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

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.     

Boundary friction for thermoelastic martensitic transformations

This paper is mainly to discuss the free energy, phase boundary friction and reversibility for thermoelastic martensitic transformations. A method is suggested to obtain, quantitatively, the energy consumed for boundary friction. The base for this calculation is the phenomenological theory suggested by authors before. Applications and results of the method for different data are studied. Comparison of this method with that of Ortin and Planes is discussed. The basic viewpoint in this paper is that the energy consumed for boundary friction converts totally into irreversible heat. This is different from the “entropy argument” of Ortin and Planes. The base of this argument is also reviewed.     

A new examination of volume fraction effects during particle coarsening

All previous studies of particle coarsening have shown that only one possible steady state particle size distribution (P.S.D.) is possible at any given volume fraction of the second phase and that the mean particle size follows a cubic growth law with time. Thus all initial P.S.D.'s will gradually approach this P.S.D. and growth rate on ageing. The present paper shows theoretically that there appear to be many possible P.S.D.'s at a given volume fraction and these all show cubic growth with time, although at different rates. It has been possible to study the effect of volume fraction on growth rates of similar P.S.D.'s. It is found that the growth rate increases with volume fraction but that the rate varies with the actual P.S.D. considered. Numerical analysis of coarsening has been carried out integrating both forwards and backwards with time. This has confirmed the existence of multiple steady state P.S.D.'s at a given volume fraction. It has also been shown that any arbitrary P.S.D. will develop towards that steady state distribution which has a similar size distribution at large radius values. Coarsening can be minimized by ensuring that the particles formed initially are all of comparable radius.     

Computer simulation of reversible martensitic transformations

This article reports the results of computer simulation studies of reversible, athermal martensitic transformations in idealized, two-dimensional crystals. The transformation is accomplished by se-quentially transforming elementary cells. The model accounts for the elastic strain developed during the transformation, assuming homogeneous elastic constants, negligible interfacial tension, and no external stress. The effects of frictional resistance to the transformation and plastic relaxation of the elastic strain are included in a simple way. The model is used to study the sources of hysteresis in the temperature-transformation (TT) curve and in the microstructural transformation path when the transformation is reversed. The central result is that some hysteresis is inevitable in a transformation of the type studied here. Even in the absence of friction and plastic relaxation, the transformation follows a path in which sequential elements of martensite relax the elastic strain of those that have previously formed. This causes the martensite to form in bursts and has the consequence that the reverse transformation does not reverse the path of the forward transformation. Friction and plastic relaxation increase hysteresis.     

A general mechanism of martensitic nucleation: Part II. FCC → BCC and other martensitic transformations

The general mechanism of martensitic nucleation by faulting from groups of existing dislocations, as proposed in Part I, is applied to the fcc → bcc, bcc → fcc, bcc → hcp, and related transformations, including mechanical twinning. Where thermodynamic data are available, the conditions at the observedM _s temperatures are consistent with nucleation from a defect composed of four or five properly spaced lattice dislocations. Examples of nucleation by faulting on the planes predicted are found in published electron microscopy. The faults are observed at the types of sites where the required dislocation groups are expected. These include grain boundaries, incoherent twin boundaries, and inclusion particle interfaces. Having defined the function of a nucleation site, mechanisms of strain induced nucleation and autocatalysis are then considered. This paper is Part II of a three-part series based on a thesis submitted by G. B. Olson for the degree of Sc.D. in Metallurgy at the Massachusetts Institute of Technology in June 1974.     

Molecular dynamics simulation of martensitic transformations in NiAI

Both thermally induced and stress-induced coherent nucleation and growth of an L1₀ martensitic phase have been examined and analyzed at the atomic level in molecular dynamics (MD) computer simulations of an ordered B2 NiAl lattice array using embedded atom method (EAM) interatomic potentials. Both heterogeneous and homogeneous nucleation are observed, the latter requiring an applied stress. The heterogeneous process occurs at ledge corners on stepped free surfaces and can be analyzed in terms of localized soft modes. The homogeneous nucleation can be understood as resulting from a strain spinodal instability which produces a morphology reminiscent of chemical spinodal decomposition. Self-accommodating martensite variants appear very early in the growth process, and all interfaces remain coherent with no detectable presence of dislocations in these early stages. Formerly Graduate Student, Department of Metallurgy, Institute of Materials Science, University of Connecticut. This article is based on a presentation made during TMS/ASM Materials Week in the symposium entitled “Atomistic Mechanisms of Nucleation and Growth in Solids,” organized in honor of H.I. Aaronson’s 70th Anniversary and given October 3“5, 1994, in Rosemont, Illinois.     

