Thermal Stresses of a Cracked Circular Hole Due to Uniform Heat Flux

Archive of Applied Mechanics (Ingenieur Archiv)

1999

Self Cite

Green's functions of the displacement boundary value problem are derived within two-dimensional thermoelasticity for a heat source in an in®nite plane with an arbitrary shaped rigid inclusion. The following two cases are considered: either rigid-body displacements and rigid-body rotations of the inclusion are allowed or no rigid-body displacements and no rigidbody rotations of the inclusion are possible. To solve these problems, fundamental solutions are developed for a point heat source, for rigid-body rotations of the inclusion, and for concentrated loads acting on the inclusion. Complex stress functions, temperature function, a rational mapping function and the thermal dislocation method are used for the analysis. In analytical examples, distributions of stresses are developed for an in®nite plane with a rectangular rigid inclusion.

“…Using the temperature function Xf that is regular outside the unit circle, the heat¯ux and temperature boundary conditions stipulated above can be expressed as in [6,7] Àk…”

Section: Solution Of Problem Amentioning

confidence: 99%

Section: Solution Of Problem Amentioning

confidence: 99%

Green's function of the displacement boundary value problem for a heat source in an infinite plane with an arbitrary shaped rigid inclusion

Yoshikawa¹,

Archive of Applied Mechanics (Ingenieur Archiv)

1999

Self Cite

“…The stress intensity factor at the crack tip C can be calculated by [1,2] K c = K 1 c -i K 2 c = 2v@ ¢'(fft) (31) where (t is the coordinate on the unit circle corresponding to the crack tip C, and (t = 1 in the studied case (Figure 3). …”

Section: Solution Of the Problem Bmentioning

confidence: 99%

“…Consequently, a number of papers dealing with the hole edge crack problem are available [1][2][3][4][5][6][7][8][9][10][11][12], among them, the rational mapping function approach is significant to solve the hole edge crack problem [1][2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Stress intensity solutions for the interaction between a hole edge crack and a line crack

Chen

1996

Int J Fract

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The principle of superposition is used to solve the problem and the original problem is converted into two particular hole edge crack problems. The remote stresses are applied at infinity in the first problem. Meantime, a dislocation distribution is assumed outside the hole contour in the second problem. Singular integral equation is proposed for the solution of the second problem, in which the right hand side of the integral equation is obtained from the solution of the first problem. The first problem as well as the elementary solution of the second problem are solved by means of the rational mapping approach. Finally, numerical examples with the calculated results of stress intensity factors are presented.

“…These facilities, in which accidents and failures caused by thermal environments and thermal loading conditions play a fatal role in the assurance of safety, stimulate the subject of thermal fracture analysis of structural components to develop at an ever higher rate. As a result, a number of technical references dealing with thermal stresses in cracked bodies have appeared, see [1,2,3] for instance.…”

Section: Introductionmentioning

confidence: 99%

Basic singular thermoelastic solutions for a crack

Zhang

1993

Int J Fract

Self Cite

Basic, singular solutions of plane thermoelasticity for an infinite medium with a crack are studied and furnished in this article. By these solutions, thermal stresses and thermal stress intensity factors in the cracked medium, under the action of a point thermal inclusion or a point heat source, can simply and exactly be evaluated. These solutions are obtained by the use of the complex function method and some quadrature techniques. In the case of a heat source, exact expressions for the temperature distribution are also derived, and some dislocation solutions are employed to obtain the final expressions for thermal stresses and thermal stress intensity factors. A number of definite integrals, with logarithmic functions as main components in their integrands, have been treated rigorously to obtain exact and closed form formulas of evaluation. This kind of definite integral is characteristic in the thermoelastic analysis of cracked bodies. Numerical values for stress intensity factors and temperature distributions are worked out and presented in tabular or graphic form.