layers, the model is continuum. An example is illustrated in Figure 3, where for clarity the number of layers has been fixed to 20. Figure 3 Continuously graded composite and corresponding Young modulus vs depth RESULTS AND DISCUSSION The 50 different microstructures generated as described in the previous section were meshed with OOF. Each mesh has about 20000 triangular elements. The thermo-elastic constants are known from Table 1, while the two Weibull parameters are assumed to be m=25 and σ0=0.1GPa for both phases. The effect of stochastic placement of the second phase on the toughness is characterized analyzing the microstructural damage evolution. We achieve this analysis placing a pre-existing surface vertical crack in each sample and incrementing the load up to the first failure. When the first element fails, local stresses are redistributed and the load can be incremented until the second failure occurs. In this manner, it is possible to track the damage evolution as the crack grows in the microstructure. Figure 4 displays the crack paths obtained for one microstructure. The elements that are damaged are colored in black. Figure 4: Damage evolution in a microstructure In order to quantify the damage accumulation, a damage parameter has been defined as the area of the damaged elements divided by the total area. This parameter is plotted vs the strain applied in Figure 5 for one single graded microstructure and a sample of the same dimension of homogeneous material (with elastic modulus equal to the average elastic modulus through depth of the graded material). As can be noted from the picture, the sample of the graded material is less damaged, thus confirming the better performance of FGM over traditional materials.
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