Heat Flux Intensity Factor Research Articles

Overall thermal conductivity of a fiber reinforced composite with partially debonded inhomogeneities

A homogenization problem for conductivity of a composite containing infinite fibers of circular cross-section with interface arc cracks is solved with the account of the orientation distribution of cracks. Solution for a single inhomogeneity with debonded zone is based on the known result on heat flux intensity factor and utilizes the connection between this quantity and resistivity contribution tensor. Maxwell's scheme is used for the homogenization procedure. The results are compared with exact numerical solution for the case when all the fibers are debonded and all the interfacial cracks have the same length and orientation. The application of the proposed approach is illustrated on the example of the recovery of information on damage accumulated in the process of hydrothermal aging.

Temperature distribution and heat flow around a crack of arbitrary orientation in a functionally graded medium

This paper investigates the heat transfer problem of an infinite functionally graded medium containing an arbitrarily oriented crack under uniform remote heat flux. In the mathematical treatment the crack is approximated as a perfectly insulating cut. By using Fourier transformation, the mixed boundary value problem is reduced to a Cauchy-type singular integral equation for an unknown density function. The singular integral equation is then solved by representing the density function with a Chebyshev polynomial-based series and solving the resulting linear equation using a collocation technique. The temperature field in the vicinity of the crack and the crack-tip heat flux intensity factor are presented to quantify the effect of crack orientation and grading inhomogeneity on the heat flow around the crack.

Heat conduction in a functionally graded medium with an arbitrarily oriented crack

To characterize the influence of cracking defect on the heat conduction in a functional graded structure, the problem of an infinite nonhomogeneous plane containing an arbitrarily oriented crack under uniform remote heat flux is considered. In the mathematical formulation the crack is approximated as a cut with temperature discontinuity. By using Fourier transformation, the mixed boundary value problem is reduced to a Cauchy-type singular integral equation for an unknown density function. The singular integral equation is then regularized by approximating the density function with a Chebyshev polynomial-based series, and the resulting linear equation is solved by using a collocation technique. Temperature distributions along the crack surface planes and the heat flux intensity factors at crack tips are calculated for quantifying the singular temperature gradient and heat flux in the neighborhood of the crack tip, and to evaluate the effects of grading inhomogeneity, crack orientation, and crack thermal permeability on the post-damage performance of the thermal system. It is shown that the inhomogeneity in thermal conductivity around crack tip results in a higher temperature gradient, and that the heat flux intensity factor is strongly influenced by crack orientation as well as material inhomogeneity.

Thermoelastic problem of steady-state heat flows disturbed by a crack at an arbitrary angle to the graded interfacial zone in bonded materials

Plane thermoelasticity solutions are presented for the problem of a crack in bonded materials with a graded interfacial zone. The interfacial zone is treated as a nonhomogeneous interlayer having spatially varying thermoelastic moduli between dissimilar, homogeneous half-planes. The crack is assumed to exist in one of the half-planes at an arbitrary angle to the graded interfacial zone, disturbing uniform steady-state heat flows. The Fourier integral transform method is employed in conjunction with the coordinate transformations of field variables in the basic thermoelasticity equations. Formulation of the current nonisothermal crack problem lends itself to the derivation of two sets of Cauchy-type singular integral equations for heat conduction and thermal stress analyses. The heat-flux intensity factors and the thermal-stress intensity factors are defined and evaluated in order to quantify the singular characters of temperature gradients and thermal stresses, respectively, in the near-tip region. Numerical results include the variations of such crack-tip field intensity factors versus the crack orientation angle for various combinations of material and geometric parameters of the dissimilar media bonded through the thermoelastically graded interfacial zone. The dependence of the near-tip thermoelastic singular field on the degree of crack-surface partial insulation is also addressed.

Thermal conductivity of a material containing cracks of arbitrary shape

The problem of thermal conductivity of a material containing microcracks of arbitrary shape (including non-flat ones) is considered. The resistivity contribution tensor of a crack – the quantity that determines the decrease in the overall conductive properties of a solid due to introduction of such cracks – is derived on the basis of the solution for the strength of a singularity of the heat flux near a crack tip (heat flux intensity factor). The approach is illustrated with several examples. It is also shown how the resistivity contribution tensor can be used to calculate effective conductive properties in the framework of various self-consistent schemes – effective media, effective field and differential scheme.

