Fatigue evaluation method and fatigue evaluation program

Abstract

To provide a fatigue evaluation method that takes into account the influence of tissue morphology on fatigue damage.SOLUTION: A fatigue evaluation method comprises: using the finite element method, calculating a shear strain range when a repeated load is applied to a part multiple m times (m is a positive integer) for each of a plurality of crystal slip systems; calculating a sum of out-of-plane components of the shear strain range; acquiring a damage index Dm, which is an index of damage to the part, based on the sum; acquiring the relation between m and the damage index Dm; acquiring a cumulative damage index DL, which is expressed by the formula, based on the relation between m and the damage index Dm.SELECTED DRAWING: Figure 17

Description

Technical Field

[0001] The present invention relates to a fatigue evaluation method and a fatigue evaluation program.

Background Art

[0002] Ensuring the safety and extending the lifespan of steel products such as automotive parts, railway vehicle parts, and bridges has become an important social issue, and there is a demand for increasing the high fatigue strength of steel materials. In order to obtain design guidelines for achieving high fatigue strength, it is necessary to establish techniques for quantifying the effects of high fatigue strength and predicting fatigue life.

[0003] Japanese Patent Application Laid-Open No. 2017-187472 discloses a fatigue evaluation method for highly accurately evaluating fatigue damage occurring in a structure when a repeated load acts on the structure. This fatigue evaluation method compares the test results of a test piece with the results of a simulation to determine whether a convergence condition is satisfied. If the convergence condition is not satisfied, the simulation conditions are adjusted. If the convergence condition is satisfied, the simulation conditions are determined, and the fatigue damage of the analysis target is evaluated using the determined simulation conditions.

[0004] Japanese Patent No. 2791174 discloses a method for evaluating the solder joint life of electronic components. This evaluation method includes a first step of obtaining the shear strain generated at the solder joint of an electric circuit device, a second step of obtaining the equivalent strain amplitude from the relationship between the equivalent strain amplitude obtained in advance from a finite element method three-dimensional thermo-elasto-plastic analysis and the above shear strain, a third step of obtaining a crack propagation speed formula showing the relationship between the crack propagation speed obtained in advance by fracture surface analysis after a temperature cycle test and the above equivalent strain amplitude, and a fourth step of obtaining the life from a life evaluation criterion formula showing the relationship between the above equivalent strain amplitude, the crack length, and the number of life cycles.

[0005] Non-Patent Document 1 describes the microstructure modeling and crystal plasticity simulation for the evaluation of fatigue cracks in α-iron. In this document, the relationship between the average shear strain amplitude and the Fatigue Indicator Parameter is discussed.

[0006] The present inventors have previously developed a fatigue evaluation method using crystal plasticity analysis and filed it as Japanese Patent Application No. 2022-003921 (Japanese Unexamined Patent Application Publication No. 2023-103073). This fatigue evaluation method includes a step of calculating the shear strain range when a repeated load is applied to a component for each of a plurality of crystal slip systems, and a step of calculating the sum of the out-of-plane component of the shear strain range of the component.

Prior Art Documents

Patent Documents

[0007]

Patent Document 1

Patent Document 2

Patent Document 3

Non-Patent Documents

[0008]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0009] In order to develop steel materials with excellent fatigue characteristics, it is necessary to grasp the stress and strain generated when a repeated load acts and to clarify the fatigue crack generation mechanism. In determining the material design guidelines, it is necessary to grasp the microscopic stress and strain depending on the microstructure such as the crystal grain size distribution and the crystal orientation distribution, and to explore the optimal microstructure for realizing high fatigue strength. Further, in order to determine whether high fatigue strength has been achieved, a fatigue evaluation method considering the influence of the microstructure on fatigue damage is required.

[0010] An object of the present invention is to provide a fatigue evaluation method and a fatigue evaluation program that take into account the influence of the microstructure on fatigue damage.

Means for Solving the Problems

[0011] A fatigue evaluation method according to an embodiment of the present invention includes a step of calculating a shear strain range when a repeated load is applied to a component m times for each of a plurality of crystal slip systems for a plurality of positive integers m using the finite element method, a step of calculating the sum of the out-of-plane direction components of the shear strain range, a step of obtaining a damage index D which is an index of damage of the component based on the sum, a step of obtaining the relationship between m and the damage index D, and a step of obtaining a cumulative damage index D represented by the following formula based on the relationship between m and the damage index D. m and, a step of obtaining a relationship between m and the damage index D m and, based on the relationship between m and the damage index D m a step of obtaining a cumulative damage index D represented by the following formula L is provided.

Number

[0012] A fatigue evaluation method according to another embodiment of the present invention is based on data of a plurality of fatigue tests performed in advance, and for each of the plurality of fatigue tests, for a plurality of positive integers m, (A) Using the finite element method, for each of a plurality of crystal slip systems, a step of calculating the shear strain range when a repeated load is applied to the test piece m times; (B) A step of calculating the sum of the out-of-plane components of the shear strain range of the test piece, and (C) Based on the sum, a step of obtaining the damage index D which is an index of damage of the test piece m ; A step of performing, a step of obtaining the relationship between m and the damage index D m ; and based on the relationship between m and the damage index D m , a step of obtaining the cumulative damage index D represented by the following formula, a step of creating a master curve which is the relationship between the cumulative damage index D L and the fatigue life, a step of obtaining the damage index D of the target part by the same steps as the above (A) to (C) L ; a step of obtaining the relationship between m and the damage index D of the target part m ; and based on the relationship between m and the damage index D of the target part m , a step of obtaining the cumulative damage index D of the target part m ; and a step of predicting the fatigue life of the target part based on the cumulative damage index D of the target part L and the master curve. L It comprises.

