FRAC-L06-CohSurfs (2)

Surface-based Cohesive Behavior Lecture 6

L6.2

Overview • Surface-based Cohesive Behavior

• Element- vs. Surface-based Cohesive Behavior • Workshop 3 (Part 2)

Modeling Fracture and Failure with Abaqus

Surface-based Cohesive Behavior

L6.4

Surface-based Cohesive Behavior • Surface-based cohesive behavior provides a simplified way to model cohesive connections with negligibly small interface thicknesses using the traction-separation constitutive model.

• It can also model “sticky” contact (surfaces can bond after coming into contact). • The cohesive surface behavior can be defined for general contact in Abaqus/Explicit and contact pairs in Abaqus/Standard (with the exception of the finite-sliding, surface-to-surface formulation). • Cohesive surface behavior is defined as a surface interaction property. • To prevent overconstraints in Abaqus/Explicit, a pure master-slave formulation is enforced for surfaces with cohesive behavior.


L6.5

Surface-based Cohesive Behavior • User interface

Abaqus/CAE

Abaqus/Standard *SURFACE INTERACTION, NAME=cohesive *COHESIVE BEHAVIOR ... *CONTACT PAIR, INTERACTION=cohesive surface1, surface2

Abaqus/Explicit *SURFACE INTERACTION, NAME=cohesive *COHESIVE BEHAVIOR ... *CONTACT *CONTACT PROPERTY ASSIGNMENT surface1, surface2, cohesive


L6.6

Surface-based Cohesive Behavior • The formulae and laws that govern surface-based cohesive behavior are very similar to those used for cohesive elements with traction-separation behavior: traction • linear elastic traction-separation, • damage initiation criteria, and

GC

• damage evolution laws.

separation

• However, it is important to recognize that damage in surface-based cohesive behavior is an interaction property, not a material property. • Traction and separation are interpreted differently for cohesive elements and cohesive surfaces: Cohesive elements Relative displacement () between the top and bottom of the cohesive layer separation Nominal strain () = Initial thickness (To) traction Nominal stress ()

Cohesive surfaces

Contact separation () Contact stress (t) =


Contact force (F) Current area (A) at each contact point

L6.7

Surface-based Cohesive Behavior • Linear elastic traction-separation behavior

• Relates normal and shear stresses to the normal and shear separations across the interface before the initiation of damage. • By default, elastic properties are based on underlying element stiffness. • Can optionally specify the properties.

• Recall this specification is required for cohesive elements. • The traction-separation behavior can be uncoupled (default) or coupled.

*COHESIVE BEHAVIOR, TYPE= { UNCOUPLED, COUPLED} Optional data line to specify Knn, Kss, Ktt


L6.8

Surface-based Cohesive Behavior • Controlling the cohered nodes

• The slave nodes to which cohesive behavior is applied can be controlled to define a wider range of cohesive interactions: Can include: • All slave nodes • Only slave nodes initially in contact

• Initially bonded node set 1• Applying cohesive behavior to all slave nodes (default)

• Cohesive constraint forces potentially act on all nodes of the slave surface. • Slave nodes that are not initially contacting the master surface can also experience cohesive forces if they contact the master surface during the analysis. *COHESIVE BEHAVIOR, ELIGIBILITY = CURRENT CONTACTS


L6.9

Surface-based Cohesive Behavior 2 Applying cohesive behavior only to slave nodes initially in contact

• Restrict cohesive behavior to only those slave nodes that are in contact with the master surface at the start of a step. • Any new contact that occurs during the step will not experience cohesive constraint forces. • Only compressive contact is modeled for new contact.

*COHESIVE BEHAVIOR, ELIGIBILITY = ORIGINAL CONTACTS


L6.10

Surface-based Cohesive Behavior 3 Applying cohesive behavior only to an initially bonded node set

(Abaqus/Standard only) • Restrict cohesive behavior to a subset of slave nodes defined using *INITIAL CONDITIONS, TYPE=CONTACT. • All slave nodes outside of this set will experience only compressive contact forces during the analysis. • This method is particularly useful for modeling crack propagation along an existing fault line.

*COHESIVE BEHAVIOR, ELIGIBILITY = SPECIFIED CONTACTS


L6.11

Surface-based Cohesive Behavior • Example: Double cantilever beam (DCB)

• Analyze debonding of the DCB model using the surface-based cohesive behavior in Abaqus/Standard. • To model debonding using surface-based cohesive behavior, • you must define: 1• contact pairs and initially bonded crack surfaces;

2• the traction-separation behavior; 3• the damage initiation criterion; and 4• the damage evolution.

• You may also 5• specify viscous regularization to facilitate solution convergence u in Abaqus/Standard.

• Note: Steps 3, 4, and 5, will be covered later in this lecture.

