In this study, a new application of the inverse analysis of the depth-sensing indentation technique based on the optimization theory has been satisfactorily demonstrated. The novel approach for determining the mechanical properties from experimental nanoindentation curves has been applied in order to generate the elastic-plastic stress-strain curves of three phases located across the joint of a like-to-like inertia friction weld of a CrMoV steel, i.e. the parent phase of tempered martensite and two child phases formed during the IFW process, martensite in the quenched and over-tempered condition. The inverse analysis carried out in this study consists of an optimization algorithm implemented in MATLAB, which compares an experimental nanoindentation curve with a predicted indentation curve generated by a 3D 2 finite element model developed using the ABAQUS software; the optimization algorithm modifies the predicted curve by changing the material properties until the best fit to the experimental nanoindentation curve is found. The optimized parameters (mechanical properties) have been used to generate the stress-strain relationships in the elastic-plastic regime that can be used to simulate numerically the effects of the variation in material properties arising from phase transformations occurring across the joint during the IFW process of a CrMoV steel.The proposed inverse analysis was capable of fitting experimental load-depth (P-h) curves produced with a Nanoindentation Nanotest NTX unit from three characteristic regions located across the joint where the above mentioned phases are known to exist. The capability of the inverse analysis to build the stress-strain relationship in the elastic-plastic regime using the optimized 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]. According to previous experimental studies, the presence of martensite in the quenched and over-tempered condition formed during the IFW of shaft sections of CrMoV steel are responsible of the 1.52:1 harder and 0.75:1 softer regions, compared to the region where the tempered martensite is located [2][3][4]. These ratios are in very good agreement with the optimized magnitudes of yield stress provided by the inverse analysis, that is, 1.54:1 for the quenched martensite and 0.68:1 for the over-tempered martensite, compared to the optimized value of yield stress of the tempered martensite.Moreover, a relative difference of less than 1.5% between the experimental and predicted maximum depth (h max ) supports the capability of the method for extracting the elastic-plastic mechanical properties defining each of the indented regions.3
Recent years have seen an increased interest in the mechanical characterisation of materials via the inverse analysis of depth-sensing indentation data; however, at low-loads both the reaction forces measured by the instrument and the contact evolution at the indenter-material interface may be severely affected by indentation size effects (ISEs). Notwithstanding the knowledge of ISE, the inverse analyses proposed to date have failed to investigate the divergence between the smallscale properties measured via indentation and the large-scale properties extracted from other techniques, e.g. tensile testing. Therefore, this study investigates the sensitivity of an inverse analysis methodology to the indentation size in relation to the size of the microstructure. The proposed inverse analysis approach is based on a multi-objective function (MOF) optimisation model that finds the combination of material properties (Young's modulus, yield stress and strain-hardening exponent) that provides the best fit to both the experimental load-displacement (P-h) curve extracted from the indentation instrument and pile-up profile of the residual imprint measured with an atomic force microscope. Therefore, the piling-up/sinking-in effect, which is strongly linked to the plastic hardening behaviour of the indented material, is considered to address the non-uniqueness issue of the inverse analysis of indentation. A Berkovich indenter was used to measure the near surface properties of three different materials, including a titanium alloy (Ti-6Al-4V), chromium-molybdenum-vanadium steel (CrMoV) and high purity copper (C110); materials have been selected to represent a wide range of ductile metallic materials so as to assess the generality of the MOF model.
This study presents a finite element (FE) model capable of predicting the final residual stress field in an inertia friction welded component of a CrMoV steel considering the elastic and inelastic components of strain resulting from mechanical deformation, temperature changes in the material and volumetric changes associated with phase transformations. The material database was improved to include the properties of the child phases involved in the polymorphic transformation during inertia friction welding (IFW) of CrMoV steels, i.e. austenite and quenched martensite, taking different approaches based on existent experimental data from the parent phase (tempered martensite) and material characterization of the heat affected zone (HAZ) in weld trials. This is the only FE model available in the literature that takes into consideration the effects induced by the transformation strain component of multiple phases in the total strain generated during IFW. Several simulations were run using this FE model in order to address for the first time the sensitivity of the final residual stress field to the individual effects of the microstructural changes, the interrelationship of multiple phases, and to different processing parameters such as the die geometry, clamping history and cooling rates.
Three different polycrystalline materials, a fine-grained martensitic steel (CrMoV), a coarsegrained high-purity copper (C110), and a two-phase microstructure titanium alloy (Ti-6Al-4V), have been selected to investigate the heterogeneity of deformation following indentation using a depth-sensing indentation instrument fitted with a Berkovich indenter. The geometry of the pile-up profiles, measured with an atomic force microscope, were observed to be very sensitive to the indentation size with respect to the size of the microstructure and the material properties and crystallographic plane of the indented grain. In contrast, neither the recovery of the area of indentation nor the degree of piling-up were affected by the presence of indentation size effects (ISE). Furthermore, based on the results of a full-3D finite element simulation, it was concluded that the misalignment of the indenter alone does not explain the significantly asymmetric piling-up in highly anisotropic materials, e.g. C110 copper, but that this is due to the crystallographic orientation of the single grain tested. In addition, the experimental results revealed that, although a thicker mechanically hardened layer formed during polishing is more prone to recovery during unloading, leading to a smaller residual indented area, the degree of piling-up is unaffected provided that the ratio of maximum depth (h max ) to the thickness of the strain-hardened layer is above unity. Moreover, on the same premise, the surface roughness and the thickness of the strain-hardened layer can be discarded as length parameters affecting hardness measurements.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.