2. Benchmark solution#

It is based on [bib.1] and [v6.08.110]. In the field of small deformations, the stress tensor \(\sigma\) being uniaxial, it is possible to calculate for each sliding system, the split resolved by: \({\tau }_{s}=\sigma :{\mu }_{s}\) with \({\mu }_{s}\) the orientation tensor defined by: \({({m}_{s})}_{\mathrm{ij}}=\frac{1}{2}({({n}_{s})}_{i}\cdot {({l}_{s})}_{j}+{({l}_{s})}_{i}\cdot {({n}_{s})}_{j})\), \({n}_{s}\) designating the normal to the sliding plane of the system \(s\) and \({l}_{s}\) the sliding direction. The evolution of plastic sliding is given for each system \(s\) by (cf. [R5.03.11]):

Case of \(\mathrm{CFC}\): For the chosen orientation, i.e. 1-5-9, the initial Schmid factors, relating the stress tensor to the various resolved splits \({\tau }_{s}\) are, for the 12 octahedral systems:

\(\begin{array}{c}\text{[}0.45784855,0.22892428,0.22892428,0.15261618,0.26707832,0.11446214,\\ 0.19840104,0.29760156,0.4960026,0.04578486,0.11446214,0.16024699\text{]}\end{array}\)

We can therefore see that the first activated sliding system will be number 9 (\(\mathrm{A3}\)), and the second will be number 1 (i.e. \(\mathrm{B4}\)).

In large deformations, or taking into account the rotation of the network, for a non-infinitesimal deformation, we must see the appearance of a third sliding system, \(\mathrm{C1}\) (12th system in Code_Aster) whose activity increases significantly, while the visco-plastic sliding of the \(\mathrm{A3}\) system no longer evolves [2].

2.1. Bibliographical references#

  1. N.Rupin Note EDF -R&D: HT24 -2010-01128-en « implementation of a new constitutive law based on dislocation dynamics for fcc materials ».

  2. Simulation of the mechanical response of austenitic stainless steel using crystalline calculations N. Rupin, J.M. Proix, F. Latourte, G. Monnet, paper at the 10th National Colloquium on Structural Calculation, 9-13 May 2011, 9-13 May 2011, Presqu’île de Giens (Var).