Strain Rate Dependent Plasticity
Strain Rate Dependent Plasticity: Theoretical Foundations
Strain Rate Dependent Plasticity
Professor, does the yield stress change with strain rate?
When metals deform at high speeds, the yield stress increases. In impacts ($\dot{\varepsilon} = 10 \sim 1000$ /s), it becomes 1.2 to 1.5 times the static yield stress.
Representative Models
| Model | Equation | Application |
|---|---|---|
| Cowper-Symonds | $\sigma_Y(1+(\dot{\varepsilon}/C)^{1/p})$ | LS-DYNA MAT_24. Most common |
| Johnson-Cook | $\sigma(1+C\ln\dot{\varepsilon}^*)$ | High-speed deformation + temperature |
| Perzyna | $\dot{\varepsilon}^p = \gamma(f/\sigma_0)^n$ | Overstress model |
Is Cowper-Symonds the most widely used?
Cowper-Symonds is standard in LS-DYNA MAT_24 for automotive crash. Representative parameters for steel (mild steel): $C = 40$ /s, $p = 5$.
Summary
Fundamentals of Viscoplasticity: Perzyna Rule
Piotr Perzyna formulated a viscoplastic model in 1963 at the Polish Academy of Sciences, where the plastic strain rate becomes a function of the overstress (difference between current stress and static yield stress). The relation $\dot{\varepsilon}_p = \gamma \langle f(\sigma,\kappa)/k \rangle^n$ allows unified treatment of creep and dynamic plasticity. This "Perzyna viscoplasticity" became the theoretical starting point for high-speed deformation analysis.
Computational Methods for Strain Rate Dependent Plasticity
FEM Settings
LS-DYNA MAT_24:
```
*MAT_PIECEWISE_LINEAR_PLASTICITY
$ ..., C, p
, , , , , , 40., 5.
```
```
*RATE DEPENDENT, TYPE=POWER LAW
D, p $ Cowper-Symonds
```
Or:
```
*RATE DEPENDENT, TYPE=JOHNSON COOK
C, eps0
```
Summary
Identification of the Cowper-Symonds Equation
The Cowper-Symonds equation σy=σ₀[1+(ε̇/D)^(1/q)] is a representative approximation for strain rate dependent yield stress. The widely cited Jones (1989) values for mild steel are D=40.4 s⁻¹, q=5. The standard procedure involves obtaining data at 10²~10⁴/s via Split Hopkinson Bar (SHPB) tests and determining the slope 1/q and D^(1/q) through least squares regression on a log-log plot.
Strain Rate Dependent Plasticity in Practice
Practical Checklist
Application to Explosive Protection Design
In IED (Improvised Explosive Device) protection analysis, the strain rate dependence of armor steel RHA (Rolled Homogeneous Armour) directly affects design quality. Set Cowper-Symonds coefficients in LS-DYNA MAT_024 to predict deformation behavior within 1ms after explosion. Practical accuracy has been verified since the 2010s through protection performance simulations for different NATO STANAG 4569 levels.
Strain Rate Dependent Plasticity: Software & Solver Comparison
Tools
LS-DYNA Strain Rate Options
LS-DYNA offers diverse SR (strain rate effect) options in material cards. For MAT_024, VP (viscoplastic flag)=0 uses equivalent plastic strain rate, VP=1 uses volumetric strain rate. MAT_019 (STRAIN_RATE_DEPENDENT_PLASTICITY) directly implements the Perzyna rule and is used for high-precision impact analysis. From R14 (2023), a diagnostic display function for effects was added.
Advanced Technology
Advanced
Crystal Plasticity and Strain Rate
In crystal plasticity theory (Crystal Plasticity), slip system
Related Topics
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