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Showing papers on "Crack closure published in 1969"


Journal ArticleDOI
TL;DR: In this article, a fracture-mechanical theory for crack propagation in brittle ceramics subjected to thermal shock is presented and the criteria of crack stability are derived for a brittle solid uniformly cooled with triaxially constrained external boundaries.
Abstract: A fracture-mechanical theory is presented for crack propagation in brittle ceramics subjected to thermal shock. The criteria of crack stability are derived for a brittle solid uniformly cooled with triaxially constrained external boundaries. Thermal stress crack instability occurs between two values of critical crack length. For short initial crack length, crack propagation occurs kinetically, with the total area of crack propagation proportional to the factor St2 (1-2v)/EG, where St is tensile strength, v is Poisson's ratio, E is Young's modulus, and G is surface fracture energy. Under these conditions the newly formed crack is subcritical and requires a finite increase in temperature difference before propagation will proceed. For long initial crack length, crack propagation occurs in a quasi-static manner and can be minimized by maximizing the thermal stress crack stability parameter Rst= [G/α2E]1/2, where α is the coefficient of thermal expansion. For heterogeneous brittle solids, such as porous refractories, the concept of an “effective flaw length” is introduced and illustrated on the basis of experimental data in the literature. The relative change in strength of a brittle solid as a function of increasing severity of thermal shock is estimated. Good qualitative agreement with literature data is found.

953 citations


Journal ArticleDOI
TL;DR: In this paper, an expression for the dynamic elastic field of a crack when one of its tips moves arbitrarily in the plane of the crack, starting from rest, was found with the help of a theorem of Bateman's.
Abstract: With the help of a theorem of Bateman's an expression is found for the dynamic elastic field of a crack when one of its tips moves arbitrarily in the plane of the crack, starting from rest. The linear isotropic theory of elasticity is used, and only states of anti-plane strain (mode III deformation) are considered. The crack is initially of finite length and subject to any static anti-plane loading. The solution obtained becomes inaccurate in regions into which disturbances reflected at the other tip have penetrated. The error is estimated for some special cases. The results are used to discuss the equation of motion of a crack tip.

191 citations


01 Jul 1969
TL;DR: Correlation between sustained load and fatigue crack growth in high strength steels for aggressive environment effects was found in this paper, where the authors showed that sustained load is correlated with fatigue crack.
Abstract: Correlation between sustained-load and fatigue crack growth in high strength steels for aggressive environment effects

112 citations


Journal ArticleDOI
TL;DR: In this article, a model for crack propagation in low endurance fatigue is described, and a rigid-plastic analysis is shown to be consistent with the observations, and the model is used to evaluate the strength of cracks in annealed aluminium, Nylon 66 and Araldite epoxy resin.
Abstract: Studies of crack growth in fatigue of annealed aluminium, Nylon 66 and Araldite epoxy resin have revealed two mechanisms, shear and tensile tearing. The former applies both to fatigue and to tensile straining under approximately plane strain conditions and requires a capacity for plastic flow within the material. The latter mechanism occurs where flow is either restricted or impossible. A model for crack propagation in low endurance fatigue is described, and a rigid-plastic analysis is shown to be consistent with the observations.

90 citations


Journal ArticleDOI
TL;DR: In this paper, the effects of gas adsorption at the crack tip and the immediate action of adsorbed surface layers on the crack while it is growing have been investigated and the critical gas pressures which are necessary to affect crack growth depend on frequency and crack rate.
Abstract: Measurements of crack growth at fatigue frequencies of 100, 1 and 1/60 Hz in some gaseous environments show that changes of crack rate with frequency can be partly or entirely due to environment, depending on the alloy The effects of oxygen, water vapor alone and water vapor in the presence of oxygen and nitrogen have been studied The critical gas pressures which are necessary to affect crack growth depend on frequency and crack rate Mechanisms for the effects observed are discussed and results are interpreted in terms of gas adsorption at the crack tip and the immediate action of adsorbed surface layers on the crack while it is growing

85 citations



Journal ArticleDOI
TL;DR: The criteria for stress corrosion crack branching in high-strength steels are shown to be (1) a constant crack velocity and (2) attainment of a critical stress intensity.

70 citations


Journal ArticleDOI
D. P. Clausing1
TL;DR: In this article, a linear elastic fracture mechanics analysis of the conditions that produce crack instability is presented, where the authors show that if the initial crack extension causes the change in crack-tip resistance to be negative with respect to the change of cracktip loading, the crack will continue to propagate even though the loading agent remains stationary, and the crack is defined as unstable.
Abstract: A linear elastic fracture mechanics analysis of the conditions that produce crack instability is presented. If the initial crack extension causes the change in crack-tip resistance to be negative with respect to the change in crack-tip loading, the crack will continue to propagate even though the loading agent remains stationary, and the crack is defined as unstable. The value of crack-tip load when the crack becomes unstable, G c, is not only a function of the plate material and thickness and fracture mode, but also depends on the specimen geometry and size, and on the compliance of the loading system. The crack-tip resistance, G R, on the other hand, is essentially a property of the plate material and thickness and fracture mode if the crack-propagation is time independent. Once G R has been experimentally determined as a function of crack-propagation distance for a particular plate material and thickness and fracture mode, the value of G e can be calculated for the same material and thickness and fracture mode for any plate configuration for which the elastic stress analysis is known.

