METHOD FOR IMPARTING IMPROVED FATIGUE STRENGTH TO WIRE MADE OF SHAPE MEMORY ALLOYS, AND MEDICAL DEVICES MADE FROM SUCH WIRE

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation application of U.S. patent application Ser. No. 13/780,238 filed on Feb. 28, 2013 which is a divisional application of U.S. Pat. No. 8,414,714 which issued on Apr. 9, 2013 which claims priority to U.S. Provisional Patent Application Ser. No. 61/110,084, entitled NANOGRAIN DAMAGE RESISTANT WIRE, filed on Oct. 31, 2008, U.S. Provisional Patent Application Ser. No. 61/179,558, entitled NANOGRAIN DAMAGE RESISTANT WIRE, filed on May 19, 2009, and U.S. Provisional Patent Application Ser. No. 61/228,677, entitled NANOGRAIN DAMAGE RESISTANT WIRE, filed on Jul. 27, 2009, the entire disclosures of which are expressly incorporated herein by reference.

BACKGROUND

1. Technical Field

The present disclosure relates to fatigue damage resistant wire and, in particular, relates to a method of manufacturing wire made of a shape memory alloy, which demonstrates improved fatigue strength properties, as well as medical devices made with such wire.

2. Description of the Related Art

Shape memory materials are materials that “remember” their original shape, and which, after being deformed, return to that shape either spontaneously or by applying heat to raise their temperature above a processing and material related threshold known as the transformation temperature. Heating to recover shape is commonly referred to in the art as “shape memory”, whereas spontaneous recovery is commonly referred to as pseudoelasticity. Pseudoelasticity, sometimes called superelasticity, is a reversible response to an applied stress, caused by a phase transformation between the austenite or parent phase and the martensite or daughter phase of a crystal. It is exhibited in shape memory alloys. Pseudoelasticity and shape memory both arise from the reversible motion of domain boundaries during the phase transformation, rather than just bond stretching or the introduction of defects in the crystal lattice. A pseudoelastic material may return to its previous shape after the removal of even relatively high applied strains by heating. For example, even if the secondary or daughter domain boundaries do become pinned, for example due to dislocations associated with plasticity, they may be reverted to the primary or parent phase by stresses generated through heating. Examples of shape memory materials include iron-chrome-nickel, iron-manganese, iron-palladium, iron-platinum, iron-nickel-cobalt-titanium, iron-nickel-cobalt-tantalum-aluminum-boron, copper-zinc-aluminum, copper-zinc-aluminum-nickel, copper-aluminum-nickel, and nickel titanium alloys. Shape memory materials can also be alloyed with other materials including zinc, copper, gold, and Iron.

Shape memory materials are presently used in a variety of applications. For example, a variety of military, medical, safety and robotic applications for shape memory materials are known. Medical grade shape memory materials are used for orthodontic wires, guide wires to guide catheters through blood vessels, surgical anchoring devices and stent applications, for example. One shape memory material in wide use, particularly in medical device applications, is a nickel-titanium shape memory material known as “Nitinol”.

Many medical grade shape memory wire products are made of biocompatible implant grade materials including “NiTi” materials. As used herein, “nickel-titanium material”, “nickel-titanium shape memory material” and “NiTi” refer to the family of nickel-titanium shape memory materials including Nitinol (an approximately equiatomic nickel-titanium, binary shape memory material) as well as alloys including nickel and titanium as primary constituents but which also include one or more additional elements as secondary constituents, such as Nitinol tertiary or quaternary alloys (Nitinol with additive metals such as chromium, tantalum, palladium, platinum, iron, cobalt, tungsten, iridium and gold).

Significant research has been dedicated to understanding how NiTi behaves in the body from the viewpoint of biological host response, but much less has been published that quantitatively correlates structure with mechanical properties.

More particularly, the fatigue properties of NiTi material have been the subject of recent research. The fatigue crack propagation behavior of Nitinol was studied in detail by McKelvey and Ritchie, as published in Fatigue-Crack Growth Behavior in the Superelastic and Shape-Memory Alloy Nitinol, Metallurgical and Materials Transactions, 32A, 2001, pgs. 731-743. McKelvey et al. observed that the crack growth propagation rate and Δ1K_th, which denotes the stress-intensity fatigue threshold in a given fatigue-crack growth scenario, were different for equivalent composition at martensite-stable and austenite-stable temperatures where the crack growth rate was generally lower at martensite-stable temperatures. They also observed that, under plane strain conditions, the heavily slipped material near the crack tip at superelastic regime temperatures remained austenitic, presumably inhibited from undergoing volume contractile, stress-induced phase transformation by the triaxial stress state, while plane stress conditions generally resulted in stress-induced martensite near the crack tip.

Wire products made of shape memory materials are manufactured by forming a relatively thick piece of hot-worked rod stock from a melt process. The rod stock is then further processed into wires by drawing the rod stock down to a thin diameter wire. During a drawing process, often referred to as a “cold working” process, a wire is pulled through a lubricated die to reduce its diameter. The deformation associated with wire drawing increases the stress in the material, and the stress eventually must be relieved by various methods of heat treatment or annealing at elevated temperatures to restore ductility, thus enabling the material to be further cold worked to a smaller diameter. Conventional wire annealing typically results in grain growth with a concomitant random crystal orientation, and the various material or fiber “textures” that are generated during cold wire drawing are mostly eliminated during conventional annealing and recrystallization. These iterative processes of cold working and annealing may be repeated several times before a wire of a desired diameter is produced and processing is completed.

Wire materials manufactured by the above processes typically contain microstructural defects, such as pores, inclusions, interstitials, and dislocations. An inclusion comprises a phase which possesses distinct properties from the primary material matrix and is divided from the matrix by a phase boundary. Inclusions may result from oxide or other metallic or non-metallic precipitate formation during primary melting or other high temperature treatment and may include carbides, nitrides, silicides, oxides or other types of particles. Inclusions may also arise from contamination of the primary melt materials or from the mold which contains the molten ingot. In the case of an interstitial, an atom occupies a site in the crystal structure at which there usually is not an atom. The atom may be a part of its host material, such as a base metal or alloying metal, or it may be an impurity. A dislocation is a linear defect around which some of the atoms of the crystal lattice are misaligned and appear as either edge dislocations or screw dislocations. Edge dislocations are caused by the termination of a plane of atoms in the middle of a crystal, while a screw dislocation comprises an internal structure in which a helical path is traced around the linear defect or dislocation line by the atomic planes of atoms in the crystal lattice. Mixed dislocations, combining aspects of screw and edge dislocations, may also occur.

Internal or external defects, such as inclusions, pores, or defects induced during wire processing may weaken the host material at the site of the defect, potentially resulting in failure of a material at the site of that defect. This weakening may be particularly acute where the defect is relatively large and/or of significantly disparate stiffness compared with adjacent dimensions of the material (such as for fine or small diameter wire). Failure of shape memory wires is more likely to occur at the site of the defect. Since inherent defects cannot be completely eliminated from the wire material, management of inherent defects and mitigation of their negative impact on wire properties is desirable.

One previously proposed solution to the problem of inherent defects has been to treat selected regions of a wire that are expected to be subjected to high strain by converting the bulk material in such regions to a different phase than the remainder of the bulk material of the wire. For example, under predetermined operating conditions, such as a predetermined operation temperature, the high strain wire regions are stabilized in a martensite phase while the lesser strain regions remain in an austenite phase. This method is therefore directed to treating predetermined regions of a wire to convert the bulk material in the regions to a more stable phase regardless of the presence, number, and location of any defects in the bulk material.

However, it may not always be possible or practical to predict what regions of a continuous wire will be subjected to high strains when portions of the wire are later incorporated into a medical device. It may also be desirable to leave defect-free portions of wire unaffected by mitigation efforts and, therefore, available to meet other design considerations. For example, a disadvantage of the above process is that for wire made of shape memory material, the regions that are stabilized in the martensite phase will lose the superelastic characteristic.

Although wires made in accordance with foregoing processes may demonstrate excellent fatigue strength, further improvements in fatigue strength are desired, particularly with reference to fatigue damage that propagates from defects.

What is needed is a method of manufacturing a wire that demonstrates improved fatigue strength, and medical devices that include such wire.

SUMMARY

The present disclosure relates to wire products, and medical devices including wire products, such as round and flat wire, strands, cables, coils, and tubing, made from a shape memory material or alloy. Defects within the material are isolated from a primary, or parent, material phase within one or more areas of stabilized secondary, or daughter, material phases that are resistant to failure, such that the wire product demonstrates improved fatigue strength. In one application, a method of mechanical conditioning in accordance with the present disclosure isolates defects in nickel-titanium or NiTi shape memory materials in localized areas or fields of a secondary material phase that are resistant to crack initiation and/or propagation, such as a martensite phase, while the remainder of the surrounding defect-free material remains in a primary material phase, such as an austenite phase, whereby the overall superelastic and/or nature of the material is preserved.

Wire products manufactured in accordance with the present disclosure maintain good mechanical properties in addition to improved fatigue performance. Increases in the strain fatigue limit for both high cycle and low cycle fatigue are observed, while shape memory or superelastic characteristics are preserved.

As discussed below and shown in the Working Examples, the amount of secondary phase material formed about the defects during the mechanical conditioning process is sufficient to either completely isolate the defects or at least partially isolate high stress concentrator areas about the defects in order to the improve fatigue strength of the material and yet, when the bulk of the material reverts back to the primary phase after the mechanical conditioning, the overall amount of remaining secondary phase material that is formed about the defects is not sufficient compromise the shape memory or superelastic characteristic of the material as a whole. In this respect, the amount of mechanical conditioning may be specifically tailored to achieve a desired balance between fatigue strength and material elasticity.

In one form thereof, the present invention provides a medical device including a wire made of a nickel-titanium shape memory material, the wire having a fatigue endurance exceeding 0.95% strain amplitude at greater than 10⁶ cycles.

In other embodiments, the medical device may include a wire having a fatigue endurance exceeding 1.1% strain amplitude at greater than 10⁶ cycles, or a fatigue endurance exceeding 1.1% strain amplitude at greater than 10⁹ cycles. In a further embodiment, the medical device may include a wire having a residual strain of less than 0.25% after being subjected to engineering strain of at least 9.5%.

In another form thereof, the present invention provides a medical device including a wire product made of a shape memory material, the shape memory material having a plurality of defects, the wire product substantially comprised of the shape memory material in a primary phase and including portions of the shape memory material comprising a secondary phase at localized regions disposed proximate respective defects, with at least some of the secondary phase portions separated by the primary phase.

The shape memory material may be a nickel-titanium shape memory material, in which the primary phase is an austenite phase, and the secondary phase portions comprise a martensite phase. The secondary phase portions may together comprise less than 15% of the shape memory material, by volume.

In a further embodiment, the shape memory material may be a nickel-titanium shape memory material, with the wire product having a fatigue endurance exceeding 0.95% strain amplitude at greater than 10⁶ cycles, a fatigue endurance exceeding 1.1% strain amplitude at greater than 10⁶ cycles, or a fatigue endurance exceeding 1.1% strain amplitude at greater than 10⁹ cycles. The wire may also have a residual strain of less than 0.25% after being subjected to engineering strain of at least 9.5%. The wire product may be selected from the group consisting of wire having a circular cross-section, wire having a non-circular cross-section, cable, coil, and tubing.

In a further form thereof, the present invention provides a method, including the steps of: providing a wire product made of a shape-set, shape memory material; mechanically conditioning the wire product by: applying an engineering stress between 700 MPa and 1600 MPa; and releasing the applied engineering stress; and incorporating the wire product into a medical device. The mechanical conditioning step may occur either prior to or after the incorporation step.

In another embodiment, the mechanical conditioning step includes: applying an engineering stress between 900 MPa and 1450 MPa; and releasing the applied engineering stress. In a further embodiment, the mechanical conditioning step includes: applying an engineering stress between 1100 MPa and 1350 MPa; and releasing the applied engineering stress. The method may further include the repeating the mechanically conditioning step at least once.

In one embodiment, the shape memory material may be a nickel-titanium shape memory material, and the mechanical conditioning step may be conducted below a martensite deformation temperature (Md) of the nickel-titanium shape memory material. The mechanical conditioning step may further include: applying the first force to the wire product in an environment having a temperature T, wherein

T=A_f±50° C.,

wherein A_f is the austenite transformation finish temperature of the nickel-titanium shape memory material. The wire product may be selected from the group consisting of wire having a circular cross-section, wire having a non-circular cross-section, cable, coil, and tubing.

