/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
ρ i ρ 0
E ν
A0 m1 m2 m3 m4
m5 m7
Fsmooth Fcut ε 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaS baaSqaaiaaicdaaeqaaaaa@3883@ Pmin
ρ C p 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)

ρ i Initial density.

(Real)

[ kg m 3 ]
ρ 0 Reference density used in the default equation of state.

Default = ρ i (Real)

[ kg m 3 ]
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.
=0
No strain rate smoothing.
= 1
Strain rate smoothing active.

(Integer)

Fcut Cutoff frequency for strain rate filtering.

(Real)

[ 1 s ]
ε 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaS baaSqaaiaaicdaaeqaaaaa@3883@ Reference strain.

(Real)

Pmin Pressure cutoff (< 0).

Default = 1030 (Real)

[ Pa ]
ρ C p Specific heat per unit volume.

(Real)

[ J m 3 K ]
T0 Initial temperature.

(Real)

[ K ]
η Heat conversion parameter 0 < η < 1.0.

(Real)

Example (Alloy)

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                   g                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW103/1/1
Magnesium alloy
#        Init. dens.          Ref. dens.
              0.0018              0.0018
#                  E                  Nu
               45000                0.28
#                 A0                  M1                  M2                  M3                  M4
               709.4             -0.0065             -0.1538                   0             -0.0261
#                 M5                  M7
                   0                   0
#            Fsmooth                Fcut                 Eps                Pmin
                   0                   0               0.010                   0
#              RhoCp                  T0                 ETA
                1.89              673.15                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata

Comments

  1. Yield stress: 1
    σ y = A 0 exp m 1 T ε m 2 ε ˙ m 3 exp m 4 ε ( 1 + ε ) m 5 T exp m 7 ε MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda WgaaWcbaGaamyEaaqabaGccqGH9aqpcaWGbbWaaSbaaSqaaiaaicda aeqaaOGaciyzaiaacIhacaGGWbWaaWbaaSqabeaacaWGTbWaaSbaaW qaaiaaigdaaeqaaSGaamivaaaakiabew7aLnaaCaaaleqabaGaamyB amaaBaaameaacaaIYaaabeaaaaGccuaH1oqzgaGaamaaCaaaleqaba GaamyBamaaBaaameaacaaIZaaabeaaaaGcciGGLbGaaiiEaiaaccha daahaaWcbeqaamaalaaabaGaamyBamaaBaaameaacaaI0aaabeaaaS qaaiabew7aLbaaaaGcdaqadaqaaiaaigdacqGHRaWkcqaH1oqzaiaa wIcacaGLPaaadaahaaWcbeqaaiaad2gadaWgaaadbaGaaGynaaqaba WccaWGubaaaOGaciyzaiaacIhacaGGWbWaaWbaaSqabeaacaWGTbWa aSbaaWqaaiaaiEdaaeqaaSGaeqyTdugaaaaa@5E6E@
    Where,
    T MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGubaaaa@39B0@
    Temperature in °C
    ε MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH1oqzaa a@3805@
    True strain ε = ε 0 + ε ¯ p MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH1oqzcq GH9aqpcqaH1oqzdaWgaaWcbaGaaGimaaqabaGccqGHRaWkcuaH1oqz gaqeamaaBaaaleaacaWGWbaabeaaaaa@3F64@
    ε ¯ p
    Equivalent plastic strain
    ε ˙
    True strain rate in s-1
    m 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaaleaacaWGTbWaaS baaWqaaiaaikdaaeqaaaaa@383A@ - m 5 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaaleaacaWGTbWaaS baaWqaaiaaikdaaeqaaaaa@383A@
    Material parameters
  2. In case of purely mechanical simulation, the temperature is computed assuming adiabatic condition:
    T = T 0 + η E int ρ C p V MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamivaiabg2 da9iaadsfadaWgaaWcbaGaaGimaaqabaGccqGHRaWkdaWcaaqaaiab eE7aOjabgwSixlaadweadaWgaaWcbaGaciyAaiaac6gacaGG0baabe aaaOqaaiabeg8aYjaadoeadaWgaaWcbaGaamiCaaqabaGccaWGwbaa aaaa@46EE@
    Where,
    Eint
    Internal energy of the element.
    η
    Taylor-Quinney coefficient used as scale of plastic energy, which transfers into heat.
    V MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvaaaa@36D2@
    Volume of the element
  3. There is no strain rate effect if m3 = 0.
  4. By default, the hydrostatic pressure is linearly proportional to volumetric strain:
    P = K μ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8akY=xipgYlh9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaamiuaiabg2da9iaadUeacqaH8oqBaaa@3E37@
    Where,
    K = E 3 ( 1 2 v ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=vipgYlh9vqqj=hEeeu0xXdbb a9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yq aiVgFr0xfr=xfr=xb9adbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4saiabg2da9maalaaabaGaamyraaqaaiaaiodadaqadaqaaiaa igdacqGHsislcaaIYaGaamODaaGaayjkaiaawMcaaaaaaaa@4101@
    Bulk modulus
    μ = ρ ρ 0 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8akY=xipgYlh9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeqiVd0Maeyypa0ZaaSaaaeaacqaHbpGCaeaacqaHbpGCdaWgaaWc baGaaGimaaqabaaaaOGaeyOeI0IaaGymaaaa@42BA@
    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.

  5. This material can be used with the material options, /HEAT/MAT, /THERM_STRESS/MAT, /EOS, and /VISC.
1 A. Hensel, T. Spittel, VEB German Publishing House for Basic Industry, Leipzig, Deutschland, 1978