Interaction of a penny-shaped crack with an elliptic crack under shear loading

Abstract

The problem of interaction between equal coplanar elliptic cracks embedded in a homogeneous isotropic elastic medium and subjected to shear loading was solved analytically by Saha et al. (1999) International Journal of Solids and Structures 36, 619-637, using an integral equation method. In the present study the same integral equation method has been used to solve the title problem. Analytical expression for the two tangential crack opening displacement potentials have been obtained as series in terms of the crack separation parameter β i up to the order β 5 i , (i = 1, 2) for both the elliptic as well as penny-shaped crack. Expressions for modes II and III stress intensity factors have been given for both the cracks. The present solution may be treated as benchmark to solutions of similar problems obtained by various numerical methods developed recently. The analytical results may be used to obtain solutions for interaction between macro elliptic crack and micro penny-shaped crack or vice-versa when the cracks are subjected to shear loading and are not too close. Numerical results of the stress-intensity magnification factor has been illustrated graphically for different aspect ratios, crack sizes, crack separations, Poisson ratios and loading angles. Also the present results have been compared with the existing results of Kachanov and Laures (1989) International Journal of Fracture 41, 289-313, for equal penny-shaped cracks and illustrations have been given also for the special case of interaction between unequal penny-shaped cracks subjected to uniform shear loading.

Validation of Crack Interaction Limit Model for Parallel Edge Cracks using Two-Dimensional Finite Element Analysis

“…Energy release rate (Parker, 1999) Micro-cracks Actual Displacement Discontinuity (Gorbatikh and Kachanov, 2000) Collinear and parallel interface cracks Mushkelishvili and Burger's vector (Han et al, 2002) Distributed parallel cracks Rotated Staggered Grid (Orlowsky et al, 2003) Parallel cracks and collinear cracks Modified Kachanov Method (Gorbatikh et al, 2007;Li et al, 2008) Inclined and offset parallel and collinear cracks Integral Equation Method (Chen, 2007;Saha and Ganguly, 2005) Offset parallel cracks Complex Stress Function Method (Sankar and Lesser, 2006) Parallel cracks Muskhelishvili and Laurent's series (Li et al, 2008) Parallel symmetric cracks Schmidt Method (Yang, 2009) Parallel surface cracks Singular Integral Method (Feng and Jin, 2009) Periodic edge cracks Fourier Integral (Yildirim et al, 2011) Parallel edge cracks Fourier and Cauchy Integral (Chen and Wang, 2012) Safety assessment of the presence of multiple cracks is commonly referred to recommended FFS codes. However, the theoretical and practical examination of the recommended FFS codes, such as ASME Boiler and Pressure Vessel Code Section XI (ASME, 1998(ASME, , 2004, API 579 (ASME, 2007), British Standard PD6495 (BSI, 1991) and BS7910 (BSI, 1997(BSI, , 2005, Nuclear Electric CEGB R6 (R6, 2006), and JSME Fitness-for-Service Code (JSME, 2000), have found that the exception of crack interaction in FFS combination rules has resulted in over-estimated and unrealistic fracture and failure predictions, particularly for closely spaced cracks.…”

Interacting Cracks Analysis Using Finite Element Method

“…Failure in pressure vessel and piping components (Moussa, Bell, & Tan, 1999;Murakami & Nasser, 1982) Collinear cracks and flat elliptical cracks Multiple site damage in aircraft structures (Gorbatikh & Kachanov, 2000;Jeong & Brewer, 1995;Jones, Peng, & Pitt, 2002;Milwater, 2010;Pitt, Jones, & Atluri, 1999) Multiple flaws and surface cracks Failure of nuclear power plant components (Kamaya, Miyokawa, & Kikuchi, 2010;Kobayashi & Kashima, 2000) Penny-shaped cracks Brittle fracture of welded structures in pressure vessels (Saha & Ganguly, 2005) Offset collinear and layered cracks…”