Grain size dependence of polycrystalline plasticity modeling in cylindrical indentation
- PDF / 22,986,221 Bytes
- 45 Pages / 595.276 x 790.866 pts Page_size
- 26 Downloads / 244 Views
ORIGINAL PAPER
Grain size dependence of polycrystalline plasticity modeling in cylindrical indentation George Z. Voyiadjis1 · Juyoung Jeong1 · Jeffrey W. Kysar2,3 Received: 12 August 2020 / Accepted: 23 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Grain boundary strengthening effect for polycrystalline copper is studied numerically using crystal plasticity in conjunction with cylindrical indentation simulations under the plane strain condition. In order to compare with an isotropic, heterogeneous continuum model a new constitutive relation is developed. This new nonlocal continuum model that encompasses the heterogeneity in yield strength based on the exponentiated Weibull function can predict the plastic properties of materials in the micron length scale. The spatial description of the deformation gradient two-point tensor is utilized to capture the intrinsic size effect in line with the subsequent deformation measures. Moreover, the total geometrically necessary dislocation density is obtained from the non-zero components of Nye dislocation density tensor. From the simulation, the relationship between the effective Green–Lagrange strain and effective stress measures is explained using the persistent long-range order and intermittent short-range order. The observation derived from the analogy between the cylindrical indentation and the progress in cylindrical voids describes how different average grain sizes of polycrystalline materials are compared with the behavior of isotropic materials. The trajectories of directions of both principal stretch and maximum shear strain explain that the internal stresses induced by cylindrical indentation either hinder or reinforce the dislocation flow, forming strain localization sporadically. The grain size dependence of polycrystalline modeling incorporates the Hall–Petch strengthening as well as the homogenization of anisotropic polycrystalline metal into the isotropic effective medium. This is a physically-based model that is used to model failure characterization in metals. Keywords Nonlocal continuum model · Exponentiated Weibull probability distribution function · Contact mechanics · Nanoindentation · Crystal plasticity finite element method · Hall–Petch effect · Homogenization
1 Introduction 1.1 Size effects One of the fundamental objectives of materials science and engineering is the strengthening due to size effects of crystalline metallic structures. Size effects in crystalline metals, particularly the Hall–Petch effect, explains the strengthening of the material by decreasing the average grain size in
B
George Z. Voyiadjis [email protected]
1
Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA 70803, USA
2
Department of Mechanical Engineering, Columbia University, New York, NY 10027, USA
3
Department of Otolaryngology-Head and Neck Surgery, Columbia University, New York, NY 10032, USA
polycrystalline metals. Dislocations control the size effects in crystalline metals, as t
