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Table of Contents
Failure criterion
RuptureCriterion
Description
RuptureCriterion
manages various failure criteria. Two parameters are common in all laws. First, the critical value C of a variable above which the element is broken. Second, the type of failure : the element is broken if the criterion is verified on one integration point (ONEBROKEN
), on all of them (ALLBROKEN
), or in average (MEANBROKEN
) over the element.
Parameters
Name | Metafor Code | Dependency |
---|---|---|
Critical value | RUPT_CRIT_VALUE | - |
Type of failure | RUPT_TYPE_CRIT | - |
IFRuptureCriterion
Description
The element is broken if an InternalField
reaches a critical value. The critical InternalField
is defined with the following command, which must be added when defining the criterion:
rc.setInternalField(IF_EPL)
for a criterion based on a critical value of the equivalent plastic strain.
BaoRuptureCriterion
Description
Bao-Wierzbicki criterion [1]. The element is broken if the variable C, defined below, reaches a critical value:
$$ C = \int_0^{\varepsilon^{pl}}\dfrac{d\varepsilon^{pl}}{\varepsilon^{f}} $$
where $\varepsilon^{f}$ is defined as:
$$ \varepsilon^{f} = \left\{ \begin{array}{ll} \infty &\mbox{if } \dfrac{p}{J_2}\leq-\dfrac{1}{3}\\ P_1 \left(\dfrac{p}{J_2} + \dfrac{1}{3}\right)^{P_2} &\mbox{if } -\dfrac{1}{3}<\dfrac{p}{J_2}\leq 0\\ P_3 \left(\dfrac{p}{J_2}\right)^2 + P_4 \dfrac{p}{J_2} + P_5 &\mbox{if } 0<\dfrac{p}{J_2}<0.4\\ \exp\left(P_6\dfrac{p}{J_2}\right) &\mbox{if } \dfrac{p}{J_2}>0.4 \end{array} \right. $$
Parameters
Name | Metafor Code | Dependency |
---|---|---|
$P_1$ | RUPT_BAO_P1 | - |
$P_2$ | RUPT_BAO_P2 | - |
$P_3$ | RUPT_BAO_P3 | - |
$P_4$ | RUPT_BAO_P4 | - |
$P_5$ | RUPT_BAO_P5 | - |
$P_6$ | RUPT_BAO_P6 | - |
HancockMackenzieRuptureCriterion
Description
Hancock and Mackenzie criterion [2]. The critical plastic strain $\varepsilon^{f}$ is defined as:
$$ \varepsilon^{f} = D_1 + D_2 \exp\left(D_3\frac{p}{J_2}\right) $$
Parameters
Name | Metafor Code | Dependency |
---|---|---|
$D_1$ | RUPT_HANCOCK_D1 | - |
$D_2$ | RUPT_HANCOCK_D2 | - |
$D_3$ | RUPT_HANCOCK_D3 | - |
JohnsonCookRuptureCriterion
Description
Johnson and Cook criterion [3]. The element is broken if the variable C, defined below, reaches a critical value: $$ C = \int_0^{\varepsilon^{pl}}\dfrac{d\varepsilon^{pl}}{\varepsilon^{f}} $$
where $\varepsilon^{f}$ is defined as:
$$ \varepsilon^{f} = \left(D_1 + D_2 \exp\left(D_3\dfrac{p}{J_2}\right)\right) \left(1 + D_4\ln\dfrac{\dot\varepsilon^{pl}}{\dot\varepsilon_0}\right) \left(1 + D_5 \dfrac{T-T_{room}}{T_{melt}-T_{room}}\right) $$
Parameters
Name | Metafor Code | Dependency |
---|---|---|
$D_1$ | RUPT_JC_D1 | - |
$D_2$ | RUPT_JC_D2 | - |
$D_3$ | RUPT_JC_D3 | - |
$D_4$ | RUPT_JC_D4 | - |
$D_5$ | RUPT_JC_D5 | - |
$\dot\varepsilon_0$ | RUPT_JC_EPSP0 | - |
Room temperature $T_{room}$ | RUPT_JC_TROOM | - |
Melting temperature $T_{melt}$ | RUPT_JC_TMELT | - |
LemaitreRuptureCriterion
Description
The element is broken if the variable C, defined below, reaches a critical value:
$$ C = \int_0^{\varepsilon^{pl}}\left(\frac{2}{3}\left(1+\nu\right) + 3\left(1-2\nu\right)\left(\frac{p}{J_2}\right)^2\right)d\varepsilon^{pl} $$
Parameters
Name | Metafor Code | Dependency |
---|---|---|
$\nu$ | RUPT_LEMAITRE_NU | - |
GoijaertsRuptureCriterion
Description
The element is broken if W, whose evolution law is defined below, reaches 1.
$$ \dot W = \dfrac{1}{C} \left<1+A\dfrac{p}{J_2}\right> \left(\varepsilon^{pl}\right)^{B} \dot\varepsilon^{pl} $$
where brackets are MacCaulay brackets:
$$ \left<x\right> = \dfrac{1}{2} \left(x + \left|x\right|\right) $$
Parameters
Name | Metafor Code | Dependency |
---|---|---|
$A $ | RUPT_GOIJAERTS_A | - |
$B $ | RUPT_GOIJAERTS_B | - |
$C $ | RUPT_GOIJAERTS_C | - |
MaximumPrincipalStrainRuptureCriterion
Description
Element failure is detected differently whether the element is globally under tension of compression. It is broken if:
$ \| \epsilon_{I} \|> $ RUPT_MPSTRAIN_TL
if $ \epsilon_{I}\ $ + $ \epsilon_{II}\ $ + $ \epsilon_{III}\ $ > 0
$ \| \epsilon_{III}\| > $ RUPT_MPSTRAIN_CL
if $ \epsilon_{I}\ $ + $ \epsilon_{II}\ $ + $ \epsilon_{III}\ $ < 0
where $\epsilon_{I} $, $ \epsilon_{II} $ and $ \epsilon_{III} $ are principal strains in decreasing order.
Parameters
Name | Metafor Code | Dependency |
---|---|---|
$A $ | RUPT_MPSTRAIN_CL | - |
$B $ | RUPT_MPSTRAIN_TL | - |
References
[1] Bao Y, Wierzbicki T. On fracture locus in the equivalent strain and stress triaxiality space. International Journal of Mechanical Sciences 2004;46:81-98.
[2] Hancock JW, Mackenzie AC. On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states. Journal of the Mechanics and Physics of Solids 1976;24:147-160.
[3] Johnson GR, Cook WH. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: 7th International Symposium on Ballistics. The Hague: The Netherlands, 1983; 541-547.