DOI: 10.5281/zenodo.14532400
title: Dataset used in the publication entitled "Grain size dependence of microscopic strain distribution in a high entropy alloy at the onset of plastic deformation"

description: Documentation for the Dataset used in the publication entitled "Grain size dependence of microscopic strain distribution in a high entropy alloy at the onset of plastic deformation"

** These datasets comprise the 2D data acquired in the face-centered cubic CoCrFeNi high entropy alloys with different grain sizes by means of high-resolution digital image correlation (HRDIC), analyzed by DefDap-0.92 software, and electron backscattered diffraction (EBSD). **** The nomination of alloys in the files are CG-HEA and FG-HEA, corresponding to the coarse-grained (average grain size: 8.8 ± 5.1 μm) and fine-grained (2.8 ± 1.5 μm) high entropy alloys, respectively, in the related publication. **** The samples were deformed in tension and the test was periodically stopped to acquire the data. The HRDIC data were acquired at macroscopic engineering strains of ~0.75%, ~1.50%, and ~2.25%. **** More details about the experimental techniques can be found in the publication "Biaobiao Yang, Xu Xu, David Lunt, Fan Zhang, Michael D. Atkinson, Yunping Li, Javier Llorca, Xiaorong Zhou, Grain size dependence of microscopic strain distribution in a high entropy alloy at the onset of plastic deformation. Acta Materialia, 2025." **

1. Fig.1(E)Grain_Size_CG_HEA.xlsx- Description: The grain size of CG-HEA acquired by EBSD before deformation, as exported by MTEX software- Number of total grains: 3815 (rows == grains)- Number of analyzed variables (features): 1 (i.e., Grain Size in um)

- Variable description by columns:        1- (Grain_size) - type: numerical (float)        Description: the equivalent circle diameter of a grain

2. Fig.1(F)Grain_Size_FG_HEA.xlsx- Description: The grain size of FG-HEA acquired by EBSD before deformation, as exported by MTEX software- Number of total grains: 29175 (rows == grains)- Number of analyzed variables (features): 1 (i.e., Grain Size in um)

- Variable description by columns:        1- (Grain_size) - type: numerical (float)        Description: the equivalent circle diameter of a grain

3. Fig.1CG-HEA_RawEBSD.ctf- Description: The raw EBSD file of CG-HEA before deformation

4. Fig.1FG-HEA_RawEBSD.ctf- Description: The raw EBSD file of FG-HEA before deformation

5. Fig.2(A,C)Stress_Strain_Curves.xlsx- Description: The engineering stress-engineering strain curve of CG and FG-HEAs during tension- Number of analyzed variables (features): 4 

- Variable description by columns:        1- (Engineering strain) - type: numerical (float)        Description: Engineering strain during deformation of CG-HEA        2- (Engineering stress) - type: numerical (float)        Description: Engineering stress reached at a given engineering strain during the deformation of CG-HEA        3- (Engineering strain) - type: numerical (float)        Description: Engineering strain during deformation of FG-HEA        4- (Engineering stress) - type: numerical (float)        Description: Engineering stress reached at a given engineering strain during the deformation of FG-HEA

6. Fig.2(B,D)Strain_Hardening_Rate.xlsx- Description: The strain hardening rate-true strain curve of CG and FG-HEAs during tension- Number of analyzed variables (features): 4 

- Variable description by columns:        1- (True strain) - type: numerical (float)        Description: True strain during deformation of CG-HEA        2- (Strain hardening rate) - type: numerical (float)        Description: Strain hardening rate reached at the given true strain during deformation of CG-HEA        3- (True strain) - type: numerical (float)        Description: True strain during deformation of FG-HEA        4- (Strain hardening rate) - type: numerical (float)        Description: Strain hardening rate reached at the given true strain during deformation of FG-HEA

7. Fig.3(A)CG-HEA_0.75%_HRDIC.txt- Description: The raw HRDIC file of CG-HEA analyzed by the DaVis software, after the deformation to a macroscopic engineering strain of 0.75%