64 citations


Journal ArticleDOI
TL;DR: In this article, the elastic-plastic solutions of externally sharply notched tension bars, produced by digital computation using the Marcal-King finite element method, have been assessed with respect to notch stress intensifications and crack opening displacements, following an initial definition of the limitations of finite mesh size.

55 citations


Journal ArticleDOI
TL;DR: In this paper, the Cottrell-Petch formulation was used to predict the probability distribution of crack orientation angles, and from these the distribution of the surface trace angles that should be observed experimentally.

47 citations


Journal ArticleDOI
TL;DR: In this paper, a theoretical model for laser-induced supersonic cracks in crystals with weak cleavage planes is developed, which predicts the crack length-time history to be expected for a given energy-time input curve.
Abstract: A theoretical model for laser-induced supersonic cracks in crystals with weak cleavage planes is developed. The crack is pictured as being driven by a laser-induced expanding plasma. The theory predicts the crack length-time history to be expected for a given energy-time input curve. The conditions for laser-induced supersonic crack production are seen to be a large input energy relative to fracture energy, a short loading time, and a weak fracture plane. The theoretical calculations are in rough agreement with experimental observations.

Journal ArticleDOI
TL;DR: In this article, it was shown that the problem of determining the crack energy and the stress intensity factor for a cruciform crack deformed by internal pressure can be reduced to that of solving an infinite system of simultaneous linear algebraic equations.

01 Apr 1969
TL;DR: In this article, a mathematical model of FATIGUE CRACK PROPAGATION is proposed, which is based on the theory that damage due to a crash at a crack tip causes a cascade of damage.
Abstract: A MECHANICAL MODEL OF FATIGUE CRACK PROPAGATION IS PROPOSED. IT HYPOTHESIZES THAT DAMAGE DUE TO STRAIN CYCLING OF THE MATERIAL AT A CRACK TIP CAUSES PROPAGATION. MASON-COFFIN'S STRAIN CYCLE FATIGUE LAW WAS USED AS FAILURE CRITERION AND MINER'S LAW WAS USED FOR DAMAGE ACCUMULATION. THE PROPOSED THEORY CORRELATES SURPRISINGLY WELL WITH DATA FOR 2024-T351 A1 AND 4340 FULLY ANNEALED STEEL. STRAINS AT A CRACK TIP WERE MEASURED BY THE MOIRE OPTICAL INTERFERENCE METHOD. THE STRAIN AT A CRACK TIP WAS PROPORTIONAL TO DELTA K SQUARE. THE RESULTS OF STRAIN MEASUREMENTS WERE USED TO CALCULATE CRACK PROPAGATION RATE. /AUTHOR/

Journal ArticleDOI
TL;DR: The results of an experiment designed to study the effect of several variables on the subcritical crack growth rate of a high-strength steel in a water environment are presented in this paper.

Journal ArticleDOI
TL;DR: In this paper, the authors showed that fatigue crack propagation is caused by cumulative damage due to strain cycling at crack tip, relating resistance to cyclic ductility to the resistance of cyclic structures.
Abstract: Fatigue crack propagation caused by cumulative damage due to strain cycling at crack tip, relating resistance to cyclic ductility

Journal ArticleDOI
TL;DR: In this paper, the Griffith crack in a thin plate, which is opened by a uniform all-round tension at infinity, is considered and partially closed in a symmetric manner by ties, idealized by point loads in the material, and the effect upon the stress intensity factors is discussed.
Abstract: The problem of a Griffith crack in a thin plate, which is opened by a uniform all-round tension at infinity, is considered. The crack is then partially closed in a symmetric manner by ties, idealized by point loads in the material, and the effect upon the stress intensity factors is discussed.


Journal ArticleDOI
TL;DR: In this article, Hull, Beardmore and Valintine (1965) showed that it is possible to insert cracks in specimens at 77°K and to subsequently test these specimens in tension at 77k without an intermediate rise in temperature.
Abstract: Cleavage cracks have been introduced into 〈100〉 axis single crystals of tungsten by a modification of the spark discharge technique used by Hull, Beardmore and Valintine (1965). It has been possible to insert cracks in specimens at 77°K and to subsequently test these specimens in tension at 77°K without an intermediate rise in temperature. Various other test conditions have also been used. From the values of fracture stress and crack length obtained, values of the effective surface energy, γ, have been determined. In analysing the results, account has been taken of the shape of the spark crack and specimen geometry and dimensions using theoretical analyses of the stress concentrations associated with cracks. Both the temperature of crack initiation and the temperature of crack propagation were found to affect γ. For specimens in which both initiation and propagation of the cracks took place at 77°K, a value of γ = 1700 ± 300 ergs/cm2 was obtained.

