Showing papers in "International Journal of Fracture in 1990"

Interface crack between two elastic layers

Abstract: A semi-infinite interface crack between two infinite isotropic elastic layers under general edge loading conditions is considered. The problem can be solved analytically except for a single real scalar independent of loading, which is then extracted from the numerical solution for one particular loading combination. Two applications of the basic solution are made which illustrate its utility: interface cracking driven by residual stress in a thin film on a substrate, and an analysis of a test specimen proposed recently for measuring interface toughness.

Determination of fracture energy, process zone longth and brittleness number from size effect, with application to rock and conerete

Abstract: The dependence of the fracture energy and the effective process zone length on the specimen size as well as the craek extension from the notch is analyzed on the basis of Ba

An analysis of decohesion along an imperfect interface

Abstract: A cohesive zone type interface model, taking full account of finite geometry changes, is used to study the decohesion of a viscoplastic block from a rigid substrate. The specific boundary value problem analyzed is a plane strain one with the imposed loading corresponding to overall uniaxial straining. The imperfection takes the form of a non-bonded portion of the interface. Dimensional considerations introduce a characteristic length into the formulation and the decohesion mode shifts from more or less uniform separation along the bond line to crack-like propagation as the ratio of block size to characteristic length increases. Field distributions prior to and accompanying propagation are displayed.

Dynamic fracture initiation and propagation in 4340 steel under impact loading

Abstract: Dynamic fracture initiation and propagation in 4340 steel was investigated experimentally using the optical method of reflected caustics combined with high speed photography. A new crack propagation testing configuration consisting of a three point bend specimen loaded in a drop weight tower was used. It was found that prior to crack initiation the stress intensity factor time record calculated using the dynamic tup load and a static formula disagrees with the actual stress intensity factor measured by caustics. During crack propagation, the crack tip velocity and stress intensity factor time records varied smoothly and repeatably allowing for a straightforward interpretation of the data. The experiments show that for the particular heat treatment of 4340 steel used, the dynamic fracture propagation toughness depends on crack tip velocity through a relation that is a material property.

Crack tip fields in ductile crystals

Abstract: Results on the asymptotic analysis of crack tip fields in elastic-plastic single crystals are presented and some preliminary results of finite element solutions for cracked solids of this type are summarized In the cases studied, involving plane strain tensile and anti-plane shear cracks in ideally plastic f c c and b c c crystals, analyzed within conventional small displacement gradient assumptions, the asymptotic analyses reveal striking discontinuous fields at the crack tip

Interlaminar shear fracture of laminated composites

Abstract: The interlaminar fracture toughness in mode II and mode III of a number of advanced composites was studied using beam type test specimens and scanning electron microscopy. Special emphasis was placed on elucidating the material aspects of the fracture process and on quantifying the effect of matrix on fracture energy. The fracture energy in mode II was independent of crack extension while that for mode III exhibited a rather probablistic “resistance” behavior that was attributed to the effect of fiber bridging. The initiation fracture energy, considered here the true measure of G IIIC , coincided with G IIC . For either mode, the interlaminar region ahead of the crack tip exhibited considerable plastic deformations, the severity that is believed to control the laminate toughness. The interlaminar fracture energy in shear, hereby denoted as G SC (=G IIC =G IIIC ), was accurately predicted from a straightforward adhesive joint fracture test provided the adhesive thickness coincide with the thickness of the interlaminar resin layer.

