The present study is concerned with the development of an inverse analysis of the depth-sensing indentation test based on a multi-objective function (MOF) optimisation model. The input data of this model are the load-displacement (P-h) curve extracted from the indentation instrument and the surface topography of the residual imprint left by the indenter after the removal of the load measured via atomic force microscopy (AFM). A Swift’s power law material model was considered to represent the indented material and thus, the output of the optimisation are the Young’s modulus (E), yield stress (σy) and strain-hardening exponent (n). The optimisation problem was designed to minimise the error between both the experimental and predicted P-h curves, i.e. the first objective, and pile-up profiles, i.e. the second objective, with the aim of addressing the non-uniqueness of the inverse analysis of indentation. A 3D FE model of the depth-sensing indentation test has been developed in ABAQUS in order to generate the predicted data from a set of trial material properties, i.e. E, σy and n. The generation of FE input files (pre-processor) and extraction of FE output files (post-processor) have been automated through MATLAB and Python subroutines. The optimisation problem was solved by the trust-region reflective algorithm available in the MATLAB Optimization ToolboxTM and thus, concisely, the model minimised the experimental and predicted data by modifying iteratively the material properties, starting from the initial guess properties specified by the user, until convergence was reached. Upon convergence, the material properties were said to describe the elastic-plastic behaviour of the indented material. A comprehensive experimental programme was carried out in order to investigate the load dependency of the indentation response of three different materials, including a steel (CrMoV), a titanium alloy (Ti-6Al-4V) and a high-purity copper (C110). The study of the topography of the residual imprints provided a better understanding of the effects of the microstructural arrangement on the plastic displacement of material beneath the indenter. The extent of piling-up was observed to be very sensitive to the difference in material properties from grain to grain and the crystallographic plane of the indented grain. Furthermore, it was concluded that the structural arrangement of the indented material may also contribute to the asymmetry observed in the pile-up profiles, in particular in materials with large grains relative to the projected area of the indenter, e.g. C110. This piece of work therefore, is suggested as a guideline for the use of height measurements of the residual imprint in the characterisation of the plastic behaviour of materials. The multi-objective function optimisation model is proved to be a step forward to the characterisation of the near-surface properties as, in contrast to the P-h curve, the residual imprint is strongly linked to the plastic behaviour of the indented material. Therefore, the physics governing the indentation problem were better represented. Therefore, the optimised P-h curve provided a very good fit to the corresponding experimental curve, to within an error of less than 2.4% and 8.4% the maximum (hmax) and residual (hr) depth, respectively, for all three materials, CrMoV steel, C110 copper and Ti-6Al-4V. Furthermore, a deviation of less than 12.4% was achieved between the area of indentation provided by the FE model and AFM instrument. Additionally, the value of maximum peak height (hpeak) was predicted with a maximum error of 11% in relation with the experimental pile-up profiles. Therefore, it was concluded that the optimised solution provided a very good representation of the complex mechanical response to indentation such that the volume of plastically displaced material as predicted by the optimised FE model was observed notably in accordance with experimental measurements. Furthermore, the complementary information provided by the second objective function allowed the model to distinguish between different materials showing identical indentation response – referred to in the literature as ‘mystical’ materials. In addition, a key outcome of this investigation suggested that stress-strain curves generated by mechanical tests performed at different scales, exhibit similar behaviour with only the magnitude of the stress increasing or decreasing depending upon the scale. Part of this thesis is dedicated to the application of the proposed inverse analysis for the characterisation of three phases located across the joint of a like-to-like inertia friction weld of SCMV steel, including martensite in the tempered, quenched and over-tempered condition. This study, characterised the generation of residual stresses into two stages: the thermal strain dominated initial cooling period that accounts for the majority of the residual stresses, and the phase transformation strain dominated final cooling period. In addition, it was concluded that at the onset of transformation from austenite to martensite, the volumetric changes experienced in the lattice relax up to 70% of the predicted tensile hoop stress found in the vicinity of the weld line near the inner surface and that the interaction of soft regions of austenite and hard regions of heat unaffected martensite accounts for up to 17% of the peak tensile stress. The indentation response of the set of optimised properties that represent each of the phases, was in very good agreement with the corresponding P-h curve and residual pile-up profile extracted from the indentation instrument and AFM, respectively. The capability of the inverse analysis to build the stress-strain relationship in the elastic-plastic regime using the optimised mechanical properties of the parent metal has been validated using experimental data extracted from the compressive test of an axisymmetric sample of tempered martensite [1]. The inclusion of the softer over-tempered martensite phase allowed the FE prediction to determine the proportion of the heat affected zone (HAZ) comprised by each phase in better agreement with the experimental weld-trial. Based on the interpretation of the microhardness test performed across the weld, the harder region formed due to the quenching process extends approximately 54% the length of the HAZ, whereas the rest 46% is comprised by the softer over-tempered martensitic phase. According to the FE prediction, the heat affected zone was composed by a proportion of 57% quenched martensite and 43% over-tempered martensite. Moreover, the distance from the weld line to the region where martensite fully tempered was observed to extend 79 and 71% the length of the HAZ, as determined by the FE model and experimental measurements, respectively. The presence of a softer region, OTM, between two harder regions, namely QM and TM, relaxed 7 to 11%, 1 to 6% and 12.8 to 15.3% the peak values of stress in the radial, axial and hoop directions respectively. A key observation from the results of the FE prediction was that the peak hoop residual stress is located at the boundary of the quenched and over-tempered martensite, and not at the edge of the heat affected zone. This observation was in agreement with the residual stress measurements published by Moat et al. [2].
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:728528 |
| Date | January 2017 |
| Creators | Iracheta-Cabrera, Omar Adrian |
| Publisher | University of Nottingham |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://eprints.nottingham.ac.uk/44781/ |
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