The indentation load-displacement behavior of six materials tested with a Berkovich indenter has been carefully documented to establish an improved method for determining hardness and elastic modulus from indentation load-displacement data. The materials included fused silica, soda–lime glass, and single crystals of aluminum, tungsten, quartz, and sapphire. It is shown that the load–displacement curves during unloading in these materials are not linear, even in the initial stages, thereby suggesting that the flat punch approximation used so often in the analysis of unloading data is not entirely adequate. An analysis technique is presented that accounts for the curvature in the unloading data and provides a physically justifiable procedure for determining the depth which should be used in conjunction with the indenter shape function to establish the contact area at peak load. The hardnesses and elastic moduli of the six materials are computed using the analysis procedure and compared with values determined by independent means to assess the accuracy of the method. The results show that with good technique, moduli can be measured to within 5%.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A53D45298E14F73B86495BBC056E16DC/S0884291400017039a.pdf/div-class-title-an-improved-technique-for-determining-hardness-and-elastic-modulus-using-load-and-displacement-sensing-indentation-experiments-div.pdf

An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments

The application of indentation techniques to the evaluation of fracture toughness is examined critically, in two parts. In this first part, attention is focused on an approach which involves direct measurement of Vickers-produced radial cracks as a function of indentation load. A theoretical basis for the method is first established, in terms of elastic/plastic indentation fracture mechanics. It is thereby asserted that the key to the radial crack response lies in the residual component of the contact field. This residual term has important implications concerning the crack evolution, including the possibility of post indentation slow growth under environment-sensitive conditions. Fractographic observations of cracks in selected “reference” materials are used to determine the magnitude of this effect and to investigate other potential complications associated with departures from ideal indentation fracture behavior. The data from these observations provide a convenient calibration of the Indentation toughness equations for general application to other well-behaved ceramics. The technique is uniquely simple in procedure and economic in its use of material.

A Critical Evaluation of Indentation Techniques for Measuring Fracture Toughness: I, Direct Crack Measurements

A Critical evaluation of indentation techniques for measuring fracture toughness

A theory for describing the evolution of the median/radial crack system in the far field of sharp-indenter contacts is developed. Analysis is based on a model in which the complex elastic/plastic field beneath the indenter is resolved into elastic and residual components. The elastic component, being reversible, assumes a secondary role in the fracture process: although it does enhance downward (median) extension during the loading half-cycle, it suppresses surface (radial) extension to the extent that significant growth continues during unloading. The residual component accordingly provides the primary driving force for the crack configuration in the final stages of evolution, where the crack tends to near-half-penny geometry. On the hypothesis that the origin of the irreversible field lies in the accommodation of an expanding plastic hardness impression by the surrounding elastic matrix, the ensuing fracture mechanics relations for equilibrium crack growth are found to involve the ratio hardness-to-modulus as well as toughness. Observations of crack evolution in soda-lime glass provide a suitable calibration of indentation coefficients in these relations. The calibrated equations are then demonstrated to be capable of predicting the widely variable median and radial growth characteristics observed in other ceramic materials. The theory is shown to have a vital bearing on important practical areas of ceramics evaluation, including toughness and strength.

Elastic/Plastic Indentation Damage in Ceramics: The Median/Radial Crack System

An examination is made of the sharp-indentation technique of strength-test precracking for toughness evaluation. The experimental approach follows that proposed by other workers but the theoretical analysis contains one vital new feature; the residual-stress term discussed in Part I of this study is now introduced explicitly into the strength formulation. This modification overcomes a major systematic discrepancy evident in the previous models and at the same time, by virtue of attendant changes in the nature of the crack stability prior to attaining a failure configuration, eliminates the need for frac-tographic measurements. Other advantages are also apparent, notably an insensitivity to postindentation radial crack extension. The main disadvantage is that only one result is obtained per specimen. Indentation/strength data from ceramics listed in Part I confirm the essential features of the theory and provide a suitable calibration factor. The method has special application to those materials which do not necessarily produce a well-defined radial crack pattern, in which case an “effective”Kc appropriate to fracture properties at the flaw level is obtained.

A Critical Evaluation of Indentation Techniques for Measuring Fracture Toughness: II, Strength Method

Residual stress effects in sharp contact cracking: Part 2 Strength degradation

The micromechanics of indentation-induced flaws in monocrystalline silicon have been studied in relation to strength determination. In the first part, the evolution of the deformation-fracture pattern during contact with a Vickers pyramid is described. Emphasis is thereby placed on the vital role of the residual component of the elastic-plastic contact field in driving the cracks. In the second part, the response of the cracks in subsequent strength testing is followed. A precursor stage of stable growth is observed prior to attaining a failure configuration, consistent with augmentation of the applied tensile (flexural) loading by the residual contact component. No detectable slow crack growth due to environmental influence is found. Nevertheless, silicon is revealed as a material of extreme susceptibility to brittle fracture, with significant strength degradation from contacts on the microscale. The relevance of this brittleness to the mechanical behaviour of silicon components as a function of fabrication and prospective service conditions is discussed.

P. Chantikul

Papers

A Critical Evaluation of Indentation Techniques for Measuring Fracture Toughness: I, Direct Crack Measurements

A Critical evaluation of indentation techniques for measuring fracture toughness

A Critical Evaluation of Indentation Techniques for Measuring Fracture Toughness: II, Strength Method

Residual stress effects in sharp contact cracking: Part 2 Strength degradation

Mechanics of strength-degrading contact flaws in silicon