8. Fig.3(B)FG-HEA_0.75%_HRDIC.txt- Description: The raw HRDIC file of FG-HEA analyzed by the DaVis software, after the deformation to a macroscopic engineering strain of 0.75%

9. Fig.3(C)CG-HEA_1.50%_HRDIC.txt- Description: The raw HRDIC file of CG-HEA analyzed by the DaVis software, after the deformation to a macroscopic engineering strain of 1.50%

10. Fig.3(D)FG-HEA_1.50%_HRDIC.txt- Description: The raw HRDIC file of FG-HEA analyzed by the DaVis software, after the deformation to a macroscopic engineering strain of 1.50%

11. Fig.3(E)CG-HEA_2.25%_HRDIC.txt- Description: The raw HRDIC file of CG-HEA analyzed by the DaVis software, after the deformation to a macroscopic engineering strain of 2.25%

12. Fig.3(F)FG-HEA_2.25%_HRDIC.txt- Description: The raw HRDIC file of FG-HEA analyzed by the DaVis software, after the deformation to a macroscopic engineering strain of 2.25%

13-15. Fig.3CG-HEA_HRDIC.(cpr, crc, and ctf)- Description: The raw EBSD file of CG-HEA before deformation, which is used to correlate with HRDIC data in 7, 9, and 11

16-18. Fig.3FG-HEA_HRDIC.(cpr, crc, and ctf)- Description: The raw EBSD file of FG-HEA before deformation, which is used to correlate with HRDIC data in 8, 10, and 12

19. Fig.3Notebook-checkpoint.ipynb- Description: The notebook contains the main scripts to analyze EBSD and HRDIC data, which can be run using the Jupyter Notebooks in the Python environment. This file was run before in the DefDap 0.92, which can be found at https://doi.org/10.5281/zenodo.3784775. In addition, the critical checkpoints to combine EBSD and HRDIC and cut dimensions for CG and FG-HEAs are also included in this file.

20. Fig.5(A)CG-HEA_0.75%_effective shear strain.xlsx- Description: 2D effective shear strain values exported from the DefDap software, for CG-HEA under a macroscopic engineering strain of 0.75%. One value corresponds to one point in the HRDIC map, and its column and line suggest the location in the x (horizontal) direction and y (vertical) direction. Here this file contains 792 columns × 744 lines, i.e. the resolution of the HRDIC map is 792 × 744 pixels. 

21. Fig.5(A)FG-HEA_0.75%_effective shear strain.xlsx- Description: 2D effective shear strain values exported from the DefDap software, for FG-HEA under a macroscopic engineering strain of 0.75%. One value corresponds to one point in the HRDIC map, and its column and line suggest the location in the x (horizontal) direction and y (vertical) direction. Here this file contains 664 columns × 627 lines, i.e. the resolution of the HRDIC map is 664 × 627 pixels. 

22. Fig.5(B)CG-HEA_1.50%_effective shear strain.xlsx- Description: 2D effective shear strain values exported from the DefDap software, for CG-HEA under a macroscopic engineering strain of 1.50%. One value corresponds to one point in the HRDIC map, and its column and line suggest the location in the x (horizontal) direction and y (vertical) direction. Here this file contains 792 columns × 744 lines, i.e. the resolution of the HRDIC map is 792 × 744 pixels.

23. Fig.5(B)FG-HEA_1.50%_effective shear strain.xlsx- Description: 2D effective shear strain values exported from the DefDap software, for FG-HEA under a macroscopic engineering strain of 1.50%. One value corresponds to one point in the HRDIC map, and its column and line suggest the location in the x (horizontal) direction and y (vertical) direction. Here this file contains 664 columns × 627 lines, i.e. the resolution of the HRDIC map is 664 × 627 pixels. 

