• Do not use tie MPCs (“General multi-point constraints,” Section 35.2.2) for the slave surface in a debonding contact pair. Abaqus is unable to resolve the overconstraint presented by the MPC and the debonded contact state. • You must have continuous master debonding surfaces. • You may be able to help the analysis converge by adding geometric nonlinearity (even if smallsliding is used for the debonding contact pair). For more information, see “Geometric nonlinearity” in “General and linear perturbation procedures,” Section 6.1.3. • For two-dimensional models with contact pairs involving higher-order underlying elements, the initially unbonded portion must extend over complete element faces. In other words, the crack tip in a two-dimensional, higher-order model must start at a corner node on the quadratic slave surfaces. The crack tip must not start at a midside node. • When the surface-to-surface contact formulation is used, at least two rows of elements should be used behind the crack front. # Tips for using the VCCT criterion in Abaqus/Explicit Crack propagation problems using the VCCT criterion analyzed in Abaqus/Explicit benefit from the robustness of the general contact algorithm in the context of an explicit time integrator. Nevertheless, as is the case in Abaqus/Standard, these analyses remain challenging given the discontinuous nature of the fracture phenomenon. The following tips will help you create a successful Abaqus/Explicit model: • Dynamic effects are of utmost relevance when assessing the results from a debonding analysis using the VCCT criterion. In most cases experimental and/or theoretical data are available in quasi-static settings. You must ensure that the Abaqus/Explicit analysis generates low ratios of kinetic energy to internal energy (1% or less). In practical terms this requirement often translates into avoiding the use of mass scaling in the model. Use smooth amplitudes to drive the loading to help reduce the kinetic energy in the model. Running the analysis over a longer period of time will not help in most cases because bond breakage is an inherently fast and localized process. • If appropriate, use damping-like behavior in the materials associated with the debonding plates to reduce dynamic vibrations. Unlike Abaqus/Standard, where a pure static equilibrium is achieved at the end of a converged increment, in Abaqus/Explicit the bond breakage at a given location is associated with a dynamic overshoot beyond the static equilibrium position. If the vibrations are significant (kinetic energy is clearly observable), the dynamic overshoot at nodes behind the crack tip may lead to premature debonding of the crack tip. • To maximize the accuracy of the debonding simulation, use quad meshes between the slave and master surfaces of the debonding surfaces. Avoid using elements with aspect ratios greater than 2. In most cases mesh refinement will help with obtaining a realistic result. • Highly mismatched critical energy values between modes tend to induce crack propagation in continuously changing directions in a manner that may be unstable and unrealistic, particularly for modes II and III. Do not use such values unless experimental data suggest so. • Use frequent field output requests to evaluate the debonding evolution as the analysis progresses. In some cases this can point to nontrivial modeling deficiencies that are difficult to identify from a simple data check analysis. • Avoid the use of other constraints involving nodes on both surfaces of the debonding interface because the cohesive contact forces will compete with the constraint forces to achieve global equilibrium. Bond breakage might be hard to interpret in these cases. # Comparing VCCT and cohesive elements Using VCCT to solve delamination problems is very similar to using cohesive elements in Abaqus. Table 11.4.3–2 describes the advantages and disadvantages of the two approaches. For an example of the use of cohesive elements, see “Delamination analysis of laminated composites,” Section 2.7.1 of the Abaqus Benchmarks Guide. This example also shows the effect of viscous regularization on the predicted force-displacement response. Table 11.4.3–2 Comparing VCCT and cohesive elements.

VCCT	Cohesive Elements
Simulation (mechanics)-driven crack propagation along a known crack surface.	Simulation (mechanics)-driven crack propagation along a known crack surface. However, cohesive elements can also be placed between element faces as a mechanism for allowing individual elements to separate.
Models brittle fracture using LEFM only.	Model brittle or ductile fracture for LEFM or EPFM. Very general interaction modeling capability is possible.
Uses a surface-based framework. Does not require additional elements.	Require definition of the connectivity and interconnectivity of cohesive elements with the rest of the structure. For accuracy, the mesh of cohesive elements may need to be smaller than the surrounding structural mesh and the associated “cohesive zone.” As a result, cohesive elements may be more expensive.
