Showing papers in "International Journal of Fracture in 1977"
TL;DR: In this article, it was shown that the work performed in the end region at the tip of a crack, where the fracture process takes place, is considered the essential work of fracture, and a constant for a particular sheet thickness.
Abstract: In a ductile material, the total work of fracture is not a material constant and linear fracture mechanics is inappropriate. The work performed in the end region at the tip of a crack, where the fracture process takes place, is considered the essential work of fracture, and a constant for a particular sheet thickness. It is shown that this essential work can be estimated from deep edge notched tension specimens by extrapolating the straight line relationship between the work of fracture and ligament length to zero ligament length.
439 citations
TL;DR: In this article, an infinite slab containing a crack and deformed at infinity to a state of finite simple shear is considered, where the material of the slab is taken to be homogeneous, isotropic, elastic, and incompressible, and the analysis is carried out for the fully nonlinear equilibrium theory of finite elasticity.
Abstract: The present paper is concerned with an infinite slab containing a crack and deformed at infinity to a state of finite simple shear. The material of the slab is taken to be homogeneous, isotropic, elastic, and incompressible, and is further assumed to belong to a class of materials which admit nontrivial states of anti-plane shear. The analysis is carried out for the fully nonlinear equilibrium theory of finite elasticity. The stress field near the crack-tips is studied in detail; one of the special materials considered is such that the shear stresses near a crack tip remain bounded, despite the presence of unbounded displacement gradients. An analogy between the crack problem in finite anti-plane shear and the problem of transonic flow of a gas past a flat plate is pointed out and discussed.
241 citations
TL;DR: In this paper, the model of an interface between two different elastic media can be changed in order to remove the logical inconsistencies present in analyses of the ideal interface currently in use, and the models, suggested in the paper, could also be interpreted as descriptions of actual diffuse interfaces formed by an adhesive layer.
Abstract: A suggestion is made as to how the model of an interface between two different elastic media can be changed in order to remove the logical inconsistencies present in analyses of the ideal interface currently in use. The models, suggested in the paper, could also be interpreted as descriptions of actual diffuse interfaces formed by an adhesive layer.
137 citations
114 citations
82 citations
TL;DR: In this article, a method of calculating stress intensity factors for branched and bent cracks embedded in an infinite body has been developed, where the branches are always assumed to be sharp cracks and are modelled by dislocation distributions.
Abstract: A method of calculating stress intensity factors for branched and bent cracks embedded in an infinite body has been developed. The branches are always assumed to be sharp cracks and are modelled by dislocation distributions. The original crack may be either sharp or of elliptical cross-section with finite root radius. Hence, the method which has a precision ±2%, is also applicable to the study of crack branches emanating from elliptical holes and, approximately, also from notches. The following detailed calculations have been made assuming mode I loading: branched sharp crack with branches of equal and different length, bent sharp crack, and one and two crack branches emanating from the crack with a finite root radius. Bending of a sharp crack under mixed mode loading has also been studied. The criteria of maximum tensile stress and maximum energy release rate used in the study of direction of crack propagation are discussed.
81 citations
TL;DR: In this paper, a computer simulation of the time dependent development of the plastic zone ahead of a crack loaded in uniform tension was performed, where the material was assumed to deform according to a creep law relating the local strain rate to the local stress.
Abstract: A computer simulation of the time dependent development of the plastic zone ahead of a crack loaded in uniform tension was performed. The material was assumed to deform according to a creep law relating the local strain rate to the local stress. The plastic zone was modelled by an array of edge dislocations coplanar with the crack. For a given time the stress was found to be uniform in a region ahead of the crack. This region increased and the local stress decreased with increasing time. The distribution of dislocations in the zone at a given time was found to be almost the same as that given by the Bilby, Cottrell and Swinden model (1963) if the friction stress in that model was replaced by an apparent friction stress equal to the uniform stress ahead of the crack. This apparent friction stress is dependent on both the applied stress and time. Assuming a critical crack opening displacement (COD) or a critical value of theJ integral,J
c, to be the criteria for the onset of the creep crack growth the initiation time can be calculated using the results of this study. A good agreement between the theory and experiment is obtained for two different CrMoV steels. This comparison with experiments suggests that the COD is an appropriate crack growth initiation parameter for both ductile and brittle materials whilstJ
cdoes not seem to be applicable in creep fracture.