24. Fig.5(C)CG-HEA_2.25%_effective shear strain.xlsx- Description: 2D effective shear strain values exported from the DefDap software, for CG-HEA under a macroscopic engineering strain of 2.25%. One value corresponds to one point in the HRDIC map, and its column and line suggest the location in the x (horizontal) direction and y (vertical) direction. Here this file contains 792 columns × 744 lines, i.e. the resolution of the HRDIC map is 792 × 744 pixels. 

25. Fig.5(C)FG-HEA_2.25%_effective shear strain.xlsx- Description: 2D effective shear strain values exported from the DefDap software, for FG-HEA under a macroscopic engineering strain of 2.25%. One value corresponds to one point in the HRDIC map, and its column and line suggest the location in the x (horizontal) direction and y (vertical) direction. Here this file contains 664 columns × 627 lines, i.e. the resolution of the HRDIC map is 664 × 627 pixels. 

26. Fig.5(D)Heterogeneity_Index.xlsx- Description: Summary of heterogeneity index of CG and FG-HEAs under various effective shear strains during deformation - Number of analyzed variables (features): 4 

- Variable description by columns:        1- (Average effective shear strain) - type: numerical (float)        Description: Average effective shear strain of CG-HEA calculated by HRDIC after deformation         2- (Heterogeneity index) - type: numerical (float)        Description: Heterogeneity index value, corresponds to the given average effective shear strain of CG-HEA after deformation. This heterogeneity index is calculated based on the 99.5th percentile of maximum in-plane effective shear strain to the average in-plane effective shear strain ratio        3- (Average effective shear strain) - type: numerical (float)        Description: Average effective shear strain of FG-HEA calculated by HRDIC after deformation         4- (Heterogeneity index) - type: numerical (float)        Description: Heterogeneity index value, corresponds to the given average effective shear strain of FG-HEA after deformation. This heterogeneity index is calculated based on the 99.5th percentile of maximum in-plane effective shear strain to the average in-plane effective shear strain ratio

27. Fig.5Normalized effective shear strain.xlsx- Description: Normalized frequencies of CG and FG-HEAs with respect to the normalized effective shear strain during deformation- Number of analyzed variables (features): 12 

- Variable description by columns:        1- (Normalized effective shear strain) - type: numerical (float)        Description: The normalized effective shear strain,  as calculated by the ratio of effective shear strain to the average effective shear strain, of CG-HEA after deformation to a macroscopic engineering strain of 0.75%        2- (Normalized frequency) - type: numerical (float)        Description: The normalized frequency is the fraction of points exhibiting a given normalized effective shear strain interval to whole HRDIC points, for CG-HEA after deformation to a macroscopic engineering strain of 0.75%        3- (Normalized effective shear strain) - type: numerical (float)        Description: The normalized effective shear strain,  as calculated by the ratio of effective shear strain to the average effective shear strain, of CG-HEA after deformation to a macroscopic engineering strain of 1.50%        4- (Normalized frequency) - type: numerical (float)        Description: The normalized frequency is the fraction of points exhibiting a given normalized effective shear strain interval to whole HRDIC points, for CG-HEA after deformation to a macroscopic engineering strain of 1.50%        5- (Normalized effective shear strain) - type: numerical (float)        Description: The normalized effective shear strain,  as calculated by the ratio of effective shear strain to the average effective shear strain, of CG-HEA after deformation to a macroscopic engineering strain of 2.25%        6- (Normalized frequency) - type: numerical (float)        Description: The normalized frequency is the fraction of points exhibiting a given normalized effective shear strain interval to whole HRDIC points, for CG-HEA after deformation to a macroscopic engineering strain of 2.25%        7-12- (Normalized effective shear strain / Normalized frequency) - type: numerical (float)        Description: Same as 1-6 but for FG-HEA

28. Fig.6(A)_Correlation_GS_SF_Strain_CG_HEA.xlsx- Description: Various strain values and microstructural features from HRDIC experiments for CG-HEA at the grain level - Number of analyzed variables (features): 12

