Elastic problem of an adhesion crack in T-junction of two orthotropic thin plates

In this study, the general solution is derived for stresses in a T-junction of two thin plates with an adhesion crack. The plates are orthotropic, and shear force is applied to the crack surface. The analysis is based on the supposition that the stresses in each plate can be approximated by the condition of plane stress. The results obtained are verified through numerical calculation using the finite element method. A singular stress field is obtained from the solution in the vicinity of a crack tip.     

The stress intensity factor for a cracked stiffened sheet repaired with an adhesively bonded composite patch

The problem of a cracked, stiffened metallic sheet adhesively bonded by a composite patch is analyzed. The composite patch is assumed to be either an infinite orthotropic sheet or an infinite orthotropic strip normal to the crack. Due to the high stress concentration around the crack and on the interface, an elliptical disbond is assumed to exist around the crack. The crack is asymmetric with respect to the stiffener's locations as well as to the patch's center. The effect of thermal stresses in curing process is also considered. The fracture problem is solved by the displacement compatibility method, using the complex variable approach and the Fourier integral transform method.The problem is dealt with in two steps. First, starting with an uncracked, patched stiffened sheet, the stress at the prospective location of the crack is determined in a closed-form solution. The second step is to introduce a crack into the stiffened patched sheet. The multivalue of the analytical formulation is treated in detail to ensure proper implement in the computer. The results show that the effect of the stiffeners on the stress intensity factor is not significant for a crack fully covered by a patch.For the repairs by Boron/Epoxy patches, the difference in KI between the infinite sheet patch and the infinite strip model is only minor (less than 5 percent) in the absence of the curing thermal stresses and it becomes more pronounced when these stresses are taken into consideration. The stress intensity factor for a crack repaired by an infinite composite strip also can be estimated with a good or reasonable accuracy via a simplified analysis in which the patch is considered as an infinite strip in the first step and is treated as an infinite sheet in the second step of the solution procedure mentioned above.The latter simplified analysis is based on the approach originally proposed by Rose for a relatively simple repair configuration. For most cases, that approach seems to work well for the repair of a stiffened sheet by an infinite composite strip with the effects of thermal stresses and a disbond included. It should be emphasized that the present methodology can apply to the problem of a crack in a metallic stiffened sheet growing beyond the patch's boundary and also to the repairs by an infinite adhesively bonded composite strip parallel to the crack.     

A multilayer hybrid-stress finite element analysis of a through-thickness edge crack in A ± 45° laminate

A solution is given for the three-dimensional stress field near a through-thickness edge crack in a thin ± 45° laminate having elastic ply moduli typical of graphite/epoxy. The stress distribution was obtained by a three-dimensional multilayer finite element analysis based on the hybrid stress model, formulated through the minimum complementary energy principle. The results indicate that the in-plane stresses of each individual ply follow the classical $\text{1}\text{√r}$ stress singularity, but that the shape of isostress contours in the crack tip region is strongly distorted from predictions based on two-dimensional anisotropic fracture mechanics theory. The interlaminar shear stresses increase rapidly as the crack tip is approached, but are restricted to a local region around the crack tip and flanks. The interlaminar normal stress is assumed to be negligible in the formulation of the analysis.     

The application of asymptotic solutions to a semi-elliptical crack at the root of a notch

This paper presents an approximate method based on asymptotic solutions for estimating the stress intensity factor K for semi-elliptic surface cracks at stress concentrations. The proposed equation for estimating K makes use of the near-notch and remote-notch solution to interpolate over the entire range from shallow to deep cracks. The near-notch solution is obtained by means of the stress concentration factor. For cracks located in the remote stress field, K is obtained by considering the crack to be located in a smooth plate with a crack depth equal to the sum of the notch depth and the actual crack depth. The accuracy of the predictions is assessed using numerical calculations and solutions found in the literature.     

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.     

Analytical solution for mode I crack orthogonal to free surface

In this paper, an analytical solution for the singular stress field near a flat crack which is orthogonal to the free surface is proposed. The singular stress field of a three-dimensional surface crack is obtained by the principle of superposition. The stresses of mode-I surface crack are derived by combining the solution of a three-dimensional crack and a second solution due to a singular traction on the free surface of a semi-infinite body. The closed form solution for the second solution is evaluated and the stress distribution at the free surface of the crack is compared with some existing results that appeared in the literature.     

