Expectable specific features of BCC crystal plastic flow and consistency with the Schmid law

Abstract

When several types of slip systems participate in crystal plasticity, the critical shear stress (CSS) of each system can suffer load orientation and sign dependencies. Variations on the CSS can result from asymmetric slip planes contributing to the plastic straining, as is the case for {112} planes in BCC crystals, and from collaboratively involved slip planes in multi-planar dislocation motions. For BCC crystals, these planes are the in-zone, cross-slip planes of each slip direction. Strictly speaking, these expectable variations do not constitute a violation of the Schmid law and not even a deviation. In order to further account for crossed non-glide stress effects between slip planes, the existing regularized forms of the classical Schmid law which do not violate the fundamentals of the criterion seem adaptable for matching with typical experimental data of both BCC and FCC structures. This is discussed and exemplified here.

Keywords:

• crystal plasticity
• plastic flow criterion
• FCC
• BCC
• asymmetric slip
• non Schmid law

Notes

1. Since there are no coplanar systems in {112} planes, the parameter does not exist.

2. (4/3)^1/2 is the limit CSS ratio for the activation of slip on a {112} plane rather than on a {110} one for uniaxial loading, in the Schmid law framework. There is no loading mode to increase further this ratio.

3. The unique scalar that is required in FCC crystals to account for this cross-slip effect should in fact be extended into a 3 × 3 “cross-slip coefficient matrix”, owing to the three different cases of G system type. This matrix being unknown so far, the three k, k′, k′′ coefficients represent a minimal form of it, for our discussion purpose.

4. For the interaction between a gliding dislocation and a previous (primary) junction product [30].

5. Typically, for directions A and B the Burgers vectors of the dislocations are a [−111]/2 and a[111]/2 and the pair energy is 3a ²/2. The junction product has Burgers vector a[022]/2 and energy 2a ².