Linear Elastic Fatigue Crack Growth Analysis

Define a Fatigue Crack Growth Analysis

The fatigue crack growth analysis capability in Abaqus/Standard is a quasi-static analysis on a structure subjected to subcritical cyclic loading. You can use the fatigue crack growth procedure to simulate two different classes of problems depending on the crack location.

At the brittle interface of laminated composites, the cyclic loading leads to interface strength degradation causing fatigue delamination growth. The onset and growth of delamination are characterized by the fracture energy release rate at the crack tip based on the Paris law (see Paris, 1961).

The other class of problems is for brittle bulk materials, in which the cyclic loading leads to material strength degradation causing fatigue crack growth along an arbitrary path. Such an approach is based on the principles of linear elastic fracture mechanics with the extended finite element method. The onset and growth of the crack are also characterized by the fracture energy release rate at the crack tip based on the Paris law (see Paris, 1961).

If both failure mechanisms (that is, discrete fatigue crack growth in the bulk brittle material and fatigue delamination growth at the brittle material interfaces) are considered within a single analysis, the most critical failure mechanism governs the actual fatigue crack growth and the damage in the region governed by the less critical failure mechanism is scaled proportionally. In the vicinity where fracture or debonding occurs, linear elastic deformation or the small scale yielding condition must be satisfied.

A fatigue crack growth analysis step can be the only step in an analysis, can follow a general or linear perturbation step, or can be followed by a general or linear perturbation step. Multiple fatigue crack growth analysis steps can be included in a single analysis. The fatigue crack growth procedure supports only constant amplitude loading—thermal, mechanical, or a combination of thermal and mechanical. You must specify the cyclic loading amplitude curves for a single loading cycle. Such a general formulation allows a wide range of loading histories such as contact or complex combinations of asynchronous loadings within a cyclic loading definition. For example, a mechanical pressure and a temperature with peaks/troughs in each can occur at different times within a single loading cycle.

The crack growth is governed by the Paris law:

\frac{d a}{d N} = c_{3} {Δ G}^{c_{4}},

where $c_{3}$ and $c_{4}$ are material constants.

For enriched elements, an equivalent form of the above Paris law based on the stress intensity factor is also available:

\frac{d a}{d N} = c_{3} {Δ K}^{c_{4}} .

Ratcliffe and Johnston (2014) and Deobald et al. (2017) proposed the following alternate form of the fatigue law which better accounts for mixed-mode fatigue crack growth:

\frac{d a}{d N} = c_{3} G_{T M a x}^{c_{4}} .

In the above expression, $G_{T M a x}$ is the total maximum strain energy release rate (as opposed to the strain energy release rate change over a cycle used in the original form of the Paris law), while $c_{3}$ and $c_{4},$ are material parameters that depend on mode mix and stress ratios. Abaqus does not support the above form of the crack growth rate equation directly, but instead allows specification of $d a / d N$ as a tabular function of $G_{T M a x}$ , the mode mix ratio, and the stress ratio.

The details of the usages of the different fatigue crack growth models are discussed in Fatigue Crack Growth Criterion for crack growth along initially partially bonded surfaces and in Fatigue Crack Growth Criterion Based on the Principles of LEFM for crack growth in enriched elements.

In addition, a user-defined fatigue crack growth law can be specified in user subroutine UMIXMODEFATIGUE.

You specify the maximum numbers of cycles, $N_{m a x}$ , when you define the fatigue crack growth analysis step.

Input File Usage

Use the following option to specify a general fatigue crack growth analysis with constant amplitude:

FATIGUE, TYPE=CONSTANT AMPLITUDE (default)
first data line
 ,  ,   $N_{m a x}$

Simplifying the Fatigue Crack Growth Analysis

The general fatigue crack growth analysis procedure described above can be simplified in some special cases if the following conditions are satisfied:

the peak or the trough value of the strain energy release rate, G, always occurs when the applied load, P, reaches its maximum or minimum value;
the strain energy release rate is proportional to the square of the applied load, P; and
the contact conditions remain unchanged during a single loading cycle.

