Simple Models for Surface Cracking
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SIMPLE MODELS FOR SURFACE CRACKING PAUL MEAKIN Central Reseach and Development Department, E. I. du Pont de Nemours and Company, P. 0. Box 80356, Wilmington, DE 19880-0356 ABSTRACT A simple model for crack growth in thin films deposited onto a substrate has been developed. This model results in the generation of cracking patterns which have a remarkably realistic appearance. In the simulations a slow crack initiation period is followed by a period of rapid crack growth in which quite linear cracks are formed. Later on the crack growth process becomes slower and less regular as the cracking process relieves much of the stress in the surface layer. In this model pre-existing defects have a large effect on the crack growth kinetics and morphology. INTRODUCTION Thin film deposits or coatings are used in a broad range of important applications to improve optical, electronic and tribological properties, corrosion resistance, wear resistance, appearance and other properties. Familiar examples include paint films, ceramic coated metal and optical coatings. Very often the performance of these systems is compromised by cracking of the thin surface layer which is a consequence of large stresses in the surface film brought about by processes such as differential contraction or expansion, phase transitions or physicochemical changes such as the drying of paint films or oxidation of metals. Very often surface cracking processes lead to the growth of cracking patterns which resemble mud cracks in a dried up lake bed. Here a simple model for this type of material failure process is described [1] and some results obtained with this model are presented. Computer Models In the model for crack growth in thin films the thin film is represent-d by a network of bonds and nodes which, in the most simple case, form a triangular network or lattice at the start of the simulation. The bonds are considered to consist of Hookean (central force) spring and the elastic energy of the surface- layer is given by E = 1/2 1 kij(,Iij-,1o) 2 ij
(1)
where 1ii is the length of the bond joining the ith and jth nodes and kij is the force constant associated with that bond. If the bond is broken, k ii = 0. At the start of a simulation the network forms a regular triangular lattice with periodic boundary conditions and the length of the bonds in the network may be larger than or smaller than the equilibrium bond length (.1o). Periodic boundary conditions were used in all of the simulations. At the start of a simulation each node in the network is attached to the substrate at its equilibrium position by a "weak" bond (Figure 1). The force exerted by this bond on the ith node Mat. Res. Soc. Symp. Proc. Vol. 130. c 1989 Materials Research Society
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Figure I
A schematic representation of a model for elastic fracture in thin films. The nodes (large dots) are connected by strong bonds to form a triangular lattice. Each node is joined to the underlying structure by a weak bond (---) at its original position at the start of the simulation. Throughout the simu
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