Experimental and Numerical Study into 3D Crack Growth from a Spherical Pore in Biaxial Compression

A series of specimens made from transparent casting resin, each with a spherical pore at the centre of specimen were tested in a polyaxial stress state with different stress ratios (sigma x/sigma y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sigma_{x} /\sigma_{y} $$\end{document}) between the lateral (the intermediate principal stress, sigma x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sigma_{x} $$\end{document}) and the axial (the major principal stress, sigma y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sigma_{y} $$\end{document}) loads, and the minor principal stress (sigma z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sigma_{z} $$\end{document} ) was equal to 0, i.e., biaxial compression. The experimental results revealed the dramatic influence of the intermediate principal stress on the mechanics of 3D crack growth from a spherical pore. In uniaxial compression, the initial spherical pore produces several differently oriented wing cracks which are relatively short, smaller than the pore diameter (referred to as wing crack wrapping). In biaxial compression even with relatively low intermediate principal stress, a large wing crack is formed growing to an extent sufficient to split the specimen. The threshold for the intermediate principal stress separating these two regimes of wing crack growth is found to be 8.5% of the major principal stress. The results obtained from finite element method modelling show that with the intermediate principal stress above this threshold the directions of most of the secondary principal stresses (tensile) along the lateral surface of the initial pore are roughly perpendicular to the intermediate principal compressive stress direction. For the intermediate principal stress below the threshold, the directions of the secondary principal tensile stresses near the lateral surface of the initial pore are distributed in radial directions with respect to the initial pore. Results of numerical modelling also show that when transition is made from spherical pore to oblate pores, this threshold increases.