BRIEF DESCRIPTION OF THE DRAWINGS

The above-mentioned and other features and advantages of this invention, and the manner of attaining them, will become more apparent and the invention itself will be better understood by reference to the following descriptions of embodiments of the invention taken in conjunction with the accompanying drawings, wherein:

FIG. 1 is a schematic view of a portion of wire having an equiaxed grain structure;

FIG. 2 is a schematic view of the portion of wire of FIG. 1 having an elongated grain structure after cold work conditioning;

FIG. 3 is a schematic view of the portion of wire of FIG. 2 having an equiaxed grain structure with smaller grains than the equiaxed grain structure of the wire in FIG. 1 after a shape set annealing process;

FIG. 4 is a schematic view illustrating an exemplary drawing process using a lubricated die;

FIG. 5 is a depiction of the processing step of conditioning a wire using a mechanical conditioning method in accordance with the present disclosure;

FIG. 6 is a depiction of the processing step of releasing the tension in the wire of FIG. 6;

FIG. 7(a) is a view of a portion of a wire having internal and external defects;

FIG. 7(b) is an fragmentary view of a defect in the wire of FIG. 7(a);

FIG. 8 is a stress-strain curve for a mechanical conditioning process in accordance with the present disclosure;

FIG. 9 is a view of a portion of a wire having internal and external defects substantially surrounded by dislocation-stabilized secondary phase;

FIG. 10(a) is a fragmentary view of a defect in the wire of FIG. 9 substantially surrounded by dislocation-stabilized secondary phase;

FIG. 10(b) is a view of a portion of a wire having internal and external defects substantially surrounded by dislocation-stabilized secondary phase;

FIG. 10(c) is a view of a portion of a wire having internal and external defects substantially surrounded by dislocation-stabilized secondary phase;

FIG. 11 is a graphical strain-life representation of rotary beam fatigue data generated in accordance with Example 1 under the following test conditions: R=−1, T=298 K, f=60 s⁻¹; environment: quiescent air, N=5 at each strain level;

FIG. 12(a) is a secondary electron (SE) image of a 100 nm deep cue mark for optical determination of defect zone;

FIG. 12(b) is an image of a transversely oriented, 10×3×0.5 μm (T×R×L) FIB-milled sharp defect;

FIG. 12(c) is an image that provides an overall view of a sharp defect zone;

FIG. 12(d) is an optical photograph of 150 μm diameter NiTi wires with cue marks evident near centerline;

FIG. 12(e) is a transverse SEM micrograph of a failed fatigue fracture specimen showing the FIB-milled sharp defect (FSD) depth corresponding to FIG. 12(b);

FIG. 13(a) shows graphical representations of cyclic tensile data for samples including overload conditioning cycle, non-conditioned, and conditioned samples, with varying test temperatures;

FIG. 13(b) is an enlarged insets showing a loading region of the graph shown in FIG. 13(a);

FIG. 13(c) is an enlarged insets showing an unloading region of the graph shown in FIG. 13(a);

FIG. 14 is a graphical representation of rotary bend fatigue data for conditioned (C) and non-conditioned (NC) samples under the following test conditions: T=300 K, rate=60 s⁻¹, R=−1, with a maximum stress error=3% and a maximum cycle count error=0.5%;

FIG. 15 is a graphical representation of single test level (1% alternating engineering strain) data for FIB-sharp defect (FSD) and FSD-conditioned (FSD-C) samples, with the extension bars in the inset representing the data spread for n=3 samples;

FIG. 16 is a bright field TEM (BF-TEM) image of an FSD crack root after mechanical conditioning, with the insets showing selected area electron diffraction patterns (SADP) for regions within (left) and outside of (right) the structurally distinct zone demarcated by a dashed line and extending approximately 0.5 μm from the crack tip;

FIG. 17 is a graphical representation of crack growth rate data inferred from high resolution scanning electron microscopy of ductile striation spacing observations and estimated stress intensity at probable crack front location based on a semi-elliptical crack in an infinite rod;

FIG. 18(a) is a graph showing cycles to failure for five sets of wire samples, where a sample from each set of wires has been mechanically conditioned with a given level of engineering stress, and where the wires were tested at a 1.25% strain level;

FIG. 18(b) is a graph showing cycles to failure for the five sets of wire samples shown in FIG. 18(a), where a sample from each set of wires has been mechanically conditioned with a given level of engineering stress, and where the wires were tested at a 1.1% strain level;

FIG. 18(c) is a graph showing cycles to failure for the five sets of wire samples shown in FIG. 18(a), where a sample from each set of wires has been mechanically conditioned with a given level of engineering stress, and where the wires were tested at a 0.95% strain level;

FIG. 18(d) is a graph showing cycles to failure for the five sets of wire samples shown in FIG. 18(a), where a sample from each set of wires has been mechanically conditioned with a given level of engineering stress, and where the wires were tested at a 0.80% strain level;

FIG. 19(a) is a stress-strain curve for five wire samples, where each wire sample was loaded using the conditioning regime indicated by the legend at the right of the figure and described in Table 2;

FIG. 19(b) is a stress-strain curve for five wire samples, where each wire sample was loaded using the conditioning regime indicated by the legend at the right of the figure and described in Table 2;

FIG. 19(c) is a stress-strain curve for five wire samples, where each wire sample was loaded using the conditioning regime indicated by the legend at the right of the figure and described in Table 2;

FIG. 19(d) is a stress-strain curve for five wire samples, where each wire sample was loaded using the conditioning regime indicated by the legend at the right of the figure and described in Table 2;

FIG. 19(e) is a stress-strain curve for five wire samples, where each wire sample was loaded using the conditioning regime indicated by the legend at the right of the figure and described in Table 2;

FIG. 20 is a graph showing the percentage of isothermally non-recoverable strain in various wire materials as a function of a mechanical conditioning parameter;

FIG. 21(a) is a section view of Drawn Filled Tubing (DFT®) wire manufactured in accordance with an embodiment of the present disclosure (DFT® is a registered trademark of Fort Wayne Metals Research Products Corporation of Fort Wayne, Ind.);

FIG. 21(b) is a cross sectional view taken along line 18B-18B of FIG. 18(a);

FIG. 22(a) is an elevation view of a braided tissue scaffold or stent including a wire made in accordance with the present process; and

FIG. 22(b) is an elevation view of a knitted tissue scaffold or stent including a wire made in accordance with the present process.

Corresponding reference characters indicate corresponding parts throughout the several views. The exemplifications set out herein illustrate preferred embodiments of the invention and such exemplifications are not to be construed as limiting the scope of the invention in any manner.

DETAILED DESCRIPTION

The present disclosure relates to wire products, and medical devices including wire products, such as round and flat wire, strands, cables, coils, and tubing, made from a shape memory material or alloy. Defects within the material are isolated from a primary, or parent, material phase within one or more stabilized secondary, or daughter, material phases that are resistant to failure, such that the wire product demonstrates improved fatigue strength. In one application, a method of mechanical conditioning in accordance with the present disclosure isolates defects in nickel-titanium or NiTi shape memory materials in localized areas or fields of a secondary material phase that are resistant to crack initiation and/or propagation, such as a martensite phase, while the remainder of the surrounding defect-free material remains in a primary material phase, such as an austenite phase, whereby the overall superelastic nature of the material is preserved.

As used herein, a “defect” refers to material defects such as crack-like defects, inclusions, dislocations, and other non-uniformities, as well as any other internal or external defects or stress risers present in a material, as well as melt intrinsic and extrinsic defects such as inclusions, porosity, voids and oxide precipitate formation after melting.

Exemplary manufacturing processes by which wires may be made in accordance with the present disclosure are set forth in Section I below, and general descriptions of the resulting physical characteristics of wires made in accordance with the present process are set forth in Section II below. Working Examples are set forth in Section III below. Applications using wires made in accordance with the present disclosure are set forth in Section IV below.

Several suitable shape memory materials may be used for forming wire products according to the present disclosure. As used herein, “shape memory material” encompasses medical grade shape memory materials including nickel-titanium or NiTi (defined above), as well as medical grade shape memory alloys including beta titanium alloys (such as Beta C that comprise primarily the beta phase at room temperature), and any other medical grade shape memory alloys exhibiting similar superelastic and/or shape memory characteristics such as tantalum-titanium, titanium-niobium, and iron-nickel-cobalt alloys. Additionally, as used herein, “shape memory material” also encompasses non-medical grade shape memory alloys such as iron-chrome-nickel, iron-manganese, iron-palladium, iron-platinum, iron-nickel-cobalt-titanium, iron-nickel-cobalt-tantalum-aluminum-boron, copper-zinc-aluminum, copper-zinc-aluminum-nickel, copper-aluminum-nickel, and nickel-titanium alloys.

Moreover, it is contemplated that various shape-memory materials having either a one-way memory effect or a two-way memory effect, and other related materials, may be subjected to the present mechanical conditioning process to achieve enhanced physical characteristics identified in the discussion below and in the corresponding Working Examples.

As discussed in detail in Section IV below, fatigue damage resistant shape memory wire made in accordance with the present disclosure may be used in medical devices such as, for example, implantable cardiac pacing, shocking and/or sensing leads, implantable neurological stimulating and/or sensing leads, wire-based stents, blood filter devices, or any other medical device application in which high fatigue strength and/or a shape memory or superelastic characteristic is desired. Wire products produced in accordance with the present disclosure may also be used in non-medical device applications in which high fatigue strength and/or a shape memory or superelastic characteristic is desired.

As used herein, “wire” or “wire product” encompasses continuous wire and wire products, such as wire having a round cross section and wire having a non-round cross section, including flat wire, as well as other wire-based products such as strands, cables, coil, and tubing.

I. DESCRIPTION OF THE PRESENT MANUFACTURING PROCESS

1. Wire Preparation

Prior to the mechanical conditioning process of the present disclosure, discussed below, wire made of a shape memory material is subjected to cold work prior to undergoing a shape set annealing process. The shape setting step imparts the primary shape memory and/or superelastic characteristics of the material prior to mechanical conditioning.

Initial preparation of a wire may involve first forming a piece of rod stock, for example, based on conventional melt processing techniques, followed by one or more iterations of conventional cold working and annealing. Referring to FIG. 1, a schematic or exaggerated view of a portion of wire 10 manufactured in accordance with conventional cold working and annealing techniques is shown. Wire 10 has been subjected to one or more, perhaps several or a very large number of, iterations of conventional cold working and annealing, as described above, to form an equiaxed crystal structure within the material of wire 10. Representative equiaxed crystals are depicted in wire 10 at 12. As used herein, “equiaxed” refers to a crystal structure in which the individual crystals 12 have axes that are approximately the same length, such that the crystals 12 collectively have a large number of slip planes, leading to high strength and ductility. However, it is not necessary that the grain structure be equiaxed. The grain structure may, for example, contain deformed grains that have been recovered to the B2 cubic austenite phase through the high temperature shape setting process described below.

Referring now to FIG. 2, prior to the shape-set anneal, wire 10 may optionally subjected to further cold work in the form of a cold work conditioning step if a nanograin microstructure is desired. As used herein, “cold work conditioning” means imparting a relatively large amount of cold work to a material, such as by wire drawing, swaging, or otherwise forming.

Referring to FIG. 4, the cold work conditioning step is performed by drawing wire 10 through a lubricated die 18 (FIG. 4) having a an output diameter D₂, which is less than diameter D₁ of the undrawn wire 10 shown in FIG. 2. In one exemplary embodiment, the cold work conditioning step by which the diameter of wire 10 is reduced from D₁ to D₂ is performed in a single draw and, in another embodiment, the cold work conditioning step by which the diameter of wire 10 is reduced from D₁ to D₂ is performed in multiple draws which are performed sequentially without any annealing step therebetween.

Further discussion of exemplary cold work conditioning processes are presented in U.S. patent application Ser. No. 12/563,062, entitled FATIGUE DAMAGE RESISTANT WIRE AND METHOD OF PRODUCTION THEREOF, filed Sep. 18, 2009, assigned to the present assignee, the disclosure of which is hereby expressly incorporated by reference herein in its entirety. The foregoing reference also discloses methods of limited annealing following the cold work conditioning to create a nanograin microstructure, which may optionally be applied to wires prior to subjecting same to the mechanical conditioning process in accordance with the present disclosure, discussed below.

Regardless of the amount of cold work imparted to the wire and/or whether cold work conditioning is used, once drawn to the desired size, and as shown in FIG. 5, wire 10 undergoes a shape setting annealing process in which it is continuously annealed under constant tension sufficient to hold the wire in a substantially linear configuration during the shape set annealing process. Shape set annealing typically occurs at a temperature between 300° C. (673 K) and 600° C. (1073 K), where the temperature is sufficiently high to restore a majority of the wire material to the primary or austenite phase. The shape setting annealing process may result in the formation of a new crystallographic structure, which may comprise nano-scale equiaxed crystals 16 in wire 10, as shown in FIG. 3. However, as noted above, an equiaxed or nanograin crystal microstructure is not required for the mechanical conditioning process described below.

2. Mechanical Conditioning

In accordance with the present disclosure, wire made of a shape memory material may be subjected to a mechanical conditioning process to improve its resistance to fatigue damage. In the present embodiment, mechanical conditioning is performed by application of a force to the wire in an environment having a temperature range within approximately 50° C. of the austenite transformation finish temperature (A_f), i.e., T=A_f±50° C.

Referring now to FIGS. 5 and 6, in the mechanical conditioning process, shape memory wire, shown in FIG. 5, in the heat set annealed condition is secured at a first end. Controlled engineering strain is applied in the direction of arrow F to a finished engineering strain, ε_C, of 0.08 to 0.14 units, wherein:

ɛ

c

=

Δ





L

L

0

,

with L_o being the initial length, and ΔL being the length increase imparted by strain.

