A Crack Close to and Perpendicular to an Interface: Resolution of Anomalous Behavior With a Cohesive Zone

2019 ◽  
Vol 86 (3) ◽  
Author(s):  
George G. Adams
Keyword(s):  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Applied Pressure ◽  
Stress Singularity ◽  
Crack Tip ◽  
Anomalous Behavior ◽  
Work Of Adhesion ◽  
Bimaterial Interface ◽  
Zone Model ◽  
Finite Distance

In this investigation, we consider a crack close to and perpendicular to a bimaterial interface. If the crack tip is at the interface then, depending on material properties, the order of the stress singularity will be equal to, less than, or greater than one-half. However, if the crack tip is located any finite distance away from the interface the stress field is square-root singular. Thus, as the crack tip approaches the interface, the stress intensity factor approaches zero (for cases corresponding to a singularity of order less than one-half) or infinity (for a singularity of order greater than one-half). The implication of this behavior is that for a finite applied pressure the crack will either never reach the interface or will reach the interface with vanishing small applied pressure. In this investigation, a cohesive zone model is used in order to model the crack behavior. It is found that the aforementioned anomalous behavior for the crack without a cohesive zone disappears and that the critical value of the applied pressure for the crack to reach the interface is finite and depends on the maximum stress of the cohesive zone model, as well as on the work of adhesion and the Dundurs' parameters.

scholarly journals Critical value of the generalized stress intensity factor for a crack perpendicular to an interface

2015 ◽  
Vol 471 (2183) ◽  
pp. 20150571 ◽  
Author(s):  
George G. Adams
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Crack Tip ◽  
Critical Value ◽  
Zone Model ◽  
Cohesive Stress ◽  
Generalized Stress Intensity Factor

When a crack tip impinges upon a bi-material interface, the order of the stress singularity will be equal to, less than or greater than one-half. The generalized stress intensity factors have already been determined for some such configurations, including when a finite-length crack is perpendicular to the interface. However, for these non-square-root singular stresses, the determination of the conditions for crack growth are not well established. In this investigation, the critical value of the generalized stress intensity factor for tensile loading is related to the work of adhesion by using a cohesive zone model in an asymptotic analysis of the separation near the crack tip. It is found that the critical value of the generalized stress intensity factor depends upon the maximum stress of the cohesive zone model, as well as on the Dundurs parameters ( α and β ). As expected this dependence on the cohesive stress vanishes as the material contrast is reduced, in which case the order of the singularity approaches one-half.

scholarly journals Adhesion and pull-off force of an elastic indenter from an elastic half-space

2014 ◽  
Vol 470 (2169) ◽  
pp. 20140317 ◽  
Author(s):  
George G. Adams
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Half Space ◽  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Elastic Half Space ◽  
Work Of Adhesion ◽  
Zone Model ◽  
Generalized Stress Intensity Factor ◽  
Elastic Punch

The adhesion between an elastic punch and an elastic half-space is investigated for plane and axisymmetric geometries. The pull-off force is determined for a range of material combinations. This configuration is characterized by a generalized stress intensity factor which has an order less than one-half. The critical value of this generalized stress intensity factor is related to the work of adhesion, under tensile loading, by using a cohesive zone model in an asymptotic analysis of the separation near the elastic punch corner. These results are used in conjunction with existing results in the literature for the frictionless contact between an elastic semi-infinite strip and half-space in both plane and axisymmetric configurations. It is found that the value of the pull-off force includes a dependence on the maximum stress of the cohesive zone model. As expected, this dependence vanishes as the punch becomes rigid in that case the order of the singularity approaches one-half. At the other limit, when the half-space becomes rigid, the stresses become bounded and uniform and the pull-off force depends linearly on the cohesive stress and is independent of the work of adhesion. Thus, the transition from fracture-dominated adhesion to strength-dominated adhesion is demonstrated.

