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Several die casting materials show different mechanical responses for specimens with different thicknesses. This can be observed in the variation of parameters, such as the Young's modulus, the tensile strength or hardness of the material in specimens with different thicknesses. In order to model this effect, we have experimentally investigated a specimen of a zinc die casting alloy. We concentrate in the modeling of the porosity distribution and its influence on the mechanical response using Mori-Tanaka proposal for incorporating porosity. The applicability of the model is shown with a simulation example. Preliminary Observations and ModelingIn the works from [1] and [2] zinc die casting alloys are investigated, observing changes in the mechanical response for specimens with different thicknesses. [2] showed that there is a thin layer at the outer surfaces of the specimens with a finer microstructure than the core material. Additionally, in [3] the porosity is considered as a common defect in die casting alloys, which increases with the thickness of the specimen. Both effects cause a thickness dependence. Microscopical investigations of the microstructure in zinc die casting specimens are performed to study the distribution of the porosity over the thickness of cylindrical, thin-walled specimens. In this work, we only concentrate on the porosity distribution as a cause of the thickness dependence.Since the porosity cannot be defined directly in dependence of the position x, we introduce a structural parameter κ( x) analogous to [4] and [5]. This parameter evolves according to a partial differential equation and provides the information, how far away a point is from the surface of the geometry. With the help of this parameter, we define the porosity distribution Φ(κ). The influence of the porosity on the model is included in the material parameters. As a first approximation, we restrict ourselves to the linear elastic range. In the Mori-Tanaka model, see [6] and [7], a representative volume element with a matrix material and inclusions is homogenized. In the case of spherical pores, the compression K 0 and shear moduli G 0 depends on a factor which decreases with a higher porosity. The boundary value problem can be summarized by the balance equation of the structural parameter κ div S + r κ = 0, with S = grad κ and r κ = α κ (1 − κ),and the balance of linear momentumThe stress is given bywhere the compression K 0 (Φ) and the shear moduli G 0 (Φ) are dependent on the porosity, E is the linearized Green strain tensor. Moreover, the porosity Φ(κ) is a function of the structural parameter κ. Implementation and Simulation ExampleIn order to solve the boundary value problem from the previous section, we express the balance equations in the weak form and discretize them in space

Zamak alloys can be found in a wide variety of components of the automotive, building, electronic, and toy industry. They are preferred to other materials for die casting foundry due to their several advantages. For example, they exhibit a low melting point which allows an economic manufacturing process, they allow the production of components with tight tolerances and are characterized by good mechanical properties. Nonetheless, these alloys show a change in their mechanical behavior over time. This phenomenon is known as aging and it is associated to microstructural transformations such as diffusion and precipitation of alloying elements and phase transformations. In this work, the influence of natural aging on the thermomechanical response is investigated with the help of tension, compression and torsion experiments and a model with aging as an internal variable is proposed.