ABAQUS粘接单元应用课件

Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Click to edit Master title style,L10.,79,Analysis of Composite Materials with Abaqus,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Click to edit Master title style,L10.,23,Analysis of Composite Materials with Abaqus,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Click to edit Master title style,Analysis of Composite Materials with Abaqus,L10.,*,Cohesive Behavior,Lecture 10,Overview,Introduction,Cohesive Element Technology,Constitutive Response in Cohesive Elements,Viscous Regularization for Cohesive Elements,Cohesive Element Examples,Surface-based Cohesive Behavior,Element- vs. Surface-based Cohesive Behavior,Note: Appendix 2 contains an in-depth discussion of modeling techniques for cohesive elements using both the interactive and keywords interfaces.,Introduction,Introduction,Cohesive behavior is useful in modeling adhesives, bonded interfaces, and gaskets.,Models separation between two initially bonded surfaces,Progressive failure of adhesives,Delamination in composites,Idealize complex fracture mechanisms with a macroscopic “cohesive law,” which relates the traction across the interface to the separation.,The cohesive behavior can be:,Element-based,Modeled with cohesive elements,Surface-based,Modeled with contact pairs in Abaqus/Standard and general contact in Abaqus/Explicit,Rail crush: Cohesive surfaces,Failed adhesive is red,(CSDMG = 1),T-peel analysis: Cohesive elements are used for modeling adhesive patches,Introduction,Element-based cohesive behavior,cohesive elements,Cohesive elements allow very detailed modeling of adhesive connections, including,specification of detailed adhesive material properties, direct control of the connection mesh, modeling of adhesives of finite thickness, etc.,Cohesive elements in Abaqus primarily address two classes of problems:,Adhesive joints,Adhesive layer with finite thickness,Typically the bulk material properties are known,Delamination,Adhesive layer of “zero” thickness,Typically the bulk material properties are not known,Introduction,The constitutive modeling depends on the class of problem:,Based on macroscopic properties (stiffness, strength) for adhesive joints,Continuum description: any Abaqus material model can be used,Modeling technique is relatively straightforward: cohesive layer has finite thickness; standard material models (including damage).,The continuum description is not discussed further in this lecture.,Based on a traction-separation description for delamination,Linear elasticity with damage,Modeling technique is less straightforward: typical applications use zero-thickness cohesive elements; non-standard constitutive law,This application is the primary focus of this lecture,Introduction,Surface-based cohesive behavior,cohesive surfaces,This is a simplified and easy way to model cohesive connections, using the traction-separation interface behavior.,It offers capabilities that are very similar to cohesive elements modeled with the traction-separation constitutive response.,However, it does not require element definitions.,In addition, cohesive surfaces can bond anytime contact is established (“sticky” contact),It is primarily intended for situations in which interface thickness is negligibly small.,It must be defined as a surface interaction property.,Damage for cohesive surfaces is an interaction property, not a material property.,The kinematics of cohesive surfaces is different from that of cohesive elements.,By default, the initial stiffness of the interface is computed automatically.,Cohesive Element Technology,Cohesive Element Technology,Element types*,3D elements,COH3D8,COH3D6,2D element,COH2D4,Axisymmetric element,COHAX4,These elements can be embedded in a model via,shared nodes or,tie constraints.,Bottom face,Top face,*Cohesive pore pressure elements are also available.,Cohesive Element Technology,Element and section definition,*ELEMENT, TYPE =,COH3D8,*,COHESIVE SECTION, ELSET =.,RESPONSE,= ,TRACTION SEPARATION,CONTINUUM,GASKET,THICKNESS,= ,SPECIFIED,GEOMETRY,MATERIAL = .,Specify thickness in dataline,(default is 1.0),Cohesive Element Technology,Default thickness of cohesive elements,Traction-separation response:,Unit thickness,Continuum and gasket response,Geometric thickness based on nodal coordinates,Cohesive Element Technology,Output variables,Scalar damage (i.e., degradation) variable,SDEG,Variables indicating whether damage initiation criteria met or exceeded,Discussed shortly,Element status flag,STATUS,Cohesive