Showing papers in "International Journal of Fracture in 1975"
TL;DR: In this paper, a theory is developed for predicting the time-dependent size and shape of cracks in linearly viscoelastic, isotropic media, and a local energy criterion of failure at the tip is introduced, which is applicable to both constant and transient tip velocities.
Abstract: A theory is developed for predicting the time-dependent size and shape of cracks in linearly viscoelastic, isotropic media First, the effect of a narrow zone of disintegrating material at the crack tip on opening displacement and on a finite stress distribution ahead of the tip is examined for elastic materials Extension to viscoelastic media is then made Although the undamaged portion of the continuum is assumed linear, no significant restrictions are placed on the nature of the zone of failing material at the crack tip and, therefore, this material may be highly nonlinear, rate-dependent, and even discontinuous Finally, formulation of the problem is completed by introducing a local energy criterion of failure at the tip which is applicable to both constant and transient tip velocities Parts II–IV, to appear in succeeding issues, will cover approximate methods of analysis and several applications of the theory
566 citations
TL;DR: In this paper, the initial energy release rate for a branch crack propagating at an arbitrary angle from an existing crack tip is obtained in a simple fashion and in closed form by using a continuity assumption.
Abstract: The initial energy release rate for a branch crack propagating at an arbitrary angle from an existing crack tip is obtained in a simple fashion and in closed form by using a continuity assumption. It is then postulated that the branch crack propagates in the direction which causes the energy release rate to be a maximum and that initiation occurs when the value of this release rate reaches a critical value. It is shown that these postulates yield results identical to the maximum stress theory, since the direction in which the maximum circumferential stress occurs is also the direction causing the maximum energy release rate.
419 citations
TL;DR: In this paper, the authors used the theory of crack growth developed in Parts I and II to predict crack velocity and failure time for an elastomer under simple uniaxial and biaaxial stress states.
Abstract: The theory of crack growth developed in Parts I and II is used to predict crack velocity and failure time for an elastomer under simple uniaxial and biaxial stress states. Included are consideration of the effect of specimen size on failure time for initially small cracks, experimental determination of fracture properties, the effect of strain level on crack propagation, and the validity of the plane strain assumption. The second half of the paper examines the effect upon crack velocity of nonlinear viscoelasticity of failing material at the crack tip in media which is otherwise linearly viscoelastic. The dependence of fracture behavior on environmental changes and aging is also considered.RésuméOn utilise la théorie de croissance de la fissure développée dans les parties I et II pour réduire la vitesse de fissuration et le temps de rupture d'un élastomére soumis à des états de contraintes uniaxiales et biaxiales. Le mémoire comporte des considérations sur l'effet de la dimension des éprouvettes sur le temps de rupture au départ de petites fissures, la détermination expérimentale des propriétés de la rupture, l'étude de l'effet du niveau de déformation sur la propagation des fissures, et de la validité d'hypothèses d'état plan de déformation.La seconde partie de l'article comporte l'examen de l'effet d'une viscoélasticité non linéaire dans la matière qui se rompt à la pointe d'une fissure, laquelle est par ailleurs sise dans un milieu caractérisé par une viscoélasticité linéaire.On considère également la manière dont le comportement à la rupture dépend du vieillissement et des changements de l'environnement.
318 citations
TL;DR: In this article, a boundary-integral equation based on the Green's function is proposed for an infinite anisotropic plate containing an exact crack. But the results of the exact crack model are not as accurate as previously published isotropic results.
Abstract: A numerical procedure based on the boundary-integral equation method, is formulated using the fundamental solution (Green's function) for an infinite anisotropic plate containing an exact crack. The boundary-integral equation developed can be solved numerically for the mode 1 and mode 2 stress intensity factors by approximating boundary data on the surface of an arbitrary body, excluding the crack surface. Thus the efficiency and generality of the boundary-integral equation method and the precision of exact crack model analyses are combined in a direct manner. The numerical results reported herein are as accurate as previously published isotropic results. The effects of material anisotropy are reported for center and double-edge cracked geometries. A path independent integral for obtaining mode 1 and mode 2 stress intensity factors directly for arbitrary loading is reported.