For the simplified fatigue crack growth analysis, you can apply a constant load with a magnitude of $P_{\max} \sqrt{(1 - α^{2})}$ (for the fracture energy release rate–based Paris law) or $P_{\max} (1 - α)$ (for the stress intensity factor–based Paris law), where $α = P_{\min} {/ P}_{\max}$ , $P_{\max}$ is the maximum applied load and $P_{\min}$ is the minimum applied load over a single cycle. At least two increments are required for each single loading cycle period when the simplified method is used.

Input File Usage

Use the following option to apply a constant load to simplify the fatigue crack growth analysis:

FATIGUE, TYPE=SIMPLIFIED
first data line
 , ,  $N_{m a x}$

Controlling the Incrementation during the Cyclic Time Period

Several automatic incrementation methods are available. Alternatively, you can use fixed time incrementation.

Automatic Incrementation

If you specify only the maximum allowable nodal temperature change in an increment, the time increments are selected automatically based on this value. Abaqus/Standard restricts the time increments to ensure that the maximum temperature change is not exceeded at any node during any increment of the analysis.

For rate-dependent constitutive equations you can limit the size of the time increment by the accuracy of the integration. The user-specified accuracy tolerance parameter limits the maximum inelastic strain rate change allowed over an increment:

t o l e r a n c e \geq ({{\dot{\bar{ε}}}^{c r} |}_{t + Δ t} - {{\dot{\bar{ε}}}^{c r} |}_{t}) Δ t,

where

t: is the time at the beginning of the increment,
$Δ t$: is the time increment (so that $t + Δ t$ is the time at the end of the increment), and
${\dot{\bar{ε}}}^{c r}$: is the equivalent creep strain rate.

To achieve sufficient accuracy, the value chosen for the accuracy tolerance parameter should be on the order of $σ_{e r r} / E$ for creep problems (where $σ_{e r r}$ is an acceptable level of error in the stress and E is a typical elastic modulus) or on the order of the elastic strains for viscoelasticity problems.

If rate-dependent constitutive equations are used in combination with a varying temperature, both controls can be used simultaneously. Abaqus/Standard chooses the increments that satisfy both criteria.

If neither the accuracy tolerance parameter nor the maximum allowable nodal temperature change is specified, Abaqus/Standard selects increment sizes based on computational efficiency.

Input File Usage

Use the following option to indicate the time increment sizes based on computational efficiency:

FATIGUE

Use the following option to specify the maximum allowable nodal temperature change:

FATIGUE, DELTMX= $Δ θ_{m a x}$

Use the following option to specify the accuracy tolerance parameter:

FATIGUE, CETOL=tolerance

Fixed Time Incrementation

If fixed time incrementation is preferred, you must specify the time increment, $Δ t,$ and the time period, T.

Input File Usage

FATIGUE, DIRECT
 $Δ t$ , T

Defining the Time Points at Which the Response Must Be Evaluated

The user-defined time incrementation for a fatigue crack growth analysis step can be augmented or superseded by specifying particular time points in the loading history at which the response of the structure should be evaluated. This feature is particularly useful if you know prior to the analysis at which time points in the analysis the load reaches a maximum and/or minimum value or when the response will change rapidly. An example is the analysis of the heating/cooling thermal cycle of an engine component where you typically know when the temperature reaches a maximum value.

When time points are used with fixed time incrementation, the time incrementation specified for the fatigue crack growth step is ignored; instead, the time incrementation precisely follows the specified time points. If time points are used with automatic incrementation, the time incrementation is variable; however, the response of the structure is evaluated at the specified time points.

The time points can be listed individually, or they can be generated automatically by specifying the starting time point, ending time point, and increment in time between the two specified time points.