Requires a pre-existing flaw at the beginning of the crack surface. Cannot model crack initiation from a surface that is not already cracked.	Can model crack initiation from initially uncracked surfaces. The crack initiates when the cohesive traction stress exceeds a critical value.

VCCT	Cohesive Elements
Crack propagates when strain energy release rate exceeds fracture toughness.	Crack propagates according to cohesive damage model, usually calibrated so that the energy released when the crack is fully open equals the critical strain energy release rate.
Multiple crack fronts/surfaces can be included.	Multiple crack fronts/surfaces can be included.
In Abaqus/Standard crack surfaces are rigidly bonded when uncracked.	Crack surfaces are joined elastically when uncracked in Abaqus/Standard.
Requires user-specified fracture toughness of the bond.	Require user-specified critical traction value and fracture toughness of the bond, as well as elasticity of the bonded surface.

# Measuring the critical strain energy release properties for VCCT You must obtain the critical strain energy release properties of the bonded surfaces for VCCT. The procedure to obtain the critical strain energy release properties is beyond the scope of this guide; however, you can refer to the following ASTM test specifications for guidance: • ASTM D 5528-94a, “Standard Test Method for Mode I Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites” • ASTM D 6671-01, “Standard Test Method for Mixed Mode I-Mode II Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites” • ASTM D 6115-97, “Standard Test Method for Mode I Fatigue Delamination Growth Onset of Unidirectional Fiber-Reinforced Polymer Matrix Composites” These test specifications can be found in the Annual Book of ASTM Standards, American Society for Testing and Materials, vol. 15.03, 2000. # Initial conditions Initial contact conditions are used to identify which part of the slave surface is initially bonded, as explained earlier. # Boundary conditions Boundary conditions should not be applied to any of the nodes on the master or slave crack surfaces, but they can be used to load the structure and cause crack propagation. Boundary conditions can be applied to any of the displacement degrees of freedom in a crack propagation analysis (“Boundary conditions in Abaqus/Standard and Abaqus/Explicit,” Section 34.3.1). In a low-cycle fatigue analysis, prescribed boundary conditions must have an amplitude definition that is cyclic over the step: the start value must be equal to the end value (see “Amplitude curves,” Section 34.1.2). # Loads The following types of loading can be prescribed in a crack propagation analysis: • Concentrated nodal forces can be applied to the displacement degrees of freedom (1–6); see “Concentrated loads,” Section 34.4.2. • Distributed pressure forces or body forces can be applied; see “Distributed loads,” Section 34.4.3. The distributed load types available with particular elements are described in Part VI, “Elements.” For a low-cycle fatigue analysis each load must have an amplitude definition that is cyclic over the step: the start value must be equal to the end value (see “Amplitude curves,” Section 34.1.2). # Predefined fields The following predefined fields can be specified in a crack propagation analysis, as described in “Predefined fields,” Section 34.6.1: • Although temperature is not a degree of freedom in stress/displacement elements, nodal temperatures can be specified as predefined fields. The specified temperature affects temperature-dependent critical stress and crack opening displacement failure criteria, if specified. • The values of user-defined field variables can be specified. These values affect field-variabledependent critical stress and crack opening displacement failure criteria, if specified. The temperatures and user-defined field variables on slave and master surfaces are averaged to determine the critical stresses and crack opening displacements. In a low-cycle fatigue analysis, the temperature values specified must be cyclic over the step: the start value must be equal to the end value (see “Amplitude curves,” Section 34.1.2). 