Number

[0013] The fatigue evaluation method according to still another embodiment of the present invention is based on the data of a plurality of fatigue tests performed in advance. For each of the plurality of fatigue tests, for a plurality of m (m is a positive integer), (A) Using the finite element method, for each of a plurality of crystal slip systems, a step of calculating the shear strain range when a repeated load is applied to the test piece m times; (B) A step of calculating the sum of the out-of-plane components of the shear strain range of the test piece, and (C) Based on the sum, a step of obtaining the damage index D which is an index of damage of the test piece m ; A step of performing, and the relationship between m and the damage index D mA step of determining the relationship with, and the cumulative damage index D represented by the following formula based on the relationship between the m and the damage index D m A step of obtaining, and the cumulative damage index D L A step of creating a master curve that is the relationship between the cumulative damage index D and the fatigue life, and the damage index D when the repeated load is applied j times (j is an arbitrary positive integer) L A step of determining the relationship between the cumulative damage index D and the damage index D j A step of obtaining, by the same steps as (A) to (C) above, the damage index D when the repeated load is applied j times to the target part L A step of determining the relationship between the damage index D of the target part and the damage index D j A step of obtaining, and a step of predicting the fatigue life of the target part based on the cumulative damage index D of the target part and the master curve j Based on the relationship between the damage index D of the target part, the damage index D, and the cumulative damage index D j A step of obtaining the cumulative damage index D of the target part L And a step of predicting the fatigue life of the target part based on the cumulative damage index D of the target part and the master curve L A step of obtaining the cumulative damage index D of the target part L And a step of predicting the fatigue life of the target part based on the cumulative damage index D of the target part and the master curve

Equation

[0014] The fatigue evaluation program according to an embodiment of the present invention causes a computer to execute each step included in any of the above fatigue evaluation methods

Advantages of the Invention

[0015] According to the present invention, it becomes possible to perform fatigue evaluation considering the influence of the tissue form on fatigue damage

Brief Description of the Drawings

[0016]

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DETAILED DESCRIPTION OF THE INVENTION

[0017] When it is difficult to experimentally evaluate microscopic stress and strain, numerical simulation becomes an effective means. Crystal plasticity analysis is a numerical analysis method that expresses the plastic deformation anisotropy of metals based on crystallographic slip, and can evaluate microscopic stress and strain at the crystal grain level.

[0018] As described above, the present inventors have previously developed a fatigue evaluation method using crystal plasticity analysis and filed an application as Japanese Patent Application No. 2022-003921 (Japanese Unexamined Patent Application Publication No. 2023-103073). The fatigue evaluation method of Japanese Unexamined Patent Application Publication No. 2023-103073 (hereinafter referred to as the "prior application publication") includes a step of calculating a shear strain range when a repeated load is applied to a component for each of a plurality of crystal slip systems, and a step of calculating a sum of out-of-plane direction components of the shear strain range. Hereinafter, the "sum of out-of-plane direction components of the shear strain range in a plurality of slip systems existing in the crystal structure" is referred to as a "damage parameter". The fatigue evaluation method of the prior application publication is a method of obtaining a damage parameter when a repeated load is applied to a component by numerical calculation such as the finite element method and evaluating the fatigue characteristics of the component based on this damage parameter.

[0019] First, although overlapping with the disclosure content of the prior application publication, a fatigue evaluation method based on this damage parameter will be described below.

[0020] [Fatigue Evaluation Method Based on Damage Parameter] The present inventor modeled a fatigue test conducted in the past and performed crystal plasticity analysis, and examined physical quantities (parameters) that can explain the distribution of fatigue damage locations observed in the experiment.

[0021] The fatigue test to be analyzed was conducted by taking a test piece having the shape shown in FIG. 1 from a test material of extra-low carbon steel. The unit of the dimensions in the figure is mm. The test piece is plate-shaped, and the dimension (thickness) in the direction perpendicular to the paper surface is 1 mm. FIG. 2 shows the crystal orientation distribution of a 0.9 mm × 0.9 mm region (region A in FIG. 1) near the center of the test piece obtained by performing crystal orientation analysis by electron backscatter diffraction (EBSD). FIG. 3 is a polycrystalline model created based on the information on crystal grain boundaries obtained by crystal orientation analysis.

[0022] As candidates for physical quantities related to fatigue damage, load direction stress, maximum principal stress, load direction plastic strain, cumulative slip, etc. were examined. However, no clear correlation was observed between the locations where these stresses or strains were high and the fatigue damage parts observed in the experiment.

[0023] As a result of further investigation, it was found that the location where "the sum of the out-of-plane components of the shear strain range in a plurality of slip systems existing in the crystal structure" is high coincides well with the fatigue damage location observed in the experiment. Fig. 4 shows the distribution of "the sum of the out-of-plane components of the shear strain range in a plurality of slip systems existing in the crystal structure" obtained by finite element method (FEM) analysis, and Fig. 5 is a diagram showing the fatigue damage locations observed in the experiment. In Fig. 5, the hatched areas are the fatigue damage locations.

[0024] Here, a detailed explanation will be given about "the sum of the out-of-plane components of the shear strain range in a plurality of slip systems existing in the crystal structure".

[0025] In crystal plasticity analysis, deformation analysis is performed assuming that plastic deformation causes shear (slip) in a specific direction along the slip plane. Fig. 6 is a diagram schematically showing the slip systems of the bcc crystal structure. In the crystal plasticity analysis of the bcc crystal structure, a total of 24 slip systems, which are the combination of 12 {110}<111> type slip systems and 12 {112}<111> type slip systems, or a total of 48 slip systems obtained by adding 24 {123}<111> type slip systems to this, are often used. In this analysis, a total of 24 slip systems, which are the combination of 12 {110}<111> type slip systems and 12 {112}<111> type slip systems, were used.

[0026] Fig. 7 is a diagram schematically showing the time change of the shear strain. The "shear strain range" is the absolute value of the difference between the shear strain at the minimum load and the shear strain at the maximum load in the final cycle of the analysis. This shear strain range is calculated for each of the above-mentioned 24 slip systems.

[0027] Fig. 8 is a diagram showing the relationship between the slip plane and the out-of-plane direction of the test piece. The out-of-plane component is extracted from the shear strain range, and the sum is obtained for all the slip systems considered (24 slip systems in this analysis). This value becomes "the sum of the out-of-plane components of the shear strain range in a plurality of slip systems existing in the crystal structure".

