Interface crack initiation at V-notches along adhesive bonding in weakly bonded polymers subjected to mixed-mode loading

In this paper, interface crack initiation at V-notches along adhesive in bonded Polycarbonate (PC) and Poly Methyl Methacrylate (PMMA) subjected to mixed-mode loading conditions was investigated based on a combined experimental, finite element and matched asymptotic analysis. The V-notch specimens with an adhesive interface starting from its tip made at different notch angles were tested under three-point bending conditions. The experimental observations show that the specimens mainly fail by cracks along the interface. Also, the load at the crack initiation increases when the notch angle increases. The computational results are then used to explain and to correlate with the experimental data. A two-fold criterion developed by Leguillon (Eur J Mech A/Solids 21:61?C72 2002) that requires a simultaneous satisfaction of both Griffith energy and stress conditions for the crack initiation at a notch in the specimen made of a homogeneous brittle material is first extended for V-notch specimens under mixed-mode loading conditions and then used to estimate the crack initiation load. The estimated loads appear to agree well with the experimental data. Finally, an inverse method is proposed to estimate the values of fracture toughness at different mode mixity ratios.     

Comparison of predictions by mode II or mode III criteria on crack front twisting in three or four point bending experiments

Whatever the external loading, a crack front in a solid tries to reach mode I loading conditions after propagation. In mode I + II, the crack kinks to annihilate mode II, kinking angle being well predicted by the principle of local symmetry (PLS) or by the maximum tangential stress criterion (MTS). In presence of mode III, the problem becomes three-dimensional and the proposed propagation criterion are not yet well proved and established. In particular in three point bending experiments (3PB) with an initially inclined crack, the crack twists around the direction of propagation to finally reach a situation of pure mode I. The aim of the paper is to compare the propagation paths predicted by two different criteria for 3PB fatigue experiments performed on PMMA. The first criterion developed by Schollmann et al. (Int J Fract 117(2):129–141, 2002), is a three-dimensional extension of the MTS criterion and predicts the local angles that annihilates mode II and III at each point of the front. The second one developed by Lazarus et al. (J Mech Phys Solids 49(7):1421–1443, 2001b), predicts an abrupt and then progressive twisting of the front to annihilate mode III. Due to presence of sign changing mode II and almost uniform mode III in the experiments, both criteria give good results. However, since mode III is predominant over mode II in the case under consideration, the global criterion gives better results. Nevertheless, the local type criterion seems to be of greater universality for practical engineering applications.     

Analysis of fracture nucleation around wellbores

International Journal of Fracture - Crack nucleation has been the subject of important contributions in the two last decades. Starting from the double criterion of Leguillon (Eur J Mech A...     

Phenomenological 3D and 1D consistent models for shape-memory alloy materials

The paper deals with the modeling and the development of a numerical procedure for the analysis of shape-memory alloy (SMA) elements in order to predict the main features of SMA devices. A 3D SMA model in the framework of small strain theory is developed starting from the thermo-mechanical model proposed by Souza et al. (Eur J Mech A/Solids 17:789–806, 1998) and modified by Auricchio and Petrini (Int J Numer Methods Eng 55:1255–1284, 2002). The aim of this paper is to propose some more modifications to the original model, to derive its consistent 1D formulation, to clarify the mechanical meaning of the material parameters governing the constitutive model. A robust time integration algorithm is developed in the framework of the finite element method and a new beam finite element is proposed. Some numerical applications and a comparison with experimental data available in literature are carried out in order to assess the ability of the proposed model to describe the SMA behavior.     

Crack tip fields in a viscoplastic solid: monotonic and cyclic loading

The asymptotic stress and strain field near the tip of a plane strain Mode I stationary crack in a viscoplastic material are investigated in this work, using a unified viscoplastic model based on Chaboche (Int J Plast 5(3):247–302, 1989). Asymptotic analysis shows that the near tip stress field is governed by the Hutchinson–Rice–Rosengren (HRR) field (Hutchinson in J Mech Phys Solids 16(1):13–31, 1968; Rice and Rosengren in J Mech Phys Solids 16(1):1–12, 1968) with a time dependent amplitude that depends on the loading history. Finite element analysis is carried out for a single edge crack specimen subjected to a constant applied load and a simple class of cyclic loading history. The focus is on small scale creep where the region of inelasticity is small in comparison with typical specimen dimensions. For the case of constant load, the amplitude of the HRR field is found to vanish at long times and the elastic K field dominates. For the case of cyclic loading, we study the effect of stress ratio on inelastic strain and find that the strain accumulated per cycle decreases with stress ratio.     

