On interface crack propagation with variable velocity for longitudinal shear problems

The antiplane strain problem of straight interface crack propagation between two elastic half-spaces under arbitrary variable loading is considered. The crack edge is specified as an arbitrary smooth function of time. It is assumed that the crack speed is less than the smaller of the shear wave velocities of two media. An integral transform method and factorization technique are used to solve the problem. The solutions are worked out for semi-infinite crack and finite crack problems. The dynamic stress intensity factors at the crack tip of the moving interface crack are given and it is found that the stress intensity factor of the interface crack is slightly higher than that in the homogeneous medium with slower shear wave velocity.     

Stress Intensity Factor of an Edge Crack in Bonded Orthotropic Materials

The article presents the problem of an edge crack under normal point loading terminating perpendicular to the surface of an orthotropic strip of finite thickness which is bonded to another orthotropic half plane. Expressing the displacements and stresses in plane strain condition in terms of harmonic functions, the problem is reduced to a pair of simultaneous integral equations with Cauchy type singularities, which are finally been solved by the Hilbert transform technique. The analytical expression of stress intensity factor (SIF) at the crack tip for large thickness of the strip is calculated, which corresponds to the weight function of a crack under normal loading. The influences of elastic constants of two different orthotropic materials, distinct arbitrary locations of normal point loading on the crack surface and length of the crack on the dynamic SIF are depicted through graphs.     

A griffith crack at the interface of two bonded dissimilar elastic half planes in which body forces are acting

The plane strain problem of determining the stress distribution in the neighbourhood of a Griffith crack situated at the interface of two bonded dissimilar isotropic half planes is investigated. Two types of loadings are considered. Firstly, the crack surfaces are subjected to arbitrary surface tractions, while the body forces are assumed to be zero everywhere in the composite plane. Secondly, there is arbitrary distribution of body forces in the upper as well as the lower half plane, while the crack surfaces are stress free. A special case of the first type of loading, namely, that in which the crack surfaces are subjected to a self equilibrating load system has been discussed separately in detail. This special case is well known in the literature and it has been used here to tackle the problem with second type of loading. Another problem whose solution has been obtained here and used to tackle the problem with the second type of loading is that in which the upper as well as the lower half plane is subjected to arbitrary distribution of body forces, but there is no crack at the interface. Particular distributions of concentrated loads in the nonhomogeneous infinite plane are discussed in detail. Analytical results are compared with the known ones in the literature and numerical results are presented grapically.     

Transient dislocation emission from a crack tip in an anisotropic elastic material

The emission of a dislocation with a general Burgers vector from the tip of a stationary semi-infinite crack in an anisotropic elastic material is examined. The dislocation is assumed to leave the crack tip along the crack extension plane at constant speed. Explicit expressions for the transient shielding stress intensity factors at the crack tip and the drag forces on the dislocations are derived. Numerical results for a class of cubic materials and two hexagonal crystals, zinc and cobalt, are given. Dislocation emission under plane stress wave loading is discussed.     

A phenomenological theory of subcritical creep crack growth under constant loading in an inert environment

The subcritical creep crack growth under constant loading is considered as due to the repeated rupture of the plastic zone in the vicinity of the crack tip. Fracture mechanics concepts are used to derive the rupture life of a centre-cracked thin sheet loaded in plane stress. The formulation is such that numerical results can readily be obtained for crack growth. Approximate analytical formulae are also given for crack growth against time.     

Partial closure of a Griffith crack under a general loading

The plane problem of a Griffith crack, partially closed under the effect of a general loading, is considered. The three cases of: a) closure at one end under a nonsymmetrical loading; b) closure at the two ends under a symmetrical loading; and c) closure at the middle under a symmetrical loading, are considered separately. Examples are given from partial closures by concentrated forces of cracks opened by a uniform tension at infinity or a parabolic pressure on the crack surface. The effect of the concentrated forces in decreasing the stress intensity factors so as to prevent crack propagation is examined.     

