An improved description of the exponential Xu and Needleman cohesive zone law for mixed-mode decohesion

Bosch, van den Mj Marco; Schreurs, Pjg Piet; Geers, Mgd Marc

doi:10.1016/j.engfracmech.2005.12.006

Cited by 260 publications

(180 citation statements)

References 46 publications

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“…The third case study highlights the sensitivity of CZMs to traction controlled mode mixity. Previous papers have typically used double cantilever beam data with uneven bending moment to validate cohesive zone performance under mode I and mixed-mode conditions (Sørensen and Jacobsen, 2003;van den Bosch et al, 2006;Park et al, 2009;Mosler and Scheider, 2011). The three case studies presented in this paper provide further challenges in the assessment of mixed-mode cohesive zone performance and should be considered in addition to double cantilever beam simulation.…”

Section: Discussionmentioning

confidence: 99%

Potential-based and non-potential-based cohesive zone formulations under mixed-mode separation and over-closure. Part I: Theoretical analysis

McGarry

Máirtín

Parry

et al. 2014

Journal of the Mechanics and Physics of Solids

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a b s t r a c tThis paper, the second of two parts, presents three novel finite element case studies to demonstrate the importance of normal-tangential coupling in cohesive zone models (CZMs) for the prediction of mixed-mode interface debonding. Specifically, four new CZMs proposed in Part I of this study are implemented, namely the potential-based MP model and the non-potential-based NP1, NP2 and SMC models. For comparison, simulations are also performed for the well established potential-based Xu-Needleman (XN) model and the non-potential-based model of van den Bosch, Schreurs and Geers (BSG model). Case study 1: Debonding and rebonding of a biological cell from a cyclically deforming silicone substrate is simulated when the mode II work of separation is higher than the mode I work of separation at the cell-substrate interface. An active formulation for the contractility and remodelling of the cell cytoskeleton is implemented. It is demonstrated that when the XN potential function is used at the cell-substrate interface repulsive normal tractions are computed, preventing rebonding of significant regions of the cell to the substrate. In contrast, the proposed MP potential function at the cell-substrate interface results in negligible repulsive normal tractions, allowing for the prediction of experimentally observed patterns of cell cytoskeletal remodelling. Case study 2: Buckling of a coating from the compressive surface of a stent is simulated. It is demonstrated that during expansion of the stent the coating is initially compressed into the stent surface, while simultaneously undergoing tangential (shear) tractions at the coating-stent interface. It is demonstrated that when either the proposed NP1 or NP2 model is implemented at the stent-coating interface mixed-mode over-closure is correctly penalised. Further expansion of the stent results in the prediction of significant buckling of the coating from the stent surface, as observed experimentally. In contrast, the BSG model does not correctly penalise mixed-mode over-closure at the stent-coating interface, significantly altering the stress state in the coating and preventing the prediction of buckling. Case study 3: Application of a displacement to the base of a bi-layered composite arch results in a symmetric sinusoidal distribution of normal and tangential traction at the arch interface. The traction defined mode mixity at the interface ranges from pure mode II at the base of the arch to pure mode I at the top of the arch. It is demonstrated that predicted debonding patterns are highly sensitive to normal-tangential coupling terms in a CZM. The NP2, XN, and BSG models exhibit a strong bias towards mode I separation at the top of the arch, while the NP1 model exhibits a bias towards mode II debonding at the base of the arch. Only the SMC model provides mode-independent behaviour in the early stages of debonding. This case study provides a practical example of the importance of the behaviour of CZMs under conditions of traction controlled mode mixity, foll...

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Section: Discussionmentioning

confidence: 99%

Potential-based and non-potential-based cohesive zone formulations under mixed-mode separation and over-closure. Part I: Theoretical analysis

McGarry

Máirtín

Parry

et al. 2014

Journal of the Mechanics and Physics of Solids

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“…In other words, if a potential traction-separation law is formulated, it is not possible to distinguish energetically between pure mode I and pure mode II, as the fracture energy is required to be independent from the fracture path. However, as pointed out by some authors [92,93], it is reasonable to assume that the work of decohesion should be path dependent, as the energy dissipated in a fracture process depends on some microstructural details that inherently make mode II different from mode I, at least at a macroscopic level. In the framework introduced above, the fracture energy path-dependency can be achieved by simply discarding Eq.…”

Section: Damaged Interface: Cohesive Traction-separation Lawsmentioning

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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“…These laws allow for different fracture energies in different mode mixities. Also, the lack of a potential introduces a path-dependency, which has a physical ground considering that cohesive zone models can describe an irreversible damage process at an interface (van den Bosch et al 2006). In this paper two cohesive zone laws are used to model the interfacial behavior in the normal and in the tangential directions.…”

Section: Cohesive Zone Modelingmentioning

confidence: 99%

Interfacial stress analysis and prediction of debonding for a thin plate bonded to a curved substrate

Lorenzis¹,

Zavarise²

2009

International Journal of Non-Linear Mechanics

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This paper focuses on the analytical and numerical modeling of the interface between a rigid substrate with simple constant curvature and a thin bonded plate. The interfacial behavior is modeled by independent cohesive laws in the normal and tangential directions, coupled with a mixed-mode fracture criterion. The newly developed analytical model determines the interfacial shear and normal stress distributions as functions of the substrate curvature, during the various behavioral stages of the interface prior to the initiation of debonding. The model is also able to predict the debonding load and the effective bond length. In the numerical model the interface is modeled by zero-thickness node-to-segment contact elements, in which both the geometrical relationships between the nodes of the discretized problem and the interface constitutive laws are suitably defined. Numerical results and comparisons between the predictions of the two models are presented.

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An improved description of the exponential Xu and Needleman cohesive zone law for mixed-mode decohesion

Cited by 260 publications

References 46 publications

Potential-based and non-potential-based cohesive zone formulations under mixed-mode separation and over-closure. Part I: Theoretical analysis

Potential-based and non-potential-based cohesive zone formulations under mixed-mode separation and over-closure. Part I: Theoretical analysis

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

Interfacial stress analysis and prediction of debonding for a thin plate bonded to a curved substrate

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