Stationary Thermoelasticity Research Articles

Thermoelastic contact problems with frictional heating and convective cooling

The contact problems with frictional heat generation are usually investigated with the idealised thermal boundary condition of perfect insulation in the separation region. This paper formulates axisymmetric and plane static thermoelasticity problems for a half-space when one boundary condition corresponds to convective heat transfer outside the contact area. The problems are reduced to the solution of Fredholm type integral equations. In each case the approximate solutions of those equations are obtained. It is established, when the influence of the heat exchange with the surrounding medium on the contact area, the contact pressure and temperature is essential and, also, when this effect is negligible.

Evaluation of T-stresses and stress intensity factors in stationary thermoelasticity by the coservation integral method

New methods for determining T-stresses and stress intensity factors in two-dimensional stationary thermoelasticity are presented. The methods utilize the path independence of J^-integral. The mutual M-integral expressed through J^-integrals provides sufficient information for determining T-stresses. The M-integral is composed of contour and domain integrals. Their integrands include the thermomechanical fields under consideration and mechanical fields corresponding to an auxiliary solution. The thermomechanical fields along the integration path and in the enclosed domain are obtained by the boundary element method. Stress intensity factors are calculated using the path independent J^-integral technique. This integral is expressed in a pure contour integral form. Numerical results for a cracked rectangular plate and thick-walled tube with internal cracks are presented.

Rißausbreitungsvorgänge in thermomechanisch belasteten Zweikomponentenmedien: Analysis und Experiment

AbstractIn dieser Arbeit wird eine Übersicht über bruchmechanische Untersuchungen zur Entstehung und Ausbreitung von Wärmespannungsrissen in einem Segment oder in der Materialgrenzfläche von zwei‐ und dreidimensionalen eingespannten Verbundstrukturen gegeben. Die resultierenden Randwertprobleme der stationären Thermoelastizitätstheorie für ungerissene und gerissene 2‐D‐ und 3‐D‐Zweikomponentenverbunde werden dabei mit Hilfe von Muskhelishvilis Methode der komplexen Potentiale sowie der FE‐Methode gelöst. Für die 2‐D‐Bimaterialien konnten dabei in den entsprechenden Querschnitten orthogonale Scharen von Hauptspannungstrajektorien erhalten werden, die einen Überblick über die thermisch induzierten Eigenspannungsfelder in den Verbundstrukturen vermitteln. Bei Anwendung eines geeigneten Rißausbreitungskriteriums, das auf der numerischen Berechnung der Gesamtenergiefreisetzungsrate einer Mixed‐Mode‐Rißausbreitung beruht, konnten schließlich die Rißwege von Wärmespannungsrissen in 2‐D‐ und 3‐D‐Bimaterialien vorhergesagt werden, die an der Schnittlinie von Materialgrenzfläche und spannungsfreier äußerer Oberfläche entstehen. Dabei zeigten im Fall der scheibenförmigen Zweikomponentenverbunde die theoretisch vorausgesagten Rißwege eine sehr gute Übereinstimmung mit aus zugehörigen Abkühlungsexperimenten erhaltenen Rißpfaden. Die bruchmechanischen Untersuchungen wurden für verschiedene Probengeometrien mit unterschiedlichen Materialkombinationen durchgeführt, die sowohl gleichförmigen als auch ungleichförmigen Temperaturverteilungen unterworfen waren. Als Ergebnis dieser Untersuchungen kann festgestellt werden, daß Wärmespannungsrisse, die sich vollständig in einem Segment eines Bimaterials ausbreiten, der Bedingung GII = 0 an der jeweiligen Rißspitze genügen, während im Falle der Grenzflächenrisse stets eine Mixed‐Mode‐Rißausbreitung vorliegt, bei der die GII‐Werte eine wichtige Rolle spielen. Weiterhin konnte bei Anwendung des vorgeschlagenen Rißausbreitungskriteriums auch der mögliche Rißablenkungswinkel ϑ* einer Grenzflächenrißspitze aus der Grenzfläche ermittelt werden, wobei auch die Dicke der Grenzschicht (interphase) berücksichtigt werden konnte.Schließlich wurden die Einflüsse dreidimensionaler Effekte auf die Wärmespannungsrißausbreitung in rotationssymmetrischen Bimaterialien unter Heranziehung der FE‐Methode sowie des bereits erwähnten Rißausbreitungskriteriums studiert. Dabei weisen die erzielten Ergebnisse für die ermittelten Rißwege sowie die zugehörigen bruchmechanischen Parameter auf einige bemerkenswerte Unterschiede zwischen den 2‐D‐ und 3‐D‐Bimaterialien hin.

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.

Boundary element method for thermoelastoplastic problems

AbstractIn this paper, we present the boundary integral formulation for inelastic stationary thermoelasticity including thermally induced non‐homogeneity. Generally, the unique BEM formulation for crack problems is achieved by using the traction boundary integral equations which are now considered in a non‐singular form. Both the two‐ and three‐dimensional boundary value problems are analysed simultaneously. Numerical examples for 2‐D problems are presented, in order to illustrate the suitability of this boundary element approach in the inelastic thermoelasticity.

