Experiments, modeling and computation of the temperature, age and size-dependent behavior of zinc die-cast materials
Final Report Abstract
The goal of the project was the investigation of the thermo-mechanical behavior of the zinc die casting alloy Zamak 5 in its solid state considering the effect of natural aging and thickness dependence. The experimental characterization of the mechanical behavior at different temperatures and aging times shows a pronounced viscoplastic material response, in which the equilibrium stress is strongly temperature-dependent and the viscosity is affected by the temperature and age. For high temperatures, the equilibrium state tends to disappear, and the viscous effects are predominant. For very low temperatures, the material behavior tends to be purely rate-independent. Natural aging influences the viscous behavior in a more pronounced way than the equilibrium behavior and this effect is more visible at room temperature than at higher or lower temperatures. Moreover, the thermo-physical properties thermal expansion, thermal conductivity and specific heat capacity as well as the shrinkage due to aging were characterized over the temperature. For the characterization of the thickness dependence, investigations with the optical microscope and scanning electron microscope were used. Moreover, investigations with the scanning electron microscope and X-ray diffractometry were used for the determination of the microstructural changes during aging. Based on the experimental results, a model of thermo-viscoplasticity for small and finite deformations was developed, in which the influence of aging was included with the help of an internal variable. Both models are based on the decomposition of the stress state into an equilibrium and an overstress part. This modeling concept shows advantages in the parameter identification process, since the parameters of the equilibrium stress part can be identified independently of the parameters in the overstress part. Since modeling and identification are closely connected, some of the material functions depending on the temperature and aging are developed during this process. The entire model is thermodynamically consistent in the sense of fulfilling the Clausius-Duhem inequality. The thickness dependence was considered for the elastic material response. A dimensionless scalar-valued order parameter is introduced, which is defined by a Helmholtz-like partial differential equation. This parameter is used to define a porosity distribution over the thickness of the specimen. The material properties are incorporated by combining the distribution of the pores with the Mori–Tanaka approach for linear elasticity. The distribution of the porosity is determined with polished cut images of the specimen. The implementation of all models is performed in the in-house finite element code TASAFEM and the viscoplasticity model is additionally implemented in Abaqus. The stress algorithm is provided for all cases. Moreover, the thermomechanical behavior with the influence of aging is validated comparing simulations of complex geometries with the experimental results. The thickness-dependent behavior was validated in the elastic range comparing the average elasticity modulus obtained from simulations with the experimental values. In conclusion, the investigations performed during this project enlarge the knowledge about the thermo-mechanical behavior of Zamak 5 and several thermal properties. Moreover, new constitutive models are available for the thermomechanical behavior with the effect of aging as well as for the elastic thickness dependence of Zamak 5, which improves the accuracy in the simulations for the design and investigation of component parts made of this material.
Publications
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Experimental characterization, material modeling, identification and finite element simulation of the thermo-mechanical behavior of a zinc die-casting alloy. International Journal of Plasticity 101, 2018, pages 74–105
Martinez Page, M. A. and Hartmann, S.
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Modeling of aging effects in a zinc die casting alloy. Technische Mechanik 38(1), 2018, pages 55–72
Martinez Page, M. A. and Hartmann, S.
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Numerical modeling of the thickness dependence of zinc die-cast materials. Computational Mechanics 62, 2018, pages 655–667
Martinez Page, M. A., Ruf, M. and Hartmann, S.
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Influence of temperature and aging on the thermal diffusivity, thermal conductivity and heat capacity of a zinc die casting alloy. Journal of Alloys and Compounds 786, 2019, pages 1060-1067
Martinez Page, M. A., Weidenfeller, B. and Hartmann, S.
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Thermo-mechanical behavior of a zinc die casting alloy considering natural aging, Doctoral Thesis, Institute of Applied Mechanics, TU Clausthal, 2019
Martinez Page, M. M.
