Study on the Effects of Grain Shape, Size and Size Distribution on the Mechanical Behavior of Metals

Abstract:

Crystal plasticity finite element (CPFE) simulations of three-dimensional representative volume elements (RVEs) enable the prediction of polycrystalline material behavior under complex loading conditions. Plastic deformation is modeled through crystallographic slip on lattice slip systems, subject to the Schmid yield criterion based on the maximum resolved shear stress (CRSS). In this work, an efficient rate-independent crystal plasticity (CP) and gradient enhanced crystal plasticity (GECP) formulation is used to investigate the influence of microstructural characteristics on the mechanical performance of FCC materials. Three-dimensional periodic RVEs with irregular grain morphologies are simulated within Abaqus/Standard to study the effects of grain size, grain size distribution, and grain shape under uniaxial loading. Comparative analyses between the CP and GECP frameworks are performed to assess the predictive capabilities and applicability for increasingly heterogeneous microstructures. The results demonstrate that GECP accurately captures grain size dependent work hardening and grain size distribution effects through the intrinsic length scale introduced by strain gradient calculations. In contrast, grain shape variations result in only minor changes in the macroscopic response for both frameworks.

• Periodical: Solid State Phenomena (Volume 390)
• Pages: 163-172
• DOI: https://doi.org/10.4028/p-cNIr4V
• Online since: April 2026
• Authors: Ruxandra Bocan*, Emin Semih Perdahcioglu, Ton van den Boogard
• Keywords: Crystal Plasticity, Gradient Enhanced Crystal Plasticity, Grain Aspect Ratio, Grain Size Distribution

References

[1] R.J. Asaro. Crystal plasticity. Journal of Applied Mechanics, 50(4b):921-934, 1983.

DOI: 10.1115/1.3167205

[2] J.F. Nye. Some geometrical relations in dislocated crystals. Acta Metallurgica, 1(2):153-162, 1953.

DOI: 10.1016/0001-6160(53)90054-6

[3] A. Acharya and J. L. Bassani. Lattice incompatibility and a gradient theory of crystal plasticity. Journal of the Mechanics and Physics of Solids, 48(8):1565-1595, 2000.

DOI: 10.1016/s0022-5096(99)00075-7

[4] N. A. Fleck, M. A. Ashby, and J. W. Hutchinson. The role of geometrically necessary dislocations in giving material strengthening. Scripta Materialia, 48(2):179-183, 2003.

DOI: 10.1016/s1359-6462(02)00338-x

[5] E S Perdahcioglu. A rate-independent crystal plasticity algorithm based on the interior point method. Computer Methods in Applied Mechanics and Engineering, 418(Part A), 2024.

DOI: 10.1016/j.cma.2023.116533

[6] B Nijhuis, E S Perdahcioglu, and A H van den Boogaard. A robust and efficient rate-independent crystal plasticity model based on successive one-dimensional solution steps. Computer Methods in Applied Mechanics and Engineering, 438(Part B), 2025.

DOI: 10.1016/j.cma.2025.117815

[7] Y. Bergstrom. A dislocation model for the stress-strain behaviour of polycrystalline alpha-fe with special emphasis on the variation of the densities of mobile and immobile dislocations. Materials Science and Engineering, 5(4):193-200, 1970.

DOI: 10.1016/0025-5416(70)90081-9

[8] E S Perdahcioglu, C Soyarslan, E E Asik, A H van den Boogaard, and S Bargmann. A class of rate-independent lower-order gradient plasticity theories: Implementation and application to disc torsion problem. Materials, 11(8), 2018.

DOI: 10.3390/ma11081425

[9] M. F. Ashby. The deformation of plastically non-homogeneous materials. Philosophical Magazine, 21(170):399-424, 1970.

DOI: 10.1080/14786437008238426

[10] L. Kudin, B. Devincre, and M. Tang. Mesoscopic modelling and simulation of plasticity in fcc and bcc crystals: Dislocation intersections and mobility. Journal of Computer-Aided Materials Design, 5:31-54, 1998.

DOI: 10.1023/a:1008648120261

[11] M. Becker. Incompatibility and Instability Based Size Effects in Crystals and Composites at Finite Elastoplastic Strains. PhD thesis, Institut für Mechanik (Bauwesen), Lehrstuhl I, Universität Stuttgart, 2006.

[12] Lawrence Berkeley National Laboratory. voro++. https://math.lbl.gov/voro++/about. html. Accessed 2025-10-15.

[13] C Geuzaine and J-F Remacle. Gmsh: A 3-d finite element mesh generator with built-in preand post-processing facilities. International Journal for Numerical Methods in Engineering, 79(11):1309-1331, 2009.

DOI: 10.1002/nme.2579

[14] R. Bocan. Study on the effects of grain shape, size and size distribution on the mechanical behavior of metals. Master's thesis, University of Twente, 2025.