Deformation and failure of a film/substrate system subjected to spherical indentation: Part 1. Experimental validation of stresses and strains derived using Hankel transform technique in an elastic film/substrate system

Our concern here is to rationalize experimental observations of failure modes brought about by indentation of hard thin ceramic films deposited on metallic substrates. By undertaking this exercise, we would like to evolve an analytical framework that can be used for designs of coatings. In Part I of the paper we develop an algorithm and test it for a model system. Using this analytical framework we address the issue of failure of columnar TiN films in Part II [J. Mater. Res. 21, 783 (2006)] of the paper. In this part, we used a previously derived Hankel transform procedure to derive stress and strain in a birefringent polymer film glued to a strong substrate and subjected to spherical indentation. We measure surface radial strains using strain gauges and bulk film stresses using photo elastic technique (stress freezing). For a boundary condition based on Hertzian traction with no film interface constraint and assuming the substrate constraint to be a function of the imposed strain, the theory describes the stress distributions well. The variation in peak stresses also demonstrates the usefulness of depositing even a soft film to protect an underlying substrate.

An Energy-Based Method for Analyzing Instrumented Spherical Indentation Experiments

Using dimensional analysis and finite element calculation, we studied spherical indentation in elastic-plastic solids with work hardening. We report two previously unknown relationships between hardness, reduced modulus, indentation depth, indenter radius, and work of indentation. These relationships, together with the relationship between initial unloading stiffness and reduced modulus, provide an energy-based method for determining contact area, reduced modulus, and hardness of materials from instrumented spherical indentation measurements. This method also provides a means for calibrating the effective radius of imperfectly shaped spherical indenters. Finally, the method is applied to the analysis of instrumented spherical indentation experiments on copper, aluminum, tungsten, and fused silica.

A New Modified Expanding Cavity Model for Characterizing the Spherical Indentation Behaviour of Bulk Metallic Glass with Pile-up

Spherical nanoindentation tests were performed on Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass and pile-ups were observed around the indenter. A new modified expanding cavity model was developed to characterize the indentation deformation behavior of strain-hardening and pressure-dependent materials. By using this model, the representative stress-strain response of this bulk metallic glass to hardness and indentation in the elastic-plastic regime were obtained taking into consideration the effect of pile-up.

Numerical Study Of Pile-Up In Bulk Metallic Glass During Spherical Indentation

Pile-up around indenter is usually observed during instrumented indentation tests on bulk metallic glass. Neglecting the pile-up effect may lead to errors in evaluating hardness, Young's modulus, stress-strain response, etc. Finite element analysis was employed to implement numerical simulation of spherical indentation tests on bulk metallic glass. A new model was proposed to describe the pile-up effect. By using this new model, the contact radius and hardness of Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass were obtained under several different indenter loads with pile-up, and the results agree well with the data generated by numerical simulation.

Numerical verification for instrumented spherical indentation techniques in determining the plastic properties of materials

 Instrumented indentation tests have been widely adopted for elastic modulus determination. Recently, a number of indentation-based methods for plastic properties characterization have been proposed, and rigorous verification is absolutely necessary for their wide application. In view of the advantages of spherical indentation compared with conical indentation in determining plastic proper-ties, this study mainly concerns verification of spherical indentation methods. Five convenient and simple models were selected for this purpose, and numerical experiments for a wide range of materials are carried out to identify their accuracy and sensitivity characteristics. The verification results show that four of these five methods can give relatively accurate and stable results within a certain material domain, which is defined as their validity range and has been summarized for each method.

Relationships between Initial Unloading Slope, Contact Depth, and Mechanical Properties for Spherical Indentation in Linear Viscoelastic Solids

Using analytical and finite element modeling, we examine the relationships between initial unloading slope, contact depth, and mechanical properties for spherical indentation in viscoelastic solids with either displacement or load as the independent variable. We then investigate whether the Oliver-Pharr method for determining the contact depth and contact radius, originally proposed for indentation in elastic and elastic-plastic solids, is applicable to spherical indentation in viscoelastic solids. Finally, the analytical and numerical results are used to answer questions raised in recent literature about measuring viscoelastic properties from instrumented spherical indentation experiments.

Determination of plastic properties by instrumented spherical indentation: Expanding cavity model and similarity solution approach

The present paper aims to develop a robust spherical indentation-based method to extract material plastic properties. For this purpose, a new consideration of-piling-up effect is incorporated into the expanding cavity model; an extensive numerical study on the similarity Solution has also been performed. As a consequence, two semi-theoretical relations between the indentation response and material plastic properties are derived, with which plastic properties of materials can be identified from a single instrumented spherical indentation curve, the advantage being that this approach no longer needs estimations of contact radius with given elastic modulus. Moreover, the inconvenience in using multiple indenters with different tip angles can be avoided. Comprehensive sensitivity analyses show that the present algorithm is reliable. Also, by experimental verification performed oil three typical materials, good agreement of the material properties between those obtained from the reverse algorithm and experimental data is obtained.

Determination Of Plastic Properties By Instrumented Spherical Indentation: Expanding Cavity Model And Similarity Solution Approach

The present paper aims to develop a robust spherical indentation-based method to extract material plastic properties. For this purpose, a new consideration of-piling-up effect is incorporated into the expanding cavity model; an extensive numerical study on the similarity Solution has also been performed. As a consequence, two semi-theoretical relations between the indentation response and material plastic properties are derived, with which plastic properties of materials can be identified from a single instrumented spherical indentation curve, the advantage being that this approach no longer needs estimations of contact radius with given elastic modulus. Moreover, the inconvenience in using multiple indenters with different tip angles can be avoided. Comprehensive sensitivity analyses show that the present algorithm is reliable. Also, by experimental verification performed oil three typical materials, good agreement of the material properties between those obtained from the reverse algorithm and experimental data is obtained.