This research study investigates the cracking processes associated with inclusion pairs of varying shape, orientation and inclusion materials. Specifically, this study summarizes a series of uniaxial compression tests on gypsum specimens with varying inclusion pair configurations. The inclusions consisted of differing materials, of contrasting Young’s Modulus (higher and lower than the matrix), shapes (hexagon, diamond, ellipse), and relative pair orientations (bridging angle). Similar cracking sequences were seen in the newly introduced inclusion pairs as in previous studies. Slightly increased debonding (usually corresponding to increased interface shearing) occurred as inclusion pairs with inclined interfaces were introduced. Coalescence behavior trended from indirect or no coalescence, to direct shear coalescence, to combined direct tensile-shear coalescence as the inclusion bridging angle was increased, similar to past studies on circular and square inclusion pairs and flaw pairs. Also, the coalescence related to inclusion interface inclination and bridging angles resembled the actual coalescence of flaw pairs with similar inclination and bridging angles.


The cracking processes in a brittle material consisting of a matrix with inclusions are important mechanisms for both natural materials (rocks) as well as synthetic composite materials (e.g. concrete). There have been many past studies regarding the cracking processes in brittle materials, which contain pre-existing cracks (called flaws) both analytically [1, 2], as well as experimentally [2, 3, 4]. Also, the cracking processes in brittle materials, which contain inclusions have been studied both analytically [6, 7, 8] and experimentally [7, 9, 10, 11, 12]. Only recently have experiments been performed with the technology capable of capturing high speed imagery to fully describe the crack propagation and coalescence behavior in a brittle material. The majority of the previous research performed on brittle materials with inclusions investigated the fracturing patterns associated with circular or rectangular (square) inclusions. The present research was conducted to develop a more detailed description of the coalescence patterns of uniaxially loaded gypsum specimens with inclusion pairs of varying shape, stiffness and orientation. Emphasis was placed on the coalescence behavior associated with the effects of varying these inclusion pair configurations.


2.1 Flaw Coalescence Studies Amongst the many experimental studies regarding flaws in brittle materials, experimental work done by Wong and Einstein [5] is particularly significant because it incorporated the use of a high speed camera to follow crack propagation and coalescence. One of the most important contributions of Wong and Einstein’s study was a proposed set of coalescence categories for different co-planar and stepped flaw pairs (Figure 2.1). These coalescence patterns will later serve as a basis for comparing the coalescence patterns seen in brittle materials containing inclusions pairs.

2.2 Inclusion Coalescence Studies Extending on the macro-scale flaw testing techniques used in the Massachusetts Institute of Technology (MIT) Rock Mechanics Laboratory, brittle material with inclusions was investigated with high speed imagery by Janeiro and Einstein [12]. That study tested 1” single square, circle, diamond, and hexagon inclusion shapes as well as 1/2" circular and square inclusions with varying inclusion material stiffness (Figure 2.2).

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