G. B. Olson

Kinetics of strain-induced martensitic nucleation

Intersections of shear bands in metastable austenites have been shown to be effective sites for strain-induced martensitic nucleation. The shear bands may be in the form of ε’ (hcp) martensite, mechanical twins, or dense bundles of stacking faults. Assuming that shear-band intersection is the dominant mechanism of strain-induced nucleation, an expression for the volume fraction of martensite vs plastic strain is derived by considering the course of shear-band formation, the probability of shear-band intersections, and the probability of an intersection generating a martensitic embryo. The resulting transformation curve has a sigmoidal shape and, in general, approaches saturation below 100 pct. The saturation value and rate of approach to saturation are determined by two temperature-dependent parameters related to the fee-bee chemical driving force and austenite stacking-fault energy. Fitting the expression to available data on 304 stainless steels gives good agreement for the shape of individual transformation curves as well as the temperature dependence of the derived parameters. It is concluded that the temperature dependence of the transformation kinetics (an important problem in the development of TRIP steels) may be minimized by decreasing the fee, bec, and hep entropy differences through proper compositional control.

A MECHANISM FOR THE STRAIN-INDUCED NUCLEATION OF MARTENSITIC TRANSFORMATIONS*

Abstract The previous work of Professor W. G. Burgers and Dr. A. J. Bogers is used to develop a mechanism of strain-induced martensitic nucleation, involving two intersecting shear systems. We distinguish between strain-induced nucleation and stress-assisted nucleation, the latter involving the same sites and embryos as does the regular spontaneous transformation. The strain-induced nucleation, on the other hand, depends on the creation of new sites and embryos by plastic deformation; this phenomenon may also contribute in a major way to autocatalytic nucleation during the course of martensitic transformation. For the case of strain-induced nucleation, it is possible to focus on specific intersecting-shear systems when the austenitic stacking-fault energy is low and e (h.c.p.) martensite can form as a part of the shear displacements. It then becomes feasible to extend the intersecting-shear mechanism from this special case to alloys of higher stacking-fault energy, where e is no longer stable relative to the austenite. It should be noted, however, that these events are very early stages in the formation of martensitic plates and relate primarily to the genesis of embryos; the actual growth start-ups which determine the operational (measured) nucleation rates may be controlled by subsequent processes.

A general mechanism of martensitic nucleation: Part I. General concepts and the FCC → HCP transformation

Consideration of the martensitic nucleation process as a sequence of steps which take the particle from maximum to minimum coherency leads to the hypothesis that the first step in martensitic nucleation is faulting on planes of closest packing. It is further postulated that the faulting displacements are derived from an existing defect, while matrix constraints cause all subsequent processes to occur in such a way as to leave the fault plane unrotated, thus accounting for the observed general orientation relations. Using basic concepts of classical nucleation theory, the stacking fault energy is shown to consist of both volume energy and surface energy contributions. When the volume energy contribution is negative, the fault energy decreases with increasing fault thickness such that the fault energy associated with the simultaneous dissociation of an appropriate group of dislocations (e.g. a finite tilt boundary segment) can be zero or negative. This condition leads to the spontaneous formation of a martensitic embryo. For the specific case of the fcc → hcp martensitic transformation in Fe-Cr-Ni alloys, the defect necessary to account for spontaneous embryo formation at the observedMs temperatures may consist of four or five properly spaced lattice dislocations. Such defects are considered to be consistent with the known sparseness of initial martensitic nucleation sites.

A constitutive model for transformation plasticity accompanying strain-induced martensitic transformations in metastable austenitic steels

Abstract We propose a constitutive model which describes the transformation plasticity accompanying strain-induced martensitic transformation in nonthermoelastic alloys. The model consists of two parts: a transformation kinetics law describing the evolution of the volume fraction of martensite and a constitutive law defining the flow strength of the evolving two-phase composite. The Olson-Cohen model for martensite volume fraction evolution is recast in a generalized rate form so that the extent of martensite nucleation is not only a function of plastic strain and temperature, but also of the stress state. A selfconsistent method is then used for predicting the resultant stress-strain behavior. The model describes both the hardening influence of the transformation product, and the softening influence of the transformation itself, as represented by a spontaneous transformation strain. The model is then implemented in a finite element program suitable for analysis of boundary value problems. Model predictions are compared with existing experimental data for austenitic steels. We present results from a few simple analyses, including tensile necking, illustrating the critical importance of stress state sensitivity in the evolution model.

