*FRACTURE CRITERION

Products Abaqus/Standard Abaqus/Explicit Abaqus/CAE

Type Model or history data in Abaqus/Standard; Model data in Abaqus/Explicit

LevelModel or Step in Abaqus/Standard; Model in Abaqus/Explicit

Abaqus/CAE Property module and Interaction module

Required parameters

DISTANCE

This parameter is required only if TYPE=COD or TYPE=CRITICAL STRESS is used.

If TYPE=CRITICAL STRESS, set this parameter equal to the distance along the potential crack surface ahead of the crack tip at which the critical stress criterion is evaluated.

If TYPE=COD, set this parameter equal to the distance behind the crack tip along the secondary surface at which the crack opening displacement is measured.

NSET

This parameter is required only if TYPE=CRACK LENGTH. Set this parameter equal to the name of the node set containing the nodes that are used to define the reference point.

TYPE

Set TYPE=CRITICAL STRESS to use the critical stress criterion at a distance ahead of the crack tip as the crack propagation criterion. This setting is available only in Abaqus/Standard.

Set TYPE=COD to use the critical value of the crack opening displacement at a distance behind the crack tip as the crack propagation criterion. This setting is available only in Abaqus/Standard.

Set TYPE=CRACK LENGTH to specify the crack length as a function of time. This setting is available only in Abaqus/Standard.

Set TYPE=ENHANCED VCCT to use the enhanced VCCT (Virtual Crack Closure Technique) criterion in which the onset and growth of a crack can be controlled by two different critical fracture energy release rates. This setting is available only in Abaqus/Standard.

Set TYPE=FATIGUE to indicate that the onset and fatigue crack growth are characterized by the relative fracture energy release rate or the relative stress intensity factor at the crack tip based on the Paris law. This setting is available only in Abaqus/Standard.

Set TYPE=VCCT to use the VCCT (Virtual Crack Closure Technique) criterion as the crack propagation criterion. The VCCT criterion uses the principles of linear elastic fracture mechanics.

Set TYPE=PRX-VCCT to use the PRX-VCCT (Progressive Release eXplicit - Virtual Crack Closure Technique) criterion as the crack propagation criterion.

Optional parameters

ANGLEMAX

This parameter is relevant only for TYPE=ENHANCED VCCT, TYPE=FATIGUE, or TYPE=VCCT in enriched elements.

Set this parameter equal to the maximum allowed change in the crack propagation angle (in degrees) between the new crack propagation direction and the previous crack propagation direction. The default is 85°.

DEPENDENCIES

This parameter is not relevant for TYPE=CRACK LENGTH.

Set this parameter equal to the number of field variable dependencies included in the data lines. If this parameter is omitted, it is assumed that the data are constant or depend only on temperature. See Material Data Definition for more information.

K-BASED

This parameter can be used only in conjunction with enriched elements with MIXED MODE BEHAVIOR=TABULAR or MIXED MODE BEHAVIOR=USER.

Include this parameter to specify a fatigue crack growth criterion based on a stress intensity factor rather than the fracture energy release rate.

LAMBDA

This parameter is relevant only for TYPE=PRX-VCCT.

Set this parameter equal to the maximum increment in damage that is allowed within each time increment. The default is LAMBDA=0.1.

MIXED MODE BEHAVIOR

This parameter is relevant only for TYPE=ENHANCED VCCT, TYPE=FATIGUE, or TYPE=VCCT.

Set MIXED MODE BEHAVIOR=BK to specify the fracture energy as a function of the mode mix by means of the Benzeggagh-Kenane mixed mode fracture criterion.

Set MIXED MODE BEHAVIOR=IRWIN to specify the effective stress intensity factor as a function of the mode mix by means of the Irwin mixed-mode fracture criterion. This option can be used only in conjunction with TYPE=FATIGUE in enriched elements.

Set MIXED MODE BEHAVIOR=POWER to specify the fracture energy as a function of the mode mix by means of a power law mixed mode fracture criterion.

Set MIXED MODE BEHAVIOR=REEDER to specify the fracture energy as a function of the mode mix by means of the REEDER mixed mode fracture criterion.

