Small strain elasto-plastic multiphase-field model

Abstract

A small strain plasticity model, based on the principles of continuum mechanics, is incorporated into a phasefield model for heterogeneous microstructures in polycrystalline and multiphase material systems (Nestler et al., Phys Rev 71:1-6, 2005). Thereby, the displacement field is computed by solving the local momentum balance dynamically (Spatschek et al., Phys Rev 75:1-14, 2007) using the finite difference method on a staggered grid. The elastic contribution is expressed as the linear approximation according to the Cauchy stress tensor. In order to calculate the plastic strain, the Prandtl-Reuss model is implemented consisting of an associated flow rule in combination with the von Mises yield criterion and a linear isotropic hardening approximation. Simulations are performed illustrating the evolution of the stress and plastic strain using a radial return mapping algorithm for single phase system and two phase microstructures. As an example for interface evolution coupling with

Modeling of crack propagation on a mesoscopic length scale

“…It has been shown in [18] that this formulation of the internal plastic energy provides the expected dissipation formulation. We derive the elastodynamic equations by calculating the variational derivative of the energy functional (1) with respect to the displacement field u [17] …”

“…By minimization of the total system energy, the models describe the propagation of cracks [7]. Extensions of this approach to plastic effects in multiphase materials are elaborated by Schneider et al [18] and applications in ferroelectric polycrystals are shown by Abdollahi and Arias [19]. Only few approaches describe crack propagation in heterogeneous materials.…”

“…Starting from a physical type model, we formulate a crack propagation model coupled with the diffusion process, and investigate the influence of water diffusion on crack propagation in glasses [16]. We extend this work by including plastic effects [18]. We extend this work by including plastic effects [18].…”

“…The main difference is the utilization of a obstacle type instead of a double-well potential, which is commonly used e.g. Thus, in [16], the crack propagation is investigated in glasses by considering the water diffusion, and the development of the plastic zone at the crack tip is analyzed in [18]. Another advantage of the model is the possibility of representing and coupling different physical fields.…”

“…This choice of locally homogenized effective flow parameters is computationally simple and numerically robust [18]. Using the Prandtl-Reuss model, the internal plastic energy density is expressed as [30] f pl (¯ pl , φ)…”