A slip transmission prediction method considering taylor factor

Abstract

This invention discloses a slip transfer prediction method considering the Taylor factor, belonging to the field of materials analysis technology. The method includes acquiring EBSD data and corresponding grain boundary morphology after deformation; extracting the slip transfer / blocking relationship and Euler angle parameters of grain pairs during actual tensile testing; calculating the Taylor factor M of each grain and obtaining the Schmidt factor under a given stress state; determining the actual active slip system by combining the slip trace and the Schmidt factor; and calculating geometric compatibility indices, including geometric compatibility factors, for candidate slip system pairs of adjacent grains. With residual Burgh's vector This invention introduces a Taylor factor and classifies slip pairs based on the Taylor factor difference ΔM. Different slip transfer prediction criteria are then fitted to the classified slip pairs to improve prediction accuracy. This invention not only enhances the accuracy of slip transfer analysis but also provides new ideas and tools for the field of materials science, possessing broad application prospects and engineering value.

Description

A slip transfer prediction method considering Taylor factor Technical Field

[0001] This invention relates to the field of materials analysis technology, and in particular to a slip transfer prediction method that takes into account the Taylor factor. Background Technology

[0002] Plastic deformation of materials essentially originates from the movement of dislocations within crystals along specific slip systems. For polycrystalline metals, when dislocations move to grain boundaries, they may undergo cross-grain boundary slip propagation or be blocked at the grain boundaries. Slip propagation / blocking behavior directly affects key failure mechanisms such as deformation uniformity, strain localization, and crack initiation and propagation. Therefore, predicting slip propagation at grain boundaries has always been a core issue in materials analysis and strengthening design.

[0003] Existing studies mostly rely on electron backscatter diffraction (EBSD) to obtain information on grain orientation and grain boundary geometry, and combine this with imaging results of the surface morphology or slip traces after deformation to characterize cross-boundary slip behavior. To achieve prediction, existing studies have proposed two types of parameters to predict the slip propagation behavior of dislocations: (1) Luster–Morris geometric compatibility factor (2) Residual Burgers vector Due to the large This alters the structure and energy of grain boundaries, inducing strain accumulation and promoting the nucleation of microcracks at grain boundaries; therefore, a smaller residual Burgers vector favors slip transfer. However, depending on... and Threshold criteria often have limited predictive accuracy and poor versatility across different material systems and loading conditions; furthermore, relying solely on the geometric matching of slip pairs to activate slip systems cannot fully reflect the differences in deformation "ease" corresponding to grain orientation. On the other hand, the Taylor factor can reflect the overall grain's response to macroscopic stress under loading conditions, but existing slip propagation prediction methods do not introduce the Taylor factor difference (ΔM) between adjacent grains to characterize the inconsistency in mechanical response between grains on both sides. This inconsistency may alter the stress-strain distribution and dislocation accumulation at grain boundaries, thereby affecting whether slip can be successfully propagated across boundaries. Summary of the Invention

[0004] The purpose of this invention is to provide a slip transfer prediction method that considers the Taylor factor, while maintaining... While ensuring geometrical compatibility of the iso-slip system, Taylor factor information is introduced to differentiate slip transfer prediction strategies under different ΔM conditions. By jointly acquiring and registering EBSD data after deformation with grain boundary / slip traces, reliable labeling of slip transfer and slip blockage is achieved. Based on the classification, criteria are fitted separately to obtain higher prediction accuracy and better engineering applicability under different microstructures and loading conditions.

[0005] To achieve the above objectives, the present invention provides a slip-transfer prediction method considering Taylor factors, comprising the following steps:

[0006] S1. Obtain EBSD data and corresponding grain boundary morphology after deformation, and extract slip transfer, slip blockage relationship and Euler angle parameters of grain pairs during actual stretching process;

[0007] S2. Calculate the Taylor factor M of each grain under a given stress state and obtain the Schmidt factor.

[0008] S3. Combine the slip trace and the Schmidt factor to determine the actual activated slip system and identify the slip system pair;

[0009] S4. For candidate slip pairs between adjacent grains, calculate the geometric compatibility index, including the geometric compatibility factor. With residual Burgh's vector ;

[0010] S5. Introduce Taylor factors and classify them according to the Taylor factor difference ΔM of the slip pairs;

[0011] S6. Fit different slip transfer prediction criteria to the slip pairs of the classification to improve prediction ability.

[0012] Preferably, S1 specifically includes the following:

[0013] S11. After tensile deformation, the sample is characterized by EBSD and Hough calibration is completed. The data is denoised using the confidence threshold. The grains are divided according to the orientation difference angle, and the grain number, average orientation and Euler angle are output.