Set MIXED MODE BEHAVIOR=TABULAR to specify the crack growth criterion directly as a function of the total maximum fracture energy release rate, mode mix ratio, and stress ratio in a mixed-mode fatigue crack growth analysis. This option can be used only in conjunction with TYPE=FATIGUE.

Set MIXED MODE BEHAVIOR=USER to specify a user-defined crack growth criterion in a mixed-mode fatigue crack growth analysis using user subroutine UMIXMODEFATIGUE. This option can be used only in conjunction with TYPE=FATIGUE.

The default is MIXED MODE BEHAVIOR=BK.

NODAL ENERGY RATE

This parameter is relevant only for TYPE=FATIGUE or TYPE=VCCT.

Include this parameter to indicate that the critical energy release rates should not be read from the data lines but should be interpolated from the critical energy release rates specified at the nodes with the NODAL ENERGY RATE option. The exponents are still read from the data lines.

NORMAL DIRECTION

This parameter can be used only in conjunction with TYPE=ENHANCED VCCT, TYPE=FATIGUE, or TYPE=VCCT for enriched elements in Abaqus/Standard.

Set NORMAL DIRECTION=MTS (default) to specify that the crack will propagate orthogonal to the direction of the maximum tangential stress when the fracture criterion is satisfied.

Set NORMAL DIRECTION=1 to specify that the crack will propagate orthogonal to the element local 1-direction when the fracture criterion is satisfied.

Set NORMAL DIRECTION=2 to specify that the crack will propagate orthogonal to the element local 2-direction when the fracture criterion is satisfied.

NPOLY

This parameter can be used only in conjunction with POSITION=NONLOCAL in enriched elements or in predefined initially partially bonded surfaces in Abaqus/Standard. It is used to specify the number of terms in the polynomial used for the moving least-squares approximation.

Set NPOLY=4 to use a linear polynomial approximation.

Set NPOLY=7 (default) to use a quadratic polynomial approximation.

Set NPOLY=10 to use a cubic polynomial approximation.

NPOWER

This parameter is relevant only for TYPE=PRX-VCCT and defines the rate of crack growth.

Set this parameter equal to a positive integer. The default is NPOWER=10.

POSITION

This parameter is relevant for TYPE=ENHANCED VCCT, TYPE=FATIGUE, TYPE=PRX-VCCT, or TYPE=VCCT in predefined initially partially bonded surfaces in Abaqus/Standard or when NORMAL DIRECTION=MTS is specified in enriched elements.

In enriched elements, set POSITION=NONLOCAL to use a moving least-squares approximation by polynomials to smooth out the normals of the individual crack facets in elements that satisfy the fracture criterion to obtain the crack propagation direction along the crack front.

In predefined initially partially bonded surfaces, set POSITION=NONLOCAL to use a moving least-squares approximation by polynomials to smooth out the tangential directions of the individual crack segments along the crack front to obtain a smoother pseudocrack tangential direction. This direction is used for calculating energy release rates under mixed-mode loading.

PROPERTIES

This parameter can be used only in conjunction with MIXED MODE BEHAVIOR=USER.

Set this parameter equal to the number of material constants being specified for a user-defined crack growth criterion in a mixed-mode fatigue crack growth analysis. The parameter value must be a nonzero value.

R CRACK DIRECTION

This parameter can be used only in conjunction with POSITION=NONLOCAL in enriched elements or in predefined initially partially bonded surfaces.

In enriched elements, set this parameter equal to the radius around the crack tip within which the elements along the crack front are included for smoothing out the normals of the individual crack facets to obtain the crack propagation direction.

In predefined initially partially bonded surfaces, set this parameter equal to the radius around the crack tip within which the elements along the crack front are included for smoothing out the tangential directions of the individual crack segments along the crack front.

The default value is three times the typical element characteristic length along the crack front in the model.

SYMMETRY

Include this parameter to compare the opening between the secondary surface and the symmetry plane to half the COD value specified. The SYMMETRY parameter is relevant only for TYPE=COD when the user is using symmetry conditions to model the problem. In this case the NORMAL parameter must be specified on the INITIAL CONDITIONS option.

TOLERANCE

Set this parameter equal to the tolerance within which the crack propagation criterion must be satisfied. The default is TOLERANCE=0.1 for TYPE=CRITICAL STRESS, TYPE=COD, and TYPE=CRACK LENGTH; for TYPE=ENHANCED VCCT, TYPE=PRX-VCCT, and TYPE=VCCT, the default is TOLERANCE=0.2.

