Multiple Cracks of a Thin Film on a Ductile Substrate
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MULTIPLE CRACKS OF A THIN FILM ON A DUCTILE SUBSTRATE Ming-Hao ZHAO, Ran FU, and Tong-Yi ZHANG a Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China ABSTRACT The present work proposes a Dugdale type model to theoretically predict the multiple cracks of a residually tensile stressed thin film on a ductile substrate. The results show that there exists a critical value, Rc, of the cracking resistance number, R. When R < Rc , the film cracks and the normalized crack spacing is determined by cracking resistance number and the stress ratio of the residual stress to the yield strength of the substrate. INTRODUCTION Residual tensile stresses in a thin film may cause film cracking when the film thickness is larger than a critical value or for a given film thickness, when the residual stress is higher than a critical value [1-7]. Considering that a film and its associate substrate have the same elastic properties, Thouless [2] and Thouless et al. [3] developed a rigorous treatment of a series of parallel cracks with the crack length as the film thickness in a residual tensile stressed film deposited an elastic substrate. Zhang and Zhao [4] further studied the thermodynamic equilibrium crack depth and spacing of a periodic array of cracks in an elastic film on an elastic substrate with the same elastic constants. Beuth [5] and Ye et al. [6] studied the cracking of thin films deposited on substrates with different elastic properties and provided complete sets of solutions and approximate formulae for practical applications. Hutchinson and Suo [7] reviewed the work by Ye et al. [6] on the possibility of penetration of surface cracks through the interface. Xia and Hutchinson [8] studied the crack patterns in thin films, wherein propagating cracks may remain straight or be curved as a consequence of crack interaction. When the substrate is ductile, the substrate yield strength has a great influence on the film cracking behavior. Studying the cracking and decohesion of thin films on ductile substrates, Hu and Evans [9] proposed a simple shear lag model, where plasticity deformation or yielding is assumed to occur along the interface. Their analytical results show that a substrate with a low yield strength enhances the tendency of film cracking but also inhibits decohesion by blunting film cracks at the interface, which may lead to multiple film-cracks. Considering the difference in elastic properties of a film from its substrate, Beuth and Klingbell [10] further investigated a single crack in a thin film bonded to an elastic-plastic substrate by numerical calculations. Good agreement between the result from the shear lag model and that from the numerical calculations has been obtained for most material combinations under the condition of Dundurs’ parameter α
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