[0014] S12. High-resolution morphology imaging was performed on the tensile-deformed sample in the region consistent with the EBSD analysis, focusing on acquiring grain boundary morphology and slip traces to form joint grain boundary-slip trace data corresponding one-to-one with the EBSD grain pairs for subsequent analysis; imaging equipment included optical microscope, scanning electron microscope, confocal microscope, and atomic force microscope.

[0015] S13. Compare the deformed surface morphology and slip trace images with the IPF diagram drawn by EBSD. For slip traces that are continuous across grain boundaries, they are determined to be "transmission" and slip traces that terminate at the boundary are determined to be "blockage". Then, they are associated with the corresponding grain pairs one by one.

[0016] Preferably, S2 specifically includes the following:

[0017] S21. Based on the given stress state, convert the grain Euler angles into an orientation matrix; for the material crystal structure, enumerate candidate slip systems, calculate the Schmitt factor of each slip system, and sort them.

[0018] S22. Under the applied load / strain conditions, determine the Taylor factor M of the grains to obtain the M value for each grain; calculate the value for adjacent grain pairs (G1, G2). For use in subsequent classification.

[0019] Preferably, the specific operation in S3 is as follows: the active slip surface is determined by matching the slip trace direction with the slip line direction predicted by crystal orientation; the slip direction with the largest Schmitt factor in the slip surface is selected as the actual active slip system.

[0020] Preferably, in S4, the geometric compatibility factor Calculated according to the Luster–Morris definition, the expression is:

[0021] ;

[0022] in for and The angle between them for and The angle between them , These are the sliding direction and the normal to the sliding surface, respectively.

[0023] Residual Burgers vector The calculation expression is: .

[0024] Preferably, step S5 specifically includes the following steps:

[0025] S51. Plot the distribution of the Taylor factor difference for the slip transfer pair and the Taylor factor difference for the slip blockage pair respectively.

[0026] S52. Analyze the differences in Taylor factor distribution caused by slip transfer and slip blockage, analyze the differences in their central tendency, dispersion, peak position and overlapping interval, identify the ΔM value characteristics corresponding to slip transfer and slip blockage, and provide a basis for threshold selection;

[0027] S53. Based on the analysis results in S52, set the Taylor factor difference threshold ΔM. And in subsequent processing, this threshold is kept unchanged, and all sliding pairs are processed according to ΔM≤ΔM. With ΔM>ΔM The data were divided into two categories for subsequent fitting of slip transfer prediction criteria.

[0028] Preferably, step S6 specifically includes the following steps:

[0029] S61. For slip pairs of different classifications, respectively using the geometric compatibility factor... With residual Burgh's vector magnitude Using the characteristic quantity, the slip transfer criterion is fitted to establish a system based on ( , () represents the determination relation of the independent variable;

[0030] S62. Set the slip transfer criterion: When >a and When the value is less than b, it is determined to be slip transfer; otherwise, it is determined to be slip blockage. Here, a and b are threshold parameters that need to be determined.

[0031] S63. Fit the classified data separately and find the optimal parameter combination (a, b) that satisfies the form of S62 within each dataset.

[0032] S64. Evaluate the effectiveness of different (a, b) combinations within each category, and select the combination with the highest accuracy as the final slip transfer criterion for that category.

[0033] Therefore, the slip propagation prediction method considering Taylor factors described above, as used in this invention, has the following beneficial effects:

[0034] 1) For the first time, the Taylor factor difference ΔM between adjacent grains is introduced into the slip transfer determination, which compensates for the shortcomings of relying solely on Taylor factor difference ΔM. and The limitations of geometric matching.

[0035] 2) Set the threshold ΔM based on ΔM By classifying the slip pairs and fitting criteria within each category, prediction accuracy is significantly improved.

[0036] 3) Establish an objective process of "ΔM distribution - difference analysis - threshold locking", and determine the fixed threshold ΔM by using the central tendency and overlapping interval of the two types of ΔM distributions: propagation and blocking. This improves the reproducibility and portability of the method.

[0037] 4) Propose >a and The dual threshold criterion <b can be optimized separately (a, b) within different ΔM categories to achieve higher global prediction accuracy and robustness.

