4.21. Cohesive Material Law

Cohesive zone materials can be used with interface elements (INTERnnn) and contact elements (CONTAnnn), as described here:

Also see Element Support for Material Models and Material Model Support for Elements for this material model.

For more information about cohesive zone materials, see Cohesive Zone Material (CZM) Model in the Theory Reference and Subroutine userCZM (Creating Your Own Cohesive Zone Material) in the Programmer's Reference.

 

4.21.1. Exponential Cohesive Zone Material for Interface Elements and Contact Elements

Interface elements and contact elements allow exponential cohesive zone materials to be used for simulating interface delamination and other fracture phenomena. To define exponential material behavior, define the material data table (TB,CZM,,,,EXPO), then specify the following material constants (TBDATA):

Constant Meaning Property
C1σmax Maximum normal traction at the interface
C2δn Normal separation across the interface where the maximum normal traction is attained
C3δt Shear separation where the maximum shear traction is attained

To define a temperature-dependent material, issue TBTEMP as shown in this input example:

TB,CZM,1,2,,EXPO     ! Activate exponential material model
TBTEMP,100.0         ! Define first temperature
TBDATA,1,σmax,δn,δt   ! Define material constants at temp 100.0
TBTEMP,200.0         ! Define second temperature
TBDATA,1,σmax,δn,δt   ! Define material constants at temp 200.0
 

4.21.2. Bilinear Cohesive Zone Material for Interface Elements and Contact Elements

Interface elements and contact elements allow bilinear cohesive zone materials to be used for simulating interface delamination and other fracture phenomena. To define bilinear material behavior, define the material data table (TB,CZM,,,,BILI), then specify the following material constants (TBDATA):

Constant Meaning Property
C1σmax Maximum normal traction
C2 Normal displacement jump at the completion of debonding
C3τmax Maximum tangential traction
C4 Tangential displacement jump at the completion of debonding
C5 α Ratio of to , or ratio of to
C6[a]βNon-dimensional weighting parameter

[a] C6 must be the constant at all temperatures.

To define a temperature-dependent material, issue TBTEMP as shown in this input example:

TB,CZM,1,2,,BILI     ! Activate bilinear CZM material model
TBTEMP,100.0         ! Define first temperature
!    Define Mode I dominated material constants at temp 100.0:
!TBDATA,1,σmax,,-τmax,,α
!
TBTEMP,200.0         ! Define second temperature
!    Define Mode I dominated material constants at temp 200.0:
TBDATA,1,σmax,,-τmax,,α

Debonding Interface Modes

Three modes of interface debonding make up bilinear CZM law:

Case Input on the TBDATA command as follows:
Mode I Dominated C1, C2, C3, C4, C5 (where C3 = -τmax)
Mode II Dominated C1, C2, C3, C4, C5 (where C1 = -σmax)
Mixed-Mode C1, C2, C3, C4, C5, C6 (where C1 = σmax and C3 = τmax)
 

4.21.3. Exponential Cohesive Zone Material for Preventing Surface Penetration

To define exponential material behavior for preventing surface penetration in SMART crack-growth simulation, define the material data table (TB,CZM,,,,CEXP), then specify the following material constants (TBDATA):

ConstantMeaningProperty
C1σnMaterial constant with a value equivalent to the maximum normal traction at the interface in the standard EXPO model
C2δnMaterial constant with a value equivalent to the normal separation in the standard EXPO model

To define a temperature-dependent material, issue TBTEMP as shown in this input example:

TB,CZM,1,2,,CEXP     ! Activate exponential material model
TBTEMP,100.0         ! Define first temperature
TBDATA,1,σn,δn       ! Define material constants at temp 100.0
TBTEMP,200.0         ! Define second temperature
TBDATA,1,σn,δn       ! Define material constants at temp 200.0

For more information, see:

 

4.21.4. Rigid Exponential Cohesive Zone Material for Interface Elements

Interface elements enable rigid exponential cohesive zone materials to be used for simulating interface delamination and other fracture phenomena.