Element Technology,Import of cohesive elements,The combination of Abaqus/Standard and Abaqus/Explicit expands the range of applications for cohesive elements.,For example, you can simulate the damage in a structure due to an impact event then study the effect of the damage on the structures load carrying capacity.,Constitutive Response in Cohesive Elements,Constitutive Response in Cohesive Elements,Delamination applications,Traction separation law,Typically characterized by peak strength (,N,) and fracture energy (,G,TC,),Mode dependent,Linear elasticity with damage,Available in both Abaqus/Standard and Abaqus/Explicit,Modeling of damage under the general framework introduced earlier,Damage initiation,Traction or separation-based criterion,Damage evolution,Removal of elements,Normal mode,Shear mode,Dependence of fracture energyon mode mix,Typical traction-separation response,Constitutive Response in Cohesive Elements,Linear elasticity with damage,Linear elasticity,Defines behavior before the initiation of damage,Relates nominal stress to nominal strain,Nominal traction to separation with default choice of unit thickness,Uncoupled traction behavior: nominal stress depends only on corresponding nominal strain,Coupled traction behavior is more general,*ELASTIC, TYPE = ,TRACTION,COUPLED TRACTION,Constitutive Response in Cohesive Elements,The elastic modulus for the traction separation law should be interpreted as a,penalty stiffness,.,For example, for the opening mode:,K,n,=,N,max,/,d,n,init,In Abaqus, nominal stress and strain quantities are used for the traction separation law.,If unit thickness is specified for the element, then the nominal strain corresponds to the separation value.,Elastic response governed by,K,n,.,If you specify a non-unit thickness for the cohesive element, you must scale your data to obtain the correct stiffness,K,n,. Example on next slide.,Displacement at damage initiation in normal (opening) mode,Constitutive Response in Cohesive Elements,Example: Peel test model,A,E,n,=K,n,h,eff,Abaqus evaluates this,which is equivalent to this,Geometric thickness (based on nodal coordinates) of the adhesive,h,geom,=,1e,-,3,Assume separation at initiation,=,1e,-,3,and,N,max,=,6.9e9,.,For,model A,: use geometric thickness,h,eff,=,h,geom,=,1e,-,3,=,/,h,eff,=,1,;,N,max,=,E,n,=,6.9e9,K,n,=,6.9e12,For,model B,: specify unit thickness,h,eff,=,1,=,/,h,eff,=,1e,-,3,;,N,max,=,6.9e9,E,n,=,K,n,=,6.9e12,B,Damage initiation,Mixed mode conditions,Maximum stress (or strain),criterion:,Output:,MAXSCRT,MAXECRT,Constitutive Response in Cohesive Elements,*,DAMAGE INITIATION,CRITERION,= ,MAXS,MAXE,Constitutive Response in Cohesive Elements,For example, for Mode I (opening mode) the MAXS condition implies damage initiates when,s,n,=,N,max,.,*Damage initiation,criterion=MAXS,290.0E6, 200.0E6, 200.0E6,Damage initiation point,N,max,T,max,S,max,Constitutive Response in Cohesive Elements,Quadratic stress (or strain) interaction criterion:,No damage initiation under pure compression,Output:,QUADSCRT,QUADECRT,*,DAMAGE INITIATION,CRITERION,= ,QUADS,QUADE,Constitutive Response in Cohesive Elements,Summary of damage initiation criteria,Maximum nominal strain criterion,*DAMAGE INITIATION, CRITERION=,MAXE,Quadratic nominal strain criterion,*DAMAGE INITIATION, CRITERION=,QUADE,Quadratic nominal stress criterion,*DAMAGE INITIATION, CRITERION=,QUADS,n,: nominal stress in the pure normal mode,s,: nominal stress in the first shear direction,t,: nominal stress in the second shear direction,n,: nominal strain in the pure normal mode,s,: nominal strain in the first shear direction,t,: nominal strain in the second shear direction,*DAMAGE INITIATION, CRITERION=,MAXS,Maximum nominal stress criterion,where,n,s, and,t,are components of relative displacement between the top and bottom of the cohesive element; and,T,o,is the original thickness of the cohesive element.,Constitutive Response in Cohesive Elements,Damage evolution,Post damage-initiation response defined by:,d,is the scalar damage variable,d =,0,:,undamaged,d =,1,:,fully damaged,d,monotonically increases,Typical damaged response,Constitutive Response in Cohesive Elements,Damage evolution is based on energy or displacement,Specify either the total fracture energy or the post damage-initiation effective displacement at failure,May depend on mode mix,Mode mix may be defined in terms of energy or traction,Area under the curve is the fracture energy,Displacement at failure in normal (opening) mode,Constitutive Response in Cohesive Elements,Displacement-based