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Dynamic shear band development in a thermally softening bimetallic body containing two voids

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Summary

We study the development of shear bands in a thermally softening viscoplastic prismatic body of square cross-section and containing two symmetrically placed thin layers of a different viscoplastic material and two elliptical voids with their major axes aligned along the vertical centroidal axis of the cross-section. One tip of each elliptical void is abutting the common interface between the layer and the matrix material. Two cases, i.e., when the yield stress of the material of the thin layer in a quasistatic simple compression test equals either five times or one-fifth that of the matrix material are studied. The body is deformed in plane strain compression at an average strain-rate of 5,000 sec−1, and the deformations are assumed to be symmetrical about the centroidal axes.

It is found that in each case shear bands initiate from points on the vertical traction free surfaces where the layer and the matrix materials meet. These bands propagate horizontally into the layer when it is made of a softer material and into the matrix along lines making an angle of ±45° with the vertical when the layer material is harder. In the former case, the band in the layer near the upper matrix/layer interface bifurcates into two bands, one propagating horizontally into the layer and then into other into the matrix material along the direction of the maximum shear stress. The band in the layer near the lower matrix/layer interface propagates horizontally first into the layer and then into the matrix material along the direction of the maximum shear stress. Irrespective of the value of the yield stress for the layer material, a band also initiates from the void tip abutting the layer/matrix interface. This band propagates initially along the layer/matrix interface and then into the matrix material along a line making an angle of approximately 45° with the vertical.

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  1. R. C. Batra & Z. G. Zhu

    Present address: Department of Mechanical and Aerospace Engineering and Engineering Mechanics, University of Missouri-Rolla, 65401-0249, Rolla, MO, USA

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    1. R. C. Batra
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    Batra, R.C., Zhu, Z.G. Dynamic shear band development in a thermally softening bimetallic body containing two voids. Acta Mechanica 86, 31–52 (1991). https://doi.org/10.1007/BF01175947

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