Key Engineering Materials Vols. 504-506

Abstract: A challenge in the design of functional parts in metal forming processes is the determination of the initial, undeformed shape such that under a given load a part will obtain the desired deformed shape. An inverse mechanical or a shape optimization formulation might be used to solve this problem, which is inverse to the standard kinematic analysis in which the undeformed shape is known and the deformed shape unknown. The objective of the inverse mechanical formulation aims in the inverse deformation map that determines the (undeformed) material configuration, where the spatial (deformed) configuration and the mechanical loads are given. The shape optimization formulation predicts the initial shape in the sense of an inverse problem via successive iterations of the direct problem. In this paper, both methods are presented using a formulation in the logarithmic strain space. An update of the reference configuration of the sheet of metal during the optimization process is proposed in order to avoid mesh distortions. A first example showed the results obtained with both methods in isotropic hyperelasticity. A second example illustrated a simplified deep drawing computed with the shape optimization formulation in isotropic elastoplasticity. From the undeformed shapes obtained with both methods the deformed shapes are acquired with the direct mechanical formulation. Compared to the target deformed shape a minor difference in node coordinates is found. The computation time is lower with the inverse mechanical formulation in hyperelasticity. The update of the reference configuration in the shape optimization formulation allowed to avoid mesh distortions but increased the computational costs.

Abstract: Pre-stressing is a technique often used in presses, and it is obtained either by wire or tape winding or by bolted rods. Pre-stressing is always performed by combining two materials: one which is tougher and used as the pre-stressing medium and one which is less resistant and used as the pre-compressed casing. Pre-stressing can be applied for several reasons: for reducing the cost of manufacturing and assembling the press frames in case of very large tonnage presses, for reducing the deflections and elongations of the frames during pressing operation, for improving the fatigue resistance of the press components, etc. In this paper a simple analytical model of loads, stresses and deformations will be proposed for pre-stressed columns. The results of the model will be validated and compared to the results of realistic FEM simulations of the behavior of the press frame in operation. The equations of the analytical models will be then used as the constraints of a global optimization algorithm, implemented with Matlab. The results clearly show that, only if the press frame structure is monolithic, it is possible to obtain a solution which is truly optimal by pre-stressing, i.e. by combination of a more expensive and high performance material with a relatively “poor” material. This conclusion seems to be robust with respect to potential noise or uncertainty issues, which in this case are mainly related to the coefficient of the objective functions.

Abstract: This paper presents a new approach for statistical analysis of process chains, including a parameter sensitivity analysis of each process step as a basis for dimension reduction, and an efficient interpolatory metamodel in order to predict new designs. A Monte Carlo alike evaluation of this metamodel results in the requested statistical information, e.g. quantiles of the output functionals. Numerical results are presented for the forming process of a ZStE340 metal blank of a B-pillar. Additionally, a brief overview of results of the process chain forming to crash is given.

Abstract: This paper deals with the identification of the anisotropic parameters using an inverse strategy. In the classical inverse methods, the inverse analysis is generally coupled with a finite element code, which leads to a long computational time. In this work an inverse analysis strategy coupled with an artificial neural network (ANN) model is proposed. This method has the advantage of being faster than the classical one. To test and validate the proposed approach an experimental cylindrical cup deep drawing test is used in order to identify the orthotropic material behaviour. The ANN model is trained by finite element simulations of this experimental test. To reduce the gap between the experimental responses and the numerical ones, the proposed method is coupled with an optimization procedure based on the genetic algorithm (GA) to identify the Cazacu and Barlat’2001 material parameters of a standard mild steel DC06.

Abstract: This paper introduces a fast and accurate procedure for determining the constants of magnesium AZ31 alloy at 713 K. The material behaviour is modelled by means of the power law relationship between the equivalent flow stress, the equivalent strain and the equivalent strain-rate within a narrow equivalent strain-rate range. Bulging tests were carried out in isothermal conditions (713 K) and at constant pressure in order to determine the material constants. It is necessary to evaluate the displacement and the thickness evolutions at the dome apex of the metal sheet. The time-displacement curve was obtained by laser measurements whereas a large number of bulging tests, interrupted at preset time intervals, were carried out to evaluate the thickness. The thickness was measured directly using a two-digit micrometer. The material constants, m, n and K were obtained in the power law relationship by means of constant pressure bulging tests coupled with the use of an inverse analysis technique. The results of comparison between experimental and numerical tests are shown and they indicate that the material constants can be accurately evaluated.

