A process for calculating fatigue and fatigue failure of structures |
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申请号 | EP13167410.3 | 申请日 | 2013-05-13 | 公开(公告)号 | EP2803968A1 | 公开(公告)日 | 2014-11-19 |
申请人 | Siemens Industry Software NV; | 发明人 | Hack, Michael; Nuhn, Peter; Liefooghe, Christophe; Strässer, Stefan; Bruyneel, Michaël; Donders, Stijn; | ||||
摘要 | In a first aspect, the instant invention relates to process for virtually predicting the durability performance of a structure enabling the optimization of the durability performance. This process comprises several steps. In a first step, the structure is modeled by a series of calculation points. Then, for each point, the stresses and strains (4) brought by load cycles (2) and defining hysteresis branches are determined (3). Then, an accumulated damage due to the load cycles is predicted (5) (6) and stored (8). For the prediction, first, using a hysteresis operator (5), a change in the stress (7) along a portion of a hysteresis branch is calculated as a function of a change in the load in time, and, second, using the change in the stress (7) and the stored accumulated damage, a change in the damage is calculated (6). Hence, also a change in the properties (14), including the stiffness, of the structure is calculated. Then, a further change in the stresses and strains (16) is calculated (15) on the basis of the change in these properties (14) to determine a new adapted hysteresis branch. Then, a further change in the stress (7) along a further portion of the adapted hysteresis branch is calculated (5) as a function of a further change in the load in time. At the end of the process, the structure is manufactured accordingly. In a second and third aspect the invention also relates to a system and software program product. | ||||||
权利要求 | |||||||
说明书全文 | The invention relates to the field of predicting durability performance and fatigue behaviour of structures. Manufacturers in the transportation, wind energy and machinery sector are increasingly using lightweight materials, since these allow delivering products with superior mechanical properties with a lower ecological foot print. Especially in the transportation (automotive, aerospace ...) the substantial deployment of lightweight design materials such as composites will be the only viable path to meeting the ever more stringent CO2 emission norms. At present, the massive deployment of lightweight materials in the industrial design and development process is however limited by the lack of predictive modeling tools to predict the macro-level behavior of lightweight materials structures. If better mechanical predictions can be made based on virtual models, the product can be optimized based on virtual simulations (rather than on late and expensive physical testing). Composite materials can typically withstand many load cycles (i.e. have a good fatigue behavior). But the first damaging events that even change the stiffness of the component occur quite early and also at quite small load cycles. For product design engineers, this means that they cannot design the product with a requirement that 'no fatigue damage should occur at all', since that would lead to typical overdesign of the structure. Instead, the engineer would like to be able to predict the fatigue behavior over the full lifetime - including the changes in stiffness, and the cross influences of the different damage mechanisms. By using the better understanding of the fatigue behavior in the product design decision process, it will be possible to achieve better, lighter and more cost-efficient designs. In automotive applications, for instance, the analysis and synthesis of fatigue loads have highly improved over the last decades. For the current cars made of metals, a mature virtual design optimization process is in place, which enables the car manufacturers to tailor their cars to be adequate for the actual usage, and to align them with the requirements of different markets, while ensuring to avoid overdesign. This involves complex load schedules for different roads with fully variable loading. In contrast, for composites materials, no mature tools are in place to virtually predict the product performance. This means that expensive physical testing approaches in a rather late stage of the design process are needed to check/validate whether the composite material design meets the requirements. The problem to be solved is to bring in place a new virtual process to predict the durability of composites structures and to include the new process in a numerical apparatus or toolset that can be used to predict and optimize the durability performance of mechanical structures. The availability of the innovative process and associated toolset will enable the industry to improve their design process for their lightweight products, achieving a better product quality at lower cost. Mandatory ingredients for such a successful methodology are:
