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As this kind of crack was never observed, it can be concluded that GI=0,012 mJ/mm2 and GII=0,04mJ/mm2 are not critical values for crack growth under PTC even if no fracture toughness are known. Then as GII values are 4 times higher than GI values, it can be deduced that the crack may propagate preferably along a local mode II.
But again this is not sure as no values of fracture toughness are known for this case.
Figure 6.8: Evolution of GII the shearing mode during 6 cycles of PTC at the interface chip/IMC
6.2.2 Crack growth in the Al metallization
At the crack tip in Al metallization, one can see Figure 6.9 that there is a large scale yielding. The evolution of the CTOD for mode I and II is plotted respectively Figure 6.10 and Figure 6.11. For the opening mode, a negative displacement represents a crack closing and a positive displacement represents a crack opening. At low temperatures the crack is open while at high temperatures the crack is closed or tends to close. The system needs about 4 cycles to stabilize. Indeed, for the first 2 cycles the crack remains always open, as its maximum and minimum CTODI are both positive. Then for the 3rd cycle the minimum CTODI reaches 0. Finally for the last 2 cycles negative values are reached, meaning that for these cycles, the crack is closed at high temperatures. During dwell times at high temperature, CTODI is staying constant meaning that layers of the crack are not moving. But for dwell times at low temperature the CTODI continues to evolve slightly inducing a slight closing movement of the crack.
Figure 6.9: Plastic strain at the crack tip in the Al metallization after PTC
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Figure 6.10: Evolution of CTODI the opening mode during 6 cycles of PTC in the Al metallization
Concerning the shearing mode of the CTOD, a negative CTODII represents a displacement to the left and a positive CTODII represents a displacement to the right for the layer above the crack compared to the layer underneath. In this case, the layer above the crack is always shifted to the left in comparison to the layer underneath. At low temperatures, the layer above the crack is moving further to the left, and at high temperatures, the layer above the crack is coming back to the right. Here also there is a shifting in displacements, as the maximum and minimum of CTODII are decreasing with increased number of cycles.
This shifting in displacement observed for both modes I and II may come from the rate dependent properties of the top solder. In the case of mode II, the system needs about 6 or even more cycles to stabilize. But the amplitude of displacements remains constant, thus calculating 6 cycles was sufficient for our analysis. During dwell times, the shear displacements at the crack tip are staying constant, thus meaning that ramping times are critical for crack growth in mode II, but not dwell times. Thus the same results in terms of crack growth in shear direction can be obtained for short or long dwell times. The amplitude of displacement is 10 times higher in mode II than in mode I. Thus the absolute maximum value of CTOD component at the new crack tip is obtained by the shearing component. According to the definition of the CTOD criterion, this means that the crack growth will occur along a local mode II direction. The values reached in this case for both mode I and II are not critical under PTC, as degradations of the Al metallization layer was not observed with this kind of test.
Figure 6.11: Evolution of CTODII the shearing mode during 6 cycles of PTC in the Al metallization
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6.2.3 Crack growth in the top IMC
Figure 6.12: von Mises stress at the crack tip at the top IMC after PTC (areas in grey have a von Mises stress superior to 500MPa)
After the 6 PTC cycles, the crack in the top IMC is open (Figure 6.12). The evolution of the ERR for opening and shearing modes is plotted respectively Figure 6.13 and Figure 6.14 for more details. For the mode I, the positive values of GI are indicating a crack opening. At high temperature the crack is almost close and at low temperature the crack is open at its maximum. For the dwell times at low temperatures, GI is not constant and continues to increase just like during ramping times. But for dwell times at high temperatures the crack keeps its quasi-closed position and does not further move. So here long dwell times can be critic for crack growth at low temperatures. The system seems to be stable approximately after 4 cycles as the maximum value seems to be constant up to the 4th cycles. The maximal values of GI reached are really low compared to the absolute maximal values reached for the shearing mode GII. Indeed absolute values of GII are about 100 times higher than values of GI.
Figure 6.13: Evolution of GI the opening mode during 6 PTC cycles in the top IMC
For the shearing mode, negative values of GII are representing a displacement to the left for the layer above the crack compared to the layer underneath. At low temperatures the layer above the crack moves to the left side and comes back to its original closed position at high temperatures. Here GII remains constant during dwell times at high temperatures, and slightly decreases for dwell time at low temperatures thus signifying that the layer above the crack tends to come back to its original position. Thus for the shearing mode, long dwell times are not critical at all in terms of crack growth. Regarding the evolution of GII, it can be noticed that the system is already stable after the first cycle.
As no fracture toughness are known for this crack in the IMC, it cannot be determined if the values reached by G are critical for crack growth under PTC. But as absolute values of GII are 100 times higher than values of
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GI, it can be deduced that the crack may propagate preferably along a local mode II. But again this is not sure as no values of fracture toughness are known for this case.
Figure 6.14: Evolution of GII the shearing mode during 6 PTC cycles in the top IMC