A wedge crack in an anisotropic material under antiplane shear

A crack emanating from the apex of an infinite wedge in an anisotropic material under antiplane shear is investigated. An isotropic wedge crack subjected to concentrated forces is first solved by using the conformal mapping technique. The solution of an anisotropic wedge crack is obtained from that of the transformed isotropic wedge crack based on a linear transformation method. Expressions for the stress intensity factor for the anisotropic wedge crack with both concentrated and distributed loads are derived. The stress intensity factors are numerically calculated for generally orthotropic wedge cracks with various crack and wedge angles as well as anisotropic parameters.     

Analysis of the distribution of thermal residual stresses in bonded composite repair of metallic aircraft structures

In this study, the distribution of the thermal residual stresses due to the adhesive curing in bonded composite repair is analysed using the finite element method. The computation of these stresses comprises all components of the structures: cracked plate, composite patch and adhesive layer. In addition, the influence of these residual stresses on the repair performance is highlighted by analysing their effect on the stress intensity factor at the crack tip. The obtained results show that the normal thermal stresses in the plate and the patch are important and the shear stresses are less significant. The level of the adhesive thermal stresses is relatively high. The presence of the thermal stresses increases the stress intensity factor at the crack tip, what reduce the repair performance.     

Prediction of fatigue crack growth under constant amplitude loading and a single overload based on elasto-plastic crack tip stresses and strains

It is generally accepted that the fatigue crack growth (FCG) depends mainly on the stress intensity factor range (ΔK) and the maximum stress intensity factor (K_max). The two parameters are usually combined into one expression called often as the driving force and many various driving forces have been proposed up to date. The driving force can be successful as long as the stress intensity factors are appropriately correlated with the actual elasto-plastic crack tip stress-strain field. However, the correlation between the stress intensity factors and the crack tip stress-strain field is often influenced by residual stresses induced in due course.A two-parameter (ΔK_tot, K_max,tot) driving force based on the elasto-plastic crack tip stress-strain history has been proposed. The applied stress intensity factors (ΔK_appl, K_max,appl) were modified to the total stress intensity factors (ΔK_tot, K_max,tot) in order to account for the effect of the local crack tip stresses and strains on fatigue crack growth. The FCG was predicted by simulating the stress-strain response in the material volume adjacent to the crack tip and estimating the accumulated fatigue damage. The fatigue crack growth was regarded as a process of successive crack re-initiations in the crack tip region. The model was developed to predict the effect of the mean and residual stresses induced by the cyclic loading. The effect of variable amplitude loadings on FCG can be also quantified on the basis of the proposed model. A two-parameter driving force in the form of: was derived based on the local stresses and strains at the crack tip and the Smith-Watson-Topper (SWT) fatigue damage parameter: D = σ_maxΔε/2. The effect of the internal (residual) stress induced by the reversed cyclic plasticity manifested itself in the change of the resultant (total) stress intensity factors controlling the fatigue crack growth.The model was verified using experimental fatigue crack growth data for aluminum alloy 7075-T6 obtained under constant amplitude loading and a single overload.     

The centrally cracked Brazilian disc: closed solutions for stresses and displacements for cracks under opening mode

Closed-form solutions for the stress and displacement fields in a centrally cracked Brazilian disc are obtained. The disc is subjected to uniformly distributed radial pressure along two finite symmetric arcs on its perimeter. The solution is based on the complex potentials method introduced by Kolosov and Muskhelisvili, and advantage is taken of a recently introduced closed-form solution for the intact Brazilian disc. Special attention is paid to the displacements of the crack lips, since they dictate whether the lips are in an opening or closing mode. The solutions obtained are valid for configurations for which the crack lips are in an opening loading mode, where there are no contact forces along the crack flanks. As well as stresses and displacements, the stress intensity factors are also determined in closed form and are found to be in good agreement with the respective values obtained from existing approximate solutions. Preliminary experimental data obtained using the digital image correlation technique support the analytically deduced conclusions for the deformation and rotation of the crack flanks.     