On the crack propagation with variable velocity

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.

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Zusammenfassung Man untersucht das ebene Problem der Ausdehnung eines geraden Risses in einem elastischen Medium unter beliebig veränderlichen Belastung. Die Örter der Ränder des Risses werden als beliebige stetige Funktionen der Zeit angenommen mit der einzigen Einschränkung daß die Rißgeschwindigkeit zu jedem Zeitpunkt kleiner ist als die Geschwindigkeit der Rayleighwelle. Die Lösung der Verteilung der ebenen Spannungskomponenten an der Rißspitze wird aufgestellt. Insbesondere werden die Spannungsintensitätsfaktoren am Riß gegeben, was die Ableitung der Rißausdehnung unter gegebenen Belastungsbedingungen ermöglicht.

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Résumé On considère le problème plan de la propagation d'une fissure droite dans un milieu élastique soumis à une charge arbitraire et variable.On spécifie que les lieux des bords de la fissure sont des fonctions monotones du temps, sous la seule réserve que la vitesse de fissuration est à tout moment inférieure à la vitesse de propagation des ondes de Rayleigh. On obtient une solution pour la distribution des composantes de la contrainte plane au voisinage de la pointe de la fissure.En particulier, des expressions du facteur d'intensité des contraintes à l'extrémité de la fissure sont fournies, qui permettent de déduire le mouvement de la fissure sous des conditions de charge déterminées.

     

A solution method for finding dynamic stress intensity factors for arbitrarily oriented cracks in transversely isotropic materials

The transient elastodynamic response of a transversely isotropic material containing a semi-infinite crack under uniform impact loading on the faces is examined. The crack lies in a principle plane of the material, but the crack front does not coincide with a principle direction. Rather, the crack front is at an angle to a principle direction and thus the problem becomes more three-dimensional in nature. Three loading modes are considered, i.e., opening, in-plane shear and anti-plane shear. The solutions for the stress intensity factor history around the crack tip are found. Laplace and Fourier transforms together with the Wiener-Hopf technique are employed to solve the equations of motion directly. The asymptotic expression of stress near the crack tip leads to a closed-form solution for the dynamic stress intensity factor for each loading mode. It is found that the stress intensity factors are proportional to the square root of time as expected. Results given here converge to known solutions in transversely isotropic materials with a crack oriented along a principle direction and isotropic materials as special cases. The results of this analysis are used to find approximate strain energy release rates for dynamically loaded penny shaped cracks.     

The green's function for a slant edge crack

The Green's functions are determined for plane edge cracks which meet the free surface at an arbitrary angle. Modes I and II stress intensification factors are found for both normal and shear loading of the crack, since coupling is found to occur between each type of loading and the two possible modes of crack-tip response.     

A surface crack in a graded coating bonded to a homogeneous substrate under dynamic loading conditions

The elastodynamic problem of a surface crack in a graded coating bonded to a homogeneous substrate under dynamic loading is considered. The coating is graded along the thickness direction and modeled as a nonhomogeneous medium with an isotropic stress-strain law. The problem is solved under the assumption of plane strain or generalized plane stress conditions. The crack surfaces are subjected to arbitrary dynamic loadings which give rise to mixed fracture modes which turn out to be uncoupled due to the fact that the crack axis is parallel to the material gradient. Using integral transforms, the resulting mixed-boundary value problem is reduced to a set of two uncoupled singular integral equations which are solved numerically to obtain the crack-tip stress intensity factors. The main objective of the paper is to study the effect of the coating thickness and nonhomogeneity parameter on the crack tip dynamic stress intensity factors for the purpose of gaining better understanding on the behavior of graded coatings.     

