The ductility of a HSLA steel at temperatures below 300 K
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I.
INTRODUCTION
H I G H strength low alloy (HSLA) steels containing niobium, vanadium, and/or other microalloying elements have found use in diverse structural applications including pipelines and automotive components. A fine ferrite grain size in conjunction with other microconstituents, a distribution of carbides/carbonitrides of V and Nb, and the dislocation substructure obtained by suitable thermomechanical processing are believed to contribute to the strength and ductility of these steels. Increasing demands for the use of these steels for transporting oil and natural gas from northern and arctic regions has led to the evaluation of their low temperature mechanical behavior. Contrary to the typically observed low ductility of plain carbon steels at subzero temperatures, ~,2 several researchers 34'5 in the past few years, including the present authors, 6 have reported an increase in the elongation to fracture of many HSLA and dual-phase steels with decreasing temperature down to 77 K. The aim of the present paper is to rationalize this low temperature behavior in terms of strain-rate sensitivity and work-hardening characteristics. Ductility is a general term commonly used to describe a material's resistance to inhomogeneous localized deformation. In the classical Consid~re 7 phenomenology, a specimen in uniaxial tension reaches an unstable condition when 0 =
do" de
- o"
111
where 0 is the work hardening rate and o" and e are true stress and true strain, respectively. If the stress-strain curve is approximated by the Hollomon equation, 8 o" = K e n
[2]
then the strain hardening exponent, n, is equal to the maximum strain for uniform elongation (as defined by Eq. [ 1l). Equations Ill and [2] provide a simple way for measuring ductility. However, in recent years many authors 9-~2 have realized that inhomogeneities in specimen geometry and in microstructure might exist even in the virgin samples. Therefore, it is more appropriate to study the problem of ductility in terms of the effect of inhomogeneities on D. TSENG and N. C. GOEL, Research Associates, and K. TANGRI, Professor and Research Director, are with Metallurgical Sciences Laboratory, Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB R3T 2N2, Canada. Manuscript submitted October 9, 1985. METALLURGICAL TRANSACTIONS A
the stability of plastic deformation. These theories9-~2 are mainly based on the constitutive relationship by Hart 9 d lno" = m d In k + y d e
[31
where m and y are, respectively, the strain rate sensitivity and work hardening coefficient and are defined by m
= [ ~ \Olnk/~.
(0 In o"~ \
de /
Combining with the assumptions such as incompressibility of the specimen material, constancy of the load along the tensile axis at a given instant, and neglecting triaxial stress state and void formation, Eq. [31 can be differentiated to yield an equation of strain gradient. For a tensile specimen c o n t a i n i n g both d e f o r m a t i o n and g e o m e t r i c a l inhomogeneities, where prestrain e0 and initial cr
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