damage evolution,Damage is a function of an effective displacement:,The post damage-initiation softening response can be either,Linear,Exponential,Tabular,Linear post-initiation response,Constitutive Response in Cohesive Elements,Keywords interface for displacement-based damage evolution,For LINEAR and EXPONENTIAL softening:,Specify the effective displacement at complete failure,d,fail,relative to the effective displacement at initiation,d,init,.,For TABULAR softening:,Specify the scalar damage variable d directly as a function of,d,d,init,.,Optionally specify the effective displacement as function of mode mix in tabular form.,Abaqus assumes that the damage evolution is mode independent otherwise.,*DAMAGE EVOLUTION, TYPE =,DISPLACEMENT, SOFTENING = ,LINEAR | EXPONENTIAL | TABULAR, MIXED MODE BEHAVIOR =,TABULAR,Constitutive Response in Cohesive Elements,Abaqus/CAE interface for displacement-based damage evolution,Constitutive Response in Cohesive Elements,Energy-based damage evolution,The fracture energy can be defined as a function of mode mix using either a tabular form or one of two analytical forms:,Power law,BK (Benzeggagh-Kenane),For isotropic failure (,G,IC,=,G,IIC,), the response is insensitive to the value of,.,Constitutive Response in Cohesive Elements,Keywords interface for energy-based damage evolution,Specify fracture energy as function of mode mix in tabular form, or,Specify the fracture energy in pure normal and shear deformation modes and choose either the POWER LAW or the BK mixed mode behavior,*DAMAGE EVOLUTION, TYPE =,ENERGY, SOFTENING = ,LINEAR | EXPONENTIAL, MIXED MODE BEHAVIOR = ,TABULAR | POWER LAW | BK, POWER =,value,Constitutive Response in Cohesive Elements,Abaqus/CAE interface for energy-based damage evolution,Constitutive Response in Cohesive Elements,Example,The preceding discussion was very general in the sense that the full range of options for modeling the constitutive response of cohesive elements was presented.,In the simplest case, Abaqus requires that you input the adhesive thickness,h,eff,and 10 material parameters:,*Elastic, type=traction,E,n, E,t, E,s,*Damage initiation, criterion = maxs,N,max, T,max, S,max,*Damage evolution, type=energy, mixed mode behavior=bk, power=,G,IC, G,IIC, G,IIIC,What do you do when you only have 1 property and the adhesive thickness is essentially zero?,Normal (opening) mode:,Traction,(nominal stress),Separation,(area under entire curve),G,IC,Cohesive material law:,Traction, Damage Evolution,Diehl, T., Modeling Surface-Bonded Structures with ABAQUS Cohesive Elements: Beam-Type Solutions, ABAQUS Users Conference, Stockholm, 2005.,Constitutive Response in Cohesive Elements,Example (contd),Common case: you know,G,TC,for the surface bond.,Assume isotropic behavior,G,IC,=,G,IIC,=,G,IIIC,=,G,TC,For MIXED MODE BEHAVIOR,=,BK, this makes the response independent of,term, so set,=,any valid input value (e.g.,1.0,),Bond thickness is essentially zero,Specify the cohesive section property thickness,h,eff,=,1.0,Nominal strains,=,separation; elastic moduli,=,stiffness,Isotropy also implies the following:,E,n,=,E,t,=,E,s,=,E,eff,(,=,K,eff,since we chose,h,eff,=,1.0,),N,max,=,T,max,=,S,max,=,T,ult,Constitutive Response in Cohesive Elements,Example (contd),Introduce concept of damage initiation ratio:,d,ratio,=,d,init,/,d,fail, where,0,d,ratio,1,.,Use,G,C,and equation of a triangle to relate back to,K,eff,and,T,ult,:,The problem now reduces to two penalty terms:,d,fail,and,d,ratio,.,Assume,d,ratio,=,.,Choose,d,fail,as a fraction of the typical cohesive element mesh size.,For example, use,d,fail,=,0.050,typical cohesive element size as a starting point.,Constitutive Response in Cohesive Elements,Example (contd),Thus, after choosing the two penalty terms, a single (effective) traction-separation law applies to all modes (normal + shear):,*Cohesive section, thickness=SPECIFIED, .,1.0,:,:,*Elastic, type=TRACTION,K,eff, K,eff, K,eff,*Damage initiation, criterion = MAXS,T,ult, T,ult, T,ult,*Damage evolution, type=ENERGY,mixed mode behavior=BK, power=,1,G,TC, G,TC, G,TC,Effective properties:,Traction,(nominal stress),Separation,(area under entire curve),G,TC,Cohesive material law:,Traction, Damage Evolution,Constitutive Response in Cohesive Elements,Example (contd),What if the response is dynamic? What about the density?,The density of the cohesive layer should also be considered a penalty quantity.,For Abaqus/Explicit, the effective density should not adversely affect the stable time increment. Diehl suggests the following