Crack Tip Stress Intensity Factor Research Articles

A note on stress intensity factors for a crack emanating from a sharp V-notch

A concise and precise formula for mode-I stress intensity factor of a short crack emanating from the bisector of a V-notch has been derived by Philipps et al. The crack tip stress intensity factor is directly evaluated via the mode-I generalized stress intensity factor of an uncracked notch. This note further supplements an accurate formula to calculate mode-III stress intensity factor for a short crack emanating from a V-notch.

Local crack plasticity and its influences on the global elastic stress field

This paper presents the background and development of a novel ‘plastic inclusion’ approach for dealing with the local plasticity which occurs at the tip of a growing fatigue crack. Localised plasticity arises from crack growth mechanisms and essentially blunts the crack, creates a reversed cyclic plastic zone, and induces shear along the crack flanks, along with the possible generation of wake contact stresses which act on the applied elastic stress field at the boundary of the elastic–plastic enclave surrounding the crack. The paper outlines the development of a meso-scale model of the elastic stress field around a growing crack that explicitly incorporates these interaction effects. The outcome is a modified crack tip stress intensity factor that includes some aspects of the magnitude of plastic wake-induced crack tip shielding and which the authors propose has the potential to help resolve some long-standing controversies associated with plasticity-induced closure. A full-field approach is developed for stress using photoelasticity and also for displacement using digital image correlation.

The effect of water penetration on crack growth in silica glass

Due to the high stresses at crack tips, stress-enhanced water diffusion into silica occurs and gives rise to a volume expansion zone around the tip. This zone leads to a fracture mechanics shielding effect. In the present paper, the diffusion equation for water into glass is solved in cylindrical coordinates including the effect of the mechanical swelling stresses on the diffusivity. As an application of the volume swelling in the crack-tip region, the shielding stress intensity factor is calculated and the relation between subcritical crack growth rate and the crack tip stress intensity factor is derived from an existing crack growth rate versus applied stress intensity factor curve. The general mathematical procedure is outlined in detail and experimental results are discussed, giving evidence for crack-tip diffusion of water and a consequent zone of swelling around the crack tip.

Numerical Analysis of Crack Propagation in Brittle Materials under Uniaxial Compression

The new simple and effective grid remeshing method on crack propagation in brittle materials is successfully introduced which is under uniaxial compression. Numerical analysis is applied to brittle materials of a single pre-existing crack considering various dip angles, lengths and friction coefficient. According to linear elastic fracture mechanics theory, we introduce node moving method to guarantee the good shape of the grid in the process of crack growth, and set contact element between the friction surfaces, and then get the crack tip stress intensity factor by using quarter singular element. The influence of length, angle and friction coefficient on crack propagation is quantitatively described. The method is consistent with the experimental results and is effective in 2D problems.

Fatigue crack growth and craze-induced crack tip shielding in polycarbonate

This paper expounds a revised characterisation of the elastic stresses ahead of a crack tip in polycarbonate which takes account of the elastic–plastic boundary stresses induced by the presence of the crazed region that surrounds a crack. The advanced experimental techniques used in this work have provided insights into fractography, identification of the crazed region and location of the crack tip position (using confocal laser scanning microscopy and scanning electron microscopy). In addition, the four-parameter model of crack tip stresses has led to modified definitions for crack tip stress intensity factors which explicitly account for craze-induced shielding effects on the fatigue crack growth rate in polycarbonate. The model is generic and offers the potential for increased understanding of fatigue crack growth in polycarbonate.

Hybrid determination of mixed-mode stress intensity factors on discontinuous finite-width plate by finite element and photoelasticity

For isotropic material structure, the stress in the vicinity of crack tip is generally much higher than the stress far away from it. This phenomenon usually leads to stress concentration and fracture of structure. Previous researches and studies show that the stress intensity factor is one of most important parameter for crack growth and propagation. This paper provides a convenient numerical method, which is called hybrid photoelasticity method, to accurately determine the stress field distribution in the vicinity of crack tip and mixed-mode stress intensity factors. The model was simulated by finite element method and isochromatic data along straight lines far away from the crack tip were calculated. By using the isochromatic data obtained from finite element method and a conformal mapping procedure, stress components and photoelastic fringes in the hybrid region were calculated. To easily compare calculated photoelastic fringes with experiment results, the fringe patterns were reconstructed, doubled and sharpened. Good agreement shows that the method presented in this paper is reliable and convenient. This method can then directly be applied to obtain mixed mode stress intensity factors from the experimentally measured isochromatic data along the straight lines.

Study on the Stress Intensity Factor of Double Cracks Parallel to and Lying on the Interface in the Cladding Material Structure

Taking the cladding material structure with double interface cracks parallel to and lying on the interface as the study object, based on the theoretical study on the crack tip stress intensity factor(SIF), using the finite element software ANSYS, the SIFs are researched by changing the crack space, crack length, thickness ratio, load and crack location. The results show that, the crack SIFs increase firstly and then decrease with the crack space increase, increase with the increases of the crack length and the load, decrease a little with the thickness ratio increase, decrease firstly and then increase with the increase of distance between the crack and the boundary.

