A new way to include the grain shape in texture simulations with the Taylor model
The use of the Hall-Petch relation in texture simulations with the Taylor-Bishop-Hill model is proposed as a mean to take into account grain shape effect. The results are compared with those obtained with the usual and relaxed constraint Taylor model for a simple texture and the consequences for the anisotropy coefficient are investigated On propose d'utiliser la relation de Hall-Petch dans les simulations de texture a l'aide du modele de Taylor-Bishop-Hill pour prendre en compte la forme des grains. Comparaison des resultats avec ceux du modele de Taylor classique ou relaxe dans le cas d'une texture simple; consequences pour le coefficient d'anisotropie
A probabilistic crystal plasticity model for modeling grain shape effects based on slip geometry
Abstract A new statistical theory is introduced that takes into account the coupling between grain size, shape and crystallographic texture during deformation of polycrystalline microstructures. A “grain size orientation distribution function” (GSODF) is used to encode the probability density of finding a grain size D along a direction (given by unit vector n ) in grains with orientation g . The GSODF is sampled from the input microstructure and is represented in a finite element mesh. During elastoplastic deformation, the evolution of grain size D (in direction θ ) and the orientation g is tracked by directly updating the GSODF probabilities using a Lagrangian probability update scheme. The effect of grain shape (e.g. in high aspect ratio grains) is modeled by including the apparent grain size as seen by various different active slip systems in the grain within the constitutive law for the slip system resistance. The prediction of texture and strains achieved by the statistical approach is compared to Taylor aggregate and finite element deformation analysis of a planar polycrystalline microstructure. The role of grain shape and size in determining plastic response is investigated and a new adaptive GSODF model for modeling microstructures with multimodal grain shapes is proposed.
Orientation distribution, elastic and plastic anisotropy in stabilized steel sheet
The texture of commercially produced stabilized steel in the temper rolled condition has been represented by a three-dimensional orientation distribution, defined by a set of coefficients of a series of generalized spherical harmonics. The coefficients have been used to calculate the elastic and plastic properties in the plane of the sheet and comparison is made between the predicted and experimental values. Errors in the experimental determination of pole figures have been analysed and estimated.