مدل سازی عددی رفتار سازه از اجزای منیزیم ریخته دیواره نازک با استفاده از یک روش از طریق پردازش

A through-process methodology for numerical simulations of the structural behaviour of thin-walled cast magnesium components is presented. The methodology consists of casting process simulations using MAGMAsoft, mapping of data from the process simulation onto a FE-mesh (shell elements) and numerical simulations using the explicit FE-code LS-DYNA. In this work, generic High Pressure Die Cast (HPDC) AM60 components have been studied using axial crushing, 3-point bending and 4-point bending tests. The experimental data are applied to obtain a validated methodology for finite element modelling of thin-walled cast components subjected to quasi-static loading. The cast magnesium alloy is modelled using a user-defined material model consisting of an elastic–plastic model based on a modified J2-flow theory and the Cockcroft–Latham fracture criterion. The fracture criterion is coupled with an element erosion algorithm available in LS-DYNA. The constitutive model and fracture criterion are calibrated both with data from material tests and data from the process simulation using MAGMAsoft.

As the lightest structural engineering metal available, magnesium is very attractive for structural automotive applications where weight saving is a matter of serious concern. With High Pressure Die Casting of magnesium and aluminium alloys, components with very complex, thin-walled geometry, like instrument panels, A and B pillars and front end structures, can be cast with a high production rate. The challenge with this production method is to optimize the process parameters with respect to the part design and the solidification characteristics of the alloy in order to obtain a sound casting without casting defects. Unbalanced filling and lack of thermal control can cause porosity and surface defects due to turbulence and solidification shrinkage. These defects can give low ductility compared to extruded materials, for instance. The HPDC method also leads to a “skin-effect”, where the microstructure of the castings near the free surfaces differs significantly from the interior as the skin region has much finer microstructure [1] and [2]. Design and production of thin-walled cast structural components for the automotive industry are challenging tasks that involve the development of alloys and manufacturing processes, structural design and crashworthiness analysis. In order to reduce the lead time to develop a new product it is necessary to use finite element analysis to ensure a structural design that exploits the material. Accurate description of the material behaviour is essential to obtain reliable results from such analyses. In order to minimize the weight of the structural component while maintaining the safety in a crash situation, the ductility of the material has to be utilized without risking un-controlled failure. Hence, a reliable failure criterion is also required, giving limits for the plastic deformations under various loading combinations. Very precise and validated constitutive models and failure criteria are available for materials such as extruded aluminium and rolled steel [3]. However, much work is still to be done in this area for thin-walled cast materials. The long-term objective of this work is to develop design and modelling tools that allow the structural behaviour of thin-walled cast components to be predicted when subjected to static and dynamic loads. In the current study, the structural behaviour of generic structural HPDC components, shown in Fig. 1 and Fig. 2, has been investigated using axial crushing, 3- point bending and 4-point bending tests.The components were cast of magnesium alloy AM60 at Hydro’s Research Centre in Porsgrunn, Norway with a Bühler SC42D 420-ton cold chamber die casting machine.

The objective of this work is to develop design and modelling tools that allow the structural behaviour of thin-walled cast components to be predicted when subjected to static and dynamic loads such as in crash situations. The approach consists of the following ingredients: casting of generic components relevant for the automotive industry, material and component testing, constitutive modelling and validation simulations using the finite element method. In the present study, a through-process methodology for numerical simulations of cast components is presented. The methodology is based on the use of both material tests and results from casting process simulation to calibrate the fracture criterion used in the finite element simulations. Experimental data consisting of axial crushing, 3-point bending, and 4-point bending tests have been applied to obtain a validated methodology for FE modelling of thin-walled cast AM60 components subjected to quasi-static loading. An elastic–plastic constitutive model based on a modified J2-flow theory, referred to as the SD model, was implemented in the FE-code LS-DYNA. The SD model is designed to model the behaviour of metals with strength differential (SD) effects, and is calibrated against uniaxial tension and uniaxial compression tests. The fracture criterion proposed by Cockcroft and Latham was adopted for the SD model, and was calibrated using experimental results (uniaxial tensile testing and 3- and 4-point plate bending). Results from numerical predictions of the material surface quality and porosity obtained from casting process simulations (MAGMAsoft) were used to give a realistic distribution of the fracture parameter Wc throughout the component. The experimental data from the uniaxial tensile tests was used together with porosity predictions to give a conservative map for the interior material ductility. Similarly, using an inverse modelling approach for the plate bending tests together with surface quality predictions, also resulting from casting process simulation, a conservative map for the skin material ductility was created. In general, experimental results presented both in this work and in previous works ([6], [7], [8] and [9]) show that there exists a relatively large scatter in the force–displacement behaviour when the HPDC components are subjected to deformation modes where the failure depends on the local tensile ductility of the material. For deformation modes where the force–displacement behaviour is controlled by local buckling much less scatter is found. The fracture criterion proposed by Cockcroft and Latham [14] linked to results from casting process simulation gave very promising results. Especially the structural ductility of components without reinforcing ribs was quite accurately predicted. For the case of 3-point bending in n-mode, the simulations gave a prediction in the brittle range of the experiments. This is in good agreement with the conservative assumptions made for the material ductility. However, a somewhat too ductile response was predicted for the case of 4-point bending of AM60 components without ribs in n-mode. This was explained with the existence of a small notch remaining from the gating system. As shown in a previous work by the authors [9], it is possible to achieve good agreement with experimental force–displacement behaviour for load cases where the deformation mainly is controlled by buckling even when a constant Wc value is assumed. Thus, the bending load cases in n-mode are more sensitive to the accuracy of the maps for material quality. However, while the FE simulations of the generic AM60 components without ribs were quite accurate compared to the experimental results, this was not the case for the components with internal ribs. Here, the simulations generally predicted a too ductile response. In order to further improve the simulations with respect to the description of structural ductility, the quality of the material ductility map should be further examined. Currently, there only exists a map for the surface material quality. Further, this quality map is a rather new development from MAGMAsoft and is still being further developed. The quality of the interior material has in this work been calibrated using porosity predictions. However, it should be noted that this must be regarded as a simple first order approximation, and a more precise map for the quality of the interior material should also be searched. As discussed previously, an alternative mapping procedure should be developed to avoid corner problems. With the current mapping procedure in MAGMAsoft, any predictions of low material quality or high porosity values at corners in the structures, such as intersection between the internal ribs, will not be mapped onto the integration points in the FE model when the corners in the structure are located at the element edges in the FE mesh. This may be the reason for prediction of a too ductile response for the AM60 components with internal ribs studied in this work. When using results from the casting process simulation (MAGMAsoft) to calibrate the Cockcroft–Latham fracture criterion, it is assumed that the elongation at fracture varies linearly with the surface quality map and porosity values for the skin material and interior material, respectively. This relation should be further examined.