Metafor

ULiege - Aerospace & Mechanical Engineering

User Tools

Site Tools


doc:user:elements:volumes:plasticity_criterion

Plastic criteria

The PlasticCriterion class manages the possibility to replace the default Von Mises plastic criterion by another one, described below.

VonMisesPlasticCriterion

Description

Isotropic plastic criterion (default in Metafor)

$$ \sqrt{\frac{3}{2}s_{ij}s_{ij}} - (\sigma_{vm} + \sigma_{visq} + \sigma_{grainSize} + \ldots) = 0 $$

Parameters

néant

Hill48PlasticCriterion

Description

Second order orthotropic plastic criterion

$$ \begin{multline} \sqrt{\frac{1}{2}} \sqrt{F (s_{22}-s_{33})^2 + G (s_{33}-s_{11})^2 + H (s_{11}-s_{22})^2 + 2 (L s_{13}^2 + M s_{23}^2 + N s_{12}^2) } \\- (\sigma_{vm} + \sigma_{visq} + \sigma_{grainSize} + \ldots) = 0 \end{multline} $$

where stresses are defined in an orthotropic frame.

Parameters

Name Metafor Code Dependency
$ F $ HILL48_F néant
$ G $ HILL48_G néant
$ H $ HILL48_H néant
$ L $ HILL48_L néant
$ M $ HILL48_M néant
$ N $ HILL48_N néant

Parameter estimation (for sheet metal)

For sheet metal, the anisotropic parameters can be estimated based on tensile tests (plastic strain of around 10%). Strains are measured along the width ($ \varepsilon_{t} $) and the thickness ($ \varepsilon_{e} $). The plastic anisotropy coefficient is then defined as : $ r = \frac{\varepsilon_{t}}{\varepsilon_{e}} $

This test is done in samples cut along the 0, 45 and 90 degrees axes to define $r_{0}$ , $_{45}$ , $r_{90}$.

A planar average is then defined as : $ r_{moy} = \frac{r_{0} + 2 r_{45} + r_{90}}{4} $

Based on tensile tests, it is not possible to estimate shear through the thickness, so L and M parameters are considered equal to 3.

  • $ F = \frac{2}{1+r_0}\frac{r_{0}}{r_{90}} $
  • $ G = \frac{2}{1+r_0} $
  • $ H = \frac{2r_{0}}{1+r_0} $
  • $ L = 3 $
  • $ M = 3 $
  • $ N = \frac{1+2r_{45}}{1+r_0}\frac{r_{0}+r_{90}}{r_{90}} $
doc/user/elements/volumes/plasticity_criterion.txt · Last modified: 2016/03/30 15:23 (external edit)