K.K. Tho

Uniqueness of reverse analysis from conical indentation tests

The curvature of the loading curve, the initial slope of the unloading curve, and the ratio of the residual depth to maximum indentation depth are three main quantitiesthat can be established from an indentation load-displacement curve. A relationship among these three quantities was analytically derived. This relationship is valid for elasto-plastic material with power law strain hardening and indented by conical indenters of any geometry. The validity of this relationship is numerically verified through large strain, large deformation finite element analyses. The existence of an intrinsic relationship among the three quantities implies that only two independent quantities can be obtained from the load-displacement curve of a single conical indenter. The reverse analysis of a single load-displacement curve will yield non-unique combinations of elasto-plastic material properties due to the availability of only two independent quantities to solve for the three unknown material properties.

Equivalency of Berkovich and conical load-indentation curves

The Berkovich indenter, which is one of the most commonly used indenter tips in instrumented indentation experiments, requires a tedious 3D finite element simulation. The indenter is widely idealized as a conical indenter of 70.3° half-angle to enable a substantially less demanding 2D axisymmetric modelling. Although the approach has been commonly adopted, limited studies have been performed to investigate possible deviations due to this simplification. The present study attempts to address the equivalency of the two indenters by performing extensively both 3D and 2D finite element analyses to simulate the load-displacement response of a wide range of elasto-plastic materials obeying power law strain-hardening during indentation for both Berkovich and conical indenters, respectively. It is demonstrated that the equivalency between these two indenters in terms of curvature of the loading curve is not valid across the range of material properties under study. However, it is established that if only the ratio of the remaining work done (WR) and the total work done (WT) of the load-indentation curve is of interest, this simplification can be adopted with satisfactory results.

Artificial neural network model for material characterization by indentation

Analytical methods to interpret the indentation load–displacement curves are difficult to formulate and solve due to material and geometric nonlinearities as well as complex contact interactions. In this study, large strain–large deformation finite element analyses were carried out to simulate indentation experiments. An artificial neural network model was constructed for the interpretation of indentation load–displacement curves. The data from finite element analyses were used to train and validate the artificial neural network model. The artificial neural network model was able to accurately determine the material properties when presented with the load–displacement curves that were not used in the training process. The proposed artificial neural network model is robust and directly relates the characteristics of the indentation load–displacement curve to the elasto-plastic material properties.

Material characterization via least squares support vector machines

Analytical methods to interpret the load indentation curves are difficult to formulate and execute directly due to material and geometric nonlinearities as well as complex contact interactions. In the present study, a new approach based on the least squares support vector machines (LS-SVMs) is adopted in the characterization of materials obeying power law strain-hardening. The input data for training and verification of the LS-SVM model are obtained from 1000 large strain?large deformation finite element analyses which were carried out earlier to simulate indentation tests. The proposed LS-SVM model relates the characteristics of the indentation load-displacement curve directly to the elasto-plastic material properties without resorting to any iterative schemes. The tuned LS-SVM model is able to accurately predict the material properties when presented with new sets of load-indentation curves which were not used in the training and verification of the model.

Finite element modelling for materials with size effect

This paper involves the formulation of the C0 finite elements incorporating the conventional mechanism-based strain gradient plasticity theory. Higher-order variables and consequently higher-order continuity conditions are not required allowing the direct applications of conventional plasticity algorithms in the existing finite element package. Implementation of the model whether analytically or computationally is efficient and straightforward as the strain gradient effect is confined in the material constitutive relation. The accuracy of the proposed elements in simulating the response of materials with strong size effect is verified through several numerical examples. The approach is applicable and valid to any materials with non-uniform plastic deformation larger than about 100 nm onwards. The proposed model becomes imperative when the deformation is less than 10 µm as classical plasticity is unable to describe the phenomenon comprehensively at this low level of deformation.

Material Characterization Based on Instrumented Indentation

Nanotechnology has emerged as a key area of technology innovation with numerous potential applications. The capability of predicting mechanical properties of materials at this scale offers critical information for device designer to materials and processing techniques. The indentation of elastic-plastic strain hardening materials which can be described by power law was investigated using the finite element method. Large deformation finite element analyses were carried out on various combinations of elasto-plastic properties covering a wide range of materials. A conical indenter with a half angle of 70.3° and a Poisson’s ratio of 0.33 were adopted throughout the study. A method has been conceived to establish the elasto-plastic properties of materials based on the load-displacement curve of instrumented indentation experiment. The method can also be applied to predict the indentation response for a given set of elasto-plastic material properties. Comprehensive studies carried out demonstrate the non-uniqueness of reverse analysis algorithms. Introduction While the measurable quantity in an indentation test is usually the hardness of the materials, the method has the potential for extracting other mechanical properties of materials. Oliver and Pharr method [1] has been widely used to extract Young’s modulus of materials from the indentation load-displacement curves. Several methods were proposed to extract the Young’s modulus, E, yield strength, Y and strain-hardening exponent, n from the load-displacement curves of instrumented indentation [2, 3, 4]. More recently, reverse analysis algorithms based on multiple indenter geometries were proposed [5, 6]. In the present study, extensive finite element analyses are carried out to investigate the response of elasto-plastic materials obeying power law strain-hardening during instrumented indentation. Forward and reverse analysis algorithms are proposed and the uniqueness of the results from the reverse analysis addressed. Finite Element Simulation Large strain-large deformation two-dimensional axisymmetric finite element analyses were carried out using ABAQUS, a commercial finite element package. The model consists of 28900 four-node, bilinear axisymmetric quadrilateral elements. Since effect of friction is negligible for indenters with half angle larger than 60° [5], frictionless contact is assumed in the analysis. A conical indenter with a half-angle of 70.3° is modeled as a rigid body. The elasticity effect of the indenter is Journal of Metastable and Nanocrystalline Materials Online: 2005-01-01 ISSN: 2297-6620, Vol. 23, pp 359-362 doi:10.4028/www.scientific.net/JMNM.23.359