The range for ε_C may be from as little as 0.06, 0.08, or 0.10 units to as much as 0.13, 0.14 0.16 units, or within any range encompassed by the foregoing values, to provide the increased benefits to the shape memory wire discussed herein. It is thought that if the end point is lower than 0.08, the mechanical conditioning may not impart the desired physical properties to the wire, as any dislocation or stress-induced secondary phase, such as martensite that is formed, may revert back to the primary or parent phase, such as austenite. In contrast, if the end point is in excess of 0.14, the wire may potentially be strained by the mechanical conditioning beyond its elastic deformation range to the extent that an undesirably large amount of plastic deformation may result.

An alternative characterization of the mechanical conditioning process of the present disclosure may be expressed as the application of engineering stress to the material. For an application of force in a tensile test as described herein, engineering stress is calculated using the following equation:

σ

e

=

P

A

0

where σ_e is the engineering stress, P is the force applied, and A₀ is the cross-sectional area of the material before application of force. In engineering stress terms, the range for Ge may be from as little as 700 MPa, 900 MPa or 1100 MPa to as much as 1350 MPa, 1450 MPa or 1600 MPa, or within any range encompassed by the foregoing values, to provide the increased benefits to the shape memory wire discussed herein.

However, it is contemplated that force may be applied to the wire or wire product using alternate stress loading regimes, such as via methods other than a tensile test, that may be more appropriate to the geometry of a particular wire product.

The temperature should be maintained below the martensitic deformation temperature, M_d, during the application of force to the wire in the mechanical conditioning process. If the temperature exceeds the martensitic deformation temperature, the bulk of the shape memory wire material will not transform to martensite upon loading, because any plastic deformation will occur in the austenite phase, and therefore the localized phase transformation mechanism would not occur. The entirety of the wire material will remain in a plastically deformed austenite state, with the austenite or primary phase containing significant plasticity and little retained martensite phase.

Referring to FIG. 6, once the desired stress or strain is applied to the wire, the force is removed and the sample is allowed to freely recover and, if the temperature is below the austenitic finish temperature, or if further recovery of the bulk material is required, heat Q is applied to drive the temperature, T to sufficiently greater than the austenitic finish temperature (i.e., T>A_f) for recovery of the bulk material, leaving the material in a state wherein defects are still isolated by a dislocation stabilized secondary phase as discussed below.

The steps of applying a controlled engineering stress or strain and subsequently removing the force to allow the sample to freely recover may repeated as few as 1, 2 or 3 times or as many as 6, 8 or 10 times, for example, to increase the amount of dislocation stabilized secondary phase within the wire material, as discussed in detail below. Thus, after one or more applications of load cycles and the attendant recovery of applied strain ε_C, the length of wire 10 is greater than its original length L₀. More particularly, the length of wire 10 after load conditioning is L₀+ps, where ps is the permanent set or isothermally non-recoverable strain resulting from plastic, pseudoplastic and other deformation mechanisms, as shown in FIG. 6. Some of this isothermally non-recoverable strain can be recovered in the bulk material by slight heating of the material as discussed above.

As discussed in more detail below in Section III, this isothermally non-recoverable strain is indicative of the amount or volume of the wire material that has been converted from the primary phase to the secondary phase and, upon recovery of the wire material, remains stabilized in the secondary material phase. These localized areas of secondary phase material isolate defects and inhibit crack propagation in the primary phase material.

For example, as calculated in Examples 3-7 below, this isothermally non-recoverable strain may be calculated by measuring the difference in wire length after load removal in a tensile test. Known tensile test devices (including the test device used for the present Working Examples) collect wire length data as the test is conducted. This data, not presented herein, is used to generate the permanent set data presented in the tables. This non-recoverable length, with the original length subtracted therefrom, gives a positive value where isothermally non-recoverable deformation has occurred (i.e., “permanent set”). This difference can then be divided by the original length, the product of which is a strain value representing the isothermally non-recoverable strain. This amount arises from a residual volume of altered material within the wire which has accommodated a given amount of strain not recovered upon load removal. The observed isothermally non-recoverable strain may be divided by the load plateau strain length, which is associated with the forward transformation from parent austenite phase to secondary, stress-induced, martensite phase, thereby providing a quantitative indication of the volume fraction of altered material within the wire.

This volume fraction, referred to as “max. volume martensite %” in Tables 3-7 below is calculated using the following formula:

V

m

=

INRS

LPSL

wherein V_M is the maximum volume fraction of secondary phase, INRS is the isothermally non-recoverable strain and LPSL is the loading plateau strain length.

The volume fraction sets an upper limit on the amount of wire material that has been converted to the secondary phase from the primary phase and remains stable at the given test temperature after load removal. That is to say, the total volume of material represented by the non-recoverable strain comprises secondary phase material, and may also comprise other non-primary phase material arising from plastically deformed primary phase material or other deformation phenomena.

It is counter-intuitive that the application of stress to a wire product at a level sufficient to initiate plastic deformation according to the present mechanical conditioning process could be beneficial for the use of that wire product in a medical device that utilizes the shape memory or superelastic characteristic of the wire product. One of ordinary skill in the art would consider a wire product made of a shape memory material that has been subjected to a stress level sufficient to induce any amount of plastic deformation to be compromised in its shape memory or superelastic characteristic and therefore unsuitable for use in a medical device in which this characteristic is desired.

II. DESCRIPTION OF MATERIAL PROPERTIES OF WIRE PRODUCTS MADE IN ACCORDANCE WITH THE PRESENT MANUFACTURING PROCESS

Wire products made of shape memory materials or alloys that have been subjected to the mechanical conditioning process of the present disclosure exhibit several novel physical characteristics and/or novel combinations of physical characteristics, including the following:

1. Isolation of Defects

Referring to FIGS. 7(a)-(b), shape memory wire 10 may have one or more defects, such as internal defects 28 and/or external defects 30. These defects may include extrinsic defects and/or intrinsic defects such as inclusions or porosity as discussed above, for example.

These defects are isolated in localized fields or areas of secondary phase material by subjecting the wire to mechanical conditioning, as exemplified by the curve shown in FIG. 8. As discussed above, this may be accomplished by applying an engineering stress (and concomitant engineering strain) so that at least some parts of wire 10 experience plastic deformation. In an exemplary embodiment of the present process, however, nearly all of the strain may be recovered upon unloading (FIG. 8).

Referring now to FIGS. 9-10(c), mechanical conditioning results in areas of dislocation stabilized B19′, R, and/or martensite, shown as secondary phase areas 26 in FIG. 10, forming proximate defects 28 in wire 10. The formation of the secondary phase areas around and/or adjacent defects 28 during mechanical conditioning helps to retard fatigue crack growth in subsequent cyclic loading in a direction emanating from defects 28, as it is known that cracks propagate more slowly in B19′, R, and/or martensite than in austenite. However, the bulk of wire 10, where defects are not present, reverts back to the austenite phase after mechanical conditioning, such that the overall wire still exhibits its shape memory or superelastic characteristic while at the same time having an enhanced degree of fatigue strength due to the isolation of defects within the secondary phase material.

Referring still to FIGS. 9-10(c), wires 10, 10′ and 10″ are shown after mechanical conditioning. As a result of mechanical conditioning in accordance with the present process, areas of dislocation stabilized secondary material phase 26 formed proximate material defects stabilize the defects. That is to say, while the bulk of the wire material reverts back to the primary phase from the secondary phase, localized areas of secondary phase material remain formed proximate material defects. This stabilization of the secondary phase areas 26 is advantageous in that it helps to retard fatigue crack growth in subsequent cyclic loading, for example, as a crack generally propagates more slowly in the secondary (i.e., martensite) phase than in the primary (i.e., austenite) phase.

Stabilization of secondary phase areas 26 is, at least in part, due to plastic deformation 27 comprising dislocations and/or dislocation networks. This plastic deformation acts to stabilize secondary phase 26 after removal of the conditioning mechanical conditioning stress or strain (when primary phase returns to the bulk of the wire material) and during subsequent service. The defect-free portions of the wire material may have less plastic deformation, or may have substantially no plastic deformation. Therefore, this defect-free material will revert back to the primary phase more readily and completely than the localized secondary phase areas near the defects, which have experienced plastic deformation.

As shown in FIGS. 10(a)-(c), the shape, size and/or spatial configuration of secondary phase 26 varies depending upon the characteristics of the defect proximate the localized secondary phase field. In general, the secondary phase field will form around the highest stress areas of the defect, and may not form at lower stress areas. This is because plastic deformation occurs most readily at the site of stress concentrators during the mechanical conditioning process; the dislocation stabilized secondary phase areas, which include some plastic deformation 27, will form at these stress concentration points even though the primary phase portions of the wire are still within a relatively elastic or pseudoelastic (where pseudoelastic is defined as elasticity associated with primary to secondary phase transformation) deformation range. Primary phase material remains present between any pair of defects that are sufficiently far apart, such that their isolation fields to not overlap.

For example, wire 10 shown in FIG. 10(a) has a secondary phase area 26 extending around substantially the entirety of defect 28. The geometry of defect 28, as well as the direction application of force F, determines the overall shape of secondary phase area 26.

As shown in FIG. 10(b), wire 10′ has defects 28′ with stabilized secondary phase areas 26′ at the highest stress concentration areas created by the application of force F. Plastic deformation 27 also occurs within secondary phase areas 26′ as discussed above. Some of secondary phase areas 26′ are adjacent one another and have overlapping boundaries, so that a defect 28′ and another nearby defect 28′ will influence one another.

Similarly, wire 10″ shown in FIG. 10(c) has multiple defects 28″ with stress fields 26″ and plastic deformation 27. Again, the stress fields 28″ form at the highest stress concentration points, which are a function of the geometry of defects 28″ and the direction of application of force F (shown as a longitudinal force along the axis of wire 10″) as well as the temperature of the material during force application.

In this manner, shape memory material wire subjected to the present mechanical conditioning process exhibits an enhanced fatigue life and fatigue strain threshold. Moreover, a shape memory wire made in accordance with the present process retains overall material properties consistent with wire in the austenitic phase, while exhibiting inhibition of crack propagation at defect sites consistent with the martensitic phase.

2. Increased High-Cycle Fatigue Resistance

As a result of the isolation of defects and/or defect boundaries (i.e. the sites along the defect/primary phase boundary most susceptible to stress concentration and crack propagation) in a secondary phase area or field, mechanical conditioning increases the fatigue life and fatigue-strain threshold of the shape memory wire. As discussed in Section III, wire conditioned in accordance with an embodiment of the present disclosure exhibited a gain in the fatigue strain limit at 100 million (10⁸ cycles of greater than 25% (FIG. 11). Also, as shown in FIG. 14, conditioned wire demonstrated an upward strain shift of greater than 20% at a 10 million (10⁷) cycle life (i.e., 1.1% engineering strain versus 0.9% engineering strain). Further, eight samples of this conditioned material survived more than 10⁹ cycles and were still running at the time conclusion of Example I discussed below.

3. Increased Damage Tolerance and Low-Cycle Fatigue Resistance

As discussed in Section III at Example 2, wire conditioning in accordance with an embodiment of the present disclosure demonstrated increased tolerance of damage to the wire. Three specimens with focused ion beam (FIB)-milled sharp defects were tested at an alternating strain of 1% in the conditioned and non-conditioned states. As shown in FIG. 15, Conditioned samples demonstrated a 50% increase in damage tolerance compared with the non-conditioned samples.

4. High Recoverable Strain, Low Residual Strain

As shown in FIGS. 13(a)-(c), greater than 8% recoverable engineering strain was observed with zero residual strain and good plateau stresses at body temperature (i.e., 310 K) after mechanical conditioning.

This recoverable strain renders wire made in accordance with the present disclosure particularly suitable for certain medical device applications. As mentioned above, this is a counter-intuitive result. Typically, wire made of a shape memory or superelastic material which has been subjected to forces sufficient to cause any plastic deformation in the wire material would be considered “damaged”, and therefore unsuitable for use in any medical device application. The surprising result of the present process is that, under proper mechanical conditioning parameters as discussed herein, wire subjected to such forces is actually superior for medical device applications.

III. EXAMPLES

The following non-limiting Examples illustrate various features and characteristics of the present invention, which are not to be construed as limited thereto.

The examples offer analysis of the effect of mechanical conditioning in fine (such as less than 250 μm diameter) Nitinol wire, and particularly of the effect of stress riser or defect isolation.

Example 1

Fatigue Resistant Nitinol Intermetallic Wire

Nanocrystalline, nominally Ti-56 wt. % Ni Nitinol wire (“NiTi wire”) was manufactured to create a superelastic, precipitate free wire with a median grain size of 50 nm. An exemplary process for creating such a wire is described in U.S. patent application Ser. No. 12/563,062, entitled FATIGUE DAMAGE RESISTANT WIRE AND METHOD OF PRODUCTION THEREOF, filed Sep. 18, 2009, the disclosure of which is hereby expressly incorporated by reference herein in its entirety.

