Fatigue Evaluation Method and Fatigue Evaluation Program

Abstract

To provide a fatigue evaluation method considering influence of fatigue damage on an organization form.SOLUTION: A fatigue evaluation method includes the steps of: calculating shear strain range for each of a plurality of crystal slip systems when load is repeatedly applied to a part: (step S4-A); and calculating a sum of outside of the part direction component in the shear strain range (step S4-B).SELECTED DRAWING: Figure 10

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 service life of steel products such as automotive parts, railway vehicle parts, and bridges are important social issues, and an increase in the high fatigue strength of steel materials is required. In order to obtain design guidelines for realizing an increase in high fatigue strength, it is necessary to establish techniques for quantifying the effects of increasing 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 in the solder joint portion 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 three-dimensional thermo-elasto-plastic analysis by the finite element method 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 simulations 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.

Prior Art Documents

Patent Documents

[0006]

Patent Document 1

Patent Document 2

Non-Patent Documents

[0007]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0008] 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 elucidate the fatigue crack generation mechanism. In determining the material design guidelines, it is necessary to grasp the microscopic stress and strain that depend on the microstructure such as the crystal grain size distribution and the crystal orientation distribution, and to search for the optimal microstructure for realizing high fatigue strength. In addition, 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.

[0009] 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

[0010] 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 for each of a plurality of crystal slip systems, and a step of calculating a sum of out-of-plane components of the shear strain range of the component.

[0011] A fatigue evaluation method according to another embodiment of the present invention includes, for each of a plurality of fatigue tests performed in advance, for each of the plurality of fatigue tests, (A) a step of calculating a shear strain range when a repeated load is applied to a test piece for each of a plurality of crystal slip systems, (B) a step of calculating a sum of out-of-plane components of the shear strain range of the test piece, and (C) a step of obtaining a damage index that is an index of damage of the test piece based on the sum, a step of creating a master curve that is a relationship between the damage index and the fatigue life, a step of obtaining a damage index of a target component by the same steps as (A) to (C) above, and a step of predicting the fatigue life of the target component based on the damage index of the target component and the master curve.

[0012] A fatigue evaluation program according to an embodiment of the present invention causes a computer to execute 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 components of the shear strain range of the component.

[0013] According to another embodiment of the present invention, a fatigue evaluation program, based on data of a plurality of fatigue tests performed in advance, for each of the plurality of fatigue tests, (A) for each of a plurality of crystal slip systems, calculates a shear strain range when a repeated load is applied to a test piece; (B) calculates a sum of out-of-plane components of the shear strain range of the test piece; and (C) obtains a damage index, which is an index of damage of the test piece, based on the sum, and then performs a step of creating a master curve that is a relationship between the damage index and the fatigue life, a step of obtaining a damage index of a target component by the same steps as (A) to (C) above, and a step of predicting the fatigue life of the target component based on the damage index of the target component and the master curve, and causes a computer to execute them.

Advantages of the Invention

[0014] According to the present invention, it becomes possible to perform fatigue evaluation considering the influence of the microstructure on fatigue damage.

Brief Description of the Drawings

[0015]

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DETAILED DESCRIPTION OF THE INVENTION

[0016] 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.

[0017] The present inventor modeled a fatigue test performed 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.

[0018] The fatigue test to be analyzed was carried out 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.

[0019] As candidates for physical quantities related to fatigue damage, the stress in the loading direction, the maximum principal stress, the plastic strain in the loading direction, the cumulative slip, etc. were examined. However, no clear correlation was recognized between the locations where these stresses or strains were high and the fatigue damage parts observed in the experiment.

[0020] 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 location of fatigue damage 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 shows the location of fatigue damage observed in the experiment. In Fig. 5, the hatched areas are the locations of fatigue damage.

[0021] Here, the "sum of the out-of-plane components of the shear strain range in a plurality of slip systems existing in the crystal structure" will be explained in detail.

[0022] In crystal plasticity analysis, deformation analysis is performed on the assumption 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 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. In this analysis, a total of 24 slip systems combining 12 slip systems of the {110}<111> type and 12 slip systems of the {112}<111> type were used.

[0023] Fig. 7 is a diagram schematically showing the time change of 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.

