Abstract
Material properties such as hardness can be dependent on the size of the indentation load when that load is small, a phenomenon known as the indentation size effect (ISE). In this work an inverse finite element method (IFEM) is used to investigate the ISE, with reference to experiments with a Berkovich indenter and an aluminium test material. It was found that the yield stress is highly dependent on indentation depth and in order to simulate this, an elastoplastic constitutive relation in which yielding varies with indentation depth/load was developed. It is shown that whereas Young's modulus and Poisson's ratio are not influenced by the length scale over the range tested, the amplitude portion of yield stress, which is independent of hardening and corresponds to the initial stress for a bulk material, changes radically at small indentation depths. Using the proposed material model and material parameters extracted using IFEM, the indentation depth-time and load-depth plots can be predicted at different loads with excellent agreement to experiment; the relative residual achieved between FE modelling displacement and experiment being less than 0.32%. An improved method of determining hardness from nanoindentation test data is also presented, which shows goof agreement with that determined using the IFEM.
Highlights
It is generally recognised that material properties, especially plasticity, relate to length scale, with materials exhibiting increased resistance to deformation at smaller length scales (Al-Rub and Voyiadjis, 2004); this has been shown by microbending and microtorsion experiments, leading to the development of a model involving strain gradient plasticity (Fleck et al, 1994), and the discovery that hardness decreases with indentation depth, until at large indentation depths a depth-independent bulk material hardness is found
A key step is selecting a material constitutive model that is able to capture the main mechanical responses of the material against an actuation of indentation; only a correct material constitutive relation can lead to a good fit between the FE simulated result and the tested, or in other words, if a sufficiently good fit can be achieved by an assumed material constitutive relation by inverse FE method (IFEM), the material constitutive relation selected is close to being correct
A method for determining material properties from indentation tests, whilst accounting for the indentation size effect has been proposed that utilizes IFEM and a novel indentation elastoplastic constitutive relation
Summary
It is generally recognised that material properties, especially plasticity, relate to length scale, with materials exhibiting increased resistance to deformation at smaller length scales (Al-Rub and Voyiadjis, 2004); this has been shown by microbending and microtorsion experiments, leading to the development of a model involving strain gradient plasticity (Fleck et al, 1994), and the discovery that hardness decreases with indentation depth, until at large indentation depths a depth-independent bulk material hardness is found. Yield stress was considered to be strain rate dependent and a function of hardening modulus This method can be used to predict hardness, only the FE simulated depth-load curve was shown and no comparison with experiments was made in the paper. Various material constitutive relations have been used in the FE simulation of ISE, only the simulated hardnesses were compared with test data in some cases (Faghihi and Voyiadjis, 2011), or only the modelled depth-load curves in others (Harsono et al, 2011; Celentano et al, 2012; Swaddiwudhipong, 2012) When both have been shown, good agreement with experimental data was not seen (Gomez and Basaran, 2006). 98.8537 0.2772 0.4992 0.3700 nanoindentation test data for the more accurate characterisation of material hardness
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