Thermal shock fracture mechanics of a cracked solid based on the dual-phase-lag heat conduction theory considering inertia effect

The generalized lagging behaviour in solids is very important in understanding heat conduction in small-scale and high-rate heating. In this paper, an edge crack in a semi-infinite medium subjected to a heat shock on its surface is studied under the framework of the dual-phase-lag (DPL) heat conduction model. The transient thermal stress in the medium without crack is obtained first. This stress is used as the crack surface traction with an opposite sign to formulate the crack problem. Numerical results of thermal stress intensity factor are obtained as the functions of crack length and thermal shock time. Crack propagation predictions are conducted and results based on the DPL model and those based on the classical Fourier heat conduction model are compared. The thermal shock strength that the medium can sustain without catastrophic failure is established according to the maximum local stress criterion and the stress intensity factor criterion.

Download Full-text

Transient Heat Conduction in Functionally Graded Hollow Cylinders and Spheres

Volume 3: Design and Analysis ◽

10.1115/pvp2012-78617 ◽

2012 ◽

Cited By ~ 1

Author(s):

A. H. Akbarzadeh ◽

Z. T. Chen

Keyword(s):

Heat Conduction ◽

Transient Heat Conduction ◽

Functionally Graded ◽

Hyperbolic Heat Conduction ◽

Phase Lag ◽

Dual Phase ◽

Conduction Theory ◽

Hollow Cylinders ◽

Fourier Heat Conduction ◽

Cylinders And Spheres

In the present work, transient heat conduction in functionally graded (FG) hollow cylinders and spheres is investigated based on the non-Fourier heat conduction theories. Since the heat transmission has been observed to propagate at a finite speed for applications with very low temperature, short-pulse thermal-heating, and micro temporal and spatial scales, dual phase lag (DPL) and hyperbolic heat conduction theories are considered in current study instead of the conventional Fourier heat conduction theory. Except the phase lags which are assumed to be constant, all the other material properties of the hollow cylinders and spheres are taken to change continuously along the radial direction according to a power-law formulation with different non-homogeneity indices. The heat conduction equations are written based on the dual phase lag theory which includes the hyperbolic heat conduction theory as well. These equations are applied for axisymmetric hollow cylinders of infinite lengths and spherically symmetric hollow spheres. Using the Laplace transform and Bessel functions, the analytical solutions for temperature and heat flux are obtained in the Laplace domain. The solutions are then converted into the time domain by employing the fast Laplace inversion technique. The exact expression is obtained for the speed of thermal wave in FG cylinders and spheres based on the DPL and hyperbolic heat conduction theories. Finally, the current results are verified with those reported in the literature based on the hyperbolic heat conduction theory.

Download Full-text