Some issues in the application of cohesive zone models for metal–ceramic interfaces

Chandra, Namas; Li, H.; Shet, C.; Ghonem, H.

doi:10.1016/s0020-7683(02)00149-x

Cited by 459 publications

(208 citation statements)

References 36 publications

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“…It is thus recommend adjusting the shape of the CZM laws to conform to the behaviour of the thin material strip or interface they are simulating. Developed CZM include triangular [17], linear-parabolic [18], polynomial [19], exponential [20] and trapezoidal laws [21]. Thus, CZM can also be adapted to simulate ductile adhesive layers, whose behaviour can be approximated with trapezoidal laws [14].…”

Section: Introductionmentioning

confidence: 99%

Modelling adhesive joints with cohesive zone models: effect of the cohesive law shape of the adhesive layer

Campilho

Banea

Neto

et al. 2013

International Journal of Adhesion and Adhesives

491

193

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Adhesively-bonded joints are extensively used in several fields of engineering. Cohesive Zone Models (CZM) have been used for the strength prediction of adhesive joints, as an add-in to Finite Element (FE) analyses that allows simulation of damage growth, by consideration of energetic principles. A useful feature of CZM is that different shapes can be developed for the cohesive laws, depending on the nature of the material or interface to be simulated, allowing an accurate strength prediction. This work studies the influence of the CZM shape (triangular, exponential or trapezoidal) used to model a thin adhesive layer in single-lap adhesive joints, for an estimation of its influence on the strength prediction under different material conditions. By performing this study, guidelines are provided on the possibility to use a CZM shape that may not be the most suited for a particular adhesive, but that may be more straightforward to use/implement and have less convergence problems (e.g. triangular shaped CZM), thus attaining the solution faster. The overall results showed that joints bonded with ductile adhesives are highly influenced by the CZM shape, and that the trapezoidal shape fits best the experimental data. Moreover, the smaller is the overlap length (LO), the greater is the influence of the CZM shape. On the other hand, the influence of the CZM shape can be neglected whe n using brittle adhesives, without compromising too much the accuracy of the strength predictions.

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Section: Introductionmentioning

confidence: 99%

Modelling adhesive joints with cohesive zone models: effect of the cohesive law shape of the adhesive layer

Campilho

Banea

Neto

et al. 2013

International Journal of Adhesion and Adhesives

491

193

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show abstract

“…In this way, initiation, propagation, branching and coalescence of microcracks stem as an outcome of the simulation, without any a priori assumptions. Several cohesive laws have been proposed [54,55], but most popular are the potential-based laws by Tvergaard [56] and Xu and Needleman [57] and the linear laws by Camacho and Ortiz [58] and Ortiz and Pandolfi [59]. Cohesive FE models for 2D microstructures have been presented by several authors.…”

Section: Introductionmentioning

confidence: 99%

A three-dimensional cohesive-frictional grain-boundary micromechanical model for intergranular degradation and failure in polycrystalline materials

Benedetti

Aliabadi

2013

Computer Methods in Applied Mechanics and Engineering

116

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In this study, a novel three-dimensional micro-mechanical crystal-level model for the analysis of intergranular degradation and failure in polycrystalline materials is presented. The polycrystalline microstructures are generated as Voronoi tessellations, that are able to retain the main statistical features of polycrystalline aggregates. The formulation is based on a grain-boundary integral representation of the elastic problem for the aggregate crystals, that are modeled as threedimensional anisotropic elastic domains with random orientation in the three-dimensional space. The boundary integral representation involves only intergranular variables, namely interface displacement discontinuities and interface tractions, that play an important role in the micromechanics of polycrystals. The integrity of the aggregate is restored by enforcing suitable interface conditions, at the interface between adjacent grains. The onset and evolution of damage at the grain boundaries is modeled using an extrinsic non-potential irreversible cohesive linear law, able to address mixed-mode failure conditions. The derivation of the traction-separation law and its relation with potential-based laws is discussed. Upon interface failure, a non-linear frictional contact analysis is used, to address separation, sliding or sticking between micro-crack surfaces. To avoid a sudden transition between cohesive and contact laws, when interface failure happens under compressive loading conditions, the concept of cohesive-frictional law is introduced, to model the smooth onset of friction during the mode II decohesion process. The incrementaliterative algorithm for tracking the degradation and micro-cracking evolution is presented and discussed. Several numerical tests on pseudo-and fully three-dimensional polycrystalline microstructures have been performed. The influence of several intergranular parameters, such as cohesive strength, fracture toughness and friction, on the microcracking patterns and on the aggregate response of the polycrystals has been analyzed. The tests have demonstrated the capability of the formulation to track the nucleation, evolution and coalescence of multiple damage and cracks, under either tensile or compressive loads.

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“…For more brittle decohesion relations, as shown for instance in the right part of Figure 2 (i.e. when the decohesion law stems from micro-cracking as in concrete or ceramics), the shape of the stress-separation relation plays a much bigger role and is sometimes even more important than the value of the tensile strength f t [9,10]. …”

Section: Formulationmentioning

confidence: 99%

“…Accordingly, the partitionof-unity property of finite element shape functions can be used in a straightforward fashion to incorporate discontinuities, and thus, cohesive-zone models in a manner that preserves their truly discontinuous character. Indeed, in conventional finite element notation, the displacement field of an element that contains a single discontinuity can be represented as (10) where N contains the standard shape functions, andā andã collect the conventional and the additional nodal degrees-of-freedom, respectively. The numerical development now follows standard lines by casting the balance of momentum in a weak format, and, in the spirit of a standard Bubnov-Galerkin method, taking a decomposition as in Equation (9) also for the test function.…”

Section: Exact Numerical Representation Of Discontinuitiesmentioning

confidence: 99%

Cohesive‐zone models, higher‐order continuum theories and reliability methods for computational failure analysis

Borst

Gutiérrez

Wells

et al. 2004

Numerical Meth Engineering

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SUMMARYA concise overview is given of various numerical methods that can be used to analyse localization and failure in engineering materials. The importance of the cohesive-zone approach is emphasized and various ways to incorporate the cohesive-zone methodology in discretization methods are discussed. Numerical representations of cohesive-zone models suffer from a certain mesh bias. For discrete representations this is caused by the initial mesh design, while for smeared representations it is rooted in the ill-posedness of the rate boundary value problem that arises upon the introduction of decohesion. A proper representation of the discrete character of cohesive-zone formulations which avoids any mesh bias can be obtained elegantly when exploiting the partition-of-unity property of finite element shape functions. The effectiveness of the approach is demonstrated for some examples at different scales. Moreover, examples are shown how this concept can be used to obtain a proper transition from a plastifying or damaging continuum to a shear band with gross sliding or to a fully open crack (true discontinuum). When adhering to a continuum description of failure, higher-order continuum models must be used. Meshless methods are ideally suited to assess the importance of the higher-order gradient terms, as will be shown. Finally, regularized strain-softening models are used in finite element reliability analyses to quantify the probability of the emergence of various possible failure modes.

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Some issues in the application of cohesive zone models for metal–ceramic interfaces

Cited by 459 publications

References 36 publications

Modelling adhesive joints with cohesive zone models: effect of the cohesive law shape of the adhesive layer

Modelling adhesive joints with cohesive zone models: effect of the cohesive law shape of the adhesive layer

A three-dimensional cohesive-frictional grain-boundary micromechanical model for intergranular degradation and failure in polycrystalline materials

Cohesive‐zone models, higher‐order continuum theories and reliability methods for computational failure analysis

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