Three-dimensional fracture analysis of thin-film debonding

Abstract: A simplified mixed-mode fracture analysis combining nonlinear thin-plate stress solutions with crack-tip elasticity results has been developed to account for local variations of G I, G II and G III in thin-film debond problems associated with large film deformations. Membrane and bending stresses from the plate analysis are matched with the crack-tip singularity solution over a small boundary region at the crack tip where the effect of geometric nonlinearity is small. Local variations in each of the individual components of the energy release rate are directly related to the “jump” in these stresses across the crack border. Specific results are presented for 1-D and elliptical planeform cracks. Deformations were induced either by a pressure acting normal to the film surface or biaxial compression or tension stresses applied to the substrate in which the loading axes and debond axes coincide. The latter type of loading involves buckling of the delaminated film. The model predictions compare well with more rigorous solutions provided the film thickness is small compared to the debond dimensions. In all cases analyzed, G III was negligible. The ratio G I/G II typically decreases with increasing load or film deformation, the rate was moderate for pressure loading while generally sharp for compression loading. Film-substrate overlap may occur for certain debond geometry and loading conditions. Prevention of this by the substrate may critically increase the energy available for crack propagation.

Micromechanics characterization of sublaminate damage

Abstract: A micromechanics analytical model is developed for characterizing the fracture behaviour of a fibre reinforced composite laminate containing a transverse matrix crack and longitudinal debonding along 0/90 interface. Both the matrix and the fibres are considered as linear elastic. A consistent shear lag theory is used to represent the stress-displacement relations. The governing equations, a set of differential-difference equations, are solved satisfying the boundary conditions appropriate to the damage configuration by making use of an eigenvalue technique. The properties of the constituents appear in the model explicitly. Displacements and stresses in the fibres and the matrix are obtained, and the growth of damage is investigated by using the point stress criterion. The investigation includes fibre stress distribution in zero degree plies, transverse crack and debonding intitiation as functions of laminate geometry, and the effect of fibre breaks in the zero degree ply on damage growth. The predicted damage growth patterns and the corresponding critical strains agree with the finite element and experimental results.

A catastrophe theory approach to fracture mechanics

Abstract: A cohesive crack model is applied to analyze the crack stability in elastic-softening materials. The shape of the global load-displacement response changes substantially by varying size-scale and keeping the geometrical shape of the structure unchanged. The softening branch becomes steeper and when the size-scale increases. A critical size-scale does exist for which the softening slope is infinite. In such a case, the load carrying capacity drastically decreases for relatively small displacement increments. Then, for larger size-scales, the softening slope becomes positive and a cusp catastrophe appears. It is proved that such a bifurcation point can be revealed by the simple LEFM condition.

Micro-mechanics of crack initiation

Abstract: Prior to the crack initiation, damage is most often localized at a scale below the size of the classical representative volume element of the continuum mechanics. This allows the stress and strain analyses in a component to neglect the strain-damage coupling at macro-scale. At the micro-scale, this coupling plays a very important role which can be emphasized by a two scale element of an elastoplastic damaged micro-element embedded in an elastic or elastoplastic macro-element. The Lin-Taylor hypothesis of strain compatibility allows the determination of the damage at micro-scale by solving the coupled constitutive equations for a given macro-strain history. It is shown how this model may be cast in the form of a post-processor of a finite element code and how a simple damage law coupled with strain constitutive equations replicates the main features of ductile or creep crack initiation, low cycle and high cycle fatigue for the case of a three-dimensional state of stress.

Large crack tip opening in thin elastic-plastic sheets

Abstract: Large deformation, three-dimensional finite element analysis has been used to study the blunting of a mode I crack tip in a thin elastic-plastic sheet. The near tip stress and deformation fields were analyzed, and the results compared with two-dimensional plane stress solutions. A double shear band was found ahead of the crack tip which created a three-dimensional zone extending several sheet thicknesses before the crack. This mechanism leads to an irregular blunt tip shape at the midplane of the sheet. Distinct differences in crack tip shape and the deformation fields were found between the perfect plasticity solution and the strain hardening solution. The analysis was also compared with experimental results obtained by other investigators.

Behavior of indentation cracks near free surfaces and interfaces

Abstract: The purpose of this research was to examine problems associated with the propagation of cracks near a free surface and near the interface of a glass/epoxy bonded system. Crack propagation was induced by placing Knoop indentations in the glass at various sites adjacent to and remote from the surface or interface. These experimental studies were supplemented by finite element stress analysis. Experiments show that for an indent parallel to the surface or interface, the initial direction of crack propagation from the indent is always toward the surface or interface and then as the crack approaches the surface or interface, the crack path deviates away from the surface. Results of finite element analysis show that the initial direction of crack propagation is in the direction normal to the maximum principal stress at the crack tip.