302 citations
TL;DR: In this paper, simple approximate relations are derived for predicting the time of fracture initiation and crack tip tip velocity in linearly viscoelastic media, assuming that the second derivative of the logarithm of creep compliance is small.
Abstract: Starting with equations developed in Part I for the opening mode of displacement, simple, approximate relations are derived for predicting the time of fracture initiation and crack tip velocity in linearly viscoelastic media. First we use the assumption that the second derivative of the logarithm of creep compliance with respect to logarithm of time is small (which is normally valid for viscoelastic materials); we next derive a relation between instantaneous values of tip velocity and stress intensity factor. This result is then used to examine some characteristics of crack growth behavior. Finally, some results are obtained for the separate problem of predicting the time at which propagation initiates.
252 citations
TL;DR: In this paper, stress intensity calculations are presented for cases of combined tensile and shear loading for a linear elastic material using functions of a complex variable, and a theory is developed to determine the direction of maximum energy release rate.
Abstract: Stress intensity calculations are presented for cases of combined tensile and shear loading for a linear elastic material. Using functions of a complex variable, a theory is developed to determine the direction of maximum energy release rate. A finite element method using virtual crack extensions is also used to determine the energy release rate for crack extensions in various directions and in particular that which gives the maximum energy release rate. Except when shear is more significant than tension, these results give good agreement with available experimental evidence. When shear is most significant, plasticity effects are probably becoming important, thereby invalidating the results of any linear theory. However, the results may still be used to determine K
I and K
II numerically from virtual crack extension calculations of J
1 and J
2 for general two-dimensional geometries.
184 citations
TL;DR: In this paper, the authors used fracture mechanics techniques to estimate the stress intensity factor for cracks with low a/2c values and the effect of the weld stress concentration factor was incorporated in the solution.
Abstract: In most of the lower fatigue strength welded joints failure occurs by the propagation of a semi-elliptical surface crack which initiates at the weld toe. In order to analyse the progress of these cracks using fracture mechanics techniques, the solution for the stress intensity factor, K, is required. Fatigue cracks in most welded joints adopt shapes which give low a/2c values (up to approximately 0.3) while solutions in the literature are more applicable to a/2c values close to 0.5. Therefore, results in the literature were used to estimate the stress intensity factor for cracks with low a/2c values. Furthermore, the effect of the weld stress concentration factor was incorporated in the solution. The accuracy of the resulting solution was confirmed by using it to determine ΔK values of weld toe cracks for which crack propagation data were available. The results agreed with the expected da/dN vs. ΔK scatterband obtained from centre-notched specimens.
174 citations
135 citations
131 citations
TL;DR: In this article, the authors considered the problem of an elastic plane containing an elastic inclusion and formulated the problem in terms of a system of singular integral equations, where both the plane and the inclusion contain a radial crack and the two cracks are collinear.
Abstract: The problem of an elastic plane containing an elastic inclusion is considered. It is assumed that both the plane and the inclusion contain a radial crack and the two cracks are collinear. The problem is formulated in terms of a system of singular integral equations. In the interesting limiting cases in which the crack tips approach the interface from either one or both sides, the dominant parts of the kernels become generalized Cauchy kernels giving rise to stress singularities of other than 13-1 power. For these unusual cases of a crack terminating at or crossing the interface stress intensity factors are defined and some detailed results are given for various crack-inclusion geometries and material combinations.
120 citations
TL;DR: In this article, the elastic stress intensity factors for arbitrary-shaped cracks in plane stress and plane strain problems were calculated using an assumed displacement hybrid finite element model, where the unknowns in the final algebraic system of equations are the nodal displacements and the elastic tensor intensity factors.