[0028] FIG. 9 is a diagram schematically showing a cross section near the surface of a test piece after a fatigue test. The protrusions and indentations (surface irregularities) observed on the surface of the test piece after the fatigue test are caused by the slip and reverse slip of crystal planes, and are considered to be the cause of crack generation. It can be inferred that the out-of-plane component of the test piece surface in the shear strain range is a physical quantity that affects this protrusion and indentation.

[0029] From the above, it has been found that the fatigue of a component can be evaluated using as an index "the sum of the out-of-plane components of the component surface in the shear strain range in a plurality of slip systems existing in the crystal structure" (damage parameter).

[0030] The inventor further examined a method for predicting the fatigue life of a target component using this damage parameter. The above-described damage parameter is a value calculated for each element of the model used in the analysis. In order to predict the fatigue life of the target component, it is effective to evaluate the degree of damage in the entire analysis region.

[0031] As an index for evaluating the degree of damage in the entire analysis region, for example, a predetermined region in the analysis region (for example, a region corresponding to the test piece surface) is considered, and a value obtained by integrating the damage parameters in this region in descending order by a predetermined ratio of the number of elements (for example, the integrated value of the top 0.5% of the damage parameters in this region) can be used.

[0032] [Influence of the number of repetitions when obtaining the damage parameter] In the prior application publication, when obtaining the damage parameter, the calculation (simulation) is terminated with a finite number of repetitions (number of cycles), and the damage parameter is obtained from the shear strain range in the final cycle. Specifically, in the prior application publication, as an example (analysis example), it is described that the fatigue life was predicted using the damage parameter when a 5-cycle load was applied and the damage index obtained therefrom. And it is described that a prediction result that agrees well with the experimental value was obtained thereby.

[0033] Thus, even when the calculation is terminated with a finite number of repetitions, predicted results that accurately match the experimental values have been obtained. On the other hand, from a theoretical perspective, the validity of terminating the calculation with a finite number of repetitions was not clear. Therefore, it was verified how the damage parameter would change as the number of repetitions increased.

[0034] Figure 10 shows the distribution of damage parameters when a fully reversed cyclic load with a stress amplitude of 160 MPa was applied 5, 10, 20, 30, 40, and 50 times, obtained by FEM analysis. As shown in Figure 10, even when the number of repetitions is changed, the position of the damaged part (the part where the damage parameter becomes relatively large) does not change, but it was found that the magnitude of the damage parameter decreases as the number of repetitions increases. The same was true when the calculation was performed with different stress amplitudes.

[0035] Figures 11 to 13 are graphs showing the relationship between the number of repetitions and the damage index when the stress amplitudes are 132 MPa, 150 MPa, and 160 MPa, respectively. In this example, the integrated value of the top 0.5% (the value averaged by the number of elements) within the target region of the damage parameter was defined as the "damage index".

[0036] As shown in Figures 11 to 13, the damage index also decreased as the number of repetitions increased. Therefore, it was suggested that the predicted value of the fatigue life might vary depending on which damage index of the number of repetitions was adopted. However, in the method of creating a master curve from the damage index and the fatigue life to predict the fatigue life as described in the prior application publication, if the number of repetitions when obtaining the damage index during master curve creation and the number of repetitions when obtaining the damage index during prediction are made the same, it is considered that no significant difference will occur. However, by taking into account the decrease in the damage index as the number of repetitions increases, there is a possibility of making a more accurate prediction.

[0037] Therefore, the inventors defined the damage index D calculated from the damage parameter when the cyclic load was applied m times (m is a positive integer) as m and the cumulative damage index D represented by the following formula as LBased on this, we came up with the idea of ​​evaluating the fatigue properties of the target parts (see Figure 14).

[0038]

number

[0039] Cumulative damage index D L is D with m ranging from 1 to infinity m Of course, there are infinite D m It is not possible to obtain m and D from the analysis results for multiple m. m Based on this relationship, the cumulative damage index D L The cumulative damage index D L As a result of evaluating the fatigue life based on the above, it was possible to predict the actual measured value with high accuracy. Furthermore, as a result of further investigation, it was found that the cumulative damage index D L The value of is the damage index D when repeated load is applied j times (j is any positive integer). j It was also found that accurate predictions could be made.

[0040] The present invention has been completed based on the above findings. Preferred embodiments of the present invention will now be described in detail.

[0041] [Fatigue assessment method] [First embodiment] 15 is a flow diagram of a fatigue evaluation method according to a first embodiment of the present invention. This fatigue evaluation method includes a step of preparing fatigue test data (step S1), a step of analyzing each of the data (step S2), a step of creating a master curve (step S3), a step of analyzing a target component (step S4), and a step of predicting the fatigue life of the target component (step S5).

[0042] The subject of application of the fatigue evaluation method according to the present embodiment is not particularly limited as long as it is a polycrystalline body, but is preferably a metal material, and more preferably a steel material (iron-based alloy).

[0043] In the following description, the "sum of the out-of-plane components of the shear strain range in a plurality of slip systems existing in the crystal structure" is referred to as the "damage parameter". In this embodiment, based on this damage parameter, a "damage index" and a "cumulative damage index", which are indicators of the damage of the test piece, are calculated. Details of the damage index and the cumulative damage index will be described later. In the fatigue evaluation method according to this embodiment, first, data of a plurality of fatigue tests performed in advance are prepared (step S1), the cumulative damage index is calculated for each of them (step S2), and a master curve showing the relationship between the cumulative damage index and the fatigue life is created (step S3). Then, the cumulative damage index is also calculated for the target part (step S4), and the fatigue life of the target part is predicted with reference to the master curve (step S5). Each step will be described in detail below.

[0044] Prepare data of a plurality of fatigue tests performed in advance (step S1). Each of the data of the fatigue tests includes, for example, information on the test piece shape, the crystal orientation distribution of the evaluation location, the load conditions (such as stress amplitude), and the fatigue life (the number of repetitions until a fatigue crack occurs, or the number of repetitions until the test piece breaks).