Finite Element (FE) Analysis (FEA) is a well-known numerical technique for modeling a mechanical structure. The model consists of many small & simple 'elements'. Each such element defines a very simple mechanical problem, e.g. a plate-like structure in which the mechanical equations are evaluated in a number of integration or calculation points. After building the numerical FEA model, one can establish a matrix equation of the complete structure, which contains the large list of simple 'elements' problems in relation to each other. Solving this equation allows approximating the mechanical behavior of the structure based on the solution of the many small elements problems. It is state of the art to base fatigue predictions on mechanical FE models. A typical result of a FEA is the mechanical prediction of the stresses & strains in the structure based on a FE model of the structure. One technique that is already known from failure prediction for metal structures is using SN-curves and linear damage accumulation. An SN-curve represents the magnitude of a stress or load cycle applied to a material as a function of the amount of cycles before fatigue failure occurs, i.e. before it breaks. The data to populate the SN-curves is typically obtained from testing, i.e. obtained from simple standardized samples of material (i.e. so-called "coupon testing"). The SN-curves are derived for a selected load direction (e.g. longitudinal or transversal load). Using the rainflow counting approach, the complex load cycles can be split up in a set of simple load cycles with different amplitudes. Using these amplitudes the number of cycles before failure can then be derived from the SN curves. Predicting failure using SN-curves can thus handle variable amplitude loads, but cannot take into account multi-axiality. A further disadvantage is that the effect of progressive damage and, thus, the reduction of the stiffness and redistribution of stress in the structure cannot be taken into account. This means that rainflow based approaches can handle stress-strain behavior and damage accumulation only in the case that there is a fixed relationship between stress and strain, and that the same stress-strain cycles always induce the same damage. Therefore, the use of SN-curves is very limited for composite structures. For variable amplitude loading it is very typical that the largest load cycles - that contribute most to the damage - take a very long time to complete, due to the many nested cycles inside. In this case the approach to only consider cycles when they are completed as in the rainflow approach can no longer be justified. Traditional fatigue damage accumulation uses rainflow counting and linear Miner-Palmgren damage accumulation. In the case of composites, one experiences that the fatigue behavior is changing over time due to several different damage mechanisms, because the damaging effects are connected to stress-strain hysteresis loops or branches. These loops are typically nested in each other, such that before one large loop closes there may be many small loops that open and close in between. So it is very typical that the largest load cycles - that contribute most to the damage - take a very long time to complete, due to the many nested cycles inside. In this case the approach to only consider cycles when they are completed as in the rainflow approach can no longer be justified. In " In " In the prior art publication " It is the object of the instant invention to overcome the above mentioned disadvantages of the prior art. The applicant does not want to restrict the scope of the invention solely to composite structures as the invention is also applicable to structures made of other materials. Therefore, the invention also applies to elastomer materials or any other material that has the property that damage accumulates in the material due to load cycles before the structure fails due to fatigue failure. Accordingly, the instant application relates, in a first aspect, to a process according to claim 1. It is an advantage that, due to the fact that a hysteresis operator is used and time steps in between the full amplitude of the load cycles are taken into account, nested loop cycles and multiple load cycles with variable amplitudes can be taken into account. It is an advantage that, due to the fact that the change in material properties is taken into account, fatigue failure for long load cycles can be predicted. These long load cycles, for example, do not represent a short distance on a virtual durability test track simulation, but may represent thousands of kilometres on a virtual test track simulation. Therefore, the prediction will be more accurate and corresponds to a real life case. It is a further advantage that, due to the fact that the accumulated damage and, hence the change in material properties, are taken into account the local redistribution of stress is accurately simulated and, hence, the prediction of the fatigue failure is more accurate. Due to the more accurate simulation of the fatigue, it is a further advantage of the instant invention that less overdesign of the composite structure is needed. This results in a lighter structure for a given set of durability and performance requirements of the structure. According to an embodiment of the first aspect the process further comprises updating the model of the composite structure to an updated model with the change in properties and, for each calculation point, new stresses and strains brought by the load cycles and defining hysteresis loops are determined. Due to the fact that the model of the composite structure is updated and the stresses and strains in the calculation points are recalculated, it is an advantage that the global redistribution of the stress, and, thus, the reduction or increase in stiffness throughout the composite structure is taken into account. A second aspect of the invention is realized by a system according to claim 8. In a third aspect the invention is realized by a software program product according to claim 11. The invention shall be better understood in light of the following description and of the accompanying drawings were