Input File Usage

Use the following options to list the time points individually:

TIME POINTS, NAME=time points name
FATIGUE, TIME POINTS=time points name

Use the following options to generate the time points automatically:

TIME POINTS, NAME=time points name, GENERATE
FATIGUE, TIME POINTS=time points name

Discrete Crack Propagation along an Arbitrary Path with the Extended Finite Element Method

Fatigue crack growth analysis in Abaqus/Standard allows the modeling of discrete crack growth along an arbitrary path based on the principles of linear elastic fracture mechanics with the extended finite element method. You complete the definition of the crack propagation capability by defining a fracture-based surface behavior and specifying the fracture criterion in enriched elements. The fracture energy release rates at the crack tips in enriched elements are calculated based on the modified virtual crack closure technique (VCCT). VCCT uses the principles of linear elastic fracture mechanics. Therefore, VCCT is appropriate for problems in which brittle fatigue crack growth occurs, although nonlinear material deformations can occur somewhere else in the bulk materials. For more information about defining fracture criteria and VCCT in enriched elements, see Modeling Discontinuities as an Enriched Feature Using the Extended Finite Element Method.

To accelerate the fatigue crack growth analysis, the damage extrapolation technique is used, which advances the crack by at least one element length after each completed cycle.

Onset and Growth of Fatigue Crack

The onset and growth of fatigue crack at an enriched element are characterized by using the Paris law, which relates the relative fracture energy release rate, $Δ G$ , to crack growth rates. Two criteria must be met to initiate fatigue crack growth:

one criterion is based on material constants, $Δ G$ , and the current cycle number, $N$ ;
the other criterion is based on the maximum fracture energy release rate, $G_{m a x}$ , which corresponds to the cyclic energy release rate when the structure is loaded up to its maximum value.

Once the onset of fatigue crack growth criterion is satisfied at the enriched elements, the crack growth rate,

\frac{d a}{d N}

, is a piecewise function based on a user-specified form of the Paris law. The criteria for fatigue crack onset and growth are discussed in detail in Fatigue Crack Growth Criterion Based on the Principles of LEFM. If you do not specify the onset criterion, Abaqus/Standard assumes that the onset of fatigue crack growth is satisfied automatically.

Damage Extrapolation Technique

If the onset of the crack growth criterion is satisfied at any crack tip in the enriched element at the end of a completed cycle, $N$ , Abaqus/Standard extends the crack length, $a_{N}$ , from the current cycle forward over a number of cycles, $Δ N$ , to $a_{N + Δ N}$ by fracturing at least one enriched element ahead of the crack tips. Given the particular fatigue crack growth form of the Paris law (as defined in Fatigue Crack Growth Criterion Based on the Principles of LEFM), combined with the known element length and likely propagation direction $Δ a_{N}_{j} = a_{N + Δ N} - a_{N}$ at the enriched elements ahead of the crack tips, the number of cycles necessary to fail each enriched element ahead of the crack tip can be calculated as $Δ N_{j}$ , where $j$ represents the enriched element ahead of the $j$ th crack tip. The analysis is set up to advance the crack by at least one enriched element per increment after the loading cycle is completed. The element with the fewest cycles is identified to be fractured, and its $Δ N_{m i n} = m i n (Δ N_{j})$ is represented as the number of cycles to grow the crack equal to its element length, $Δ a_{N}_{m i n} = m i n (Δ a_{N}_{j})$ . The most critical element is completely fractured with a zero constraint and a zero stiffness at the cracked surfaces at the end of the completed cycle. As the enriched element is fractured, the load is redistributed, and a new fracture energy release rate must be calculated for the enriched elements ahead of the crack tips for the next cycle. This capability allows at least one enriched element ahead of the crack tips to be fractured after each completed cycle and precisely accounts for the number of cycles needed to cause fatigue crack growth over that length.

