Use this model to represent the strength behavior of materials, typically metals, subjected to large strains, high strain rates and high temperatures. Such behavior might arise in problems of intense impulsive loading due to high velocity impact.
With this model, the yield stress varies depending on strain, strain rate and temperature.
The model defines the yield stress Y as
where
 = effective plastic strain |
 = normalized effective plastic strain rate |
| TH = homologous temperature = (T-Troom)/(Tmelt -Troom) |
The five material constants are A, B, C, n and m.
The expression in the first set of brackets gives the stress as a function of
strain when
= 1.0 sec-1 and
TH = 0 (for laboratory experiments at room temperature).
The constant A is the basic yield stress at low strains while B and n represent the
effect of strain hardening.
The expressions in the second set of brackets represent the effects of strain rate on the yield strength of the material. The reference strain rate against which the material data was measured is used to normalize the plastic strain rate enhancement. 1.0/second is used by default.
The expression in the third set of brackets represents thermal softening such that the yield stress drops to zero at the melting temperature Tmelt.
The plastic flow algorithm used in this model has an option to reduce high frequency oscillations that are sometimes observed in the yield surface under high strain rates. A first order strain rate correction is applied by default. An additional implicit strain rate correction is available that can be used in cases where the first order strain rate correction doesn’t suffice, although at the cost of extra CPU time usage.
The Johnson-Cook strength model can be used in all element types and in combination with all equations of state and failure properties.
Note: A specific heat capacity property should be defined to enable the calculation of temperature hence thermal softening effects.
| Name | Symbol | Units | Notes |
|---|---|---|---|
| Initial Yield Stress | A | Stress | |
| Hardening Constant | B | Stress | |
| Hardening Exponent | n | None | |
| Strain Rate Constant | C | None | |
| Thermal Softening Exponent | m | None | |
| Melting Temperature | Tmelt | Temperature | |
| Reference Strain Rate | None | Units fixed at 1/sec Default = 1.0 | |
| Strain Rate Correction | None | Option List: None 1st Order (Default) Implicit |
Custom results variables available for this model:
| Name | Description | Solids | Shells | Beams |
|---|---|---|---|---|
| EFF_PL_STN | Effective Plastic Strain | Yes | Yes* | Yes* |
| EFF_PL_STN_RATE | Effective Plastic Strain Rate | Yes | Yes* | Yes* |
| TEMP | Temperature** | Yes | Yes* | Yes* |
| SUBL_EPS | Effective sublayer plastic strain | No | Yes | No |
*Resultant value over shell/beam section.
**Temperature will be non-zero only if a specific heat capacity is defined.