[0045] The crystal orientation distribution is preferably obtained by measuring the test piece used in the fatigue test by EBSD or the like, but data of the crystal orientation distribution of the same type of material may be substituted. Also, when performing a plurality of fatigue tests by changing the load conditions with the same material, it may be assumed that all the test pieces have the same crystal orientation distribution.

[0046] In order to create a master curve, data of at least two levels of fatigue tests measured by changing the load conditions are required. It is preferable that the data of the fatigue tests have three or more levels.

[0047] Analyze each of the data of the plurality of fatigue tests (step S2). FIG. 16 is a flowchart of the step (step S2) of analyzing each of the data of the plurality of fatigue tests. The step of analyzing each of the data (step S2) is the damage index D when cyclic loading is applied m times for a plurality of positive integers m mThe step of obtaining (step S2-1), and the relationship between m and the damage index D m The step of obtaining the relationship between (step S2-2), and m and the damage index D m From the relationship between and, the cumulative damage index D L The step of obtaining (step S2-3) is provided.

[0048] The step of obtaining the damage index D m (step S2-1) includes: (A) for each of a plurality of crystal slip systems, the step of calculating the shear strain range when the test piece is subjected to m repeated loads (step S2-1-A); (B) the step of calculating the sum of the out-of-plane components of the shear strain range in the test piece surface direction (i.e., the damage parameter) (step S2-1-B); and (C) the step of calculating the damage index D m based on the damage parameter (step S2-1-C). These analyses can be performed, for example, by FEM analysis.

[0049] As the slip systems used in this analysis, although not limited to these, for example, in the fcc crystal structure, 12 slip systems of the {111}<110> type can be used. In the crystal plasticity analysis of the bcc crystal structure, as described above, a total of 24 slip systems combining 12 slip systems of the {110}<111> type and 12 slip systems of the {112}<111> type, or a total of 48 slip systems obtained by adding 24 slip systems of the {123}<111> type to this, are often used. Instead of these, for example, analysis may be performed using 12 slip systems of the {110}<111> type.

[0050] Also, in the hcp crystal structure, for example, the following slip systems can be used.

Number

[0051] For each of the target crystal slip systems, calculate the shear strain range when a repeated load is applied to the test piece m times (step S2-1-A). The shear strain range changes with each cycle due to work hardening. The shear strain range considering work hardening can be obtained, for example, using the equations described in D. Pierce, R.J. Asaro, A. Needleman, Acta metall., vol.30(1982), pp.1087-1119.

[0052] Calculate the sum of the out-of-plane components of the shear strain range on the test piece surface (step S2-1-B). More specifically, extract the out-of-plane component of the shear strain range (the component in the direction perpendicular to the surface of the test piece) from the relationship between the slip plane and the global coordinate system, and calculate the sum for all crystal slip systems considered in step S2-1-A. In this embodiment, this sum is referred to as the "damage parameter". A location where this damage parameter is large can be evaluated as a location where cracks are likely to occur due to repeated loading.

[0053] Based on the damage parameter, calculate the "damage index D m " described below (step S2-1-C). The above-described damage parameter is a value calculated for each element of the model used in the analysis. As an index for evaluating the degree of damage in the entire analysis region, calculate the "damage index D m ".

[0054] The damage index is calculated based on the damage parameter within a predetermined region in the analysis region. More specifically, for example, the damage index D m can be obtained based on the following equation (1) or equation (2).

Equation

[0055] As described above, by obtaining the damage index D m it is possible to evaluate the degree of damage in the entire analysis region regardless of the way the analysis model is divided.

[0056] In addition, when the number of elements in the analysis model is the same in the process of analyzing the fatigue test data (step S2) and the process of analyzing the target component (step S4), the damage index D m may be obtained based on the following formula (3). The meanings of N, s, and d i are the same as those in formulas (1) and (2).

Equation

[0057] The region to be considered is, for example, a region that can be predicted to be easily damaged (where stress is likely to concentrate). Specifically, it is a region corresponding to the outermost layer of the test piece, holes, steps, grooves, regions near defects or scratches, etc. The region to be considered may be the entire analysis target region.

[0058] s is preferably less than 1.00 (less than 100%), more preferably 0.05 or less (5% or less), still more preferably 0.005 or less (0.5% or less), and even more preferably 0.001 or less (0.1% or less).

[0059] Through the above steps, the damage index D m for a specific m is calculated. In the step of obtaining the damage index D m (step S2-1), the damage index D m is calculated for a plurality of m. The number of damage indices D m to be calculated only needs to be 2 or more. The larger the number of damage indices D m calculated, the more accurately the relationship between m and the damage index D m can be obtained. On the other hand, the calculation cost increases. The damage index Dm The number is preferably 3 or more, more preferably 5 or more.

[0060] Next, the relationship between m and the damage index D m is obtained (step S2-2). Specifically, for example, m and the damage index D m are subjected to regression analysis to obtain an approximate function that describes the damage index D m .

[0061] From the relationship between m and the damage index D m , the cumulative damage index D L is obtained (step S2-3). Specifically, for example, the cumulative value (sum) up to the number of repetitions n of the damage index D m obtained above is expressed as a function of n, and the limit as n → ∞ is obtained to obtain the cumulative damage index D L .

[0062] By performing the above steps for each of the data of a plurality of fatigue tests, the cumulative damage index D L is calculated for each of the data of the plurality of fatigue tests.

[0063] From the cumulative damage index D L obtained in step S2 and the fatigue life obtained in the fatigue test, a master curve showing the relationship between the cumulative damage index D L and the fatigue life is created (step S3).

[0064] Next, crystal plasticity analysis is similarly performed on the target part to be subjected to fatigue evaluation (step S4). FIG. 17 is a flowchart of the process of analyzing the target part (step S4). The process of analyzing the target part (step S4) includes a step (step S4-1) of obtaining the damage index D m when repeated loading is applied m times for a plurality of m (m is a positive integer), a step (step S4-2) of obtaining the relationship between m and the damage index D m , and a step (step S4-3) of obtaining the cumulative damage index D m from the relationship between m and the damage index D L .