A new boundary integral equation method of three-dimensional crack analysis

Introducing the mode II and mode III dislocation densities W ₂(y) and W ₃(y) of two variables, a new boundary integral equation method is proposed for the problem of a plane crack of arbitrary shape in a three-dimensional infinite elastic body under arbitrary unsymmetric loads. The fundamental stress solutions for three-dimensional crack analysis and the limiting formulas of stress intensity factors are derived. The problem is reduced to solving three two-dimensional singular boundary integral equations. The analytic solution of the axisymmetric problem of a circular crack under the unsymmetric loads is obtained. Some numerical examples of an elliptical crack or a semielliptical crack are given. The present formulations are of basic significance for further analytic or numerical analysis of three-dimensional crack problems.     

High-cycle fatigue mechanisms in 1045 steel under non-proportional axial-torsional loading

Detailed microscopic analyses have been made on the high-cycle mechanisms in 1045 steel under various stress-controlled axial-torsional loadings. A special attention has been paid to a critical example of non-proportional loading, i.e., 90° out-of-phase loading with different stress ratios. The replica technique has been used to monitor crack initiation and propagation from the microstructure scale. The orientations of persistent slip bands and Stage I cracks are in good agreement with the critical plane concept. The evolutions of crack length with cycle life as well as the crack aspect ratios depend on the loading condition. However at a given life, the data are consolidated in terms of crack depth versus cycle life. The McDiarmid parameter correlates stress-life data under proportional loadings. However, it underestimates fatigue lives under out-of-phase loading at high stress ratio and it overestimates them in the case where all planes experience the same shear stress amplitude (stress ratio = 0.5). More damaging mechanisms are involved in crack initiation and crack propagation. It is recommended to test the fatigue performance of materials in this last condition that involves the worst damage mechanisms.     

On the stress wave induced curving of fast running cracks — a numerical study by a time-domain boundary element method

Summary Fast crack propagation in dynamically loaded plane structures is investigated. The major point of interest is the evolution of the crack trajectory under the influence of stress waves which are generated and repeatedly reflected at the specimen boundaries. Since these waves may lead to arbitrary mixed-mode and time-dependent loading of the crack tip, both the direction and speed of crack advance are determined from a fracture criterion.Starting point is a system of time-domain boundary integral equations which describes the initial boundary value problem of a linear elastic body containing an arbitrarily growing crack. The unknown displacements and/or tractions on the exterior boundary and the displacement jumps across the crack are computed numerically by a collocation method in conjunction with a time-stepping scheme. Crack growth is modelled by adding new boundary elements of constant length at the running crack tip.The method proves to be of sufficient accuracy when applied to problems treated with other numerical techniques. Moreover, the simulation of dynamic crack propagation under various geometry and loading conditions enables the reproduction and analysis of complex phenomena observed experimentally.     

A method for tracking internal crack propagation in railhead

This paper presents a method for tracking two-dimensional propagation of internal cracks, in particular vertical split head (VSH) defects, due to contact loading in railhead. Generalised curved crack is assumed to have present in the railhead and its propagation is simulated by solving interaction of arbitrary shaped cracks successively. Furthermore, the finite shape of the rail section is also modelled as the continuous distribution of dislocation within an infinite plane. Crack propagation is simulated using the criterion of vanishing of Mode II stress intensity factors (SIF) at crack tips. Examples are provided for tracking the propagation of pre-existing internal cracks in railheads turning into VSH defects under centric contact loading.     

The stress intensity factors for pressed cracks in arbitrary shapes

A boundary element method (BEM) was specially developed for a crack under crack face pressure in arbitrary two-dimensional problems. It is based on the basic stress solutions for an infinite plane with a crack loaded by body forces and moment at arbitrary point, which were derived by Erdogan from the Kolosov-Muskhelishvili fundamental functions, and the basic solution for a crack in an infinite plate under crack surface pressure, so that the crack surface need not be modelled. Therefore, minimal modelling efforts are needed to obtain stress intensity factors with the method and its accuracy was established by comparing the obtained results with the exact SIF results and acceptable results for various problems of arbitrary shapes and loadings.     