In a first step (1), a model of the composite structure of which the durability performance will be predicted is obtained. In this first step, this is done be modelling the structure by a series of elements comprising one or more calculation points. This may be a Finite Element (FE) model. As well known in the art, such a model divides the structure into a series of simple elements and the interaction between every element of the structure is described by a simple equation whereas, when the structure as a whole would be considered, a set of complex partial differential equations would have to be solved. Such a model typically comprises the geometrical properties of the structure and how it is divided into a series of these simple elements. Next to this, the model also comprises how external forces act on the structure and further comprises the material properties of the structure such as, for example, the stiffness of the structure. In An illustrative example of such a structure is shown in Fatigue failure in a composite structure will occur when the structure is submitted to a series of load cycles, i.e. external force(s) that vary in amplitude over time. In order to predict the durability performance, the process also needs these load cycles as an input. In In a next step (3) of the process, the stresses and strains (4) brought by the load cycles (2) are determined. Due to the forces induced by the load cycles and comprised in the model of the structure, stress will build up along the structure. Stress is well known to express the internal forces that neighbouring elements or particles of a continuous material exert on each other. Stress is typically expressed in Megapascals (MPa) or Newtons per square millimetre (N/mm2). The calculation of these stresses and strains may be done using a Finite Element (FE) Solver (3) that performs a Finite Element Analysis (FEA) taking as input the Nominal FE model (1). The FE Solver thus also takes as input how external forces act on the structure and the material properties as also defined by the FE model (1). As a result the FE solver will calculate the displacements at the so-called nodes. From these it calculates the related stresses (denoted by σ) and strains (denoted by ε) values in every element. These stresses may be calculated for a number of calculation points in the element. For composite structures this is typically done also at the different plies. In all the calculation points where the stresses and strains are calculated, the fatigue analysis may be performed. The strain indicates the displacement of an element of the structure caused by the stress. As it is a relative measure, it is defined by the ratio between the local displacement and the global displacement. In the example of The process then proceeds to steps (5) and (6) where an accumulated damage due to the load cycles (2) is predicted and stored (8). These steps will now be explained in more detail. Step (3) will relate the stresses and strains to the external forces or loads, but only for a static case, i.e. only for non-varying external forces (22). However, to predict the fatigue of the composite structure, the process also needs to take into account the complex variation of the load in time defined by the Load Histories (2). When a structure is submitted to such load cycles, the relation between the stresses and the strains (4) obtained from the FE Solver in every calculation point of the structure will exhibit a memory effect. In other words, the strain is not only dependent on the material but also on the history of the stress, i.e. how the path to the stress was established. This is illustrated in In a step (5), using a hysteresis operator (5), a change in the stress (7) along a portion of the hysteresis loop is now calculated as a function of a change in the load in time. Based on the load histories (2) and the output of the FE Solver (3), a hysteresis operator will calculate the stress σ1 (7) (see Referring to the example of the beam in In a further step (6), using the change in the stress (7) from step (5) and the stored accumulated damage, a change in the damage is calculated (6), and, hence, a change in the properties (14), including the stiffness, of the structure in each calculation point is also calculated. As the process is an iterative process, when executing step (6) for the first time the value of the accumulated damage will have an initial predetermined value, zero for example. In a composite structure, every load cycle (31) will produce a change in damage inside the structure. After a certain amount of cycles, the total sum of all the changes in damage, i.e. the accumulated damage, will exceed a certain threshold and fatigue failure will occur. In composite structures the change in damage or progressive damage may be characterized as follows: In other words, the change in damage El is the stiffness of the material in a direction l dl is the total accumulated