[0065] Damage index D m The step of obtaining the damage index D (step S4-1) is the same as the step of obtaining the damage index D m in FIG. 16. Similar to the step of obtaining the damage index D (step S2-1), it includes: (A) a step of calculating the shear strain range when an m-time repeated load is applied to the target part for each of a plurality of crystal slip systems (step S4-1-A); (B) a step of calculating the sum of the out-of-plane components of the shear strain range (i.e., the damage parameter) of the part (step S4-1-B); and (C) a step of calculating the damage index D m based on the damage parameter (step S4-1-C).

[0066] The step of obtaining the relationship between m and the damage index D m (step S4-2), and the step of obtaining the cumulative damage index D m from the relationship between m and the damage index D L (step S4-3) can be performed in the same manner as the step of obtaining the relationship between m and the damage index D m explained in FIG. 16 (step S2-2) and the step of obtaining the cumulative damage index D m from the relationship between m and the damage index D L (step S2-3). Thus, the cumulative damage index D L of the target part can be obtained.

[0067] The target part is preferably made of the same type of material as the test piece used for creating the master curve, and more preferably made of a material having the same chemical composition. On the other hand, the crystal orientation distribution of the test piece used for creating the master curve and the crystal orientation distribution of the target part may be the same or different. However, it is preferable that the target part is made of a material having the same crystal orientation distribution as the crystal orientation distribution of the test piece used for creating the master curve.

[0068] Finally, based on the cumulative damage index D L of the target part obtained in step S4 and the master curve obtained in step S3, the fatigue life of the target part is predicted (step S5).

[0069] Referring to FIGS. 18 to 22, an example of the fatigue evaluation method described above will be described. As an example of data from a plurality of fatigue tests, for the same material, the stress amplitude σ is changed to σ1, σ2, …, σ k Consider the data of the fatigue test performed. FIG. 18 is a diagram (S-N curve) showing the relationship between the stress amplitude σ and the fatigue life (the number of repetitions until a fatigue crack occurs, or the number of repetitions until the test piece breaks).

[0070] First, perform the above-described crystal plasticity analysis on the data of the fatigue test with the stress amplitude σ being σ1, and obtain the cumulative damage index D L,σ=σ1 in the data of the fatigue test with the stress amplitude σ being σ1. For this purpose, first, for a plurality of m (m is a positive integer), calculate the damage index D m,σ=σ1 when the repeated load with the stress amplitude σ being σ1 acts m times.

[0071] For each element of the analysis model, calculate the damage parameter d m,σ=σ1 when the repeated load with the stress amplitude σ being σ1 acts m times. FIG. 19 is a diagram schematically showing the frequency distribution of the damage parameter d m,σ=σ1 . Based on the damage parameter d m,σ=σ1 and a predetermined s, calculate the damage index D m,σ=σ1 when the repeated load with the stress amplitude σ being σ1 acts m times.

[0072] Calculate the damage index D m,σ=σ1 for a plurality of m, and obtain the relationship between m and the damage index D m,σ=σ1 . FIG. 20 is a diagram schematically showing the relationship between m and the damage index D m,σ=σ1 . Perform a regression analysis on m and the damage index D m to obtain an approximate function g(m) that describes the damage index D m,σ=σ1 . Express the cumulative value (sum) up to the number of repetitions n of this damage index D m,σ=σ1 as a function of n, and obtain the cumulative damage index D L,σ=σ1 by finding the limit as n → ∞.

[0073] When the stress amplitude σ is σ2, …, σ kFor the data of the fatigue test as well, crystal plasticity analysis is similarly performed to calculate the cumulative damage indices D L,σ=σ2 , …, D L,σ=σk . The fatigue lives N1, N2, …, N k obtained from the fatigue test and the cumulative damage indices D L,σ=σ1 , D L,σ=σ2 , …, D L,σ=σk are associated with each other to obtain a master curve for predicting the fatigue life (Fig. 21). In the master curve, D L is represented as a function f of N as follows. D L = f(N)

[0074] For the target part to be evaluated for fatigue as well, a similar crystal plasticity analysis is performed to obtain the cumulative damage index D X . The fatigue life of the part is obtained by finding N corresponding to the cumulative damage index D X from the inverse function of f (Fig. 22). N = f -1 (D X )

[0075] Above, the fatigue evaluation method according to the first embodiment of the present invention has been described. According to this embodiment, fatigue evaluation considering the influence of the microstructure on fatigue damage becomes possible.

[0076] [Second Embodiment] Fig. 23 is a flowchart of the fatigue evaluation method according to the second embodiment of the present invention. This fatigue evaluation method further includes a step (step S6) of obtaining the relationship between the damage index D j and the cumulative damage index D L when a repeated load is applied j times (j is an arbitrary positive integer) in addition to the steps included in the fatigue evaluation method according to the first embodiment (Fig. 15). Also, the content of the step of analyzing the target part (step S7) is different from the step of analyzing the target part in the first embodiment (step S5 in Fig. 15).

[0077] In this embodiment, after the step of analyzing each of the data (step S2), the damage index D when a repeated load is applied j times (j is an arbitrary positive integer)j and the cumulative damage index D L to obtain the relationship therebetween (step S6). In FIG. 23, the step of obtaining the relationship between the damage index D j and the cumulative damage index D L is arranged after the step of obtaining the master curve (step S3). However, the step of obtaining the relationship between the damage index D j and the cumulative damage index D L may be performed after the step of analyzing each of the data (step S2), and may also be performed before the step of obtaining the master curve (step S3).

[0078] When the repeated load is applied j times (j is an arbitrary positive integer), it is known that there is a correlation between the damage index D j and the cumulative damage index D L . In the present embodiment, based on the damage index D j and the cumulative damage index D L obtained in the step of analyzing each of the data (step S2), the relationship between the damage index D j and the cumulative damage index D L is obtained. Specifically, for example, the damage index D j and the cumulative damage index D L are subjected to regression analysis to obtain the cumulative damage index D L as a function of the damage index D j .