Simulation of Crack Initiation at the Interface Edge Between Sub-Micron Thick Films Under Creep by Cohesive Zone Model

2008 ◽  
Author(s):  
Do Van Truong
Keyword(s):  
Crack Initiation ◽  
Cohesive Zone ◽  
Damage Mechanics ◽  
Cohesive Zone Model ◽  
Thick Films ◽  
Stress Singularity ◽  
Zone Model ◽  
Cohesive Law ◽  
Micro Cantilever ◽  
Interface Edge

Delamination between sub-micron thick films is initiated at an interface edge due to creep deformation, and leads to the malfunction of microelectronic devices. In this study, the cohesive zone model approach with a cohesive law based on damage mechanics was developed to simulate crack initiation process at an interface edge between film layers under creep. Delamination experiments using a micro-cantilever bend specimen with a Sn/Si interface were conducted. The parameters charactering the cohesive law were calibrated by fitting displacement-time curves obtained by experiments and simulations. In addition, the order of the stress singularity, which increases with time and has a significant jump in its value at the crack initiation, was investigated.

scholarly journals Modelling of crack initiation in adhesively bonded Joint

2012 ◽  
Vol 3 (3) ◽  
pp. 221-227
Author(s):  
H. Al Ali ◽  
M.A. Wahab
Keyword(s):  
Crack Initiation ◽  
Cohesive Zone ◽  
Damage Mechanics ◽  
Cohesive Zone Model ◽  
Stress Singularity ◽  
Strain Energy Release ◽  
Continuum Damage Mechanics ◽  
Zone Model ◽  
Adhesively Bonded ◽  
Adhesively Bonded Joint

 In this paper, a review of some techniques proposed in the literature for modelling crackinitiation in adhesively bonded joints is presented. The techniques reviewed are: a) the singular intensityfactor, b) the inherent flaw size, c) Cohesive-zone model (CZM) and d) Continuum Damage Mechanics(CDM). The singular intensity factor characterizes the stress singularity at the corner point and can beused as a failure criterion to predict crack initiation. The inherent flaw method technique assumes that asmall crack having a fraction of millimetres is initiated at the singular point in order to develop a fracturemechanics criterion for crack initiation. The strain energy release rate for an un-cracked specimen is usedto determine the size of the inherent flaw. The cohesive zone model (CZM) technique is based ondefining parameters from fracture mechanics test specimens and using them to model failure of the joints.Continuum Damage Mechanics makes use of thermodynamics principles in order to derive a damageevolution law. In this damage evolution law the damage variable (D) is expressed as a function of numberof cycles, applied stress range and triaxiality function. Furthermore, the possibility of using the eXtendedFinite Element Method (XFEM) to predict crack initiation is elaborated.

scholarly journals Numerical Simulation of Fatigue Crack Growth Rate and Crack Retardation due to an Overload Using a Cohesive Zone Model

2014 ◽  
Vol 891-892 ◽  
pp. 777-783 ◽  
Author(s):  
Sarmediran Silitonga ◽  
Johan Maljaars ◽  
Frans Soetens ◽  
Hubertus H. Snijder
Keyword(s):  
Finite Element ◽  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Propagation ◽  
Crack Growth ◽  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Crack Tip ◽  
Zone Model ◽  
Cohesive Elements

In this work, a numerical method is pursued based on a cohesive zone model (CZM). The method is aimed at simulating fatigue crack growth as well as crack growth retardation due to an overload. In this cohesive zone model, the degradation of the material strength is represented by a variation of the cohesive traction with respect to separation of the cohesive surfaces. Simulation of crack propagation under cyclic loads is implemented by introducing a damage mechanism into the cohesive zone. Crack propagation is represented in the process zone (cohesive zone in front of crack-tip) by deterioration of the cohesive strength due to damage development in the cohesive element. Damage accumulation during loading is based on the displacements in the cohesive zone. A finite element model of a compact tension (CT) specimen subjected to a constant amplitude loading with an overload is developed. The cohesive elements are placed in front of the crack-tip along a pre-defined crack path. The simulation is performed in the finite element code Abaqus. The cohesive elements behavior is described using the user element subroutine UEL. The new damage evolution function used in this work provides a good agreement between simulation results and experimental data.

