Stress intensity factors for circumferential semielliptical surface cracks in a pipe under thermal loading

Stress intensity factors are calculated at the deepest point and at the surface points of circumferential semielliptical surface cracks in a thermally shocked pipe. The method of calculation is based on weight functions following a proposal by Munz et al. Numerical values of the stress intensity factors are given for a wide range of crack depths and crack lengths considering a pipe with a wall thickness to inner radius ratio of $\text{1}\text{10}$.     

Fatigue strength assessment of initial semi-elliptical cracks located at a hole

In the present paper, the residual strength of a pin-loaded lug and a finite plate, both with a semi-elliptical crack emanating from a hole, is examined. A new analytical methodology, based on Fracture Mechanics concepts, is proposed to analyse the crack propagation process in terms of life estimation and crack front evolution. Firstly, the stress field and the stress intensity factor are computed by applying both analytical and numerical approaches. Then, the two-parameter driving force model proposed by Kujawski is implemented for the fatigue life estimation and the crack front evolution. The validity of model here employed is assessed through the comparison between crack growth calculations and experimental data available in the literature, such comparison shows a quite good correlation for the crack and geometrical configurations here examined.     

an experimental investigation into the mechanics of deep semielliptical surface cracks in mode i loading

An experimental investigation was made of the surface deformation and extent of plastic yielding associated with relatively deep semielliptical surface cracks in plates subjected to tensile loading. Data were gathered from sheet Ti-6A1-4V and Fe-3Si, the latter material being employed to study, by the electrolytic etching technique, the plastic zones in various planes intersecting the crack. Available analytical models were applied to calculate the stress intensity factors, and the experimental data were used to examine various models for predicting plastic zone sizes.     

Stress intensity factors for coalescing and single corner flaws along a hole bore in a plate

The objective of this paper is to describe the effects of crack interaction on stress intensity factors for two symmetric coplanar corner flaws located along a hole bore. This numerical analysis employes the Finite Element-Alternating Method to determine Mode I stress intensity factors for single and coalescing corner flaws. Using single flaw stress intensity factors as a reference, analysis of crack size and shape effects on $\text{K}{}_{\mathrm{I}}$ for coalescing corner flaws indicates the stress intensity factor for crack points along the hole bore increases as the crack tip separation distance decreases. Interaction effects are not experienced by hole bore crack points when the crack tip separation distance is equal to or greater than half of the largest corner flaw dimension.     

Crack onset and propagation stability from a circular hole under biaxial loading

The brittle crack initiation from a circular hole in an infinite slab subjected to remote biaxial loading is investigated by means of the coupled finite fracture mechanics criterion, focussing on the behaviour of the average energy release rate. The work then analyzes the stability/instability of crack growth, following the terminology put forward by Weißgraeber et al. (Eng Fract Mech 168:93–104, 2016). Depending on the loading biaxiality and on the ratio between the crack advance and the hole radius, the crack propagation could reveal to be either unstable (positive geometries), or stable (negative geometries). Furthermore, it is shown that stable paths could follow unstable paths and vice-versa, leading to locally positive/globally negative or locally negative/globally positive configurations, which are discussed in detail case by case.     

Crack–surface displacements for cracks emanating from a circular hole under various loading conditions

The purpose of this paper is to calculate and develop equations for crack–surface displacements for two‐symmetric cracks emanating from a circular hole in an infinite plate for use in strip‐yield crack‐closure models. In particular, the displacements were determined under two loading conditions: (1) remote applied stress and (2) uniform stress applied to a segment of the crack surface (partially loaded crack). The displacements were calculated by an integral‐equation method based on accurate stress–intensity factor equations for concentrated forces applied to the crack surfaces and those for remote applied stress or for a partially loaded crack surface. A boundary‐element code was also used to calculate crack–surface displacements for some selected cases. Comparisons made with crack–surface displacement equations previously developed for the same crack configuration and loading showed significant differences near the location where the crack intersected the hole surface. However, the previous equations were fairly accurate near the crack‐tip location. Herein an improved crack–surface displacement equation was developed for the case of remote applied stress. For the partially loaded crack case, only numerical comparisons were made between the previous equations and numerical integration. A rapid algorithm, based on the integral‐equation method, was developed to calculate these displacements. Because cracks emanating from a hole are quite common in the aerospace industry, accurate displacement solutions are crucial for improving life‐prediction methods based on the strip‐yield crack‐closure models.     