Thermal effect of plastic dissipation at the crack tip on the stress intensity factor under cyclic loading

Plastic dissipation at the crack tip under cyclic loading is responsible for the creation of an heterogeneous temperature field around the crack tip. A thermomechanical model is proposed in this paper for the theoretical problem of an infinite plate with a semi-infinite through crack under mode I cyclic loading both in plane stress or in plane strain condition. It is assumed that the heat source is located in the reverse cyclic plastic zone. The proposed analytical solution of the thermo-mechanical problem shows that the crack tip is under compression due to thermal stresses coming from the heterogeneous stress field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum and its range) is calculated analytically for the infinite plate and by finite element analysis. The heat flux within the reverse cyclic plastic zone is the key parameter to quantify the effect of dissipation at the crack tip on the stress intensity factor.     

Fatigue crack growth analysis using 2-D weight function

A method for crack growth analysis of planar cracks under arbitrary Mode I loading is presented in the paper. The method is based on the point-load (2-D) weight function used for the calculation of stress intensity factors. An algorithm for the analysis of fatigue crack growth of planar cracks, and validation results supporting the entire methodology is also discussed. Application examples of the proposed method for crack growth analysis under arbitrary Mode I stress fields are presented as well.     

The evolution of the stress–strain fields near a fatigue crack tip and plasticity-induced crack closure revisited

The evolution of the stress–strain fields near a stationary crack tip under cyclic loading at selected R‐ratios has been studied in a detailed elastic–plastic finite element analysis. The material behaviour was described by a full constitutive model of cyclic plasticity with both kinematic and isotropic hardening variables. Whilst the stress/strain range remains mostly constant during the cyclic loading and scales with the external load range, progressive accumulation of tensile strain occurs, particularly at high R‐ratios. These results may be of significance for the characterization of crack growth, particularly near the fatigue threshold. Elastic–plastic finite element simulations of advancing fatigue cracks were carried out under plane‐stress, plane‐strain and generalized plane‐strain conditions in a compact tension specimen. Physical contact of the crack flanks was observed in plane stress but not in the plane‐strain and generalized plane‐strain conditions. The lack of crack closure in plane strain was found to be independent of the material studied. Significant crack closure was observed under plane‐stress conditions, where a displacement method was used to obtain the actual stress intensity variation during a loading cycle in the presence of crack closure. The results reveal no direct correlation between the attenuation in the stress intensity factor range estimated by the conventional compliance method and that determined by the displacement method. This finding seems to cast some doubts on the validity of the current practice in crack‐closure measurement, and indeed on the role of plasticity‐induced crack closure in the reduction of the applied stress intensity factor range.     

Transient analysis of multiple parallel cracks under anti-plane dynamic loading

The problem of a homogeneous linear elastic body containing multiple non-collinear cracks under anti-plane dynamic loading is considered in this work. The cracks are simulated by distributions of dislocations and an integral equation relating tractions on the crack planes and the dislocation densities is derived. The integral equation in the Laplace transform domain is solved by the Gaussian–Chebyshev integration quadrature. The dynamic stress intensity factor associated with each crack tip is calculated by a numerical inverse Laplace scheme. Numerical results are given for one crack and two or three parallel cracks under normal incidence of a plane horizontally shear stress wave.     

A STUDY ON FATIGUE CRACK GROWTH UNDER OUT-OF-PHASE COMBINED LOADINGS

Abstract— Fatigue tests were performed on thin-walled tubular specimens of S45C steel under tension-compression, pure torsion, in-phase and out-of-phase axial-torsional loadings. The relationship between cracking behaviour and stress components on the crack plane was investigated. Measurement of microcrack density showed that microcracking was governed predominantly by the shear stress amplitude acting on the crack plane for all loading conditions. The failure crack was formed by coalescence of many cracks initiated near the maximum shear planes. The cracks grew turning their orientation to the direction perpendicular to the maximum normal stress. The transition of crack orientation occurred at relatively longer crack lengths at a higher stress ratio. The crack growth behaviour for all loading modes can be correlated using an equivalent strain intensity parameter based on shear and normal strains on the crack plane.