Hydrogen assisted intergranular cracking in steels

McMahon suggested that interface decohesion at grain-boundary carbides and precipitates is the mechanism of hydrogen assisted intergranular cracking, HAIC, in high strength steels. In general, cleavage of grain-boundary carbides, adhesion failure or interface decohesion at grain-boundary carbides and precipitates, and crack-tip shear slip along the grain boundary could be the mechanisms of HAIC. Hydrogen reduces cleavage strength, adhesion strength and the resistance to shear slip; therefore, hydrogen assists intergranular cracking. A method of identifying such mechanisms is suggested. A generalized theory of hydrogen assisted cracking is deduced. Brittle crystals cleave on their cleavage planes. Cleavage cracking of such crystals is anisotropic. When the crack-tip stress intensity factor, K, is low, the tortuous cracking process from the anisotropy results in rapidly increasing Stage-I crack growth rate with respect to K. The mechanism of the crack growth threshold, K TH, is also discussed.

Crack-Tip Shielding Effect on Fatigue Crack Propagation in Porous Silicon Carbide

A sharply notched specimen of porous silicon carbide with porosity of 37% was fatigued under four-point bending. The opening displacement of a fatigue crack was measured at several positions along cracks by using scanning electron microscopy. The crack propagation curve was divided into stages I, II, and III. The crack propagation rate first decreased with crack extension in stage I and became constant in stage II. In stage III, the crack propagation rate increased again. The range of crack opening displacement measured in SEM was lower than that calculated from the applied load range by FEM, suggesting that the anomalous variation of the crack propagation rate with crack extension was caused by crack-tip shielding due to crack face contact. The crack-tip stress intensity factor was estimated as a true crack driving force from the relation between the crack opening displacement and the applied load. The amount of crack-tip shielding increased very quickly with crack extension, reducing the crack-tip stress intensity factor in stage I. In stage II, the increasing applied stress intensity factor is balanced by the increase in the crack-tip shielding. The crack-tip stress intensity factor increases with crack extension in stage III.

Transient near tip fields in crack dynamics

Transient effects of stress-strain fields in the vicinity of a stationary crack tip under high rate loads are discussed. Exact analytical solutions to near tip stresses are compared to fields prescribed by leading terms (one or several) of Williams asymptotic expansion. Influence of load application mode, time (or, which is the same, distance from a crack tip) and Poisson’s ratio on this discrepancy is extensively examined. Some effects connected with crack tip propagation speed are also discussed. Significant inconsistencies between real (or received in numerical solutions of state equations - e.g. finite element computations) crack tip fields and stress intensity factor (SIF) singular field observed by numerous researchers are explained. The scope of problems where SIF field can be used for correct prediction of dynamic stress-strain fields in the crack tip region is established. Possibility to correctly approximate fields that are not SIF dominated, accounting additional terms of Williams expansion, is studied.

The interaction between a screw dislocation and a piezoelectric fiber composite with a wedge crack

The interaction problem between a screw dislocation and a piezoelectric fiber composite with a semi-infinite wedge crack is investigated in this paper. The piezoelectric media are assumed to be transversely isotropic with the poling direction along the x3 direction. The screw dislocation considered here involves a Burgers vector parallel to the poling direction with a line force and a line charge being applied at the core of the dislocation. Both cases of the screw dislocation located at the matrix and inclusion are observed. The analytical derivation is based on the complex variable and the conformal mapping methods. The exact solutions are obtained to calculate the forces on the dislocation and the crack-tip stress and electric displacement intensity factors. Based on these results, the anti-shielding and shielding effects for different loadings, material combinations, and geometric configurations are discussed in detail.

On an antiplane crack problem for functionally graded elastic materials

This paper examines an antiplane crack problem for a functionally graded anisotropic elastic material in which the elastic moduli vary quadratically with the spatial coordinates. A solution to the crack problem is obtained in terms of a pair of integral equations. An iterative solution to the integral equations is used to examine the effect of the anisotropy and varying elastic moduli on the crack tip stress intensity factors and the crack displacement. doi:10.1017/S1446181111000551

Analysis on the Expansion of Surface Crack in Asphalt Pavement

The relationship between surface crack tip stress intensity factor and calculated parameters of pavement structure is discussed and finite element models based on the fracture mechanics theory is created. From the study in this paper, the following conclusions can be drawn: As the load increases, stress intensity factor will decrease, and it may promote spread of the crack. Surface layer modulus has a great influence on stress intensity factor. In the condition of the same crack depth, stress intensity factor increases while surface layer modulus increases, stress intensity factor decreases gradually while the thickness of the surface layer increases. As base layer modulus increasing, stress intensity factor of surface layer decreases. With the increase of the modulus of subbase layer, stress intensity factor of surface layer decreases gradually. The earthen foundation module has a little big influence. With the increase of the earthen foundation module, stress intensity factor will decrease, so it can delay the appearance of the crack.