Theory and finite element computations of a unified cyclic phase transformation model for monocrystalline materials at small strains

After a survey the refined numerical treatment and verification is presented for a rate-independent macroscopic unified PT material model (including mass conservation with respect to phase fractions and covexified free energy) by Govindjee and Miehe (Comput Methods Appl Mech Eng 191:215–238, 2001) for describing SME and SE effects within a linear kinematic setting. Special attention is given to temperature dependent PTs. The material model was implemented into ABAQUS via the UMAT material interface in 2004. Validation of this PT model is carried out with experimental data supplied by Xiangyang et al. (J Mech Phys Solids 48:2163–2182, 2000), using 3D finite element computations. Experimentally gained material data from different sources are used and numerical results of energy barriers for PTs are given. Another feature is the simulation of suppressed shape memory effects by quasiplastic temperature induced PT. Furthermore, a plane strain problem is treated with comparisons of butterfly shaped expansions of martensitic PT and plastic deformation, correspondingly.     

Failure mechanisms in granular media: a discrete element analysis

This paper attempts to numerically validate the concept of diffuse failure using a discrete element method. First, the theoretical background is reviewed, and it is shown how the kinetic energy of a system, initially at rest after a loading history, is likely to abruptly increase under the effect of disturbances. The vanishing of the second-order work thus constitutes a basic ingredient, related to both the pioneering work of Hill (J Mech Phys Solids (6):236–249, 1958) and the notion of bifurcation applied to geomechanics (Vardoulakis and Sulem in Bifurcation analysis in geomechanics, Chapman & Hall Publisher, London, 1995). Discrete numerical simulations were performed on homogeneous three-dimensional specimens, and the three basic conditions that must be satisfied in order to observe a failure mechanism are numerically checked. Finally, this work illustrates the phenomena that are likely to affect in situ slopes, for instance, when the loading (due to weather conditions or human activities) meets the three basic conditions for a failure mechanism to develop.     

The effects of shear and near tip deformations on energy release rate and mode mixity of edge-cracked orthotropic layers

In this paper semi-analytical expressions are derived for the energy release rate and the stress intensity factors of edge-cracked homogeneous and orthotropic layers subject to arbitrary generalized end forces. The expressions are accurate for long and short cracks. Following the work of Li et al. [Li S, Wang J, Thouless MD. The effects of shear on delamination in layered materials. J Mech Phys Solids 2004;52(1):193-214] for isotropic bi-material layers, the derivation extends the method proposed by Suo [Suo ZG. Delamination specimens for orthotropic materials. J Appl Mech 1990;57(3):627-34] for axial forces and bending moments in order to include the contribution of the shear forces. The shear contribution to the fracture parameters depends on the shear deformations along the layer and the elastic near tip deformation of the material. Li et al. [Li S, Wang J, Thouless MD. The effects of shear on delamination in layered materials. J Mech Phys Solids 2004;52(1):193-214] derived semi-analytical expressions for the fracture parameters that depend on the crack tip stress resultants, the elastic constants and five numerically-determined constants globally describing the effect of shear. In this paper analogous constants are derived for orthotropic layers and defined by semi-analytical expressions that highlight their physical significance and allow separation of the different contributions. The derivation is based on the assumption that the near tip deformation can be described by means of relative rotations between the cross sections of the different sub-layers at the crack tip (root rotations). The root rotations depend linearly on the crack tip stress resultants through compliance coefficients that are derived numerically in the paper for a wide range of orthotropic materials. Applications to different mixed mode delamination and peeling problems, for which accurate two-dimensional finite element solutions can be found in the literature, highlight the accuracy of the proposed expressions.     