Abstract: This work deals with comparing the prediction of the development of rolling textures by using a homogenization method that is based on a homogeneous reference material. The proposed homogenization scheme, assuming constant stress polarisations in each phase, has in a natural way the potential to model the transition between Taylor- and Sachs-type textures. Therefore, the stiffness ef the hemogeneous reference material has to be varied between infinitely stiff and infinitely compliant. In the present study, texture evolution during rolling is simulated, showing that the application of different comparison materials in the homogenization scheme leads to the development of different main texture characteristics (Cube, Cu, Bs, Goss) in the orientation distribution function. For efficiently carrying out the rolling simulations using the proposed method, the measured texture information of the bulk aluminum sample is representatively reduced by using a partitioning technique of the orientation space.

Abstract: Aluminum sheets used for beverage cans show a significant anisotropic plastic material behavior in sheet metal forming operations. In a deep drawing process of cups this anisotropy leads to a non-uniform height, i.e., an earing profile. The prediction of this earing profiles is important for the optimization of the forming process. In most cases the earing behavior cannot be predicted precisely based on phenomenological material models. In the presented work a micromechanical, texture-based model is used to simulate the first two steps (cupping and redrawing) of a can forming process. The predictions of the earing profile after each step are compared to experimental data. The mechanical modeling is done with a large strain elastic visco-plastic crystal plasticity material model with Norton type flow rule for each crystal. The response of the polycrystal is approximated by a Taylor type homogenization scheme. The simulations are carried out in the framework of the finite element method. The shape of the earing profile from the finite element simulation is compared to experimental profiles.

Abstract: In this paper the capabilities of Associated Flow Rule (AFR) and non-AFR based finite element models for sheet metal forming simulations is investigated. In case of non-AFR, Hill’s quadratic function used as plastic potential function, makes use of plastic strain ratios to determine the direction of effective plastic strain rate. In addition, the yield function uses direction dependent yield stress data. Therefore more accurate predictions are expected in terms of both yield stress and strain ratios at different orientations. We implemented a modified version of the non-associative flow rule originally developed by Stoughton [1] into the commercial finite element code ABAQUS by means of a user material subroutine UMAT. The main algorithm developed includes combined effects of isotropic and kinematic hardening [2]. This paper assumes proportional loading cases and therefore only isotropic hardening effect is considered. In our model the incremental change of plastic strain rate tensor is not equal to the incremental change of the compliance factor. The validity of the model is demonstrated by comparing stresses and strain ratios obtained from finite element simulations with experimentally determined values for deep drawing steel DC06. A critical comparison is made between numerical results obtained from AFR and non-AFR based models

Abstract: Two non-quadratic orthotropic yield functions called Yld2011-18p (containing 18 param-eters) and Yld2011-27p (containing 27 parameters) are proposed. The formulations are based on theestablished concept of linear transformations operating on the stress deviator. Application examplesreveal the capabilities of both yield functions to accurately describe complex plastic anisotropy ofsheet metals.

Abstract: As close as you watch them, the materials (especially metals) present discontinuities that can easily be qualified as strong. Dislocations, structures formed by these dislocations, phases and grains are all discontinuities, also sources of heterogeneity, with effects on material behavior that are not really well reproduced by a model based on a continuity assessment. Consequently, the materials should be considered as a set of compartments with different behaviors. This promotes an alternative way to define models. A coherent modeling process is probably the integration of the different behaviors of the material compartments within the global model. The objective is here to build an efficient elasto(visco)plastic model of the mechanical behavior of titanium combining compartmentalized behaviors. After setting the frame of the study, which is of primary importance, the proposed modeling process is running as follows (i) choose a local behavior, (ii) identify the parameters of crystalline texture that must be integrated into the simulation and (iii) finally formulate a way of combining local compartments behaviors. The intrinsic properties of Finite Element codes are used to achieve the integration of the whole system.