Showing papers in "International Journal of Fracture in 1983"
258 citations
TL;DR: In this paper, the effect of material rate sensitivity on the localization of deformation in a porous visco-plastic solid is examined under plane strain tension and axisymmetric tension conditions.
Abstract: The effect of material rate sensitivity on the localization of deformation in a porous visco-plastic solid is examined under plane strain tension and axisymmetric tension conditions. The plastic flow rule proposed by Gurson [3], modified to account for material rate sensitivity, is adopted to model the plastic softening behavior that arises due to void nucleation and growth. An initial imperfection in the form of a planar band is assumed and a material instability is sought as the deformation proceeds.
194 citations
193 citations
TL;DR: In this paper, the authors investigated the stability of straight crack paths and showed that the straight crack path is unstable, i.e. that tip to tip coalescence will not take place.
Abstract: The experimentally known phenomenon that originally collinear mode I cracks seem to avoid each other before coalescence is studied by investigating the stability of straight crack paths. To this end a periodic array of approximately collinear but slightly curved cracks is considered. Stress intensity factors for modes I and II are derived and the growth of originally straight cracks under mode I conditions is studied after introduction of a disturbance that forces the cracks to deviate from a straight path. It is shown that the straight crack path is unstable, i.e. that tip to tip coalescence will not take place.
148 citations
TL;DR: In this article, the authors proposed a new approach based on maximum tangential principal stress (MTPS) to predict the angle of crack extension, critical load and unstable crack paths.
Abstract: Predictions for the angle of crack extension, critical load and unstable crack paths based on the criteria of maximum tangential stress (MTS), maximum tangential strain (MTSN) and strain energy density (SED) for angled slit and elliptical cracks under uniaxial tensile loading are compared. The tangential stress associated with the MTS criterion need not be a principal stress and a new approach to this criterion is suggested. A criterion based on maximum tangential principal stress (MTPS) is proposed. Predictions by these two criteria are compared. Some difficulties associated with the application of the SED criterion are indicated. A new basis, which permits a unification of all the criteria in respect of prediction of critical load, is suggested. Some of the results have been compared with data available in the literature.
112 citations
TL;DR: In this article, the weight function method was used to calculate stress intensity factors for a semi-elliptical surface crack in a plate exposed to stress gradients, and the stress intensity factor was calculated for a plate with respect to a fixed number of cracks.
Abstract: The weight function method is used to calculate stress intensity factors for a semi-elliptical surface crack in a plate exposed to stress gradients.
104 citations
TL;DR: In this article, the dislocation free zone at the tip of a mode III shear crack is analyzed using a pile-up of screw dislocations parallel to the crack front.
Abstract: The dislocation free zone at the tip of a mode III shear crack is analyzed. A pile-up of screw dislocations parallel to the crack front, in anti-plane shear, in the stress field of a crack has been solved using a continuous distribution of dislocations. The crack tip remains sharp and is assumed to satisfy Griffith's fracture criteria using the local crack tip stress intensity factor. The dislocation pile-up shield the sharp crack tip from the applied stress intensity factor by simple addition of each dislocation's negative contribution to the applied stress intensity value. The analysis differs substantially from the well known BCS theory in that the local crack tip fracture criteria enters into the dislocation distributions found.
90 citations
TL;DR: In this article, a quasi-static crack growth in a finite brittle solid is examined, and a solution method which accounts for the finite geometry and the applied boundary conditions is presented.
Abstract: The problem of a slightly non-collinear, quasi-static crack growth in a finite brittle solid is examined. A solution method which accounts for the finite geometry and the applied boundary conditions is presented. The approach uses the results of the first order perturbation solution for non-collinear crack extension from the tip of a semi-infinite straight crack, in an alternating solution scheme which takes into account the effect of the finite geometry and the boundary conditions in an iterative manner. For illustration, a slightly slanted Griffith crack under biaxial loading is examined.
87 citations
TL;DR: In this paper, the authors proposed the cyclic J-integral as a criterion for fatigue crack growth, which is evaluated as a generalized force on dislocations to be moved or the energy flow rate to be dissipated to heat by the dislocation movements in an element just attached to the fatigued crack tip during one cycle of loading.
