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The intrinsic relationship of the thermal stress intensity factor and temperature difference between the upper and lower surface of the crack have been studied in this paper. The results show the thermal stress intensity factor is always proportional to the temperature difference between the upper and lower crack surface, and the ratio depends only on material parameters and crack length, but is independent of loading condition. For a finite medium problem, the above conclusion is still valid by simply adding a size related correction factor. When the size of medium is 10 times larger than the crack size, the size related correction factor is less than 1.019, that is, the error is less than 2%. Our conclusion provides a theoretical basis to estimate the localization thermal stress intensity factor simply by measuring the temperature difference of the crack surface. [ABSTRACT FROM AUTHOR]

In this work, the bending response of Euler–Bernoulli beam is analyzed with three nonlocal strain gradient model with high-order boundary conditions and modified nonlocal strain and stress gradient models, in which the integral constitutive equation is transformed to an equivalent differential equation with two extra constraint equations. The corresponding differential equations are solved uniquely by the Laplace transformation and its inverse version. Under different boundary and loading conditions, the inconsistency of a nonlocal strain gradient model is examined extendedly, and consistent softening and toughening responses can be observed while using modified nonlocal strain and stress gradient model. [ABSTRACT FROM AUTHOR]

This article investigates the failure modes of the structure composed of a soft matrix and a hard line inhomogeneity under uniform remote thermo-mechanical loading. The inhomogeneity is assumed to be thermally permeable and the thermal expansion-induced stretch of the inhomogeneity is incorporated. For arbitrary uniform remote stresses and heat flux, the explicit solution to the full stress field in the matrix is derived by solving the corresponding Riemann-Hilbert problem, and the critical condition for the failure modes of the structure is obtained. The effects of the direction of the remote heat flux and those of the mismatch of thermal expansions on the failure modes of the structure are illustrated via numerical examples. It is shown that the heat-induced failure modes of the structure are distinct at the two tips of the inhomogeneity and are either interface puncture or interface separation depending on the direction of the remote heat flux and the disparity between the thermal expansion coefficients of the inhomogeneity and matrix. In addition, the heat flux-induced stress intensity factors at the inhomogeneity tips are found to be proportional to a 3 / 2 where a is the half-length of the inhomogeneity, indicating that the failure of the structure may be more sensitive to thermal loading other than mechanical loading. [ABSTRACT FROM AUTHOR]

The thermoelastic problem of a stretchable rigid line inhomogeneity at a bimaterial interface is considered. The closed-form solution is presented and the explicit expressions of the stress at the tip of the rigid line inhomogeneity are derived. The effects of thermal expansion of rigid line on the stress intensity factors are investigated. It is found that the singularity of stress maintains the same structure, and the stresses possess an apparent oscillatory character, as in the case of a rigid line without the effects of thermal expansion. However, there is a significant difference in the coefficient of the singular behavior of the stresses at the tip of rigid line, which is due to the temperature changes. [ABSTRACT FROM AUTHOR]

The multilayer ferroelectric actuator (MFA) with electrodes is an important smart structure and it has found wide application in engineering. Under the applied electric–elastic loads, the local stress concentration will be intensified near the tips of electrodes, and it finally may lead to the failure of the MFA. On the other hand, the temperature-dependent behavior of ferroelectrics results in the novel evolutions of local stresses and microstructure in the MFA under different temperature environments. In this work, the different temperature-induced nonlinear behavior and electroelastic field concentration around the electrode tip in the MFA is studied based on a phase-field approach containing the time-dependent Ginzburg–Landau equation. Using three-dimensional nonlinear finite element method, the temperature-induced domain switching behavior of the MFA and the evolution of the local stress near the electrode tips are simulated under different loadings and temperatures. It is found that the maximum tensile stress ahead of the electrode tip increases as the temperature increases from room temperature to a critical temperature. However, over the critical temperature, the stress decreases significantly due to the ferroelectric–paraelectric phase transition, which implies that by optimizing the environmental temperature, the local stress concentrations can be controlled. [ABSTRACT FROM AUTHOR]

The two-dimensional problem of a crack in thermoelectric materials is studied in this research. The general solution is derived based on the complex variable method. For the case of a crack subjected to remote electric current and heat flow, the solutions are obtained in closed-form. The results show that the fields of heat flow, electric current, and stress exhibit traditional square-root singularity at the crack tip. The remote electric current produces both type I and II stress intensity factor. Furthermore, the stress intensity factor has a linear relationship with the heat flux, but a non-linear relationship with the electric current. [ABSTRACT FROM PUBLISHER]

The thermal stress field in a functionally graded coating on a parabolic substrate, where the material properties vary along the thickness direction, is considered. The closed-form solutions of thermal stresses related to compositional gradient, coating thickness and substrate curvature were obtained based on force and moment balances, and then numerical results are presented for several special examples. It is found that the magnitude and distribution of thermal stress in the functionally graded coating system with general geometrical shape can be designed properly by controlling the compositional gradient, coating thickness and substrate curvature. [ABSTRACT FROM PUBLISHER]

Thermoelectroelastic solution is derived for the generalized two-dimensional problem of edge cracks originating from an elliptical hole in a piezoelectric solid based on complex variable method. First, the heat complex function is solved, and then the expressions for the complex potentials and field intensity factors are presented under the electrically impermeable boundary condition. Numerical analysis is also made to discuss the influences of crack length and heat flux on the electroelastic fields and fields intensity factors. It is found that the heat flux has great effect on the stress intensity factors for the mode II cracks, but its influence on the stress intensity factors for the mode I cracks and the intensity factors of electric displacements is not significant. [ABSTRACT FROM PUBLISHER]

This paper presents the non-axisymmetric two-dimensional problem of thermal stresses in a functionally graded plate with a circular hole based on complex variable method. With using the method of piece-wise homogeneous layers, the general solution for the plate having radial arbitrary elastic properties is derived when it is subjected to uniform heat flux at infinity, and then numerical results are presented for several special examples. It is found that the stress around the circular hole in the functionally graded material plate can be effectively reduced by choosing the proper change ways of the radial elastic properties. [ABSTRACT FROM AUTHOR]

Using the Stroh formalism combined with the analytical continuation principle of Muskhelishvili, the Green's functions for a line heat source in a piezoelectric solid with a parabolic boundary are obtained in closed form. The obtained Green's functions not only satisfy all the given boundary conditions, but also ensure the displacement and electric potential to be single-valued. As special cases, the solutions for a piezoelectric half-plane are also presented, and they are shown to be consistent with previous works. [ABSTRACT FROM AUTHOR]