Elastoplastic Phase Transformation Model Of Shear Band Forming In Amorphous Alloys

The phenomena of strain localization have been widely observed in experiments and nature,such as kinking band in unidirectional fiber reinforced composite,kinking band in rock,lüders band in fine grain low carbon steel,shear band in sand and so on.When the phenomena of strain localization appear in materials,shear band and regions outside the shear band can betreated as two-phase piecewise-homogeneous deformation.Strain and stress are different in these two regions.The strain in shear band is bigger than other regions.Calculating out the stress and strain inside and outside the shear bandsof amorphous alloys is helpful to kown mechanical behavior of materials and improve material application safety.Amorphous alloy,also known as metallic glass,is a kind of amorphous material made of a variety of metals.The earliest discovery of amorphous alloys was more than 50 years ago.The appearance of amorphous alloys has injected fresh blood into the fields of physics,materials and other fields,enriching their research content.Amorphous alloy has the characteristics of high strength,high fracture toughness and corrosion resistance.Therefore,it has attracted the attention and interest of many scholars.Many experiments carried out by scholars have shown that shear bands will occur in amorphous alloys with axial tension and compression,and these shear bands can be regarded as a strain localization phenomenon.Some scholars have pointed out that the shear bands in amorphous alloys are the key factors that affect their plastic deformation.The plastic deformation of amorphous alloy is mainly concentrated in the shear band and the fracture of amorphous alloys is often in the direction of the main shear band.Therefore,the study of the deformation of shear bands in amorphous alloys is of great help for the popularization and application of amorphous alloys.In this paper,the shear band is considered as a strain localization phenomenon,the shear bands in amorphous alloys and the regions outside the shear bands are considered as different phases,and the occurrence of shear bands is regarded as a phase transformation behavior.When the shear band appears,the displacement at the boundary of the shear band is continuous.But the deformation gradient are discontinuous.The stress and deformation gradients need to satisfy jump conditions.At the same time,the strain energy of the material will also change at the phase boundry and it must satisfy the Maxwell relation.According to the conditions required for phase transformation,We can write down the governing equations of phase transformation.By solving the governing equations,the stress and strain inside and outside the shear band,the shear band inclination angle and the Maxwell stress can be obtained.Finally,we select the relevant amorphous alloy experiments,solving the stress and strain inside and outside shear band,the shear band inclination angleand the Maxwell stress with the phase transformation model.The calculated results are in good agreement with the experimental results...