This parameter can also be used in a fatigue crack growth analysis (TYPE=FATIGUE) with gradual release of the debonding forces in debonding nodes when DEBONDING FORCE=RAMP is used on the DEBOND option. Set this parameter equal to the tolerance within which the scalar damage parameter reaches the value 1.0, resulting in the complete release of the debonding force. The default is 0.05.

UNSTABLE GROWTH TOLERANCE

Set this parameter equal to the tolerance within which the unstable crack propagation criterion must be satisfied for multiple nodes at and ahead of the crack tip to be allowed to debond without the cut back of increment size in one increment when the TYPE=PRX-VCCT or VCCT criterion is satisfied for an unstable crack problem.

If this parameter is included without a specified value, the default value is infinity.

VISCOSITY

This parameter applies only to Abaqus/Standard analyses and can be used only in combination with TYPE=ENHANCED VCCT or TYPE=VCCT.

Set this parameter equal to the value of the viscosity coefficient used in the viscous regularization. The default value is 0.0.

Data lines to define the critical stress criterion (TYPE=CRITICAL STRESS)

First line

Normal failure stress, $σ^{f}$ .
Shear failure stress, $τ_{1}^{f}$ .
Shear failure stress, $τ_{2}^{f}$ . (Not applicable in two dimensions.)
Temperature.
First field variable.
Second field variable.
Etc., up to four field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than four)

Fifth field variable.
Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the critical stress criterion as a function of temperature and/or field variables.

Data lines to define the crack opening displacement criterion (TYPE=COD)

First line

Critical crack opening displacement, $δ_{c}$ .
Cumulative crack length.
Temperature.
First field variable.
Second field variable.
Etc., up to five field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than five)

Sixth field variable.
Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the crack opening displacement criterion as a function of temperature and/or field variables.

Data lines to define the crack length versus time criterion (TYPE=CRACK LENGTH)

First line

Total time (not step time).
Crack length, l, from the reference point.
Etc., up to four time/length pairs per line. Crack length must be given as an increasing function of time.

Repeat this data line as often as necessary to define the crack length as a function of time.

Data lines to define the onset and growth of a crack for the enhanced VCCT criterion (TYPE=ENHANCED VCCT) for MIXED MODE BEHAVIOR=BK or REEDER

First line

Mode I critical energy release rate for onset of a crack, $G_{I C}$ .
Mode II critical energy release rate for onset of a crack, $G_{I I C}$ .
Mode III critical energy release rate for onset of a crack, $G_{I I I C}$ .
Mode I critical energy release rate for crack propagation, $G_{I C}^{P}$ .
Mode II critical energy release rate for crack propagation, $G_{I I C}^{P}$ .
Mode III critical energy release rate for crack propagation, $G_{I I I C}^{P}$ .
Exponent, $η$ .
Temperature.

Subsequent lines (only needed if the DEPENDENCIES parameter has a nonzero value)

First field variable.
Second field variable.
Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the critical energy rates and exponent as a function of temperature and field variables.

Data lines to define the onset and growth of a crack for the enhanced VCCT criterion (TYPE=ENHANCED VCCT) for MIXED MODE BEHAVIOR=POWER

First line

Mode I critical energy release rate for onset of a crack, $G_{I C}$ .
Mode II critical energy release rate for onset of a crack, $G_{I I C}$ .
Mode III critical energy release rate for onset of a crack, $G_{I I I C}$ .
Mode I critical energy release rate for crack propagation, $G_{I C}^{P}$ .
Mode II critical energy release rate for crack propagation, $G_{I I C}^{P}$ .
Mode III critical energy release rate for crack propagation, $G_{I I I C}^{P}$ .
Exponent, $a_{m}$ .
Exponent, $a_{n}$ .

Second line

Exponent, $a_{o}$ .
Temperature.
First field variable.
Second field variable.
Etc., up to six field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than six)

Seventh field variable.
Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the critical energy rates and exponents as a function of temperature and field variables.

