Dislocation substructure as a function of strain in a dual-phase steel
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INTRODUCTION
T H E R E have been many investigations concerning the relationship between microstructure and mechanical properties of dual-phase steels. ~,2,3The microstructures of dualphase steels are complex, and may consist of mixtures of martensite, retained ferrite (ferrite present at the intercritical annealing temperature), epitaxial ferrite (ferrite formed by transformation of austenite by epitaxial growth on retained ferrite during cooling from the intercritical annealing temperature), retained austenite, and various types of ferritecarbide aggregates. Rarely have all of the microstructural features been taken into account in correlation of mechanical properties with microstructure. For some properties, differentiation of the various components of complex dual-phase steel microstructures appears to be unnecessary. For example, ultimate tensile strength is a linear function of volume fraction martensite in most dual-phase steels. 4'5 However, the strain-dependent flow stress is a more complex function of dual-phase microstructures. 5 The latter complexity may be related to the high density of unpinned dislocations in the ferrite immediately adjacent to the martensite patches in dual-phase steels 6,v and the heterogeneous dislocation distributions and variable strain hardening characteristics of the retained and epitaxial ferrite which make up the matrix of dual-phase steels. 6,8 Several theoretical models have been proposed to explain the deformation behavior of dual-phase steels. 9 ~2 Most of these models treat each constituent of the microstructure as a continuum, and the mechanical properties of each constituent are assumed to be independent of the other elements in the microstructure. Another assumption of many of these models is that the martensite deforms to approximately the same extent as the ferrite. However, the results of several studies indicate that the deformation of a dual-phase steel is inhomogeneous, with the strain in the ferrite much greater than the strain in the martensite. 7'~3-15 A mechanism which is based on the accumulation of dislocations in a material which deforms inhomogeneously has been proposed by D.A. KORZEKWA, formerly Research Assistant at the Colorado School of Mines, is now Research Engineer, Los Alamos Scientific Laboratory, Los Alamos, NM 87544. D.K. MATLOCK, Charles E Fogarty Professor, and G. KRAUSS, AMAX Foundation Professor, are with the Department of Metallurgical Engineering, Colorado School of Mines, Golden, CO 80401. Manuscript submitted June 15, 1983.
METALLURGICAL TRANSACTIONS A
Ashby, ~6 and cited 7 as responsible for the high work hardening rates typical of dual-phase steels. Unlike most steels, the stress-strain behavior of dualphase steels frequently cannot be approximated by a simple parabolic function over the entire strain range, i.e., dualphase steels do not exhibit single n values. 4'6 Analysis with constitutive equations has indicated that the stress-strain curve of a dual-phase steel may be divided into as many as three strain regions, each de
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