66 citations
TL;DR: In this article, it has been shown that the threshold stress intensity depends more on the elastic modulus rather than on any other material property in agreement with many experimental results, and that the stress intensity can be related to the stress necessary to nucleate a dislocation at the crack tip.
Abstract: It has been shown that the ratio of threshold stress intensity for fatigue crack growth to the shear modulus is nearly a constant for many materials This implies that fatigue crack growth is related to some fundamental phenomenon occurring at the crack tip In the following a dislocation model has been developed to predict the threshold stress intensity It is shown that the stress intensity can be related to the stress necessary to nucleate a dislocation at the crack tip The most important outcome of the present analysis is that the threshold stress intensity depends more on the elastic modulus rather than on any other material property in agreement with many experimental results
61 citations
TL;DR: In this paper, the authors show that the assumption that the probability of survival is the product of the probabilities of survival of the structure for the principal stresses applied individually is generally unconservative and therefore the approximation serves as a lower bound to the failure probability.
Abstract: A frequently used approximate treatment of fracture statistics for polyaxial stress states assumes that the probability of survival is the product of the probabilities of survival of the structure for the principal stresses applied individually. The present paper shows that this assumption is generally unconservative and therefore the approximation serves as a lower bound to the failure probability. A simple technique is given for finding an upper bound in cases of biaxial tension provided the uniaxial fracture behavior is described satisfactorily by Weibull's two-parameter formula. The upper bound is a good approximation when in high stress regions the stresses are equibiaxial, or nearly so, as in laterally loaded or spinning disks.
57 citations
56 citations
TL;DR: In this article, the Paris equation for fatigue crack growth is explained in relation to the crack closure concept suggested by Elber, and it is concluded that the exponent parameter m reflects mainly the dependency of crack closure behavior on ΔK.
Abstract: The two parameters, C and m, which characterize the Paris equation for fatigue crack growth are explained in relation to the crack closure concept suggested by Elber. It is proposed that the range of effective incremental change in stress intensity factor (ΔK) needed for crack growth should have a second power correlation with the growth rate. The crack growth is essentially determined by cumulative damage to the material in cycled plastic zone near the crack tip, and is relatively insensitive to the applied ΔK-values and the mechanical properties of material. However, the crack closure behavior is expected to depend on both the stress range and the material properties. Thus it is concluded that the exponent parameter m reflects mainly the dependency of crack closure behavior on ΔK. For example, in the case of m=4 the crack opening level increases linearly with increase in ΔK, while in the case of m=2 it remains constant. It is suggested that the cyclic straining at the crack tip possibly varies with ΔK, thus changing primarily the crack closure behavior rather than the damage accumulation process in the plastic zone.
TL;DR: In this article, a theory of crack propagation, resulting from the application of a monotonic increasing applied stress, in a linear viscoelastic material, is derived based upon an energy balance fracture criterion.
Abstract: A theory of crack propagation, resulting from the application of a monotonic increasing applied stress, in a linear viscoelastic material, is derived based upon an energy balance fracture criterion. It is shown that for a Maxwell solid the crack growth law can be derived either from a global energy balance taking full account of the energy dissipation resulting from viscoelastic flow, or from a local energy balance taking account of the dissipation in the failure zones. The local energy balance method allows the derivation of the crack growth law for more general linear viscoelastic solids. The theory predicts the well known Griffith condition for fracture when the material is simply linear elastic. For a crack having failure zones in a linear viscoelastic solid the growth law for a constant applied stress is where c(t) is the time dependent half-crack length, 641-1 is the yield or crazing stress in the failure zone, K(t) is the time dependent stress intensity factor, Γ is the fracture energy, ν is Poisson's ratio and J(t) is the uniaxial creep function of the viscoelastic material. This growth law is valid if either J(t)≡0 for all times t>0 (i.e. a Maxwell solid) or if 641-1 641-2 641-3
TL;DR: In this paper, the concept of a crack driving force was formally introduced to molecular rate theory and the basic thermodynamic relations were derived for steady state crack propagation using assumptions similar to those well accepted in theories of deformation based on thermally activated dislocation motion.
