Thermoelastic analysis of a partially insulated crack in a strip under thermal impact loading using the hyperbolic heat conduction theory

In this paper, the transient temperature and thermal stresses around a partially insulated crack in a thermoelastic strip under a temperature impact are obtained using the hyperbolic heat conduction theory. Fourier and Laplace transforms are applied and the thermal and mechanical problems are reduced to solving singular integral equations. Numerical results show that the hyperbolic heat conduction parameters, the thermal conductivity of crack faces, and the geometric size of the strip have significant influence on the dynamic temperature and stress field. The results based on hyperbolic heat conduction show much higher temperature and much more dynamic thermal stress concentrations in the very early stage of impact loading comparing to the Fourier heat conduction model. It is suggested that to design materials and structures against fracture under transient thermal loading, the hyperbolic model is more appropriate than the Fourier heat conduction model.     

Debonding of a thermoelastic material from a rigid substrate at any constant speed: thermal relaxation effects

Summary A linear isotropic thermoelastic half-space is debonded from a rigid insulated substrate at constant speed by moving shear and normal line loads. A dynamic steady state is examined, and an exact transform solution for the related problem of an insulated half-space subjected to a moving zone of specified surface displacements is obtained. Asymptotic forms are extracted that are valid near the zone edge and for high speeds, and which highlight thermal relaxation effects. They are used to derive analytical results for debonding at any constant speed. In particular, field variables on the debonded surface and the still-bonded interface are given for the sub-Rayleigh, super-Rayleigh/subsonic, lower and upper transonic, and supersonic speed ranges. The degenerate cases that arise at the three body wave speeds and at twice the rotational wave speed are also given. Calculations for the dynamic fracture energy rate and debonding zone temperature change at sub-Rayleigh speeds in 4340 steel indicate that thermal relaxation enhances energy rate, but mutes thermal response. The latter effect, however, itself decreases as the Rayleigh speed is approached.     

The influence of thermal relaxation and thermal damping on transient processes with cyclic boundary conditions

Variants of the differential equation of heat conduction in a solid body, which follow from the Fourier and Cattaneo–Vernotte hypotheses and the Lykov equation, are considered. A boundary value problem describing temperature fields in a body (cylinder) upon cyclic heat transfer with cold and hot media is formulated. An analytical solution to the boundary value problem with a hyperbolic differential equation of heat conduction with allowance for thermal relaxation and temperature damping with cyclic boundary conditions of the third kind is given. The thermal transient processes calculated by the classical heat conductance equation and hyperbolic equation of heat conduction on the axis of the cylinder at different values of factors such as the ratio of the thermal damping time to the thermal relaxation time, the duration of cyclic periods, the Fourier relaxation number, and the Biot number are compared. A conclusion is made that the theory of regenerative air heater should be improved by taking into account thermal relaxation and thermal damping in the nozzle and measurements of the thermal relaxation and thermal damping times of the corresponding materials.     

Thermal relaxation effects in rapid sliding contact with friction

Summary. A rigid die slides at constant sub-critical speed on a homogeneous, isotropic linear coupled thermoelastic half-space. Friction exists, and a dynamic steady state of plane strain is considered. An exact integral transform solution for the related problem of moving surface traction is obtained, and asymptotic expressions valid when thermal relaxation is prominent are extracted.These are used to derive an analytic solution for the sliding problem, and formulas for contact zone size and location, and unilateral constraints imposed by non-tensile contact and non-positive frictional work rate. Expressions for three body wave speeds and a Rayleigh wave speed show, save for the rotational wave case, clear dependence on thermoelastic coupling and thermal relaxation.Calculations for 4340 steel show that the problem eigenvalue is similar to its isothermal counterpart for high sliding speeds, but that the average contact zone temperature increase is less pronounced than when classical Fourier heat conduction effects dominate. Calculations for a hypothetical material similar to steel show that increasing the thermal relaxation time can in effect suppress both the Rayleigh wave and second sound body wave.     

Thermal stresses near a penny-shaped crack in an elastic sphere embedded in an infinite elastic space

This paper gives an analysis of the distribution of thermal stresses in a sphere which is bonded to an infinite elastic medium. The thermal and the elastic properties of the sphere and the elastic infinite medium are assumed to be different. The penny-shaped crack lies on the diametral plane of the sphere and the centre of the crack is the centre of the sphere. By making a suitable representation of the temperature function, the heat conduction problem is reduced to the solution of a Fredholm integral equation of the second kind. Using suitable solution of the thermoelastic displacement differential equation, the problem is then reduced to the solution of a Fredholm integral equation, in which the solution of the earlier integral equation arising from heat conduction problem occurs as a known function. Numerical solutions of these two Fredholm integral equations are obtained. These solutions are used to evaluate numerical values for the stress intensity factors. These values are displayed graphically.     

