Electrothermal stress in conducting particulate composites

Abstract

Electrothermal–mechanical interaction plays an important role in controlling the performance of electromechanical structures and field-assisted processes. The understanding of electrothermal–mechanical behavior of a material requires the analyses of Joule heating and thermomechanical deformation. In this study, we analyze the current-induced thermal stress in a conducting composite consisting of conducting spherical inclusions at dilute concentration. Assuming that there is no interaction among conducting inclusions, we obtain closed-form solutions of local temperature and thermal stress. The thermal stress created by Joule heating is proportional to the square of electric current density (electric field intensity) and the von-Mises stress reaches the maximum value at the interface between the spherical inclusion and the matrix. Large electric current will likely cause local delamination along the interface.

Appendix

The coefficients of $\tilde{a}_{n}$ and $\tilde{b}_{n}$ are listed below,

$$ \tilde{a}_{0} = \frac{{\left( {1 + \chi^{2} } \right)}}{2\chi }\frac{{\rho_{\text{m}} }}{{\kappa_{\text{m}} }} + \frac{{\left( {1 - 2\chi } \right)^{2} }}{6\chi }\frac{{\rho_{\text{s}} }}{{\kappa_{\text{s}} }}\left( {1 + \frac{{2\kappa_{\text{s}} }}{{\kappa_{\text{m}} }}} \right) $$

(75)

$$ \tilde{b}_{0} = 0 $$

(76)

$$ \tilde{a}_{2} = \frac{1}{{3\chi R^{2} (3 + 2\kappa_{\text{s}} /\kappa_{\text{m}} )}}\frac{{\rho_{\text{m}} }}{{\kappa_{\text{m}} }}\left( {(\chi - 5)(\chi + 1) + (1 - 2\chi )^{2} -\left[ {2 + \frac{{3\kappa_{\text{m}} }}{{\kappa_{\text{s}} }}} \right]\frac{{\rho_{\text{s}} }}{{\rho_{\text{m}} }}} \right) $$

(77)

$$ \tilde{b}_{2} = \frac{1}{3\chi }\frac{{2R^{3} (1 + \chi )}}{{3 + 2\kappa_{\text{s}} /\kappa_{\text{m}} }}\frac{{\rho_{\text{m}} }}{{\kappa_{\text{m}} }}\left[ {( - 1 + 2\chi ) + (1 + \chi )\frac{{\kappa_{\text{s}} }}{{\kappa_{\text{m}} }}} \right] $$

(78)

$$ \tilde{a}_{n} = \tilde{b}_{n} = 0 \; \quad \; {\text{for}}\;n = 1 {\text{ and}}\;n > 2 $$

(79)