Dependence of ductile crack formation in tensile tests on stress triaxiality, stress and strain ratios

An experimental and numerical study on ductile crack formation in tensile tests was conducted. Five different specimens including flat specimens, smooth round bars, notched bars (two types) and flat-grooved plates were investigated. Von Mises equivalent strain to crack formation, stress triaxiality, and stress and strain ratios at critical locations, were obtained. Accuracy of the Bridgman formulas for stresses in necked round bars, and McClintock's model for flat-grooved plates, were studied. A relationship between the stress triaxiality and equivalent strain to crack formation was determined in a high stress triaxiality range for Al 2024-T351. More importantly, it was found that equivalent strain and stress triaxiality are the two most important factors governing crack formation, while stress and strain ratios cause secondary effects. It appears possible to make a good prediction of crack formation with equivalent strain and stress triaxiality.     

Transient thermal stress intensity factors for an internal longitudinal semi-elliptical crack in a thick-walled cylinder

In this paper, the stress intensity factors are derived for an internal semi-elliptical crack in a thick-walled cylinder subjected to transient thermal stresses. First, the problem of transient thermal stresses in a thick-walled cylinder is solved analytically. Thermal and mechanical boundary conditions are assumed to act on the inner and outer surfaces of the cylinder. The quasi-static solution of the thermoelasticity problem is derived analytically using the finite Hankel transform and then, the stress intensity factors are extracted for the deepest point and the surface points of the semi-elliptical crack using the weight function method. The results show to be in accordance with those cited in the literature in the special case of steady-state problem. Using the closed-form relations extracted for the transient thermal stress intensity factors, some conclusive results are drawn.     

Numerical investigation of through crack behaviour under welding residual stresses

Numerous engineering structures operate under the presence of residual stresses resulting from welding or other manufacturing processes. In the present work, the effect of typical residual stress fields on stress intensity factors and crack propagation angle of cracks developing into the residual stress field under mixed mode loading conditions is studied. For the calculations a numerical methodology based on linear elastic finite element analysis is used. The presented results provide a useful tool for an efficient assessment of the influence of residual stress field on the crack evolution behaviour.     

Numerical study on fatigue crack growth in railway wheels under the influence of residual stresses

Accurate prediction of fatigue crack growth on railway wheels and the influence of residual stresses by finite element method (FEM) modeling can affect the maintenance planning. Therefore, investigation of rolling contact fatigue and its effect on rolling members life seem necessary. The objective of this paper is to provide a prediction of rolling contact fatigue crack growth in the rail wheel under the influence of stress field from mechanical loads and heat treatment process of a railway wheel. A 3D nonlinear stress analysis model has been applied to estimate stress fields of the railway mono-block wheel in heat treatment process. Finite element analysis model is presented applying the elastic–plastic finite element analysis for the rail wheel under variable thermal loads. The stress history is then used to calculate stress intensity factors (SIFs) and fatigue life of railway wheel. The effect of several parameters, vertical loads, initial crack length and friction coefficient between the wheel and rail, on the fatigue life in railway wheels is investigated using the suggested 3-D finite element model. Three-dimensional finite element analysis results obtained show good agreement with those achieved in field measurements.     

Computation of stress intensity factors of interface cracks based on interaction energy release rates and BEM sensitivity analysis

Stress intensity factors of bimaterial interface cracks are evaluated based on the interaction energy release rates. The interaction energy release rate is defined based on the energy release rates of a cracked body, corresponding to two independent loading conditions, actual field and an auxiliary field, and is related to the sensitivities of the potential energies for crack extensions. The potential energy of a cracked body is expressed with a domain integral, which is converted to a boundary integral expression by applying the divergence theorem. By differentiating this expression with the crack length, a boundary integral expression for the interaction energy release rate is obtained. The boundary integral representation for the interaction energy release rate involves the displacement, the traction, and their sensitivity coefficients with respect to the crack length. The boundary element sensitivity analyses are used to calculate these quantities accurately. A regularized boundary integral equation relating the boundary displacement and traction is differentiated with respect to an arbitrary shape parameter to derive the regularized boundary integral equation for the sensitivity coefficients of the boundary displacement and traction. The proposed approach is applied to several cracks in dissimilar media and the results are compared with those obtained by the conventional approach based on the extrapolation method. The analytical displacement and stress solutions for an interface crack between two infinite dissimilar media subjected to uniform stresses at infinity are used to give the auxiliary field, in which the values of the stress intensity factors are known. It is demonstrated that the present method can give accurate results for the stress intensity factors of various bimaterial interface cracks under coarse mesh discretizations.     

