Concept Of Representative Strain Research Articles

Investigation of Stress-Strain Constitutive Behavior of Intermetallic Alloys

AbstractThe study aims to estimate the stress-strain constitutive behavior of intermetallic compounds (IMCs) observed in a solder interconnect from experimental nanoindentation responses through a modified analysis procedure for improved solution robustness based on Cheng and Cheng's and Dao et al.'s models. On the basis of parametric finite element nanoindentation simulation and dimensional analysis together with the concept of representative strain, a set of universal dimensionless functions are established, by which a forward and reverse analysis algorithm are created to predict nanoindentation responses from given elastoplastic properties and vice versa, respectively. The proposed analysis procedure is validated through comparison with the experimental nanoindentation responses and limited literature data. The results show that the proposed analysis procedure is an effective means for plastic property characterization of micro/nanoscale IMCs. The representative strain is found to be 0.056, which differs from the Dao et al.'s and Giannakopoulos and Suresh's estimate. Besides, though generally brittle and hard in nature, the IMCs in a micro/nanoscale thickness show high plasticity, and comprise a yield strength surpassing most typical engineering metals.

A New Three-Dimensional Numerical Model of Rough Contact: Influence of Mode of Surface Deformation on Real Area of Contact and Pressure Distribution

Surface roughness causes contact to occur only at discrete spots called microcontacts. In the deterministic models real area of contact and pressure field are widely evaluated using Flamant and Boussinesq equations for two-dimensional (2D) and three-dimensional (3D), respectively. In this paper, a new 3D geometrical contact approach is developed. It models the roughness by cones and uses the concept of representative strain at each asperity. To discuss the validity of this model, a numerical solution is introduced by using the spectral method and another 3D geometrical approach which models the roughness by spheres. The real area of contact and the pressure field given by these approaches show that the conical model is almost insensitive to the degree of isotropy of the rough surfaces, which is not the case for the spherical model that is only valid for quasi-isotropic surfaces. The comparison between elastic and elastoplastic models reveals that for a surface with a low roughness, the elastic approach is sufficient to model the rough contact. However, for surfaces having a great roughness, the elastoplastic approach is more appropriate to determine the real area of contact and pressure distribution. The results of this study show also that the roughness scale modifies the real contact area and pressure distribution. The surfaces characterized by high frequencies are less resistant in contact and present the lowest real area of contact and the most important mean pressure.

A dual conical indentation technique based on FEA solutions for property evaluation

The sharp indenters such as Berkovich and conical indenters have a geometrical self-similarity so that we can obtain only one parameter from an indentation loading curve, which makes different materials have the same load–displacement relation. Most studies to evaluate elastic–plastic properties by using the geometrical self-similar indenter have therefore tried to use dual/plural indentation techniques, on the basis of the concept of representative strain/stress varying with the indenter angle. However, any suggested representative concept is not universally operative for real materials. In this work, we suggest a method of material property evaluation without using the concept of representative strain. We begin the work by studying the characteristics of load–depth curves of conical indenters via finite element (FE) method. From FE analyses of dual-conical indentation, we investigate the relationships between indentation parameters and load–depth curves. The projected contact diameter is expressed as a function of the indenter angle, tip-radius, and material properties, which allows us to simply predict the elastic modulus. Two mapping functions for two indenter angles (45° and 70.3°) are presented to find the two unknowns (yield strain and strain-hardening exponent) via dual indentation technique. The method provides elastic modulus, yield strength and strain-hardening exponent with an average error of less than 5%. The method is valid for any elastically deforming indenters. We also discuss the sensitivity of measured properties to the load–displacement curve variation, and the difference between conical and Berkovich indenters.

Determination of plastic properties of polycrystalline metallic materials by nanoindentation: experiments and finite element simulations

Nanoindentation experiments at low indentation depths are strongly influenced by micromechanical effects, such as the indentation size effect, pile-up or sink-in behaviour and crystal orientation of the investigated material. For an evaluation of load–displacement data and a reconstruction of stress–strain curves from nanoindentations, these micromechanical effects need to be considered. The influence of size effects on experiments were estimated by comparing the results of finite element simulation and experiments, using uniaxial stress–strain data of the indented material as input for the simulations. The experiments were performed on conventional and ultrafine-grained copper and brass, and the influence of the indentation size effect and pile-up formation is discussed in terms of microstructure. Applying a pile-up correction on Berkovich and cube-corner indentation data, a piecewise reconstruction of stress–strain curves from load–displacement data is possible with Tabor's concept of representative strain. A good approximation of the slope of the stress–strain curve from the indentation experiments is found for all materials down to an indentation depth of 800 nm.

Recovery of microindents in a nickel–titanium shape-memory alloy: A “self-healing” effect

The thermally induced recovery of microscopic deformation in a nickel–titanium shape-memory alloy was examined. Surface deformation was simulated by indenting the alloy in the martensite phase at room temperature using both spherical and pyramidal indenters. We show that deformation in spherical microindents can be almost completely reversed by moderate heating. Partial recovery was observed for pyramidal impressions formed by a Vickers indenter and the recovery ratio was independent of the indentation depth. The observations were rationalized using the concept of representative strain and maximum stress under the spherical and pyramidal indenters.