[0024] 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 in all the slip systems considered (24 slip systems in this analysis) is obtained. This value is 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] FIG. 9 is a diagram schematically showing a cross section near the surface of a test piece after a fatigue test. The protrusions and depressions (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 depression.

[0026] 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 part in the shear strain range in a plurality of slip systems existing in the crystal structure". The present invention has been completed based on the above findings. Hereinafter, embodiments of the present invention will be described in detail.

[0027] [Fatigue Evaluation Method] FIG. 10 is a flowchart of a fatigue evaluation method according to an 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).

[0028] The application target of the fatigue evaluation method according to the present embodiment is not particularly limited as long as it is a polycrystal, but is preferably a metal material, and more preferably a steel material (iron-based alloy).

[0029] 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 the present embodiment, based on this damage parameter, a "damage index", which is an index of damage to the test piece, is calculated. Details of the damage index will be described later. In the fatigue evaluation method according to the present embodiment, first, data of a plurality of fatigue tests performed in advance are prepared (step S1), the damage index is calculated for each of them (step S2), and a master curve representing the relationship between the damage index and the fatigue life is created (step S3). Then, the 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.

[0030] Prepare data of a plurality of fatigue tests performed in advance (step S1). Each of the fatigue test data includes, for example, information on the test piece shape, the crystal orientation distribution at the evaluation location, the loading 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).

[0031] 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 loading conditions with the same material, it may be assumed that all the test pieces have the same crystal orientation distribution.

[0032] To create a master curve, data of at least two levels of fatigue tests measured by changing the loading conditions are required. It is preferable that there are three or more levels of the fatigue test data.

[0033] Analyze each of the data from a plurality of fatigue tests (step S2). Specifically, for each of the data from a plurality of fatigue tests, perform the following steps: (A) For each of a plurality of crystal slip systems, calculate the shear strain range when a repeated load is applied to the test piece (step S2-A); (B) Calculate 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-B); and (C) Calculate the damage index based on the damage parameter (step S2-C). These analyses can be performed, for example, by FEM analysis.

[0034] As the slip systems used for 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.

[0035] Also, in the hcp crystal structure, for example, the following slip systems can be used.

Number

[0036] For each of the target crystal slip systems, calculate the shear strain range when a repeated load is applied to the test piece (step S2-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 formula described in D. Pierce, R.J. Asaro, A. Needleman, Acta metall., vol.30(1982), pp.1087-1119. In fatigue tests, a repeated load of thousands to hundreds of thousands of cycles may be applied. However, when calculating the shear strain range by FEM analysis, it is realistic to cut off the calculation at a few cycles from the perspective of calculation cost and calculate the shear strain range at the final cycle.

[0037] Calculate the sum of the out-of-plane components of the shear strain range on the test piece surface (step S2-B). More specifically, extract the out-of-plane components of the shear strain range on the test piece surface from the relationship between the slip plane and the global coordinate system, and calculate the sum for all the crystal slip systems considered in step S2-A. In this embodiment, this sum is called the "damage parameter". A location with a large damage parameter can be evaluated as a location where cracks are likely to occur due to repeated loading.

[0038] Based on the damage parameter, calculate the "damage index" described below (step S2-C). The above-described damage parameter is a value calculated for each element of the model used in the analysis. Calculate the "damage index" as an index for evaluating the degree of damage in the entire analysis region.

[0039] The damage index is calculated based on the damage parameter. The damage index may be, for example, the sum of the damage parameters of all the elements of the analysis model. The damage index may also be the sum of the damage parameters of a predetermined size or more among the damage parameters of all the elements of the analysis model.

[0040] Alternatively, a predetermined percentage of elements may be extracted in descending order of the damage parameter, and the sum of these may be used as the damage index. That is, the total number of elements is N, the predetermined percentage is s (0 < s < 1), and the k-th largest damage parameter is dk Taking (k = 1, 2, 3, …, N), D represented by the following formula may be used as the damage index.

Equation

[0041] Also, among all the elements of the analysis model, only the part related to the crack, more specifically, the elements corresponding to the outermost layer part of the test piece, may be extracted, and the damage index may be calculated based on the damage parameters of the extracted elements. For example, the elements corresponding to the outermost layer part of the test piece may be extracted, and from these, in order from the ones with larger damage parameters, a predetermined percentage of elements may be extracted, and the sum of these may be used as the damage index.