Progressive Delamination Growth along a Predefined Path at Interfaces

Fatigue crack growth analysis in Abaqus/Standard also allows the modeling of progressive delamination growth at the interfaces in laminated composites. The interface along which the delamination (or crack) propagates must be indicated in the model using a fracture criterion definition. The fracture energy release rates at the crack tips in the interface elements are calculated based on the virtual crack closure technique (VCCT). VCCT uses the principles of linear elastic fracture mechanics. Therefore, VCCT is appropriate for problems in which brittle fatigue delamination growth occurs along predefined surfaces, although nonlinear material deformations can occur in the bulk materials. For more information about defining fracture criteria and VCCT, see Crack Propagation Analysis.

To accelerate the fatigue crack growth analysis, the damage extrapolation technique is used, which releases at least one element length at the crack tip along the interface after each completed cycle. When both brittle fatigue delamination at interfaces and discrete crack growth in bulk materials are considered in an analysis, failure occurs first at the weakest link.

Onset and Growth of Fatigue Delamination

The onset and growth of fatigue delamination at a defined crack interface are characterized by using the Paris law, which relates the relative fracture energy release rate, $Δ G$ , to crack growth rates. Two criteria must be met to initiate fatigue delamination growth:

one criterion is based on material constants, $Δ G$ , and the current cycle number, $N$ ;
the other criterion is based on the maximum fracture energy release rate, $G_{m a x}$ , which corresponds to the cyclic energy release rate when the structure is loaded up to its maximum value.

Once the onset of the delamination growth criterion is satisfied at the interface, the delamination growth rate,

\frac{d a}{d N}

, is a piecewise function based on a user-specified form of the Paris law. The criteria for fatigue delamination onset and growth are discussed in detail in Fatigue Crack Growth Criterion. If you do not specify the onset criterion, Abaqus/Standard assumes that the onset of fatigue crack growth is satisfied automatically.

Damage Extrapolation Technique at the Interface Elements

If the onset of delamination growth criterion is satisfied at any crack tip in the interface at the end of a completed cycle, $N$ , Abaqus/Standard extends the crack length, $a_{N}$ , from the current cycle forward over a number of cycles, $Δ N$ , to $a_{N + Δ N}$ by releasing at least one element at the interface. Given the particular fatigue crack growth form of the Paris law (as defined in Fatigue Crack Growth Criterion), combined with the known node spacing $Δ a_{N}_{j} = a_{N + Δ N} - a_{N}$ at the interface elements at the crack tips, the number of cycles necessary to fail each interface element at the crack tip can be calculated as $Δ N_{j}$ , where j represents the node at the jth crack tip. The analysis is set up to release at least one interface element per increment after the loading cycle is completed. The element with the fewest cycles is identified to be released, and its $Δ N_{m i n} = m i n (Δ N_{j})$ is represented as the number of cycles to grow the crack equal to its element length, $Δ a_{N}_{m i n} = m i n (Δ a_{N}_{j})$ . The most critical element is completely released with a zero constraint and a zero stiffness at the end of the completed cycle. As the interface element is released, the load is redistributed, and a new relative fracture energy release rate must be calculated for the interface elements at the crack tips for the next cycle. This capability allows at least one interface element at the crack tips to be released after each completed cycle and precisely accounts for the number of cycles needed to cause fatigue crack growth over that length.

Controlling Element Fracture

In the following discussion, the terms damage, fracture, and debonding are used in a generic sense to describe the process by which the internal forces at the crack-tip nodes are reduced to zero as they transition from an uncracked to a fully cracked state. At the end of each cycle, Abaqus utilizes the stress state at the nodes of the current crack front to determine the state of damage at each node. The following fundamental assumptions govern the fracture process:

The most critical element ahead of the current crack front undergoes complete damage.
The total cycle count increases by $Δ N_{m i n}$ , the number of cycles (based on the Paris law) needed to fracture the most critical element.
In addition to elements forecast to be fully or almost fully damaged after $Δ N_{m i n}$ cycles, additional elements are also allowed to partially fracture if they are within certain tolerances (described below) in the current cycle.

