مدل سازی عددی رفتار سازه از اجزای منیزیم ریخته دیواره نازک

Axial crushing, 3-point bending and 4-point bending tests have been performed in order to establish an experimental database of the behaviour of generic high pressure die cast (HPDC) AM60 structural components. In this paper, 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 HPDC structural components are modelled in LS-DYNA using shell elements. The cast magnesium alloy is modelled using both the classical J2-flow theory and an elastic–plastic model based on a non-associated J2-flow theory. In the latter, the constitutive model includes the Cockcroft–Latham fracture criterion, which is coupled with an element erosion algorithm available in LS-DYNA. It is further possible to define the fracture criterion as a Gauss-distributed stochastic parameter to allow for heterogeneities in the cast material. The constitutive model and fracture criterion are calibrated with data from tension and compression tests. Comparison of experimental and predicted behaviour of HPDC components gives promising results. It is found that the strength difference between uniaxial compression and tension has little influence on the numerical simulations. The fracture criterion of Cockcroft and Latham seems to be an effective approach to predict failure in HPDC components.

Growing concerns for economy, environment and functionality have led to increased use of light-metals in the load carrying structure and safety components of cars. With high pressure die casting (HPDC) 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 the method is to optimise 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 for instance extruded materials. Design and production of thin-walled cast structural components for the automotive industry are challenging tasks, involving 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 (FE) 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. To minimise the weight of the structural component while maintaining the safety in a crash situation, the ductility of the material has to be utilised without risking un-controlled failure. Hence, a reliable failure criterion is also required, giving limits for the plastic deformations under various loading combinations. Quite precise and validated constitutive models and failure criteria are available for materials such as extruded aluminium and rolled steel (Lademo, 1999). For thin-walled cast materials, however, much work is still to be done. 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 with the use of axial crushing, 3- and 4-point bending experiments. 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 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 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, high pressure die cast AM60 components were subjected to axial crushing and 3- and 4-point bending. Laboratory experiments and explicit finite element simulations with shell elements were performed. Only quasi-static loading conditions were considered. An elastic–plastic constitutive model based on a non-associated extended 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 (1968) was adopted for the SD model, and can be defined as a Gauss-distributed stochastic parameter. This option makes it possible to introduce material inhomogeneities in the cast material and reproduce the stochastic nature of the casting process. That is, components cast with equal process parameters can get a different distribution of the material properties. In general, experimental results presented both in this work and by Dørum et al. (2003) show that there exists a relatively large scatter in the force–deformation 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–deformation behaviour is controlled by local buckling much less scatter is found. From numerical simulations with LS-DYNA, it was found that both the classical J2-flow theory and the SD model capture the structural behaviour of the generic AM60 components with reasonable accuracy. Thus, for the load cases studied here, it can be concluded that the reported strength differential effect in the cast AM60 material found from uniaxial tension and compression tests have no significant influence on the accuracy of the numerical simulations in terms of force–deformation behaviour. This observation is related to the fact that the measured force–deformation characteristics can be viewed as an integrated response, where the applied force at a given displacement is a function of the stress and strain distribution in the component. Consequently, whether the difference in compressive and tensile yield stresses influence the global response depends upon the load case and the geometry of the component. Even if the J2-flow theory captures the force–deformation behaviour for these cases, it does not have the ability to reproduce the uniaxial properties of the AM60 material. Further, existing experimental data for other die cast magnesium alloys, such as the AE42 alloy, show that the SD effect can be significantly larger (tensile yield strength equal to 145 MPa and compressive yield strength equal to 103 MPa) (Hydro Magnesium, 1998). Largest deviation from the experimental force–deformation characteristics was found in the simulations of single components with ribs subjected to axial loading. This deviation may be due to inaccurate description of both the geometrical and material inhomogeneities. No experimental data are available concerning the material quality of the components with reinforcing ribs. However, several surface defects can be found by visual inspection. The fracture criterion proposed by Cockcroft and Latham (1968) gave promising results. Especially the structural ductility of components subject to axial crushing and bending in the u-mode was quite accurately predicted using a constant value of Wc. The reason for the good agreement in these cases is related to the evolution of local plastic strains with increasing global deformation after the buckling load has been reached. Here, a small increase in global deformation results in a relatively large increase in local plastic strains. Thus, the accuracy of the prediction of failure in terms of global force–deformation behaviour is not very dependent on the accuracy of the Wc parameter. For the case of bending in n-mode, the simulations using a constant value of Wc predicted too ductile response. To represent the scatter found in the experimental force–deformation behaviour and the scatter in local tensile ductility, two series of simulations were run with the critical plastic work in the fracture criterion introduced as a stochastic Gauss-distributed variable. The Gauss distribution was generated from experimental results provided by Laukli (2002). With this approach, a better agreement with the experiments was observed. In this work, the fracture criterion is only used in combination with the SD model. However, for the load cases studied here, the fracture criterion would probably give equally good agreement with the experiments also if it had been implemented in the J2-flow plasticity model. For the load cases axial crushing and bending in the u-mode, the simulations where fracture criterion is not included make it possible to see how the material failure affects the softening branch of the force–deformation characteristics after the buckling load has been reached. In order to further improve the simulations with respect to the description of structural ductility, a more realistic distribution of the inhomogeneity present in the components should be included in the FE-models. Thus, a coupling between a die casting process simulation and the pre-processor for the final FE-simulations should be considered.