Cracking in Thin Films and Substrates
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CRACKING IN THIN FILMS AND SUBSTRATES P. STAHLEt AND C.F. SHIHt tDepartment of Technology, Uppsala University, Uppsala, Sweden tDivision of Engineering, Brown University, Providence, RI, USA ABSTRACT A crack terminating perpendicularly at the bimaterial interface is analyzed. Stress distributions for a broad range of elastic moduli and yield strength mismatch are discussed. These results can be used to understand the effect of mechanical properties mismatch on the competition between crack deflecting into the interface and crack penetrating into the base material. The role of microdefects near the interface is explored. INTRODUCTION Coatings can improve the electrical and mechanical properties of the coated structure. The interface between the coating and the substrate is often the site for the initiation of flaws which can eventually cause the structure to fracture. A systematic series of experiments in which the coated beams were loaded to fracture has been carried out by Johansson et al. (1988) [1]. These mono-crystalline silicon beams (with dimensions 1 x 10 x 100prm) were coated with titanium, titanium nitrate and aluminium, respectively. Through different processing techniques, coatings of different thicknesses (0.1-0.6pm) and different crystallographic orientations were produced. They observed that aluminum coatings strengthened the coated structure by a larger amount than was anticipated by the increased cross section of the beam. In contrast, titanium and especially titanium nitrate coatings weakened the structure. Our investigation is motivated by the above experimental observations (and similar observations reported by other investigators) and is aimed at explaining the role of mechanical properties of the film and the substrate on the competing fracture processes. BOUNDARY VALUE PROBLEM Consider a film containing a crack terminating perpendicularly at the bimaterial interface as depicted in Fig. 1. The elastic properties of the substrate, designated material 1, are characterized by Young's Modulus E 1 and Poisson's ratio v1, while those for the film, designated material 2, are characterized by E 2 and v2 . The substrate and the film behave as perfectly plastic materials upon reaching their respective yield stresses c0 and aaO. When both materials are elastic, Zak and Williams [2) showed that the stresses near the tip of the crack become unbounded according to a - r" where r is the distance to the crack tip and -1 < s < 0. Assume that the characteristic dimensions of the substrate axe much larger than the film thickness d. Suppose the coating is subjected to an uniform tensile residual stress of o,' in the y direction. By dimensional considerations, the stresses surrounding the crack tip can be written as
Crilol' = )(r/d)'g 3(O), where the parameter A is a function of the body geometry and the load case. angular function gii(O) is normalized so that g22(0) equals unity. More generally, the stresses may be written as roj = K(23rr). gMi(a). Mat. Res. Soc. Symp. Proc. Vol. 239. 01992 Materials Research Soc
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