The fracture mechanics of bi-material systems

Banerjee, Anuradha (2003) The fracture mechanics of bi-material systems. PhD thesis, University of Glasgow.

Abstract

A stationary crack normal to the boundary between two elastically mismatched solids such that the crack tip is located at the interface is studied analytically and computationally. Eigenvalue expansions establish the first two terms of the asymptotic expansion of the plane strain elastic stress fields for mode I and mode II loading. The second order term was determined as a function of elastic mismatch for a thin cracked film on a substrate and for a thin cracked lamina between two substrates. Elastic-plastic analysis was performed when one of the solids was fully elastic and the other solid was elastic perfectly-plastic. Analytic and numerical solutions of the asymptotic stress fields were developed in small strain yielding. The angular span at the crack tip was composed of elastic and plastic sectors. Analytic solution of the stresses in plastic sectors was based on slip line theory and the stresses in the elastic sectors were developed using solutions to semi-infinite problems. Numerical solutions obtained using boundary layer formulations were in close agreement with the analytic results. When the crack was located in plastic solid, the elastic solid ahead of the crack develops a logarithmic singularity. The effect of the T-stress on the extent of plasticity on the flanks is determined. Interest is mainly focussed on the case when the crack is in an elastic solid and the material ahead is elastic perfectly-plastic. Solutions are developed at different levels of elastic mismatch, mode mixity and T-stress. Mode I fields are identified to be parameterised by the constraint ahead of the crack tip which depends on the elastic mismatch and the T-stress. The effect of constraint on the competition between interface failure and penetration is discussed. A crack located in an interfacial zone between two plastically dissimilar solids in which toughness and yield strength were assumed to interpolate linearly across the zone, has been studied both analytically and computationally. The problem is an idealisation of a crack in the heat affected zone between a weld and parent plate in which the mechanical properties are dependent on position or a crack in a solid subject to a non-uniform temperature field. Due to the gradation in yield strength, even under a remote mode I load the plastic zone shapes are asymmetric about the crack plane resulting in a non-unity plastic mixity at the crack tip. Plane strain asymptotic stress fields under conditions of small scale yielding and non-hardening plasticity have been constructed by assembling elastic and plastic sectors using slip line theory. The numerical solutions using boundary layer formulations are in close agreement with the analytic solutions. From the asymptotic field under assumption of local homogeneity, higher plastic mismatch and compressive T-stress result in higher inclination of the crack extension plane towards the solid of higher yield strength. Failure is also modelled using a weakest link model which allows initiation of cleavage failure within the plastic zone and not necessarily at the crack tip. Mismatch in yield strength and toughness show opposing effects on the crack extension direction, the plastic mismatch favours crack initiation in the softer material while toughness mismatch favours crack initiation in less tough material.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: Mechanical engineering.
• Colleges/Schools: College of Science and Engineering > School of Engineering
• Supervisor's Name: Hancock, Prof. John
• Date of Award: 2003
• Depositing User: Enlighten Team
• Unique ID: glathesis:2003-71418
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 10 May 2019 10:49
• Last Modified: 04 Jun 2021 13:47
• URI: https://theses.gla.ac.uk/id/eprint/71418