- Variable description by columns:        1- (GrainID) - type: numerical (integer)        Description: The IDs of all grains in CG-HEA before deformation        2- (Grain Area) - type: numerical (float)        Description: The areas of the grains in CG-HEA before deformation        3- (Max. Schmid factor) - type: numerical (float)        Description: The maximum Schmid factor for 12 {111} <110> slip systems of a given grain in CG-HEA before deformation, as calculated based on the grain orientation and uniaxial macroscopic stress        4- (Strain50) - type: numerical (float)        Description: The 50th percentile of the in-plane effective shear strain of a given grain in CG-HEA after deformation to a macroscopic engineering strain of 0.75%        5- (Strain99) - type: numerical (float)        Description: The 99.5th percentile of the in-plane effective shear strain of a given grain in CG-HEA after deformation to a macroscopic engineering strain of 0.75%        6- (MeanStrain) - type: numerical (float)        Description: The mean value of in-plane effective shear strain of a given grain in CG-HEA after deformation to a macroscopic engineering strain of 0.75%        7-9- (Strain50, Strain99, MeanStrain) - type: numerical (float)        Description: Same as 4-6 but for in CG-HEA after deformation to a macroscopic engineering strain of 1.50%        10-12- (Strain50, Strain99, MeanStrain) - type: numerical (float)        Description: Same as 4-6 but for in CG-HEA after deformation to a macroscopic engineering strain of 2.25%

29. Fig.6(B)_Correlation_GS_SF_Strain_FG_HEA.xlsx- Description: Various strain values and microstructural features from HRDIC experiments for FG-HEA at the grain level - Number of analyzed variables (features): 12

- Variable description by columns:        1-12 (***) -         Description: Same as last .xlsx file (Fig.6(A)_Correlation_GS_SF_Strain_CG_HEA.xlsx) but for in FG-HEA

30. Fig.8(A)CG-HEA_GrainArea_SlippingSystems.xlsx- Description: Summary of grain areas for grains exhibiting different slip characteristics for CG-HEA after deformation to a macroscopic engineering strain of 1.50%- Number of analyzed variables (features): 4

- Variable description by columns:        1- (Free slip) - type: numerical (float)         Description: The grains containing no clear slip traces        2- (Single slip) - type: numerical (float)         Description: The grains containing slip traces corresponding to one slip system        3- (Double slip) - type: numerical (float)         Description: The grains containing slip traces corresponding to two slip systems        4- (Triple slip) - type: numerical (float)         Description: The grains containing slip traces corresponding to three slip systems

31. Fig.8(B)FG-HEA_GrainArea_SlippingSystemss.xlsx- Description: Summary of grain areas for grains exhibiting different slip characteristics for FG-HEA after deformation to a macroscopic engineering strain of 1.50%- Number of analyzed variables (features): 4

- Variable description by columns:        1-4 (***) -         Description: Same as last .xlsx file (Fig.8(A)CG-HEA_GrainArea_SlippingSystems.xlsx) but for in FG-HEA

32. Fig.9(A)CG-HEA_Schmid factor.xlsx- Description: The Schmid factors of all active slip systems in CG-HEA acquired by Relative Displacement Ratio (RDR) analysis after deformation to a macroscopic engineering strain of 1.50%- Number of total grains: 261 (rows == total number of active slip systems)- Number of analyzed variables (features): 1 (i.e., Schmid factor)

- Variable description by columns:        1- (Schmid factor) - type: numerical (float)        Description: The Schmid factor of the active slip system of a given grain in CG-HEA, as calculated based on the grain orientation and uniaxial macroscopic stress

33. Fig.9(B)FG-HEA_Schmid factorr.xlsx- Description: The Schmid factors of all active slip systems in FG-HEA acquired by Relative Displacement Ratio (RDR) analysis after deformation to a macroscopic engineering strain of 1.50%- Number of total grains: 131 (rows == total number of active slip systems)- Number of analyzed variables (features): 1 (i.e., Schmid factor)