To define rigid exponential material behavior, define the material data table (TB,CZM,,,,REXP), then specify the following material constants (TBDATA):

Constant Meaning Property
C1σmax Maximum normal traction at the interface
C2δcn Normal separation across the interface where the maximum normal traction is attained
C3δct Shear separation where the maximum shear traction is attained

To define a temperature-dependent material, issue TBTEMP as shown in this input example:

TB,CZM,1,2,,EXPO        ! Activate exponential material model
TBTEMP,100.0            ! Define first temperature
TBDATA,1,σmax,δcn,δct   ! Define material constants at temp 100.0
TBTEMP,200.0            ! Define second temperature
TBDATA,1,σmax,δcn,δct   ! Define material constants at temp 200.0

For more information, see Material Model – Rigid Exponential Behavior in the Theory Reference.

 

4.21.5. Friction in Cohesive Zone Material for Interface Elements

Interface elements enable frictional cohesive zone materials to be used for simulating interface delamination and other fracture phenomena. To define friction behavior, define the material data table (TB,CZM,,,,FRIC), then specify the following material constants (TBDATA):

Constant Meaning Property
C1µCoefficient of friction for isotropic friction
C2bConstant cohesion
C3Kt Penalty stiffness for sticking
C4τmaxMaximum equivalent frictional stress τmax, where regardless of the magnitude of the contact pressure, sliding occurs if the magnitude of the equivalent frictional stress reaches this value.

To define a temperature-dependent material, issue TBTEMP as shown in this input example:

TB,CZM,1,2,,FRIC        ! Activate exponential material model
TBTEMP,100.0            ! Define first temperature
TBDATA,1, µ, b, Kt,τmax ! Define material constants at temp 100.0
TBTEMP,200.0            ! Define second temperature
TBDATA,1, µ, b, Kt,τmax ! Define material constants at temp 200.0

For more information, see Material Model – Frictional Behavior in the Theory Reference.

 

4.21.6. Linear Cohesive Zone Material for Preventing Surface Penetration

To define linear material behavior for preventing surface penetration in SMART crack-growth simulation, define the material data table (TB,CZM,,,,CLIN), then specify the following material constant (TBDATA):

ConstantMeaningProperty
C1KPenalty slope

To define a temperature-dependent material, issue TBTEMP as shown in this input example:

TB,CZM,1,2,,CLIN     ! Activate linear material model
TBTEMP,100.0         ! Define first temperature
TBDATA,1,K1          ! Define material constants at temp 100.0
TBTEMP,200.0         ! Define second temperature
TBDATA,1,K2          ! Define material constants at temp 200.0

For more information, see:

 

4.21.7. Viscous Regularization of Cohesive Zone Material for Interface Elements and Contact Elements

Interface elements and contact elements allow viscous regularization to be used for stabilizing interface delamination. Viscous regularization is valid with the exponential cohesive zone material model (TBOPT = EXPO) and the bilinear cohesive zone material model (TBOPT = BILI).

To define viscous regularization parameters, issue TB,CZM,,,,VREG, then specify the following material constant (TBDATA):

Constant Meaning Property
C1ζDamping coefficient

To define a temperature-dependent material, issue TBTEMP as shown in this input example:

TBTEMP,100.0      ! Define first temperature
TBDATA,1,c1       ! Define damping coefficient at temp 100.0
TBTEMP,200.0      ! Define second temperature
TBDATA,1,c1       ! Define damping coefficient at temp 200.0

For more information, see Viscous Regularization in the Mechanical APDL Theory Reference.

 

4.21.8. Cohesive Zone Material for Contact Elements

To model interface delamination, also known as debonding, the contact elements support an additional cohesive zone material model with bilinear behavior. This model allows two ways to specify material data.

Bilinear Material Behavior with Tractions and Separation Distances

To define bilinear material behavior with tractions and separation distances, issue the TB,CZM,,,,CBDD command, then specify the following material constants via the TBDATA command:

Constant Meaning Property
C1σmax Maximum normal contact stress[a]
C2 Contact gap at the completion of debonding
C3τmax Maximum equivalent tangential contact stress[a]
C4 Tangential slip at the completion of debonding
C5ηArtificial damping coefficient
C6 βFlag for tangential slip under compressive normal contact stress; must be 0 (off)  or 1 (on)
C7αPower law exponent for mixed-mode debonding (default = 2)

[a] For contact elements using the force-based model (see the description of KEYOPT(3) for CONTA175 and CONTA177), input a contact force value for this quantity.