Abstract: This paper deals with a procedure to calculate the elastic stress intensity factors for arbitrary-shaped cracks in plane stress and plane strain problems. An assumed displacement hybrid finite element model is employed wherein the unknowns in the final algebraic system of equations are the nodal displacements and the elastic stress intensity factors. Special elements, which contain proper singular displacement and stress fields, are used in a fixed region near the crack tip; and the interelement displacement compatibility is satisfied through the use of a Lagrangean multiplier technique. Numerical examples presented include: central as well as edge cracks in tension plates and a quarter-circular crack in a tension plate. Excellent correlations were obtained with available solutions in all the cases. A discussion on the convergence of the present solution is also included.
TL;DR: In this article, a stress intensity factor solution is developed for a large plate containing radial hole cracks loaded with arbitrary crack face pressure, defined as the unflawed hoop stress surrounding a mechanical fastener.
Abstract: A stress intensity factor solution is developed for a large plate containing radial hole cracks loaded with arbitrary crack face pressure. When the pressure is defined as the unflawed hoop stress surrounding a mechanical fastener, stress intensity factor calibrations are readily computed by the linear superposition principle. Results obtained in this manner agree well with previous solutions determined for open holes loaded in remote tension. The potential usefulness of the present analysis is further demonstrated with application to specific fastener configurations, including interference fit fasteners, pin-loaded plates, and cold-worked holes.
TL;DR: In this article, the application of stress intensity factors derived from linear elastic fracture mechanics (LEFM) to fracture at creep temperatures has been considered and it is shown that a LEFM approach is inapplicable to predicting creep crack growth rates, whilst the net section stress is found to correlate well with the crack growth rate.
Abstract: The application of stress intensity factors derived from linear elastic fracture mechanics (LEFM) to fracture at creep temperatures has been considered. From tensile creep rupture tests on single edge notched and notched centre hole specimens of solution treated A.I.S.I. type 316 stainless steel, it is shown that a LEFM approach is inapplicable to predicting creep crack growth rates, whilst the net section stress is found to correlate well with the crack growth rates. These observations have been explained by considering the creep relaxation that takes place at the notch root, smoothing out the local stresses and thus making the LEFM stress distribution inapplicable. The resulting stress distribution supports the observation that the net section stress is a successful criterion on which to predict creep rupture in stainless steel.
TL;DR: In this article, the authors considered the plane problem of propagation of a straight crack in an elastic medium under arbitrary variable loading, and the locations of the edges of the crack were specified as arbitrary smooth functions of time under the only restriction that crack speed at any instant of time is less than the velocity of Rayleigh wave.
Abstract: The plane problem of propagation of a straight crack in an elastic medium under arbitrary variable loading is considered. The locations of the edges of the crack are specified as arbitrary smooth functions of time under the only restriction that crack speed at any instant of time is less than the velocity of Rayleigh wave. Solution for the distribution of plane stress components near the crack tip is obtained. In particular, expressions for stress intensity factors at the crack are given, which thus makes it possible to deduce the crack motion under given loading conditions.
TL;DR: In this article, the authors studied the formation of submicroscopic cracks in polymers under load by small-angle X-ray scattering, and the main regularities of crack formation under different loading conditions have been analyzed.
Abstract: Formation of incipient submicroscopic cracks in polymers under load have been studied by small-angle X-ray scattering. The main regularities of crack formation under different loading conditions have been analyzed. The connection between the submicrocrack concentration and the deformation of a stressed polymer has been shown. The main parameters of crack formation defining the strength properties of a polymer, i.e., the size of initial submicrocracks transverse to the axis of loading, which is determined by the structural heterogeneity of a material, and the concentration of submicrocracks before rupture, have been established. The analysis of the quantitative correlation between these parameters allows one to formulate the main statements regarding the micromechanics of polymer fracture. From comparing the volume and surface parameters of crack formation of a stressed polymer, the dominating role of the surface in the process of fracture has been demonstrated.
TL;DR: The failure of an axially strained polymer solid having a fibrous structure is caused by formation, coalescence, and growth of microcracks up to critical size crack, which then propagates catastrophically through the cross-section of the sample as mentioned in this paper.