The resulting wire was drawn through diamond drawing dies beginning at a diameter of 0.230 mm and ending at a diameter of 0.177 mm to yield a retained cold work level of about 40% cold work. The wire was then continuously annealed at a temperature of 773K-873K for less than 60 seconds, to yield a 50 nm grain size as verified by TEM electron microscopy scanning. Specifically, field emission scanning electron microscopy or transmission electron microscopy (TEM) is used to gather an image containing, for example, several hundred crystals or grains exhibiting strong grain boundary contrast. Next, the image is converted to a binary format suitable for particle measurement. Resolvable grains are modeled with ellipsoids and subsequently measured digitally yielding statistics regarding the crystal or grain size, such as the average size, maximum size, and minimum size. The resulting average crystal size is taken to be the average crystal size for the material from which the sample was taken. Grain size verification is discussed in detail in U.S. patent application Ser. No. 12/563,062, entitled FATIGUE DAMAGE RESISTANT WIRE AND METHOD OF PRODUCTION THEREOF, filed Sep. 18, 2009, incorporated by reference above.

After annealing, the wire of the present Example was subjected to cyclic tensile testing and was determined to exhibit pseudoelasticity out to greater than 10% engineering strain. A first wire sample was preserved at this point in the process.

The remainder of the wire was then subjected to mechanical conditioning, as described in detail above, by loading the wire to about 12% axial engineering strain (i.e., 0.12 units), completely releasing the load, reloading to about 12% engineering strain, and once again completely releasing the load. A second wire sample was preserved after this point in the process.

The first and second wire samples were subjected to rotary beam fatigue testing. Referring now to FIG. 11, the first, non-mechanically conditioned sample generated data curve 100 exhibiting a 100 M cycle engineering strain limit of about 0.85% at N=10 data points, shown by right most data point 100′ of the curve 100. The second, mechanically conditioned sample generated data curve 102 exhibiting a 100 M cycle engineering strain limit of about 1.1% at N=10 data points, exemplifying a greater than 25% gain in the fatigue strain limit at 100 M cycles, shown by right most data point 102′ of curve 102.

Example 2

Mechanical Conditioning of Superelastic NiTi Wire for Improved Fatigue Resistance

In this example, the effects of mechanical overload conditioning of superelastic wire and the possibility of increased fatigue damage resistance associated with near-defect, plasticity-locked phase transformation were investigated. In thin wires, where plane stress dominates, it is expected that sufficient loading will result in phase transformation near the largest or shape-conducive crack-like defects, such as constituent inclusion particles, before conversion of the bulk, defect-free material.

1. Experimental Technique

Samples for this Example were subjected to a total engineering strain departure, measured by crosshead extension, of about 11.5%. Conditioning was applied by approaching the martensitic yield point at 295 K using strain-rate-controlled loading in order induce some dislocation locking of stress-transformed material in the vicinity of stress concentrators. Referring now to FIG. 8, the conditioning cycle comprises a strain-controlled ramp to a stress level of 1240 MPa engineering stress, resulting in an engineering strain of about 11.5%, followed by a 3 second hold, and finishing with a strain-controlled ramp to zero load.

In order to prepare samples for this Example, Nitinol wire with an ingot austenite start temperature, AS, of 243 K, having Ti-56 wt. % Ni was repetitively drawn and annealed from a diameter of 2 mm to a diameter of 177 μm in accordance with the process described above. At this stage, wires were continuously annealed at 770 to 800 K. Final cold working was completed using diamond dies to draw round wire with a diameter of 150 μm prior to continuous, reel-to-reel annealing at 750 to 780 K under constant engineering stress for less than 60 seconds to effect linear shape setting. The final wire comprised a room-temperature-superelastic Nitinol wire with an active austenitic finish temperature, A_f, of 280 K and an approximately 120 nm thick, dark brown oxide layer similar to that disclosed in an article by the present inventor entitled “Structure-Property Relationships in Conventional and Nanocrystalline NiTi Intermetallic Alloy Wire” and published in the Journal of Materials Engineering and Performance, February 2008, ISSN 1544-1024, pgs. 1-6, the entire disclosure of which is hereby expressly incorporated by reference herein.

Focused ion beam (FIB)-milled sharp defects 202 (“FSD”) were then milled into material 200 of each sample in order to act as preferential sites of incipient fatigue crack formation and to facilitate user-defined damage localization and monitoring. An FEI dual-beam (Nova 200 NanoLab) focused ion beam (FIB) with in situ scanning electron microscopy (SEM) was used to simultaneously monitor samples by SEM during the FIB milling process. A 30 keV Ga+ ion beam was used to precisely mill transverse defects into wire specimens at a 0.50 nA beam current. Defects 202 were of consistent dimension measuring 10 μm transverse length by 3 μm radial depth by 0.5 μm axial surface width, an example of which is shown in FIGS. 12(a)-(e). Cue lines 204 (FIG. 12(a)) were milled into the oxide surface at a depth of about 50 nm on either side of each sharp defect in order to enhance optical detection for accurate placement in fatigue test gages after removal from the SEM chamber. As shown in FIGS. 12(a)-(e), the cue lines were of sufficient depth to create a visually detectible gradient associated with the reduced oxide thickness, while shallow enough to minimize undesirable mechanical impact.

Electron microscopy of fracture surfaces was carried out using a Hitachi S4800 field emission SEM (FE-SEM) operated at 10 to 20 kV. Transmission electron microscopy samples were extracted and prepared using the FIB/SEM dual beam equipment previously mentioned with an in situ sample manipulator for thin foil removal and transport to TEM grids. Additional details regarding this method can be found in the article by the present inventor, which is incorporated by reference herein above, namely the article entitled “Structure-Property Relationships in Conventional and Nanocrystalline NiTi Intermetallic Alloy Wire” and published in the Journal of Materials Engineering and Performance, February 2008, ISSN 1544-1024, pgs. 1-6. TEM imaging and diffraction experiments were carried out on a 200 kV machine equipped with a LaB₆ emitter (Tecnai 20, FEI Company, Oregon).

Cyclic and monotonic uniaxial tensile properties were measured at an ambient temperature of 295 K at a strain rate of 10⁻³ s⁻¹ using an Instron Model 5565 Tensile Test Bench equipped with pneumatic, smooth face grips. Six hundred grit emery-cloth was used to reduce grip-specimen interface slip. Elevated temperature testing was completed on an equivalent tensile bench fitted with an environmental chamber capable of maintaining a temperature of 310±0.5 K.

Fatigue behavior was characterized using rotary beam fatigue test equipment manufactured by Positool, Inc., at a test rate of 60 s⁻¹ in ambient 298 K air. The test rate was chosen at a rate significantly higher than physiological loading frequencies to promote expediency. Data have recently been presented by Robertson and Ritchie, in an article entitled “In vitro fatigue-crack growth and fracture toughness behavior of thin-walled superelastic Nitinol tube for endovascular stents: A basis for defining the effect of crack-like defects”, published in Biomaterials 28, 2007, pgs. 700-709, suggesting that high rate testing may well estimate in vivo fatigue failure lifetimes.

As shown in FIGS. 13(a)-13(c), specimens from each group, non-conditioned (NC) and conditioned (C), were tested at alternating engineering strain (½ peak-to-peak amplitude) levels ranging from 0.8 to 1.6% to a maximum of about 10⁹ cycles or 200 days test time. Further, specimens with FSD 202 were tested at 1% engineering strain before and after conditioning. The FSD zone was located at the apex of the fatigue bend by optical positioning using the cue marks 204 as guides.

2. Results

The resulting tensile data is shown graphically in FIGS. 13(a)-(c). As noted above, the conditioning cycle comprised a strain-controlled ramp to a stress level of 1240 MPa engineering stress followed by a 3 second hold, finishing with a strain-controlled ramp to zero load. This conditioning cycle generated data curve 220, shown in FIGS. 13(a)-(c). The total engineering strain departure for this cycle, measured by crosshead extension, was 11.5%. Conditioning initially resulted in 0.3% residual strain comprising both plastic and pseudo-plastic strain contributions.

The martensite to austenite reversion plateau stress associated with unloading was significantly reduced during unloading from the conditioning cycle, but was observed to elevate in subsequent testing to 8% engineering strain. Some of this effect can be accounted for by strain rate differences: the conditioning cycle was run at a significantly higher strain rate than the 8% test cycles. High strain rates can cause heating during loading and cooling during unloading resulting in increasing stress hysteresis. Further testing of a C sample at body temperature (310 K) generated data curve 226 depicted on FIGS. 13(a)-(c) by circular marks 226′, showing elevation of the unloading plateau stress to levels greater than an NC sample at 295 K, shown as data curve 222 with square-shaped marks 222. This result was consistent with known test temperature-plateau stress relationships.

The conditioned sample at 295 K, shown as curve 224 on FIGS. 13(a)-(c) with triangle-shaped marks 224′, exhibited a downward shift in the unloading plateau stress. This can be attributed to plastic deformation, some of which may be directly beneficial to resistance against subsequent fatigue crack growth. The lack of significant shift in the strain length of the plateaus indicates that plastic deformation to the overall microstructure was minimal during overload conditioning.

FIG. 14 illustrates the observed differences in fatigue performance for conditioned wire specimens, shown as data curve 230 with triangular-shaped marks 230′, versus non-conditioned (NC) wire specimens, shown as data curve 232 with triangular-shaped marks 232′. The conditioning resulted in an upward strain shift of greater than 20% at the 10⁷ cycle life (i.e., 1.1% engineering strain versus 0.9% engineering strain). Eight samples of the conditioned material survived more than 10⁹ cycles and were still running at the time conclusion of the experiment.

As shown in FIG. 15, three FSD specimens in each of the NC and C states were tested at an alternating strain of 1%. In this case, the FSD-C group generated data bar graph 242, showing an average of 21,228 cycles to failure with a margin of error indicated at the top of the bar. The FSD-NC group generated data bar graph 240, showing an average of 14,196 cycles to failure with a margin of error indicated at the top of the bar. Thus, the conditioned wire samples outperformed the non-conditioned samples by 50%. All FSD samples failed considerably before the non-FSD samples; this is attributable to the geometry of the FIB-milled defects, which were purposefully milled larger and sharper than the 2-6 μm inclusion particles typically found at fatigue failure sites in this grade of Nitinol wire in order to direct site-specific, locatable failure for study.

A microstructurally distinct region resulting from the mechanical conditioning was found within an approximately 500 nm radius of the approximately 10 nm width FSD crack root. FIG. 16 shows the results of TEM work performed to help elucidate mechanisms giving rise to mechanical property changes associated with the mechanical conditioning. The selected area diffraction patterns 250, 252 in FIG. 16, outside of and within the distinct FSD concentration zone respectively, reveal significant differences in contributing bright field contrast signal. A typical polycrystalline, B2 pattern 250 was observed at approximately 1 μm from the crack tip, while the selected area diffraction pattern adjacent to the root, shown as 252, revealed what appears to be superimposed diffuse rings, B2 polycrystalline reflections, as well as some evidence of ½ (110) reflections associated with the B19′ martensitic phase. Also evident is a significant increase in dislocation density and associated contrast.

The diffuse (110) rings observed within the FSD zone, shown in the left and upper-right insets of FIG. 16, may be related to partial amorphization and/or due to (110) reflection splitting and the presence of ½(110) reflections associated with a mixed B2-B19′ structure.

The narrowest ductile striations were observed in conditioned samples near the FSD incipient crack front. High resolution SEM (HR-SEM) analysis of fatigue failure sites in NC and C specimens was completed and the stress intensity was estimated based on the probable crack front location at the examined site using assumptions of a semi-elliptical crack in an infinite cylinder. Referring to FIG. 17, a crack growth rate plot as a function of the estimated stress intensity factor (not taking into account crack closure effects) is shown, with square-shaped marks 260 indicating data on non-conditioned material and triangle-shaped marks 262 indicating conditioned material. The difference between the two data sets may suggest martensitic growth rate inhibition.

In this example, it has been demonstrated that mechanical conditioning of superelastic NiTi wire results in improved fatigue performance, while maintaining good mechanical properties. In addition, greater than 8% recoverable engineering strain was observed with zero residual strain and good plateau stresses at body temperature after mechanical conditioning. Further, an increase in the strain fatigue limit of greater than 20% at 10⁷ cycles is observed in conditioned versus non-conditioned wire with an observed increase in low cycle life of 50%. The tensile overload conditioning treatment also resulted in a mixed-phase microstructure in the vicinity of stress concentrators that comprises increased dislocation density and possible plasticity-induced or roughness-induced crack closure.

The presence of plasticity in the FSD region may also contribute to increased fatigue performance due to residual stresses which offset the effective crack-opening stress intensity range. The reduction in the operating stress intensity range can serve to increase the effective ΔK_th fatigue threshold (defined above) thereby elevating the strain load level required to initiate or maintain crack growth. The mixed microstructure may also promote crack front tortuosity thereby precluding crack arrest associated with roughness-induced closure at near-threshold crack growth conditions.

