Stress-strain relations for age hardened AlMgSi alloys, measured with necking corrections and modelled based on TEM characterization
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Age hardening Al-Mg-Si(-Cu) alloys, like other aluminium alloys, are increasingly utilized due to the combination of cost-saving, easy fabrication, and good mechanical properties. Yield strength and work hardening are important criteria for design and thermomechanical processing optimization of novel Al-Mg-Si(-Cu) alloys. The main motivation of this work is to gain deep understandings on the yield strength and work hardening criteria of Al-Mg-Si(-Cu) alloys, by precisely measured equivalent stress-strain relations until fracture using a robust optical measurement technique, quantitative microstructure investigations using transmission electron microscopy, and a modelling framework strongly linking the precipitates evolutions with mechanical properties. A robust image processing algorithm and corresponding python software were developed for precise measurement of stress-strain curves until fracture. The images and synchronised force data were acquired during uniaxial tensile tests from an optical measurement setup. The radius of the minimal cross-sectional area a and the radius of curvature of the necking contour R were measured during tensile test, used as input for analytical necking corrections, as well as finite element inverse modelling for verification. The combination of the optimized light environment and the image processing algorithm deals with the surface roughness of the specimen, while not compromise the accuracy of the measurements. To demonstrate and validate this new technique, image recording by a digital camera and synchronized force measurements were made for an isotropic, commercially pure aluminium alloy and for an axisymmetric, peak aged AA6082 alloy. Inverse modelling by finite element simulations were used to assess the accuracy of analytical corrections of the stress-strain curves. Uniaxial tensile tests with the optical measurement setup on axisymmetric tensile specimens of an AA6082 alloy artificially aged at different times, were performed at room temperature, 100°C and 150°C. During these tests, specimen contour images and corresponding force data were experimentally obtained. These data were then processed by the software. A new empirical model was furtherly proposed based on the experimental necking geometry ratio a/R as a function of the strain after onset of necking ε-εu, generalizing the one parameter Le Roy model to a two-parameter nonlinear model. The new empirical model describes the strain and necking geometry ratio a/R relations, shows first a nonlinear transition, followed by a linear asymptotic relationship. The nonlinear region increases with increasing temperature and ageing times. The proposed model, combined with Gromada’s necking correction method, was verified by finite element modelling analysis and applied for more accurate determination of the equivalent stress-strain curve until fracture. The measured equivalent stress-strain curves were furtherly used for study on precipitate and mechanical properties. Precipitate evolutions at a range of ageing conditions in three Al-Mg-Si(-Cu) alloys were investigated by transmission electron microscopy (TEM), scanning precession electron diffraction (SPED) and electron energy loss spectroscopy (EELS). Higher material yield strength correlated well with a refined precipitate microstructure comprising higher number densities of smaller precipitates. Three different strengthening models (Holmedal , Esmaeili , NaMo ) were used for predicting the strength of the alloys and furtherly the ductility was discussed. An improved modelling framework on strength and work hardening is proposed. The detailed TEM data were then applied to calculate the stress contribution from precipitates using the strength model by Holmedal . A modified Kernel Density Estimation (KDE) method with gaussian kernel was used instead of the commonly used log-normal distribution integrated in the model, this results in a mathematical representation of the precipitate size distributions that is closer to the experimental statistics. The work hardening behaviour of tensile tests at various ageing conditions was analysed, and it was concluded that the presence of the precipitates strongly enhance dynamic recovery at strains larger that 15-20%, where the peak aged condition shows no work hardening at all. At strains up to this limit, the model by Cheng et al.  was tested but applying more precise estimates for solute contribution to the dislocation-based stress and a refined account of GNDs based on the detailed precipitate size distribution. The GND mechanism, firstly proposed by Ashby  turned out to predict a too strong work hardening. Instead, a new model is suggested for slip length restrictions due to precipitates, based on counting precipitates obstacles as dislocation pinning points somehow similar as the dislocations restrict the slip length. This new model modification resulted in a model predicting the work hardening behaviour of the alloys up to 10-15% strain in good agreement with the experimental results. The large experimental data as well as the given models will be of importance in future alloy and process development and serve as a useful reference in the development of large model framework for the Al-Mg-Si(-Cu) system.