Stress distribution in discontinuous fibres in a model composite

In order to calculate stress distribution in unidirectional discontinuous fibres embedded in a metal matrix, a method based on the shear-lag analysis was proposed. Using this method, the influence of fibre length, interfacial bonding strength, distance between fibre ends in the longitudinal direction, and applied strain to composite on both stress distribution and average stress of fibres was estimated for a number of examples.     

Dynamic propagation of a finite crack in a micropolar elastic solid

Summary The dynamic propagation of a finite crack under mode-I loading in a micropolar elastic solid is investigated. By using an integral transform method, a pair of two-dimensional singular integral equations governing stress and couple stress is formulated in terms of displacement transverse to the crack, macro and micro rotations, and microinertia. These equations are solved numerically, and solutions for dynamic stress intensity and couple stress intensity factors are obtained by utilizing the values of the strengths of the square root singularities in macrorotation and the gradient of microrotation at the crack tips.     

Visco-elastoplastic stress concentration in a strip with a circular hole

The visco-elastoplastic stress concentration in a strip with a circular hole has been investigated for various rates of increase of stress by means of the photo-rheological method, using specimens of celluloid at 65C. The stress concentration factors at the stress raiser are considerably influenced by the stress rate. Such an effect cannot be analysed by ordinary photoplasticity in which the time effect is not taken into account.     

The influence of a finite stringer on the stress intensities around cracks in plates

The influence of a stringer embedded in a plate, containing a number of cracks of arbitrary shape and arbitrarily oriented relatively to the stringer, on the stress field and the stress intensity factors at the tips of the cracks was studied by using the method of singular integral equations. An exact expression for the complex stress function was given for the most general case. The method was applied to an example of an arbitrarily oriented internal crack relatively to the position of the stringer and the influence of its orientation on the stress intensity factor was determined numerically. The method constitutes a potential technique for solving problems of stress concentrations and intensities in reinforced plates.     

Surface dislocation model of a dislocation in a two-phase medium

The surface dislocation method developed earlier for solving the free surface boundary problem is now extended to the two-phase interface boundary problem wherein a lattice dislocation is situated in one of the phases. The interface is planar where two semi-infinite half spaces of different elastic properties are joined. The interface consists of four surface arrays of dislocations, two in each phase, so that the continuity of two stress components and two displacement components is maintained. The continuous distribution of dislocations is employed to arrive at the distribution function representing the surface arrays. The Airy stress functions for the two phases are derived and shown to give the same result as that obtained earlier by other methods. The distortions involved across the interface are represented in terms of simple surface arrays to show the advantage of the surface dislocation model. The stress field around the dislocation in the two-phase medium is plotted and the effect of the shear modulus of the second phase and of Poisson's ratio discussed. The advantages of applying the surface dislocation model either by the continuous distribution method or the discrete dislocation method are indicated.     

Fracture mechanics analysis of a crack in a residual stress field

The standard definition of the J integral leads to a path dependent value in the presence of a residual stress field, and this gives rise to numerical difficulties in numerical modelling of fracture problems when residual stresses are significant. In this work, a path independent J definition for a crack in a residual stress field is obtained. A number of crack geometries containing residual stresses have been analysed using the finite element method and the results demonstrate that the modified J shows good path-independence which is maintained under a combination of residual stress and mechanical loading. It is also shown that the modified J is equivalent to the stress intensity factor, K, under small scale yielding conditions and provides the intensity of the near crack tip stresses under elastic-plastic conditions. The paper also discusses two issues linked to the numerical modelling of residual stress crack problems-the introduction of a residual stress field into a finite element model and the introduction of a crack into a residual stress field.     

Calculation of stress intensity factors for a longitudinal semi-elliptical crack in a finite-length thick-walled cylinder

The purpose of this paper is to present the effect of finite boundary on the stress intensity factor of an internal semi-elliptical crack in a pressurized finite-length thick-walled cylinder  ( R _i/ t = 4)  . The three-dimensional finite element method, in conjunction with the weight function method, is used for computing the stress intensity factor at the deepest and surface points of an axial semi-elliptical crack in a cylinder. The transition aspect ratios, the aspect ratios in which the maximum stress intensity factor translates from the deepest to the surface points of the crack, are calculated for different relative depths and cylinder lengths. The results show that the stress intensity factor increases as the cylinder length decreases, especially at the corner point of the crack compared with the deepest point. The major advantage of this paper is that a closed-form expression is extracted for the stress intensity factor at the surface point of a semi-elliptical crack, which experiences higher changes due to the effect of the finite boundary of the cylinder.     