Establishing K1c from eccentrically fatigue cracked small circumferentially grooved cylindrical specimens

Abstract: The authors have earlier proposed a practical method of using a small cylindrical circumferentially notched and fatigue cracked specimen to measure K 1c This specimen has a machined “Vee” groove, from the root of which, is grown a fatigue crack using rotating bending This specimen is then broken in tension and K 1c thus established In practice however a significant proportion of the final ligaments after fatigue cracking are eccentric and some are non-circular Finite element analysis has been carried out on a spectrum of final ligament sizes and eccentricities, leading to a relationship for determining K 1c from such eccentrically cracked specimens The results using this relationship are compared with experimental data

Treatment of singularities in cracked bodies

Abstract: Three-dimensional finite-element analyses of middle-crack tension (M-T) and bend specimens subjected to mode I loadings were performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements with collapsed, non-singular elements at the crack front. The displacements and stresses from the analysis were used to estimate the power of singularities using a log-log regression analysis along the crack front. The analyses showed that finite-sized cracked bodies have two singular stress fields. The near-field singular stress has the form σ =C0(θ,z)r-/12' +D0 (0,ϕ)R λ σ The first term is the cylindrical singularity with the power -1/2 and is dominant over the middle 96 percent (for Poisson's ratio = 0.3) of the crack front and becomes nearly zero at the free surface. The second singularity is a vertex singularity with the vertex point located at the intersection of the crack front and the free surface. The second singularity is dominant at the free surface and becomes nearly zero away from the boundary layer. The thickness of the boundary layer depends on Poisson's ratio of the material and is independent of the specimen type. The thickness of the boundary layer was about 0%, 2%, 4%, and 5% of the total specimen thickness for Poisson's ratio of 0.0, 0.3, 0.4, and 0.45, respectively.

A hybridized displacement discontinuity and indirect boundary element method to model fracture propagation

Abstract: In mechanical modelling of fracture propagation, complications arise from the stress concentrations at the fracture tips and nonlinear responses caused by opening/closing of fractures, by nonlinear constitutive relations of fracture surfaces sliding on each other, and by fracture propagation. The hybridized Displacement Discontinuity and Indirect Boundary Element Method described in this paper avoids problems associated with other numerical methods when analyzing fracture propagation. The method, which includes analytical influence functions and thus makes numerical integration unnecessary, is described in the first part of this paper. In the second part a number of examples are given in which a variety of fracture propagation problems in two dimensions are modelled with the hybridized method. These examples include classical problems in which tension is applied to cracked plates but also others where shearing is applied. Comparisons with solutions obtained by other authors are shown to be satisfactory.

Elastic-plastic and asymptotic fields of interface cracks

Abstract: In previous analyses [1, 2, 13], and full-field computational investigations, we found that the near tip plastic fields of cracks on a bimaterial interface do not have a separable form of the HRR type. Nevertheless they appear to be nearly separable in an annular region well within the plastic zone. Asymptotically, as the crack tip is approached, the material system responds like that of a plastically deforming solid bonded to a rigid substrate; in particular, the stress and strain fields in the more compliant (lower hardening) material behave like those of a material with identical plastic properties bonded to a rigid substrate. Furthermore, the asymptotic fields of the interface crack bear strong similarities to mixed mode HRR fields for the homogeneous medium characterized by the plastic properties appropriate to the more (plastically) compliant material. In this investigation, we elucidate the behaviour of the material system over two length scales which are physically relevant, namely, distances comparable to the dominant plastic zone and the crack tip opening displacement. The latter is approximately given by the plastic zone size times and the relevant yield strain. Over length scales comparable to the dominant plastic zone, the stress fields are governed by the characteristics of the weaker (lower yield strength) material. On the other hand, the near tip plastic fields are governed by the strain hardening characteristics of the more plastically compliant (lower hardening) material.