-u Initial crack

Note: Only the Keywords interface is illustrated in the example; the Abaqus/CAE interface is illustrated in the workshop exercise. Modeling Fracture and Failure with Abaqus

Cohesive interface

L6.12

Surface-based Cohesive Behavior 1 • Define contact pairs and initially bonded crack surfaces

• The initially bonded portion of the slave surface (i.e., node set bond) is identified with the *INITIAL CONDITIONS, TYPE=CONTACT option.

bond

TopSurf

BotSurf

Note: Frictionless contact is assumed.

*NSET, NSET=bond, GENERATE 1, 121, 1 *SURFACE, NAME=TopSurf _TopBeam_S1, S1 *SURFACE, NAME=BotSurf _BotBeam_S1, S1 *CONTACT PAIR, INTER=cohesive TopSurf, BotSurf *INITIAL CONDITIONS, TYPE=CONTACT TopSurf, BotSurf, bond slave surface master surface


a list of slave nodes that are initially bonded

L6.13

Surface-based Cohesive Behavior 2• Define traction-separation behavior

• In this model, the cohesive behavior is only enforced for the node set bond. • Use the ELIGIBILITY=SPECIFIED CONTACTS parameter to enforce this behavior.

• Recall the default elastic properties are based on underlying element stiffness. Here we specify the properties. bond

TopSurf

BotSurf

t Kn (Ks , Kt)

1

 Kn, Ks, and Kt: normal and tangential stiffness components

... *CONTACT PAIR, INTER=cohesive TopSurf, BotSurf *INITIAL CONDITIONS, TYPE=CONTACT TopSurf, BotSurf, bond *SURFACE INTERACTION, NAME=cohesive *COHESIVE BEHAVIOR, ELIGIBILITY=SPECIFIED CONTACTS 5.7e14, 5.7e14, 5.7e14 Optional

Kn

Ks


Kt

L6.14

Surface-based Cohesive Behavior • Damage modeling for cohesive surfaces • Damage of the traction-separation response for cohesive surfaces is defined within the same general framework used for cohesive elements. • The difference between the two approaches is that for cohesive surfaces damage is specified as part of the contact interaction properties.

t



tnmax tsmax , ttmax





 nmax  smax ,  tmax





 nf  sf ,  t f





tnmax , tsmax , and ttmax : peak values of the contact stress

 nmax ,  smax , and tmax : peak values of the contact separation

 nf ,  sf , and  t f : separations at failure


L6.15

Surface-based Cohesive Behavior • User interface

Abaqus/CAE

Abaqus/Standard *SURFACE INTERACTION, NAME=cohesive *COHESIVE BEHAVIOR *DAMAGE INITIATION *DAMAGE EVOLUTION *CONTACT PAIR, INTERACTION=cohesive surface1, surface2

Abaqus/Explicit *SURFACE INTERACTION, NAME=cohesive *COHESIVE BEHAVIOR *DAMAGE INITIATION *DAMAGE EVOLUTION *CONTACT *CONTACT PROPERTY ASSIGNMENT surface1, surface2, cohesive


L6.16

Surface-based Cohesive Behavior • Damage initiation criteria Maximum stress criterion

Maximum separation criterion

 tn ts tt  MAX  max , max , max  1 ts tt   tn

  n s  t  MAX  max , max , max  1 s  t    n

*DAMAGE INITIATION, CRITERION=MAXS

*DAMAGE INITIATION, CRITERION=MAXU

tnmax , tsmax , ttmax

Quadratic stress criterion 2

2

2

 nmax ,  smax , tmax

Quadratic separation criterion 2

2

2

 tn   ts   tt   max    max    max   1  tn   ts   tt 

  n    s   t   max    max    max   1   n    s   t 

*DAMAGE INITIATION, CRITERION=QUADS

*DAMAGE INITIATION, CRITERION=QUADU

tnmax , tsmax , ttmax tn: normal contact stress in the pure normal mode ts: shear contact stress along the first shear direction tt: shear contact stress along the second shear direction

 nmax ,  smax , tmax

n: separation in the pure normal mode s: separation in the first shear direction t: separation in the second shear direction

Note: Recall the damage initiation criteria for the cohesive elements: if the initial constitutive thickness To = 1, then  = /To = . In this case, the separation measures for both approaches are exactly the same. Modeling Fracture and Failure with Abaqus

L6.17

Surface-based Cohesive Behavior • Example: Double cantilever beam 3• Define the damage initiation criterion

• The quadratic stress criterion is specified for this problem.

bond

TopSurf

BotSurf

... *CONTACT PAIR, INTER=cohesive TopSurf, BotSurf *INITIAL CONDITIONS, TYPE=CONTACT TopSurf, BotSurf, bond *SURFACE INTERACTION, NAME=cohesive *COHESIVE BEHAVIOR, ELIGIBILITY=SPECIFIED CONTACTS 5.7e14, 5.7e14, 5.7e14 *DAMAGE INITIATION, CRITERION=QUADS 5.7e7, 5.7e7, 5.7e7

tnmax

tsmax


ttmax

L6.18

Surface-based Cohesive Behavior • Damage evolution

• For surface-based cohesive behavior, damage evolution describes the degradation of the cohesive stiffness. • In contrast, for cohesive elements damage evolution describes the degradation of the material stiffness. • Damage evolution can be based on energy or separation (same as for cohesive elements). • Specify either the total fracture energy (a property of the cohesive interaction) or the post damage-initiation effective separation at t failure.

