Simplified fractal FEA model for the estimation of the Young’s modulus of Ti foams obtained by powder metallurgy

• A new reduced fractal model is introduced.
• The effect of the porosity on Young’s modulus for Ti foams was analyzed.
• Experimental results and FEA estimations highly agreed.
• The introduction of the fractal model improved the estimated results.

This work reports the introduction of a new finite elements model, for the estimation of the Young’s modulus (E) of metallic foams obtained by means of powder metallurgy using a Space Holder Phase (SHP). The model is based on the reduction of the volume, and the replication of the expected porosity distribution as fractal using two different pore sizes, which depend on the SHP. Ti foams with porosities ranging from 30% to 70% were experimentally obtained and characterized to validate the model. The effect of the porosity on the Young’s modulus for the Ti foams was estimated using the proposed model, and compared to the experimental values. Estimations obtained were in excellent agreement with the experimental results, with relative errors ranging from 0.8% to 11.2%. Both, experimental and estimated values for E showed important decreases as the porosity increases: e.g. E estimations were 37.1 and 9.3 GPa for porosities of 30% and 70%, respectively. The results demonstrated the fractal behavior of the porosity for the experimental metallic foams, as well as the efficacy of the proposed model for predicting the mechanical properties of these materials, being an important tool for their design and manufacture.

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