13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- possibility of shear band formation. As is known, 45 corresponds to the direction of the maximum shear stress, which is usually the shear direction of crystalline alloys. However, shear bands for MGs are predicted to form at the angles normally >45º in tension while <45º in compression (see Fig. 2), consistent with the experimental observations in MGs [28]. This deviation of shear direction from the maximum shear stress can be partly attributed to the pressure effect which usually cannot be ignored in MGs [24-27]. In addition, the c also shows an obvious dependence on dilatancy factor β. With increasing β, the minimum value of c decreases in tensile case while increases in compressive case. It means that shear dilatancy promotes the shear banding in tension while impedes that in compression. In Fig. 2, the minimum point of c in tension is relatively lower than that in compression. Due to this asymmetry, strain localization in tensile part is usually easier than that in compressive part. Fig. 2 Dependence of con θ for α=0.1 and different β both on tensile side (the blue curves) and on compressive side (the red curves). The inclination angle of shear banding θ versus the dilatancy factor for different is plotted by Fig.3. We interestingly find that is a little bigger than 45 for both tension and compression even excluding the pressure sensitivity and dilatancy ( 0 and 0 ). This is attributed to the specific stress state and depends on the Poisson ratio [20]. Increasing or , the inclination angle increases in tensile part while decreases in compressive part, showing a asymmetrical deviation from 45º. This prediction is similar to those results of uniaxial loading (tension and compression) from continuum and molecular simulations [31, 32]. For Vit-1, the pressure sensitive factor is around 0.1 [33]. Ranging from 0 to 0.5, the shear band angles are predicted to be 47º ~54º and 38º ~44º, respectively in tension and compression. Actually, the shear band angles observed in the experiment are 55º on tensile side and 40º on compressive side. In the above discussion, the Poisson ratio is set to be a constant 0.36 for Vit-1.
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