A rate dependent kinetic theory of fracture for polymers

Abstract: In this paper we develop a rate dependent theory of fracture for polymers valid for variable stress histories. The theory is developed within the framework of the kinetic theory of fracture of solids and compared to experiments for variable stress history loadings. A significant aspect of the theory is the introduction of a crack damage state variable which quantifies submicroscopic crack damage prior to macroscopic failure of the material. A first order differential equation governing the time evolution of the crack damage variable is developed based on first principles of statistical physics. The theory is shown to accurately predict the ultimate stress of polymethyl-methacrylate for constant stress rate loadings ranging over 5 orders of magnitude as well as variable stress histories which include creep and stress rate conditions. Furthermore, the theory predicts qualitatively correct results for submicrocrack concentration under both constant stress and constant stress rate conditions.

On some path independent integrals and their use in fracture of nonlinear viscoelastic media

Abstract: In certain cases it is possible to construct work potentials and J-like path-independent integrals for monolithic or composite nonlinear viscoelastic media. In this paper we discuss some situations in which such quantities exist and are useful in the study of quasi-static initiation and continuation of crack growth. The so-called quasi-elastic approximation and a constitutive equation in the form of a single hereditary integral provide the basis for using J or J-like integrals as fracture characterizing parameters during initiation and the early stages of crack growth. It is also shown that in some cases with significant crack growth the instantaneous crack speed can be characterized in terms of a similar path-independent integral. The problem of characterizing growth of large cracks in viscoelastic media with micro-damage is discussed briefly.

Stress intensity factor analysis for part-elliptical cracks in structures

Abstract: A method based on the generalized weight function theory is used for solving three-dimensional linear elastic fracture mechanics problems. A complete system of equations of the weight function method (WFM) has been obtained for the calculation of stress intensity factors (SIF) for part-elliptical cracks subjected to arbitrary normal loading.

Influence of damage on crack-tip fields under small-scale-creep conditions

Abstract: The growth of a sharp crack typically is accompanied by a damage or fracture process zone that propagates with the crack tip. The present understanding of the transient crack-tip fields under small-scale-creep conditions is limited primarily to analyses based upon creep flow rules that neglect damage. In this paper, Kachanov-type creep-damage constitutive equations are developed that include the dilatational creep that arises from caviation and microcrack damage. A finite element calculation demonstrates the effects of this type of creep-damage behavior on the asymptotic, singular crack-tip fields.

Plastic η-factor (η p )

Abstract: Slip line field solutions for several commonly used fracture mechanics specimens are summarized From these solutions analytic expressions of the plastic η p factors are derived These results are then compared with those η p factors obtained using the EPRI's finite element analyses for power law strain hardening materials in order to assess the extent to which they can be approximately applied in J-integral tests with these specimens containing both deep and shallow cracks It appears that in the deep crack specimens the η p factors are approximately equal for all hardening materials implying that the η p factors derived from slip line field solutions are accurate enough for J-integral evaluation In the shallow crack specimens, with the exception of the double-edge cracked panels and pure bend specimens, the η p factors do not agree very well and reasons for the discrepancies are discussed

Mechanics and micromechanisms of fatigue crack growth in brittle solids

Abstract: This paper is concerned with the mechanics and micromechanisms of stable mode I crack growth in brittle solids subjected to compression—compression fatigue and tension—tension fatigue loads. Constitutive models, results of finite element analyses, and experimental observations are described for monolithic ceramics and ceramic-matrix composites, plain concrete, and a transformation-toughened ceramic in an attempt to deduce a general theory on the origin of mode I fracture in notched plates under uniaxial cyclic compression at room temperature. An analysis of the residual stress field which develops at elevated temperatures in response to power law creep and far-field compressive cyclic loads is also presented. The principal “driving force” for mode I fracture in cyclic compression is the generation of a near-tip zone of residual tension, when the deformation at the notch-tip leaves permanent strains upon unloading from the far-field compressive stress. The results indicated that materials with very different microscopic deformation mechanisms, i.e., microcracking, dislocation plasticity, martensitic transformation, interfacial debonding/slip, or creep, exhibit a macroscopically similar, stable fracture under far-field cyclic compression because the zone of residual tension is embedded in material which is elastically strained in compression. It is shown that cyclic compression loading offers a unique method for fatigue precracking notched specimens of brittle solids prior to tensile fracture testing, whereby an unambiguous interpretation of the critical stress intensity factors for crack initiation and growth can be achieved. Fatigue crack growth characteristics of a transformation-toughened ceramic and a creeping ceramic composite under tension—tension fatigue loads are also discussed.

