Key Engineering Materials Vols. 554-557

Abstract: A series of mechanical tests in different specimen orientations was performed to study the anisotropic behavior of an IF steel (DC06). State-of-the-art polycrystalline models Alamel [1], VPSC [2], as well as the classical FC Taylor model were employed to predict flow stress curves. A two-stage Voce law was used to describe the single crystal shear stress-accumulated shear strain relationship. In this approach, the textural hardening and the dislocation hardening are effectively modeled separately. Results demonstrate that both the Alamel and VPSC models could reproduce the flow stress curves adequately. Also, the quantitative agreement of texture prediction is used to validate the model predictions. It is concluded that the better performance of grain interaction models compared to the FC Taylor model is mainly due to an improved prediction of the slip inside the constituting grains, and not in particular due to an improved prediction of texture evolution.

Abstract: A physically based elasto-visco-plastic constitutive model is presented and compared to experimental results for three different mild steels. The experiments consist of tensile tests at strain rates up to 103 s-1 and reverse shear tests. The model requires significantly fewer material parameters compared to other visco-plasticity models from the literature while exhibiting very good accuracy. Accordingly, the parameter identification is simple and intuitive, requiring a relatively small set of experiments. The strain-rate sensitivity modeling is not restricted to a particular hardening law and thus provides a general framework in which advanced hardening equations can be adopted. The model was eventually used as the basis for a homogenization approach at the phase scale; preliminary investigations showed the benefit of such an approach, where microstructure-relevant data can explicitly enter the model and may be used for material design simulations.

Abstract: In this study, suitable distinct stress integration algorithms for advanced anisotropic models with mixed hardening, and their implementation in finite element codes, are discussed. The constitutive model studied in the present work accounts for advanced (non-quadratic) anisotropic yield criteria, namely, the Barlat et al. 2004 model with 18 coefficients (Yld2004-18p), combined with a mixed isotropic-nonlinear kinematic hardening law. This phenomenological model allows for an accurate description of complex plastic yielding anisotropy and Bauschinger effects, which are essential for a reliable prediction of deep drawing and springback results using numerical simulations.In the present work distinct algorithm classes are analysed: (i) a semi-explicit algorithm that accounts for the sub-incrementation technique; (ii) the cutting-plane approach (semi-implicit integration); and (iii) the fully-implicit multi-stage return mapping procedure, based on the control of the potential residual. The numerical performance of the developed algorithms is inferred by benchmarks in sheet metal forming processes. The quality of the solution is assessed and compared to reference results. In the end, an algorithmic and programming framework is provided, suitable for a direct implementation in commercial Finite Element codes, such as Abaqus (Simulia) and Marc (MSC-Software) packages.

Abstract: A continuum-based plasticity approach is considered to model the anisotropic hardening response of hexagonal closed packed (hcp) materials. A Cazacu-Plunkett-Barlat (CPB06) yield surface is modified to create anisotropic hardening in terms of the accumulated plastic strain. The anisotropy and asymmetry parameters are replaced with saturation-type functions and the new modified model is then optimized globally to fit the material response. Furthermore, the effect of the number of linear stress transformations performed on the deviatoric stress tensor is investigated on the capability of the model to capture the response from the experiments. By increasing the number of stress transformations, more flexibility is obtained. However, increasing the number of stress transformations increases the arithmetic calculations involved in the material model. The proposed approach is an effective and time efficient method to create material models with complex evolving tension/compression behavior.

Abstract: Textures of rolled sheets are typically orthotropic along the mid-thickness plane, where the material undergoes plane strain compression. At the surface and in the subsurface layers, however, the achievement of the orthotropic symmetry can be impeded due to friction between the sheet and the rolls. The through-thickness strain distribution and texture have been found to also depend on the rolling draught [1], the load exerted on the rolls, the temperature and the rolling speed. Valid predictions of the influence of the shear deformation on the development of the microstructure and texture are not only important for controlling structural characteristics of the as-deformed material, but are also a pre-requisite to the investigation of the recrystallization process upon annealing. A recent experimental study of the texture development in heavily rolled aluminum revealed that the texture in each subsurface layer was dominated by one of the symmetric variants of the “copper” component. To investigate the conditions under which such variant selection is expected, a crystal plasticity theory combined with several mean-field as well as full-field scale-transition schemes is applied in the present work. Model predictions are compared to the texture development measured by EBSD in samples rolled to high and ultrahigh strains.

Abstract: The numerical simulation of sheet metal forming processes needs the accurate identification of the material parameters, for a given constitutive model. This identification can follow different methodologies and different sets of experimental data can be used, which lead to distinct sets of material parameters. In order to accurately compare the results of several methodologies, it is necessary to guarantee uniformity of their presentation. In this work, the correspondence between sets of parameters of the Hill’48 criterion is explored. The meaning of the “isotropic values” of the parameters associated with the out-of-plane stresses components is discussed and a required condition is proposed, in order to properly compare numerical simulation results obtained by using different input sets of constitutive parameters, identified by different procedures. Finite element simulations of complex shaped forming process, involving strain-path changes, are carried out in order to support the analysis.