[0038] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0039] Figure 1 is a flowchart of a method according to an embodiment of the present invention;

[0040] Figure 2 is an implementation architecture diagram of an embodiment of the present invention;

[0041] Figure 3 is an IPF diagram and grain numbering of an embodiment of the present invention;

[0042] Figure 4 shows partial grain Euler angle data from an embodiment of the present invention;

[0043] Figure 5 shows grain boundary / slip trace images obtained in the same region according to an embodiment of the present invention, showing only the range of 2-3 grains;

[0044] Figure 6 is a histogram of the frequency distribution of Taylor factor difference of the slip transfer pair according to an embodiment of the present invention;

[0045] Figure 7 is a histogram of the frequency distribution of Taylor factor difference of the sliding blocking pair according to an embodiment of the present invention;

[0046] Figure 8 is a comparison diagram of the theoretical slip surface trace and the actual slip surface trace of an embodiment of the present invention. The selected range is the range within the red box in Figure 5.

[0047] Figure 9 shows the calculation of the slip pair according to an embodiment of the present invention. Screenshot of data with Δb;

[0048] Figure 10 shows the implementation results of the slip transfer prediction method according to an embodiment of the present invention. Detailed Implementation

[0049] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0050] Unless otherwise defined, the technical terms or scientific terms used in this invention shall have the ordinary meanings as understood by those of ordinary skill in the field to which this invention pertains. The "first", "second" and similar terms used in this invention do not denote any order, quantity or importance, but are only used to distinguish different components. Words such as "comprising" or "including" mean that the elements or objects appearing before this word cover the elements or objects listed after this word and their equivalents, without excluding other elements or objects. Words such as "connected" or "coupled" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Upper", "lower", "left", "right", etc. are only used to represent relative positional relationships. When the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0051] Example 1

[0052] The present invention provides a slip transfer prediction method considering the Taylor factor. The flow is shown in Figures 1 and 2. The basic idea is to introduce the difference in Taylor factors between adjacent grains and the residual Burgers vector on the basis of the traditional geometric compatibility factor to characterize the difference in the loading responses on both sides of the grain boundary; obtain "transfer / blocking" samples based on the registration of EBSD after deformation and slip traces, determine the actually activated slip systems under a given stress state and calculate ( , , ΔM); select a threshold ΔM to classify the samples, and optimize (a, b) in the form of a double threshold of >a and <b within each classification; thus achieving highly accurate and generalizable prediction of cross-grain boundary slip transfer.

[0053] First, some concepts with similar forms are explained:

[0054] Slip system: The slip system is the basic unit of crystal slip deformation, composed of a slip plane and the slip direction thereon, representing the possible spatial orientations that can be selected during the plastic deformation of the crystal. The activation of the slip system will generate slip traces on the grain surface. If the slip traces can cross the grain boundary and enter the adjacent grain, it is slip transfer; if it is blocked at the grain boundary, it is slip blocking.

[0055] Slip pair: That is, a slip transfer pair or a slip blocking pair. During the tensile process, the relationship between two adjacent grains will ultimately lead to two results: slip transfer and slip blocking; therefore, these two grains and the relationship between these two grains can be collectively referred to as a slip pair, specifically a slip transfer pair and a slip blocking pair;

[0056] Slip system pair: After determining the actual active slip system of the grain through S3 below, the slip pair is described more specifically as a slip system pair. Compared with the slip pair, the slip system pair adds one piece of information, namely the actual active slip system of each grain.

[0057] The specific flow of the method in this embodiment is shown in Figures 1 and 2, including the following steps:

[0058] S1. Obtain EBSD data and corresponding grain boundary morphology after deformation, and extract slip transfer, slip blockage relationships, and Euler angle parameters of grain pairs during the actual tensile process; specifically including the following:

[0059] S11. After tensile deformation, the sample is characterized by EBSD and Hough calibration is completed. The data is denoised using the confidence threshold. The grains are divided according to the orientation difference angle, and the grain number, average orientation and Euler angle are output.

[0060] S12. High-resolution morphology imaging was performed on the tensile-deformed sample in the region consistent with the EBSD analysis, focusing on acquiring grain boundary morphology and slip traces to form joint grain boundary-slip trace data corresponding one-to-one with the EBSD grain pairs for subsequent analysis; imaging equipment included optical microscope, scanning electron microscope, confocal microscope, and atomic force microscope.

[0061] S13. Compare the deformed surface morphology and slip trace images with the IPF diagram drawn by EBSD. For slip traces that are continuous across grain boundaries, they are determined to be "transmission" and slip traces that terminate at the boundary are determined to be "blockage". Then, they are associated with the corresponding grain pairs one by one.

[0062] The IPF diagrams, grain numbers, partial grain Euler angle data, and grain boundary / slip trace images of the same region obtained in this embodiment are shown in Figures 3-5.