A Superposition Framework for Discrete Dislocation Plasticity

2004 ◽  
Vol 71 (6) ◽  
pp. 805-815 ◽  
Author(s):  
M. P. O’Day ◽  
W. A. Curtin
Keyword(s):  
Boundary Conditions ◽  
Crack Growth ◽  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Bimaterial Interface ◽  
Homogeneous Material ◽  
Plastic Behavior ◽  
Zone Model ◽  
Discrete Dislocation ◽  
Wide Range

A superposition technique is introduced that allows for the application of discrete dislocation (DD) plasticity to a wide range of thermomechanical problems with reduced computational effort. Problems involving regions of differing elastic and/or plastic behavior are solved by superposing the solutions to i) DD models only for those regions of the structure where dislocation phenomena are permitted subject to either zero traction or displacement at every point on the boundary and ii) an elastic (EL) (or elastic/cohesive-zone) model of the entire structure subject to all desired loading and boundary conditions. The DD subproblem is solved with standard DD machinery for an elastically homogeneous material. The EL subproblem requires only a standard elastic or elastic/cohesive-zone finite element (FE) calculation. The subproblems are coupled: the negative of the tractions developed at the boundaries of the DD subproblem are applied as body forces in the EL subproblem, while the stress field of the EL subproblem contributes a driving force to the dislocations in the DD subproblem structure. This decomposition and the generic boundary conditions of the DD subproblem permit the DD machinery to be easily applied as a “black-box” constitutive material description in an otherwise elastic FE formulation and to be used in a broader scope of applications due to the overall enhanced computational efficiency. The method is validated against prior results for crack growth along a plastic/rigid bimaterial interface. Preliminary results for crack growth along a metal/ceramic bimaterial interface are presented.

scholarly journals The J-integral for mixed-mode loaded cracks with cohesive zones

2020 ◽  
Vol 227 (1) ◽  
pp. 79-94
Author(s):  
Johannes Scheel ◽  
Alexander Schlosser ◽  
Andreas Ricoeur
Keyword(s):  
Cohesive Zone ◽  
Mixed Mode ◽  
Cohesive Zone Model ◽  
Crack Tip ◽  
Constitutive Law ◽  
Zone Model ◽  
J Integral ◽  
Cohesive Law ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement

AbstractThe J-integral quantifies the loading of a crack tip, just as the crack tip opening displacement (CTOD) emanating from the cohesive zone model. Both quantities, being based on fundamentally different interpretations of cracks in fracture mechanics of brittle or ductile materials, have been proven to be equivalent in the late 60s of the previous century, however, just for the simple mode-I loading case. The relation of J and CTOD turned out to be uniquely determined by the constitutive law of the cohesive zone in front of the physical crack tip. In this paper, a J-integral vector is derived for a mixed-mode loaded crack based on the cohesive zone approach, accounting for the most general case of a mode-coupled cohesive law. While the $$J_1$$ J 1 -coordinate, as energy release rate of a straight crack extension, is uniquely related to the cohesive potential at the physical crack tip and thus to the CTOD, the $$J_2$$ J 2 -coordinate depends on the solution of the specific boundary value problem in terms of stresses and displacement gradients at the cohesive zone faces. The generalized relation is verified for the Griffith crack, employing solutions of the Dugdale crack based on improved holomorphic functions.

scholarly journals Prediction of delamination strength at interface between thin film and substrate by cohesive zone model

2006 ◽  
Vol 28 (4) ◽  
pp. 252-262 ◽  
Author(s):  
Do Van Truong ◽  
Hiroyuku Hirakata ◽  
Takayuki Katamura
Keyword(s):  
Thin Film ◽  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Electronic Device ◽  
Stress Singularity ◽  
Zone Model ◽  
Cohesive Law ◽  
Gold Thin Film ◽  
Different Shapes ◽  
Interface Edge

An electronic device consists of multi-layered submicron-thick films, and delamination often takes place at an interface edge because of the stress singularity near the edge. Since the stress singularity at an interface edge depends on the edge shape, the fracture mechanics concept cannot be used to compare the delamination strength between the components with different shapes. This paper aims to predict the delamination strength at the interface edge with arbitrary shape using a cohesive zone model. Two different experiments are conducted for a gold thin film on a silicon substrate to calibrate the cohesive law. The validity of the approach is then discussed.

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