Journal ArticleDOI
TL;DR: In this article, a fracture criterion was developed from the Sih-Hartranft bending theory, which, when modified to account for precatastrophic crack extension, agreed well with the experiments in regions where the crack remained open at fracture.
Abstract: Experiments were performed on cracked plates loaded in combined extension and approximately cylindrical bending. A fracture criterion was developed from the Sih-Hartranft bending theory, which, when modified to account for precatastrophic crack extension, agreed well with the experiments in regions where the crack remained open at fracture and appeared to provide a lower bound in the region where crack closure occurred.

Journal ArticleDOI
TL;DR: In this article, a vanadium modification of 4340 alloy was used for stress corrosion testing of precracked specimens in a cantilever beam apparatus, and the effect of these plastic zones on the fracture paths was demonstrated.
Abstract: Stress corrosion testing of a vanadium modification of 4340 alloy was conducted using precracked specimens in a cantilever beam apparatus. Plastic zones at the crack tip were determined using optical interference measurements, and the effect of these plastic zones on the fracture paths was demonstrated. Crack propagation rates were measured for steels of varying yield strengths (140–205 ksi). Electron fractographs and photomicrographs associated with the fracture through plastic zone are presented. Crack propagation rates were shown to vary inversely with the yield strength of the steel with the overall failure time being related to both the propagation rate and the fracture toughness of the material.

Journal ArticleDOI
TL;DR: In this article, a model is suggested to estimate the creep life of a material containing wedge cracks, and failure occurs when the crack opening displacement at the tip attains a critical level and the predictions are compared with experimentally determined stress rupture relationships.
Abstract: A model is suggested to estimate the creep life of a material containing wedge cracks. The model considers that failure occurs when the crack opening displacement at the tip attains a critical level and the predictions are compared with experimentally determined stress rupture relationships.

Journal ArticleDOI
TL;DR: In this article, the growth of fatigue cracks in aluminum alloys was studied by microscopic observation of the surface of the specimen and electron fractography. And the results of analysis for the growth by Master curve method showed that there were two stages of the growth and only the 1st stage depended on ageing conditions.
Abstract: Fatigue crack propagation in aluminum alloys was studied in thin plate under plane bending the microscopic observation of the surface of specimen and electron fractography.There were two types of fatigue crack propagation according to the conditions of ageing. One was a continuous growth type; for instance, in Al-1.5%Mg2Si alloy after natural ageing, the fatigue crack was generated at the central hole of the specimen and was developed to grow up until final failure. The other was a discontinuous propagation type; for instance, the fatigue crack of the above alloy, fully age-hardened, predominantly propagated by the linking of many isolated cracks.The results of analysis for the growth of fatigue crack by Master curve method showed that there were two stages of the growth and only the 1st stage depended on ageing conditions. The rate of growth in the 2nd stage would be a function of the product of grass strain amplitude, eG and a square root of half crack length, √l. The transition from the 1st to the 2nd stage also depended on the ageing conditions.The examination of the fatigue fracture by electron fractography showed that characteristic feature of the fracture suface depended on the stage of crack growth and the ageing conditions. The 1st stage was the shear mode of crack growth and the surface was often characterized by parallel lamellae along the direction of the growth of the crack. The 2nd stage was the tensile mode of crack growth and the surface was characterized by the striations normal to the local direction of the crack growth. Each striation represented the position of the front oftranscrystalline crack at each load cycle. There were observed two types of striations; ductile and brittle. However, the latter was observed only in aluminum alloys fully age-hardened.

Journal ArticleDOI
TL;DR: In this paper, thermal stress and displacement fields in elastic solid weakened by crack outside of circular region, noting plastic zone size and energy dissipation, and noted that the plastic zone was smaller than the elastic solid.