[0063] S2. Calculate the Taylor factor M for each grain under a given stress state and determine the Schmidt factor; specifically, this includes the following:

[0064] S21. Based on the given stress state, convert the grain Euler angles into an orientation matrix; for the material crystal structure, enumerate candidate slip systems, calculate the Schmitt factor of each slip system, and sort them.

[0065] S22. Under the applied load / strain conditions, determine the Taylor factor M of the grains to obtain the M value for each grain; calculate the value for adjacent grain pairs (G1, G2). For use in subsequent classification.

[0066] The statistical results calculated in this embodiment are shown in Figures 6 and 7. In the slip transfer pairs, 85.54% of the slip pairs have a Taylor factor difference of less than 0.6, while the Taylor factor difference of the slip blocking pairs shows a uniform distribution.

[0067] S3. Combine the slip trace and Schmidt factor to determine the actual active slip system and identify the slip system pair. The specific operation is as follows: match the slip trace direction with the slip line direction predicted by crystal orientation to determine the active slip surface; select the slip direction with the largest Schmidt factor in the slip surface as the actual active slip system. In this embodiment, it is shown in Figure 8. The selected range is shown in the red box in Figure 5. The four red lines represent four different slip surfaces, which are calculated. Compare with the trace of the actual sample. The red trace parallel to the trace of the actual grain is the actual active slip surface.

[0068] S4. For candidate slip pairs between adjacent grains, calculate the geometric compatibility index, including the geometric compatibility factor. With residual Burgh's vector Geometric compatibility factor Calculated according to the Luster–Morris definition, the expression is:

[0069] ;

[0070] in for and The angle between them for and The angle between them , These are the sliding direction and the normal to the sliding surface, respectively.

[0071] Residual Burgers vector The calculation expression is: The specific data used in this embodiment is shown in Figure 9.

[0072] S5. Introduce Taylor factors and classify the slip pairs based on the Taylor factor difference ΔM; specifically, this includes the following steps:

[0073] S51. Plot the distribution of the Taylor factor difference for the slip transfer pair and the Taylor factor difference for the slip blockage pair respectively.

[0074] S52. Analyze the differences in Taylor factor distribution caused by slip transfer and slip blockage, analyze the differences in their central tendency, dispersion, peak position and overlapping interval, identify the ΔM value characteristics corresponding to slip transfer and slip blockage, and provide a basis for threshold selection;

[0075] S53. Based on the analysis results in S52, set the Taylor factor difference threshold ΔM. And in subsequent processing, this threshold is kept unchanged, and all sliding pairs are processed according to ΔM≤ΔM. With ΔM>ΔM The data is divided into two categories for subsequent fitting of slip transfer prediction criteria. In this embodiment, the classification threshold ΔM is determined based on the results obtained in S2. The value is set at 0.6, and based on this, all slip pairs are divided into... and Two categories.

[0076] S6. Fit different slip transfer prediction criteria to the slip pairs of the classification to improve predictive power. Specifically, this includes the following steps:

[0077] S61. For slip pairs of different classifications, respectively using the geometric compatibility factor... With residual Burgh's vector magnitude Using the characteristic quantity, the slip transfer criterion is fitted to establish a system based on ( , () represents the determination relation of the independent variable;

[0078] S62. Set the slip transfer criterion: When >a and When the value is less than b, it is determined to be slip transfer; otherwise, it is determined to be slip blockage. Here, a and b are threshold parameters that need to be determined.

[0079] S63. Fit the classified data separately and find the optimal parameter combination (a, b) that satisfies the form of S62 within each dataset.

[0080] S64. Evaluate the effectiveness of different (a, b) combinations within each category, and select the combination with the highest accuracy as the final slip transfer criterion for that category.

[0081] In this embodiment, for group 1: The fitting accuracy was 91.01%. >0.968589 and Values ​​<0.187593 are considered "transmitted," otherwise "blocked." For group 2, The fitting accuracy was 96.85%. >0.888307 and Values ​​<0.321873 are classified as "transmitting"; otherwise, they are classified as "blocking". The overall accuracy rate is 92.85%. See Figure 10 for details.

[0082] Therefore, this invention employs the aforementioned slip propagation prediction method that considers the Taylor factor, incorporating the Taylor factor difference ΔM between adjacent grains into the slip propagation determination, thus overcoming the limitations of relying solely on... and Geometric matching limitations; setting a threshold ΔM based on ΔM By classifying the slip pairs and fitting criteria within each category, prediction accuracy is significantly improved. An objective process of "ΔM distribution - difference analysis - threshold locking" is established, and a fixed threshold ΔM is determined by utilizing the central tendency and overlap interval of the propagation / blocking ΔM distributions. To improve the reproducibility and portability of the method; to propose >a and The method employs a dual threshold criterion of <b, which can be optimized separately (a, b) within different ΔM categories to achieve higher global prediction accuracy and robustness. This method not only enhances the accuracy of slip transfer analysis but also provides new ideas and tools for the field of materials science, with broad application prospects and engineering value.

