Capturing the influence of surface constraints in small and thin samples using polycrystalline plasticity theory

Abstract

A rate-dependent, single-crystal plasticity model for face-centred cubic crystal structures has been implemented into a large strain elastic - plastic, finite-element code to examine the mechanical influence of the reduced surface constraints of relatively small polycrystalline aggregates. The implemented model simulates deformation of a polycrystal composed of cubic grains where each grain is a single finite element. Mechanical constraint is varied by changing (a) specimen thickness and (b) specimen volume, relative to grain size. Numerical uniaxial tensile tests have been performed to a strain level of 0.01. Direct and statistical examination of the model results revealed the reduced flow stress of grains at specimen surfaces, edges and corners. The results of these simulations are in good agreement with previous experimental studies which suggest that 5 - 10 grains across the minimum dimension of a structure are necessary to approximate true continuum polycrystalline response.

Cyclic response of electrodeposited copper films. Experiments and elastic–viscoplastic mean-field modeling

“…With such time consuming calculations, the number of grains considered is usually limited (from 10 to hundreds of grains). Buchheit et al (1997) showed that specimens with approximately five grains in the thickness have a macroscopic response which is consistent with continuum polycrystalline behavior (where surface constraints may be neglected). Keller and Hug (2017) confirmed these results by considering FE calculations and experiments on Nickel films.…”

Investigation of three-dimensional aspects of grain-scale plastic surface deformation of an aluminum oligocrystal

“…Thirdly, surface strain localization in most of these studies was measured using digital image correlation (DIC) methods, which work by tracing pattern changes on the strained sample surface. Finally, the simulation tool predominantly used in these works was the finite element crystal plasticity (FEMCP) method, which provides a computational framework capable of addressing the complexity of the problem, including the mechanical grain interaction, the sample geometry, the loading boundary condition, the grain topology, the grain orientation changes (or texture evolution), the microstructure information and the hardening response of the crystal (Kalidindi et al, 1992;Beaudoin et al, 1996;Sarma and Dawson, 1996;Buchheit et al, 1997;Mika and Dawson, 1999;Bate, 1999). …”

Plastic heterogeneities of a copper multicrystal deformed in uniaxial tension: experimental study and finite element simulations

“…In most cases, an ideal polycrystal is imagined and relatively few attempts have been made to simulate the behavior of an actual sample [12,13], one of the reasons being that for a sample with more than one layer of grains, if surface observations provide a lot of detail about the strains and crystal orientation in the surface layer, the boundary conditions imposed by the deeper layers of material cannot be assessed. The problem of number of through thickness grains is addressed in the work by Buchheit et al [14], but on an ideal polycrystal. Most of these simulations use a hardening rule derived from Asaro and Needleman [15], where quantities similar to critical shear rates are linearly related to glide velocities through a constant hardening matrix which in its simplest form has only two dierent kinds of term, the diagonal term for self-hardening and the o-diagonal for latent hardening.…”