Modes I/II SIF of a diametrically compressed Brazilian disc having a central inclined crack with frictional surfaces

Abstract

An in‐house finite element code was used to analyse a diametrically compressed isotropic homogeneous Brazilian disc having a central inclined crack with frictional surfaces for the evaluation of its corresponding modes I and II stress intensity factor (SIF). One‐half of the disc was successfully idealized. The coefficient of friction between the crack surfaces ranged from 0 to 1 in steps of 0.1. Relative crack length ratios of 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, and 0.7 were analysed with crack angles up to 90° in steps of 5°. The crack angle corresponding to the transition from a mixed mode I/II to a pure mode II decreases with increasing the relative crack length ratio. An increase in the relative crack length ratio leads to an increase in the range of crack angles corresponding to a partially closed crack. The crack angle at which fully closed sliding crack surfaces commences is 30° independent of the relative crack length ratio and the friction coefficient. With the same relative crack length ratio and increasing the friction coefficient, there is a corresponding decrease in the crack angle for the maximum mode II SIF. With a decrease in the relative crack length ratio or the friction coefficient, the crack angle beyond which the crack surfaces become in a fully sticking mode decreases resulting in zero mode II SIF. Generally, mode II SIF decreases with increasing the friction coefficient between the crack surfaces. Good agreement has been generally obtained with relevant results found in the literature.

Numerical evaluation of mode I/II SIF of quasi-brittle materials using cracked semi-circular bend specimen

“…Instead, a fine mesh was constructed around the crack tip. That idealization proved its adequacy in similar analyses (Hammouda et al, 2002(Hammouda et al, , 2003a(Hammouda et al, , 2003b(Hammouda et al, , 2004(Hammouda et al, , 2007(Hammouda et al, , 2017Fayed, 2008;Fayed et al, 2008).…”

“…Hammouda and Fayed (2017) found that da/a = 0.008 was sufficient to get an accurate solution for their problem. The ratio da/a in the present work was decided based on the results of similar pilot exercises in which the several da/a ratios 0.002, 0.004, 0.006 and 0.008 were also invoked to compare the resulting computed stress intensity factors.…”

Mixed‐mode stress intensity factors via centrally cracked Brazilian disc with wide‐range controlling parameters

“…The determination of relevant SIFs is the main objective of related numerical and analytical works. The numerical methods include the finite element method, 16–20 the boundary element method, 21,22 the discrete element method, 23 and the finite difference technique 12 . That led to some analytical and numerical solutions for those disc systems.…”

“…Pure mode II SIF exists in the case of having the crack tip closed with sliding crack surfaces. In case of frictional crack surfaces, crack tip can be in a sticking contact mode leading to zero K II 13,17 . Researchers have paid attention both numerically and analytically in addressing closed cracks having pure mode II operating with either smooth or frictional crack surfaces.…”

Wide‐range and accurate mixed‐mode weight functions and stress intensity factors for cracked discs

“…3 During the past decades, various methods and solutions have been proposed to obtain SIFs for the cracked discs subjected to various boundary conditions. [4][5][6][7][8][9][10][11][12] Using the dislocation method, an important and closed-form SIF solution was given by Atkinson et al, 5 for the centrecracked disc subjected to diametrically concentrated compressive forces. The explicit SIFs for several crack lengths and crack inclinations were given in the form of infinite series.…”