A constitutive theory and modeling on deviation of shear band inclination angles in bulk metallic glasses
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Mo Lia) School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332 (Received 24 February 2009; accepted 6 May 2009)
A constitutive theory for metallic glasses is established that is based mainly on the Drucker-Prager model and a free-volume theory. The primary emphasis of this theory is on volume dilatation and its consequences on mechanical responses in metallic glasses that have been known from studies in both experiments and atomistic simulations. We also implemented the constitutive theory in a finite element modeling scheme and conducted numerical modeling of deformation of a metallic glass under plane-strain tension and compression. In particular, we focused our attention on the deviation of the shear band inclination angle, a commonly observed phenomenon for metallic glasses. We found very good qualitative agreement with available experimental data on shear band inclination angle and stress-strain relation. We also give a detailed discussion on different constitutive models, in particular the Coulomb-Mohr model, in the context of predicting the shear band inclination angle.
I. INTRODUCTION
The unique and outstanding mechanical properties are largely the impetus for the intensive research on bulk metallic glass (BMG) in the past decade. An overwhelming number of studies have shown that the plastic deformation of BMGs follows different yield criterion from that of the von Mises type,1–10 which was tested and used extensively in polycrystalline metals and alloys. The convincing evidence is the deviation of the shear band inclination angle (SBIA) from the classical 45 predicted by the von Mises criterion.1–5,9,10 SBIA is defined as the angle between the shear plane and the loading direction in a uniaxial loading mode. One can find a list of these angles for different kinds of BMGs, summarized, for example, by Lund and Schuh11,12 as well as Zhang et al.13 Although scattered, the data show a clear trend in the range of 2745 in compressive loading and 4858 in tensile loading. One possible explanation is that because the metallic glasses have relatively large elastic strain at yielding, the SBIA could be caused by the elastic unloading. However, our results show that such an effect is small (i.e., less than 10 for the sample loaded up to the elastic strain at 2– 3%).14 The deviation of the SBIA suggests that the yielda)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2009.0306
2688
http://journals.cambridge.org
J. Mater. Res., Vol. 24, No. 8, Aug 2009 Downloaded: 21 Mar 2015
ing of BMGs is not dominated by shear stress alone. A possibility is that it should involve normal stress.5,6 A quick solution is hence to invoke the Coulomb-Mohr (CM) yield criterion that is well known in soil mechanics and granular matters to give slip directions different from 45 . As shown in an atomistic simulation11 with a slip plane implicitly introduced, one can indeed see the CM type of relation linking the applied normal stress perpendicular
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