노즐 이종금속용접부의 내면 보수용접부에서 수치해석법을 이용한 PWSCC 균열성장해석

In this paper, crack propagation analyses in the inner diameter (ID) repair weld of the dissimilar metal weldment of a nozzle were performed using a finite element alternating method (FEAM). To calculate the theoretical solution for the crack tip stress intensity factor, a weak type singular integral equation consisted of crack surface traction and dislocation density function was constructed and solved in conjunction with the FEAM. A two-dimensional axisymmetric finite element nozzle model was prepared and ID repair welding was simulated. An initial crack, 10% depth of weld thickness, was assumed and crack propagation trajectory from the initial crack to the 75% depth of thickness was calculated using the FEAM. Crack growth versus time curve was also calculated and compared with the curves obtained from ASME code method. With the method constructed in this paper, crack propagation trajectory and crack growth time were calculated automatically and effectively.

A Failure Criterion for Cracked Rock Mass under Seepage Pressure and Confining Pressure

The existence of water affects the mechanical properties of cracked rock mass. Taking into account the friction generated by the crack closure, the stress intensity factor of the center cracked plate subjected to compression and seepage pressure was obtained through the theoretical analysis and numerical calculation of the boundary collocation method. The results show that crack tip stress intensity factor increases with the increasing of the seepage pressure, but decreases with the increasing of crack surface friction and the confining pressure. Finally a failure criterion for cracked rock mass under seepage pressure and confining pressure is developed.

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.

Dynamic interaction of multiple arbitrarily oriented planar cracks in a piezoelectric space: A semi-analytic solution

The problem of determining the electro-elastic fields around arbitrarily oriented planar cracks in an infinite piezoelectric space is considered. The cracks which are acted upon by a transient load are either electrically impermeable or permeable. A semi-analytic method based on the theory of exponential Fourier transformation is proposed for solving the problem in the Laplace transform domain. The Laplace transforms of the jumps in the displacements and electric potential across opposite crack faces are determined by solving a system of hypersingular integral equations. Once these displacement and electric potential jumps are obtained, the displacements and electric potential and other physical quantities of interest, such as the crack tip stress and electric displacement intensity factors, can be computed with the help of a suitable algorithm for inverting Laplace transforms. The stress and electric displacement intensity factors are computed for some specific cases of the problem.

Computational Modeling of Surface Fracture of Polyethylene Acetabular Cup in Total Artificial Hip Replacement

In this paper, a crack analysis model based on finite element method and virtual crack extension technique was proposed to investigate the occurrence of surface fracture of polyethylene acetabular cup under gait loadings. To this, a simplified hip joint model was created for facture analysis. The stress intensity factor (SIF) at crack site was estimated and used to evaluate the propagation of the surface crack. Current results show that under normal gait loading, the SIF at crack tip within polyethylene cup was predicted to be lower than the fatigue threshold of polyethylene material. However, under the heel strike instant, the crack tip SIF exceeds the fracture strength of polyethylene subject to gamma radiation, which may drive the crack to propagate to final fracture. Overall, the presented analysis model has demonstrated the probability of severe surface damage occurring in polyethylene cup under impact walking conditions. This provides a valuable reference to the improvement of the mechanical properties or design of bearing materials in clinical orthopedic application.

An Axisymmetric Problem of a Partially Insulated Crack Embedded in a Graded Layer Bonded to a Homogeneous Half-Space Under Thermal Loading

The elastic-static problem of a partially insulated axisymmetric crack embedded in a graded coating bonded to a homogeneous substrate subjected to thermal loading is considered. The coating's gradient is parallel to the axisymmetric direction and is orthogonal to the crack plane. The graded coating is modeled as a nonhomogeneous medium with an isotropic constitutive law. Using Hankel transform, the heat conduction and the plane elasticity equations are converted into singular integral equations, which are solved numerically to yield the temperature distribution and the crack tip stress intensity factors. The Finite Element Method was additionally used to model the crack problem. The main objective of this paper is to study the influence of the material nonhomogeneity, partial insulation of the crack faces and the crack position on the stress intensity factors for the purpose of gaining better understanding on the behavior of graded coatings.

A boundary integral approach for plane analysis of electrically semi-permeable planar cracks in a piezoelectric solid

A plane electro-elastostatic problem involving arbitrarily located planar stress free cracks which are electrically semi-permeable is considered. Through the use of the numerical Green's function for impermeable cracks, the problem is formulated in terms of boundary integral equations which are solved numerically by a boundary element procedure together with a predictor–corrector method. The crack tip stress and electric displacement intensity factors can be easily computed once the boundary integral equations are properly solved.