Contact Mechanics Of Layered Structures

Abstract

Contact mechanical study of layered structures is useful to various fields of engineering, such as - mechanical engineering, civil engineering, materials engineering and biomechanics. Thin hard film coating on a compliant substrate used in cutting tool industry is an example of a layered structure. The protective coating saves the substrate from fracture and wear. However, due to film material brittleness, fracture in the films is of concern. We have developed an analytical model for a film-substrate bilayer system under normal contact loading, which helps us to obtain the stress distribution in the film and fracture behaviour. Our contact model is based on Hankel’s Transform technique, where we assume a Hertzian pressure boundary condition. At each depth of penetration of the indenter in the film-substrate system, we estimate effective modulus of the system based on Gao’s approach. We have validated our analysis by surface strain measurements and photoelastic stress study in the film on a substrate. Experimental observations from literatures show the dependence of different fracture modes in a thin hard film with columnar structure on film thickness and substrate plasticity. We perform fracture analysis, a parametric study of the fracture modes in the film under contact loading. When the film thickness is small and the substrate is relatively hard (e.g. tool steel), the film and the substrate deform conformally under contact loading and the columns of TiN slide against each other into the substrate. On the other hand, when the film is thicker and the substrate is soft (e.g. mild steel or aluminium), the strain mismatch between the film and substrate acts as an added traction at the interface and drives cracks, such as radial tensile stress driven bending cracks that start from the interface at the center of indentation; maximum shear stress driven inclined shear crack that starts inside the film and propagate at an angle to the indentation axis and tensile stress driven edge crack that starts from the free surface outside the contact. We can draw a fracture map based on these calculations which provides a guide to select film thickness depending on the substrate hardness, so that the benign mode of damage, i.e., columnar shear occurs in the film. Apart from generating the fracture map, we can obtain rationale for different fracture phenomenon in the film by studying the indentation stress field. Principal tensile stresses, responsible for driving edge cracks from the free surface outside the contact, become compressive as one approaches the substrate if the substrate is compliant. The cracks therefore do not penetrate deep into the film rather curve away from the axis of indentation. At the transition zone from one mode of damage to other in the fracture map, different modes of fracture may co-exist. The whole column may not shear, rather the shear can start from somewhere in the middle of the film, where the shear stress is maximum and it can end without reaching the interface. The indentation energy is then dissipated in other forms of damage. The contact analysis is further applied to TiN /AlTiN multilayered films having similar elastic properties. Experimental observations suggest that with decreasing layer thickness the fracture resistance of the multilayers increase and some plastic yielding occurs at the top layers of the film. However no substantial change in strain capacity (Hardness/ Young’s Modulus) of the film is observed. Hence we attribute the increase of fracture resistance of multilayers to film plasticity and mimic it by reducing the modulus of the film. The analysis validates the propensity of edge cracking and transgranular cracking as they decrease with increasing number of layers in a multilayer. We next extend our bilayer analysis to a more general trilayer problem where the moduli of the layers vary by several orders. The test system here is a mica-glue-glass system which is used in surface force apparatus experiments. Gao’s trilayer analysis is used to fit the experimental data obtained from surface force apparatus experiments, where a glass sphere indents the trilayer. The parallel spring model used in Gao’s approximation is found to be inadequate to rationalize the experimental data. We have modified Gao’s formulations by reducing the problem to a bilayer problem where the layers are the first layer (in contact) and an equivalent layer which has properties determined by a rule of mixture of the properties of all the layers excluding the top layer set out as a set of springs in series. The modified formulations give a better fit to the experimental data and it is validated from nanoindentation experiments on the same system. The formulation is used to obtain the compression of the glue, which contributes significantly to the deformation of the trilayer system in the SFA experiments. Thus, the analysis can be used to deconvolute the influence of glue in the actual mechanical response of the system in an SFA experiment, which has so far been neglected.