Boundary element analysis of stress intensity factor KI in some two-dimensional dynamic thermoelastic problems

This paper presents a numerical technique for the calculation of stress intensity factor as a function of time for coupled thermoelastic problems. In this task, effect of inertia term considering coupled theory of thermoelasticity is investigated and its importance is shown.A boundary element method using Laplace transform in time-domain is developed for the analysis of fracture mechanic considering dynamic coupled thermoelasticity problems in two-dimensional finite domain. The Laplace transform method is applied to the time-domain and the resulting equations in the transformed field are discretized using boundary element method. Actual physical quantities in time-domain is obtained, using the numerical inversion of the Laplace transform method.The singular behavior of the temperature and stress fields in the vicinity of the crack tip is modeled by quarter-point elements. Thermal dynamic stress intensity factor for mode I is evaluated using J-integral method. By using J-integral method effects of inertia term and other terms such as strain energy on stress intensity factor may be investigated separately and their importance may be shown. The accuracy of the method is investigated through comparison of the results with the available data in literature.     

Mean stress dependence of the thermoelastic constant

The SPATE 8000 thermoelastic stress analyser has been used to demonstrate the mean stress dependence of the thermoelastic constant. This dependence has potential application in the measurement of residual stress provided the material has not yielded.     

Applications of thermoelastic stress analysis to composite materials

A number of applied thermoelastic stress analysis (TSA) studies on composite components and assemblies are described, for the purpose of illustrating the potential of the technique for use with composite materials.     

Determination of stress intensity factor solutions for cracks in finite-width functionally graded materials

A generalized method to determine the stress intensity factor equations for cracks in finite-width specimens of functionally graded materials (FGMs), based on force balance in regions ahead of the crack tip is provided. The method uses the Westergaard's stress distribution ahead of the crack in an infinite plate and is based on the requirement of isostrain deformation of layers of varying moduli ahead of the crack tip. It is shown that the modified Westergaard equation describes the normal stress distribution and the singular stress state ahead of the crack tip in a reasonably accurate manner. Based on this, closed-form analytical equations for the stress intensity factors of cracks in finite-width center cracked specimens were derived. Comparisons of the K values from the analytical equations with that obtained from FEM simulations indicate that the derived stress intensity factor equations for FGMs are reasonably accurate. For the finite-width center-cracked-tension (CCT) specimen, the errors are less than 10% for most of the crack lengths for materials with the outer layer modulus ratios varying from 0.2 to 5. The stress intensity factors were found to be sensitive to the absolute values of moduli of the layers, the modulus ratio of the outer layers as well as the nature of gradation including the increasing and the decreasing functional forms. The stress intensity factor equations are convenient for engineering estimates of stress intensity factors as well as in the experimental determinations of fracture toughness of FGMs.     

Calculation of stress intensity factor from stress concentration factor

Using the general formulas of stress concentration factor, methods for calculating stress intensity factor are mentioned.These methods make use of the several known values of stress concentration and radius of curvature at the point of stress concentration to form expression of stress concentration factor. Values of stress concentration from handbooks or experiments and others can be used.This paper deals with plane elastic, longitudinal shearing and thin plate bending problem.     

Green's functions for the stress intensity factor evolution in finite cracks in orthotropic materials

The elastodynamic response of an infinite orthotropic material with finite crack under concentrated loads is examined. Solution for the stress intensity factor history around the crack tips is found. Laplace and Fourier transforms are employed to solve the equations of motion leading to a Fredholm integral equation on the Laplace transform domain. The dynamic stress intensity factor history can be computed by numerical Laplace transform inversion of the solution of the Fredholm equation. Numerical values of the dynamic stress intensity factor history for some example materials are obtained. This solution can be used as a Green's function to solve dynamic problems involving fini te cracks.     

A method of determining the time dependence of the dynamic stress intensity factor in impact tests

A document delivered at the 1st All-Union Conference on Fracture Mechanics of Materials, Lvov, October 20–22, 1987.     

Analysis of the stress intensity factor dependence with the crack velocity using a lattice model

In this work, the influence of crack propagation velocity in the stress intensity factor has been studied. The analysis is performed with a lattice method and a linear elastic constitutive model. Numerous researchers determined the relationship between the dynamic stress intensity factor and crack propagation velocity with experimental and analytical results. They showed that toughness increases asymptotically when the crack tip velocity is near to a critical. However, these methods are very complex and computationally expensive; furthermore, the model requires the use of several parameters that are not easily obtained. Moreover, its practical implementation is not always feasible. Hence, it is usually omitted. This paper aims to capture the physics of this complex problem with a simple fracture criterion. The selected criterion is based on the maximum principal strain implemented in a lattice model. The method used to calculate the stress intensity factor is validated with other numerical methods. The selected example is a finite 2D notched under mode I fracture and different loads rates. Results show that the proposed model captures the asymptotic behaviour of the SIF in function of crack speed, as reported in the aforementioned models.     