Elastic-plastic analysis of frictionless contact at interfacial crack tips

Abstract: The asymptotic elastic behavior of an interfacial crack occurring between two dissimilar isotropic media is reviewed. Distinct solutions, based on differing assumptions regarding crack-face boundary conditions, can be generated. The assumption of traction-free faces generally leads to oscillatory singular asymptotic fields which mathematically cause crack-face interpenetration, an inconsistency which can be alleviated by alternatively assuming asymptotic frictionless contact. For predominant tensile loading, the elastically-calculated ratio of contact length to crack size is typically very small, but may become appreciable when shear loading is applied. In either case, the singular crack-tip stresses cannot be sustained in materials capable of limited plastic flow, and small scale yielding (SSY) should be considered. In an extension of previous work [11], we identify conditions for SSY within surrounding dominant elastic regions of both traction-free and frictionless contact types. For the latter case, approximate closed form expressions for the plastic zone size and shape are obtained as the locus of points where the elastically-calculated Mises stress equals the tensile yield strength, σ ys ,. The maximum extent of this plastic zone is approximately 3K II c2 /2σ ys 2 , where K II c , is the closed crack-tip bimaterial stress intensity factor. Precise SSY numerical calculations for an elastic/perfectly-plastic material atop a rigid substrate indicate that the asymptotic stress field in the plastically-deforming material is composed of two fan regions and two constant state regions. Within the plastic zone, the interfacial and crack-face tractions asymptotically reach constant values. Compressive crack-face tractions persist even when contained inelastic crack-tip deformation is included.

Mixed mode fracture initiation and trajectory prediction under random stresses

Abstract: A method is developed for estimating (i) confidence intervals on the initial direction of crack extension and (ii) the probability of crack initiation in plane stress and plane strain problems The method accounts for the uncertainty in applied stresses, fracture toughness, and crack geometry It is based on classical theories of linear fracture mechanics for homogeneous isotropic materials, a computer code for deterministic fracture mechanics analysis (FRANC) and first and second order structural reliability algorithms (FORM/SORM) Several examples are presented to demonstrate the use and generality of the proposed method for probabilistic fracture mechanics analysis

Experimental and numerical studies of the J-integral for a surface flaw

Abstract: Applied J-integral values for a surface cracked tensile panel are experimentally evaluated by measuring strain and displacement quantities along an instrumented contour located on the longitudinal symmetry plane. Nonlinear, 3-D, finite-element analyses are employed to obtain corresponding estimates of the contour and area integral contributions to a 3-D J-integral. Finite element results indicate that the area integral contribution is negligibly small on the symmetry plane; the fracture driving force is thus adequately characterized by the experimental contour values. Detailed comparisons of the experimental and numerical results (crack mouth opening displacement, J-values, and strains along the contour) reveal that the one-quarter symmetric, finite element model accurately predicts the panel response for overall (gauge length) strains approaching 1.6 times the material yield strain, beyond which the observed deformation patterns exhibited globally asymmetric shear bands.

