Thermal Stress Intensity Factors Research Articles

THERMAL STRESSES INTENSITY FACTOR FOR FUNCTIONALLY GRADIENT PLATE WITH AN EDGE CRACK

Thermal stress problems of a functionally gradient plate as one of the advanced high-temperature materials capable of withstanding the extreme temperature environments, with and without an edge crack, are discussed One of the most important problems of the thermal stress in the functionally gradient plate with the crack are how to decrease the thermal stress intensity factor and how to determine the optimally continuous profile of the composition of the plate. The functionally gradient plate is subjected to a cycle of heating and cooling on the ceramics surface of the plate. The material properties of the functionally gradient plate are dependent on the temperature and the position. The optimally continuous profile of the composition of the plate is discussed. The numerical results for thermal stresses and the thermal stress intensity factor are shown for many temperature conditions and for many continuous profiles of the composition of the plate.

STRESS INTENSITY FACTORS OF MULTIPLE RADIAL EDGE CRACKS AT A CIRCULAR HOLE IN AN INFINITE PLATE DUE TO ROTATING HEAT SOURCE

We analyze the stress intensity factors for multiple-edge cracks emanating from a circular hole in an infinite plate with a moving heat source rotating around the circular hole. Numerical calculations for the stress intensity factors are carried out for the case of two radial edge cracks. The interference effects on the stress intensity factors with the included angle between two radial cracks are investigated, and the effects of the angular velocity on the results are also considered In addition, for the case of standing heat source, we attempt to measure the thermal stress intensity factors using the strain gage We compare the experimental results with the current numerical results.

Thermal Stress Analysis of a Subsurface Inclined Crack Subjected to a Point Heat Source

The thermoelastic response of a subsurface inclined crack under the application of a point heat source is studied in this paper. Based on the complex variable theory and the method of analytical continuation, the problem is formulated by two stress functions and a temprature function which are enforced to satisfy the interface condition. The singular integral equations for both the temperature field and thermoelastic field are derived by taking dislocation functions along the crack border such that both the insulated condition and traction-free condition are satisfied on the crack surface. Numerical results of the thermal stress intensity factors for different geometric configurations are discussed in detail and provided in graphical form. The results obtained in this study will be helpful in understanding the problems of seismology generated by thermal loading in a cracked body.

Determination of thermal shock stress intensity factor for elliptical crack by modified Vainshtok's weight function method

Vainshtok's weight function method is modified. The thermal shock stress intensity factors for elliptical surface cracks in the thin and thick walled cylinders are determined. The present results are compared with previous solutions and shown to be in good agreement with them. For the thick and thin walled cylinders, the thermal shock stress intensity factor increases at the beginning and decreases finally with elapsed time, and is decreased also by increasing the crack ratio and crack depth ratio.

STUDY OF AN EDGE CRACK PROBLEM IN A SEMI-INFINITE FUNCTIONALLY GRADED MEDIUM WITH TWO DEVIENSIONALLY NONHOMOGENEOUS COEFFICIENTS OF THERMAL EXPANSION UNDER THERMAL LOAD

The crack problem in semi-infinite functionally graded materials (FGMs) under thermal load is considered The main objective of this work is to reduce the thermal stress by assigning an appropriate value of the coefficient of thermal expansion, which changes in two directions. It is assumed that the coefficient of thermal expansion is exponentially dependent on x- and y-directions as $. From the formulation of the problem it reduces to a singular integral equation with a simple Cauchy type kernel. This singular integral equation has the derivative of the crack surface displacement as the density function. The thermal stress intensity factor can be calculated versus the mechanical nonhomogeneous parameters of the assumed FGMfrom the solution of the singular integral equation. Then from the calculated values of the thermal stress intensity factor the appropriate values of the nonhomogeneous parameters of the coefficient of thermal expansion and the mechanical nonhomogeneous parameters of the material can be ...

Determination of stress intensity factor for embedded elliptical crack in turbine rotor

The stress intensity factor (SIF) for an embedded elliptical crack in a turbine rotor and the thermal shock stress intensity factor for a semi-elliptical surface crack in a finite plate are determined by means of Vainshtok's weight function method. The solution for the semi-elliptical surface crack is in good agreement with the previous one. The value of the SIF for the embedded elliptical crack in the turbine rotor under centrifugal and thermal loading is larger at the crack contour near the inner radius surface and almost constant at the opposite crack contour. The SIF decreases by increasing the crack ratio, and the distance between the inner radius surface and the crack center.