[0042] The damage index may also be calculated by methods other than the above. The damage index may be any one calculated based on the damage parameter. For example, it is also conceivable to use the maximum value of the damage parameter or the number of elements whose damage parameter is equal to or greater than a predetermined magnitude as the damage index.

[0043] Through the above steps, the damage index is calculated for each of the data of a plurality of fatigue tests.

[0044] From the damage index obtained in step S2 and the fatigue life obtained in the fatigue test, a master curve representing the relationship between the damage index and the fatigue life is created (step S3).

[0045] Next, for the target part to be subjected to fatigue evaluation, crystal plasticity analysis is similarly performed (step S4). Specifically, (A) 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 target part (step S4-A), (B) a step of calculating the sum of the out-of-plane direction components of the shear strain range (i.e., the damage parameter) (step S4-B), and (C) a step of calculating the damage index based on the damage parameter (step S4-C) are performed.

[0046] The target component 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 component may be the same or different.

[0047] Finally, based on the damage index of the target component obtained in step S4 and the master curve obtained in step S3, the fatigue life of the target component is predicted (step S5).

[0048] With reference to FIGS. 11 to 15, an example of the above-described fatigue evaluation method will be described. As an example of data from a plurality of fatigue tests, consider data from fatigue tests performed on the same material with the stress amplitude σ changed to σ1, σ2, …, σ k FIG. 11 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) N.

[0049] First, the above-described crystal plasticity analysis is performed on the data of the fatigue test with the stress amplitude σ being σ1, and the damage parameter d is calculated for each element of the analysis model. FIG. 12 is a diagram schematically showing the frequency distribution of the damage parameter d in the fatigue test with the stress amplitude σ being σ1. Based on the damage parameter d, the damage index D1 in the data of the fatigue test with the stress amplitude σ being σ1 is calculated. In FIG. 13, as an example, the sum obtained by extracting in a predetermined ratio in descending order of the damage parameter d is taken as the damage index D1.

[0050] For the data of the fatigue tests with the stress amplitudes σ being σ2, …, σ k as well, crystal plasticity analysis is similarly performed to calculate the damage indices D2, …, D k (FIG. 13). By correlating the fatigue lives N1, N2, …, N k obtained from the fatigue tests with the damage indices D1, D2, …, D k a master curve for predicting the fatigue life is obtained (FIG. 14). In the master curve, D is represented as a function f of N as follows. D = f(N)

[0051] For the target component to be evaluated for fatigue, similar crystal plasticity analysis is also performed to obtain the damage index D X (Fig. 15). The fatigue life of the component is obtained as follows: N corresponding to D X is obtained from the inverse function of f (Fig. 16). N = f -1 (D)

[0052] The fatigue evaluation method according to an embodiment of the present invention has been described above. According to this embodiment, fatigue evaluation considering the influence of the microstructure on fatigue damage becomes possible.

[0053] 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 process of receiving fatigue test data, a process of analyzing each data, a process of creating a master curve, a process of analyzing a target component, and a process of predicting the fatigue life of the target component. Also according to this embodiment, fatigue evaluation considering the influence of the microstructure on fatigue damage becomes possible.

Example

[0054] Hereinafter, the present invention will be described more specifically by way of examples (analysis examples). The present invention is not limited to these examples.

[0055] A past fatigue test was modeled and crystal plasticity analysis was performed. 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.

[0056]

Table 1

[0057] The fatigue test was performed by taking a test piece having 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.

[0058]

Table 2

[0059] Note that the stress amplitudes actually tested 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.

[0060] Measuring the 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. Figure 2 shows the crystal orientation distribution of a 0.9 mm × 0.9 mm region (region A in Figure 1) near the center of the test piece obtained by performing crystal orientation analysis by EBSD on the test piece used in the test at a stress amplitude of 132 MPa. Figure 3 is a polycrystalline model created based on the grain boundary information obtained by crystal orientation analysis. Note that since there was no EBSD analysis information for the test pieces in the fatigue tests at stress amplitudes of 150 MPa and 160 MPa, the same polycrystalline model as Figure 3 was used.

[0061] Figure 17 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 0.05 mm portion from the surface out of the 1 mm test piece thickness was extracted in the test piece thickness direction, and the analysis was performed assuming that 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 5-cycle load was applied at the stress amplitude condition in the fatigue test at the right end.