• May depend on mode mix



tnmax tsmax , ttmax



• Mode mix may be defined in terms of energy or traction

GTC









 nf  sf ,  t f





L6.19

Surface-based Cohesive Behavior • Separation-based damage evolution

• Damage is a function of an effective separation:



n

2

t



tnmax tsmax , ttmax

Linear postinitiation response



  s2   t2

• As with cohesive elements, the post damage-initiation softening response can be either: • Linear • Exponential • Tabular









 nf  sf ,  t f





L6.20

Surface-based Cohesive Behavior • Separation-based damage evolution (cont’d)

• Usage:

*DAMAGE EVOLUTION, TYPE = DISPLACEMENT, SOFTENING = { LINEAR | EXPONENTIAL | TABULAR }, MIXED MODE BEHAVIOR = TABULAR


L6.21

Surface-based Cohesive Behavior • Energy-based damage evolution

• As with cohesive elements, the energy-based damage evolution criterion can be defined as a function of mode mix using either a tabular form or one of two analytical forms: Power law 



Benzeggagh-Kenane (BK) 

 GI   GII   GIII        1  GIC   GIIC   GIIIC 



 Gshear  GIC   GIIC - GIC     GTC G  T  where Gshear  GII  GIII GT  GI  Gshear


L6.22

Surface-based Cohesive Behavior • Energy-based damage evolution (cont’d)

• Usage:

*DAMAGE EVOLUTION, TYPE = ENERGY, SOFTENING = { LINEAR | EXPONENTIAL}, MIXED MODE BEHAVIOR = { TABULAR | POWER LAW | BK }, POWER = value


L6.23

Surface-based Cohesive Behavior • Example: Double cantilever beam 4 • Define damage evolution

• The energy-based damage evolution based on the BK mixed mode behavior is specified.

GIC   GIIC



G  - GIC   shear   GTC  GT 

bond

TopSurf

BotSurf

... *CONTACT PAIR, INTER=cohesive TopSurf, BotSurf *INITIAL CONDITIONS, TYPE=CONTACT TopSurf, BotSurf, bond *SURFACE INTERACTION, NAME=cohesive *COHESIVE BEHAVIOR, ELIGIBILITY=SPECIFIED CONTACTS 5.7e14, 5.7e14, 5.7e14 *DAMAGE INITIATION, CRITERION=QUADS 5.7e7, 5.7e7, 5.7e7 *DAMAGE EVOLUTION, TYPE=ENERGY, MIXED MODE BEHAVIOR=BK, POWER=2.284 280.0, 280.0, 280.0



GIC

GIIC


GIIIC

L6.24

Surface-based Cohesive Behavior • Viscous regularization

• Can be specified to facilitate solution convergence in Abaqus/Standard for surface-based cohesive behavior when stiffness degradation occurs. • Output: • Energy associated with viscous regularization: ALLCD

*DAMAGE STABILIZATION


L6.25

Surface-based Cohesive Behavior • Example: Double cantilever beam 5 • Specify a viscosity coefficient for

the cohesive surface behavior

bond

TopSurf

BotSurf

... *CONTACT PAIR, INTER=cohesive TopSurf, BotSurf *INITIAL CONDITIONS, TYPE=CONTACT TopSurf, BotSurf, bond *SURFACE INTERACTION, NAME=cohesive *COHESIVE BEHAVIOR, ELIGIBILITY=SPECIFIED CONTACTS 5.7e14, 5.7e14, 5.7e14 *DAMAGE INITIATION, CRITERION=QUADS 5.7e7, 5.7e7, 5.7e7 *DAMAGE EVOLUTION, TYPE=ENERGY, MIXED MODE BEHAVIOR=BK, POWER=2.284 280.0, 280.0, 280.0 *DAMAGE STABILIZATION 1.e-5

viscosity coefficient,




L6.26

Surface-based Cohesive Behavior • Example: Double cantilever beam

• Summary of the input for the traction-separation response Cohesive elements *COHESIVE SECTION, MATERIAL=cohesive, RESPONSE=TRACTION SEPARATION, ELSET=coh_elems, CONTROLS=visco , 0.02 *MATERIAL, NAME=cohesive *ELASTIC, TYPE=TRACTION 5.7e14, 5.7e14, 5.7e14 *DAMAGE INITIATION, CRITERION=QUADS 5.7e7, 5.7e7, 5.7e7 *DAMAGE EVOLUTION, TYPE=ENERGY, MIXED MODE BEHAVIOR=BK, POWER=2.284 280.0, 280.0, 280.0 *SECTION CONTROLS, NAME=visco, VISCOSITY=1.e-5