[0079] As an example of data of a plurality of fatigue tests, consider data of fatigue tests performed by changing the stress amplitude σ to σ1, σ2,..., σ k for the same material. In this case, in the process of calculating the cumulative damage index D L,σ=σ1 , the value of the damage index D j,σ=σ1 is obtained. Similarly, the values of the damage index D j,σ=σ2 ,..., D j,σ=σk are also obtained. From these data, an approximate function h(D L ) of the cumulative damage index D j can be obtained (see FIG. 24).

[0080] FIG. 25 is a flowchart of the process of analyzing the target component (step S7). The process of analyzing the target component (step S7) includes a step of obtaining a damage index D j when a repeated load is applied j times (step S7-1), and a step of obtaining a cumulative damage index D j from the relationship between the damage index D L and the cumulative damage index D L (step S7-2).

[0081] The step of obtaining the damage index D j (step S7-1) includes: (A) a step of calculating the shear strain range when a repeated load of j times is applied to the target component for each of a plurality of crystal slip systems (step S7-1-A); (B) a step of calculating the sum of the out-of-plane component of the shear strain range with respect to the component surface (i.e., the damage parameter) (step S7-1-B); and (C) a step of calculating the damage index D j based on the damage parameter (step S7-1-C).

[0082] In the first embodiment, in the process of analyzing the target component (step S4), similar to the process of analyzing each piece of data (step S2), the damage index D m is obtained for a plurality of m, the relationship between m and the damage index D m is obtained, and the cumulative damage index D L is calculated from this relationship. In contrast, in this embodiment, based on the relationship between the damage index D j obtained in step S6 (FIG. 23) and the cumulative damage index D L , the cumulative damage index D j can be calculated from one damage index D L . Therefore, the calculation cost can be significantly reduced.

[0083] j can be any positive integer, but from the perspective of calculation cost, it is preferably a small value. j is preferably 5 or less, more preferably 3 or less, and even more preferably 1. It has been found that sufficient accuracy can be obtained even when j is set to 1.

[0084] The fatigue evaluation method according to the second embodiment of the present invention has been described above. Also according to this embodiment, fatigue evaluation considering the influence of the microstructure on fatigue damage becomes possible.

[0085] [Fatigue Evaluation Program] The above-described fatigue evaluation method can also be realized as a computer program. The fatigue evaluation program according to an embodiment of the present invention causes a computer to execute a step of receiving data of a fatigue test, a step of analyzing each of the data, a step of creating a master curve, a step of analyzing a target part, and a step of predicting the fatigue life of the target part. The fatigue evaluation program according to another embodiment of the present invention causes a computer to execute a step of receiving data of a fatigue test, a step of analyzing each of the data, a step of creating a master curve, a step of obtaining the relationship between the damage index D j and the cumulative damage index D L when a repeated load is applied j times (j is an arbitrary positive integer), a step of analyzing a target part, and a step of predicting the fatigue life of the target part. Also according to these embodiments, fatigue evaluation considering the influence of the microstructure on fatigue damage becomes possible.

Example

[0086] Hereinafter, the present invention will be described more specifically by way of examples (analysis examples). The present invention is not limited to these examples.

[0087] [Prediction of Fatigue Life by Cumulative Damage Index D L A crystal plasticity analysis was performed by modeling a fatigue test conducted in the past. The test material used in the fatigue test to be analyzed is an extra-low carbon steel having the chemical composition shown in Table 1.

[0088]

Table 1

[0089] ​The fatigue test was conducted by taking test pieces with the shape shown in Fig. 1 from this test material. The unit of the dimensions in the figure is mm. The test piece is plate-shaped, and the dimension (thickness) in the direction perpendicular to the paper surface is 1 mm. The results of the fatigue test are shown in Table 2.

[0090]

Table 2

[0091] Note that the stress amplitudes actually applied in the test were two levels of 132 MPa and 160 MPa, and the fatigue crack initiation life at a stress amplitude of 150 MPa is an estimated value obtained by interpolating the test results of the above two conditions.

[0092] Measuring the crystal grain shape of the entire test piece and performing crystal plasticity analysis is not reasonable in terms of measurement work and calculation costs. Therefore, only the vicinity of the center of the test piece was taken as the analysis target. Fig. 2 shows the crystal orientation distribution of a 0.9 mm × 0.9 mm region (region A in Fig. 1) near the center of the test piece used in the test with a stress amplitude of 132 MPa, obtained by performing crystal orientation analysis using EBSD. Fig. 3 is a polycrystalline model created based on the information on grain boundaries obtained by crystal orientation analysis. Note that since there was no EBSD analysis information for the test pieces of the fatigue tests at stress amplitudes of 150 MPa and 160 MPa, the same polycrystalline model as Fig. 3 was used.

[0093] Fig. 26 is a diagram showing the boundary conditions of the FEM analysis. For the purpose of estimating fatigue damage on the test piece surface, only a portion of 0.05 mm from the surface out of the 1 mm test piece thickness was taken out in the test piece thickness direction, and the analysis was performed assuming that crystal grains with the same shape and the same crystal orientation continued in the thickness direction. The total number of elements was 49575. A symmetric boundary was set at the left end of the analysis region, and a load was applied up to 50 cycles at the stress amplitude condition in the fatigue test at the right end.

[0094] By FEM analysis, the shear strain range of each slip system was calculated. From the relationship between the slip plane and the global coordinate system, the component of the shear strain range in the out-of-plane direction of the test piece (here, the z direction) was extracted, and the sum (damage parameter) for these 24 slip systems (a total of 24 slip systems combining 12 slip systems of the {110}<111> type and 12 slip systems of the {112}<111> type) was calculated.

[0095] Figures 27, 28, and 29 show the distributions of the damage parameter when cyclic loads with stress amplitudes of 132 MPa, 150 MPa, and 160 MPa are applied for 5 cycles, respectively. From Figures 27 to 29, it can be seen that as the stress amplitude increases, the locations where the damage parameter increases expand.

[0096] Figures 30, 31, and 32 show the frequency distributions of the damage parameter when cyclic loads with stress amplitudes of 132 MPa, 150 MPa, and 160 MPa are applied for 5 cycles, respectively. The frequency distributions in Figures 30 to 32 were obtained for the elements corresponding to the test piece surface among all the elements of the analysis model (see Figure 33).

