A Finite Element Investigation Of Brittle Fracture During Spherical Nanoindentation Of Thin Hard Films

Abstract

Hard ceramic films of micrometric thickness deposited on a soft metallic substrate have ushered in a new era in the fabrication of structural, tribological, microelectronic and optical components. The mechanical performance of these components is however critically dependent on the strength and toughness of these films as well as on those of the film-substrate interface. Recent studies have shown that cylindrical and radial cracks can propagate through the film during nanoindentation tests with spherically tipped and pointed indenters, resulting in steps in the load versus displacement curve. In this thesis, the mechanics of fracture of thin hard films bonded to soft substrates, during nanoindentation is studied by carrying out finite element analyses. The role of plastic yielding in the substrate on the above issue is examined. Another important objective of this work is to propose a method by which finite element simulations can be employed to interpret nanoindentation test results and yield information related to the fracture behaviour of hard films.

To this end, axisymmetric finite element analyses of spherical nanoindentation of a TiN film of thickness t = 1 //m, on a steel substrate are carried out. Numerical algorithms for large deformation, contact simulation and computation of energy release rate are employed in the analyses. The film is assumed to be linear elastic, whereas, an elastic-plastic constitutive model is used for the substrate.

A nanoindentation analysis of the uncracked film is first carried out. The development of plastic yielding in the substrate and its influence on the load P versus penetration h characteristics is examined. The stress fields around the indenter for different depths of indentation are studied. The results show that the radial stress attains a tensile peak at the film surface, just outside the indented zone. However, it becomes compressive with increasing distance below the surface. Interestingly, a tensile radial stress prevails at the film-substrate interface at large indentation depth. The shear stress increases to a peak value at a distance of 0.052 to OAt below the film surface depending upon the radial location and then reduces.

Next, circumferential cracks extending downwards from the film surface are introduced at different radial distances R from the axis of symmetry. Finite element analyses are carried out till the indented zone extends almost up to the crack surface. The energy release rate J is computed as a function of indentation depth for different crack lengths c (in the range from O.lt to 0.9t). The results show that shallow cracks are essentially under Mode II loading with closure of crack faces caused by compressive radial stresses. However, a mixed-mode state prevails if the crack length is large (c > 0.62), with crack faces opening out due to tensile radial stress near the film-substrate interface. The variation of J with c/t for cracks located at different radial distances R is examined. It is found that for small R, there is a decreasing branch in the J versus c variation between c = 0.2i to 0.75£ which indicates that crack extension in this range will be stable. On the other hand, for large R, J increases monotonically with c/t which implies that unstable fracture of the full film thickness will occur following crack initiation.

A composite nomogram is generated in the P — h plane where constant J lines are plotted along with load-displacement curves for different crack lengths. If now a nanoindentation (experimental) load-displacement behaviour is superimposed on this nomogram, the initial crack length (of a pre-existing flaw), the final crack length and fracture energy of the film can be inferred.

In the last part of the thesis, the effect of the substrate yield strength on the indentation mechanics is studied. It is found that upon decreasing the yield strength, the load at a given indentation depth decreases while the residual depth at unloading increases. Also, the energy release rate for a given radial location and crack length reduces considerably at large depths of indentation.