atom

micro

macro

A

B

C
CP-FEM

CP-FEM: Crystal Plasticity – Finite Element Method
Definition:Finite element method restricting the mechanical degrees of freedom to the crystallographic slip and twin systems of the crystal.
Explanation:The Finite Element Method (FEM) can be viewed as a quasi-standard for simulating micromechanical deformation processes. In the standard form, the materials are modelled as continuum that can be elastically and/or plastically deformed. However, it is known since the 1930s that crystals deform plastically by the motion of dislocations along specific shear directions and planes. This dislocation motion creates a shear of the crystal lattice on distinct planes in distinct directions. In terms of a continuum method as FEM, this means that the plastic part of the deformation has to be built from these elementary shears. The resulting method has been called as CP-FEM. The first simulation using this approach haa been performed by Peirce et al. in 1982. Since then, the CP-FEM has developed into a versatile tool for describing the mechanical response of crystalline materials on all length scales from single crystals to engineering parts (Roters et al. 2010 a/b). While it originally accounted for dislocation slip as the only deformation mechanism, there now exist extensions of CP-FEM, that also account for other deformation mechanisms such as the twinning induced plasticity (→TWIP) and the transformation induced plasticity (→TRIP).
Picture /
Figure /
Diagram:

Two examples for the application of CP-FEM. (a) Simulation of a mini tensile sample resolving the grain structure. (b) Simulation of a deep drawing experiment using macro texture data.
SFB-Link:The constitutive model developed for TWIP steels is also implemented in the framework of CP-FEM.
References:Peirce D., Asaro R.J., Needleman A.; Acta Metall. 30, 1982, p 1087
Roters F., Eisenlohr P., Hantcherli L., Tjahjanto D.D., Bieler T.R., Raabe D.; Acta Mater. 58, 2010, p 1152
Roters F. Eisenlohr P., Bieler T.R., Raabe D.; Crystal Plasticity Finite Element Methods, 2010 WILEY-VCH