Introduction to Examples 3-7

For examples 3-7, various wire materials were tested in a similar manner for comparison to one another. FIGS. 18(a)-(d) show results for wire materials from each of Examples 3-7, with each Figure representing a different strain condition (as indicated on each respective Figure). Table 1, below, indexes the Example materials:

TABLE 1

Index of Example Materials for Examples 3-6

Austenitic

Nominal

Actual

Shape Set

Surface

Finish

Nitinol

Composition

Diameter

Temperature

Finish

Temperature Af

Example

type

(weight %)

(mm)

(K)

Description

(K)

3

NiTi #1

56Ni—Ti

0.151

740-800

Oxide

280

4

NiTi #2

55.8Ni—0.25Cr—Ti

0.269

740-800

Oxide

283

5

NiTi #4

55.8Ni—Ti

0.302

740-800

Oxide

298

6

NiTi #1

56Ni—Ti

0.076

740-800

Etched

288

7

NiTi #1

56Ni—Ti

0.638

740-800

Polished

291

FIGS. 19(a)-(e) also show results for wire materials from each of Examples 3-7, with each Figure representing a stress-strain curve for a corresponding Example. Table 2, below, indexes the mechanical conditioning regimes applied to each wire product shown in FIGS. 19(a)-(e). The “regime” number corresponds to a given curve on each figure, as indicated by the corresponding number on the legend at the right side of each of FIGS. 19(a)-(e), where, the digit preceding the decimal point in X.X refers to the Example (e.g. 1, 2, 3, 4, and 5 correspond to Examples 3, 4, 5, 6, and 7 respectively), and the digit following the decimal point corresponds to regimes 1, 3, 4, 6, and 7 given below in Table 2.

TABLE 2

Index of Conditioning Regimes for Examples 3-6

Regime (See

Hold stress

also legends at

Ramp rate

(MPa) (See also

right of FIGS.

(engineering

X-axes in FIGS.

19(a)-(e))

strain/min)

18(a)-(d))

1

0.10

700

3

0.10

1100

4

0.10

1240

6

0.10

1400

7

0.10

1500

Results shown in Tables 3-7 show data used to create FIGS. 19(a)-19(e) respectively. Thus, Tables 3-7 correspond with Examples 3-7, respectively.

Example 3

Mechanical Conditioning of Superelastic NiTi Wire for Improved Fatigue Resistance

In this example, the effects of mechanical overload conditioning of superelastic wire and the possibility of increased fatigue damage resistance associated with near-defect, plasticity-locked phase transformation were further investigated over a broader range of loads as compared to Example 2.

1. Experimental Technique

Samples for this Example were subjected to a total engineering strain departure, measured by crosshead extension, ranging from about 8% to 12.5% Conditioning was applied by approaching the martensitic yield point at 295 K using strain-rate-controlled loading in order induce some dislocation locking of stress-transformed material in the vicinity of stress concentrators. Referring now to FIG. 19(a), the conditioning cycle comprises a strain-controlled ramp to five stress levels of 700, 1100, 1240, 1400, and 1500 MPa engineering stress, resulting in an engineering strain of about 8.3%, 9.8%, 10.3%, 11.1% and 12.2% respectively, followed by a 3 second hold, finishing with a strain-controlled ramp to zero load.

In order to prepare samples for this Example, Nitinol wire with an ingot austenite start temperature, As, of 243 K, having Ti-56 wt. % Ni was repetitively drawn and annealed from a diameter of 2 mm to a diameter of 201 μm in accordance with the process described above. At this stage, wires were continuously annealed at 950 to 1000 K. Final cold working was completed using diamond dies to draw round wire with a diameter of 151 μm prior to continuous, reel-to-reel annealing at 750 to 780 K under constant engineering stress for 40 to 80 seconds to effect linear shape setting. The final wire comprised a room-temperature-superelastic Nitinol wire with an active austenitic finish temperature, A_f, of 280 K and an approximately 120 nm thick, dark brown oxide layer similar to that disclosed in an article by the present inventor entitled “Structure-Property Relationships in Conventional and Nanocrystalline NiTi Intermetallic Alloy Wire” and published in the Journal of Materials Engineering and Performance, February 2008, ISSN 1544-1024, pgs. 1-6, which is incorporated by reference above.

Cyclic and monotonic uniaxial tensile properties were measured at an ambient temperature of 295 K at a strain rate of 10⁻³ s⁻¹ using an Instron Model 5565 Tensile Test Bench equipped with pneumatic, smooth face grips. Six hundred grit emery-cloth was used to reduce grip-specimen interface slip.

Fatigue behavior was characterized using rotary beam fatigue test equipment manufactured by Positool, Inc., at a test rate of 60 s⁻¹ in ambient 298 K air. The test rate was chosen at a rate significantly higher than physiological loading frequencies to promote expediency.

As shown in FIGS. 18(a)-(d), three specimens from each group at each conditioning cycle, ranging from 0 MPa which indicates non-conditioned wire to 1500 MPa which indicates the maximum conditioning load used, were tested at alternating engineering strain (½ peak-to-peak amplitude) levels ranging from 0.80 to 1.25% strain to a maximum of about 10⁶ cycles. The total samples tested for each conditioning load regime for each sample was 12 resulting in a total of 72 fatigue samples tested for this portion of the study. Samples which did not fracture after 10⁶ cycles were stopped and recorded.

2. Results

The resulting tensile data is shown graphically in FIGS. 18(a)-(d) as line 1 on each curve. As noted above, the conditioning cycle comprised a strain-controlled ramp to a stress level of 0, 700, 1100, 1240, 1400 or 1500 MPa engineering stress, as indicated along the horizontal axis of the plot, followed by a 3 second hold, finishing with a strain-controlled ramp to zero load.

This conditioning cycle generated data curves 1.1, 1.3, 1.4, 1.6 and 1.7 shown in FIG. 19(a). The total engineering strain departure for respective cycles, measured by crosshead extension, was about 0%, 8.3%, 9.8%, 10.3%, 11.1% and 12.2% for increasing load levels respectively. Conditioning resulted in residual strains (i.e. isothermally non-recoverable strains) of respectively 0%, 0.19%, 0.20%, 0.24%, 0.17%, ad 7.3% respectively.

FIGS. 18 (a) to (d) illustrate the observed differences in fatigue performance for non-conditioned (e.g. 0 load level on x-axis) and conditioned wire specimens (700, 1100, 1240, 1400, and 1500 MPa on the x-axis) The conditioning resulted in an upward cycle life shift of at least 55% and 3000% at the 1.25% and 0.95% alternating strain test levels respectively at a conditioning load level of 1240 MPa. An overall upward trend in lifetime for a given test strain level was observed for increasing conditioning load through 1500 MPa. Most samples of the material conditioned at greater than 1240 MPa survived more than 10⁶ cycles and were still running at the time of conclusion of the experiment for test strain levels below 0.95%.

FIG. 19(a) illustrates the observed tensile behavior during load conditioning of each sample. In each case, an upper bound of the maximum volume of retained martensite was calculated as described above based on the ratio of isothermally non-recoverable strain to the strain length of the load plateau. FIG. 20 illustrates the positive correlation between isothermally non-recoverable strain and conditioning load. Non-recoverable strain was less than 0.17% for all samples conditioned below 1400 MPa resulting in a max. volume of retained martensite estimate of 3.7% for the same samples loaded below 1400 MPa.

In this Example, it has been demonstrated that mechanical conditioning of superelastic NiTi wire results in improved fatigue performance, while maintaining good mechanical properties. In addition, less than 3.7% of the matrix was left in the martensite phase after load removal for conditioning below 1400 MPa with a concomitant maximum isothermally non-recoverable strain of 0.17%. Further, an increase in the strain fatigue life of greater than 3000% at 10⁶ cycles is observed in wire conditioned at 1240 MPa versus non-conditioned wire while maintaining good elastic properties suitable for said medical device applications.

Example 4

Mechanical Conditioning of Superelastic NiTi Wire for Improved Fatigue Resistance

In this Example, the effects of mechanical overload conditioning of superelastic wire and the possibility of increased fatigue damage resistance associated with near-defect, plasticity-locked phase transformation were further investigated over a broader range of loads as compared to Example 2 using a high strength chromium doped tertiary Nitinol compound.

1. Experimental Technique

Samples for this Example were subjected to a total engineering strain departure, measured by crosshead extension, ranging from about 7.7% to 13.1% Conditioning was applied by approaching the martensitic yield point at 295 K using strain-rate-controlled loading in order induce some dislocation locking of stress-transformed material in the vicinity of stress concentrators. Referring now to FIG. 19(b), the conditioning cycle comprises a strain-controlled ramp to five stress levels of 0, 700, 1100, 1240, 1400, and 1500 MPa engineering stress, resulting in an engineering strain of about 0%, 7.7%, 9.6%, 10.2%, 11.3%, and 13.1% respectively, followed by a 3 second hold, finishing with a strain-controlled ramp to zero load.

In order to prepare samples for this Example, Nitinol wire with an ingot austenite start temperature, As, of about 235 K, having Ti-55.8 wt. % Ni-0.25 wt % Cr was repetitively drawn and annealed from a diameter of 2 mm to a diameter of 361 μm in accordance with the process described above. At this stage, wires were continuously annealed at 950 to 1000 K. Final cold working was completed using diamond dies to draw round wire with a diameter of 269 μm prior to continuous, reel-to-reel annealing at 750 to 780 K under constant engineering stress for 40 to 80 seconds to effect linear shape setting. The final wire comprised a room-temperature-superelastic Nitinol wire with an active austenitic finish temperature, Af, of 283 K and an approximately 120 nm thick, dark brown oxide layer similar to that disclosed in an article by the present inventor entitled “Structure-Property Relationships in Conventional and Nanocrystalline NiTi Intermetallic Alloy Wire” and published in the Journal of Materials Engineering and Performance, February 2008, ISSN 1544-1024, pgs. 1-6, which is incorporated by reference above.

Cyclic and monotonic uniaxial tensile properties were measured at an ambient temperature of 295 K at a strain rate of 10⁻³ s⁻¹ using an Instron Model 5565 Tensile Test Bench equipped with pneumatic, smooth face grips. Six hundred grit emery-cloth was used to reduce grip-specimen interface slip.

Fatigue behavior was characterized using rotary beam fatigue test equipment manufactured by Positool, Inc., at a test rate of 60 s⁻¹ in ambient 298 K air. The test rate was chosen at a rate significantly higher than physiological loading frequencies to promote expediency.

As shown in FIGS. 18 (a) to (d), three specimens from each group at each conditioning cycle, ranging from 0 MPa which indicates non-conditioned wire to 1500 MPa which indicates the maximum conditioning load used, were tested at alternating engineering strain (½ peak-to-peak amplitude) levels ranging from 0.80 to 1.25% strain to a maximum of about 10⁶ cycles. The total samples tested for each conditioning load regime for each sample was 12 resulting in a total of 72 fatigue samples tested for this portion of the study. Samples which did not fracture after 10⁶ cycles were stopped and recorded.

2. Results

The resulting tensile data is shown graphically in FIG. 19(b). As noted above, the conditioning cycle comprised a strain-controlled ramp to a stress level of 0, 700, 1100, 1240, 1400 or 1500 MPa engineering stress, as indicated along the horizontal axis of the plot, followed by a 3 second hold, finishing with a strain-controlled ramp to zero load. This conditioning cycle generated data curves 2.1, 2.3, 2.4, 2.6 and 2.7 shown in FIG. 19(b). The total engineering strain departure for respective cycles, measured by crosshead extension, was about 0%, 7.7%, 9.6%, 10.2%, 11.3%, and 13.1% for increasing load levels respectively. Conditioning resulted in residual strains (i.e. isothermally non-recoverable strains) of respectively 0%, 0.07%, 0.09%, 0.35%, 0.18%, and 2.23% respectively.

FIGS. 18 (a)-(d) illustrate the observed differences in fatigue performance for non-conditioned (e.g. 0 load level on x-axis) and conditioned wire specimens (700, 1100, 1240, 1400, and 1500 MPa on the x-axis) The conditioning resulted in an upward cycle life shift of at least 46% and 2500% at the 1.25% and 0.95% alternating strain test levels respectively at a conditioning load level of 1240 MPa. An overall upward trend in lifetime for a given test strain level was observed for increasing conditioning load through 1500 MPa. Most samples of the material conditioned at greater than 1240 MPa survived more than 10⁶ cycles and were still running at the time of conclusion of the experiment for test strain levels below 0.95%.

FIG. 19(b) illustrates the observed tensile behavior during load conditioning of each sample. In each case, an upper bound of the maximum volume of retained martensite was calculated as described above based on the ratio of isothermally non-recoverable strain to the strain length of the load plateau. FIG. 20 illustrates the positive correlation between isothermally non-recoverable strain and conditioning load. Non-recoverable strain was less than 0.35% for all samples conditioned below 1400 MPa resulting in a max volume of retained martensite estimate of 5.9% for the same samples loaded below 1400 MPa.

In this Example, it has been demonstrated that mechanical conditioning of superelastic NiTi wire results in improved fatigue performance, while maintaining good mechanical properties. In addition, less than 5.9% of the matrix was left in the martensite phase after load removal for conditioning below 1400 MPa with a concomitant maximum isothermally non-recoverable strain of 0.35%. Further, an increase in the strain fatigue life of greater than 2500% at 10⁶ cycles is observed in wire conditioned at 1240 MPa versus non-conditioned wire while maintaining good elastic properties suitable for said medical device applications.