- Variable description by columns:        1- (Schmid factor) - type: numerical (float)        Description: The Schmid factor of the active slip system of a given grain in FG-HEA, as calculated based on the grain orientation and uniaxial macroscopic stress

34. Fig.9(C)CG-HEA_Slip systems ranking.xlsx- Description: The ranking of all active slip systems in CG-HEA acquired by Relative Displacement Ratio (RDR) analysis after deformation to a macroscopic engineering strain of 1.50%- Number of total grains: 261 (rows == total number of active slip systems)- Number of analyzed variables (features): 1 (i.e., slip systems ranking)

- Variable description by columns:        1- (slip systems ranking) - type: numerical (integer)        Description: The Schmid factor ranking of active slip systems among 12 possible slip systems at grain level; the Schmid factor decreased from 1 to 12                1: 1st (the highest Schmid factor for {111} <110> slip system)                2: 2nd                3: 3rd                4: 4th                5: 5th                6: 6th                7: 7th                8: 8th                9: 9th                10: 10th                11: 11th                12: 12th (the lowest Schmid factor for {111} <110> slip system)

35. Fig.9(D)FG-HEA_Slip systems ranking.xlsx- Description: The ranking of all active slip systems in FG-HEA acquired by Relative Displacement Ratio (RDR) analysis after deformation to a macroscopic engineering strain of 1.50%- Number of total grains: 131 (rows == total number of active slip systems)- Number of analyzed variables (features): 1 (i.e., slip systems ranking)

- Variable description by columns:        1- (slip systems ranking) - type: numerical (integer)        Description: The Schmid factor ranking of active slip systems among 12 possible slip systems at grain level; the Schmid factor decreased from 1 to 12                1: 1st (the highest Schmid factor for {111} <110> slip system)                2: 2nd                3: 3rd                4: 4th                5: 5th                6: 6th                7: 7th                8: 8th                9: 9th                10: 10th                11: 11th                12: 12th (the lowest Schmid factor for {111} <110> slip system)

36. Fig.S2(A)KAM_CG_HEA.xlsx- Description: The Kernel Average Misorientation (KAM, in degree) of CG-HEA acquired by EBSD before deformation, as exported by MTEX software- Number of total grains: 3815 (rows == grains)- Number of analyzed variables (features): 1 (i.e., KAM in degree)

- Variable description by columns:        1- (Kernel Average Misorientation) - type: numerical (float)        Description: The Kernel Average Misorientation within one given grain, a measure of local grain misorientation

37. Fig.S2(B)KAM_FG_HEA.xlsx- Description: The Kernel Average Misorientation (KAM, in degree) of FG-HEA acquired by EBSD before deformation, as exported by MTEX software- Number of total grains: 29175 (rows == grains)- Number of analyzed variables (features): 1 (i.e., KAM in degree)

- Variable description by columns:        1- (Kernel Average Misorientation) - type: numerical (float)        Description: The Kernel Average Misorientation within one given grain, a measure of local grain misorientation

38. Fig.S2(C)SchmidFactor_CG_HEA.xlsx- Description: The Schmid factor of CG-HEA acquired by EBSD before deformation, as exported by MTEX software- Number of total grains: 3815 (rows == grains)- Number of analyzed variables (features): 1 (i.e., Schmid factor)

- Variable description by columns:        1- (Schmid factor) - type: numerical (float)        Description: It represents the highest Schmid factor of 12 {111} <110> slip systems in each grain

39. Fig.S2(D)SchmidFactor_FG_HEA.xlsx- Description: The Schmid factor of FG-HEA acquired by EBSD before deformation, as exported by MTEX software- Number of total grains: 29175 (rows == grains)- Number of analyzed variables (features): 1 (i.e., Schmid factor)

- Variable description by columns:        1- (Schmid factor) - type: numerical (float)        Description: It represents the highest Schmid factor of 12 {111} <110> slip systems in each grain