Cohesive surfaces *SURFACE INTERACTION, NAME=cohesive *COHESIVE BEHAVIOR, ELIGIBILITY=SPECIFIED CONTACTS 5.7e14, 5.7e14, 5.7e14 *DAMAGE INITIATION, CRITERION=QUADS 5.7e7, 5.7e7, 5.7e7 *DAMAGE EVOLUTION, TYPE=ENERGY, MIXED MODE BEHAVIOR=BK, POWER=2.284 280.0, 280.0, 280.0 *DAMAGE STABILIZATION 1.e-5


L6.27

Surface-based Cohesive Behavior • Results

u2 = 0.006

Cohesive elements

Failed cohesive elements

u2 u2 = 0.006

Cohesive surfaces

u2


Element- vs. Surface-based Cohesive Behavior

L6.29

Element- vs. Surface-based Cohesive Behavior Preprocessing

• Cohesive elements • Gives you direct control over the cohesive element mesh density and stiffness properties. • Constraints are enforced at the element integration points. • Refining the cohesive elements relative to the connected structures will likely lead to improved constraint satisfaction and more accurate results.

• Cohesive surfaces

Integration points on an 8-node cohesive element

• Are easily defined using contact interactions and cohesive interaction properties. • A pure master-slave in formulation is used.

• Constraints are enforced at the slave nodes. • Refining the slave surface relative to the master surface will likely lead to improved constraint satisfaction and more accurate results .


L6.30

Element- vs. Surface-based Cohesive Behavior Initial configuration:

• Cohesive elements • Must be bonded at the start of the analysis.

• Once the interface has failed, the surfaces do not re-bond. • Cohesive surfaces

• Can bond anytime contact is established (i.e., “sticky” contact behavior). • Cohesive interface need not be bonded at the start of the analysis. • You can control whether debonded surfaces will stick or not stick if contact occurs again. • By default, they do not stick.


L6.31

Element- vs. Surface-based Cohesive Behavior Constitutive behavior:

• Cohesive elements • Allow for several constitutive behavior types:

• Traction-separation constitutive model • Including multiple failure mechanisms

• Continuum-based constitutive model • For adhesive layers with finite thickness • Uses conventional material models

• Uniaxial stress-based constitutive model • Useful in modeling gaskets and/or single adhesive patches

• Cohesive surfaces • Must use the traction-separation interface behavior. • Intended for bonded interfaces where the interface thickness is negligibly small.

• Only one failure mechanism is allowed. Modeling Fracture and Failure with Abaqus

L6.32

Element- vs. Surface-based Cohesive Behavior Influence on stable time increment (Abaqus/Explicit only):

• Cohesive elements

 Le  t    c d  

• Often require a small stable time increment.

• Cohesive elements are generally thin and sometimes quite stiff. • Consequently, they often have a stable time increment that is significantly less than that of the other elements in the model. • Cohesive surfaces • Cohesive surface behavior with the default cohesive stiffness properties is formulated to minimally affect the stable time increment. • Abaqus uses default contact penalties to model the cohesive stiffness behavior in this case. • You can specify a non-default cohesive stiffness values. • However, high stiffnesses may reduce the stable time increment.


L6.33

Element- vs. Surface-based Cohesive Behavior Mass:

• Cohesive elements • The element material definitions include mass.

• Cohesive surfaces • Do not add mass to the model.

• Indented for thin adhesive interfaces; thus, neglecting adhesive mass is appropriate for most applications. • However, nonstructural mass can be added to the contacting elements if necessary.


L6.34

Element- vs. Surface-based Cohesive Behavior Summary:

• Cohesive elements • Are recommended for more detailed adhesive connection modeling.

• Additional preprocessing effort (and often increased computational cost) is compensated for by gaining: • Direct control over the connection mesh • Additional constitutive response options • E.g., model adhesives of finite thickness

• Cohesive surfaces • Provides a quick and easy way to model adhesive connections. • Negligible interface thicknesses only • Surfaces can bond anytime contact is established (“sticky” contact) • Model contact adhesives, Velcro, tape, and other bonding agents that can stick after separation.


Workshop 3 (Part 2)

L6.36

Workshop 3 (Part 2) • Crack growth in a three-point bend specimen using surface-based cohesive behavior • Repeat the element-based exercise using surface-based behavior • Use default traction-separation elastic properties • Compare with element-based results


FRAC-L06-CohSurfs (2)

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