Size Dependency of Elastic and Plastic Properties of Metallic Polycrystals Using Statistical Volume Elements
Source abstract
Abstract
We present an efficient approach to evaluate the size dependency of elastic and plastic properties of metallic polycrystalline materials. Specifically, we consider different volume fractions of ferrite and martensite phases for the construction of three macroscopic domains. Statistical Volume Elements (SVEs) of different sizes are extracted from these domains using the moving window method. Linear and Crystal Plasticity (CP) simulations provide elastic and plastic properties of the SVEs such as the bulk and shear moduli, yield strength, and hardening modulus. We use a variation-based criterion to determine the Representative Volume Element (RVE) size of these properties. This RVE size corresponds to a size beyond which the given property can be idealized as homogeneous. We also use anisotropy indices and an additional RVE size criterion to determine the size limits beyond which these properties can be idealized as isotropic. Numerical results show that the plastic properties often reach their homogeneity and isotropy limits at larger sizes compared to elastic properties. This effect is more pronounced for the hardening modulus compared to the yield strength.
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Research context
OpenAlex topics: Microstructure and mechanical properties · Composite Material Mechanics · Aluminum Alloys Composites Properties
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Mechanical, Aerospace, and Biomedical Engineering Department, University of Tennessee, Knoxville, TN 37996, USA
Funding
Air Force Office of Scientific Research
References (68)
Show source-provided references
1. Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications10.1016/j.actamat.2009.10.058 ↗
2. Microstructural randomness versus representative volume element in thermomechanics10.1115/1.1410366 ↗
3. Numerical homogenization of N-component composites including stochastic interface defects10.1002/(SICI)1097-0207(20000220)47:5<1001::AID-NME814>3.0.CO;2-V ↗
4. Kriging-based approximate stochastic homogenization analysis for composite materials10.1016/j.cma.2007.12.011 ↗
5. A microscopic failure probability analysis of a unidirectional fiber reinforced composite material via a multiscale stochastic stress analysis for a microscopic random variation of an elastic property10.1016/j.commatsci.2012.05.008 ↗
6. Stochastic homogenization analysis of a porous material with the perturbation method considering a microscopic geometrical random variation10.1016/j.ijmecsci.2013.10.001 ↗
7. Random field modeling of elastic properties using homogenization10.1061/(ASCE)0733-9399(2001)127:1(27) ↗
8. Computational micromechanics of composites: The effect of particle spatial distribution10.1016/j.mechmat.2005.06.026 ↗
9. Modeling the effect of mesoscale randomness on concrete fracture10.1016/j.probengmech.2005.11.002 ↗
10. Characterization of random composites using moving-window technique10.1061/(ASCE)0733-9399(2000)126:4(389) ↗
11. Elastic properties of reinforced solids: Some theoretical principles10.1016/0022-5096(63)90036-X ↗
12. Scaling to RVE in random media10.1016/bs.aams.2016.07.001 ↗
13. Elastic and strength properties of statistical volume elements: Determination of isotropic and homogeneous size limits10.1016/j.compstruc.2022.106959 ↗
14. Analysis of heterogeneous composites based on moving-window techniques
15. Effect of boundary condition and statistical volume element size on inhomogeneity and anisotropy of apparent properties10.1016/j.mechmat.2022.104408 ↗
16. Determination of the size of the representative volume element for random composites: Statistical and numerical approach10.1016/S0020-7683(03)00143-4 ↗
17. Estimating fatigue sensitivity to polycrystalline Ni-base superalloy microstructures using a computational approach10.1111/j.1460-2695.2007.01159.x ↗
18. A random field-based method to estimate convergence of apparent properties in computational homogenization10.1016/j.cma.2017.10.027 ↗
19. On statistical strain and stress energy bounds from homogenization and virtual testing10.1016/j.euromechsol.2014.11.003 ↗
20. Scale-Dependent Homogenization of Inelastic Random Polycrystals10.1115/1.2912999 ↗
21. Microstructure and property based statistically equivalent RVEs for intragranular γ- γ’microstructures of Ni-based superalloys10.1016/j.actamat.2018.07.034 ↗
22. Microstructure and property based statistically equivalent RVEs for polycrystalline-polyphase aluminum alloys10.1016/j.ijplas.2018.12.002 ↗
23. Estimation of the size of the RVE for isotropic copper polycrystals by using elastic–plastic finite element homogenisation10.1016/j.commatsci.2009.12.014 ↗
24. Representative volume element size determination for viscoplastic properties in polycrystalline materials10.1016/j.ijsolstr.2018.09.011 ↗
25. Crystal plasticity finite element analysis for René88DT statistical volume element generation10.1088/0965-0393/23/3/035003 ↗
