Gradient crystal plasticity including dislocation-based work-hardening and dislocation transport. (June 2015)

• Record Type: Journal Article
• Authors: Wulfinghoff, Stephan; Böhlke, Thomas
• Is Part Of: International journal of plasticity. Volume 69(2015:Jun.)
• Page Start: 152
• Page End: 169
• Publication Date: 2015-06
• Subjects: Crystal plasticity -- Dislocations -- Particulate reinforced material -- Numerical algorithms -- Gradient plasticity; Plasticity -- Periodicals; Plasticité -- Périodiques; Plasticity; Periodicals; 620.11233
• DOI: 10.1016/j.ijplas.2014.12.003
• Languages: English
• ISSNs: 0749-6419

Abstract

Abstract: This work aims at the formulation of a gradient crystal plasticity model which incorporates some of the latest developments in continuum dislocation theory and is, at the same time, well-suited for a three-dimensional numerical implementation. Specifically, a classical continuum crystal plasticity framework is extended by taking into account continuous dislocation density and curvature field variables which evolve according to partial differential equations (Hochrainer et al., 2014; Ebrahimi et al., 2014). These account for dislocation transport and curvature-induced line-length production and have been derived from a higher-dimensional continuum dislocation theory. The dislocation density information is used to model work hardening as a consequence of dislocation entanglement. A composite microstructure is simulated consisting of a soft elasto-plastic matrix and hard elastic inclusions. The particles are assumed to act as obstacles to dislocation motion, leading to pile-ups forming at the matrix–inclusion interface. This effect is modeled using gradient plasticity with a simplified equivalent plastic strain gradient approach (Wulfinghoff et al., 2013) which is used here in order to allow for an efficient numerical treatment of the three-dimensional numerical model. A regularized logarithmic energy is applied which is intended to approximate the higher order gradient stress of the statistical theory of Groma et al. (2003). Highlights: A gradient crystal plasticity model using continuum dislocation dynamics is proposed. The model is well-suited for a three-dimensional numerical implementation. Dislocation density and curvature field variables evolve according to PDEs. A composite microstructure is simulated. Strain gradient effects are modeled by an equivalent plastic strain gradient.