[0097] From the frequency distributions under each stress amplitude condition, the sum of the damage parameters up to the top 0.5% was determined as the damage index D m Specifically, based on the following formula (1) averaged by the number of elements, the damage index D m (D5) was determined when the number of repetitions m was 5.

Equation

[0098] Similarly, the damage index D m was determined when the number of repetitions m was 10, 20, 30, 40, and 50.

[0099] Figures 11 to 13 are graphs showing the relationship between the number of repetitions m and the damage index D when the stress amplitudes are 132 MPa, 150 MPa, and 160 MPa, respectively. As shown in Figures 11 to 13, there is a correlation between the number of repetitions m and the damage index D, which is represented by the following formula (4). m As shown in Figures 11 to 13, there is a correlation between the number of repetitions m and the damage index D m and it is represented by the following formula (4). D m = a2 × exp(a1·m)…(4) In the above formula, exp(x) means the x-th power of the Napier number e. a1 and a2 are constants, and they take the values in Table 3 below according to the stress amplitude conditions. Note that the relationship between the number of repetitions m and the damage index D m is not limited to this functional form.

[0100]

Table 3

[0101] Since the damage index D in formula (4) m can be interpreted as the damage progressing during the m-th repetition, it is more appropriate to use the cumulative value of the damage index D m for predicting the fatigue life in terms of correspondence with the actual phenomenon. From formula (4), the cumulative value D m of the damage index D up to the number of repetitions n is represented by the following formula (5). s is represented by the following formula (5).

[0102]

Equation

[0103] Figure 14 is a graph showing the relationship between the number of repetitions n and the cumulative value D m of the damage index D up to the number of repetitions n. As the number of repetitions n increases, the cumulative value D s approaches a certain value, and that value can be obtained by the following formula. s approaches a certain value, and that value can be obtained by the following formula.

[0104]

Equation

[0105] Hereinafter, this D L is referred to as the cumulative damage index.

[0106] By correlating this cumulative damage index D L with the fatigue life N under each stress amplitude condition, the master curve in Fig. 34 was obtained. This master curve is expressed by the following equation. D L = 1.27×10 10 ·N -3.24 Note that the master curve is not limited to the above functional form.

[0107] The fatigue life under other test conditions can be obtained by calculating the cumulative damage index D L from crystal plasticity analysis and substituting it into the following equation (A) to find the corresponding fatigue life.

Equation

[0108] To verify the validity of this prediction equation (A), fatigue tests of other steel materials were analyzed. For the extra-low carbon steel shown in Fig. 35 (average crystal grain size 389 μm), crystal plasticity analysis was carried out under the condition of fully reversed cyclic loading with a stress amplitude of 121 MPa, and the cumulative damage index D L was obtained and the fatigue life was predicted from equation (A). As shown in Fig. 36, results in good agreement with the experimental fatigue life were obtained.

[0109] [Prediction of fatigue life by conversion from the damage index D5 at 5 cycles of repetition to the cumulative damage index D L In the above-described fatigue life prediction method, it is necessary to increase the number of repetitions in crystal plasticity analysis to obtain the cumulative damage index D L , which also increases the computational cost. To reduce the computational cost, it is desirable to obtain the cumulative damage index D L with as few repetitions as possible.

[0110] Fig. 37 shows the damage index D5 when cyclic loading is applied 5 times and the cumulative damage index D LIt is a graph showing the relationship with. As shown in FIG. 37, there is a correlation between the damage index D5 and the cumulative damage index D L and it was found that the cumulative damage index D L can be expressed by the following formula (B) using the damage index D5. D L = 0.021327·ln(D5 + 8.0347×10 -5 ) + 0.20110…(B)

[0111] Therefore, the damage index D5 can be converted to the cumulative damage index D L using the above formula (B), and the fatigue life can be predicted using formula (A).

[0112] To verify the validity of this prediction method, fatigue tests of extra-low carbon steels with different crystal grain sizes but the same chemical composition were analyzed. The fatigue life prediction results by the method of converting the damage index D5 to the cumulative damage index D L are shown in FIG. 38. For comparison, the fatigue life prediction results using the damage index D5 are shown in FIG. 39. In the fatigue life prediction results by the method of converting the damage index D5 to the cumulative damage index D L , all the results were within 1 / 2 to 2 times the error, which is said to have good accuracy in fatigue life prediction.

[0113] [Expansion to the number of repetitions j times] If the cumulative damage index D L can be obtained from the results at a number of repetitions less than 5 times, it will lead to a further reduction in the calculation cost. Therefore, similar to the case of the number of repetitions of 5 times, when the number of repetitions is 1 time, 10 times, 30 times, and 50 times, the damage index was converted to the cumulative damage index D L and the fatigue life was predicted respectively. The results are shown in FIG. 40.

[0114] As shown in FIG. 40, it was found that even in the cases other than the number of repetitions of 5 times, the prediction results are equivalent to those in the case of the number of repetitions of 5 times. From this, the cumulative damage index D j from the damage index D LIt has been found that it can be predicted. In particular, it has been found that the fatigue life can be predicted even from the damage index D1 with a repetition number of 1. Fig. 41 shows the fatigue life prediction results by the method of converting the damage index D1 into the cumulative damage index D L as shown.

[0115] As described above, embodiments of the present invention have been described. However, the above-described embodiments are merely examples for carrying out the present invention. Therefore, the present invention is not limited to the above-described embodiments, and within the scope of the invention, the above-described embodiments can be appropriately modified and implemented.