THERMOELASTIC PROBLEM OF STEADY-STATE HEAT FLOW DISTURBED BY A CRACK PERPENDICULAR TO THE GRADED INTERFACIAL ZONE IN BONDED MATERIALS

The plane thermoelasticity equations are used to investigate the steady-state nonisothermal crack problem for bonded materials with a graded interfacial zone. The interfacial zone is modeled as a nonhomogeneous interlayer having continuously varying thermoelastic moduli in the exponential form between the dissimilar, homogeneous half-planes. A crack is assumed to exist in one of the half-planes oriented perpendicular to the nominal interface, disturbing a uniform heat flow. Based on the method of Fourier integral transform, formulation of the crack problem is reduced to solving two sets of Cauchy-type singular integral equations for temperature and thermal stress fields. The heat-flux intensity factors and the thermally induced mode II stress intensity factors are defined in order to characterize the singular behavior of temperature gradients and thermal stresses, respectively, in the vicinity of the crack tips. In the numerical results, the values of heat-flux and thermal-stress intensity factors are presented for various combinations of material and geometric parameters of the dissimilar media bonded through a thermoelastically graded interfacial zone. The influence of crack-surface partial conductance on the near-tip temperature and thermal stress fields is also addressed.

THERMAL STRESS PROBLEM FOR MIXED HEAT CONDUCTION BOUNDARY AROUND AN ARBITRARILY SHAPED HOLE WITH CRACK UNDER UNIFORM HEAT FLUX

This article deals with a thermal stress problem for thermal conduction around an arbitrarily shaped hole with a crack under uniform heat flux. Two cases for the hole edge and the crack faces are assumed: adiabatic and isothermal conditions or vice versa (isothermal and adiabatic). A closed-form solution is obtained using conformal mapping, dislocation functions, and the complex variable method. Results of temperature, heat flux, stress, and stress intensity factor are illustrated.

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.

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.

Thermal problem of curvilinear cracks in bonded dissimilar materials with a point heat source

Boundary value problems for a circular-arc crack embedded in dissimilar materials under the application of a point heat source are formulated and solved in closed form. Based on the Hubert problem formulation and a special technique of analytic continuation, exact solutions of the temperature and temperature gradient are obtained in an explicit form. It is found that the temperature gradients or heat fluxes near the crack tips of a curved crack possess the characteristic inverse square-root singularity in terms of the radial distance away from the crack tip which is the same as those obtained for a straight crack between dissimilar materials. Due to this singular behavior, the heat flux intensity factor is introduced to measure the thermal energy intensification cumulated in the vicinity of the crack tip. Numerical results for the temperature and heat flux intensity factor are provided in graphic form. It is shown that the thermal system having a smaller crack length would make the heat flux intensity factor lower. Consequently, the thermal energy intensification is diminished.

Thermal problem of curvilinear cracks in bonded dissimilar materials

Boundary problems for a circular insert bonded partially to the interior of an infinite medium of another material under an uniform heat flow are formulated and solved in closed form. The unbonded portions of the interface may be regarded as circular arcs of discontinuities or curved cracks. By application of the complex function theory dealing with sectionally holomorphic functions, the present problem is reduced to the solution of the problem of linear relationship or Hilbert problem. Exact solution is given for an example of a single circular-arc crack. It is found that the temperature gradients or heat flux near the tips of a curved crack possess the characteristic inverse square-root singularity in terms of the radial distance away from the crack tip which is the same as those obtained for a straight crack between dissimilar materials. Due to this singular behavior, the heat flux intensity factor is introduced to measure the thermal energy intensification cumulated in the vicinity of the crack tip. Numerical results for the temperature and heat flux intensity factor are provided in graphic forms. It is shown that the material of a circular insert having a lower heat conductivity would make the heat flux intensity factor smaller. Consequently, the thermal energy intensification is diminished.

Thermal interface crack problems in dissimilar anisotropic media

The fundamental nature of an interface crack between dissimilar anisotropic media under the uniform heat flux is studied. Based on the Hilbert problem formulation and a special technique of analytical continuation, a simple and compact version of general solutions for the thermal field are given. The temperature gradients or heat fluxes are found to possess the characteristic inverse square-root singularity in terms of the radial distance from the crack tip. Due to this singular behavior, the heat flux intensity factor is then introduced to quantify the thermal energy cumulated in the neighborhood of the crack tip. Some numerical examples are given for the application of the final results to the intensity factor of heat flux as well as the full field solutions of temperature. It is very interesting to see that the solutions associated with the dissimilar media can be easily obtained from the corresponding problem associated with the homogeneous media by a simple substitution of their own material properties. In general, the system possesses the symmetric properties of the thermal conductivity coefficients which can make the heat flux intensity factor smaller. Consequently, the thermal energy intensification is diminished.