13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- Figure 2. Schematic of the laminate of study with the applied boundary conditions (combined loading in 4-point bending flexure and residual stresses from sintering process). An initial crack is introduced in the first layer Table 1. Young’s modulus (E), Poisson’s ratio ( ν), Coefficient of Thermal Expansion ( α), Flexural Strength ( σf), Fracture Toughness (KIc) and Fracture Energy (Gc) of the layer materials Material E [GPa] ν [-] α x10-6 [K-1] σf [MPa] KIc [MPa.m1/2] Gc [J/m2] ATZ 390±10 0.22 9.8±0.2 422±30 3.2±0.1 25±2 AMZ 280±10 0.22 8±0.2 90±20 2.6±0.1 23±2 In order to show the influence of the level of residual stresses on the propagation of the crack (i.e. deflection or bifurcation), three configurations with different volume ratio of the material components were considered and calculated. The total height of the laminate WS was kept constant WS =3mm and the thicknesses of the layers (tATZ and tAMZ) were thus given by the chosen volume ratio – see (Table 2). The residual stresses corresponding to the chosen volume ratio configuration were calculated using the classical laminate theory by considering of ΔT = –1230°C (temperature between sintering and room temperature) and material properties given in the Table 1. The calculated residual stresses are listed in Table 2 as well. Table 2. Layer thicknesses and corresponding residual stresses in the ATZ and AMZ layer for three different volume ratios of ATZ and AMZ material (WS=const.=3mm) VATZ/VAMZ (tATZ/tAMZ) tATZ [mm] tAMZ [mm] σres,ATZ [MPa] σres,AMZ [MPa] 2 (1.6) 0.400 0.250 +292 –585 5 (4.0) 0.500 0.125 +140 –695 8 (6.4) 0.533 0.083 +90 –730 2.2 Description of computational approach In order to decide about the type of further crack propagation (single or double crack penetration) and/or about further crack propagation direction, a change of the potential energy –δΠ for the crack increments in all possible propagation directions has to be calculated. Direction and/or type of propagation is selected such that δΠ attains a maximum value (where maximum of energy is released by the fracture process). However one should note that the energy release rate (ERR) for Mat. A ( EA, νA, αA) Mat. B ( EB, νB, αB) Layer A - ATZ (tA, nA) Layer B - AMZ (tB, nB) (nB= nA -1) LS=50 mm WS = 3 mm So=40 mm Si=20 mm F/2 F/2 ΔT=-1230°C Initial crack VA= tA.nA VB= tB.nB z x y
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