Thermal stresses in a thin circular disc of orthotropic material due to an instantaneous point heat source

Summary In this paper, we have analysed the transient plane thermal stress problem of a circular disc of orthotropic material with instantaneous point heat source. The variation of with time along different radius vectors is exhibited graphically and compared with that of the isotropic case.

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Wärmespannungen in einer dünnen Kreisscheibe aus orthotropem Material zufolge einer punktförmigen instantanen Wärmequelle

Zusammenfassung In dieser Arbeit wurde das instationäre ebene Wärmespannungsproblem einer Kreisscheibe aus orthotropem Material zufolge einer punktförmigen instantanen Wärmequelle untersucht. Die Veränderung von über die Zeit für verschiedene Radien ist graphisch dargestellt und wird mit dem isotropen Fall verglichen.

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Nomenclature r, polar coordinates - T temperature rise - ² ratio of conductivities - ² thermal diffusivity in -direction - J _n Bessel function ofn-th order - t time - p introduced in equation (2) - h heat transfer coefficient - a radius of circular disc - f(r, ) temperature distribution at initial state - r ₀, ₀ a point on the disc - T ₀ strength of point heat source - Dirac delta function - F stress function in two dimensions - ₁, ₂ coefficient of thermal expansion - a ₁₁,a ₁₂,a ₂₂,a ₆₆ elastic constants With 9 Figures     

Temperature stresses due to a heat source located on one side of a straight wedge

A heat source acts on one side of a straight wedge with adiabatic boundaries. The temperature stresses are determined in terms of the displacement potential and Airy stress function.     

Thermal stresses in a viscoelastic trimaterial with a combination of a point heat source and a point heat sink

A general solution for a thermoviscoelastic trimaterial combined with a point heat source and a point heat sink is presented in this work. Based on the method of analytic continuation associated with the alternation technique, the solutions to the heat-conduction and thermoelastic problems for three dissimilar, sandwiched media are derived. A rapidly convergent series solution for both the temperature and stress field, expressed in terms of an explicit general term of the corresponding homogeneous potential, is obtained in an elegant form. The hereditary integral in conjunction with the Kelvin–Maxwell model is applied to simulate the thermoviscoelastic properties, while a thermorheologically simple material is considered. Based on the correspondence principle, the Laplace transformed thermoviscoelastic solution is directly determined from the corresponding thermoelastic one. The real-time solution can then be solved numerically by taking the inverse Laplace transform. A typical example concerning the interfacial stresses generated from a combined arrangement of a heat source and sink are discussed in detail. The corresponding thin-film problem is also discussed.     

Interaction between a point heat source and a nonuniformly coated circular inclusion

This paper investigates the interaction between a point heat source and a nonuniformly coated circular inclusion under plane deformation. Based on the complex variable theory and conformal mapping in conjunction with the analytical continuation method, the general expressions of the temperature, displacements, and stresses for three dissimilar media are derived explicitly in a series form. Numerical results are provided for some particular examples to investigate the effect of material combinations on the interfacial stresses. The derived analytical solution can also be used as a fundamental solution for the boundary element method as well as for other physical models, including welding and cutting.     

Temperature stresses in a circular plate with a central crack induced by a heat source

L'viv Polytechnic Institute, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 30, No. 2, pp. 125–127, March–April, 1994.     

Transient thermal stresses in a transversely isotropic finite circular cylinder due to an arbitrary internal heat-generation

The transient thermal stresses in a transversely isotropic, finite, solid, circular cylinder resulting from a unsteady-state, axisymmetrical temperature field are examined. A general method of solution based upon a set of stress functions is presented for the case of an arbitrary internal heat-generation. The temperature field is exactly determined by combined use of finite Fourier-cosine and finite Hankel transforms. Numerical calculations are carried out for various cases of the thermal and elastic anisotropies of the materials.     

Effects of phase lags on wave propagation in an infinite solid due to a continuous line heat source

The present work is concerned with the wave propagation in a homogeneous, isotropic and unbounded solid due to a continuous line heat source under the theory of thermoelasticity with three phase-lags (Roychoudhari in J Therm Stress 30:231?C238, 2007). For the solution of the problem, we employ a potential function approach together with Laplace and Hankel transform method. Analytical expressions for the distributions of different fields like temperature, displacement and stresses inside the medium are derived by inverting Laplace transforms in an approximate manner for small values of time. The problem is illustrated by computing numerical values of the field variables for a particular material. The theoretical as well as numerical results are compared with the corresponding results for other theories of thermoelasticity reported earlier.     