Abstract: The definition of the cyclic J-integral is offered and its physical significance for fatigue crack growth is discussed using the Dugdale model on the assumption that the crack closure, cycle dependent creep deformation, and crack extension under cycling can be neglected. It is shown that the cyclic J-integral for small scale yielding is equivalent to theJ-integral for linear elastic crack independent of loading processes, while the value for large scale yielding varies with the loading processes. However, in both cases, the cyclicJ-integral remains constant during the reversal of loading under a constant stress range, if the first monotonic loading stage is excluded. In this situation, the cyclicJ-integral can be applied as a criterion for fatigue crack growth, since it is evaluated as a generalized force on dislocations to be moved or the energy flow rate to be dissipated to heat by the dislocation movements in an element just attached to the fatigued crack tip during one cycle of loading. It is suggested that the available experimental data of different materials for fatigue crack growth can be generalized to a unified formulation on the basis of the energy criterion. It is also deduced that the threshold ΔJ corresponding to ΔKth should be larger than 4γ where γ is the surface energy of the material. Finally the operational definition of the cyclicJ-integral on single loadversus displacement curves is given for center cracked plate with wide uncracked ligaments in tension.
85 citations
TL;DR: In this paper, the relative importance of internal gas pressurization and stress-wave-induced circumferential tensions for extending radial cracks originating at the borehole walls was investigated.
Abstract: Explosive loading in borehole configurations has been investigated to assess the relative importance of internal gas pressurization and stress-wave-induced circumferential tensions for extending radial cracks originating at the borehole walls. Simple calculations of an extending crack (with and without confining pressure) were performed to estimate an upper bound on crack length resulting solely from internal pressurization for comparison with the crack length resulting solely from tensile stresses. These calculations indicated that a internal gas pressure could increase the crack length by a factor of 10 to 100 (no confining pressure) or 3 to 25 [6.9-MPa (1000-psi) confining pressure] compared with the tensile stresses acting alone. Simple laboratory experiments were performed using 3.2 × 10−3m diameter (1/8in.) by 1.52 × 10−1m long (6 in.) borehole charges centered in a 1.3 × 10−2m diameter (1/2in.) borehole in transparent Plexiglas cylinders 3 × 10−1m in diameter by 3 × 10−1m long (12in. by 12in.) to verify these computational results. Two tests were performed: one with a thin (5.08 × 10−4m) steel liner to contain the explosive gases and one without a liner so that the explosive gases could enter and pressurize the fractures. A confining pressure of 6.9 MPa (1000 psi) was applied to the Plexiglas cylinders in both experiments to better simulate field conditions and to contain the cracks within the cylinder; all other experimental conditions were identical. These experiments indicated that the primary effect of the explosive gases was to increase crack length by a factor of five to ten compared with the tensile stresses acting alone, in approximate agreement with the predictions.
81 citations
TL;DR: In this paper, the internal stress and displacement fields for a body in an external applied stress field, and containing a prescribed distribution of penny shaped cracks, are constructed as expansions in the parameter space.
Abstract: Statistical solutions for the internal stress and displacement fields are constructed for a body in an external applied stress field, and containing a prescribed distribution of penny shaped cracks. From the fields, a stress-strain relationship is calculated for the body, and effective elastic moduli are derived. The fields are constructed as expansions in the parameter
$$\overline {Na^3 }$$
wich is assumed small (N is the crack density, anda is the crack radius). Angular integrals over the distribution function are performed for two special cases that represent a bedded crack distribution, and an isotropic crack distribution. A criterion for the validity of the use of these quasistatic results in dynamical calculations is presented.
TL;DR: In this article, an analytical comparison of a standard and a side-grooved compact tension specimen was performed using 3-13 finite element techniques in the elastic regime as well as under large-scale yielding conditions.
Abstract: This paper presents an analytical comparison of a standard and a side-grooved compact tension specimen. Both specimens were analyzed using 3-13 finite element techniques in the elastic regime as well as under large-scale yielding conditions. The standard specimen reveals large variations of both the crack opening displacement and the energy release rate along the crack front clearly indicating that the crack will tend to propagate in a tunneling mode. The side-grooved specimen, on the other hand, provides a much more uniform variation of both parameters thereby promoting both flat fracture and a uniform crack growth. The results clearly indicate that for ductile materials loaded well into the plastic range, a much more uniform fracture process can be obtained with the side-grooved specimen.
