An analysis of shear stress in a soft material under mode III fracture - Grewal, Harishpal Singh (2018)
The motivation behind this study is to identify the shear stresses (both in plane and out of plane) around a crack of a mode III fracture of a soft material and see its associated behaviours. This will be done by plotting individual graphs based on different notch angles (four in this report) and from there, plotting collectively the stress in each of the nine directions of stresses. For example, T_xx at 96 degrees, T_yy at 96 degrees etc. The formulas to plot the collective graphs will be further elaborated in the formulation and results section. From this graph plotted collectively, the maximum value of the stress at each alpha value can be analysed and the distance from the crack line at which the maximum shear stress occurs. The meaning of crack line in this paper refers to the location of the notch angle, for example if the notch angle of concern is 96 degrees, then the crack line would be the line at the 96-degree mark with respect to the reference line (Figure 1). The reason for studying the angle at which the maximum stress occurs is that it gives an indication on how far from the crack surface or line does this maximum value occur. For example, if for a 96-degree crack surface (i.e. α=96), the maximum stress occurs at 86 degrees, the author will be able to know that is 0.89 or 89% away from the reference line. From all these data, the author is looking for the difference between linear and non-linear stresses. To calculate and analyse the stress in an efficient manner, an infinitesimal element would be studied as shown in Figure 2. The entire structure would be teared as shown in by the symbols in Figure 1. Due to the complex nature of the equations, mathematical program, Wolfram Mathematica will be utilized to set up equations and plot graphs which will be useful for the study.