David Rowcliffe

Analysis and prediction of thermal shock in brittle materials

Abstract The indentation quench method has been studied through both experiments and modeling. Practical results are obtained for alumina, whisker reinforced alumina, cermet and high speed steel. The crack growth vs temperature difference curves show no crack growth at very low Δ T s, stable crack growth at medium Δ T s and unstable crack growth above a certain Δ T (Δ T U ) and these regimes are explained in the analysis. The stable and unstable crack growth are governed by the combination of residual and thermal stress. An expression has been derived for the prediction of thermal shock resistance and it is shown that the fracture toughness is of great importance. The presence of residual stress results in the greater sensitivity of the indentation-quench method compared to other approaches, and also makes it possible to define specific values of Δ T adapted to specific applications. The method can be used to explore susceptibility to thermal fracture in a range of brittle materials on condition that it is possible to insert an indentation precrack.

Controlled indentation : a general approach to determine mechanical properties of brittle materials

This paper presents a general methodology to analyse the experimentally-obtained loading cycle of indentation load-depth (P-h) results for Vickers indentation, in combination with a newly-developed FEM analysis. Through a detailed analysis of the load-depth curves, information related to various mechanical properties, including hardness, yielding stress, strain hardening, surface displacement and plastic zone size, are obtained. The experimentally-reported indentation P-h curves for 11 different glasses and ceramics have been analysed in detail. Comparisons between calculated and experimental P-h curves show good agreement for most of the materials examined here.

The Hertzian stress field and formation of cone cracks—I. Theoretical approach

Abstract A complete three-dimensional solution has been derived for the Hertzian stress field. The solution was used to define an expression for the largest tensile stress under a spherical indenter. A numerical method was developed to solve the fracture mechanics equation related to cone crack formation, leading to a simple expression for fracture toughness. Examination of the relation between load, cone crack size and stress intensity showed that the critical stress intensity factor is independent of load and crack size. This suggests a new method to determine fracture toughness of brittle materials using Hertzian indentation.

The Hertzian stress field and formation of cone cracks—II. Determination of fracture toughness

Abstract A method for determining the fracture toughness by Hertzian indentation has been developed. Three materials, a ceramic matrix composite, a fine grained Al2O3 and glass, were indented by a spherical WC/Co indenter at various loads. The samples were then sectioned and polished and the length of the Hertzian cone cracks were measured. The fracture toughness was found to be independent of cone crack length and indentation load. Values of fracture toughness for the ceramic composite, the fine grained Al2O3 and soda-lime glass were 6.7, 3.77 and 0.8 MPa m 1 2 respectively.

Finite element analysis of substrate effects on indentation behaviour of thin films

The substrate effects on indentation behaviour of thin films are analysed using finite element (FE) method. There is no universal critical penetration depth beyond which the substrate effects come in. The critical penetration depth is dependent on the combination of the film and the substrate and more sensitive to differences in the elastic properties than in the plastic properties of the film/substrate system. The FE simulation results of the effects of the substrate on the elastic modulus and the hardness of the film/substrate system have also been compared with the empirical models of Doerner and Bhattacharya, respectively.

Nanoindentation on diamond-like carbon and alumina coatings

A linear relationship of the square of indentation hardness and the inverse of penetration depth predicted by the mechanism-based strain gradient (MSG) theory has been used to derive the coating-only hardness of the hard coatings and the critical penetration depth, where the influence of the soft substrate comes in. The ratio of the critical penetration depth to the coating thickness is approximately 0.2 for both diamond-like-carbon (DLC) and alumina coatings and almost independent of the coating thickness. Observation of residual indents on both DLC and alumina coatings by atomic force microscopy (AFM) reveals that plastic deformation occurs in the hard coatings when the penetration depth is smaller than the critical depth. With further penetration, partial lateral cracks first initiate in the middle of the quadrants between the radial plastically deformed grooves induced by the indenter edges, then propagate to the corner of the indent and connect with one another to form an annular crack. With the increase of the penetration depth more annular cracks are created and form a growth ring of cracks. A significant delamination may occur at the centre of the indent for a deep enough penetration.

