Application of the Generalized Schmid Law in Multiscale Models: Opportunities and Limitations

• Published in: Microstructural Design of Advanced Engineering Materials pp. 19 - 40
• Main Author: Houtte, Paul
• Format: Book Chapter
• Language: English
• Published: Weinheim, Germany Wiley‐VCH Verlag GmbH & Co. KGaA 14.08.2013
• Subjects: critical resolved shear stress (CRSS); crystal plasticity; edge dislocation; Schmid law; Schmid tensors; strain rate tensor
• ISBN: 9783527332694; 3527332693
• DOI: 10.1002/9783527652815.ch02

The generalized Schmid law is means to identify active slip systems in a ductile crystal subjected to a stress described by a tensor. It is used as the corner stone of models that relate the imposed plastic strain tensor to the stress deviator in a single crystal or in a grain of polycrystalline material. It can be used very well at the length scale of individual crystals, for example, to model the relationship between local stress and plastic strain rate, or to predict the lattice spin upon plastic deformation. Multiscale models for plastic deformation, linking the crystal length scale with the macroscopic length scale, can also make good use of the generalized Schmid law (or of the approximately equivalent visco‐plastic crystal model). Applications include the prediction of deformation textures and of the plastic anisotropy of a polycrystalline material with a known texture. Examples of such models are the Taylor–Bishop–Hill theory, grain interaction models, self‐consistent models, the crystal‐plasticity finite element method, and the crystal‐plasticity fast Fourier transformation method. They can be used as an essential component in a through process modeling setup. They also play a key role in models used for computer‐aided design of entire components such as car bodies. The length scales bridged by such models are: crystal, macroscopic, sometimes even the engineering level (entire component).