26. Determination of the RVE size for polycrystal metals to predict monotonic and cyclic elastoplastic behavior: Statistical and numerical approach with new criteria10.1016/j.euromechsol.2018.04.011 ↗
27. Investigating mesh sensitivity and polycrystalline RVEs in crystal plasticity finite element simulations10.1016/j.ijplas.2019.06.001 ↗
28. A classification of higher-order strain-gradient models–linear analysis10.1007/s00419-002-0202-4 ↗
29. Nonlocal damage theory
30. Gradient enhanced damage for quasi-brittle materials10.1002/(SICI)1097-0207(19961015)39:19<3391::AID-NME7>3.0.CO;2-D ↗
31. The variational approach to fracture10.1007/s10659-007-9107-3 ↗
32. Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations10.1002/nme.2861 ↗
33. Size effect10.1016/S0020-7683(99)00077-3 ↗
34. Plasticity in small-sized metallic systems: Intrinsic versus extrinsic size effect10.1016/j.pmatsci.2011.01.005 ↗
35. Grain size-dependent crystal plasticity constitutive model for polycrystal materials10.1016/j.msea.2017.07.087 ↗
36. Numerical study of the size-dependent deformation morphology in micropillar compressions by a dislocation-based crystal plasticity model10.1016/j.ijplas.2016.09.001 ↗
37. A crystal plasticity model that accounts for grain size effects and slip system interactions on the deformation of austenitic stainless steels10.1016/j.ijplas.2022.103249 ↗
38. A cosserat crystal plasticity and phase field theory for grain boundary migration10.1016/j.jmps.2018.03.006 ↗
39. Scale-dependent homogenization of random composites as micropolar continua10.1016/j.euromechsol.2014.08.010 ↗
40. Hardening and strengthening behavior in rate-independent strain gradient crystal plasticity10.1016/j.euromechsol.2017.09.006 ↗
41. Large-scale 3D random polycrystals for the finite element method: Generation, meshing and remeshing10.1016/j.cma.2011.01.002 ↗
42. DREAM. 3D: A digital representation environment for the analysis of microstructure in 3D10.1186/2193-9772-3-5 ↗
43. Statistically equivalent representative volume elements (SERVE) for material behaviour analysis and multiscale modelling10.1080/09506608.2023.2246766 ↗
44. Roters, F., Eisenlohr, P., Bieler, T.R., and Raabe, D. (2011). Crystal Plasticity Finite Element Methods: In Materials Science and Engineering, John Wiley & Sons.10.1002/9783527631483 ↗
45. Simulation of local material properties based on moving-window GMC10.1016/S0266-8920(01)00022-4 ↗
46. Application of variational concepts to size effects in elastic heterogeneous bodies10.1016/0022-5096(90)90041-2 ↗
47. A robust and efficient hybrid solver for crystal plasticity10.1016/j.ijplas.2023.103773 ↗
48. High-performance full-field crystal plasticity with dislocation-based hardening and slip system back-stress laws: Application to modeling deformation of dual-phase steels10.1016/j.jmps.2019.103750 ↗
49. Integrated experimental–simulation analysis of stress and strain partitioning in multiphase alloys10.1016/j.actamat.2014.07.071 ↗
50. Predicting elastic anisotropy of dual-phase steels based on crystal mechanics and microstructure10.1016/j.ijmecsci.2018.12.021 ↗
51. A strategy for synthetic microstructure generation and crystal plasticity parameter calibration of fine-grain-structured dual-phase steel10.1016/j.ijplas.2019.10.002 ↗
52. On the size of RVE in finite elasticity of random composites10.1007/s10659-006-9076-y ↗
53. Order relationships for boundary conditions effect in heterogeneous bodies smaller than the representative volume10.1016/0022-5096(94)90022-1 ↗
54. Geometric partitioning schemes to reduce modeling bias in statistical volume elements smaller than the scale of isotropic and homogeneous size limits10.1016/j.cma.2022.114772 ↗
55. Elasticity and Anelasticity of Metals10.1021/j150474a017 ↗
56. The elastic anisotropy of crystals10.1063/1.1709819 ↗
57. Heterogeneous Anisotropy Index and scaling in two-phase random polycrystals10.1007/s00707-018-2114-6 ↗
58. Universal elastic anisotropy index10.1103/PhysRevLett.101.055504 ↗
59. Nye, J.F. (1985). Physical Properties of Crystals: Their Representation by Tensors and Matrices, Oxford University Press.
60. Anisotropy degree of elastic materials
61. Effect of Volume Element Geometry on Convergence to a Representative Volume10.1115/1.4043753 ↗
62. Effect of microstructural variations on the failure response of a nano-enhanced polymer: A homogenization-based statistical analysis10.1007/s00466-020-01934-x ↗
63. Matheron, G. (1971). The Theory of Regionalized Variables and Its Applications, Vol. 5, École National Supérieure des Mines.
64. Lantuejoul, C. (2002). Geostatistical Simulation: Models and Algorithms, Springer Science & Business Media.
65. Automated homogenization-based fracture analysis: Effects of SVE size and boundary condition10.1016/j.cma.2018.11.009 ↗
66. Voronoi tessellation based statistical volume element characterization for use in fracture modeling10.1016/j.cma.2018.02.025 ↗
67. RVE Problem: Mathematical aspects and related stochastic mechanics10.1016/j.ijengsci.2019.103169 ↗
68. Malyarenko, A., and Ostoja-Starzewski, M. (2020). Tensor Random Fields in Continuum Mechanics. Encyclopedia of Continuum Mechanics, Springer.10.1007/978-3-662-55771-6_71 ↗