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Showing papers on "Crack closure published in 2000"


Journal ArticleDOI
TL;DR: In this article, a two-dimensional model of a film bonded to an elastic substrate is proposed for simulating crack propagation paths in thin elastic films and the existence of spiral paths is demonstrated.
Abstract: A two-dimensional model of a film bonded to an elastic substrate is proposed for simulating crack propagation paths in thin elastic films. Specific examples are presented for films subject to equi-biaxial residual tensile stress. Single and multiple crack geometries are considered with a view to elucidating some of the crack patterns which are observed to develop. Tendencies for propagating cracks to remain straight or curve are explored as a consequence of crack interaction. The existence of spiral paths is demonstrated.

352 citations


Journal ArticleDOI
TL;DR: In this article, a crystallographic model is proposed which takes into account both crack-plane twist and tilt effects on crack retardation at grain boundaries, and studies of short fatigue crack growth in an Al-Li 8090 alloy plate provide evidence that supports the model.

336 citations


01 Jan 2000
TL;DR: In this paper, the authors explain from fracture mechanics principles that the common size e•ect observed in fracturetoughness and energy measurements of many engineering materials including concrete, reinforced composites and even coarse-grained ceramics are in fact similar to what has been observed in the well-studied elastic-plasticfracture of metals.
Abstract: This study explains from the fracture mechanics principles that the common size e•ect observed in fracturetoughness and energy measurements of many engineering materials including concrete, fiber reinforced compositesand even coarse-grained ceramics are in fact similar to what has been observed in the well-studied elastic–plasticfracture of metals. The conditions required for measurements of the material constant, the plane strain fracturetoughness K IC , of metals are akin to those required to avoid such a size e•ect on the fracture toughness and energyof concrete and other composites. Using the common yield strength and plain strain fracture toughness criteria areference crack length a is defined in this study, which is then used to introduce a simple asymptotic function. Theasymptotic analysis shows that the size e•ect on fracture toughness and energy of a heterogeneous material such asconcrete will be inevitable if the relative crack measured by the crack ratio a=a or the remaining ligament ratio–Wyaƒ=a is too close to one. This relative crack needs to be around 10 or even higher to avoid the size e•ectinfluence. Experimental results and previous models are compared with the current asymptotic analysis. # 2000Elsevier Science Ltd. All rights reserved.

225 citations


Journal ArticleDOI
TL;DR: In this article, the authors used edge cracks by edge impact (LECEI) for generating high rates of crack tip shear (mode-II) loading and showed that the energy consumption of a mode-II crack tip stress field is larger than an equivalent mode-I crack tip field, and the remaining driving energy for any failure process is higher than for the case of equivalent failure initiation conditions.
Abstract: The technique of loading edge cracks by edge impact (LECEI) for generating high rates of crack tip shear (mode-II) loading is presented. The LECEI-technique in combination with a gas gun for accelerating the impactor is used to study the high rate shear failure behaviour of three types of materials. Epoxy resin (Araldite B) shows failure by tensile cracks up to the highest experimentally achievable loading rate; steel (high strength maraging steel X2 NiCoMo 18 9 5) shows a failure mode transition: at low rates failure occurs by tensile cracks, at higher rates, above a certain limit velocity, failure by adiabatic shear bands is observed; aluminum alloy (Al 7075) shows failure due to shear band processes in the high rate regime, but this failure mode is observed over the entire range of lower loading rates, even down to quasi-static conditions. Characteristics of the failure modes are presented. When transitions are observed in the failure process from tensile cracks to shear bands the limit velocity for failure mode transition depends on the bluntness of the starter crack the failure is initiated from: The larger the bluntness of the starter crack the higher the critical limit velocity for failure mode transition. The data indicate that adiabatic shear bands require and absorb more energy for propagation than tensile cracks. Aspects of the energy balance controlling mode-II instability processes in general are considered. Effects very different than for the mode-I instability process are observed: When failure by a tensile crack occurs under mode-II initiation conditions, a notch is formed between the initiated kinked crack and the original starter crack, and, at this notch a compressive stress concentration builds up. The energy for building up this stress concentration field is not available for propagation of the initiated kinked crack. The energy density of a mode-II crack tip stress field, however, when compared to an equivalent mode-I crack tip field, is considerably larger, and, consequently, the remaining driving energy for any mode-II initiated failure process, nevertheless, is higher than for the case of equivalent mode-I initiation conditions. Furthermore, mode-II crack tip plastic zones are considerably larger than equivalent mode-I crack tip plastic zones. Consequently, validity conditions for linear-elastic or small scale yielding failure behaviour are harder to fulfill and possibilities for the activation of nonlinear high energy ductile type failure processes are enhanced. Speculations on how these effects might favour failure by high energy processes in general and by shear bands processes in particular for conditions of high rate shear mode-II loading are presented.