TL;DR: In this article, the elasticity problem for a long hollow circular cylinder containing an axisymmetric circumferential crack subjected to general nonaxismmetric external loads is considered.
Abstract: The elasticity problem for a long hollow circular cylinder containing an axisymmetric circumferential crack subjected to general nonaxisymmetric external loads is considered. The problem is formulated in terms of a system of singular integral equations with the Fourier coefficients of the derivative of the crack surface displacement as density functions. The stress intensity factors and the crack opening displacement are calculated for a cylinder under uniform tension, bending by end couples, and self-equilibrating residual stresses.
TL;DR: In this article, the authors used Fourier transforms and the Wiener-Hopf technique in conjunction with plane elastostatics to examine the singular crack tip stress field in the Double Cantilever Beam (DCB) specimen.
Abstract: Fourier transforms and the Wiener-Hopf technique are used in conjunction with plane elastostatics to examine the singular crack tip stress field in the Double Cantilever Beam (DCB) specimen With terms of orderh
2/a
2 retained in the series expansion, the dimensionless stress intensity factor is found to be
$$Kh^{\tfrac{1}{2}} /P = (12)^{\tfrac{1}{2}} (a/h + 06728 + 00377h^2 /a^2 )$$
, in whichP is the magnitude of the concentrated forces per unit thickness, a is the distance from the crack tip to the points of load application, andh is the height of each cantilever beam This result is quite similar to the expression
$$Kh^{\tfrac{1}{2}} /P = 346a/h + 238$$
, which Gross and Srawley obtained by fitting a line to discrete results from their boundary collocation analysis Still another expression,
$$Kh^{\tfrac{1}{2}} /P = [12\{ (a/h + 06)^2 + \tfrac{1}{3}\} ]^{\tfrac{1}{2}}$$
, obtained by Ripling, Mostovoy and Patrick from a strength of materials approach combined with compliance measurements, although somewhat different in form from the present results, also yields accurate values ofK for thea/h-range of practical interest (2 ⩽a/h ⩽ 10) The present result serves as both a confirmation and a refinement of the Gross and Srawley formula For this reason, and because of its simplicity, the present result should be useful in the derivation of other simple and parametrically appropriate equations for the analysis of data from DCB specimen tests
TL;DR: The creep crack growth behavior of a type 316 stainless steel was characterized at 594°C (1100°F) using precracked single edge notch specimens loaded in displacement rate control as discussed by the authors.
Abstract: The creep crack growth behavior of a type 316 stainless steel was characterized at 594°C (1100°F) using precracked single edge notch specimens loaded in displacement rate control. The steady-state crack growth rate, da/dt, correlated with J-integral and did not correlate with C*. The creep crack growth behavior in this material and temperature is compared with our previous creep crack growth rate data on a Cr-Mo-V steel at 538°C (1000°F) and on type 304 stainless steel at 594°C in which da/dt correlated with C*. A detailed discussion is included on why in some materials creep crack growth rate correlates with J integral and in others it correlates with C*.
TL;DR: In this paper, an analysis of the stress intensity factor due to residual stress is made for a crack perpendicular to the welding joint in a large plate, where the residual stress distribution is represented by a simple function which is chosen to satisfy the physical requirements for residual stress and to simulate the commonly observed distribution.
Abstract: An analysis of the stress intensity factor due to the residual stress is made for a crack perpendicular to the welding joint in a large plate. The residual stress distribution is represented by a simple function which is chosen to satisfy the physical requirements for the residual stress and to simulate the commonly observed distribution. The stress intensity factor is obtained using customary method based on the superposition principle. The function chosen for the residual stress distribution leads to an exact expression of the stress intensity factor in a simple closed form. The solution yields somewhat conservative values of the stress intensity factor for large cracks and it may be conveniently used for practical applications.
