/FAIL/EMC

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
/FAIL/EMC/`mat_ID`/`unit_ID`
`a`		`n`		`b`₀		`c`

Card 2

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
$γ$ $γ$		${\dot{ε}}_{0}$ ${\dot{ε}}_{0}$

Optional Line

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`fail_ID`

Definitions

Field	Contents	SI Unit Example
`mat_ID`	Material identifier. (Integer, maximum 10 digits)
`unit_ID`	Unit Identifier. (Integer, maximum 10 digits)
`a`	Hosford exponent. Default = 1.0 (Real)
`n`	Stress state sensitivity exponent. (Real)
`b`₀	Strain to fracture for uni-axial tension. 2 Default = 1.0 (Real)
`c`	Friction parameter for triaxiality. Default = 0.0 (Real)
$γ$ $γ$	Strain rate sensitivity parameter. (Real)
${\dot{ε}}_{0}$ ${\dot{ε}}_{0}$	Reference strain rate. Default = 10³⁰ (Real)	$[\frac{1}{s}]$ $[\frac{1}{s}]$
`fail_ID`	(Optional) Failure criteria identifier. 3 (Integer, maximum 10 digits)

Example (Metal)

Fracture parameters could be identified with tests like uniaxial tension ( $η = 1 / 3, θ = 1$ $η = 1 / 3, θ = 1$ ), pure shear ( $η = 0, θ = 0$ $η = 0, θ = 0$ ), and axisymmetric compression ( $η = 2 / 3, θ = - 1$ $η = 2 / 3, θ = - 1$ ).

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                 Mg                  mm                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW84/1/1
Swift-voce (metal)
#              RHO_I
                8E-9
#                  E                  NU
             206000.                0.30
#                P12                 P22                 P33               QVOCE               BVOCE
                -0.5                  1.                  3.            524.0000                 25.
#                G11                 G22                 G33                  K0               ALPHA
                -0.5                  1.                  3.                100.                 0.5
#                 AN                EPS0                  NN               CEPSP               DEPS0
               1000.             0.00128               0.200               0.014              0.0011
#                ETA                  CP                TINI                TREF               TMELT
                 0.9              420e+8                 293                293.               1700.
#              MTEMP              DEPSAD
               0.921               1.379
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FAIL/EMC/1/1
#         exponent_a          exponent_n              coef_b              coef_c
                 1.9                 0.2                0.20                 0.0
#               GAMA               DEPS0
                 0.0                 1.0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

The failure criteria is calculated as:(1)
$D_{f a i l} = \sum Δ D > 1$ $D_{f a i l} = \sum Δ D > 1$

Where,(2)
$Δ D = \frac{Δ {\bar{ε}}_{p}}{{\bar{ε}}_{p, f a i l}}$ $Δ D = \frac{Δ {\bar{ε}}_{p}}{{\bar{ε}}_{p, f a i l}}$

Where,(3)
${\bar{ε}}_{p, f a i l} = b \cdot {(1 + c)}^{\frac{1}{n}} \cdot {{[\frac{1}{2} ({(f_{1} - f_{2})}^{a} + {(f_{2} - f_{3})}^{a} + {(f_{1} - f_{3})}^{a})]}^{\frac{1}{a}} + c (2 η + f_{1} + f_{3})}^{- \frac{1}{n}}$ ${\bar{ε}}_{p, f a i l} = b \cdot {(1 + c)}^{\frac{1}{n}} \cdot {{[\frac{1}{2} ({(f_{1} - f_{2})}^{a} + {(f_{2} - f_{3})}^{a} + {(f_{1} - f_{3})}^{a})]}^{\frac{1}{a}} + c (2 η + f_{1} + f_{3})}^{- \frac{1}{n}}$

Where, $f_{1}$ $f_{1}$ , $f_{2}$ $f_{2}$ and $f_{3}$ $f_{3}$ are functions of the Lode angle $θ$ $θ$ :(4)
$f_{1} = \frac{2}{3} cos [\frac{π}{6} (1 - θ)]$ $f_{1} = \frac{2}{3} cos [\frac{π}{6} (1 - θ)]$
(5)
$f_{2} = \frac{2}{3} cos [\frac{π}{6} (3 + θ)]$ $f_{2} = \frac{2}{3} cos [\frac{π}{6} (3 + θ)]$
(6)
$f_{3} = - \frac{2}{3} cos [\frac{π}{6} (1 + θ)]$ $f_{3} = - \frac{2}{3} cos [\frac{π}{6} (1 + θ)]$

With(7)
$θ = 1 - \frac{2}{π} arccos [\frac{3 \sqrt{3}}{2} \frac{J_{3}}{{(J_{2})}^{3 / 2}}]$ $θ = 1 - \frac{2}{π} arccos [\frac{3 \sqrt{3}}{2} \frac{J_{3}}{{(J_{2})}^{3 / 2}}]$

Where, $η$ $η$ is the traixiality $η = \frac{σ_{m}}{σ_{V M}} = \frac{I_{1}}{3 \sqrt{3 J_{2}}}$ $η = \frac{σ_{m}}{σ_{V M}} = \frac{I_{1}}{3 \sqrt{3 J_{2}}}$ .
The coefficient, b is computed as:
$b = b_{0} [1 + γ \ln (\frac{{\dot{\bar{ε}}}_{p}}{{\dot{\bar{ε}}}_{0}})]$ $b = b_{0} [1 + γ \ln (\frac{{\dot{\bar{ε}}}_{p}}{{\dot{\bar{ε}}}_{0}})]$ if ${\dot{\bar{ε}}}_{p} > {\dot{\bar{ε}}}_{0}$ ${\dot{\bar{ε}}}_{p} > {\dot{\bar{ε}}}_{0}$ else $b = b_{0}$ $b = b_{0}$
The fail_ID is used with /STATE/BRICK/FAIL and /INIBRI/FAIL for brick. There is no default value. If the line is blank, no value will be output for failure model variables in the /INIBRI/FAIL (written in .sta file with /STATE/BRICK/FAIL for brick).