13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- length, width and thickness directions and when the material deforms more in width direction than thickness direction to produce a higher r-value, it has improved formability. The contribution of each strain component to r-value and q- value may provide insight into the origin of the anomalous relationship between formability and r-value for AZ31. Fig. 7 shows the relationship between the q-value and strain for the three materials. It is seen in Fig. 7 that AZ31 has the highest q-value, i.e. most of the deformation is actually concentrated in the width direction while AA5754 has the lowest q-values, with least deformation along the width direction. 0.00 0.50 1.00 1.50 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Global true strain Contraction ratio, q AZ31 AA5754 IF steel Fig. 7 q-value development in three alloys Fig. 8 shows the thickness strain in the three materials calculated using the incompressibility criterion. It is clear that there is very little thinning in AZ31, consistent with the q-value results in Fig. 7. Fig. 8 Thickness strain evolution in three alloys. Note that ‘‘average’’ denotes thickness strain estimated from both tensile strain and width strain from given gage lengths while ‘‘point’’ denotes thickness strain at a point within necked area.
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