A plasticity-corrected stress intensity factor for fatigue crack growth in ductile materials under cyclic compression

For prediction of the fatigue crack growth (FCG) behavior under cyclic compression, a plasticity-corrected stress intensity factor (PC-SIF) range ΔK_pc is proposed on the basis of plastic zone toughening theory. The FCG behaviors in cyclic compression, and the effects of load ratio, preloading and mean load, are well predicted by this new mechanical driving force parameter. Comparisons with experimental data showed that the proposed PC-SIF range ΔK_pc is an effective single mechanical parameter capable of describing the FCG behavior under different cyclic compressive loading conditions.     

Single edge-crack stress intensity factor solutions

Weight function arguments and a boundary collocation technique are used to re-examine the stress intensity factor solutions to several classic two-dimensional linear elastic single edge-crack configurations. Limits to applicability and the solutions to the three and four-point bend, pure bending, eccentrically loaded tension, and other boundary condition problems are extracted from the solution to the uniformly loaded single edge-cracked configuration. A simple representation of the asymptotic behavior is proposed and a common expression that captures the full range of crack length to specimen width ratio is presented.     

Dynamic stress intensity factor due to concentrated loads on a propagating semi-infinite crack in orthotropic materials

The elastodynamic response of an infinite orthotropic material with a semi-infinite crack propagating at constant speed under the action of concentrated loads on the crack faces is examined. Solution for the stress intensity factor history around the crack tip is found for the loading modes I and II. Laplace and Fourier transforms along with the Wiener-Hopf technique are employed to solve the equations of motion. The asymptotic expression for the stress near the crack tip is analyzed which lead to a closed-form solution of the dynamic stress intensity factor. It is found that the stress intensity factor for the propagating crack is proportional to the stress intensity factor for a stationary crack by a factor similar to the universal function k(v) from the isotropic case. Results are presented for orthotropic materials as well as for the isotropic case.     

Stress intensity factor analysis for an interface crack between dissimilar isotropic materials under thermal stress

Thermal stresses, one of the main causes of interfacial failure between dissimilar materials, arise from different coefficients of linear thermal expansion. Two efficient numerical procedures in conjunction with the finite element method (FEM) for the stress intensity factor (SIF) analysis of interface cracks under thermal stresses are presented. The virtual crack extension method and the crack closure integral method are modified using the superposition method. The SIF analyses of some interface crack problems under mechanical and thermal loads are demonstrated. Very accurate mode separated SIFs are obtained using these methods.     

Evaluation of stress intensity factor under pure shear stress in orthotropic material

Various types of composite materials are currently being developed and used for automobiles, airplanes, ships and other structures in response to required service conditions which are getting increasingly more severe. Of growing importance under such circumstances is the study of stress analysis and fracture mechanics for these composite material structures. Particularly, the primary concern in design of structures and machines should be the initiation of cracks due to excessive deformation, delamination in material or other material defects. In evaluating safety, it is indispensable from the structural design point of view that K value should be known by an analysis conducted in advance. In this study, stress intensity factor (mode II) under a pure shear stress was obtained using the photoelastic method and caustic method and applying an isotropic material and orthotropic material (copper fibre epoxy composite (CFEC) developed by the authors), each containing the crack. Results were compared with theoretical values. As a result, this method was found useful and the effect of the direction of the primary axis of this material on the stress intensity factor was clarified.     

Applications of thermoelastic stress analysis

Recent advances in infra-red technology have permitted SIRA Ltd to develop a highly sensitive instrument for full field experimental stress analysis. The calibration and performance of this instrument (SPATE) is being evaluated on a wide range of structural materials and engineering components at NEL, and techniques have been developed to extend the instrument to wide band random loading applications. SPATE has proved to be a very successful and convenient instrument for performing non-contacting experimental stress analysis on full scale engineering structures, and its extension to random loading conditions using specially developed signal processing software has produced a completely unique facility at NEL.     

Threshold range and opening stress intensity factor in fatigue

The fatigue threshold, ΔK_th, is strongly influenced by the stress-ratio, ie by the loading conditions. Results for a Ti6A14V alloy show that a ΔK exists for non-propagating fatigue cracks which is independent of loading conditions. This ΔK is called the fatigue tolerance range and is denoted by ΔK^K. The fatigue tolerance range corresponds to that part of the ΔK_th during which the fatigue crack is open. Arguments that the fatigue tolerance range has to be explicitly incorporated in equations predicting fatigue crack growth rates are presented.     

Evaluation of the stress intensity factor for cracks in elastomers

We analyze the applicability of the method of the J-integral to the solution of problems of fracture mechanics for structures made of low-compressible elastomers. The components of the J-integral are computed by the method of equivalent three-dimensional integration. To take into account weak compressibility, we use the finite-element moment scheme. Lugansk Agricultural Institute, Lugansk, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 81–85, July–August, 1999.