Stress intensity factors for a surface-breaking crack in a half-plane subject to contact loading

Modes I and II stress intensity factors are derived for a crack breaking the surface of a half-plane which is subject to various forms of contact loading. The method used is that of replacing the crack by a continuous distribution of edge dislocations and assume the crack to be traction-free over its entire length. A traction free crack is achieved by cancelling the tractions along the crack site that would be present if the half-plane was uncracked. The stress distribution for an elastic uncracked half-plane subject to an indenter of arbitrary profile in the presence of friction is derived in terms of a single Muskhelishvili complex stress function from which the stresses and displacements in either the half-plane or indenter can be determined. The problem of a cracked half-plane reduces to the numerical solution of a singular integral equation for the determination of the dislocation density distribution from which the modes I and II stress intensity factors can be obtained. Although the method of representing a crack by a continuous distribution of edge dislocations is now a well established procedure, the application of this method to fracture mechanics problems involving contact loading is relatively new. This paper demonstrates that the method of distributed dislocations is well suited to surface-breaking cracks subject to contact loading and presents new stress intensity factor results for a variety of loading and crack configurations.     

Fatigue life of a friction welded joint with a circular crack in the centre

This paper compares the calculated fatigue life with the tested life, for an embedded crack in the friction weld between two axially loaded rods. The initial crack is caused by lack of fusion in the centre of the friction weld. The radius for the initial circular crack is 5–6 mm. The stress intensity factors for the crack are calculated with the weight function method. It was found that a relatively high axial tensile residual stress must exist in the centre, to get the crack to grow sufficiently fast. An approximation for the residual stress distribution is used in the calculation. The calculation gives about 30% longer median lives than the fatigue tests. That might depend on uncertainties in material data and/or the fact that the tensile stress in the centre is higher than expected. The paper also shows that the integrals in the weight function method can be solved by a standard mathematics program.     

KI of a circumferential crack emanating from an ellipsoidal cavity obtained by the crack tip stress method in FEM

In high hardness steel, fatigue crack appears from a microcavity in most cases. Therefore, it is important to know the stress intensity factor of a crack emanating from the cavity. Recently, a method for calculating the highly accurate values of two-dimensional stress intensity factors was proposed by Nisitani, based on the usefulness of the stress values at a crack tip calculated by FEM. This method is called the crack tip stress method. In this paper, the crack tip stress method is extended to the problems of an infinite solid having an ellipsoidal cavity with a circumferential crack emanating from the cavity subjected to tension.     

Stress Concentration in a Pipeline with Surface Hollow in the Form of a Semiellipsoid of Revolution

For the analysis of stress concentration in the region of a local hollow in a pipeline in the form of a semiellipsoid of revolution, we use a computational model based on the three-dimensional problem of a layer subjected to biaxial tension. The numerical analysis of this problem is performed with the help of a semianalytic finite-element method by using bilinear quadrangular elements. We deduce an engineering formula for the evaluation of the maximum stress intensity factors.     

Role of plasticity on interface crack initiation from a free edge and propagation in a nano-component

In order to elucidate the role of plasticity on interface crack initiation from a free edge and crack propagation in a nano-component, delamination experiments were conducted by a proposed nano-cantilever bend method using a specimen consisting of ductile Cu and brittle Si and by a modified four-point bend method. The stress fields along the Cu/Si interface at the critical loads of crack initiation and crack propagation were analyzed by the finite element method. The results reveal that intensified elastic stresses in the vicinity of the interface edge and the crack tip are very different, although the Cu/Si interface is identical in both experiments. The plasticity of Cu was then estimated on the basis of the nano-cantilever deflection measured by in situ transmission electron microscopy. The plasticity affects the stress fields; the normal stress near the interface edge is intensified while that near the crack tip is much reduced. Both the elasto-plastic stresses are close to each other in the region of about 10 nm. This suggests that the local interface fracture, namely, the crack initiation at the interface edge and the crack propagation along the interface, is governed by elasto-plastic normal stress on the order of 10 nm.     