Example 5

Mechanical Conditioning of Superelastic NiTi Wire for Improved Fatigue Resistance

In this Example, the effects of mechanical overload conditioning of superelastic wire and the possibility of increased fatigue damage resistance associated with near-defect, plasticity-locked phase transformation were further investigated over a broader range of loads as compared to Example 2 using a Nitinol with warmer transformation temperatures as compared to Examples 2 and 3.

1. Experimental Technique

Samples for this Example were subjected to a total engineering strain departure, measured by crosshead extension, ranging from about 8.3% to 12.8% Conditioning was applied by approaching the martensitic yield point at 295 K using strain-rate-controlled loading in order induce some dislocation locking of stress-transformed material in the vicinity of stress concentrators. Referring now to FIG. 19 (c), the conditioning cycle comprises a strain-controlled ramp to five stress levels of 0, 700, 1100, 1240, and 1400 MPa engineering stress, resulting in an engineering strain of about 0%, 8.3%, 10%, 10.8%, and 12.8% respectively, followed by a 3 second hold, finishing with a strain-controlled ramp to zero load.

In order to prepare samples for this Example, Nitinol wire with an ingot austenite start temperature, A_s, of about 255 K, having Ti-55.8 wt. % Ni was repetitively drawn and annealed from a diameter of 2 mm to a diameter of 380 μm in accordance with the process described above. At this stage, wires were continuously annealed at 950 to 1000 K. Final cold working was completed using diamond dies to draw round wire with a diameter of 302 μm prior to continuous, reel-to-reel annealing at 750 to 780 K under constant engineering stress for 40 to 80 seconds to effect linear shape setting. The final wire comprised a room-temperature-superelastic Nitinol wire with an active austenitic finish temperature, A_f, of 298 K and an approximately 120 nm thick, dark brown oxide layer similar to that disclosed in an article by the present inventor entitled “Structure-Property Relationships in Conventional and Nanocrystalline NiTi Intermetallic Alloy Wire” and published in the Journal of Materials Engineering and Performance, February 2008, ISSN 1544-1024, pgs. 1-6, which is incorporated by reference above.

Cyclic and monotonic uniaxial tensile properties were measured at an ambient temperature of 295 K at a strain rate of 10⁻³ s⁻¹ using an Instron Model 5565 Tensile Test Bench equipped with pneumatic, smooth face grips. Six hundred grit emery-cloth was used to reduce grip-specimen interface slip.

Fatigue behavior was characterized using rotary beam fatigue test equipment manufactured by Positool, Inc., at a test rate of 60 s⁻¹ in ambient 298 K air. The test rate was chosen at a rate significantly higher than physiological loading frequencies to promote expediency.

As shown in FIGS. 18 (a) to (d), three specimens from each group at each conditioning cycle, ranging from 0 MPa which indicates non-conditioned wire to 1400 MPa which indicates the maximum conditioning load used, were tested at alternating engineering strain (½ peak-to-peak amplitude) levels ranging from 0.80 to 1.25% strain to a maximum of about 10⁶ cycles. The total samples tested for each conditioning load regime for each sample was 12 resulting in a total of 60 fatigue samples tested for this portion of the study. Samples which did not fracture after 10⁶ cycles were stopped and recorded.

2. Results

The resulting tensile data is shown graphically in FIG. 19 (c). As noted above, the conditioning cycle comprised a strain-controlled ramp to a stress level of 0, 700, 1100, 1240, or 1400 MPa engineering stress, as indicated along the horizontal axis of the plot, followed by a 3 second hold, finishing with a strain-controlled ramp to zero load. This conditioning cycle generated curves 3.1, 3.3, 3.4, and 3.6 shown in FIG. 19(c). The total engineering strain departure for respective cycles, measured by crosshead extension, was about 0%, 8.3%, 10%, 10.8%, and 12.8% for increasing load levels respectively. Conditioning resulted in residual strains (i.e. isothermally non-recoverable strains) of respectively 0%, 0.03%, 0.13%, 1.1%, and 7.31% respectively.

FIGS. 18 (a) to (d) illustrate the observed differences in fatigue performance for non-conditioned (e.g. 0 load level on x-axis) and conditioned wire specimens (700, 1100, 1240, and 1400 MPa on the x-axis) The conditioning resulted in an upward cycle life shift of at least 116% and 2400% at the 1.25% and 0.95% alternating strain test levels respectively at a conditioning load level of 1240 MPa. An overall upward trend in lifetime for a given test strain level was observed for increasing conditioning load through 1400 MPa. Most samples of the material conditioned at greater than 1240 MPa survived more than 10⁶ cycles and were still running at the time of conclusion of the experiment for test strain levels below 0.95%.

FIG. 19(c) illustrates the observed tensile behavior during load conditioning of each sample. In each case, an upper bound of the maximum volume of retained martensite was calculated as described above based on the ratio of isothermally non-recoverable strain to the strain length of the load plateau. FIG. 20 illustrates the positive correlation between isothermally non-recoverable strain and conditioning load. Non-recoverable strain was less than about 1% for all samples conditioned below 1240 MPa resulting in a max. volume of retained martensite estimate of about 17% for the same samples loaded below 1240 MPa.

In this Example, it has been demonstrated that mechanical conditioning of superelastic NiTi wire results in improved fatigue performance, while maintaining good mechanical properties. In addition, less than about 17% of the matrix was left in the martensite phase after load removal for conditioning below 1240 MPa with a concomitant maximum isothermally non-recoverable strain of about 1%. Further, an increase in the strain fatigue life of greater than 2400% at 10⁶ cycles is observed in wire conditioned at 1240 MPa versus non-conditioned wire while maintaining good elastic properties suitable for said medical device applications.

Example 6

Mechanical Conditioning of Superelastic NiTi Wire with an Etched Surface Finish for Improved Fatigue Resistance

In this Example, the effects of mechanical overload conditioning of superelastic wire and the possibility of increased fatigue damage resistance associated with near-defect, plasticity-locked phase transformation were further investigated over a broader range of loads as compared to Example 2 and in a finer diameter using a Nitinol with an etched surface finish comprising a substantially oxide-free surface.

1. Experimental Technique

Samples for this Example were subjected to a total engineering strain departure, measured by crosshead extension, ranging from about 7.8 to 11.9% Conditioning was applied by approaching the martensitic yield point at 295 K using strain-rate-controlled loading in order induce some dislocation locking of stress-transformed material in the vicinity of stress concentrators. Referring now to FIG. 19 (d), the conditioning cycle comprises a strain-controlled ramp to five stress levels of 0, 700, 1100, 1240, 1400 and 1500 MPa engineering stress, resulting in an engineering strain of about 0%, 7.8%, 9.5%, 10%, 10.8%, and 11.9% respectively, followed by a 3 second hold, finishing with a strain-controlled ramp to zero load.

In order to prepare samples for this Example, Nitinol wire with an ingot austenite start temperature, A_s, of about 246 K, having Ti-56 wt. % Ni was repetitively drawn and annealed from a diameter of 2 mm to a diameter of 102 μm in accordance with the process described above. At this stage, wires were continuously annealed at 950 to 1000 K. Final cold working was completed using diamond dies to draw round wire with a diameter of 76 μm prior to continuous, reel-to-reel annealing at 750 to 780 K under constant engineering stress for 40 to 80 seconds to effect linear shape setting. The final wire comprised a room-temperature-superelastic Nitinol wire with an active austenitic finish temperature, A_f, of 288 K and an etched, substantially oxide-free surface finish.

Cyclic and monotonic uniaxial tensile properties were measured at an ambient temperature of 295 K at a strain rate of 10⁻³ s⁻¹ using an Instron Model 5565 Tensile Test Bench equipped with pneumatic, smooth face grips. Six hundred grit emery-cloth was used to reduce grip-specimen interface slip.

Fatigue behavior was characterized using rotary beam fatigue test equipment manufactured by Positool, Inc., at a test rate of 60 s⁻¹ in ambient 298 K air. The test rate was chosen at a rate significantly higher than physiological loading frequencies to promote expediency.

As shown in FIGS. 18 (a) to (d), three specimens from each group at each conditioning cycle, ranging from 0 MPa which indicates non-conditioned wire to 1500 MPa which indicates the maximum conditioning load used, were tested at alternating engineering strain (½ peak-to-peak amplitude) levels ranging from 0.80 to 1.25% strain to a maximum of about 10⁶ cycles. The total samples tested for each conditioning load regime for each sample was 12 resulting in a total of 72 fatigue samples tested for this portion of the study. Samples which did not fracture after 10⁶ cycles were stopped and recorded.

2. Results

The resulting tensile data is shown graphically in FIG. 19 (d). As noted above, the conditioning cycle comprised a strain-controlled ramp to a stress level of 0, 700, 1100, 1240, 1400 or 1500 MPa engineering stress, as indicated along the horizontal axis of the plot, followed by a 3 second hold, finishing with a strain-controlled ramp to zero load. This conditioning cycle generated curves 4.1, 4.3, 4.4, 4.6 and 4.7 shown in FIG. 19(d). The total engineering strain departure for respective cycles, measured by crosshead extension, was about 0%, 7.8%, 9.5%, 10%, 10.8%, and 11.9% for increasing load levels respectively. Conditioning resulted in residual strains (i.e. isothermally non-recoverable strains) of respectively 0%, 0.09%, 0.14%, 0.29%, 0.26% and 7.2% respectively.

FIGS. 18 (a) to (d) illustrate the observed differences in fatigue performance for non-conditioned (e.g. 0 load level on x-axis) and conditioned wire specimens (700, 1100, 1240, 1400 and 1500 MPa on the x-axis) The conditioning resulted in an upward cycle life shift of at least 7.2% and 2600% at the 1.25% and 0.95% alternating strain test levels respectively at a conditioning load level of 1240 MPa. An overall upward trend in lifetime for a given test strain level was observed for increasing conditioning load through 1500 MPa. Most samples of the material conditioned at greater than 1240 MPa survived more than 10⁶ cycles and were still running at the time of conclusion of the experiment for test strain levels below 0.95%.

FIG. 19(d) illustrates the observed tensile behavior during load conditioning of each sample. In each case, an upper bound of the maximum volume of retained martensite was calculated as described above based on the ratio of isothermally non-recoverable strain to the strain length of the load plateau. FIG. 20 illustrates the positive correlation between isothermally non-recoverable strain and conditioning load. Non-recoverable strain was less than about 0.29% for all samples conditioned below 1240 MPa resulting in a max. volume of retained martensite estimate of about 4.7% for the same samples loaded below 1400 MPa.

In this Example, it has been demonstrated that mechanical conditioning of superelastic NiTi wire results in improved fatigue performance, while maintaining good mechanical properties. In addition, less than about 4.7% of the matrix was left in the martensite phase after load removal for conditioning below 1400 MPa with a concomitant maximum isothermally non-recoverable strain of about 0.29%. Further, an increase in the strain fatigue life of greater than 2600% at 10⁶ cycles is observed in wire conditioned at 1240 MPa versus non-conditioned wire while maintaining good elastic properties suitable for said medical device applications.

Example 7

Mechanical Conditioning of Superelastic NiTi Wire with a Polished Surface Finish for Improved Fatigue Resistance

In this Example, the effects of mechanical overload conditioning of superelastic wire and the possibility of increased fatigue damage resistance associated with near-defect, plasticity-locked phase transformation were further investigated over a broader range of loads as compared to Example 2 and in a larger diameter using a Nitinol with an etched and mechanically polished surface finish comprising a substantially oxide-free surface.

1. Experimental Technique

Samples for this Example were subjected to a total engineering strain departure, measured by crosshead extension, ranging from about 7.5 to 13.1% Conditioning was applied by approaching the martensitic yield point at 295 K using strain-rate-controlled loading in order induce some dislocation locking of stress-transformed material in the vicinity of stress concentrators. Referring now to FIG. 19 (d), the conditioning cycle comprises a strain-controlled ramp to five stress levels of 0, 700, 1100, 1240, 1400 and 1500 MPa engineering stress, resulting in an engineering strain of about 0%, 7.5%, 9.6%, 10.3%, 11.6%, and 13.1% respectively, followed by a 3 second hold, finishing with a strain-controlled ramp to zero load.

In order to prepare samples for this Example, Nitinol wire with an ingot austenite start temperature, A_s, of about 249 K, having Ti-56 wt. % Ni was repetitively drawn and annealed from a diameter of 2 mm to a diameter of 813 μm in accordance with the process described above. At this stage, wires were continuously annealed at 950 to 1000 K. Final cold working was completed using diamond dies to draw round wire with a diameter of 638 μm prior to continuous, reel-to-reel annealing at 750 to 780 K under constant engineering stress for 60 to 150 seconds to effect linear shape setting. The final wire comprised a room-temperature-superelastic Nitinol wire with an active austenitic finish temperature, A_f, of 291 K and an etched, substantially oxide-free and mechanically polished surface finish.