Evaluation of Axisymmetric Steady Thermal Stress and Thermal Stress Intensity Factor in Kassir's Nonhomogeneous Infinite Body with a Penny-Shaped Crack

In this work, a theoretical analysis of the axisymmetric thermal stress problem and the associated thermal stress intensity factor KI is developed for Kassir's nonhomogeneous body with a penny-shaped crack with radius a subjected to a uniform heat supply from the crack surfaces. Assuming that the thermal conductivity λ, shear modulus of elasticity G and coefficient of linear thermal expansion α vary with the axial coordinate z according to the relations λ(z)=λo(|z/a|+1)β, G(z)=Go(|z/a|+1)m and a(z) = αo(|z/a|+1)n, the axisymmetrical steady temperature solution is obtained. Then, the associated thermal stress distribution and the thermal stress intensity factor at the crack tip are evaluated theoretically using the method of superposition. Numerical calculations are carried out for three different cases taking into account the nonhomogeneity of the above-mentioned material properties, and the numerical results obtained are shown in graphical form. The influences of the nonhomogeneous material properties on the temperature distribution, the corresponding thermal stress distribution and the stress intensity factor are examined.

Performance of quarter-point boundary elements in analysing thermally stressed kinked and curved cracks

The performance of quarter-point and traction-singular quarter-point boundary elements, dealing with kinked and curved thermal cracks, is investigated. These special crack-tip elements simulate correctly the r 1 2 and r −1 2 near-tip behavior of temperature/displacement and heat flux/thermal stress fields, respectively. The well-known displacement and traction-based formulas are generalized for any crack configuration and used for the evaluation of heat flux and mixed-mode thermal stress intensity factors. The two-dimensional stationary thermoelasticity problem is solved via the boundary-only element method, through which volume discretization is completely eliminated. It is demonstrated by the conducted numerical experiments that present results converge to the exact ones, obtained from the literature, when the crack-tip element size tends to zero. The accuracy of the proposed method is maintained at high levels for all crack configurations considered, without the need for a dense mesh. This conclusion stands even for cracks nearly zero in size, thus rendering the method a potent tool for thermal crack initiation and extension analysis.

Thermal stress intensity factor for functionally gradient half space with an edge crack under thermal load

The aim of this work is to investigate the thermal stress intensity factor of a functionally gradient half space with an edge crack under a steady heat flux. All material properties of the functionally gradient half space, except for the coefficient of linear thermal expansion, are exponentially dependent on the distance from the boundary of the plate. The coefficient of linear thermal expansion is assumed to be two-dimensionally dependent. The problem is reduced to a singular integral equation by using the Fourier transform. The thermal stress intensity factor versus the nonhomogeneous material parameters is calculated and represented in figures. The numerical results show that thermal stress intensity factor is dramatically decreased when the material nonhomogeneous parameters are appropriately selected.

Thermal fracture of functionally gradient ceramics

An edge crack in a strip of functionally gradient ceramics (FGC) is studied under thermal loading conditions. Two FGC materials are considered, i.e., one with a spatial variation of shear modulus and the other with a spatial variation of thermal conductivity. Thermal stress intensity factors (TSIF) are numerically calculated based on singular integral equations derived for the dislocation density along the crack faces. It is shown that: (a) for the FGC with a graded shear modulus, the TSIF are reduced for crack lengths longer thanl c b and remain approximately the same as those of a homogeneous material for shorter crack lengths, wherel c is about 0.065 andb is the width of the strip; and (b) for the FGC with a thermal conductivity gradient, the TSIF are generally lower compared with those for the bonded two-layer material.

Thermal Stress Analysis in Functionally Gradient Plate with a Crack.

Functionally gradient materials (FGMs) are advanced high-temperature materials capable of withstanding extreme temperature enviroments, and are produced by continuous change of two material components. In this work a FGM plate of PSZ and Ti-6Al-4V is suddenly heated and suddenly cooled on the ceramic surface side and is kept cool on the metal surface side. The transient thermal stress and the stress intensity factors are calculated by a finite-element method (FEM). Crack propagation from an edged crack on the surface of ceramics side and the optimum distribution of materials are shown and discussed from the calculated thermal stress and stress intensity factors.

Thermal stress intensity factor for functionally gradient half space with an edge crack under thermal load

Thermal stress intensity factor for functionally gradient half space with an edge crack under thermal load

Thermal Stress Intensity Factor of Semi-Infinite Crack due to Crack Face Heating.

The stress intensity factor of a semi infinite crack in an infinite plate under a transient and quasistatic thermal stress field generated by a point heat source acting on a crack surface was analyzed. A typical stress around a point heat source is severe compression in the vicinity of the point of heat, then it turns positive value as the distance from the point of heat increases and finally it becomes zero at infinity. Therefore, in the crack surface heating, a wide contact region of crack surface was found just around the heat source, but the crack surfaces gradually open each other due to the positive stress away from the point of heat and the singular stress appears at the crack tip. A crack tip stress intensity factor was obtained as a function of heating time and/or velocity of the moving heat source and the degree of heat dissipation from surfaces of thin plate to the atmosphere. Two types of different technique for determining an extent of the contact length and stress intensity factor were proposed. It was found that the SIF is significantly influenced by the degree of heat dissipation from the plate surfaces in the case of crack face heating with moving heat source.

Rotation at the crack tip under uniform heat flow in an infinite medium

A complex analysis of rigid body rotation is presented. The crack-tip rotation for a line crack subjected to steady uniform heat flow is obtained in terms of thermal stress intensity factor in shear mode of the crack, the material and thermal parameters and coordinates of points close to the crack tip. The shear strip configuration is analysed on the basis of rotation and displacement at the end of the shear strip.