Claims

1. A step of calculating a shear strain range when a repeated load is applied to a component m times for each of a plurality of crystal slip systems for a plurality of m (m is a positive integer) using the finite element method; A step of calculating the sum of the out-of-plane direction components of the shear strain range of the component; A damage index D which is an index of damage of the component based on the sum; ｍ A step of obtaining; A step of obtaining the relationship between m and the damage index D; ｍ A step of obtaining; Based on the relationship between the m and the damage index D; ｍ A step of obtaining a cumulative damage index D represented by the following formula; A fatigue evaluation method comprising. Ｌ 【Equation 1】

2. Based on the data of a plurality of fatigue tests performed in advance, for each of the plurality of fatigue tests, for a plurality of m (m is a positive integer), (A) A step of calculating a shear strain range when a repeated load is applied to a test piece m times for each of a plurality of crystal slip systems using the finite element method, (B) A step of calculating the sum of the out-of-plane direction components of the shear strain range of the test piece, and (C) A step of obtaining a damage index D which is an index of damage of the test piece based on the sum; ｍ A step of obtaining; A step of performing; A step of obtaining the relationship between m and the damage index D; ｍ A step of obtaining; Based on the relationship between the m and the damage index D; ｍ A step of obtaining a cumulative damage index D represented by the following formula; Ｌ A step of obtaining; A step of creating a master curve which is the relationship between the cumulative damage index D and the fatigue life; Ｌ A step of obtaining the damage index D of the target component by the same steps as (A) to (C) above; A step of obtaining; ｍ A step of obtaining; A step of obtaining the relationship between m and the damage index D of the target component; ｍ A step of obtaining; Based on the relationship between the m and the damage index D of the target part ｍ to obtain the cumulative damage index D of the target part Ｌ and a step of Based on the cumulative damage index D of the target part Ｌ and the master curve, predicting the fatigue life of the target part. A fatigue evaluation method comprising: [Figure 2]

3. Based on the data of a plurality of fatigue tests performed in advance, for each of the plurality of fatigue tests, for a plurality of m (m is a positive integer), (A) Using the finite element method, for each of a plurality of crystal slip systems, calculating the shear strain range when a repeated load is applied to the test piece m times; (B) calculating the sum of the out-of-plane components of the shear strain range of the test piece; and (C) obtaining the damage index D which is an index of damage of the test piece based on the sum ｍ and a step of performing; a step of obtaining the relationship between m and the damage index D ｍ and based on the relationship between the m and the damage index D ｍ obtaining the cumulative damage index D represented by the following formula Ｌ and a step of creating a master curve which is the relationship between the cumulative damage index D Ｌ and the fatigue life; obtaining the relationship between the damage index D when a repeated load is applied j times (j is an arbitrary positive integer) ｊ and the cumulative damage index D Ｌ and obtaining the damage index D when a repeated load is applied to the target part j times by the same steps as (A) to (C) above ｊ and a step of based on the relationship between the damage index D of the target part ｊ and the damage index D ｊ and the cumulative damage index D Ｌ obtaining the cumulative damage index D of the target part ＬA step of obtaining, the cumulative damage index D of the target component Ｌ and a step of predicting the fatigue life of the target component based on the master curve, a fatigue evaluation method. 【Equation 3】

4. Using the finite element method, for a plurality of m (m is a positive integer), for each of a plurality of crystal slip systems, a step of calculating the shear strain range when a repeated load is applied to the component m times, a step of calculating the sum of the out-of-plane direction components of the shear strain range of the component, based on the sum, the damage index D which is an index of damage of the component ｍ a step of obtaining, a step of obtaining the relationship between m and the damage index D ｍ and, based on the relationship between m and the damage index D ｍ a step of obtaining the cumulative damage index D represented by the following formula, a fatigue evaluation program for causing a computer to execute. Ｌ 【Equation 4】

5. Based on the data of a plurality of fatigue tests performed in advance, for each of the plurality of fatigue tests, for a plurality of m (m is a positive integer), (A) Using the finite element method, for each of a plurality of crystal slip systems, a step of calculating the shear strain range when a repeated load is applied to the test piece m times, (B) a step of calculating the sum of the out-of-plane direction components of the shear strain range of the test piece, and (C) based on the sum, a step of obtaining the damage index D which is an index of damage of the test piece ｍ a step of performing, a step of obtaining the relationship between m and the damage index D ｍ and, based on the relationship between m and the damage index D ｍ a step of obtaining the cumulative damage index D represented by the following formula, Ｌ the cumulative damage index D Ｌ a step of creating a master curve showing the relationship with the fatigue life; a step of obtaining a damage index D of the target part by the same steps as the above (A) to (C); ｍ a step of obtaining; a step of obtaining the relationship between m and the damage index D of the target part; ｍ a step of obtaining; a step of obtaining the cumulative damage index D of the target part based on the relationship between the m and the damage index D of the target part; ｍ a step of obtaining; Ｌ a step of obtaining; a step of predicting the fatigue life of the target part based on the cumulative damage index D of the target part and the master curve; a fatigue evaluation program for causing a computer to execute. Ｌ 【Equation 5】

6. Based on the data of a plurality of fatigue tests performed in advance, for each of the plurality of fatigue tests, for a plurality of m (m is a positive integer), (A) a step of calculating the shear strain range when a repeated load is applied m times to a test piece for each of a plurality of crystal slip systems using the finite element method; (B) a step of calculating the sum of the out-of-plane components of the shear strain range of the test piece; and (C) a step of obtaining a damage index D which is an index of damage of the test piece based on the sum; ｍ a step of obtaining; a step of performing; a step of obtaining the relationship between m and the damage index D; ｍ a step of obtaining; a step of obtaining the cumulative damage index D represented by the following formula based on the relationship between the m and the damage index D; ｍ a step of obtaining; Ｌ a step of obtaining; a step of creating a master curve showing the relationship between the cumulative damage index D and the fatigue life; Ｌ a step of obtaining the relationship between the damage index D when a repeated load is applied j times (j is an arbitrary positive integer) and the cumulative damage index D; a step of obtaining; ｊ a step of obtaining; Ｌ a step of obtaining; ​The step of obtaining the damage index D when a repeated load is applied to the target part j times by the same steps as the above (A) to (C), ｊ and the step of, Based on the relationship between the damage index D of the target part ｊ and the damage index D ｊ and the cumulative damage index D Ｌ the step of obtaining the cumulative damage index D of the target part, Ｌ and the step of, Based on the cumulative damage index D of the target part Ｌ and the master curve, the step of predicting the fatigue life of the target part, a fatigue evaluation program that causes a computer to execute. 【Equation 6】

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