/MAT/LAW103 (HENSEL-SPITTEL)
Block Format Keyword This law represents an isotropic elastic-plastic material at high temperature using Hensel-Spittel yield stress formula. The yield stress is a function of strain, strain rate and temperature. This material law can be used with an equation of state /EOS.
This material is often used in hot forging simulations. The law parameters are valid only for a given range of temperature and strain rate. This material law is compatible with solid and SPH elements only.
Format
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
/MAT/LAW103/mat_ID/unit_ID or /MAT/HENSEL-SPITTEL/mat_ID/unit_ID | |||||||||
mat_title | |||||||||
ρi | ρ0 | ||||||||
E | ν | ||||||||
A0 | m1 | m2 | m3 | m4 | |||||
m5 | m7 | ||||||||
Fsmooth | Fcut | ε0 | Pmin | ||||||
ρCp | T0 | η |
Definition
Field | Contents | SI Unit Example |
---|---|---|
mat_ID | Material
identifier. (Integer, maximum 10 digits) |
|
unit_ID | Unit Identifier. (Integer, maximum 10 digits) |
|
mat_title | Material
title. (Character, maximum 100 characters) |
|
ρi | Initial
density. (Real) |
[kgm3] |
ρ0 | Reference density used in
the default equation of state. Default = ρi (Real) |
[kgm3] |
E | Initial Young's
modulus. (Real) |
[Pa] |
ν | Poisson's
ratio. (Real) |
|
A0 | Stress
parameter. (Real) |
[Pa] |
m1 | Material parameter
1. (Real) |
|
m2 | Material parameter
2. (Real) |
|
m3 | Material parameter
3. (Real) |
|
m4 | Material parameter
4. (Real) |
|
m5 | Material parameter
5. (Real) |
|
m7 | Material parameter
7. (Real) |
|
Fsmooth | Smooth strain rate flag.
(Integer) |
|
Fcut | Cutoff frequency for
strain rate filtering. (Real) |
[1s] |
ε0 | Reference
strain. (Real) |
|
Pmin | Pressure cutoff (<
0). Default = 1030 (Real) |
[Pa] |
ρCp | Specific heat per unit
volume. (Real) |
[Jm3⋅K] |
T0 | Initial
temperature. (Real) |
[K] |
η | Heat conversion parameter
0 <
η
< 1.0. (Real) |
▸Example (Alloy)
Comments
- Yield stress:
1
(1) σy=A0expm1Tεm2˙εm3expm4ε(1+ε)m5Texpm7εWhere,- T
- Temperature in °C
- ε
- True strain ε=ε0+ˉεp
- ˉεp
- Equivalent plastic strain
- ˙ε
- True strain rate in s-1
- m1 - m5
- Material parameters
- In case of
purely mechanical simulation, the temperature is computed assuming adiabatic
condition:
(2) T=T0+η⋅EintρCpVWhere,- Eint
- Internal energy of the element.
- η
- Taylor-Quinney coefficient used as scale of plastic energy, which transfers into heat.
- V
- Volume of the element
- There is no strain rate effect if m3 = 0.
- By default, the
hydrostatic pressure is linearly proportional to volumetric
strain:
(3) P=KμWhere,- K=E3(1−2v)
- Bulk modulus
- μ=ρρ0−1
- Volumetric strain
An additional Equation of State (/EOS) card can refer to this material to model a nonlinear dependency between hydrostatic pressure and volumetric strain.
- This material can be used with the material options, /HEAT/MAT, /THERM_STRESS/MAT, /EOS, and /VISC.