Data lines to define the low-cycle fatigue onset and crack growth criterion (TYPE=FATIGUE) for MIXED MODE BEHAVIOR=BK or REEDER

First line

Material constant for fatigue crack initiation, $c_{1}$ .
Material constant for fatigue crack initiation, $c_{2}$ .
Material constant for fatigue crack growth, $c_{3}$ .
Material constant for fatigue crack growth, $c_{4}$ .
Ratio of energy release rate threshold used in the Paris law over the equivalent critical energy release rate, $\frac{G_{t h r e s h}}{G_{C}}$ .
Ratio of energy release rate upper limit used in the Paris law over the equivalent critical energy release rate, $\frac{G_{p l}}{G_{C}}$ .
Mode I critical energy release rate, $G_{I C}$ .
Mode II critical energy release rate, $G_{I I C}$ .

Second line

Mode III critical energy release rate, $G_{I I I C}$ .
Exponent, $η$ .
Temperature.
First field variable.
Second field variable.
Etc. up to five field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than five)

Sixth field variable.
Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the constants used in the Paris law, critical energy rates, and exponents as a function of temperature and field variables.

Data lines to define the low-cycle fatigue onset and crack growth criterion (TYPE=FATIGUE) for MIXED MODE BEHAVIOR=POWER

First line

Material constant for fatigue crack initiation, $c_{1}$ .
Material constant for fatigue crack initiation, $c_{2}$ .
Material constant for fatigue crack growth, $c_{3}$ .
Material constant for fatigue crack growth, $c_{4}$ .
Ratio of energy release rate threshold used in the Paris law over the equivalent critical energy release rate, $\frac{G_{t h r e s h}}{G_{C}}$ .
Ratio of energy release rate upper limit used in the Paris law over the equivalent critical energy release rate, $\frac{G_{p l}}{G_{C}}$ .
Mode I critical energy release rate, $G_{I C}$ .
Mode II critical energy release rate, $G_{I I C}$ .

Second line

Mode III critical energy release rate, $G_{I I I C}$ .
Exponent, $a_{m}$ .
Exponent, $a_{n}$ .
Exponent, $a_{o}$ .
Temperature.
First field variable.
Second field variable.
Third field variable.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than three)

Fourth field variable.
Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the constants used in the Paris law, the critical energy rates, and exponents as a function of temperature and field variables.

Data lines to define fatigue crack growth criterion (TYPE=FATIGUE) for MIXED MODE BEHAVIOR=IRWIN

First line

Material constant, $c_{3}$ , for fatigue crack growth based on $\frac{d a}{d N} = c_{3} Δ K_{e f f}^{c_{4}}$ .
Material constant, $c_{4}$ , for fatigue crack growth based on $\frac{d a}{d N} = c_{3} Δ K_{e f f}^{c_{4}}$ .
Ratio of equivalent stress intensity factor threshold used in the Paris law over the equivalent critical stress intensity factor, $\frac{K_{t h r e s h}}{K_{C}}$ . The default is 0.01.
Ratio of equivalent stress intensity factor upper limit used in the Paris law over the equivalent critical stress intensity factor, $\frac{K_{p l}}{K_{C}}$ . The default is 0.85.
Equivalent critical stress intensity factor, $K_{C}$ .
Constant coefficient, $A$ , defined in $Δ K_{e f f} = \sqrt{A \times Δ K_{I}^{2} + B \times Δ K_{I I}^{2} + C \times \frac{1}{1 - ν} Δ K_{I I I}^{2}}$ .
Constant coefficient, $B$ , defined in $Δ K_{e f f} = \sqrt{A \times Δ K_{I}^{2} + B \times Δ K_{I I}^{2} + C \times \frac{1}{1 - ν} Δ K_{I I I}^{2}}$ .
Constant coefficient, $C$ , defined in $Δ K_{e f f} = \sqrt{A \times Δ K_{I}^{2} + B \times Δ K_{I I}^{2} + C \times \frac{1}{1 - ν} Δ K_{I I I}^{2}}$ .

Second line (leave blank if no temperature or field variables are specified)

Temperature.
First field variable.
Second field variable.
Etc., up to seven field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than seven)

Eighth field variable.
Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the constants used in the Paris law and the critical stress intensity factor as a function of temperature and field variables.