Crack originating from a corner of a square hole

A crack originating from a corner of a square hole is analyzed as a plane elastic problem. Muskhelishvili's method and the rational mapping function of the sum of fractional expressions are used. A closed solution is obtained. Stress distributions and stress intensity factors are investigated for some angles of the corner of the hole and crack lengths. The T-shaped crack is analyzed as a special case. The stress intensity at the opposite corner to the corner with the crack is investigated. Three loading states of uniform tension in the direction of the x and y axes and pure shear are considered.     

Crack formation as a result of hole coalescence

Translated from Fiziko-Khimicheskaya Mekhanika Materialov, No. 1, pp. 26–32, January–February, 1988.     

Simulating Crack Trajectories from a radially loaded hole

A procedure for determining the trajectory of growth of a crack in the neighbourhood of a stress-raising feature is described, The method relies on first determining the underlying stress field, and then formulating an integral equation along the (generally) curvilinear contour of the crack, which ensures that its surfaces remain traction free. The crack tip stress intensities are calculated, from which an increment of growth is found using the ^max criterion. The technique is then applied to the determination of the growth trajectory for a crack growing from a circular hole loaded by pressing a pin against its boundary.     

Multiple cracks in a half-space under contact loading

This paper develops a semi-analytic solution for multiple cracks in an isotropic half-space under contact loading. The solution takes into account interactions among all the cracks as well as the interactions between the cracks and the loading body. In formulating the governing equations for the subsurface crack problem, each crack of mixed modes I and II is modeled as a continuous distribution of climb and glide dislocations with unknown densities. Such a treatment converts the original contact problem concerning an inhomogeneous half-space into a homogeneous half-space contact problem, for which governing equations with unknown surface contact areas and normal pressure and tangential tractions within the areas can be conveniently formulated. All the unknowns in the governing equations are determined by means of iteration. The iterative process is performed until the convergence of the half-space surface displacements, which are the sum of the displacements due to the surface contact load and subsurface cracks. The solution is validated by the finite element method. Numerical examples are calculated to demonstrate the generality of the solution.     

Crack growth of physically small cracks

This paper shows how, for physically small cracks, the unified crack growth model, also referred to as Unigrow, can be related to the generalized Frost and Dugdale crack growth model. We also show how this formulation can be used to predict the crack growth history of a range of experimental tests.     

Crack face contact for a hexahedral-based XFEM formulation

Taking into account arbitrary crack geometries, crack closure generally occurs independently of the load case. As the standard eXtended Finite Element Method (XFEM) does not prevent unphysical crack face penetration in this case, a formulation allowing for crack face contact is proposed in terms of a penalty formulation for normal contact. The discretization is developed for non-planar cracks intersecting hexahedral elements in an arbitrary manner. Typical problems of many crack face contact implementations within the XFEM, like locking or the introduction of additional degrees of freedom, are avoided by projecting the contact contribution onto the hexahedral element nodes. The method is tested by means of suitable numerical examples, finally presenting an application in form of a multiscale setup with arbitrarily arranged micro cracks in the vicinity of a macro crack front.     

Axial cracks on both sides of a hole in a cylindrical shell

The problem of a cylindrical shallow shell with axial cracks on both sides of a hole is investigated by use of the expressions in the context of Muskhelishvili's complex potentials by means of comformal mapping. The values of bending stresses and displacements around a hole for the shell are shown in Tables and variation of moment and stress intensity factors at the tip of the cracks are also illustrated.

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Résumé On étudie le problème d'un réservoir cylindrique à paroi mince présentant des fissures axiales de chaque côté d'un orifice, en utilisant les expressions développées par représentation conforme dans le contexte des potentiels complexes de Muskhelishvili.On fait apparaître dans des tables les valeurs des contraintes de flexion et les déplacements dans la portion du réservoir autour de l'orifice et on montre par ailleurs la variation du moment et des facteurs d'intensité de contraintes à l'extérieur des fissures.

     

Crack opening displacements of Vickers indentation cracks

Vickers indentation cracks are an appropriate tool to determine the crack-tip toughness K_I0 and, possibly, the bridging relation of ceramics with an R-curve behaviour from the total crack opening displacements. Two contributions to the total crack opening displacement field are addressed. First, the residual stresses occurring in the uncracked body are considered and then, the contact stresses generated by preventing crack face penetration are computed. The COD solution resulting from the superposition of residual and contact displacements is given and an analytical expression is provided. Near-tip displacements are represented by the first terms of series expansions. As an example of application, an evaluation of the actual stress intensity factor is presented for a window glass 1 h after Vickers indentation.