Abstract: Steady state crack propagation in solids is analyzed as a thermally activated process. The fracture mechanics concept of a crack driving force is formally introduced to molecular rate theory. This representation of crack propagation appears to be, in many aspects, similar to that of the motion of a dislocation under a shear stress across thermal obstacles. The basic thermodynamic relations are derived for steady state crack propagation using assumptions similar to those well accepted in theories of deformation based on thermally activated dislocation motion.
TL;DR: In this article, the basic equations for the representation of crack tip plasticity by an inclined strip yield superdislocation model are derived and the results are put into a form suitable for the analysis of fatigue and other stable crack growth processes.
Abstract: The basic equations for the representation of crack tip plasticity by an inclined strip yield superdislocation model are derived. The results are put into a form suitable for the analysis of fatigue and other stable crack growth processes. Specialization of the general results for small-scale yielding under a fixed load is also given. The crack tip crack-opening displacement obtained for this situation is compared with finite element and other more rigorously obtained results and found to be in quite good agreement.
TL;DR: Linear elastic crack-tip solutions for twelve different shapes of cracked body of interest, are given in this article, which assist the user of fracture mechanics in that they carry out the interpolative step accurately and therefore may be usefully incorporated in other crack computational procedures.
Abstract: Linear elastic crack-tip solutions for twelve different shapes of cracked body of interest, are given. The purpose is to provide efficient “closed” formulations of data previously presented in a tabular or graphical manner. The formulae assist the user of fracture mechanics in that they carry out the interpolative step accurately and therefore may be usefully incorporated in other crack computational procedures, such as fatigue crack growth prediction, crack-tip plasticity corrections, etc. The method used to generate the formulae can be applied to other cracked body geometries.
TL;DR: In this paper, the formation of fracture mirrors was investigated for specimens of a soda-lime-silicate glass tested in tension, four point flexure, and three-point flexure.
Abstract: The formation of fracture mirrors was investigated for specimens of a soda-lime-silicate glass tested in tension, four point flexure, and three point flexure. The dimensions of the mirror region are dependent on the macrostress state of the specimen at fracture. An energy balance approach, incorporating a kinetic term is applied to explain mirror formation and the macrostress state differences.
TL;DR: In this paper, an integral for non-elastic material whose value is determined by the magnitude of the singularities at the tip of a crack but which may be evaluated mainly far away from the crack, where the state of deformation may be determined numerically with higher accuracy than near the crack was proposed.
Abstract: An integral has been proposed for a non-elastic material whose value is determined by the magnitude of the singularities at the tip of a crack but which may be evaluated mainly far away from the crack, where the state of deformation may be determined numerically with higher accuracy than near the crack. The integral is intended for situations when plasticity is too great for linear elastic fracture mechanics to be appropriate, but may be related to the stress intensity factors in the linear elastic case. Its value has been calculated for a central or edge crack in a uniformly loaded and unloaded plate with a non-work-hardening elastic plastic material when the loading is either tension or longitudinal shear. It has also been calculated for a non-work-hardening material for a central sloping crack under tension and for a central crack under a quadratic temperature gradient for which previously suggested contour integrals are no longer path independent even in the linear elastic case.
TL;DR: In this article, the authors extended small bending models for the peeling of an elastic strip from a rigid substrate to large bending, and found that the present large bending analysis and the conventional models based on energy considerations predict the same dependence of peel force on peel angle.
Abstract: Previous small bending models for the peeling of an elastic strip from a rigid substrate are extended to large bending. Computational results obtained by an initial value method are presented. One finding is that the present large bending analysis and the conventional models based on energy considerations predict the same dependence of peel force on peel angle.
TL;DR: In this paper, a finite element method for determining the stress intensity factor in a cracked elastic sheet is presented, where special cracked elements are placed around each crack tip; in each special element the stresses and displacements are derived from the exact stress function while the continuity of the displacements at the nodes is satisfied in a least square sense.