Allowing partial damage in some elements helps ensure a relatively smooth (that is, nonjagged) new crack front. The traction at a crack-tip node is either removed immediately upon fracture or ramped down gradually (see Specifying How a Debonding Force Is Released after a Fracture Criterion Is Met in Abaqus/Standard).

For the discussion that follows, it is convenient to introduce a damage variable that is defined in an “incremental” (defined in terms of cycle increments) framework as:

D_{N + Δ N} = D_{N} + Δ D,

with

Δ D = \frac{\frac{d a}{d N} Δ N_{\min}}{a_{N}},

where

$D_{N + Δ N}$ and $D_{N}$: are the scalar damage variables at the end of cycles $N + Δ N$ and $N$ , respectively, and
$a_{N}$: is the length of the element ahead of a current crack front node.

The value of $D$ varies between 0 (undamaged state) and 1 (fully damaged state), with intermediate values indicating partial damage at a crack-tip node. At the beginning of the analysis ( $N = 0$ ), the initial damage at each crack-tip node is $D_{0} = 0$ . At the end of the first completed cycle increment, $Δ N$ , the crack-tip node for the most critical element satisfies the condition $Δ D = 1$ , and, hence, is fully released.

For other crack-tip nodes, $0 \leq Δ D < 1$ , and these nodes are either undamaged or only partially damaged. The partial damage is governed by the damage variable, $D$ . Abaqus reduces the effective length of partially damaged elements as:

Δ a_{N}^{e f f} = (1 - D) Δ a_{N} .

The reduced effective length is used for the next crack growth calculations based on the Paris law.

Two criteria are available to control the partial fracture of the elements ahead of the current crack front:

A cycle-based criterion that is based on a tolerance value, $Δ D_{N t o l}$ .
A damage-based criterion that is based on a tolerance value, $Δ D_{D t o l}$ .

If neither tolerance is specified, the damage-based criterion, with a default $Δ D_{D t o l} = 0.25$ , is assumed to be in effect. If both tolerances are specified, the damage-based tolerance takes precedence. Using a damage-based tolerance allows you to choose the tolerance independent of the cycle increment size during the analysis.

In addition to satisfying one of the two criteria outlined above, crack front nodes are only fractured partially if such fracture helps ensure overall self-similar crack propagation, which is a fundamental assumption of the VCCT method. In other words, not all nodes that are eligible for partial fracture based on either the cycle-based or the damage-based criterion actually undergo partial fracture.

Cycle-Based Criterion for Partial Damage

For a cycle-based criterion, all elements ahead of the current crack front that satisfy the following criterion are eligible for partial fracture:

\frac{L o g Δ N_{j} - L o g Δ N_{m i n}}{L o g Δ N_{m i n}} \leq Δ D_{N t o l} .

A typical value of $Δ D_{N t o l}$ that provides a balance between accuracy and performance is 0.1.

Input File Usage

Use the following option to specify a cycle-based tolerance for determining the elements that are eligible for partial fracture:

FATIGUE
first data line
 ,   ,   ,  ,   $Δ D_{N t o l}$ ,

Damage-Based Criterion for Partial Damage

For a damage-based criterion, all elements ahead of the current crack front that satisfy the following criterion are eligible for partial fracture:

D_{N + Δ N} \geq 1 - Δ D_{D t o l} .

Thus, for the default choice of

Δ D_{D t o l} = 0.25

, all elements ahead of crack tip nodes where

D_{N + Δ N} \geq 0.75

are partially released.

Input File Usage

Use the following option to specify a damage-based tolerance for determining the elements that are eligible for partial fracture:

FATIGUE
first data line
 ,   ,   ,  ,  ,  $Δ D_{D t o l}$

Influence of Tolerance Parameters on Accuracy and Performance

If a small tolerance is specified, fewer elements along the crack front are eligible for fracture during any given cycle increment $Δ N$ . In this case, more cycle increments in total (with a smaller size for each cycle increment) are required to propagate an initial crack to its final allowable crack length. This approach results in a more accurate solution, although at a higher computational cost.