On the computation of mode I and II thermal shock stress intensity factors using a boundary‐only element method

AbstractA time domain boundary‐only element method is used for the analysis of fractured planar bodies, subjected to thermal shock type loads. The uncoupled quasistatic thermoelasticity equations are solved without the need for domain discretization. The singular behaviour of the temperature and displacement fields, in the vicinity of the crack tip, is modelled by quarter‐point elements. Transient thermal stress and heat flux intensity factors are evaluated from computed nodal values, using the well‐known displacement and traction formulas. The accuracy of the method, the stability of the solution and the dependence on space‐time discretization is investigated through comparison of present results with analytical and computational ones, taken from the literature. For mode I and mixed mode two‐dimensional problems examined, the method proved to be a potent tool for fracture analysis in presence of severe thermal shock loads, even in the microcrack size range. Potent in the sense that, it is very stable and cost effective from the space‐time discretization point of view.

Numerical thermo-elastic analysis of singularities in two-dimensions

Linear elastic two-dimensional problems with singular points subjected to steady-state temperature distribution are considered. The stress tensor in the vicinity of the singular points exhibits singular behavior characterized by the strength of the singularity and the associated thermal stress intensity factors (TSIFs). It is shown that the TSIFs and the strength of the stress singularity can be obtained using the principle of complementary energy together with the modified Steklov method and the p-version of the finite element method. Importantly, the proposed method is applicable not only to singularities associated with crack tips, but also to multi-material interfaces and non-homogeneous materials. Numerical results of crack-tip singularities in a rectangular plate and singular points associated with a two-material inclusion are presented.

Solutions of thermoelastic crack problems in bonded dissimilar media or half-plane medium

The two-dimensional thermoelastic crack problem in bonded dissimilar media or in a half-plane medium is considered. The proposed method for solving this problem consists of two parts. In the first part, complex potential functions are derived which are enforced to satisfy the continuity conditions across the interface, while the second part consists of the derivation of singular integral equations by introducing the dislocation functions along the crack border which are solved numerically. For both half-plane and two bonded half-plane problems associated with an insulated crack, the thermal stress intensity factors are computed numerically by using the appropriate interpolation formulae. The results compared with those of the homogeneous case given in the literature show that the method proposed here is effective, simple and general.

Some Basic Thermoelastic Problems for Nonhomogeneous Structural Materials

The focus of this review is on the method of analytical development of thermoelastic problems for nonhomogeneous materials, such as functionally gradient materials (FGM). For such nonhomogeneous materials, both the thermal and mechanical material constants are described by the function of the variable of the coordinate system. Then, the governing equations for the temperature field and the associated thermoelastic field become of nonlinear form in general cases. Therefore, the theoretical treatment is very difficult and the exact solution for the temperature and the thermoelastic field is almost impossible to obtain. This nonlinear equation system is usually treated by introducing some linearization technique with appropriate theoretical approximation. In this review, the method of some analytical developments for the heat conduction problem and the associated thermal stress problem of a body with nonhomogeneous material properties is explained briefly, and some boundary value problems of technical interest, such as optimization problems for material nonhomogeneity and the problems of thermal stress intensity factor for a body with a crack, are discussed.

TRANSIENT THERMAL STRESSES IN A CLADDED SEMI-INFINITE MEDIUM CONTAINING AN UNDERCLAD CRACK

The transient thermal stress problem for a cladded medium containing an underclad crack is studied within the two-dimensional framework of uncoupled, quasi-static thermoelasticity. The cladded medium is modeled such that a thin cladding is bonded to a substrate via a transitional layer. The cladding and the transitional layer are represented as homogeneous strips, while the substrate is regarded as a half-plane having a crack oriented normal to its surface. The transient thermal loading is prescribed in the form of a gradual or sudden cooldown applied at the medium bounding surface. The flexibility / stiffness matrix approach is introduced as an efficient means of formulating the proposed crack problem. Subject to equivalent transient thermal tractions acting on the location of the crack, a Cauchy-type singular integral equation is derived and solved numerically. Transient thermal stress intensity factors are then evaulated to demonstrate the response of the underclad crack as functions of various geometr...

Thermal stress intensity factors for partially insulated interface crack under uniform heat flow

Hilbert problems are derived to evaluate thermal stress intensity factors for a partially insulated crack subjected to vertically uniform heat flow in infinite bonded dissimilar material. In the case of a fully insulated crack surface, the present solutions of thermal stress intensity factors are reduced into the same as the previous results. For the homogeneous material, the mode II thermal stress intensity factor only exists. However, in the bonded dissimilar material, both mode I and II thermal stress intensity factors are obtained. Specially, in this case, the mode II thermal stress intensity factor is dominant. Also, thermal stress intensity factors are strongly influenced by the material properties. Thermal stress intensity factors decrease when the degree of insulation decreases.