Method to determine the plastic properties of bulk materials by nanoindentation

Abstract The indentation of elastic-plastic strain-hardened material with a conical indenter was investigated using the finite-element method. The influence of the ratio of the elastic recovered depth h e to the maximum penetration depth h max on the deformation behaviour of the material and its relationship with the material parameters [sgrave] y/E and n were analysed. The finite-element results were compared with the results of Berkovich indentations on single-crystal aluminium, single-crystal tungsten, nickel, lead, fused silica and BK7 glass. It is found that h e/h max can be directly related to the elastic-plastic properties [sgrave] y/E and n of a material, which determine the deformation behaviour of materials. The pile-up and sinking-in behaviour of the material during indentation is controlled by both strain hardening and h e/h max. No pile-up occurs for materials with n > 0.3; for materials with n < 0.3, the critical value of h e/h ma? for pile-up and sinking-in is 0.12. The hardness of a material measured by indentation is a function of the stress at about 10% plastic strain for both soft and hard materials. Direct comparison of finite-element results with experimental indentations shows good agreement. Based on the analysis, a method that can be used to estimate the plastic properties of bulk materials is proposed.

Vickers indentations in glass—II. Comparison of finite element analysis and experiments

Abstract This paper presents a comparison of a three-dimensional finite element numerical analysis of Vickers indentation with an experimentally observed indentation load—depth ( P—h ) relation on soda-lime glass. Several mechanical properties, such as yielding stress, strain hardening and elastic modulus, are then estimated from the analysis of the experimental P—h curve. This paper also compares the experimentally-measured residual stress field around a Vickers indentation at the surface of glass with an FEM numerical calculation. The FEM calculation uses Mises elastoplasticity to describe the residual stress state at the unloading. The comparison shows a very good agreement between the numerical calculation and the experimental results for the P—h relation, the Mises stress and the hydrostatic stress. The results further confirm that the residual stress field close to the indentation is a non-equal bi-axial stress field, which is not circular in shape but reflects the shape of the indentation impression. The formation of radial cracks also causes significant modification of the stress field. The FEM analysis shows that the P—h relation can provide much useful information on mechanical properties using the analysis developed here.

Vickers indentations in glass. I: Residual stress fields and iso-stress contour maps

Abstract This paper describes an experimental approach to measure the residual stress field around Vickers indentations in soda-lime glass. The method uses a small indentation as a microprobe to measure the residual stress at a specific position near a large indentation. Extensive experiments have been performed and the residual stresses field around a 45 N Vickers indentation were mapped. The relation between the residual stress and the distance from the indentation was determined along several specific directions from the indentation based on numerical regression. The residual stress field around the Vickers indentation is a non-equal bi-axial stress field. Both residual tensile stress and compressive stress show a power law relation with distance from the indentation. These relations are angle dependent. The iso-stress contours of both residual tensile and compressive stresses are then determined from the experiments. A self-calibration experiment, i.e. indentation on pre-stressed glass bending bars, was specially designed to confirm the accuracy of the experiments and the analysis. The present experiments and the analysis are accurate as long as the residual stress is larger than 10 MPa.

Analysis of penetration curves produced by sharp indentations on ceramic materials

Abstract Indentation load–penetration curves from sharp indentations (Vickers indentation and nanoindentation) on several ceramic materials were analysed using newly developed three-dimensional finite-element (FEN numerical models, based on elastic and elastoplastic calculations. The results have led to a general methodology to analyse the penetration curves obtained from both Vickers indentations and nanoindentations on bulk materials. It is found that it is necessary to proceed with separate analyses for the loading and unloading curves, although the analyses are related. Through a detailed analysis of the load–depth curves, information related to various compressive mechanical properties is obtained from different portions of the load–penetration curves. From the loading curve, the hardness, yielding stress, strain hardening, surface displacement and plastic zone size are obtained, whereas the elastic modulus is obtained from the unloading curve. Experimentally reported indentation load–penetration cur...