Plane-strain mixed-mode near-tip fields in elastic perfectly plastic solids under small-scale yielding conditions

Abstract: Within the context of the small-strain approach, plane-strain mixed-mode near-tip fields of a stationary crack in an elastic perfectly plastic Mises solid under small-scale yielding conditions are examined by finite element methods. Steady-state stress fields in the immediate vicinity of the crack tip are obtained as the remote loading of the elastic K-field increases. Asymptotic crack-tip solutions consisting of constant stress sectors, centered fan sectors, and an elastic sector are then constructed accordingly. The asymptotic crack-tip stress solutions agree well with the numerical results for a whole spectrum of mixed-mode loadings. Our mixed-mode near-tip solution with an elastic sector differs from that of Saka et al. by one (plastic) constant stress sector situated between the elastic sector and the neighbouring fan sector. The effect of the existence of the elastic sector on the near-tip fields is discussed in the light of the computational results. The plastic mixity factor of the near-tip field is given as a function of the elastic mixity factor of the prescribed K-field. This function is well bounded by that of the perfectly plastic limit of the corresponding solutions for power-law hardening materials given by Shih. Some issues pertaining to the numerical procedures such as the implementation of the small-scale yielding assumption are also addressed.

Observations on high strain rate crack growth based on a strip yield model

Abstract: In the past, analytical models have been developed for the study of rapid crack growth in a rate-dependent elastic—plastic material under conditions that permit crack advance in a cleavage mode, and separately for rapid crack advance in an elastic—plastic material when the crack advances by means of a local ductile mechanism. However, models suitable for study of rapid crack growth that permit either mode of crack advance, with the operative mode being determined by which of two competing fracture criteria prevails, have been elusive. Here, the process of dynamic tensile crack growth in a material is studied under small scale yielding conditions with the crack tip plastic zone modeled as a strip yield zone extending ahead of the advancing crack tip. Following Glennie [1] and others, rate dependence of plastic flow is taken into account by assuming that the cohesive stress in the yield zone depends linearly on the local rate of opening of the yield zone. The conditions under which a crack can advance steadily according to either of two criteria are considered. A crack tip opening criterion is identified with a locally ductile mode, and a critical stress condition is identified with a cleavage mode. The analysis leads to conditions among the applied stress intensity factor, the crack speed and the material viscosity that are necessary for sustained crack growth in either case, with the implication that the criterion that is easiest to satisfy will establish the mode by which the crack advances.

New integral equation approach for the crack problem in elastic half-plane

Abstract: This paper presents an elementary solution for the crack problem in elastic half-plane. The elementary solution corresponds to the following conditions: (1) a point dislocation placed at some point of the upper half-plane, (2) a fixed or free boundary for the elastic half-plane, (3) zero stresses at the remote plane. After using the distributed dislocation functions to be unknowns and taking the resultant force functions along the crack borders to be the right hand terms of the integral equation, a new integral equation with the log singular kernel is obtained. Numerical procedure for the solution of the integral equation is proposed and several examples are given.

Finite element analysis of void growth in elastic-plastic materials

Abstract: Three-dimensional finite element computations have been carried out for the growth of initially spherical voids in periodic cubic arrays and for initially spherical voids ahead of a blunting mode I plane strain crack tip. The numerical method is based on finite strain theory and the computations are three-dimensional. The void cubic arrays are subjected to macroscopically uniform fields of uniaxial tension, pure shear and high triaxial stress. The macroscopic stress—strain behavior and the change in void volume were obtained for two initial void volume fractions. The calculations show that void shape, void interaction and loss of load carrying capacity depend strongly on the triaxiality of the stress field. The results of the finite element computation were compared with several dilatant plasticity continuum models for porous materials. None of the models agrees completely with the finite element calculations. Agreement of the finite element results with any particular constitutive model depended on the level of macroscopic strain and the triaxiality of the remote uniform stress field. For the problem of the initial spherical voids directly ahead of a blunting mode I plane strain crack tip, conditions of small scale yielding were assumed. The near tip stress and deformation fields were obtained for different void-size-to-spacing ratios for perfectly plastic materials. The calculations show that the holes spread towards the crack tip and towards each other at a faster rate than they elongate in the tensile direction. The computed void growth rates are compared with previous models for void growth.