NUMERICAL MODELLING OF A 3D RAIL RCF 'SQUAT'-TYPE CRACK UNDER OPERATING LOAD

The analysis is based on the 3D FE model of the rail Rolling-Contact-Fatigue (RCF) 'squat'-type crack, which tends to be common in tracks with high-speed passengers and mixed traffic. The model incorporates the section of rail and a wheel of real geometry, in which the wheel is rolling over the running band of rail containing the 'squat'-type crack. The state of stress in the vicinity of the crack front is determined, and consequently the values and ranges of the stress intensity factors (SIFs) K_I , K _II and K III at the crack front are calculated for the cycle of rolling. To simulate loading conditions occurring in practice, residual, bending and thermal stresses acting in the presence of the tractive force were taken into account. The results indicate a significant role of face friction and tractive force in the loading mechanism at the 'squat'. The longitudinal and lateral residual stresses may also influence the loading cycles, especially for the cases with reduced friction between the crack faces. Reduction of the face friction coefficient to values close to zero creates conditions for crack propagation driven by the shear mode mechanism. These results were obtained under a project sponsored by the ERRI D173 Committee, Utrecht, The Netherlands.     

Symmetric Edge Cracks in an Orthotropic Strip Under Normal Loading

The problem of two edge cracks of finite length, situated symmetrically in an orthotropic infinite strip of finite thickness 2 h, under normal point loading has been discussed. The displacements and stresses in plane strain conditions are expressed in terms of two harmonic functions. The problem is addressed by seeking the solution of a pair of simultaneous integral equations with Cauchy type singularities solved by finite Hilbert Transform technique. For large h, analytical expression for the stress intensity factor at the crack tip is obtained.     

A definition and evaluation procedure of generalized stress intensity factors at cracks and multi-material wedges

This paper proposes a definition of generalized stress intensity factors that includes classical definitions for crack problems as special cases. Based on the semi-analytical solution obtained from the scaled boundary finite-element method, the singular stress field is expressed as a matrix power function with its dimension equal to the number of singular terms. Not only real and complex power singularities but also power-logarithmic singularities are represented in a unified expression without explicitly determining the type of singularity. The generalized stress intensity factors are evaluated directly from the scaled boundary finite-element solution for the singular stress field by following standard stress recovery procedures in the finite element method. The definition and evaluation procedure are valid to multi-material wedges composed of any number of isotropic and anisotropic materials. Numerical examples, including a cracked homogeneous plate, a bimaterial plate with an interfacial crack, a V-notched bimaterial plate and a crack terminating at a material interface, are analyzed. Features of this unified definition are discussed.     

CYCLIC CRACK RESISTANCE OF WELDED JOINTS WITH NON-UNIFORM FIELDS OF RESIDUAL WELDING STRESSES

Abstract— The use of linear elastic fracture mechanics to describe the kinetics of fatigue fracture of welded joints with high welding residual stresses (WRS) is experimentally evaluated in this paper. A correction analysis is used to show that the crack propagation rate of cracks in joints, as a function of the applied stress intensity factor, is linear on a log-log scale in the Paris regime when non-uniform fields of WRS are superimposed on the applied cyclic loading. It is shown that crack growth rates in joints with high WRS do not depend on the characteristics of the loading cycle. The parameters of the Paris exponential equation are determined by the initial WRS distribution, by the range of cyclic stresses and by the load ratio. A method for calculating the cyclic crack resistance of joints is proposed which explicitly allows for a non-uniform field of WRS that influences the fatigue crack growth rate.     

Photoelastic and theoretical analyses of cracked frames

Photoelastic and theoretical analyses have been carried out to investigate the effect of cracks on the behaviour of two hinged portal frames subjected to two symmetrical vertical concentrated loads. The distribution of internal shear and normal stresses are obtained at different sections at various crack depth ratio. Also, values of stress intensity factor are obtained based on the measured local stress values.Based on the present result, an increase in normal stresses occurred at sections far from the crack location and a decrease in stresses occurred at sections close to the crack location. This is due to the fact that a redistribution in internal forces occurred due to crack presence. It is also noticed that a localized shear stress is created in a pure bending zone due to crack presence, the size of this zone is increased as crack size increased. Good agreement is obtained between experimental and theoretical results.