210 citations


Journal ArticleDOI
TL;DR: A fracture mechanics study of cortical bone is presented to investigate the contribution, development morphology of microcracking in cortical bone during crack propagation and provides a detailed account of mocrocrack formation and contribution towards the propagation of a fracture crack.

201 citations


Journal ArticleDOI
TL;DR: In this article, the authors evaluated the effect of various fatigue parameters on the onset of crack initiation in a component subjected to constant amplitude plain fatigue and found that the maximum strain amplitude at the contact interface was an important parameter for fretting fatigue crack initiation.

172 citations


Journal ArticleDOI
TL;DR: In this paper, mixed-mode crack tip deformations and fracture parameters in glass-filled epoxy beams with cracks normal to the elastic gradient were studied and a companion finite element model was developed and validated by the measurements.

169 citations


Journal ArticleDOI
TL;DR: In this paper, the authors used a cohesive zone model to simulate the micromechanical process of void growth and coalescence of voided cells and showed that the cohesive zone parameters for ductile tearing, cohesive strength and energy, are generally dependent on the amount of crack growth, specimen geometry and size.

169 citations


Journal ArticleDOI
TL;DR: In this article, a small scale yielding around a plane strain mode I crack is analyzed using discrete dislocation dynamics, where the dislocations are all of edge character, and are modeled as line singularities in an elastic material.
Abstract: Small scale yielding around a plane strain mode I crack is analyzed using discrete dislocation dynamics. The dislocations are all of edge character, and are modeled as line singularities in an elastic material. At each stage of loading, superposition is used to represent the solution in terms of solutions for edge dislocations in a half-space and a complementary solution that enforces the boundary conditions. The latter is non-singular and obtained from a finite element solution. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation are incorporated into the formulation through a set of constitutive rules. A relation between the opening traction and the displacement jump across a cohesive surface ahead of the initial crack tip is also specified, so that crack growth emerges naturally from the boundary value problem solution. Material parameters representative of aluminum are employed. For a low density of dislocation sources, crack growth takes place in a brittle manner; for a low density of obstacles, the crack blunts continuously and does not grow. In the intermediate regime, the average near-tip stress fields are in qualitative accord with those predicted by classical continuum crystal plasticity, but with the local stress concentrations from discrete dislocations leading to opening stresses of the magnitude of the cohesive strength. The crack growth history is strongly affected by the dislocation activity in the vicinity of the growing crack tip.

158 citations


Journal ArticleDOI
TL;DR: In this paper, the authors show that finite element analyses using standard fatiguedamage formulations exhibit an extreme sensitivity to the spatialdiscretisation of the problem, which is caused by the fact that the underlying continuum model predicts instantaneous, perfectly brittle crack growth as soon as a crack has been initiated.
Abstract: Continuum damage mechanics can be used to model the initiation and growthof fatigue cracks. However, finite element analyses using standard fatiguedamage formulations exhibit an extreme sensitivity to the spatialdiscretisation of the problem. The mesh sensitivity is caused by the factthat the underlying continuum model predicts instantaneous, perfectlybrittle crack growth as soon as a crack has been initiated. The growth ofdamage localises in a vanishing volume during this instantaneous growth.This localisation is not so much due to loss of ellipticity of theproblem, but is caused by the fact that the damage rate is singular at thecrack tip. The damage rate singularity can be removed by the introductionof higher-order deformation gradients in the constitutive modelling. As aresult, crack growth at a finite rate and with ! a positive amount of energydissipation is predicted. Finite element analyses converge to thissolution and are thus no longer pathologically dependent on the spatialdiscretisation.

149 citations


Journal ArticleDOI
TL;DR: In this article, the authors used the indentation quench method to explore susceptibility to thermal fracture in a range of brittle materials on condition that it is possible to insert an indentation precrack.