TL;DR: In this article, a study of fatigue crack propagation in mode III (antiplane shear) for A469 and A470 commercial rotor steels (tensile strength 621 and 764 MN/m2 respectively) using torsionally-loaded circumferentially-notched cylindrical specimens was made.
Abstract: A study has been made of fatigue crack propagation in mode III (anti-plane shear) for A469 and A470 commercial rotor steels (tensile strength 621 and 764 MN/m2 respectively) using torsionally-loaded circumferentially-notched cylindrical specimens. For crack growth under both small-and large-scale yielding conditions, radial mode III crack propagation rates are observed to be similar in both steels and to be uniquely related to the plastic intensity range 163-1 per cycle, provided friction, abrasion and interlocking between sliding crack faces is minimized by the application of a small tensile mean load. Over the range studied (i.e., ≈10-6 to 10-1 mm/cycle), mode III growth rates (dc/dN)III are found to be independent of load ratio (for R=−1.0 and −0.5) and to be a power law function of 163-1 or the mode III cyclic crack tip displacement. When compared to mode I crack growth at equivalent cyclic crack tip displacements, however, crack propagation rates in mode III are seen to be two orders of magnitude smaller than in mode I. Based on fractographic evidence of elongated voids, parallel to the crack front, at the tip of the fatigue crack, several models for mode III crack growth are proposed utilizing the concept that mode III crack advance occurs by the initiation and coalescence of voids formed at inclusions directly ahead of the crack tip. By considering the linkage of these voids to take place by mode II shear parallel to the main crack front, expressions for the mode III crack propagation rate are developed based either on considerations of the local mode II crack tip displacementsor the mode II accumulated crack tip strain (computed from the Coffin-Manson damage relationship). Whereas both types of models predict mode III growth rates to be a small fraction of the cyclic crack tip displacements per cycle, the damage accumulation model in particular is found to provide excellent agreement with experimentally measured growth rates in the present rotor steels.
TL;DR: In this paper, the conditions of crack length, pulse amplitude, and pulse duration predicted by each criterion for crack instability under stress wave loads are presented and compared, and a data base was generated by performing plate impact experiments on epoxy specimens embedded with thin circular disks that acted as internal penny-shaped cracks.
Abstract: Previously proposed dynamic crack instability criteria are reviewed. The conditions of crack length, pulse amplitude, and pulse duration predicted by each criterion for crack instability under stress wave loads are presented and compared. To discriminate among these criteria, a data base was generated by performing plate impact experiments on epoxy specimens embedded with thin circular disks that acted as internal penny-shaped cracks. The observed instability behavior of these cracks under 2-µs stress pulses of various amplitudes was best described by a criterion that requires the dynamic stress intensity to exceed the dynamic fracture toughness for a certain minimum time.
TL;DR: In this paper, a velocity gauge was devised to measure the crack length with good accuracy over the whole range of speeds of interest, and a suspension of graphite particles was applied by spraying or by screen-printing over the surface where the crack is expected to propagate.
Abstract: ck growth. Only a few of the available methods [i] are able to measure continuously the crack length, a, with good accuracy over the whole range of speeds of interest. Moreover, they often make use of the specific properties of metallic specimens. Polymers, which are relevant here, and ceramics must, therefore, be tested by another method. A velocity gauge has been devised to fill this gap. A suspension of graphite particles is applied by spraying or by screen-printing over the surface where the crack is expected to propagate. A small quantity of binder facilitates handling without giving the gauge specific fracture properties. It is, indeed, intended that the particles follow locally exactly the behaviour of the specimen. The critical parameter is, therefore, the crack opening displacement (COD). Particles with diameters greater than the COD are liable to form bridges over the crack. Particle sizes in the order of I ~m were used satisfactorily with polymeric samples. The thickness of the layer should be as small as possible, a homogeneous layer of about 5 zm being obtainable in practice. Silver-ink electrodes permit the creation of a quasi-linear electric field. It is proposed that two such lines be drawn on the graphite, parallel to the crack using a drawing pen. Due to the high resistivity of graphite, as compared to metals, usual Ohmmeters are suitable for measuring the gauge resistance. Fig. 1 shows the final arrangement of the gauge. The initial resistance R measured between the electrodes is dependent on the restivity of [he graphite PC and the dimensions of the gauge, thickness ~, length l, and width b
TL;DR: In this paper, a newly developed specimen was proposed for use in accurately measuring K, which was used for the first time in the measurement of Kiic, and it has been shown that most cracks will be loaded in a mixed mode field.
