PSI - Issue 5

Danuta Miedzińska et al. / Procedia Structural Integrity 5 (2017) 484– 491 Danuta Miedzińska / Structural Integrity Procedia 00 (2017) 000 – 000 For 2D structures the series of FE models were developed, which had 10 × 10 , 20 × 20 … 100 × 100 grains. Similarly for 3D structures the FE models of 10 × 10 × 10 , 20 × 20 × 20 … 100 × 100 × 100 grains were built. Three models of each dimension with different randomization were develop to achieve the averaged results that are independent from microstructure. The porosity of all models was 0.5. The characteristic dimension of a grain was 1 0 × 10  m for 2D model and 1 0 × 10 × 10  m for 3D model. The uniaxial compression test was carried out with the use of LS Dyna computer code.. The linear elastic material model with Young modulus of = 780 GPa and Poisson’s ratio of  = 0.3 for solid phase was applied. The calculations results were presented in Figure 2 and 3 as the dependence between a substituted Young modulus achieved in numerical analyses and number of elements in a model. For 2D models it is strictly visible, that for 10 × 10 grains model the result is non physical, and the results stabilizations appears for 80 × 80 grains model. For 3D models such results stabilizations appears for 40 × 40 × 40 grains model. 487 4

Fig. 2. FE analyses results for RVE calculations for 2D models.

Fig. 3. FE analyses results for RVE calculations for 3D models.

3. Method of FGM numerical homogenization

For the purpose of modeling of functionally graded materials the computer application was developed with the use of VBA code. The elements in the model are drawn with on the base of assessed randomization (statistic distribution – linear or normal one) with the use of the application. For the drawings the Excel RAND function was used. The function RAND() returns a pseudo-random integral number, so the sequence will contain the repeating series of numbers, if is long enough. Coupling of random numbers, like in Wichman – Hill procedure, allows to generate 10 13 of numbers before repetition appears. In case of some Diehard tests the achieved results were incorrect, because in