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 in Abaqus/Standard and Abaqus/Explicit,” Section 34.2.1). Alternatively, you can ramp the temperatures back to their initial condition values, as described in “Predefined fields,” Section 34.6.1. # Material options Any of the mechanical constitutive models in Abaqus/Standard can be used to model the mechanical behavior of the cracking material. See Part V, “Materials.” # Elements Regular, rectangular meshes give the best results in crack propagation analyses. Results with nonlinear materials are more sensitive to meshing than results with small-strain linear elasticity. First-order elements generally work best for crack propagation analysis. Line spring elements cannot be used in crack propagation analysis. The VCCT, enhanced VCCT, and low-cycle fatigue criteria not only support two-dimensional models (planar and axisymmetric) but also three-dimensional models with contact pairs involving first-order underlying elements (solids, shells, and continuum shells). In Abaqus/Standard use of the VCCT or enhanced VCCT criterion in two-dimensional models with contact pairs involving higher-order underlying elements is limited to crack fronts that are aligned with the corner nodes of the higher-order element faces. Use of the low-cycle fatigue criterion with contact pairs involving higher-order underlying elements is not supported. # Output Unless otherwise stated, the following discussions in this section are applied only to the critical stress, critical crack opening displacement, and crack length versus time criteria. At the start of an analysis Abaqus/Standard will scan the partially bonded surfaces and identify all of the crack tips that are present in the model. The initial contact status of all of the slave surface nodes is printed in the data (.dat) file. At this stage Abaqus/Standard will explicitly identify all the crack tips and mark them as crack 1, crack 2, etc. The slave and master surfaces that are associated with these cracks are also identified. The initial contact status of all of the slave surface nodes is also printed in the data (.dat) file for the VCCT, enhanced VCCT, and low-cycle fatigue criteria. # Printing crack propagation information to the data file By default, crack propagation information will be printed to the data file during the analysis. For each crack that is identified Abaqus/Standard will print out the initial and current crack-tip node numbers, accumulated incremental crack length (distance from the initial crack tip to the current crack tip, measured along the slave surface), and the current value of the user-specified fracture criterion used. Crack propagation information cannot be printed to the data file in Abaqus/Explicit. Input File Usage: \*DEBOND, SLAVE=slave, MASTER=master Abaqus/CAE Usage: Interaction module: Special→Crack→Create: Type: Debond using VCCT, Write output to DAT file every n increments For example, if the crack opening displacement criterion is used, the printed output during the analysis will appear as follows in the data file:

CRACK TIP LOCATION AND ASSOCIATED QUANTITIES
CRACK	SLAVE	MASTER	INITIAL	CURRENT	CUMULATIVE	CRITICAL
NUMBER	SURFACE	SURFACE	CRACKTIP	CRACKTIP	INCREMENTAL	COD
			NODE #	NODE #	LENGTH
$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$

# Writing crack propagation information to the results file In Abaqus/Standard you can choose to write the crack propagation information to the results (.fil) file. Input File Usage: \*DEBOND, SLAVE=slave, MASTER=master, OUTPUT=FILE Abaqus/CAE Usage: Writing crack propagation information to the results file is not supported in Abaqus/CAE. # Writing crack propagation information to both the data file and the results file In Abaqus/Standard you can write the crack propagation information to both the data and the results files. Input File Usage: \*DEBOND, SLAVE=slave, MASTER=master, OUTPUT=BOTH Abaqus/CAE Usage: Writing crack propagation information to both the data file and the results file is not supported in Abaqus/CAE. # Controlling the output frequency In Abaqus/Standard you can control the output frequency in increments. By default, the crack-tip location and associated quantities will be printed every increment. Specify an output frequency of 0 to suppress crack propagation output. Input File Usage: \*DEBOND, SLAVE=slave, MASTER=master, FREQUENCY=f Abaqus/CAE Usage: Interaction module: Special→Crack→Create: Type: Debond using VCCT, Write output to DAT file every n increments # Output variables The following bond failure quantities can be requested as surface output (see “Output to the data and results files,” Section 4.1.2; “Abaqus/Standard output variable identifiers,” Section 4.2.1; and “Abaqus/Explicit output variable identifiers,” Section 4.2.2) for all fracture criteria: DBT The time when bond failure occurred. For the VCCT, enhanced VCCT, and lowcycle fatigue criteria, this is the time when debonding initiates. DBSF