damage The following equation related to the curve in whereby Xl is the static strength constant that indicates at which stress static value the structure will be permanently damaged , and c1, c2, c3, c4 and c5 are constants related to the material obtained by stress measurement of material samples, and dl is the total accumulated damage in a direction I of the structure. The above equations are just an example on how to derive the change in damage and properties of the structure, but the invention is not limited thereto. In general the calculation of the change in damage may directly use characterization data relating the change in damage and properties to the accumulated damage and to the change in the stress as illustrated by The new value of the accumulated damage is then derived from the previous value of the accumulated damage and the progressive damage just obtained. This new value is then stored as state information (8) as part of the material properties until a next iteration of the process. Similarly, a new value of the stiffness El, which is a material property, is calculated. Referring to the example of the beam of As the material stiffness has changed due to the accumulation of damage in the material, the hysteresis curve (41) as depicted in Referring to the example of the beam of After step (15), the process arrives back at step (5) where a further change in the stress (7) along a further portion of said adapted hysteresis branch is calculated (5) as a function of a further change in the load in time. Referring to With the new stress value σ2' at time step t2 the process then moves again to step (6) where the progressive damage and new value of the stiffness is obtained as described before. The iteration along steps (5), (6) and (15) then continues while continuously updating the state information (8), i.e. the material memory (e.g. hysteresis branch position) and the change in properties of the material (e.g. stiffness and accumulated damage). At a certain time tn in the load cycles (2) one of the calculation points in the composite structure will exceed a certain damage accumulation value (and thus related stiffness value) and, thus, fatigue failure will occur. At that moment, the durability performance of the composite structure is known because it is known at which time in the Load Histories (2) the fatigue failure would occur. At that time, the obtained fatigue property of the composite structure might be satisfactory and the structure may be manufactured with the material properties and dimensions as specified by the nominal FE model (1). If not satisfactory the composite structure and, hence, the model can be adapted and the prediction of the durability performance is repeated. This way optimization of the durability performance of the composite structure can be obtained. Referring to the example of the beam, when going through the iterative steps (5), (6) and (15), at a certain time tn in a certain calculation point of the beam the damage accumulation would be as such that the stiffness is too low. In other words, the beam would bend too much according to the requirements or it would just break. When it is decided to redo the FEA analysis, the state of the system is saved using the state information (8):
Then, the changes in the material properties, e.g. the stiffness, are applied to the finite element model (12) and, hence, a damaged FE model and, thus, an updated model (13) is obtained. Then, updated stresses and strains (4) are calculated by the FE Solver (3) and the hysteresis operator resumes where it had stopped. According to a second aspect of the invention, the invention also relates to a system for performing the process according to the first aspect of the invention. An embodiment of such a system is illustrated in The system comprises a means (81) for modelling the composite structure by a series of simple elements comprising one or more calculation points. This may be done by a computer where a model of a composite structure is drawn using the input devices (mouse, keyboard, ...) of the computer. Using the computer, the model is then further finalized by defining the elements and thus the FE model, the external forces and material properties. Furthermore, the means (81) may also comprise a scanning device to digitize a physical prototype of the structure and a computer on which the FE model is further finalized. The system further comprises a means (82) for determining the load histories (2) and, thus, load cycles. The afore-mentioned means may comprise another computer or the same computer as comprised in the means (81) for determining the load cycles by simulation. The means (82) may also comprise a test setup to measure the load cycles by an actual physical experiment. The system may further comprise a computing means (83) for performing the steps (3), (5), (6), (9), (12) and (15) of the process according to the first aspect of the invention. These steps may be written in programming language and compiled to run on a processor (85) which is comprised within the computing means (83). The means (83) may further comprise storage (86) for keeping track of the state information (8). This storage could be the RAM memory or hard drive of the computing means (83). The system further comprises a means (84) for manufacturing the composite structure accordingly. |