rule:,The Abaqus Analysis Users Manual provides additional guidelines for determining a cohesive element density that minimizes the effect on the stable time increment in Abaqus/Explicit.,D,t,stable,=,stable time increment without cohesive elements in the model,f,t2D,= 0.32213,(for cohesive elements whose original nodal coordinates relate to zero element thickness),Constitutive Response in Cohesive Elements,Example: Double-cantilever beam (DCB),Alfano and Crisfield (2001),Pure Mode I,Displacement control,Analyzed using 2D (CPE4I) elements,Delamination assumed to occur along a straight line,Beams: Orthotropic material,Cohesive layer: Traction-separation with damage,The cohesive properties are given next slide.,Initial crack,u,-,u,Cohesive layer (set:,coh_elems,),Constitutive Response in Cohesive Elements,Properties: adhesive,Interactive interface,Constitutive Response in Cohesive Elements,Keywords interface,Note:,More details on modeling of this problem using cohesive elements are discussed in Appendix 2 “Cohesive Element Modeling Techniques;” the relevant results will be discussed later in section “Surface-based Cohesive Behavior.”,*COHESIVE SECTION, ELSET=coh_elems, MATERIAL=cohesive, RESPONSE=TRACTION SEPARATION, THICKNESS=SPECIFIED 1.0, 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, 280 , 280,Viscous Regularization for Cohesive Elements,Viscous Regularization for Cohesive Elements,Cohesive elements have the potential to cause numerical difficulties in the following cases,Stiff cohesive behavior may lead to reduced maximum stable time increment in Abaqus/Explicit,Potentially addressed through selective mass scaling,Unstable crack propagation may lead to convergence difficulties in Abaqus/Standard,Potentially addressed through built-in viscous regularization option specific to cohesive elements,Viscous Regularization for Cohesive Elements,User interface for viscous regularization,*,COHESIVE SECTION,CONTROLS,=,control1,*SECTION CONTROLS, NAME =,control1,VISCOSITY,=,factor,Add-on,transverse shear stiffness may provide additional stability,*,COHESIVE SECTION,*TRANSVERSE SHEAR STIFFNESS,Output,Energy associated with viscous regularization: ALLCD,More details on viscous regularization are discussed in Appendix 2,Cohesive Element Examples,Cohesive Element Examples,Composite components in aerospace structures (Courtesy: NASA,),Stress concentrations around stiffener terminations and flanges,Residual thermal strains at the interface at room temperature,Analysis of the effects of residual strains on skin/stiffener debonding,Delamination initiation and propagation,Beginning of separation,After separation,Abaqus/Standard simulation of skin/stiffener debonding,Example Problem 1.4.5,Cohesive layers,Cohesive Element Examples,Delamination of a composite,This model is a representative of composite delamination.,It comprises 3 layers of composite with adhesive layers applied between composite layers.,The composite delaminates under the impact of a heavy mass displayed in light greenish shade in the animation.,Cohesive Element Examples,Lap joint analysis,Lap joints are created by laying one material on top of another and bonding them together,For example: bonding materials using an adhesive or fasteners,Connection type influences characteristic of joint,Adhesive connection (covered here),Compliance and thickness of adhesive,Fastener connection,Stiffness of fastener,Material A,Material B,Single-Lap Joint,Cohesive Element Examples,Mesh of the lap joint modeled using both solid and shell elements,2536 C3D8I and S4R elements,Transition from solid to shell elements is accomplished using the surface-based shell-to-solid coupling constraint.,2116 COH3D8 elements,Linear elastic material is used for the cohesive layer,100 psi modulus of elasticity (compared to 10.E6 for aluminum),0.4 Poissons ratio,Note that the cohesive element layer is initially of zero thickness, and the mesh density is finer than the connected regions,Cohesive Element Examples,The evolution of deformation of the lap joint with a compliant adhesive layer,Surface-based Cohesive Behavior,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.,Surface-based Cohesive Behavior,User interface,*SURFACE INTERACTION, NAME=,cohesive,*COHESIVE BEHAVIOR,.,*CONTACT PAIR, INTERACTION=,cohesive,surface1,surface2,Abaqus/Standard,*SURFACE INTERACTION, NAME=,cohesive,*COHESIVE BEHAVIOR,.,*CONTACT,*CONTACT PROPERTY ASSIGNMENT,surface1,surface2,cohesive,Abaqus/Explicit,Abaqus/CAE,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:,l