Interaction of dynamic mode-I cracks with inclined interfaces

In this paper, we report on an experimental study of the deflection/penetration behavior of dynamic mode-I cracks propagating at two different crack velocities (slower and faster) toward inclined weak interfaces of three dissimilar angles (α): 30°, 45° and 60°. A simple wedge-loading specimen configuration as proposed by Xu et al. [Xu LR, Huang YY, Rosakis AJ. Dynamic crack deflection and penetration at interface in homogenous materials: experimental studies and model predictions. J Mech Phys Solids 2003;51:461-86], made of brittle Homalite-100, is used. A modified Hopkinson bar setup is used to achieve well-controlled impact loading conditions. Dynamic photoelasticity in conjunction with high-speed photography is used to capture real-time isochromatics associated with deflected/penetrated cracks.     

A combined dislocation—cohesive zone model for fracture in a confined ductile layer

The collective dislocation behavior near a crack tip in a ductile layer sandwiched between two brittle solids is analyzed via two-dimensional dislocation dynamics (DD) simulations that incorporate a cohesive zone (CZ) model. The cohesive crack tip is treated as part of a much larger finite crack confined in the ductile layer. The underlying boundary value problem is formulated with a set of boundary integral equations and numerically evaluated with a collocation method. The fracture energy of the layered composite material is shown to be strongly correlated with the layer thickness and is directly influenced by the cohesive strength of the ductile layer (Hsia KJ et al. (1994) J Mech Phys Solids 6 877–896).     

Introduction of damage evolution in a scale transition approach for highly-filled particulate composites

The present paper deals with a non-conventional scale transition for modelling the behaviour of highly-filled particulate composites, starting from a methodology initially proposed by Christoffersen [Christoffersen J. Bonded granulates. J Mech Phys Solids 1983;31:55–83] and recently extended by Nadot et al. [Nadot C, Dragon A, Trumel H, Fanget A. Damage modelling framework for viscoelastic particulate composites via a scale transition approach. J Theor Appl Mech 2006;44(3):553–83] in presence of damage. The model thus obtained is here completed with several ingredients allowing to describe damage evolution and in particular a defect nucleation criterion as well as a closure criterion. These criteria are formulated in terms of displacement, and so as to ensure continuity in terms of macroscopic stress. They are finally introduced in an iterative numerical solving procedure which allows to follow damage evolution as a discrete sequence of interfacial debonding including also eventual closure of defects.     

Elastic property prediction by finite element analysis with random distribution of materials for tungsten/silver composite

In the present numerical study, we introduce a finite element analysis for heterogeneous materials via a random distribution of materials to predict effective elastic properties. With this random distributing strategy, a large scale parametric analysis via finite element becomes feasible for the multi-phase heterogeneous solids. Taking a well-documented tungsten–silver bi-continuous material as an example, the numerical prediction provided here for the effective properties is checked by experimental testing data available in open publication. Discussions on the present finite element prediction and other approaches are also made by comparing with Hashin and Shtrikman (J Mech Phys Solids 11:127–140, 1963) bounds in the composite mechanics.     

Crack deflection in a biaxial stress state

Cotterell and Rice theory (Int J Fract 16(2):155–169, 1980) on the kinking of a crack submitted to a biaxial loading in a homogeneous material is revisited. Using both an energetic and a stress fracture criteria (Leguillon, Eur J Mech A/Solids 21:61–72, 2002) allows defining a positive threshold of the T-stress T _c below which no branching can occur (Selvarathinam and Goree, Eng Fract Mech 60(5–6):543–561, 1998) provided the inhomogeneities size is small compared to the Irwin length. The absence of such a threshold would definitely condemn experimental procedures like the double-cantilever beam (DCB) or compact tension (CT) tests, which result in a positive T-stress at the crack tip. The stress intensity factors K _I and T are computed using a contour integral. Calculations provide a very good agreement with the analytical results of the infinite Centrally Notched (CN) plate in tension for instance. An asymptotic analysis makes it possible to define the branching angle as a discontinuous function of T with a jump from 0° to some significant positive value as T reaches T _c . Furthermore, for non vanishing K _II , a similar analysis is carried out, a positive T-stress increases the kinking angle due to K _II alone.     