Journal ArticleDOI
TL;DR: In this article, the authors used the moire-fringe technique for the determination of displacement fields in test specimens of magnesium, 7075-T6 and 7178-t6 aluminum alloys.
Abstract: Experimentally determined crack-opening displacements of stationary and running cracks and of inclined stationary cracks in centrally notched plates are reported in this paper The moire-fringe technique was used for the determination of displacement fields in test specimens of magnesium, 7075-T6 and 7178-T6 aluminum alloys Experimentally determined crack-opening displacements were compared with corresponding re ults based on theoretical models of Westergaard, Dugdale, Craggs and Craggs-Dugdale In addition, normal-strain fields derived from the moire-fringe data were compared with static or dynamic strain fields of these theoretical models The results of this investigation indicate that while the Dugdale crack is a fair model of a stationary crack in ductile materials, the Craggs crack appears to be a better representation of a running crack in the ductile materials investigated

Journal ArticleDOI
TL;DR: In this article, a statistical model for the tensile fracture of parallel fiber composites is based on a stress criterion for crack propagation, and the stresses in fiber which surround a crack nucleus are evaluated and the number and size of such nuclei are evaluated statistically.
Abstract: A statistical model for the tensile fracture of parallel fiber composites is based on a stress criterion for crack propagation. The stresses in fiber which surround a crack nucleus are evaluated and the number and size of such nuclei are evaluated statistically. Failure is predicted when, statistically, a new break is expected at any crack nucleus. The predictions of this model are in good agreement with measured tensile strength, the variation of strength with size, the variability of tensile fracture srength, the very small creep strain, and the observed mechanism of fracture of fiberglass composites.

Journal ArticleDOI
TL;DR: In this article, the relationship between the strain energy release rate and the displacements of the surfaces of an extending crack in an elastic, tensile member is examined, and it is shown that G can be expressed in terms of the volume of the deformed crack provided that any stresses applied to crack surfaces are uniform.
Abstract: The relationship between the strain energy release rate, G, and the displacements of the surfaces of an extending crack in an elastic, tensile member is examined It is shown that G can be expressed in terms of the volume of the deformed crack provided that any stresses applied to crack surfaces are uniform This form is especially useful for superposition applications as it depends linearly on displacements The strain energy release rate is calculated from crack volumes for a crack in an infinite sheet and for two cases of a crack in an infinite solid: (a) a penny-shaped crack subjected to internal pressure as well as axial stress, and (b) an elliptical crack loaded by axial stress The importance of the shape of the propagating crack is demonstrated by the elliptical crack by considering various shapes for the propagating crack such as preferential propagation along a diameter or propagation as an ellipse of invariant shape A discussion of the distinction between a fracture criterion based on the strain energy release rate and one based on the stress intensity factor is presented

Journal ArticleDOI
TL;DR: In this article, the construction of harmonic functions from which the stresses and displacements in an infinite solid containing an elliptical crack and conducting heat under steady-state conditions may be obtained.

Journal ArticleDOI
TL;DR: In this paper, rotating bending and torsional fatigue tests of plain and notched steel specimens with electropolished surfaces were carried out, and the main results obtained are as follows.
Abstract: Rotating bending and torsional fatigue tests of plain and notched steel specimens with electropolished surfaces were carried out. The main results obtained are as follows. (1) The maximum shear stresses in the crack initiation limit of torsional fatigue are determined only by the stress gradient X independently of the notch depth as in the case of bending fatigue. (2) When the values of X are equal, the maximum shear stress in the crack initiation limit of torsional fatigue is about 1.2 times that of bending fatigue. (3) The surface states of notch roots after 107 cycles of the limit stress for crack initiation in torsional fatigue are similar to each other irrespective of the maximum stress repeated on the notch root, as in the case of bending fatigue. The fatigue damages at the crack initiation limit under torsional stresses are severer than the ones under bending stresses. (4) The mechanism of non-propagation of a crack in torsional notched specimens is different from that in bending notched specimens.

Journal ArticleDOI
TL;DR: In this paper, the visibility of fatigue fracture striations appears to be governed by the conditions existing along the crack front, in that they were only observed in regions where a state approximating to plane strain existed.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the strength of solids as a function of crack dimension varies in a way different from that predicted by the Griffith-Irwin theory of fracture if the range of the initial crack length is chosen to be of the order of a certain characteristic length l*, this length is related to the stress intensity factor (K) and the yield stress magnified by a constraint factor (Y) appropriate to a given stress field.
Abstract: The prime objective of this work is to show that the strength of solids as a function of crack dimension varies in a way different from that predicted by the Griffith-Irwin theory of fracture if the range of the initial crack length is chosen to be of the order of a certain characteristic length l*. This length is related to the stress intensity factor (K) and the yield stress magnified by a constraint factor (Y) appropriate to a given stress field. In other words, a characteristic quantity l*=K2/2πY2 determines the limits of applicability of the Griffith-Irwin theory. The second objective is to introduce time as a meaningful variable in fracture mechanics and to study its effect upon the strength. This is done by accepting a certain model which allows for linear time-dependent behaviour of the matrix in which the crack is embedded, and by assuming that the non-linear effects due to large plastic and viscous deformations are confined to the Dugdale-type narrow zones in the crack plane. As the final result we obtain in place of one (static) curve of strength against crack length a continuous time spectrum of such curves, each of which is valid for a different moment t. A simple `cut-ends cigar' model of a crack is proposed to describe the effects of plasticity (small-scale yielding) and time on fracture.