Abstract
Most current analysis of nano-indentation test data assumes the sample to behave as an isotropic, homogeneous body. In practice, engineering materials such as structural steels, titanium alloys and high strength aluminium alloys are multi-phase metals with microstructural length scales that can be the same order of magnitude as the maximum achievable nano-indentation depth. This heterogeneity results in considerable scatter in the indentation load-displacement traces and complicates inverse analysis of this data. To address this problem, an improved and optimised inverse analysis procedure to estimate bulk tensile properties of heterogeneous materials using a new ‘multi-objective’ function has been developed which considers nano-indentation data obtained from several indentation sites. The technique was applied to S355 structural steel bulk samples as well as an autogenously electron beam welded sample where there is a local variation of material properties. Using the new inverse analysis approach on the S355 bulk material resulted in an error within 3% of the experimental yield strength and strain hardening exponent data, which compares to an approximate 9% error in the yield strength and an 8% error in the strain hardening exponent using a more conventional approach to the inverse analysis method. Applying the new method to indentation data from different regions of an S355 steel weld and using this data as an input into an FE model of the cross-weld, tensile data from the FE model resulted matching the experimentally measured properties to within 5%, confirming the efficacy of the new inverse analysis approach.
Highlights
The inverse analysis of nano-indentation data has attracted increasing interest in the scientific community because of its potential to predict and measure elastic-plastic properties in local areas for different material applications, from coatings to welds, which would be difficult to test otherwise using more standard testing methodologies [1,2,3,4,5,6,7,8,9].The inverse indentation problem aims to identify the unknown tensile properties of a material from only the load-depth trace obtained from experimental indentation testing
The study undertaken and described in this paper aims to develop and validate a more robust methodological approach for inverse analysis of experimental load-depth nano-indentation data measured from heterogeneous materials
A second phase of the validation process comprised applying the inverse analysis technique to investigate the tensile properties of a weld generated by butt welding two S355 plates together using electron beam technology (Fig. 2)
Summary
The inverse analysis of nano-indentation data has attracted increasing interest in the scientific community because of its potential to predict and measure elastic-plastic properties in local areas for different material applications, from coatings to welds, which would be difficult to test otherwise using more standard testing methodologies [1,2,3,4,5,6,7,8,9].The inverse indentation problem aims to identify the unknown tensile properties of a material from only the load-depth trace obtained from experimental indentation testing. There are three main inverse analysis techniques that can be employed to extract tensile properties of materials from instrumented indentation experimental data: the representative stress-strain method [10,11,12,13,14,15,16,17], iterative FEA [1,2,3,4,5,7,9], and artificial neural networks [18,19,20]. This paper is concerned only with the inverse analysis technique by iterative FE simulations For this approach, in order to approximately solve the inverse problem for a given material, finite element models of the experimental set up are analysed. The combination of elasticplastic material properties used in the FE model that result in the simulated load-depth curve matching the experimental curve are assumed to be the elastic-plastic properties of the material being investigated
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