Examples of the Influence of Residual stresses on Fracture

Generally compressive residual stresses increase the resistance of a part to fracture while tensile residual stress degrades strength. It will be shown that the local compressive residual stresses and the subsurface cracks produced by scribing, at very low loads, are responsible for the low tensile strength of glass specimens. Also, if metal parts containing surface cracks are subjected to pressure such as shot-peening, which produces high near surface residual compressive stresses, the initial end of the crack will experience tensile loading. This paper explains these phenomena using procedures based on LEFM. A method for residual stress measurement using LEFM solutions is also reviewed. 1. BEAR, Inc. Berkeley, CA 94710 e-mail: weilicheng@home.com 2. James Fife, Professor Emeritus Dept. of Mech. Eng., University of California Berkeley, CA 94720 e-mail: finnie@me.berkeley. edu Introduction The literature on cracking due to a sliding indenter, a process often referred to as scribing or scratching, goes back 80 years ago, when Griffith’s classic work appeared. The scribing process will be described, and it is seen that “median” cracks propagate downwards, below the indenter, in glass at loads as low as 0.014 N. The present work is based on loading a sub-surface crack and analyzes the effect of loading rate in a moist environment in a different manner from previous work by others. The present wok estimates the strength of glass in the presence of subsurface flaws produced by scratching. An upper bound is observed by considering an inert environment. A lower bound is obtained for the strength of glass in moist air. A related problem is the residual stresses induced by shot-peening or laser surface treatment. These are shown to have a profound effect on surface flaw detection. It is also shown that the solutions for LEFM leads to a new method for residual stress measurement. The Strength of Glass Following Scribing The scribing process shown in Fig. 1 introduces a zone of deformation under the indenter which we describe as “the plastic zone” due to a combination of compression and shear. The first crack to form, described as the median crack, propagates from the base of the plastic zone as shown in Fig. 2. Currently, the concept that surface flaws are inherent in glass is a common concept. For example, in the well known book by McClintock and Argon (1966) it is stated that “In some brittle solid, such as inorganic glass, cracks are formed only at the free surfaces”. To study this assumption, we take a simple model in which the inherent flaw is treated as an edge crack and residual stresses are ignored. Taking a fracture toughness K of 0.76 MN/m and fracture stress of soda lime glass IC 3/2 in a moist environment of 70 MPa leads to an estimate of crack size of a = [K /(1.12 σ)] /π = 30 μm. Ic 2 Immediately, we can draw two contradictory conclusions, first, such a flaw size should be detectable by optical or scanning electron microscope (SEM). Second, to our knowledge no such surface cracks have been observed directly. It is tempting by saying that the crack faces are touching. However, SEM examination of glass subjected to bending loads, which should separate the faces of a closed crack, has not revealed cracks. This suggests that strength impairing flaws are so close to the surface that they may be removed by surface melting or etching. v(a, s) ' MU MF *F ' 0 ' 1 E )m a 0 KI(a) MK f I (a,s) MF da vr(a) ' 2.9 Fr E ) aH( b a ) with H( b a ) ' b a % m 1