Abstract: The object of this note is to report on a newly developed specimen which is proposed for use in accurately measuring K . Since it has Ilc been generally assumed that mode I displacement is dominant, most investigations to date have concentrated on this failure mode; it seems clear however, that most cracks will be loaded in a mixed mode field. Moreover, mode II deformations may dominate as for example in the spar web of an airplane wing. Several specimens have appeared in the literature [1,2,3,4] to measure Kiic, each of which has various deficiencies.
TL;DR: In this paper, a theoretical model relating fracture toughness expressed as JIC and bulge ductility for a material exhibiting linear elastic behavior at low temperature and elastic-plastic behavior at higher temperatures is proposed.
Abstract: A theoretical model relating fracture toughness expressed as JIC and bulge ductility {ie71-1} for a material exhibiting linear elastic behavior at low temperature and elastic-plastic behavior at higher temperatures is proposed. This model shows a variation of JIC with {ie71-2} for linear elastic behavior and JIC with {ie71-3} for elastic-plastic behavior. The model contains three constants to be determined experimentally for a given material, specimen geometry and testing conditions. A case study on 1045 steel in the temperature range −60 to 25°C confirms the validity of the model. The experimental results help in determining the size of the fracture zone ahead of the crack as well as the mechanisms for crack blunting and crack growth.
TL;DR: In this article, the influence of gravity on the gas-dynamical process driven by the piston is discussed in terms of characteristic theory, and the flow field is given quantitatively.
Abstract: Two local solutions, one perpendicular and one parallel to the direction of solar gravitational field, are discussed. The influence of gravity on the gas-dynamical process driven by the piston is discussed in terms of characteristic theory, and the flow field is given quantitatively. For a typical piston trajectory similar to the one for an eruptive prominence, the velocity of the shock front which locates ahead the transient front is nearly constant or slightly accelerated, and the width of the compressed flow region may be kept nearly constant or increased linearly, depending on the velocity distribution of the piston. Based on these results, the major features of the transient may be explained. Some of the fine structure of the transient is also shown, which may be compared in detail with observations.
TL;DR: In this article, a micromechanistic model of warm pre-stressing is extended to predict the combined effects of pre-straining and strain ageing on the cleavage fracture toughness of ferritic steels.
Abstract: A micromechanistic model of warm pre-stressing is extended to predict the combined effects of warm pre-stressing and strain ageing on the cleavage fracture toughness of ferritic steels The crack tip stress distribution after a cycle of pre-straining and strain ageing is estimated by superposition of the appropriate monotonic loading stress distributions The Ritchie, Knott and Rice model of cleavage fracture and its associated fracture criterion are employed in conjunction with the crack tip stress distribution to predict the critical stress intensity factor after warm pre-stressing and strain ageing Illustrative calculations are presented, based upon the published material's properties of a high nitrogen mild steel Available experimental data for pressure vessel steels bear out the form of the predictions At low temperatures, and after heavy pre-loads, the benefits of warm pre-stressing dominate strain ageing induced embrittlement and the toughness is apparently enhanced At higher temperatures, or after small pre-loads, however, strain ageing dominates and the apparent toughness is reduced Various assumptions and approximations inherent in the model are discussed These generally tend to render the predictions conservative Finally it is noted that the model should be equally applicable to the prediction of the combined effect of warm pre-stressing and neutron irradiation on the cleavage fracture toughness of ferritic steels
TL;DR: In this paper, a singular integral equation (with a kernel with a logarithmic singularity) was proposed for the crack problem inside an elastic medium under plane or antiplane conditions.
Abstract: A new singular integral equation (with a kernel with a logarithmic singularity) is proposed for the crack problem inside an elastic medium under plane or antiplane conditions. In this equation the integral is considered in the sense of a finite-part integral of Hadamard because the unknown function presents singularities of order −3/2 at the crack tips. The Galerkin and the collocation methods are proposed for the numerical solution of this equation and the determination of the values of the stress intensity factors at the crack tips and numerical results are presented. Finally, the advantages of this equation are also considered.
