On the Mechanics of Indentation Induced Lateral Cracking
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On The Mechanics of Indentation Induced Lateral Cracking Xi Chen1 1 Department of Civil Engineering and Engineering Mechanics, Columbia University New York, NY 10027 ABSTRACT The mechanics governing the lateral cracks that form when a hard object plastically penetrates a ceramic is presented. The roles of indentation load, penetration depth and work of indentation are all highlighted, as are the influences of the mechanical properties of the substrate. The three dimensional axisymmetric problem for an annular crack driven by a rigid spherical or conical indenter pushed into a semi-infinite half-space of elastic-perfectly plastic material is solved using numerical methods. The region of highest tensile stress is identified corresponding to the location where a crack is most likely to nucleate. This location coincides with the depth below the surface where the crack will expand parallel to the surface under mode I conditions. The solutions have been validated by comparison with measurements of the cracks that form upon Vickers indentation. The basic formula for the crack radius has been used to predict trends in cracking upon static penetration. INTRODUCTION When a small indenter plastically penetrates a ceramic, a pattern of cracks often forms around the impression, as the indenter is removed. Some cracks extend radiallyoutward and penetrate the ceramic normal to the surface. Others nucleate beneath the surface and enlarge laterally, parallel to the surface [1-5]. Indentation-induced radial cracking has become the basis for a method that can be used to estimate the fracture toughness [2, 3, 6-10]. Moreover, detailed analysis has been conducted for the radial cracks that form upon machining and during particle impact, which degrade the strength Figure 1. Schematic showing of the lateral crack [11, 12]. Lateral cracks have not been system. The spherical indentation (with load P ) on an elastic-plastic solid leaves an impression with characterized to a comparable extent. Yet, projected contact radius a . The lateral crack is such cracks participate in equally important annular with length c , which forms just outside the phenomena. Lateral cracks at the interface plastic zone, at distance d below the free surface. between thin films and substrates can be used to estimate the interface toughness [13, 14]. Such cracks are also responsible for the abrasive wear and erosion of ceramics and ceramic coatings [15-18]. The role of these cracks in the erosion and foreign object damage experienced by thermal barrier oxides used in gas turbines, when impacted by small particles in the gas stream, is of current interest [15-18]. The objective of this article is to present a rigorous mechanics analysis of lateral cracking (Fig. 1), that can be used to understand and characterize these phenomena.
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A suite of careful Vickers indentation experimental measurements of lateral cracks in transparent ceramics and glasses (symbols in Fig. 2) remains the sole basis for characterization [4]. Namely, based on these measurem
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