Fraction of stress at bond failure that still remains. DBS All components of remaining stress in the failed bond. DBS1i 1i component of stress in the failed bond that remains ( ). For the VCCT, enhanced VCCT, and low-cycle fatigue criteria, the following additional variables can be also requested as surface output (see “Output to the data and results files,” Section 4.1.2): 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). OPENBC Relative displacement behind crack when the fracture criterion is met. CRSTS All components of critical stress at failure CRSTS1i 1i component of critical stress at failure ( ). ENRRT All components of strain energy release rate. ENRRT1i 1i component of strain energy release rate ( ). EFENRRTR Effective energy release rate ratio, $\frac { G _ { e q u i v } } { G _ { e q u i v C } }$ Gequiu GequiuC Surface output requests provide the usual output of contact variables in addition to the above quantities. The bond failure quantities must be requested explicitly; otherwise, only the default output for contact will be given. Abaqus/CAE provides support for the visualization of time-history plots and X–Y plots of the variables that are written to the output database. # Contour integrals Contour integrals can be requested for two-dimensional crack propagation analyses performed using the critical stress, critical crack opening displacement, or crack length versus time fracture criteria. If the contours are chosen so that the crack tip passes through the contour, the contour value will go to zero (as it should). Therefore, in crack propagation analysis contour integrals should be requested far enough from the crack tip that the crack tip does not pass through the contour, which is easily done by including all nodes along the bond surface in the crack-tip node set specified. See “Contour integral evaluation,” Section 11.4.2, for details on contour integral output. # Input file template Abaqus/Standard analysis ```c *HEADING ... *BOUNDARY Data lines to specify zero-valued boundary conditions *INITIAL CONDITIONS, TYPE=CONTACT (, NORMAL) Data lines to specify initial conditions *SURFACE, NAME=slave Data lines to define slave surface *SURFACE, NAME=master Data lines to define master surface ** *CONTACT PAIR slave, master ** *STEP (, NLGEOM) *STATIC or *VISCO or *COUPLED TEMPERATURE-DISPLACEMENT *DEBOND, SLAVE=slave, MASTER=master Data lines to define debonding amplitude curve *FRACTURE CRITERION, TYPE=type, DISTANCE or NSET Data lines to define fracture criterion *BOUNDARY Data lines to define zero-valued or nonzero boundary conditions *CLOAD and/or *DLOAD and/or *TEMPERATURE and/or *FIELD ``` Data lines to define loading ** *CONTOUR INTEGRAL, CONTOURS=n, TYPE=type **Contour integrals can be requested in a two-dimensional crack propagation analysis *CONTACT PRINT DBT, DBSF, DBS *EL PRINT JK, *END STEP ** *STEP *DIRECT CYCLIC, FATIGUE *DEBOND, SLAVE=slave, MASTER=master *FRACTURE CRITERION, TYPE=FATIGUE Data lines to define material constants used in Paris law and fracture criterion *BOUNDARY Data lines to define zero-valued or nonzero cyclic boundary conditions *CLOAD and/or *DLOAD and/or *TEMPERATURE and/or *FIELD Data lines to define cyclic loading ** *END STEP ** Abaqus/Explicit analysis *HEADING ... *BOUNDARY Data lines to specify zero-valued boundary conditions *SURFACE, NAME=slave Data lines to define slave surface *SURFACE, NAME=master Data lines to define master surface ** *CONTACT CLEARANCE, NAME=clearance_name, SEARCH NSET=initially_bonded_nodeset_name *SURFACE INTERACTION, NAME=interaction_name *COHESIVE BEHAVIOR Data lines to specify elastic behavior *FRACTURE CRITERION, TYPE=VCCT, MIXED MODE BEHAVIOR=BK ** *STEP *DYNAMIC, EXPLICIT \*CONTACT \*CONTACT CLEARANCE ASSIGNMENT Data lines to assign a clearance name to a surface pair \*CONTACT PROPERTY ASSIGNMENT Data lines to assign a surface interaction to a surface pair \*END STEP \*\* # Additional references • Benzeggagh, M., and M. Kenane, “Measurement of Mixed-Mode Delamination Fracture Toughness of Unidirectional Glass/Epoxy Composites with Mixed-Mode Bending Apparatus,” Composite Science and Technology, vol. 56, p. 439, 1996. • Reeder, J., S. Kyongchan, P. B. Chunchu, and D. R.. Ambur, “Postbuckling and Growth of Delaminations in Composite Plates Subjected to Axial Compression” 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Denver, Colorado, vol. 1746, p. 10, 2002. • Wu, E. M., and R. C. Reuter Jr., “Crack Extension in Fiberglass Reinforced Plastics,” T and M Report, University of Illinois, vol. 275, 1965.