Stress state of transversally isotropic body with elliptical crack in the presence of a uniform heat flux at its surface

An explicit solution of the state thermoelasticity problem is constructed for an infinite transversally isotropic body containing an internal elliptical crack in the isotropy plane. It is assumed that a uniform heat flux is specified at the crack surface and the body is free of external loads. Values of the stress-intensity coefficients depending on the heat flux, the crack dimensions, and the thermoelastic properties of the material are obtained. Note that the analogous problem was considered for an isotropic body. The static thermoelasticity problem for a transversally isotropic body with an internal elliptical crack at whose surface linear temperature variation is specified was solved.

Thermoelastic strain in a parabolic cylinder

An exact solution of the inner and outer problems of static thermoelasticity is obtained for an isotropic parabolic cylinder whose surface temperature is representable by a Fourier integral in one variable and by Weber functions in the other variable. The boundary surface is assumed free from external forces.

The stationary problem of thermoelasticity for a plate with a heated slit

We consider the stationary heat conduction and thermoelasticity problem for a plate that whose lateral surfaces are thermally insulated and which has a slit on whose edges a constant temperature is maintained. The heat conduction problem is solved using a modified logarithmic single-layer potential by reducing it to integral equations.

Computation of strip yield lengths for a crack in 2-d stationary thermoelasticity using the BEM

The boundary element method is presented for determining the strip yield lengths (Dugdale model) for a crack in 2-d (two-dimensional) stationary thermoelasticity. It is shown that the length of the strip yield zone can be computed economically by combination of the BEM with the Bueckner singular field. Once the strip yield length has been determined the computation of of unknown crack opening displacements is reduced to the solution of a crack problem without singularity in the crack tip. Extension of the computational method for Dugdale model solutions into the stationary thermoelasticity is practical because of large yielding at the crack tip under thermal loading. Examples of the edge-cracked rectangular bar and tube, subjected to temperature gradient, are used to illustrate the boundary integral formulation for the solution of strip yield zones.

General problem of static thermoelasticity for a transversely isotropic cone

General problem of static thermoelasticity for a transversely isotropic cone

Thermoelastic state of a medium, containing a thermally insulated ellipsoidal cavity, when subjected to a uniform heat flow

This article examines a problem of static thermoelasticity for an isotropic medium with an ellipsoidal cavity. The orientation of the cavity relative to the heat flow is assumed to be arbitrary. The solution of the problem is constructed in closed form and is expressed through incomplete elliptic integrals of the first and second kinds. In cases when the ellipsoid degenerates into a spheroid or sphere, the stress-strain state can be written in elementary functions of the ellipsoidal coordinate.

Boundary element method analysis of stationary thermoelasticity problems in non‐homogeneous media

AbstractThis paper presents an advanced BEM formulation for the solution of stationary problems of thermoelasticity taking into consideration the thermally induced non‐homogeneity. An iterative scheme is used to determine the displacement fields because the formulation contains a domain‐type integral with displacements. As compared with the existing BEM formulation, this one does not contain a domain integral of the temperature field and, furthermore, the integral representation of stresses is written in the regularized from. Consequently, all the integrals can be computed numerically by using the regular Gaussian quadrature.

Improved Computation of Thermal Stresses in Stationary Thermoelasticity Using Boundary Elements

We have implemented numerically and tested two schemes for computation of internal stresses in 2-d stationary thermoelasticity. As expected, both the nonregularized and regularized schemes fail as the internal point approaches the boundary

Quasistatic thermal crack extension in the interfaces of bounded self-stressed multiphase compounds

Abstract The quasistatic growth of straight interface cracks in thermally loaded brittle multiphase solids consisting of two circular segments of brittle materials with different thermoelastic properties which are glued together at the interface with a special glass seal has been investigated. The resulting mixed boundary-value problems of the stationary plane thermoelasticity have been solved by applying the finite element method. Moreover, fracture mechanical data like crack surface displacements and strain energy release rates governing the propagation behavior of a quasistatic extending thermal interface crack have been calculated. The data obtained have been compared with the results of special cooling experiments in multiphase composite structures in which curved thermal cracks in one of the circular segments occur.

Some representations of the solutions of boundary value problems of two-dimensional static thermoelasticity

Exact solutions are obtained for special boundary value problems of linear thermoelasticity of a homogeneous anisotropic cylindrical body in the case when force and displacement in definite directions are given on the cross-sectional contour. These directions can vary consistently along the contour. The exact solutions of the special problems are used as the representations of solutions of other boundary value problems and to reduce a boundary value problem to the solution of a certain one-dimensional singular integral equation. The integral equation for an orthotropic strip is obtained as an illustration.