Stress intensity factors of a central interface crack in a bonded finite plate and periodic interface cracks under arbitrary material combinations

Although a lot of interface crack problems were previously treated, few solutions are available under arbitrary material combinations. This paper deals with a central interface crack in a bonded finite plate and periodic interface cracks. Then, the effects of material combination and relative crack length on the stress intensity factors are discussed. A useful method to calculate the stress intensity factor of interface crack is presented with focusing on the stress at the crack tip calculated by the finite element method.     

A finite element model of the stress field in a star-shaped inclusion

The elastic stress field in the neighborhood of an inclusion in the shape of a five-pointed star embedded in a homogeneous matrix subject to a remote uniaxial strain is determined using the finite element method in both plane stress and plane strain. The results do not support a recent preliminary analytical result that both the individual stress components and the effective stress distribution inside the inclusion should be uniform.     

Analysis of the stress field in front of a notch

We performed the analytic, numerical, and experimental analyses of stresses in front of a sharp notch with an aim to establish a proper fracture criterion for the prediction of the onset of crack propagation from the notch. We reconsidered the Williams approach to the analysis of the general structure of the stress field. The finite-element method was used to deduce a formula for the stress concentration factor for a given geometry of the specimen. The method of caustics was used to obtain new relations for the stress concentration factors in front of the notch. We also carried out experimental investigations by the method of caustics and used the experimental data to postulate a fracture criterion. Department of Mechanical Engineering, Kielce University of Technology, Kielce, Poland. Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 34, No. 5, pp. 101–107, September–October, 1998.     

Stress concentration around a strongly oblate spheroidal cavity in a transversely isotropic medium

Expressions for the Eshelby tensor of a strongly oblate spheroidal region in a transversely isotropic medium are given explicitly. Based on the equivalent inclusion method, three dimensional stress concentration around the spherodal cavity subjected to remote uniform loading is analyzed and the associated stress concentration factor is determined. Analogously to two-dimensional blunted cracks, the so called stress rounding factor is introduced so that the connection between the crack tip stress and the stress intensity factor in linear fracture mechanics is established. Numerical values of the stress rounding factor for several representative cases of transversely isotropic symmetry are given.     

An estimation of plastic zones in a plate with a central hole

A method is described for estimating the size of the plastic zone developing around a central hole in a finite width plate subjected to a monotonically increasing tensile load from a knowledge of the elastic stress field only. The plate is assumed to be subjected to plane stress conditions and to be made from an elastic, linearly strain-hardening material. Yielding is considered to occur when the Mises criterion is satisfied. Stresses within the plastically deformed area of the plate are evaluated by means of the Prandtl-Reuss incremental flow rule together with strains increments calculated from the elastic stress distributions. The predicted plastic zone sizes correlate well with those determined experimentally by other workers.     

Analysis of an internal crack in a finite anisotropic plate

In this paper the boundary collocation method is presented for computing the stress intensity factors for an internal crack in a finite anisotropic plate. The stress functions are assumed such that they can represent the stress singularity at the crack tips, satisfying not only the governing equations of the anisotropic plate theory in the domain, but also the stress-free conditions on the crack surfaces. Therefore, only the boundary conditions of the plate need to be considered, and they can be satisfied approximately by the Boundary Collocation Method. Numerical examples demonstrated that the proposed method gives satisfactory results compared with the existing solutions.     

Contact stress distributions in a turbine disc dovetail type joint - a comparison of photoelastic and finite element results

Two dimensional photoelastic frozen stress techniques were used to investigate the stress distributions of an axially loaded dovetail joint as is found in the design of some turbine blade-disc fixings. The internal stress distributions were obtained by the shear difference method and were compared to results obtained by using the finite element method. It was found that steep principal stress gradients were present immediately below the contact surfaces in the zone adjacent to the fillet radius of the dovetail fixing, which could be an important consideration in the fatigue strength of the joint. The finite element model used gave the same trends of stress as the photoelastic model, predicted higher peak principal stresses and did not exhibit the same detailed variations of stress distribution.     

Thermal Mismatch Stress of a Spherical Inclusion in a Cubic Crystal

The thermal stress induced in a spherical inclusion by the difference of the thermal expansion coefficiences of the inclusion and its embedding matrix is considered. Both the inclusion and the matrix are assumed to be of cubic symmetry. Eshelby’s equivalent inclusion method is used to solve the problem. A smple expression for the determination of thermal mismatch stress is thus derived. Some numerical examples are provided.