Cyclic and monotonic uniaxial tensile properties were measured at an ambient temperature of 295 K at a strain rate of 10⁻³ s⁻¹ using an Instron Model 5565 Tensile Test Bench equipped with pneumatic, smooth face grips. Six hundred grit emery-cloth was used to reduce grip-specimen interface slip.

Fatigue behavior was characterized using rotary beam fatigue test equipment manufactured by Positool, Inc., at a test rate of 60 s⁻¹ in ambient 298 K air. The test rate was chosen at a rate significantly higher than physiological loading frequencies to promote expediency.

As shown in FIGS. 18 (a) to (d), three specimens from each group at each conditioning cycle, ranging from 0 MPa which indicates non-conditioned wire to 1500 MPa which indicates the maximum conditioning load used, were tested at alternating engineering strain (½ peak-to-peak amplitude) levels ranging from 0.80 to 1.25% strain to a maximum of about 10⁶ cycles. The total samples tested for each conditioning load regime for each sample was 12 resulting in a total of 72 fatigue samples tested for this portion of the study. Samples which did not fracture after 10⁶ cycles were stopped and recorded.

2. Results

The resulting tensile data is shown graphically in FIG. 19 (e). As noted above, the conditioning cycle comprised a strain-controlled ramp to a stress level of 0, 700, 1100, 1240, 1400 or 1500 MPa engineering stress, as indicated along the horizontal axis of the plot, followed by a 3 second hold, finishing with a strain-controlled ramp to zero load. This conditioning cycle generated data curves 5.1, 5.3, 5.4, 5.6 and 5.7 shown in FIG. 19(e). The total engineering strain departure for respective cycles, measured by crosshead extension, was about 0%, 7.5%, 9.6%, 10.3%, 11.6%, and 13.1% for increasing load levels respectively. Conditioning resulted in residual strains (i.e. isothermally non-recoverable strains) of respectively 0%, 0.21%, 0.40%, 0.61%, 2.17%, and 7.84% respectively.

FIGS. 18 (a) to (d) illustrate the observed differences in fatigue performance for non-conditioned (e.g. 0 load level on x-axis) and conditioned wire specimens (700, 1100, 1240, 1400 and 1500 MPa on the x-axis) The conditioning resulted in an upward cycle life shift of at least 54% at the 0.95% alternating strain test levels respectively at a conditioning load level of 1240 MPa. An overall upward trend in lifetime for a given test strain level was observed for increasing conditioning load through 1500 MPa. Most samples of the material conditioned at greater than 1240 MPa survived more than 10⁶ cycles and were still running at the time of conclusion of the experiment for test strain levels below 0.80%.

FIG. 19(e) illustrates the observed tensile behavior during load conditioning of each sample. In each case, an upper bound of the maximum volume of retained martensite was calculated as described above based on the ratio of isothermally non-recoverable strain to the strain length of the load plateau. FIG. 20 illustrates the positive correlation between isothermally non-recoverable strain and conditioning load. Non-recoverable strain was less than about 0.61% for all samples conditioned below 1240 MPa resulting in a max. volume of retained martensite estimate of about 11% for the same samples loaded below 1240 MPa.

In this Example, it has been demonstrated that mechanical conditioning of superelastic NiTi wire results in improved fatigue performance, while maintaining good mechanical properties. In addition, less than about 11% of the matrix was left in the martensite phase after load removal for conditioning below 1240 MPa with a concomitant maximum isothermally non-recoverable strain of about 0.61%. Further, an increase in the strain fatigue life of greater than 54% at 10⁶ cycles is observed in wire conditioned at 1240 MPa versus non-conditioned wire while maintaining good elastic properties suitable for said medical device applications.

TABLE 3

Tensile Data for Various Wire Samples, see Examples 3-6, FIG. 19(a)

Strain level

1.1

Engr.

1.3

Engr.

1.4

Engr.

1.6

Engr.

1.7

Engr.

Engr.

Stress

Engr.

Stress

Engr.

Stress

Engr.

Stress

Engr.

Stress

Strain

(MPa)

Strain

(MPa)

Strain

(MPa)

Strain

(MPa)

Strain

(MPa)

0

0

0

0

0

0

0

0

0

0

0.0019

106.7

0.0020

108.5

0.0009

51.2

0.0016

86.8

0.0010

55.8

0.0154

655.3

0.0132

601.7

0.0047

295.3

0.0053

315.4

0.0048

287.4

0.0157

614.5

0.0163

680.2

0.0134

626.4

0.0085

431.0

0.0096

461.7

0.0201

644.5

0.0180

591.1

0.0170

686.4

0.0139

630.5

0.0135

614.8

0.0523

643.1

0.0195

635.8

0.0209

612.7

0.0189

642.5

0.0160

663.5

0.0796

639.8

0.0513

636.2

0.0305

636.1

0.0462

657.7

0.0393

621.6

0.0817

699.7

0.0747

638.4

0.0701

634.9

0.0612

631.2

0.0579

624.2

0.0821

716.8

0.0784

635.4

0.0753

643.3

0.0766

642.1

0.0787

631.7

0.0826

700.5

0.0797

669.7

0.0793

690.4

0.0793

665.2

0.0804

680.6

0.0746

431.8

0.0822

739.3

0.0826

755.0

0.0824

748.1

0.0856

809.0

0.0718

360.0

0.0899

933.9

0.0866

854.4

0.0872

870.6

0.0948

1036.8

0.0688

293.9

0.0968

1100.3

0.1006

1189.9

0.0953

1082.6

0.1083

1341.4

0.0646

222.5

0.0974

1116.1

0.1012

1201.9

0.1075

1351.4

0.1209

1500.8

0.0633

206.7

0.0976

1114.3

0.1019

1218.4

0.1082

1353.9

0.1223

1508.2

0.0618

190.8

0.0969

1092.6

0.1026

1234.8

0.1105

1400.7

0.1202

1427.7

0.0593

171.7

0.0921

891.0

0.1030

1245.6

0.1113

1406.2

0.1184

1353.7

0.0558

160.0

0.0801

460.0

0.1033

1243.3

0.1084

1286.7

0.1096

1012.9

0.0526

168.1

0.0774

381.8

0.1012

1157.5

0.1069

1225.5

0.0940

463.0

0.0461

160.4

0.0742

303.2

0.0985

1043.9

0.1007

970.9

0.0798

100.3

0.0393

178.4

0.0705

225.0

0.0887

662.5

0.0788

240.8

0.0734

4.9

0.0288

170.2

0.0667

165.6

0.0791

358.0

0.0725

116.4

0.0729

0.1

0.0233

169.8

0.0615

113.5

0.0745

246.1

0.0640

33.1

0.0727

0.0

0.0113

167.4

0.0584

106.0

0.0691

149.6

0.0590

39.1

0.0063

169.4

0.0540

111.2

0.0651

103.4

0.0511

33.0

0.0019

0.0

0.0426

113.7

0.0585

84.8

0.0440

35.5

0.0309

112.0

0.0520

91.9

0.0352

38.7

0.0074

113.2

0.0435

93.6

0.0265

35.2

0.0044

92.9

0.0335

95.8

0.0152

67.2

0.0030

53.3

0.0262

93.2

0.0115

56.6

0.0020

0.0

0.0174

81.9

0.0048

25.7

0.0122

99.3

0.0017

0.0

0.0089

111.8

0.0062

76.2

0.0029

17.0

0.0024

0.0

load plateau

0.0663

0.0690

0.0658

0.0654

0.0652

length (strain) →

unload plateau

0.0627

0.0648

0.0627

0.0623

0.0071

length (strain) →

permanent set

0.0019

0.0020

0.0024

0.0017

0.0727

(strain) →

max volume fraction

2.9%

2.8%

3.7%

2.6%

100.0%

martensite (%) →

TABLE 4

Tensile Data for Various Wire Samples, see Examples 3-6, FIG. 19(b)

Strain level

2.1

Engr.

2.3

Engr.

2.4

Engr.

2.6

Engr.

2.7

Engr.

Engr.

Stress

Engr.

Stress

Engr.

Stress

Engr.

Stress

Engr.

Stress

Strain

(MPa)

Strain

(MPa)

Strain

(MPa)

Strain

(MPa)

Strain

(MPa)

0

0

0

0

0

0

0

0

0

0

0.0052

313.2

0.0009

49.5

0.0009

51.0

0.0007

37.9

0.0008

44.9

0.0107

540.7

0.0047

278.5

0.0047

277.4

0.0044

268.7

0.0046

274.8

0.0148

647.1

0.0092

470.9

0.0093

470.0

0.0090

464.1

0.0092

469.4

0.0152

645.2

0.0165

668.0

0.0166

668.5

0.0163

671.1

0.0164

670.8

0.0159

650.8

0.0205

641.1

0.0205

634.1

0.0203

632.2

0.0204

638.9

0.0164

654.0

0.0253

640.1

0.0253

627.5

0.0251

647.9

0.0252

647.7

0.0170

657.3

0.0584

649.5

0.0584

644.5

0.0582

624.2

0.0583

641.6

0.0245

650.4

0.0694

646.7

0.0695

641.9

0.0692

642.2

0.0694

644.0

0.0684

641.0

0.0728

655.8

0.0728

658.1

0.0726

666.4

0.0727

656.6

0.0734

637.0

0.0757

702.2

0.0757

701.7

0.0755

701.9

0.0756

701.7

0.0743

652.5

0.0782

749.1

0.0782

743.7

0.0780

747.0

0.0781

746.1

0.0749

666.0

0.0901

1006.6

0.0901

1000.8

0.0899

1007.8

0.0900

999.6

0.0763

697.5

0.0928

1059.7

0.0941

1088.6

0.0938

1097.3

0.0939

1084.7

0.0767

706.1

0.0932

1061.0

0.0970

1149.8

0.0967

1159.7

0.0969

1145.1

0.0767

696.1

0.0936

1070.4

0.0992

1189.1

0.1003

1230.4

0.1004

1213.8

0.0653

386.6

0.0944

1087.2

0.1000

1195.9

0.1059

1326.9

0.1060

1310.6

0.0603

304.9

0.0951

1103.2

0.1007

1210.8

0.1084

1345.7

0.1114

1384.3

0.0553

260.5

0.0955

1109.7

0.1014

1226.5

0.1091

1352.0

0.1169

1440.2

0.0506

244.2

0.0955

1104.3

0.1021

1239.8

0.1099

1363.8

0.1199

1442.0

0.0446

249.3

0.0953

1098.4

0.1022

1240.6

0.1102

1369.1

0.1202

1438.8

0.0361

260.2

0.0919

961.0

0.1022

1236.0

0.1106

1377.1

0.1219

1454.3

0.0183

258.0

0.0877

800.9

0.1022

1231.9

0.1112

1385.9

0.1239

1475.3

0.0158

267.6

0.0867

762.9

0.1016

1210.2

0.1113

1388.1

0.1260

1488.8

0.0086

232.7

0.0827

626.9

0.0976

1045.7

0.1118

1396.0

0.1279

1497.3

0.0071

218.2

0.0792

518.0

0.0941

905.5

0.1123

1401.5

0.1309

1499.0

0.0053

192.6

0.0759

428.1

0.0908

780.5

0.1128

1399.3

0.1287

1417.2

0.0028

113.0

0.0707

313.8

0.0856

601.6

0.1129

1397.9

0.1252

1281.9

0.0008

22.5

0.0671

255.5

0.0820

493.4

0.1106

1307.1

0.1162

952.8

0.0007

0.0

0.0634

210.8

0.0783

393.2

0.1087

1230.3

0.1114

787.8

0.0588

185.1

0.0737

291.6

0.1041

1047.3

0.1060

614.2

0.0540

179.0

0.0689

212.5

0.0993

864.9

0.0943

298.8

0.0517

180.0

0.0666

184.7

0.0970

781.4

0.0908

222.1

0.0469

186.4

0.0618

148.3

0.0922

617.6

0.0864

141.9

0.0323

190.5

0.0472

152.9

0.0851

407.8

0.0820

78.7

0.0205

191.7

0.0354

166.8

0.0777

237.4

0.0779

35.3

0.0096

180.8

0.0245

165.2

0.0735

169.3

0.0750

14.6

0.0069

148.3

0.0218

154.2

0.0679

108.1

0.0708

3.0

0.0038

55.4

0.0187

152.5

0.0618

81.8

0.0660

10.7

0.0017

0.2

0.0166

155.5

0.0568

91.8

0.0627

14.5

0.0009

0.0

0.0158

163.8

0.0541

94.1

0.0506

16.1

0.0110

152.6

0.0508

101.1

0.0335

14.0

0.0064

104.3

0.0324

101.4

0.0260

5.4

0.0049

55.6

0.0154

98.9

0.0231

1.2

0.0039

13.1

0.0076

49.0

0.0223

0.0

0.0035

0.0

0.0039

0.2

0.0018

0.0

load plateau

0.0601

0.0592

0.0592

0.0592

0.0592

length (strain)

unload plateau

0.0596

0.0662

0.0654

0.0717

0.0485

length (strain)

permanent set

0.0007

0.0009

0.0035

0.0018

0.0223

(strain)

max vol. fraction

1.2%

1.5%

5.9%

3.1%

37.6%

martensite (%)

TABLE 5

Tensile Data for Various Wire Samples, see Examples 3-6, FIG. 19(c)

Strain level

3.1

Engr.