[0083] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A slip transfer prediction method considering Taylor factors, characterized in that, Includes the following steps: S1. Obtain EBSD data and corresponding grain boundary morphology after deformation, and extract slip transfer, slip blockage relationship and Euler angle parameters of grain pairs during actual tensile process; S2. Calculate Taylor factor M of each grain under a given stress state and obtain Schmidt factor; S3. Combine slip trace and Schmidt factor to determine the actual active slip system and determine slip system pairs. S4. For candidate slip pairs between adjacent grains, calculate the geometric compatibility index, including the geometric compatibility factor. With residual Burgh's vector ； S5. Introduce Taylor factors and classify slip pairs based on the Taylor factor difference ΔM. Specifically, this includes the following steps: S51. Plot distribution maps of the Taylor factor differences for slip-transfer pairs and slip-blocking pairs respectively; S52. Analyze the differences in Taylor factor distributions between slip-transfer and slip-blocking pairs, examining their central tendency, dispersion, peak positions, and overlapping intervals, identifying the ΔM value characteristics corresponding to slip-transfer and slip-blocking, and providing a basis for threshold selection; S53. Set the Taylor factor difference threshold ΔM based on the analysis results of S52. And in subsequent processing, this threshold is kept unchanged, and all sliding pairs are processed according to ΔM≤ΔM. With ΔM > ΔM The data is divided into two categories for subsequent fitting of slip transfer prediction criteria; S6, different slip transfer prediction criteria are fitted to the categorized slip pairs to improve prediction ability; specifically, this includes the following steps: S61, for slip pairs of different categories, using geometric compatibility factors... With residual Burgh's vector magnitude Using the characteristic quantity, the slip transfer criterion is fitted to establish a system based on ( ， S62. Set the slip transfer criterion: when... >a and When <b, it is determined to be slip transfer; otherwise, it is determined to be slip blockage, where a and b are threshold parameters to be determined; S63, fit the classified data respectively, and find the optimal parameter combination (a, b) that satisfies the form of S62 within each dataset; S64, evaluate the effect of different (a, b) combinations within each classification, and select the combination with the highest accuracy as the final slip transfer criterion for that classification.

2. The slip-transfer prediction method considering Taylor factors according to claim 1, characterized in that, S1 specifically includes the following: S11, EBSD characterization of the sample after tensile deformation, and Hough calibration; noise reduction of the data using confidence thresholds, grain division based on orientation difference angles, and output of grain number, average orientation, and Euler angle; S12, high-resolution morphology imaging of the sample after tensile deformation in the region consistent with EBSD analysis, focusing on acquiring grain boundary morphology and slip traces, forming grain boundary-slip trace joint data corresponding one-to-one with EBSD grain pairs for subsequent analysis; imaging equipment includes optical microscope, scanning electron microscope, confocal microscope, and atomic force microscope; S13, matching the deformed surface morphology and slip trace images with the IPF map drawn by EBSD, determining "transmission" for continuous slip traces across grain boundaries, and determining "blockage" for slip traces terminating at the boundary, and associating them one-to-one with the corresponding grain pairs.

3. The slip-transfer prediction method considering Taylor factors according to claim 2, characterized in that, S2 specifically includes the following: S21, converting the Euler angles of the grains into an orientation matrix based on the given stress state; enumerating candidate slip systems for the material's crystal structure, calculating and sorting the Schmidt factor of each slip system; S22, obtaining the Taylor factor M of the grains under the applied load / strain conditions, and acquiring the M value for each grain; calculating the Taylor factor M for adjacent grain pairs (G1, G2). For use in subsequent classification.

4. The slip-transfer prediction method considering Taylor factors according to claim 1, characterized in that, The specific operation in S3 is as follows: the active slip surface is determined by matching the slip trace direction with the slip line direction predicted by crystal orientation; the slip direction with the largest Schmitt factor in the slip surface is selected as the actual active slip system.

5. The slip-transfer prediction method considering Taylor factors according to claim 3, characterized in that, In S4, the geometric compatibility factor Calculated according to the Luster–Morris definition, the expression is: ;in for and The angle between them for and The angle between them 、 These represent the slip direction and the slip surface normal, respectively; the residual Burgers vector. The calculation expression is: 。

Images