Abstract: The failure of an axially strained polymer solid having a fibrous structure is caused by formation, coalescence, and growth of microcracks up to critical size crack, which then propagates catastrophically through the cross-section of the sample. The primary candidates for microcrack formation are the ends of microfibrils where the material connection by tie molecules to the rest of the sample is almost completely interrupted. The opening of microcracks and sliding motion of fibrillar elements ruptures locally the most strained taut tie molecules and, thus, produces radicals detectable by ESR. But, chain rupture is the consequence and not the cause of displacement of the strong fibrillar elements. It also does not substantially affect the load carrying properties of the sample which mainly depend on the lateral autoadhesion of microfibrils and fibrils and on their quasi-viscous resistance to axial displacement. Hence, one has to reject the completely inadequate models trying to base the observed load-elongation curve of such samples on the load carrying properties of those tie molecules which are eventually ruptured upon straining. Some examples of these models are treated explicitly.
TL;DR: In this article, a power type expression for fatigue crack growth was derived and the frequency dependence for this power function type was obtained, and reasonable agreement with experimental results from the literature was obtained.
Abstract: Dislocation group dynamics theory is used to deduce a power type expression for fatigue crack growth. In general, the results reflect only a single rate process, and thus one activation energy which is small compared to those in usual rate processes. The frequency dependence for this power function type fatigue crack growth rate was also obtained, and yield reasonable agreement with experimental results from the literature.
TL;DR: In this article, the transition from ductile to brittle failure is shown to be both rate and thickness dependent, and an increasing percentage of the incidence of brittle failure with rate rather than a sharp transition is explained in terms of a distribution of toughness values introduced by variations in the notching method.
Abstract: Test data is described for polycarbonate single edge notch specimens at a range of loading rates and two thicknesses at 20°C. The transition from ductile to brittle failure is shown to be both rate and thickness dependent. The effects may be described in terms of a plane stress and a plane strain fracture toughness coupled with a rate dependent yield stress and a plastic zone size to thickness ratio criterion. An increasing percentage of the incidence of brittle failure with rate rather than a sharp transition is noted and explained in terms of a distribution of toughness values introduced by variations in the notching method.
TL;DR: In this article, the effect of mean stress on fatigue crack propagation has been investigated, mainly in steels and aluminium alloys, and fundamental explanations of the effects of stress on mean stress are discussed.
Abstract: Most investigations of fatigue crack propagation have been carried out using pulsating tension loading and rate of crack propagation (da/dN) expressed in terms of range of stress intensity factor (ΔK). However, mean stress can have a significant effect on da/dN, so that generally it should be expressed in terms of mean and range of stress intensity factor. Literature relating to the effect of mean stress on da/dN, mainly in steels and aluminium alloys, is reviewed in the present report. Empitical relationships which allow the correlation of crack propagation data obtained at different mean stresses, crack propagation theories which predict the effect of mean stress, and fundamental explanations of the effects of mean stress are discussed. Suggestions for future research are made.
TL;DR: In this paper, it was pointed out that the Weibull multiaxial treatment of brittle strength contains limitations which are not present in the more familiar uniaxual formulation.
Abstract: It is pointed out that the Weibull multiaxial treatment of brittle strength contains limitations which are not present in the more familiar uniaxial formulation. Provided these limitations are satisfied, it is possible to use tension or bending data to predict multiaxial behavior when at least one principal stress is tensile. This is illustrated for the Brazilian disk test (diametral compression of a disk). Predictions based on bending tests agree well with observed strength values in disk tests on two types of rocks.
TL;DR: In this paper, two different crack monitoring techniques are used on two different sample geometries, PTC [I0] and CT [II], and two heats of A1 2219-T851, but otherwise equal testing conditions, to characterize closure more fully.
