# [LEGACY] Multiaxial Control with Constant Strain Rate

This example (`tutorials/triaxSLR`

) covers the biaxial deformation of an HCP polycrystal at a constant strain rate. Loads are applied normal to the surface, maintaining proportional macroscopic load ratios of \(-1\):\(0\):\(1\) for the \(x\):\(y\):\(z\) directions, respectively. Load tolerance options are prescribed and latent hardening is enabled, as well as saturation strength evolution. The primary loading direction is set to be in the \(x\) direction, and the strain rate is doubled on the second step. Elemental values for the equivalent plastic strain and plastic work are output, along with the nodal coordinates and surface-integrated forces. Material parameters are those for the \(\alpha\) phase of Ti-6Al-4V and are provided in the below tables. The latent parameters are input values to the hardening interaction matrix [CARSON17]. Illustrations of the results are provided in the below figures.

Phase |
Type |
\(C_{11}\) [MPa] |
\(C_{12}\) [MPa] |
\(C_{13}\) [MPa] |
\(C_{44}\) [MPa] |
---|---|---|---|---|---|

\(\alpha\) |
HCP |
\(169.66 \times 10^3\) |
\(88.66 \times 10^3\) |
\(61.66 \times 10^3\) |
\(42.50 \times 10^3\) |

Phase |
\(m\) [-] |
\(\dot{\gamma_{0}}\) [1/s] |
\(h_{0}\) [MPa] |
\(g_{s0}\) [MPa] |
\(m^\prime\) [-] |
\(\dot{\gamma_{s}}\) [1/s] |
\(n\) [-] |
\(c/a\) [-] |
---|---|---|---|---|---|---|---|---|

\(\alpha\) |
0.01 |
1.0 |
190.0 |
530.0 |
1.1 |
1.0 |
1.0 |
1.587 |

Phase |
\(g_0\) (basal) [MPa] |
\(g_0\) (prismatic) [MPa] |
\(g_0\) (pyramidal) [MPa] |
\(h_{diag}\) [-] |
\(h_{1}-h_{7}\) [-] |
---|---|---|---|---|---|

\(\alpha\) |
390.0 |
468.0 |
663.0 |
1.0 |
1.4 |