The opposite is true if a large tolerance is specified. In this case, more elements along the crack front are eligible for fracture during any given cycle increment. Therefore, fewer cycle increments in total (with a larger size for each cycle increment) are likely required to propagate an initial crack to its final allowable crack length. This approach might be computationally more efficient. However, the predicted total number of cycles taken to propagate an initial crack to its final allowable crack size might be less conservative. In addition, the use of a very large tolerance (for example, 0.95) might violate the self-similar crack growth assumption that is fundamental to the VCCT method, resulting in a jagged (not smoothing) crack front.

Figure 1 illustrates how the change of tolerance influences the predicted response of cycle number versus crack length in a mixed-mode fatigue crack growth analysis when compared to a benchmark solution (Krueger et al, 2020). Reducing the tolerance from 0.25 to 0.1 results in an almost identical response; however, the solution with a tolerance of 0.1 was computationally more expensive. For a larger tolerance, the predicted total number of cycles taken to propagate an initial crack to its final allowable crack length is somewhat nonconservative.

Initial Conditions

Initial values of stresses, temperatures, field variables, solution-dependent state variables, etc. can be specified (see Initial Conditions).

Boundary Conditions

Boundary conditions can be applied to any of the displacement or rotation degrees of freedom. During the analysis, prescribed boundary conditions in a general fatigue crack growth step must have an amplitude definition that is cyclic over the step: the start value must be equal to the end value (see Amplitude Curves). However, prescribed boundary conditions in a simplified fatigue crack growth analysis must have a constant value. If the analysis consists of several steps, the usual rules apply (see Boundary Conditions). At each new step, the boundary condition can either be modified or completely defined. All boundary conditions defined in previous steps remain unchanged unless they are redefined.

Loads

The following loads can be prescribed in a fatigue crack growth analysis step:

Concentrated nodal forces can be applied to the displacement degrees of freedom (1–6); see Concentrated Loads.
Distributed pressure forces or body forces can be applied; see Distributed Loads. The distributed load types available with particular elements are described in the Abaqus Elements Guide.

During the general fatigue crack growth analysis, each load must have an amplitude definition that is cyclic over the step where the start value must be equal to the end value (see Amplitude Curves). However, each load must have a constant value in a simplified fatigue crack growth analysis. If the analysis consists of several steps, the usual rules apply (see About Loads). At each new step, the loading can either be modified or completely defined. All loads defined in previous steps remain unchanged unless they are redefined.

Predefined Fields

The following predefined fields can be specified in a fatigue crack growth analysis step, as described in Predefined Fields:

Temperature is not a degree of freedom in a fatigue crack growth analysis step, but nodal temperatures can be specified as a predefined field. The temperature values specified in a general fatigue crack growth analysis must be cyclic over the step: the start value must be equal to the end value (see Amplitude Curves). If the temperatures are read from the results file, you should specify initial temperature conditions equal to the temperature values at the end of the step (see Initial Conditions). Alternatively, you can ramp the temperatures back to their initial condition values, as described in Predefined Fields. Any difference between the applied and initial temperatures causes thermal strain if a thermal expansion coefficient is given for the material (Thermal Expansion). The specified temperature also affects temperature-dependent material properties, if any. In a simplified fatigue crack growth analysis, the temperature values specified must be constant.
The values of user-defined field variables can be specified. These values affect only field-variable-dependent material properties, if any. The field variable values specified in a general fatigue crack growth analysis must be cyclic over the step. The field variable values must be constant in a simplified fatigue crack growth analysis step.