TL;DR: In this article, an integral transform method is used to find the solution of the equation of motion from the linear theory for a homogeneous, isotropic elastic material, which resolves the problem into an integral equation.
Abstract: In an earlier paper [6] we have studied the case of interaction of shear waves with a crack centrally situated in an infinite elastic strip; we, in this paper, extend the study to the case of two coplanar Griffith cracks. An integral transform method is used to find the solution of the equation of motion from the linear theory for a homogeneous, isotropic — elastic material. This method resolves the problem into an integral equation. It has been observed that shear waves with frequencies less than a parameter depending on the width of the wave guide can only propagate. The integral equation is solved numerically for a range of values of wave frequency, width of strip and the inter-crack distance. These solutions are used to calculate the dynamic stress intensity factor. The results are shown graphically.
TL;DR: In this paper, a tapered load-sharing rule is considered which distributes the nominal load of a failed fiber among its four nearest neighbors, with the two adjacent fibers taking a greater proportion of the load.
Abstract: This paper continues the study of the chain-of-bundles model for the statistical strength of composite materials by focusing carefully on the localized load redistribution in two-dimensional composites. A tapered load-sharing rule is considered which distributes the nominal load of a failed fiber among its four nearest neighbors, with the two adjacent fibers taking a greater proportion of the load. We consider three distinct probabilistic techniques of analysis and find that the basic probability structure for the distribution for composite strength turns out to be the same as for the idealized local load-sharing in earlier work; however, the median strength of the composite rises moderately due to the milder overloads on the fibers adjacent to breaks, while the presence of small overloads on more distant fibers has almost no effect on strength. Also, the variability in composite strength tends to decrease mildly, due to a slight increase in the critical fracture sequence size leading to catastrophic failure. Again, the Weibull distribution arises as a key model for the strength of unidirectional composites, and we give accurate approximations for its parameters.
TL;DR: In this paper, the authors compared the results of Tweed and Rooke and Newman for a single crack and two symmetric cracks, and showed that the ratio of the two K factors is the same for both symmetric and single cracks.
Abstract: Numerical results for the stress intensity factor of a crack at the edge of a hole in an infinite sheet were published by Bowie [i], Newman [2], and Tweed and Rooke [3]. Bowie solved this problem for both a single crack and two symmetric cracks, see inset of Figure i. Newman treated the results for two symmetric cracks, and Tweed and Rooke for a single crack. The results of Bowie will be compared to those of the other two sources. The prime reason for doing so was a comparison between K factors for a single crack and two symmetric cracks. The ratio of the two K factors is
TL;DR: In this article, the relationship between crack growth rate dc/dN and T appears to be a material property, independent of testpiece geometry, and the tearing energy, T is substantially independent of crack length.
Abstract: Repeated deformation of rubber cylinders in compression causes cracks to initiate at tensile stress concentrations (eg. bond edges). The cracks grow to remove the rubber which at maximum deformation bulges outside the original profile of the cylinder. The results are analysed in terms of fracture mechanics. The tearing energy, T is substantially independent of crack length. The relation between crack growth rate dc/dN and T appears to be a material property, independent of testpiece geometry.
TL;DR: In this paper, a discussion of the validity of the arrest condition in a linear theory is made based upon experimental results and the inverse problem is also considered, i.e. to predict the crack growth event, the arrest length and the corresponding stress intensity factors when the crack propagation toughness is known for the material.
Abstract: Crack arrest experiments are performed on edge-notched specimens of a high strength steel. The crack velocity and the displacements at the boundaries are continuously measured during the experiments. This information is then used in a subsequent FEM analysis to evaluate the dynamic stress intensity factor before and after crack arrest. Dynamic effects are seen to influence the process a considerable time after the arrest. A discussion of the validity of the arrest condition in a linear theory is made based upon experimental results. The inverse problem is also considered, i.e. to predict the crack growth event, the arrest length and the corresponding stress intensity factors when the crack propagation toughness is known for the material. The predicted values are shown to exhibit good agreement with the experimental results.