Abstract: Crack closure at positive stress levels [i] is currently being investigated as a mechanism to explain variations in fatigue crack growth rate caused by changes in the testing conditions. Compliance [i-3], resistivity [4-6], optical [7,8], and acoustical [9,10] measurements, extensively used to monitor crack growth, yield information about crack closure. Correlation between the various results is quite difficult, however, since different monitoring techniques, sample geometries, materials, etc. have been involved. In the present investigation two of the above crack monitoring techniques are used on two different sample geometries, PTC [I0] and CT [ii], and two heats of A1 2219-T851, but otherwise equal testing conditions, to characterize closure more fully.
TL;DR: In this paper, the authors used IR spectroscopy to find how the applied mechanical stress imposed upon a sample is distributed among the interatomic bonds and determined the maximum stress on interatomic bond by the magnitude of the breaking stress on them.
Abstract: Infrared (IR) spectroscopy is used to find how the applied mechanical stress imposed upon a sample is distributed among the interatomic bonds. The distribution is highly heterogeneous: 80–95% of the bond population experience stresses close to the applied stress, the stress on the rest of the bond population varies over a wide range and reaches 1000–2000 kg/mm2. The overstressed interatomic bonds lie in the amorphous regions of the polymer and are oriented in the direction of the mechanical force. The maximum stress on interatomic bonds is determined by the magnitude of the breaking stress on them. The breaking stress is shown to be a function of the applied stress, time, and temperature. This dependence is due to scission of stressed bonds induced by thermal fluctuations.
TL;DR: In this article, the elasticity solution and the stress intensity factors for a finite crack in one of the materials of a bimaterial composite were determined for an arbitrary orientation and distance from the straight interface, and the solution for general stress boundary conditions on the crack surface was presented in the form of coupled Fredholm integral equations of the second kind.
Abstract: Two-dimensional elasticity solution and the stress intensity factors are determined for a finite crack in one of the materials of a bimaterial composite. The crack has an arbitrary orientation and distance from the straight interface. The solution for general stress boundary conditions on the crack surface is presented in the form of coupled Fredholm integral equations of the second kind. Numerical values of the stress intensity factors are computed for various crack orientations, distances from the interface, and different combinations of material properties when the boundary conditions are uniform pressure and uniform shear stress.
TL;DR: In this paper, the electron spin resonance (ESR) technique has led to detailed information on the number, location, and production kinetics of molecular fracture points and the possible impact of these ESR results on existing statistical, mechanical, kinetic, and continuum-mechanical fracture models.
Abstract: The investigation of stress induced chain scission by the electron spin resonance (ESR) technique has led to detailed information on number, location, and production kinetics of molecular fracture points. These data are reported here. The possible impact of these ESR results on existing statistical, mechanical, kinetic, and continuum-mechanical fracture models is discussed.
TL;DR: In this article, the authors describe an analytical technique which may be used in connection with the general problem of bonded wedges containing radial cracks, which consists of the reduction of the related dual integral equations of the problem to a singular integral equation in a systematic manner, and described by applying it to a relatively simple antiplane shear problem.
Abstract: The primary aim of this paper is to describe an analytical technique which may be used in connection with the general problem of bonded wedges containing radial cracks. The technique consists of the reduction of the related dual integral equations of the problem to a singular integral equation in a systematic manner, and is described by applying it to a relatively simple anti-plane shear problem. The paper also presents the results of various numerical examples and the closed form solution for the special case of two bonded wedges with equal angles and an interface crack.
TL;DR: In this article, a technique for dealing with the problem of an elastic domain containing an arbitrarily oriented internal crack is presented, which is formulated as a system of integral equations for a fictitious layer of body forces imbedded in the plane along a closed smooth curve encircling the original domain.
Abstract: A technique is presented for dealing with the problem of an elastic domain containing an arbitrarily oriented internal crack. The problem is formulated as a system of integral equations for a fictitious layer of body forces imbedded in the plane along a closed smooth curve encircling the original domain. The problems of a half plane with a crack in the neighborhood of its free boundary and of an infinite strip containing a symmetrically located internal crack with an arbitrary orientation are considered as examples. In each case the stress intensity factors are computed and are given as functions of the crack angle.