Material Options

Most material models that describe mechanical behavior are available for use in a fatigue crack growth analysis. The inelastic definition in a material point must be used in conjunction with the linear elastic material model (Linear Elastic Behavior), the porous elastic material model (Elastic Behavior of Porous Materials), or the hypoelastic material model (Hypoelastic Behavior).

The following material properties are not active during a fatigue crack growth analysis: acoustic properties, thermal properties (except for thermal expansion), mass diffusion properties, electrical conductivity properties, piezoelectric properties, and pore fluid flow properties.

Rate-dependent yield (Rate-Dependent Yield), rate-dependent creep (Rate-Dependent Plasticity: Creep and Swelling), and two-layer viscoplasticity (Two-Layer Viscoplasticity) can also be used during a fatigue crack growth analysis.

However, in the vicinity where fracture or debonding occurs, linear elastic deformation or the small scale yielding condition must be satisfied.

Elements

Any of the stress/displacement elements in Abaqus/Standard can be used in a fatigue crack growth analysis (see Choosing the Appropriate Element for an Analysis Type). However, when modeling fatigue crack growth based on the principles of linear elastic fracture mechanics with the extended finite element method, only first-order continuum stress/displacement elements and second-order stress/displacement tetrahedral elements can be associated with an enriched feature (see Modeling Discontinuities as an Enriched Feature Using the Extended Finite Element Method).

Output

In addition to the standard output identifiers available in Abaqus (Abaqus/Standard Output Variable Identifiers), whole element and surface variables are available.

The following whole element variables are available with the extended finite element method:

STATUSXFEM: Status of the enriched element. (The status of an enriched element is 1.0 if the element is completely cracked, 0.0 if the element is not. If the element is partially cracked, the value lies between 1.0 and 0.0.)
CYCLEINIXFEM: Number of cycles to initialize the crack at the enriched element.
CYCLEXFEM: Number of cycles to fracture at the enriched element.
ENRRTXFEM: All components of strain energy release rate.

The following additional surface output variables can be also requested along a predefined path at interfaces:

CSDMG: Overall value of the scalar damage variable.
BDSTAT: Bond state. The bond state varies between 1.0 (fully bonded) and 0.0 (fully unbonded).
CYCLE: Number of cycles to debond.
ENRRT: All components of strain energy release rate.
CRKLENGTH: Accumulated crack length. It is measured starting from the unbonded nodes immediately behind the initial crack front. As the crack tip nodes debond, the debonded element length is added to the accumulated crack length.

Limitations

The fatigue crack growth procedure supports only constant amplitude loading—thermal, mechanical, or a combination of thermal and mechanical. Several fatigue crack growth analysis steps can be used for an analysis with variable amplitude loading with each step having a constant amplitude loading.

Significant inaccuracy in fatigue prediction can occur if the fatigue procedure is used for cases that depart significantly from linear elastic response near a crack. See Low-Cycle Fatigue Analysis Using the Direct Cyclic Approach for discussion of simulation fatigue crack growth involving ductile materials.

Input File Template

The following is an example using the general fatigue crack growth analysis procedure:

HEADING
…
ENRICHMENT, TYPE=PROPAGATION CRACK, INTERACTION=INTERACTION,
ELSET=ENRICHED
BOUNDARY
Data lines to specify zero-valued boundary conditions
INITIAL CONDITIONS
Data lines to specify initial conditions
AMPLITUDE
Data lines to define amplitude variations
**
MATERIAL
Options to define material properties
SURFACE, INTERACTION=INTERACTION
SURFACE BEHAVIOR
FRACTURE CRITERION, TYPE=FATIGUE
Data lines to define material constants used in the Paris law and  fracture criterion in the bulk 
material for enriched elements
**
SURFACE, NAME=secondary
Data lines to define the secondary surface at the delamination interface
SURFACE, NAME=main
Data lines to define the main surface at the delamination interface
CONTACT PAIR
secondary, main
TIME POINTS, NAME=T1
**
STEP (,INC=)
Set  INC equal to the maximum number of increments in a single loading cycle
FATIGUE, TYPE=CONSTANT AMPLITUDE, TIME POINTS=T1
Data line to define time increment, cycle time, minimum time increment allowed, and maximum time increment allowed
Data line to define minimum increment in number of cycles, maximum increment in number of cycles, total number of cycles, , tolerance for the least number of cycles to fracture
DEBOND, SECONDARY=secondary, MAIN=main
FRACTURE CRITERION, TYPE=FATIGUE
Data lines to define material constants used in the Paris law and  fracture criterion at the interface
**
BOUNDARY, AMPLITUDE=
Data lines to prescribe zero-valued or nonzero boundary conditions
CLOAD and/or DLOAD, AMPLITUDE=
Data lines to specify loads
TEMPERATURE and/or FIELD, AMPLITUDE=
Data lines to specify values of predefined fields
**
END STEP