Journal ArticleDOI
TL;DR: In this article, a path independent J integral for a crack in a residual stress field is obtained and the modified J is equivalent to the stress intensity factor, K, under small scale yielding conditions and provides the intensity of the near crack tip stresses under elastic-plastic conditions.
Abstract: The standard definition of the J integral leads to a path dependent value in the presence of a residual stress field, and this gives rise to numerical difficulties in numerical modelling of fracture problems when residual stresses are significant. In this work, a path independent J definition for a crack in a residual stress field is obtained. A number of crack geometries containing residual stresses have been analysed using the finite element method and the results demonstrate that the modified J shows good path-independence which is maintained under a combination of residual stress and mechanical loading. It is also shown that the modified J is equivalent to the stress intensity factor, K, under small scale yielding conditions and provides the intensity of the near crack tip stresses under elastic-plastic conditions. The paper also discusses two issues linked to the numerical modelling of residual stress crack problems-the introduction of a residual stress field into a finite element model and the introduction of a crack into a residual stress field.

Journal ArticleDOI
TL;DR: In this paper, the effects of residual stresses arising from thermal expansion mismatch are taken into account, and a series of very useful inter-relationships between thermo-elastic constants for damaged and corresponding undamaged laminates are derived.

Journal ArticleDOI
TL;DR: In this article, the authors explored key computational issues that aAect analyses employing the computational cell methodology to predict crack growth in ductile metals caused by void growth and coalescence.

Journal ArticleDOI
TL;DR: In this article, the role of simulated FOD in affecting the initiation and early growth of small surface fatigue cracks in a Ti-6Al-4V alloy, processed for typical turbine blade applications was investigated.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the tensile strain relaxation in AlxGa1−xN layers of different compositions epitaxially grown on GaN/sapphire.
Abstract: Relaxation of tensile strain in AlxGa1−xN layers of different compositions epitaxially grown on GaN/sapphire is investigated. Extended crack channels along 〈211¯0〉 directions are formed if the aluminum content exceeds a critical value, which decreases with increasing layer thickness. This process is found to limit the average strain energy density to a maximum value of 4 J/m2. By calculating the stress distribution between cracks and the strain energy release rate for crack propagation, the relaxed strain as measured by x-ray diffraction is correlated to the crack density, and the onsets of crack channeling and layer decohesion are fitted to a fracture toughness of 9 J/m2. Moreover, the crack opening at the surface is found to linearly increase with the stress. Annealing of samples above the growth temperature introduces additional tensile stress due to the mismatch in thermal expansion coefficients between the layer and substrate. This stress is shown to relieve not only by the formation of additional cr...

Journal ArticleDOI
Pommier1, Bompard1
TL;DR: In this paper, the effect of overloads, underloads and stress ratio on plasticity-induced crack opening level was examined for different'model' materials for different finite element analyses were conducted using ABAQUS.
Abstract: The effect of overloads, underloads and stress ratio on plasticity-induced crack opening level is examined for different ‘model’ materials. This study is focused on the consequences of the Bauschinger effect on the crack opening level. Various finite element analyses were conducted using ABAQUS to test these effects, involving the Chaboche constitutive equations that take into account both the Bauschinger effect of the material and its cyclic hardening or softening. The cyclic plastic behaviour of the material is found to strongly affect the crack behaviour after an overload or an underload. The experimental data obtained on a 0.4% carbon mild steel confirm the numerical results.

Journal ArticleDOI
TL;DR: In this paper, the authors evaluated the roughness of the fracture surface of acrylamide gels and measured the fracture energy taking into account of roughness to clarify the effects of crack speed and cross-link density on fracture energy.
Abstract: To clarify effects of crack speed and cross-link density on the fracture energy of acrylamide gels, we evaluated the roughness of the fracture surface and measured the fracture energy taking into account the roughness. The fracture energy increases linearly with crack speed Vin a fast crack speed region, and the increasing rate of fracture energy with V decreases with increasing cross-link density in the gels. In a slow crack speed region the fracture energy depends on crack speed more strongly than in the fast crack speed region. This indicates that a qualitative change exists in the fracture process of the gels.

Journal ArticleDOI
TL;DR: In this paper, the multiscale nature of cracking in ferroelectric ceramics is explored in relation to the crack growth enhancement and retardation behavior when the direction of applied electric field is reversed with reference to that of poling.


