Plastic instability in U-notched bend specimens of spheroidized AIS11090 steel
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I.
INTRODUCTION
W H I L E extensive studies have been performed on the ductile fracture of notched specimens of steel, both in tension ~ and in bend tests, 2-7 the critical events at the notch root at crack initiation are not clearly understood. For bend tests, the concentration of strain along the characteristic slip traces (surfaces of tangential velocity discontinuity) has been postulated to govern ductile fracture behavior. 8 Since the strain is a maximum at the notch surface, some critical surface perturbation 9'~~is expected to lead to the formation of localized bands of plastic instability, with subsequent crack nucleation within them. Indeed, current plasticity theory for plastic flow bifurcation9 predicts critical strains for the development of periodic surface irregularities and, subsequently, localized shear bands in the bulk. 9'H-13 In view of the above developments, this research was undertaken with the objectives of characterizing surface and bulk plastic instabilities for U-notched bend specimens, thereby testing the new theories, and distinguishing the initiation of surface and bulk microcracks. Spheroidized AISI 1090 steel was selected for the experiments because some results were already available for this material. TM The present work also provides background for a following paper on the influence of hydrogen on the initiation of plastic instability.
strain localization has been predicted by various authors 9'H'13 as a bifurcation phenomenon in plasticity theory. For the present case of a U-notched bend specimen, we specialize to the middle portion of the notch where the flow approximates plane strain behavior.
Surface Instabilities and Strain Bifurcation Instabilities in the form of surface waviness have been predicted in terms of a strain bifurcation analysis in the approximation of a finite strain deformation model for a nonlinear elastic solid. 9 For such a hyperelastic solid, strain bifurcation can occur when a vertex or comer develops on the yield surface in principal stress space when nonlinear J2 deformation theory is used. The general condition for bifurcation in the surface mode is given in that theory by 9
4N*
4/x*
"~ o'2/
where the instantaneous shearing moduli are given by ~* = ~
1[
E,-
(E~-E,) 1+
(
1 )2 cosa +~sinc~
sin
= E,/3 when a = 0 or 7r II.
[2]
and
THEORY
1
A. Prediction of Maximum Principal Strain at Onset of Surface Wave Bifurcation and Shear Localization The equations governing incremental equilibrium in a homogeneous, time-dependent, pure deformation process can be described in terms of a current yield (flow) surface and plastic strain trajectories in principal stress and strain space. When the yield surface suffers a loss of ellipticity, a shear band bifurcation becomes possible. 13The boundaries of the emergent shear bands correspond to the associated characteristic slip traces. The condition for the onset of such O . A . ONYEWUENYI, formerly Graduate Student at The Ohio State University, is now Metallurgist, Shell Development Company, Houston, TX 77
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