Strain Hardening of Hadfield Manganese Steel

The plastic flow behavior of Hadfield manganese steel in uniaxial tension and compression is shown to be greatly influenced by transformation plasticity phenomena. Changes in the stress-strain (σ−ε) curves with temperature correlate with the observed extent of deformation twinning, consistent with a softening effect of twinning as a deformation mechanism and a hardening effect of the twinned microstructure. The combined effects give upward curvature to the σ−ε curve over extensive ranges of plastic strain. A higher strain hardening in compression compared with tension appears to be consistent with the observed texture development. The composition dependence of stacking fault energy computed using a thermodynamic model suggests that the Hadfield composition is optimum for a maximum rate of deformation twinning. Comparisons of the Hadfield steel with a Co-33Ni alloy exhibiting similar twinning kinetics, and an Fe-21Ni-lC alloy deforming by slip indicate no unusual strain hardening at low strains where deformation is controlled by slip, but an unusual amount of structural hardening associated with the twin formation in the Hadfield steel. A possible mechanism of anomalous twin hardening is discussed in terms of modified twinning behavior (pseudotwinning) in nonrandom solid solutions.

First principles determination of the effects of phosphorus and boron on iron grain boundary cohesion.

Toward an electronic level understanding of intergranular embrittlement and its control in steels, the effects of phosphorus and boron impurities on the energy and electronic properties of both an iron grain boundary and its corresponding intergranular fracture surface are investigated by the local density full potential augmented plane wave method. When structural relaxations are taken into account, the calculated energy difference of phosphorus in the two environments is consistent with its measured embrittlement potency. In contrast to the nonhybridized interaction of iron and phosphorus, iron-boron hybridization permits covalent bonding normal to the boundary contributing to cohesion enhancement. Insights into bonding behavior offer the potential for new directions in alloy composition for improvement of grain boundary-sensitive properties.

Interphase-boundary dislocations and the concept of coherency

Abstract The discrete-lattice concept of coherency applied to interphase boundaries and the elasticcontinuum concept applied to enclosed particles are shown to be mutually consistent. In line with these concepts, a general discrete dislocation description of interphase-boundary structure is developed. It is shown that a coherent interface can contain partial dislocations which we call transformation or ‘coherency’ dislocations. These dislocations accomplish the transformation lattice deformation between the two phases and maintain continuity of the lattice. They are capable of conservative climb and/or glide during the transformation, but their motion is restricted to the plane of the dislocation loop. Strain energy associated with the coherency dislocations can be reduced by misfit or ‘anticoherency’ dislocations, generally having lattice Burgers vectors and producing a lattice-invariant deformation which disrupts the uniformity of the lattice correspondence across the interface and thereby reduces coherency. The anticoherency dislocations move as conventional dislocations.

Stress-assisted isothermal martensitic transformation: Application to TRIP steels

Low-temperature plastic flow in TRIP steels has been found to be controlled by stress-assisted isothermal martensitic transformation. For these conditions, the thermodynamics and kinetic theory of martensitic transformations leads directly to constitutive relations predicting the dependence of flow stress on temperature, strain, strain-rate, and stress-state, consistent with the observed behavior of TRIP steels. Guidelines are obtained for the control of temperature sensitivity, σ -ɛ curve shape, and stress-state effects to achieve novel mechanical properties.

Kinetics of F.C.C. → B.C.C. heterogeneous martensitic nucleation—I. The critical driving force for athermal nucleation

Abstract Employing available experimental data for athermal f.c.c. → b.c.c. martensitic transformation in binary, ternary and multicomponent Fe-base alloys, a model is developed and tested for the critical driving force at the M s temperature. Incorporating the theory of solid solution hardening, we describe the composition dependence of the athermal frictional work for martensitic interface motion governing the kinetics of barrierless heterogeneous nucleation. The available data suggests that the composition dependence of the athermal frictional work is of the same form as that for slip deformation. We have evaluated the athermal strengths of 14 alloying elements Al, C, Co, Cr, Cu, Mn, Mo, N, Nb, Ni, Si, Ti, V and W from the experimental data. Except for Al, Ni and Co, the athermal strengths of the common substitutional alloying elements are similar in magnitude, while the interstitial solutes C and N exert a stronger influence. Previously proposed superposition laws are used to account for the presence of multiple solutes having different athermal strengths. With an improved assessment of the magnetic parameters of alloy systems, the model predicts M s temperatures within ±40 K for M s > 300 K where thermal contributions to the frictional work can be neglected.

A general mechanism of martensitic nucleation: Part III. Kinetics of martensitic nucleation

The growth of martensitic fault embryos in the fault plane, the development of their interfacial structure, and the thickening of the embryos normal to the fault plane are examined as possible rate limiting steps in the total martensitic nucleation process. Growth of the embryos in the fault plane appears the most probable rate limiting step, capable of accounting for both the observed isothermal and athermal kinetic behavior depending on the parameters (such as activation volume) which control the motion of the transformational dislocations. The thermally activated nucleation of dislocation loops responsible for lattice invariant deformations is a possible rate limiting step for some isothermal transformations, though such deformations are not required for all martensitic transformations. Embryo thickening by the nucleation of discrete loops of transformation dislocations appears improbable in bulk material; instead, a plausible pole mechanism for embryo thickening is presented which incorporates existing “forest” dislocations intersected by embryos growing in the fault plane. Lattice softening phenomena may lower the critical chemical driving force for nucleation, but are not essential for martensitic nucleation by the proposed faulting mechanism.