A dynamic analysis of unstable crack propagation and arrest in the DCB test specimen

Kanninen, M. F.

doi:10.1007/bf00035502

Cited by 268 publications

(146 citation statements)

References 11 publications

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“…The most common solution for ∆ comes from the beam on a linear-elastic foundation approach which assumes a stiffness of k s such that the stress, σ, versus displacement, u, relationship for the cohesive zone at the crack tip is as shown in Figure 4a [1,5]. For this case:…”

Section: The Linear-elastic Stiffness Approachmentioning

confidence: 99%

Cohesive zone models and the plastically deforming peel test

Georgiou

Hadavinia

Ivanković

et al. 2003

The Journal of Adhesion

106

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The peel test is a popular test method for measuring the peeling energy between flexible laminates. However, when plastic deformation occurs in the peel arm(s) the determination of the true adhesive fracture energy, G c , from the measured peel load is far from straightforward.Two different methods of approaching this problem have been reported in recently published papers, namely: (a) a simple linear-elastic stiffness approach, and (b) a critical, limiting maximum stress, σ max , approach. In the present paper, these approaches will be explored and contrasted. Our aims include trying to identify the physical meaning, if any, of the parameter σ max and deciding which is the better approach for defining fracture, when suitable definitive experiments are undertaken.Keywords: cohesive zone models; fracture mechanics; laminates; peel tests; plastic deformation. 2 INTRODUCTIONThe peel test is a popular test method for measuring the peeling energy between flexible laminates [e.g. [1][2][3]. The simple single-arm form is shown in Figure 1a and the 'T-peel' variant is illustrated in Figure 1b. For the former test method, the total energy input, G, is related to the applied steady-state peel load, P, the width, b, of the specimen and the peel angle, θ, by:(1 cos )and for the 'T-peel' we essentially have two such specimens 'back-to-back', each with 2 π θ = , such that:This value of G includes the adhesive fracture energy, G c , and any plastic work done in bending the peeling arm(s). The value of the adhesive fracture energy, G c , is assumed to be a 'characteristic' property of the adhesive, or interface, and ideally independent of geometrical details of the peel test such as the thickness, h, of the peel arm and the peel angle, θ.However, the value of G c would, of course, be expected to typically be dependent upon the test rate and temperature, since we are dealing with viscoelastic materials.When only elastic deformation occurs in the peeling arm there is no energy dissipation, so that c G G = . However, in many cases, there is a rather complex bending and unbending process, as shown, for 2 π θ = in Figure 2a where the peeling arm is initially bent and then gradually straightened as the peeling proceeds. A schematic diagram of the bending moment, M/b, per unit width in the peel arm and the inverse of the local radius, 1/R, of curvature at the peel front is shown in Figure 2b and the area under the curve is the plasticenergy dissipated in bending. When a non-work hardening material is used for the peel arm, the moments tend to the plastic limit:3 where M p is the fully plastic moment, y σ is the yield stress and h is the thickness of the peel arm, and for large values of the plastic-energy dissipation:A crucial factor in the analysis is the root rotation, o θ , illustrated in Figure 3. This arises from stretching of the substrate peeling arm before it debonds and reduces the plastic work done such that the proportion of G going into plastic work,Considering now only the 90° peel test, and assuming o θ to be small, then...

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Section: The Linear-elastic Stiffness Approachmentioning

confidence: 99%

Cohesive zone models and the plastically deforming peel test

Georgiou

Hadavinia

Ivanković

et al. 2003

The Journal of Adhesion

106

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“…11(b). It can be seen that the opening-rate-dependence even under the static loading regime produces a significantly longer crack than the quasistatic solution, which can be calculated from the static DCB deflection relationship [31]:…”

Section: Static Quasi-explicit Czm Resultsmentioning

confidence: 98%

Dynamic fracture analysis by explicit solid dynamics and implicit crack propagation

Crump

Ferté²,

Jivkov

et al. 2017

International Journal of Solids and Structures

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Combining time-dependant structural loading with dynamic crack propagation is a problem that has been under consideration since the early days of fracture mechanics.Here we consider a method to deal with this issue, which combines a set-valued opening-rate-dependant cohesive law, a quasi-explicit solver and the eXtended Finite Element Method of representing a crack. The approach allows a propagating crack to be mesh-independent while also being dynamically informed through a quasi-explicit solver. Several well established experiments on glass (Homolite-100) and Polymethyl methacrylate (PMMA) are successfully modelled and compared against existing analytical solutions and other approaches in 2D up until the experimentally observed branching speeds. The comparison highlights the robustness of ensuring energy is conserved globally by treating a propagating phenomenological crack-tip implicitly, while taking advantage of the computational efficiency of treating the global dynamics explicitly.

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“…Two different testing conditions, in the following referred to as A and B, have been simulated consid- ering V 0 = 4 µm and V 0 = 14 µm respectively. According to the analytical solutions proposed, for instance, in [52,53], in the first case the crack stops propagating after reaching a plateau value, whereas an unstable fracture propagation is expected in the second case. The adopted unstructured finite element mesh, featuring quadratic 10-node tetrahedral elements, is characterized by an element size equal to 25 µm around the beam axis; this size allows an accurate enough resolution of the stress field within the cohesive zone, whose length is = 55 µm.…”

Section: Double Cantilever Beammentioning

confidence: 99%

Coupled domain decomposition–proper orthogonal decomposition methods for the simulation of quasi-brittle fracture processes

Corigliano

Confalonieri

Dossi

et al. 2016

Adv. Model. and Simul. in Eng. Sci.

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In this paper, we discuss a strategy to reduce the computational costs of the simulation of dynamic fracture processes in quasi-brittle materials, based on a combination of domain decomposition (DD) and model order reduction (MOR) techniques. Fracture processes are simulated by means of three-dimensional finite element models in which use is made of cohesive elements, introduced on-the-fly wherever a cracking criterion is attained. The body is initially subdivided into sub-domains; for each sub-domain MOR is obtained through a proper orthogonal decomposition (POD) of the equations governing its evolution, until when it starts getting cracked. After crack inception within a sub-domain, the solution is switched back to the original full-order model for that sub-domain only. The computational gain attained through the coupled use of DD and POD thus depends on the geometry of the body, on the topology of sub-domains and, on top of all, on the spreading of cracking induced by load conditions. Numerical examples concerning well-established fracture tests are used for validation, and the attainable reduction of the computing time is discussed at varying decomposition into sub-domains, even in the absence of a full exploitation of parallel computing potentialities.

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A dynamic analysis of unstable crack propagation and arrest in the DCB test specimen

Cited by 268 publications

References 11 publications

Cohesive zone models and the plastically deforming peel test

Cohesive zone models and the plastically deforming peel test

Dynamic fracture analysis by explicit solid dynamics and implicit crack propagation

Coupled domain decomposition–proper orthogonal decomposition methods for the simulation of quasi-brittle fracture processes

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