Abstract: This paper presents a finite element method for determining the stress intensity factor in a cracked elastic sheet. Special cracked elements are placed around each crack tip; in each special element the stresses and displacements are derived from the exact stress function while the continuity of the displacements at the nodes is satisfied in a least square sense. A general procedure for evaluating the stiffness matrix of a cracked isotropic, or orthotropic, element is presented, and the numerical results obtained are compared with exact analytical results.
TL;DR: In this article, the authors discussed the physical meaning of the J-integral as a fracture criterion in the elastic-plastic regime and pointed out the distinction between J taken in the Eshelby [2] sense, where only elastic strains and distortions are used in evaluating the integral, as opposed to the form commonly used in elasticplastic continuum calculations, where total strain and distortion are used.
Abstract: In a recent paper Vitek and Chell [i] discussed the physical meaning of the J-integral as a fracture criterion in the elastic-plastic regime. They pointed out the distinction between J taken in the Eshelby [2] sense, where only elastic strains and distortions are used in evaluating the integral, as opposed to the form commonly used in elastic-plastic continuum calculations, where total strains and distortions are used. In the former case the integral has the physical meaning of the force on all singularities and inhomogeneities enclosed by the contour of integration and clearly will be path dependent if, in changing the contour, singularities and/or inhomogeneities are omitted or included. In contrast the physical meaning of the integral employed in continuum calculations is not clear, although it has been argued that it characterizes the crack tip environment.
TL;DR: In this paper, the authors derived an equation for the crack growth rate under creep conditions, where the authors assumed that the cavities grow by power law creep in the elastic crack tip stress field and provided the stress dependence of the crack velocity through the elastic stress intensity factor.
Abstract: An equation is derived for the crack growth rate under creep conditions. In the model, the propagation of a grain boundary crack is controlled by the plastic growth of cavities located in the grain boundaries ahead of the crack. It is assumed that the cavities grow by power law creep in the elastic crack tip stress field. Hence, the stress dependence of the crack velocity is provided through the elastic stress intensity factor, i.e., dC/dt=BK
. The cavity spacing, λ, appears as an important factor in the coefficient,B ∝ λ−(p−2)/2. At large values of λ, corresponding to less severe creep damage in the grain boundaries, the above equation would predict very low values for the crack velocity. Under such conditions, we suggest that another mechanism, whose stress dependence is provided through the net section stress, becomes active, i.e., dC/dt=B′σ
net
′
. Since λ increases with decreasing applied stress, one should observe the σnet correlation at low stresses. The results of recent creep crack growth experiments which tend to support this hypothesis are presented.
TL;DR: In this paper, the authors investigated the nature of the singular stress field developed at the point where a crack intersects the bonded interface of a bimaterial full-plane by the complex variable method.
Abstract: The nature of the singular stress field developed at the point where a crack intersects the bonded interface of a bimaterial full-plane was investigated by the complex variable method. The crack lips were assumed to be under homogeneous stress, displacement or mixed boundary conditions. The order of the singularity was shown to be dependent on both the geometry and the four elastic constants of the two materials of the composite. Graphs showing the variation of the stress singularity with the aforementioned parameters were given. Valuable results indicating how the stress singularity depends on the geometry, the elastic constants and the boundary conditions of the cracked composite full-plane were derived.
TL;DR: In this paper, the authors used interference of the +1st and -1st order diffracted beams from a 1000 lines/mm phase-type grating on the specimen surface for the measurement of strain distribution at the tip of a propagating fatigue crack in a steel plate having a central crack.
Abstract: The moire fringe multiplication method which used interference of the +1st and -1st order diffracted beams from a 1000 lines/mm phase-type grating on the specimen surface was applied to the measurement of strain distribution at the tip of a propagating fatigue crack in a steel plate having a central crack. The sensitivity of the measurement was equivalent to the sensitivity obtained from a 2000 lines/mm grating on the specimen when the conventional moire fringe method is used. The gage length was of the order of 10μm. The result of the measurement of strain distribution was applied to the estimation of the fatigue crack propagation rate.