Temperature-rate-dependent thermoelastic interactions due to a line heat source

Summary Temperature-rate-dependent thermoelasticity theory is employed to study thermoelastic interactions due to a continuous line source in a linear, homogeneous and isotropic unbounded solid. Laplace and Hankel transforms are employed to solve the problem. Explicit expressions for temperature and stress fields are obtained for small time approximation. Numerical results for a copper material are presented.     

On stresses induced in a thermal barrier coating due to indentation testing

Instrumented indentation has been suggested as a method to determine interfacial fracture toughness of thermal barrier coatings. However, in a previous experimental study we showed that the results are ambiguous. In this work, we investigate the experimental results by numerical simulations incorporating the material microstructure. In the numerical simulations, based on finite element analyses, the stress fields that are associated with the loading and unloading of the indenter are investigated. By comparing these stress fields to the damage observed in the experimental study, including crack path and interfacial delaminations, we explain key findings from the experimental observations. Our results suggest that indentation testing of multilayered coated structures might not induce the delamination in the overall weakest interface and therefore the test results must be evaluated with care.     

Thermoelastic interactions without energy dissipation due to a line heat source

Summary The linear theory of thermoelasticity without energy dissipation is employed to study thermoelastic interactions due to a continuous line source of heat in a homogeneous and isotropic unbounded solid. Laplace and Hankel transforms are employed to solve the problem. Exact expressions, in closed form, for the temperature and stress fields are obtained. Numerical results for a hypothetical, copper-like material are presented with the view of illustrating the theoretical results.     

Application of the decomposition method to thermal stresses in isotropic circular fins with temperature-dependent thermal conductivity

Summary A stress-field of a perfect elastic isotropic circular fin with variable thermal conductivity is obtained. The thermal conductivity is considered temperature dependent. The nonlinear conduction-convection-radiation heat transfer equation of the circular fins subjected to the nonlinear boundary conditions is solved by Adomian's double decomposition method. The thermal stress distribution is obtained by direct integration of the temperature distribution. Fow low temperature difference between the fin base and the ambiance, the effect of thermal conductivity on pure convection and convection-radiation is important and can be negligible in pure radiation.     

Thermal deformation in a thin circular plate due to a partially distributed heat supply

In this paper, we develop an integral transform to determine temperature distribution in a thin circular plate, subjected to a partially distributed and axisymmetric heat supply on the curved surface, and study the thermal deformation. The results, obtained in series form in terms of Bessel’s functions, are illustrated numerically.     

A three-dimensional treatment of transient thermal stresses in a transversely isotropic semi-infinite circular cylinder subjected to an asymmetric temperature on the cylindrical surface

Summary This paper deals with a three-dimensional transient thermal stress problem in a transversely isotropic semi-infinite circular cylinder subjected to an asymmetrical temperature on the cylindrical surface and a convective heat loss on the surfaces. In analyzing the problem, the generalized Fourier transform to a temperature and the modified transversely isotropic potential functions method to stresses are used. For the numerical example, the temperature and the thermal stresses are calculated for a grafite which belongs under a transverse isotropy, and compared with the values under isotropic conditions. The effects of the various anisotropies of the material properties on the temperature and the thermal stresses are studied.With 15 Figures     

Local heating of an anisotropic body by a circular heat source

The solution and analysis of the two-dimensional nonstationary heat-conduction problem are presented for an anisotropic (orthotropic) body heated by a circular heat source.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 5, pp. 828-835, May, 1988.     

Transient thermal stresses in a rectangular plate due to variation of heat-transfer coefficients on upper and lower surfaces

In this paper, a method is presented for the determination of the transient temperature and thermal stresses in a thin finite rectangular plate subjected to the distinct thermal boundary conditions of the third kind at the four edges and allowing the variation of heat-transfer coefficients on the upper and lower surfaces of the plate.     

Epicenter motion of a transversely isotropic elastic half-space due to a suddenly applied buried point source

A linear, transversely isotropic, elastic half-space is excited by a suddenly applied buried point source. The stress free surface of the half-space is normal to the axis of material symmetry. An integral transform solution is found for a restricted class of materials. Explicit results are given for the normal component of the epicenter displacement. Numerical results are tabulated and discussed for nine hexagonal crystals.     

The treatment of thermal and residual stresses in fracture assessments

The behaviour of a crack under combined mechanical and thermal/residual loads is described in terms of a reference stress or equivalent mechanical loading. The reference stress can be readily established from a knowledge of the stress intensity factor for the thermal/residual load, the magnitude of the mechanical load, and the material stress-strain curve. The result enables the J-integral to be evaluated and is also used to define a procedure for the inclusion of thermal/residual stresses in the CEGB defect assessment method (R6). In particular, a detailed procedure is given for treating thermal/residual stresses in recent revisions of R6 which cater for structures made of materials which strongly work-harden.