Dugdale plastic zone model of a penny-shaped crack in a magnetoelectroelastic cylinder under magnetoelectroelastic loads

This paper extends the Dugdale plastic zone to the penny-shaped crack problem for a magnetoelectroelastic (MEE) cylinder, where the crack surfaces are assumed to be magnetoelectrically permeable. Using potential function theory and Hankel transform method, the present boundary value problem is translated into solving a sectionalized Fredholm integral equation of the second kind. The non-singular field solutions are analyzed, and the effects of the applied MEE loads and geometric dimension on the width of plastic zone and crack opening displacements are evaluated. Numerical results show that for the considered model, each of the far-field MEE combination load λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}, the far-field magnetoelectric combination load λEH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _{\mathrm{EH}}$$\end{document} and the purely mechanical load σ0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma _0$$\end{document} applied in the far field, respectively, plays an important role in the present fracture analysis. For a given mechanical load and a fixed crack configuration, the negative magnetoelectric loads are prone to promote the crack growth and propagation than the positive ones. These should be helpful for the design and manufacture of MEE materials and devices.