Journal ArticleDOI
TL;DR: In this paper, the problem of a fatigue crack approaching an interface in a bi-material and an interlayer is investigated, and it is shown that the bifurcation of the crack in the vicinity of the interface occurs when the crack propagates from the weak to the strong material, and the relatively large effect of the extremely small thermal mismatch on the crack propagation behavior.
Abstract: The problem of a fatigue crack approaching an interface in a bi-material and an interlayer is experimentally investigated. Cracks propagating perpendicular to the sharp ferritic steel – ferritic steel interface are studied. The elastic and thermal expansion properties are nearly identical, only the plastic properties are different. The previously reported, theoretically predicted slowdown of the growth rate in the case of a weak/strong transition and the acceleration in the case of a strong/soft transition are verified. Two surprising results are: the bifurcation of the crack in the vicinity of the interface when the crack propagates from the weak to the strong material, and the relatively large effect of the extremely small thermal mismatch on the crack propagation behavior.

Journal ArticleDOI
TL;DR: In this paper, the behavior of concrete subjected to flexural fatigue loading is studied, where the crack propagation caused by quasi-static and fatigue loads is described in terms of fracture mechanics.
Abstract: In this paper the behavior of concrete subjected to flexural fatigue loading is studied. Notched concrete beams were tested in a three-point bending configuration. Specimens were subjected to quasi-static cyclic and constant amplitude fatigue loading. The cyclic tests were performed by unloading the specimen at different points in the postpeak part of the quasi-static loading response. Low cycle, high amplitude fatigue tests were performed to failure using four different load ranges. The crack mouth opening displacement was continuously monitored throughout the loading process. Crack propagation caused by quasi-static and fatigue loads is described in terms of fracture mechanics. It is shown that the crack propagation in the postpeak part of the quasi-static load response is predicted using the critical value of the mode I stress intensity factor (\IK\DIC\N). The ultimate deformation of the specimen during the fatigue test is compared with that from the quasi-static test; it is demonstrated that the quasi-static deformation is insufficient as a fatigue failure criterion. It is observed that crack growth owing to constant-amplitude fatigue loading comprises two phases: a deceleration stage where there is a decrease in crack growth rate with increasing crack length, followed by an acceleration stage where the rate of crack growth increases at a steady rate. The crack length where the rate of crack growth changes from deceleration to acceleration is shown to be equal to the crack length at the peak load of the quasi-static response. Analytical expressions for crack growth in the deceleration and acceleration stages are developed, wherein the expressions for crack growth rate in the deceleration stage are developed using the \iR-curve concept, and the acceleration stage is shown to follow the Paris law. It is observed that the crack length at failure for constant amplitude fatigue loading is comparable to that of the corresponding load in the postpeak part of the quasi-static response. Finally, a fracture-based fatigue failure criterion is proposed.

Journal ArticleDOI
TL;DR: In this article, the authors developed a damage model for concrete materials exhibiting a residual hysteretic behavior at a fixed level of damage, which is obtained by coupling damage mechanics and friction phenomena.
Abstract: This paper is concerned with the development of a damage model for concrete materials exhibiting a residual hysteretic behaviour at a fixed level of damage. This feature is obtained by coupling damage mechanics and friction phenomena. In its complete form, the damage variable by means of which the stiffness decrease is obtained in an orthotropic second-order tensor. Its evolution is governed by the tensile part of the strain tensor. The sliding between the crack lips is assumed to have a plasticity-like behaviour with non-linear kinematic hardening. The sliding stress depends on the level of damage. Such a model assumes the evolution of two yield surfaces: a fracture one and a sliding one. If unilateral effects need to be taken into account for cyclic loading analysis (crack closure modelling), the damage evolution remains isotropic. The effectiveness of this model in reproducing a part of damping when subjected to dynamic loading is exemplified through two structural case studies. Copyright © 2000 John Wiley & Sons, Ltd.

Journal ArticleDOI
TL;DR: In this article, the authors derived analytical expressions to quantify the effect and evaluate the effective crack driving force for smooth and abrupt variations in yield stress, which can be used to optimize graded materials and interface and interlayer transitions so that the fracture resistance increases.

Journal ArticleDOI
TL;DR: In this paper, the interaction between a semi-infinite crack and a screw dislocation under antiplane mechanical and in-plane electrical loading in a linear piezoelectric material is studied in the framework of linear elasticity theory.
Abstract: The interaction between a semi-infinite crack and a screw dislocation under antiplane mechanical and in-plane electrical loading in a linear piezoelectric material is studied in the framework of linear elasticity theory. A straight dislocation with the Burgers vector normal to the isotropic basal plane near a semi-infinite crack tip is considered. In addition to having a discontinuous electric potential across the slip plane, the dislocation is subjected to a line-force and a line-charge at the core. The explicit solution for the model is derived by means of complex variable and conformal mapping methods. The classical 1/√r singularity is observed for the stress, electric displacement, and electric field at the crack tip. The force on a screw dislocation due to the existence of a semi-infinite crack subjected to external electromechanical loads is calculated. Also, the effect of the screw dislocation with the line-force and line-charge at the core on the crack-tip fields is observed through the field intensity factors and the crack extension force.