A criterion for brittle fracture in U-notched components under mixed mode loading

A failure criterion is proposed for brittle fracture in U-notched components under mixed-mode static loading. The criterion, called UMTS, is developed based on the maximum tangential stress criterion and also a criterion proposed in the past for mode I failure of rounded V-shaped notches [Gomez FJ, Elices M. A fracture criterion for blunted V-notched samples. Int J Fracture 2004;127:239-64]. Using the UMTS criterion, a set of fracture curves are derived in terms of the notch stress intensity factors. These curves can be used to predict the mixed mode fracture toughness and the crack initiation angle at the notch tip. An expression is also obtained from this criterion for predicting fracture toughness of U-notched components in pure mode II loading. It is shown that there is a good agreement between the results of UMTS criterion and the experimental data obtained by other authors from three-point bend specimens.     

On Comparison of Experiment and Theory for Ultrasonic Attenuation in Polycrystalline Niobium

In this communication comparison of experimental attenuation results in polycrystalline niobium (Zeng et al., J. Nondestruct. Eval. 29:93–103, 2010) with scattering-induced attenuation models is reexamined. Reasonable agreement is found between those results and the standard Stanke and Kino model (in J. Acoust. Soc. Am. 75:665–681, 1984) contradicting the conclusions of Zeng et al.     

Analysis of in-plane transonically propagating interface crack with a finite contact zone

The report of Lambros and Rosakis [(1995) J Mech Phys Solids 43(2): 169–188] has focused attention on steady-state transonic interfacial crack growth accounting for the phenomenon of crack face contact in elastic/rigid bimaterial but could not handle issues relating to energy transmission across the interface. The present paper attempts to provide a complete explicit expression of the asymptotic fields induced by transonically propagating interfacial crack in elastic/elastic bimaterial for in-plane case. The energy distribution on the contact area, crack tip and two singular characteristic lines is analysed thoroughly and compared with the dynamic separated J-integrals. The length of the contact zone is also discussed briefly by establishing energy fracture criterion that satisfies contact condition. The two-dimensional in-plane asymptotic deformation field surrounding the contact area of a crack propagating transonically along an elastic/elastic bimaterial interface is observed and discussed thoroughly.     

The resistance curve for subcritical cracks near the threshold

Thermodynamic analysis of brittle fracture specimens near the threshold developed by Rice (Thermodynamics of quasi-static growth of Griffith cracks, J Mech Phys Solid 26:61–78, 1978) is extended to specimens undergoing microstructural changes. The proposed extension gives rise to a generalization of the threshold concept that mirrors the way the resistance curve generalizes the fracture toughness. In the absence of experimental data, the resistance curve near the threshold is constructed using a basic lattice model.     

A variational void coalescence model for ductile metals

We present a variational void coalescence model that includes all the essential ingredients of failure in ductile porous metals. The model is an extension of the variational void growth model by Weinberg et al. (Comput Mech 37:142–152, 2006). The extended model contains all the deformation phases in ductile porous materials, i.e. elastic deformation, plastic deformation including deviatoric and volumetric (void growth) plasticity followed by damage initiation and evolution due to void coalescence. Parametric studies have been performed to assess the model’s dependence on the different input parameters. The model is then validated against uniaxial loading experiments for different materials. We finally show the model’s ability to predict the damage mechanisms and fracture surface profile of a notched round bar under tension as observed in experiments.     

Slip modes and partitioning of energy during dynamic frictional sliding between identical elastic–viscoplastic solids

The effect of plasticity on dynamic frictional sliding along an interface between two identical elastic–viscoplastic solids is analyzed. The configuration considered is the same as that in Coker et al. (J Mech Phys Solids 53:884–992, 2005) except that here plane strain analyses are carried out and bulk material plasticity is accounted for. The specimens have an initial compressive stress and are subject to shear loading imposed by edge impact near the interface. The material on each side of the interface is modeled as an isotropically hardening elastic–viscoplastic solid. The interface is characterized as having an elastic response together with a rate- and state-dependent frictional law for its inelastic response. Depending on bulk material properties, interface properties and loading conditions, frictional slip along the interface can propagate in a crack-like mode, a pulse-like mode or a train-of-pulses mode. Results are presented for the effect of material plasticity on the mode and speed of frictional slip propagation as well as for the partitioning of energy components between stored elastic energy, kinetic energy, plastic dissipation in the bulk and frictional dissipation along the interface. Some parameter studies are carried out to explore the effects of varying the interface elastic stiffness and the impact velocity.