The following is an example using the simplified fatigue crack growth analysis procedure:

HEADING
…
ENRICHMENT, TYPE=PROPAGATION CRACK, INTERACTION=INTERACTION,
ELSET=ENRICHED
BOUNDARY
Data lines to specify zero-valued boundary conditions
INITIAL CONDITIONS
Data lines to specify initial conditions
AMPLITUDE
Data lines to define a constant load equal to  $P_{\max} \sqrt{(1 - α^{2})}$ 

**
MATERIAL
Options to define material properties
SURFACE, INTERACTION=INTERACTION
SURFACE BEHAVIOR
FRACTURE CRITERION, TYPE=FATIGUE
Data lines to define material constants used in the Paris law and  fracture criterion in the bulk 
material for enriched elements
**
SURFACE, NAME=secondary
Data lines to define the secondary surface at the delamination interface
SURFACE, NAME=main
Data lines to define the main surface at the delamination interface
CONTACT PAIR
secondary, main
TIME POINTS, NAME=T1
**
STEP (,INC=)
Set  INC equal to the maximum number of increments in a single loading cycle (at least two increments are required)
FATIGUE, TYPE=SIMPLIFIED, TIME POINTS=T1
Data line to define time increment, cycle time, minimum time increment allowed, and maximum time increment allowed
Data line to define minimum increment in number of cycles, maximum increment in number of cycles, total number of cycles, , tolerance for the least number of cycles to fracture
DEBOND, SECONDARY=secondary, MAIN=main
FRACTURE CRITERION, TYPE=FATIGUE
Data lines to define material constants used in the Paris law and  fracture criterion at the interface
**
BOUNDARY, AMPLITUDE=
Data lines to prescribe zero-valued or nonzero boundary conditions
CLOAD and/or DLOAD, AMPLITUDE=
Data lines to specify loads
TEMPERATURE and/or FIELD, AMPLITUDE=
Data lines to specify values of predefined fields
**
END STEP

References

Deobald, L., G. Mabson, S. Engelstad, M. Rao, M. Gurvich, W. Seneviratne, S. Perera, T. O'Brien, G. Murri, J. Ratcliffe, C. Davila, N. Carvalho , and R. Krueger, “Guidelines for VCCT-Based Interlaminar Fatigue and Progressive Failure Finite Element Analysis,” NASA/TM-2017-219663, 2017.
Krueger, R., L. Deobald, and H. Gu, “A Benchmark Example for Delamination Growth Predictions Based on the Single Leg Bending Specimen under Fatigue Loading,” Advanced Modeling and Simulation in Engineering Sciences, vol. 7, no. 11, 2020.
Paris, P., M. Gomaz , and W. Anderson, “A Rational Analytic Theory of Fatigue,” The Trend in Engineering, vol. 15, 1961.
Ratcliffe, J., and W. Johnston, “Influence of Mixed Mode I-Mode II Loading on Fatigue Delamination Growth Characteristics of a Graphite Epoxy Tape Laminate,” Proceedings of American Society for Composites 29th Technical Conference, 2014.