Journal ArticleDOI
TL;DR: In this paper, the mechanisms of fatigue-crack propagation in ceramics and intermetallics are examined through a comparison of cyclic crack-growth behavior in ductile and brittle materials.

Journal ArticleDOI
TL;DR: In this paper, the macroscopic work of fracture of the material is computed as a function of the crack velocity and the parameters characterizing the fracture process zone and the solid.

Journal ArticleDOI
TL;DR: In this paper, a linear elastic model of the stress concentration due to contact between a rounded flat punch and a homogeneous substrate is presented, with the aim of investigating fretting fatigue crack initiation in contacting parts of vibrating structures including turbine engines.
Abstract: A linear elastic model of the stress concentration due to contact between a rounded flat punch and a homogeneous substrate is presented, with the aim of investigating fretting fatigue crack initiation in contacting parts of vibrating structures including turbine engines. The asymptotic forms for the stress fields in the vicinity of a rounded punch-on-flat substrate are derived for both normal and tangential loading, using both analytical and finite element methods. Under the action of the normal load, P, the ensuing contact is of width 2b which includes an initial flat part of width 2a. The asymptotic stress fields for the sharply rounded flat punch contact have certain similarities with the asymptotic stress fields around the tip of a blunt crack. The analysis showed that the maximum tensile stress, which occurs at the contact boundary due to tangential load Q, is proportional to a mode II stress intensity factor of a sharp punch divided by the square root of the additional contact length due to the roundness of the punch, Q/(√(b − a)√πb). The fretting fatigue crack initiation can then be investigated by relating the maximum tensile stress with the fatigue endurance stress. The result is analogous to that of Barsom and McNicol where the notched fatigue endurance stress was correlated with the stress intensity factor and the square root of the notch-tip radius. The proposed methodology establishes a ‘notch analogue’ by making a connection between fretting fatigue at a rounded punch/flat contact and crack initiation at a notch tip and uses fracture mechanics concepts. Conditions of validity of the present model are established both to avoid yielding and to account for the finite thickness of the substrate. The predictions of the model are compared with fretting fatigue experiments on Ti–6Al–4V and shown to be in good agreement.

Journal ArticleDOI
TL;DR: In this paper, a finite element finite element (FE) model was built to simulate fatigue crack closure behavior in polycarbonate polysilicon. But the model was not applied to analyze the crack growth rate.

Book
24 Jan 2000
TL;DR: In this paper, the authors proposed a method to estimate the fracture toughness of a plane strain fracture by measuring the growth rate of fatigue crack. But the method was not suitable for the case of small scale yielding cracks.
Abstract: Introduction: Summary References Fracture toughness: Introduction Energy approach to brittle fracture Stress intensity factors Some Mode I stress intensity factor solutions Limitations of the stress intensity factor approach Effects of small scale yielding Slant crack growth in thin sheets Effect of thickness on fracture toughness Effect of notch acuity on fracture toughness R-curves General yielding fracture mechanics Summary References. Plane strain fracture toughness testing: Introduction Specimen types Offset procedure Fatigue precracking Specimen size requirements Klc- Charpy correlations Chevron notch tests Summary References. Fatigue crack growth: Introduction Use of stress intensity factors Fatigue crack growth rate data Mechanisms of fatigue crack growth Threshold for fatigue crack growth Overall fatigue crack growth behaviour Crack closure Short cracks Fatigue crack growth under variable amplitude loading Weighted average stress range Cycle counting Summary References. Fatigue crack growth testing: Introduction Specimen types Specimen size requirement Fatigue precracking Crack path requirement Data reduction The threshold and near threshold crack growth rates Summary References. Fatigue crack paths: Introduction Crack path stability in two dimensions Crack growth from an initial mixed Modes I and II crack Constraints on crack paths in three dimensions Constraints on crack fronts in three dimensions Mode I crack growth in three dimensions Slant crack growth in thin sheets Summary References. Applications: Introduction Modelling of irregular cracks Static failure Constant amplitude fatigue crack growth Variable amplitude fatigue crack growth Proof test logic Leak-before-break Summary References.