3.3

Engr.

3.4

Engr.

3.6

Engr.

Engr.

Stress

Engr.

Stress

Engr.

Stress

Engr.

Stress

Strain

(MPa)

Strain

(MPa)

Strain

(MPa)

Strain

(MPa)

0

0

0

0

0

0

0

0

0.0003

16.0

0.0009

52.2

0.0007

37.7

0.0006

32.1

0.0048

237.0

0.0047

230.8

0.0044

239.5

0.0043

232.3

0.0105

450.1

0.0095

406.1

0.0092

420.0

0.0091

410.1

0.0138

550.1

0.0122

509.7

0.0119

525.8

0.0118

512.5

0.0173

544.5

0.0151

556.9

0.0149

570.7

0.0147

563.6

0.0358

527.9

0.0305

529.6

0.0303

539.6

0.0302

550.0

0.0618

529.2

0.0522

523.1

0.0519

538.8

0.0518

513.0

0.0733

549.4

0.0618

523.1

0.0615

543.5

0.0614

530.4

0.0748

571.5

0.0630

510.2

0.0628

534.2

0.0627

539.5

0.0785

631.8

0.0662

525.3

0.0659

548.4

0.0658

522.6

0.0802

661.4

0.0687

529.5

0.0684

552.7

0.0683

507.3

0.0807

664.3

0.0716

543.2

0.0713

567.4

0.0712

536.6

0.0813

673.7

0.0755

590.1

0.0753

609.2

0.0752

591.3

0.0820

686.2

0.0797

668.3

0.0794

670.0

0.0793

663.0

0.0827

700.6

0.0841

767.6

0.0838

761.7

0.0837

758.2

0.0832

709.6

0.0901

908.9

0.0899

899.3

0.0897

896.7

0.0831

701.3

0.0969

1060.2

0.0976

1069.0

0.0975

1068.7

0.0801

591.9

0.0973

1059.3

0.1001

1118.4

0.1000

1118.5

0.0746

411.1

0.0979

1070.4

0.1043

1193.2

0.1045

1200.1

0.0711

316.3

0.0983

1078.4

0.1046

1184.5

0.1075

1244.7

0.0666

219.2

0.0988

1089.9

0.1051

1191.0

0.1112

1293.0

0.0601

128.9

0.0994

1103.9

0.1059

1204.6

0.1166

1346.2

0.0536

100.1

0.0998

1107.3

0.1066

1218.6

0.1186

1337.7

0.0444

100.8

0.0992

1078.3

0.1076

1236.3

0.1197

1345.4

0.0424

102.4

0.0975

1004.8

0.1077

1238.6

0.1199

1348.3

0.0371

108.2

0.0931

821.3

0.1079

1235.3

0.1205

1355.8

0.0306

107.0

0.0877

611.1

0.1080

1232.6

0.1212

1364.3

0.0249

107.5

0.0829

445.7

0.1034

1040.9

0.1218

1370.6

0.0209

111.3

0.0796

343.7

0.1001

903.4

0.1223

1374.5

0.0159

109.8

0.0754

234.2

0.0959

738.9

0.1228

1378.9

0.0101

100.7

0.0706

134.6

0.0911

563.4

0.1235

1383.3

0.0059

78.9

0.0671

80.0

0.0876

445.1

0.1239

1386.1

0.0031

43.4

0.0648

53.3

0.0853

374.5

0.1242

1387.8

0.0021

17.8

0.0640

45.1

0.0845

350.1

0.1244

1388.4

0.0006

2.2

0.0627

34.6

0.0832

314.7

0.1245

1389.3

0.0003

0.0

0.0596

17.8

0.0801

233.3

0.1249

1391.5

0.0567

12.8

0.0772

167.0

0.1253

1393.4

0.0531

15.1

0.0736

100.4

0.1258

1395.6

0.0510

15.6

0.0716

68.2

0.1261

1396.7

0.0485

18.0

0.0691

36.9

0.1264

1398.2

0.0458

22.0

0.0664

11.4

0.1267

1399.6

0.0446

23.7

0.0651

2.6

0.1269

1400.2

0.0433

24.1

0.0639

2.0

0.1271

1400.6

0.0333

26.7

0.0539

2.0

0.1281

1399.7

0.0306

26.5

0.0511

2.0

0.1256

1303.2

0.0279

27.4

0.0484

2.0

0.1229

1197.3

0.0217

23.0

0.0422

2.0

0.1166

960.1

0.0167

22.8

0.0372

13.7

0.1116

779.5

0.0140

18.3

0.0345

17.6

0.1089

686.3

0.0102

9.8

0.0307

19.4

0.1052

563.2

0.0063

0.4

0.0268

19.6

0.1012

441.7

0.0019

0.5

0.0224

18.1

0.0968

318.9

0.0013

0.0

0.0180

14.7

0.0924

208.9

0.0141

8.3

0.0885

121.9

0.0116

3.2

0.0860

73.7

0.0109

0.0

0.0837

34.4

0.0806

1.2

0.0731

0.0

load plateau

0.0664

0.0646

0.0633

0.0675

length (strain)

unload plateau

0.0598

0.0658

0.0606

0.0075

length (strain)

permanent set

0.0003

0.0013

0.0109

0.0731

(strain)

max volume fraction

0.4%

1.9%

17.3%

100.0%

martensite (%)

TABLE 6

Tensile Data for Various Wire Samples, see Examples 3-6, FIG. 19(d)

Strain level

4.1

Engr.

4.3

Engr.

4.4

Engr.

4.6

Engr.

4.7

Engr.

Engr.

Stress

Engr.

Stress

Engr.

Stress

Engr.

Stress

Engr.

Stress

Strain

(MPa)

Strain

(MPa)

Strain

(MPa)

Strain

(MPa)

Strain

(MPa)

0

0

0

0

0

0

0

0

0

0

0.0063

344.2

0.0037

195.8

0.0029

158.3

0.0024

127.7

0.0022

119.3

0.0108

520.9

0.0059

276.6

0.0050

239.7

0.0046

229.8

0.0043

211.8

0.0133

606.8

0.0076

335.0

0.0066

296.5

0.0063

294.0

0.0059

270.9

0.0158

644.6

0.0098

410.4

0.0087

372.3

0.0085

367.3

0.0080

341.4

0.0188

613.0

0.0119

498.4

0.0108

461.2

0.0106

448.9

0.0101

426.9

0.0218

635.5

0.0139

574.4

0.0127

534.1

0.0126

529.7

0.0120

503.2

0.0258

633.3

0.0161

625.0

0.0148

576.3

0.0148

596.8

0.0140

556.0

0.0308

623.0

0.0171

627.8

0.0158

585.0

0.0158

619.5

0.0151

569.8

0.0358

637.5

0.0206

631.5

0.0191

582.2

0.0193

630.6

0.0184

576.1

0.0403

638.8

0.0249

596.2

0.0233

556.1

0.0236

596.0

0.0226

539.8

0.0485

606.7

0.0293

591.9

0.0275

561.4

0.0280

634.6

0.0268

544.2

0.0668

614.5

0.0332

631.1

0.0312

581.7

0.0319

621.6

0.0305

578.1

0.0733

626.7

0.0403

622.8

0.0381

586.4

0.0390

628.7

0.0374

572.2

0.0745

662.3

0.0561

614.6

0.0533

559.5

0.0548

622.2

0.0526

564.7

0.0750

671.1

0.0618

621.3

0.0587

560.3

0.0605

615.9

0.0580

571.1

0.0756

687.8

0.0633

629.5

0.0602

580.9

0.0620

627.9

0.0595

572.1

0.0762

700.6

0.0661

599.2

0.0629

571.0

0.0648

608.4

0.0622

575.9

0.0767

711.5

0.0704

633.3

0.0670

575.6

0.0691

617.3

0.0663

573.1

0.0771

720.3

0.0741

633.6

0.0706

570.7

0.0728

623.8

0.0699

579.1

0.0776

729.8

0.0778

696.1

0.0741

619.8

0.0765

658.5

0.0734

595.5

0.0767

702.1

0.0808

771.2

0.0770

693.4

0.0795

735.8

0.0763

669.4

0.0740

605.1

0.0847

872.9

0.0808

788.7

0.0834

834.0

0.0801

760.8

0.0700

483.3

0.0891

988.3

0.0850

892.8

0.0878

949.9

0.0843

863.6

0.0662

393.5

0.0915

1054.0

0.0873

948.0

0.0902

1012.6

0.0865

927.3

0.0615

306.7

0.0921

1062.2

0.0906

1042.0

0.0936

1104.8

0.0899

1014.4

0.0572

254.7

0.0926

1072.8

0.0937

1120.0

0.0969

1190.8

0.0930

1093.3

0.0537

231.9

0.0931

1088.1

0.0967

1190.4

0.1010

1290.1

0.0970

1193.3

0.0502

231.4

0.0936

1100.9

0.0972

1193.8

0.1042

1337.2

0.1005

1275.6

0.0452

231.0

0.0940

1111.5

0.0976

1200.4

0.1046

1350.1

0.1034

1335.9

0.0405

235.6

0.0943

1121.8

0.0980

1210.2

0.1050

1355.4

0.1063

1387.3

0.0392

232.5

0.0948

1132.9

0.0985

1223.1

0.1055

1366.6

0.1105

1447.9

0.0372

229.3

0.0945

1124.8

0.0990

1238.3

0.1061

1380.9

0.1120

1440.1

0.0347

228.3

0.0934

1071.7

0.0991

1239.9

0.1062

1382.7

0.1122

1439.3

0.0317

227.7

0.0917

997.2

0.0993

1247.0

0.1065

1389.6

0.1124

1442.2

0.0297

228.9

0.0895

906.9

0.0996

1251.1

0.1068

1394.0

0.1127

1443.3

0.0255

230.4

0.0869

802.3

0.0998

1257.5

0.1071

1400.9

0.1130

1448.4

0.0235

231.8

0.0852

736.5

0.1000

1260.7

0.1073

1406.4

0.1132

1451.1

0.0205

223.7

0.0815

606.5

0.0995

1240.7

0.1077

1414.0

0.1137

1457.8

0.0182

225.8

0.0798

549.2

0.0979

1160.1

0.1079

1419.0

0.1139

1459.9

0.0157

227.6

0.0772

472.3

0.0954

1044.6

0.1082

1421.9

0.1143

1467.0

0.0130

225.4

0.0752

417.1

0.0935

961.4

0.1083

1423.1

0.1145

1469.6

0.0092

222.3

0.0731

363.5

0.0914

874.3

0.1069

1357.3

0.1148

1474.9

0.0072

222.4

0.0707

310.6

0.0891

779.1

0.1045

1251.5

0.1151

1478.9

0.0020

150.0

0.0674

250.9

0.0860

659.2

0.1012

1110.7

0.1155

1484.5

0.0010

75.0

0.0657

225.5

0.0843

597.0

0.0995

1036.4

0.1157

1486.3

0.0009

0.0

0.0629

193.1

0.0816

502.9

0.0967

919.4

0.1161

1490.9

0.0607

172.9

0.0795

436.5

0.0945

834.3

0.1164

1492.7

0.0579

160.3

0.0768

357.3

0.0917

725.4

0.1167

1496.4

0.0542

154.2

0.0733

264.8

0.0880

593.6

0.1172

1501.1

0.0494

161.9

0.0687

174.8

0.0832

439.3

0.1178

1506.8

0.0458

159.4

0.0652

121.4

0.0796

335.0

0.1182

1510.6

0.0427

155.4

0.0622

91.0

0.0765

261.1

0.1186

1511.7

0.0395

158.5

0.0591

73.2

0.0733

197.1

0.1187

1478.2

0.0375

157.3

0.0572

71.6

0.0713

163.8

0.1168

1425.1

0.0341

161.1

0.0539

69.4

0.0679

118.9

0.1134

1282.1

0.0302

166.9

0.0502

67.5

0.0640

85.0

0.1097

1123.1

0.0269

165.2

0.0470

71.3

0.0607

70.6

0.1066

994.2

0.0215

164.2

0.0418

77.9

0.0553

77.5

0.1014

788.7

0.0172

165.1

0.0377

75.9

0.0510

80.4

0.0972

634.1

0.0130

164.5

0.0337

75.8

0.0468

79.0

0.0932

495.0

0.0083

160.4

0.0291

80.2

0.0421

84.5

0.0887

350.3

0.0042

139.0

0.0252

77.5

0.0380

85.2

0.0847

241.7

0.0014

0.0

0.0229

76.3

0.0356

84.8

0.0824

183.3

0.0208

74.3

0.0334

83.8

0.0803

136.0

0.0181

76.3

0.0306

79.3

0.0776

83.7

0.0145

72.2

0.0269

80.6

0.0741

25.2

0.0133

69.9

0.0256

75.6

0.0728

8.4

0.0124

66.8

0.0247

72.9

0.0720

0.0

0.0058

71.1

0.0178

79.5