[0062] By FEM analysis, the shear strain range (the difference between the maximum value and the minimum value at the 5th cycle) 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 (here the z direction) of the test piece surface 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.

[0063] Figures 18, 19, and 20 show the distributions of damage parameters when the stress amplitudes are 132 MPa, 150 MPa, and 160 MPa, respectively. From Figures 18 to 20, it can be seen that as the stress amplitude increases, the locations where the damage parameters increase expand.

[0064] Figures 21, 22, and 23 show the frequency distributions of damage parameters when the stress amplitudes are 132 MPa, 150 MPa, and 160 MPa, respectively. The frequency distributions in Figures 21 to 23 were obtained for the elements corresponding to the specimen surface (see Figure 24) among all the elements of the analytical model. 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, and by correlating it with the fatigue life N under each stress amplitude condition, the master curve in Figure 25 was obtained. This master curve is expressed by the following equation. D = 0.739e -0.000891N In this case, the master curve was expressed by an exponential function, but the master curve is not limited to an exponential function.

[0065] The fatigue life under other test conditions can be obtained by determining the damage index D from crystal plasticity analysis and substituting the corresponding fatigue life into the following equation (A). N = -(1 / 0.000891N)ln(D / 0.739) ··· Equation (A)

[0066] To verify the validity of this prediction equation (A), the fatigue tests of other steel materials were analyzed. The test material is an extra-low carbon steel with the same chemical composition as in Table 1 but different crystal grain sizes. The crystal orientation distribution of this test material is shown in Figure 26. The average crystal grain size of this test material is 100 μm, while the average crystal grain size of the test material shown in Figure 2 is 400 μm. Test specimens with the same shape as in Figure 1 were taken from this test material and fatigue tests were carried out. The test conditions and test results are shown in Table 3.

[0067]

Table 3

[0068] Based on the information of crystal grain boundaries obtained by crystal orientation analysis, a polycrystalline model was created, and crystal plasticity analysis was performed under the stress amplitude conditions shown in Table 3. The damage index D was determined and substituted into Equation (A) to predict the fatigue life N. The results are shown in Fig. 27. The error between the predicted value and the experimental value was about -30%. The prediction was made within 1 / 2 to 2 times the error, which is generally considered to have good accuracy in fatigue life prediction, thus confirming the validity of this fatigue evaluation method.

[0069] The embodiments of the present invention have been described above. However, the above-described embodiments are merely examples for implementing the present invention. Therefore, the present invention is not limited to the above-described embodiments, and it is possible to appropriately modify the above-described embodiments and implement them without departing from the gist of the present invention.

Claims

1. For each of a plurality of crystal slip systems, a step of calculating a shear strain range when a repeated load is applied to a component, and a step of calculating the sum of the out-of-plane direction components of the shear strain range of the component, a fatigue evaluation method.

2. Based on data of a plurality of fatigue tests performed in advance, for each of the plurality of fatigue tests, (A) For each of a plurality of crystal slip systems, a step of calculating a shear strain range when a repeated load is applied to a test piece, (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 which is an index of damage of the test piece based on the sum, a step of performing, a step of creating a master curve which is the relationship between the damage index and the fatigue life, a step of obtaining the damage index of the target component by the same steps as (A) to (C) above, a step of predicting the fatigue life of the target component based on the damage index of the target component and the master curve, a fatigue evaluation method.

3. For each of a plurality of crystal slip systems, a step of calculating a shear strain range when a repeated load is applied to a component, and a step of calculating the sum of the out-of-plane direction components of the shear strain range of the component, a fatigue evaluation program for causing a computer to execute.

4. Based on data of a plurality of fatigue tests performed in advance, for each of the plurality of fatigue tests, (A) For each of a plurality of crystal slip systems, a step of calculating a shear strain range when a repeated load is applied to a test piece, (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 which is an index of damage of the test piece based on the sum, a step of performing, a step of creating a master curve which is the relationship between the damage index and the fatigue life, a step of obtaining the damage index of the target component by the same steps as (A) to (C) above, a step of predicting the fatigue life of the target component based on the damage index of the target component and the master curve, a fatigue evaluation program for causing a computer to execute.

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