To define a temperature-dependent material, issue TBTEMP as shown in this input example:

TB,CZM,1,2,,CBDD     ! Activate bilinear material model with tractions 
                     ! and separation distances
TBTEMP,100.0         ! Define first temperature
TBDATA,1,σmax, ,τmax, ,η,β     ! Define material constants at temp 100.0
TBDATA,7,α
TBTEMP,200.0                      ! Define second temperature
TBDATA,1,σmax, ,τmax, ,η,β     ! Define material constants at temp 200.0
TBDATA,7,α

Bilinear Material Behavior with Tractions and Critical Fracture Energies

Issue TB,CZM with TBOPT = CBDE to define bilinear material behavior with tractions and critical fracture energies, then specify the following material constants (TBDATA).

Constant Meaning Property
C1σmax Maximum normal contact stress[a]
C2Gcn Critical fracture energy density (energy/area) for normal separation[b]
C3τmax Maximum equivalent tangential contact stress[a]
C4Gct Critical fracture energy density (energy/area) for tangential slip[b]
C5ηArtificial damping coefficient
C6βFlag for tangential slip under compressive normal contact stress; must be 0 (off)  or 1 (on)
C7αPower law exponent for mixed-mode debonding (defaults to 2)

[a] For contact elements using the force-based model (KEYOPT(3)) for CONTA175 and CONTA177), input a contact force value for this quantity.

[b] For contact elements using the force-based model (KEYOPT(3)) for CONTA175 and CONTA177), this quantity is critical fracture energy.

To define a temperature-dependent material, issue TBTEMP as shown in this input example:

TB,CZM,1,2,,CBDE                  ! Activate bilinear material model with 
                                  ! tractions and facture energies 
TBTEMP,100.0                      ! Define first temperature
TBDATA,1,σmax,Gcn,τmax,Gct,η,β       ! Define material constants at temp 100.0
TBDATA,7,α
TBTEMP,200.0                      ! Define second temperature
TBDATA,1,σmax,Gcn,τmax,Gct,η,β       ! Define material constants at temp 200.0
TBDATA,7,α

Debonding Modes

Debonding involves separation of surfaces forming an interface. The direction of separation determines the debonding mode. The program detects the debonding mode based on material data that you input for normal and tangential directions:

  • Mode I debonding involves separation normal to the interface. It is activated by inputting data items C1, C2, and C5 on the TBDATA command.

  • Mode II debonding involves slip tangent to the interface. It is activated by inputting data items C3, C4, and C5 on the TBDATA command.

  • Mixed-mode debonding involves both normal separation and tangential slip. It is activated by inputting data items C1, C2, C3, C4, C5, C6, and C7 on the TBDATA command.

Debonding

When friction is defined between contact surfaces undergoing debonding, tangential stress is calculated as the maximum between the tangential stress as governed by the debonding model and the tangential stress as governed by the friction law.

 

4.21.9. Post-Debonding Behavior at the Contact Interface

When the cohesive zone material defined at a contact interface is completely debonded, the contact behavior at that interface is changed to standard contact (KEYOPT(12) = 0) by default. This default behavior can be changed for certain CZM materials.

For the cohesive zone materials with bilinear material behavior (TBOPT = CBDD, CBDE or BILI on the TB command), you can specify that the cohesive zone interface be “healed” if the surfaces come into contact again after debonding. To activate this option, use the TBFIELD,CYCLE command to define the CZM material as a function of healing cycle number. You can use multiple TBFIELD commands to specify the material properties for any number of healing cycles, but be sure to start with a cycle number of zero.

For example, the following commands specify healing of the CZM interface if the contact surfaces come into contact after they are completely debonded:

TB,CZM,1,,,CBDE                  ! Activate the CBDE bilinear material behavior
TBFIELD,CYCLE,0                  ! Initial CZM definition (before healing)
TBDATA,1,σmax,Gcn,τmax,Gct,η,β    ! CZM properties
TBFIELD,CYCLE,1                  ! CZM definition for first healing cycle
TBDATA,1, ...                    ! CZM properties to be used after first healing

When the contact interface is completely debonded and the surfaces come into contact again, the debonding parameter is set to 0 thus effectively healing the CZM. The healing cycle is incremented by one and the appropriate material data is interpolated for this healing cycle.

This healing option is only available when one of the supported cohesive zone materials is used with contact elements. It is not available when a cohesive zone material is used with interface elements.