Abstract: The effects of different constitutive models in sheet metal forming are investigated by considering the cylindrical and square cup drawing and V-bending processes. Numerical analyses are performed by employing eight different constitutive models. These are elastic plastic constitutive model with isotropic hardening, elastic plastic constitutive model with kinematic hardening, elastic plastic constitutive model with combined hardening, power law isotropic plasticity, piecewise linear isotropic plasticity, three-parameter Barlat, anisotropic plasticity and transversely anisotropic elastic plastic models. The simulations are performed for three different materials, St12 steel, Al-5182 aluminum and stainless steel 409 Ni, by using a commercial finite element code. A number of experiments are carried out and the experimental and analytical results are utilized to evaluate the results of simulations.

Abstract: ±Abstract. By applying the new quantum mechanics and relativistic mathematical model, proposed by Muñoz-Andrade, on the experimental results reported previously by Aghaie-khafri and Adhami [5], the true activation energy for hot deformation of 15-5 PH stainless steel is obtained over the temperature range of 900-1150°C and strain rates varying between 0.001 and 0.5s-1. It is interesting to contrast the results of this theoretical work with the main results of the apparent activation energy obtained for the same data, but applying the common methodology. It is shown that the true activation energy increased as the hot deformation is increased. Moreover, the true activation energy decreased as the strain rate is increased. The mean value of the true activation energy (289 kJ/mol) at high strain rate, ξ=0.5s-1, for dynamic recrystallization over the temperature range of 900-1150°C is in a closed agreement with the value of activation energy for self-diffusion in γ iron (280 kJ/mol) in dissimilarity of the result of the apparent activation energy (49221 kJ/mol) obtained beforehand by Aghaie-khafri and Adhami [5]. The results obtained in this work by the quantum mechanics and relativistic mathematical model are widely satisfactory; because essentially they are over the crucial limitations of the common methodology to obtain the activation energy at each thermo-mechanical metalworking condition. Keywords: Activation Energy, Hot Deformation, Dynamic Recrystallization, Quantum Mechanics, Special Relativity Theory.

Abstract: Low alloyed steels produced by continuous casting are thermomechanically treated to achieve final high mechanical properties, meaning a good combination of strength and toughness. The hot deformation mechanisms of a micro-alloyed steel containing up to 0.1wt% of V is studied by means of hot compression tests using a Gleeble^® 3800 device. Austenitization of samples is carried out at 1150°C during 2 minutes followed by cooling to the deformation temperature at 1Ks-¹ in the range of 750 – 1150°C. The studied strain rate range is from 0.01 to 80 s^-1 and the total true strain achieved is of 0.7. In situ water quenching is applied after the deformation to freeze the microstructure and avoid any post dynamic effect. The Ar₃ temperature is determined by dilatometry experiments to be 725°C for the used cooling rate. The stress values obtained from the compression tests are evaluated at different strains to determine the strain rate sensitivity and flow instability maps and thus, to predict the formability of the material in the range of studied deformation parameters. These maps are correlated to the microstructure at specific deformation parameters.

Abstract: Nowadays, precision Computer Controlled Optical Surfacing (CCOS) and processes like Ion Beam Finishing (IBF) or Magneto-Rheological Finishing (MRF) allow manufacturing of fused silica optics with nanometer precision. However, High spatial frequency defects remain on the optics and need to be previously smoothed. Full aperture semi-flexible polishing tools can be used, as they can guarantee uniform pressure on low frequency patterns to preserve the pre-formed aspherical shape while maintaining a high pressure differential on high frequency defects, thus smoothing them. That behavior can be obtained with tools that combine a continuous flexible layer for low frequency compliance and a fractionate viscoelastic polishing layer for high frequency defect polishing. The main goals of this study are predicting smoothing efficiency and form control of different tools, and then determining the best tool to achieve a good balance between them. To do this, a multiscale model is developed. First, at the whole tool scale, for a given aspherical shape, the largest misfit between tools and surfaces is mathematically determined, depending on machining parameters. Then a finite-element parametric study is performed and yields for the flexible layer the best mechanical properties and thickness as well as the optimal applied force to achieve pressure homogeneity at the global aspherical shape level. Second, at the viscoelastic polishing layer level, the Discrete Element Method (DEM) is used to investigate the tool – workpiece interface. A model based on the viscoelastic cohesive beam method is developed, thus allowing taking into account the polishing layer’s dynamic response depending on the excitation frequency. The optical surface is also modeled by interpenetrated discrete elements, paving the way for a full-DEM model of the polishing layer – workpiece interface. Smoothing simulations are separated in two steps : the first one is the initial pressure application, leading to an initial state of full tool – surface contact with an homogeneous pressure. Then the tool is moved over the surface and the dynamic pressure is calculated depending on defect and polishing layer properties as well as tool kinematics. By analyzing the pressure differential on defects it becomes possible to calculate the smoothing efficiency of a given polishing layer and therefore optimize its properties depending on the defects that need to be smoothed.