Transient thermal response near dynamically-loaded cracks during dislocation generation

Summary As a step in considering thermal effects prior to dynamic fracture or the development of fully-plastic crack edge zones, a transient 2-D study of edge dislocation generation near cracks in a fully-coupled thermoelastic solid is considered. Dynamic loading is provided either by SV-wave diffraction or tension, and no heat sources are imposed upon the solid. Despite the existence of characteristic lengths in the governing equations, exact solutions to the required mixed boundary/initial value problems are obtained in the multiple transform space, and time transforms extracted by an inversion process similar to the used in classical wave propagation. From them, the temperature changes at the dislocation edges for short times after generation are developed. These show that dislocation motion and dislocation-crack interaction produce constant temperature changes that are small. However, the results for mirror pairs separating at low speeds suggest that, as dislocation arrays form in the process of plastic zone development near the crack edge, the temperature increases could well become important.     

Thermal stress singularities at tips of a crack in a semi-infinite medium under uniform heat flow

In the framework of plane thermoelastic problems is discussed the thermal stress field near the tips of an arbitrarily inclined crack in an isotropic semi-infinite medium with the thermally insulated edge surface under uniform heat flow. The crack is replaced by continuous distributions of quasi-Volterra dislocations corresponding to line heat sources and edge dislocations, and we obtain a set of simultaneous singular integral equations for dislocation density functions, whose solution is given in the forms of series in terms of Tchebycheff polynomials of the first kind. By means of this method, the thermal stress singularities at the crack tips are estimated exactly and the stress intensity factors can be readily evaluated. Numerical results are given for the particular case where the surface of the inclined crack is maintained at constant temperature and the heat supplied across the surface of the crack vanishes as a whole. The effects of the distance from the crack tip to the edge surface of the semi-infinite medium and the angle of inclination of the crack on the stress intensity factors and the initial direction of crack extension are shown graphically.     

Stress intensity factor analysis of an interface crack between dissimilar anisotropic materials under thermal stress using the finite element analysis

New numerical methods were presented for stress intensity factor analyses of two-dimensional interfacial crack between dissimilar anisotropic materials subjected to thermal stress. The virtual crack extension method and the thermal M-integral method for a crack along the interface between two different materials were applied to the thermoelastic interfacial crack in anisotropic bimaterials. The moving least-squares approximation was used to calculate the value of the thermal M-integral. The thermal M-integral in conjunction with the moving least-squares approximation can calculate the stress intensity factors from only nodal displacements obtained by the finite element analysis. The stress intensity factors analyses of double edge cracks in jointed dissimilar isotropic semi-infinite plates subjected to thermal load were demonstrated. Excellent agreement was achieved between the numerical results obtained by the present methods and the exact solution. In addition, the stress intensity factors of double edge cracks in jointed dissimilar anisotropic semi-infinite plates subjected to thermal loads were analyzed. Their results appear reasonable.     

Feeble interfaces in bimaterials

Summary In the present paper, the thermal and thermo-elastic response of a bi-material to temperature changes is analyzed, when its interface exhibits a simultaneous weakness in traction transferring and heat flow conducting (feeble interface). Such a pathological behavior of an interface is described by two sets of constitutive relationships relating the heat flow passing through the interface to the temperature jump and the interfacial components of the traction to those of the displacement jump. The bimaterial model considered is that of a circular inhomogeneity in an elastic matrix with linear forms of the constitutive relationships. When the solutions of both heat conduction and thermoelastic problems with a perfect interface are known, the corresponding problems with a feeble interface are reduced to the solution of two dislocation problems: a heat conduction problem with an appropriate temperature dislocation applied across the interface, and an elasticity problem with an appropriate displacement dislocation of Somigliana type acting across the interface. For both dislocation problems, general representations of their solutions in terms of two-phase potential functions of complex variables are provided. Detailed analytical results are given for a circular inhomogeneity with a feeble interface disturbing a linear distribution of the temperature change in the matrix. In this case, the stress field within the inhomogeneity has a linear distribution and it vanishes for the limiting case of a sliding interface. For a specific value of the interface parameter H, which characterizes the thermal imperfection, there are no shear stresses within the inhomogeneity. Finally, since the constitutive laws describing the thermal and mechanical interface behavior correlate tensors of different order, the resulting fields in the system are drastically affected by the inhomogeneity size.     

基于非傅里叶热传导对热冲击下带裂纹厚壁圆筒的分析

随着科学技术、工业水平的发展,传统的傅里叶导热在极端条件下不再适用。基于双曲型单相延迟非傅里叶热传导方程,推导了热冲击下有限元方程,编写了有限元算法程序,研究了在热冲击载荷下含裂纹厚壁圆筒结构的热力学响应,计算出厚壁圆筒在非经典传热条件下的温度场、位移场和裂纹尖端应力强度因子的数值解,分析不同热冲击载荷、不同裂纹长度、不同相位延迟下非傅里叶热传导的波动性效应以及温度应力强度因子的变化,得到相应的结论。为非经典工程条件下,带裂纹厚壁圆筒构件的可靠性以及构件的优化设计提供了数值上的参考。