Data lines to define fatigue crack growth criterion (TYPE=FATIGUE) for MIXED MODE BEHAVIOR=TABULAR

First line

Crack growth rate, $\frac{d a}{d N}$ in log scale.
Total maximum energy release rate, $G_{T M a x}$ in log scale.
Mode mix ratio, $\frac{G_{I I M a x} + G_{I I I M a x}}{G_{T M a x}}$ .
Local stress ratio, $\frac{G_{T M i n}}{G_{T M a x}}$ .
Temperature.
First field variable.
Second field variable.
Third field variable.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than three)

Fourth field variable.
Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the crack growth rates as a function of energy release rate, mode mix ratio, local stress ratio, temperature, and field variables.

Data lines to define fatigue crack growth criterion (TYPE=FATIGUE) for MIXED MODE BEHAVIOR=TABULAR, K-BASED

First line

Constant coefficient, $A$ , defined in $Δ K_{e f f} = \sqrt{A \times Δ K_{I}^{2} + B \times Δ K_{I I}^{2} + C \times \frac{1}{1 - ν} Δ K_{I I I}^{2}}$ .
Constant coefficient, $B$ , defined in $Δ K_{e f f} = \sqrt{A \times Δ K_{I}^{2} + B \times Δ K_{I I}^{2} + C \times \frac{1}{1 - ν} Δ K_{I I I}^{2}}$ .
Constant coefficient, $C$ , defined in $Δ K_{e f f} = \sqrt{A \times Δ K_{I}^{2} + B \times Δ K_{I I}^{2} + C \times \frac{1}{1 - ν} Δ K_{I I I}^{2}}$ .

Second line

Crack growth rate, $\frac{d a}{d N}$ , in log scale.
Effective stress intensity factor range of a load cycle, $Δ K_{e f f} = \sqrt{A \times Δ K_{I}^{2} + B \times Δ K_{I I}^{2} + C \times \frac{1}{1 - ν} Δ K_{I I I}^{2}}$ , in log scale.
Mode mix ratio, $\frac{\sqrt{B \times K_{I I M a x}^{2} + C \times \frac{1}{1 - ν} K_{I I I M a x}^{2}}}{\sqrt{A \times K_{I M a x}^{2} + B \times K_{I I M a x}^{2} + C \times \frac{1}{1 - ν} K_{I I I M a x}^{2}}}$ .
Local stress ratio, $\frac{\sqrt{A \times K_{I M i n}^{2} + B \times K_{I I M i n}^{2} + C \times \frac{1}{1 - ν} K_{I I I M i n}^{2}}}{\sqrt{A \times K_{I M a x}^{2} + B \times K_{I I M a x}^{2} + C \times \frac{1}{1 - ν} K_{I I I M a x}^{2}}}$ .
Temperature.
First field variable.
Second field variable.
Third field variable.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than three)

Fourth field variable.
Etc., up to eight field variables per line.

Repeat this set of data lines (exclude the first line) as often as necessary to define the crack growth rates as a function of the effective stress intensity factor range, mode mix ratio, local stress ratio, temperature, and field variables.

Data lines to define fatigue crack growth criterion (TYPE=FATIGUE) for MIXED MODE BEHAVIOR=USER

First line

Give the material constants, eight per line.

Repeat this data line as often as necessary to define all material constants.

Data lines to define the VCCT criterion (TYPE=VCCT) or PRX-VCCT criterion (TYPE=PRX-VCCT) for MIXED MODE BEHAVIOR=BK or REEDER

First line

Mode I critical energy release rate, $G_{I C}$ .
Mode II critical energy release rate, $G_{I I C}$ .
Mode III critical energy release rate, $G_{I I I C}$ .
Exponent, $η$ .
Temperature.
First field variable.
Second field variable.
Third field variable.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than three)

Fourth field variable.
Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the critical energy rates and exponent as a function of temperature and field variables.

Data lines to define the VCCT criterion (TYPE=VCCT) or PRX-VCCT criterion (TYPE=PRX-VCCT) for MIXED MODE BEHAVIOR=POWER

First line

Mode I critical energy release rate, $G_{I C}$ .
Mode II critical energy release rate, $G_{I I C}$ .
Mode III critical energy release rate, $G_{I I I C}$ .
Exponent, $a_{m}$ .
Exponent, $a_{n}$ .
Exponent, $a_{o}$ .
Temperature.
First field variable.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than one)

Second field variable.
Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the critical energy rates and exponents as a function of temperature and field variables.