Massive and martensitic transformations in the Ag−Al system

The Ag?Al system in the composition range of stability of the high temperature β phase exhibits two-phase field characteristics which make it an ideal system for examining massive phase transformations. Experiments have established that the β phase can be retained to room temperature following cooling rates of the order of 10⁵ deg per sec. Subsequently, the M_s temperatures have been determined for the composition range Ag-24.4 to 25.0 at. pct Al. Since the ζ phase can also be retained, it has been possible to examine the β→ζ _m , β→μ _m and ζ→μ _m 3composition-invariant, nonmartensitic phase transformation at a single composition. In addition, the two high-temperature phases, β and ζ, are associated with a congruent point at Ag-24.5 at. pct Al, the width of the two-phase field increasing at higher and lower aluminum concentrations. This has permitted an investigation of the morphology of the ζ _m -product for a range of compositions and cooling rates, the latter determining the extent of undercooling at which the reaction occurs. In particular, that morphology representative of a given degree of supercooling has been compared for several compositions and the interdependence of cooling rate and parent/product coherency (as revealed by the shape of the resulting ζ _m -phase) has been examined.     

Stabilization of retained austenite due to partial martensitic transformations

The stabilization effect of retained austenite has been studied using FeNiC alloys with M_s temperatures below 0°C via a two-step cooling procedure, i.e. the samples were first cooled to a temperature (T_a) below M_s temperature and then heated to room temperature (RT), after being held at RT for a while, the samples were recooled to low temperatures (23 or 82 K) and then heated to RT. It was found that, during the second step of cooling, the martensitic transformation occurred at a temperature of M_s′ which was lower than T_a. With increasing the amount of martensite formed during the first cooling, the difference in the martensitic transformation starting temperatures, ΔM_s = M_s − M_s′, increased. The mechanism of the stabilization of retained austenite during the second step of cooling is proposed to be mainly due to the inhibition effect produced by the previously formed martensite. The aging processes, which retard the growth of the previously formed martensite plates and reduce the number of the available nucleation sites, are the necessary conditions for the above mechanism to operate. By simplifying the internal resisting stress acting on the retained austenite due to the existence of martensite phase as a hydrostatic compressive stress, which increases with increasing the amount of martensite, the change in ΔM_s is discussed from a thermodynamic point of view.     

X-ray study of phase transformations in martensitic Ni-Al alloys

The formation of the Ni₅Al₃ and Ni₂Al phases in Ni-Al alloys with L1o ↔ B2 thermoelastic martensitic transformation has been studied by X-ray analysis. Ni₅Al₃ can form both the L1o and B2 structures, but the kinetics of L1o → Ni₅Al₃ and B2 → Ni₅Al₃ reactions are significantly different. A homogeneous mechanism for the former reaction and a mechanism of precipitation and growth for the latter are proposed. Ni₂Al forms from the B2 structure by the complex rearrangement of atoms. The initial stage of this reaction proceeds very rapidly and involves segregation of Ni atoms into Ni-rich zones leading to a Ni depletion in the surrounding regions. The nucleation of Ni₂Al retards the Ni₅Al₃ formation, so preaging in the B2 region affects the kinetics of the L1o → Ni₅Al₃ reaction on further aging in the L1o region. The microstructural mechanism for this effect is suggested.     

氧化铈掺杂氧化锆的等温和非等温马氏体相变

Martensitic transformation behavior was studied for zirconia containing 4%～10% CeO2 (in mole fraction) by using a dilatometric method. The Ms (Martensite start temperature) decreased near linearly with increasing CeO2. Different transformation modes were observed depending on the composition and cooling rate. ZrO2 containing 6% CeO2 showed isothermal transformation behavior, whereas ZrO2 containing 9% and 10% CeO2 showed athermal transformation behavior. However, ZrO2 containing 8% CeO2 showed either isothermal or athermal transformations behavior depending on the cooling rate. A TTT (Time-Temperature-Transformation) diagram was proposed for ZrO2 containing 8% CeO2.     

Comparison of interfacial structure-related mechanisms in diffusional and martensitic transformations

Some central problems in understanding the similarities of and the differences between ledgewise martensitic and ledgewise diffusional growth are examined. Martensitic growth can be described in terms of a lattic correspondence and a plane undistorted by the shear transformation. Diffusional growth can be similarly described in some cases but not in others. On the basis of the Sutton-Balluffi definitions of glissile and sessile boundaries, only misfit dislocations (on terraces or risers) or orthogonal sets of disconnections provide a truly sessile interface. When closely spaced structural ledges (now termed “structural disconnections”) are present during diffusional growth, they must have been glissile in the formation of a local equilibrium structure during the initial stages of growth. Once they are in local equilibrium and evenly spaced, however, they can only move synchronously because of their local strain interaction. Under these circumstances, extrinsic sources of growth ledges are required to move such interfaces in a diffusional manner. During martensitic growth, however, disconnections in the form of transformation dislocations can move freely in a synchronous manner. Also, on this basis, the apparent (undistorted) habit plane is generally useful in deducing the transformation mechanism during martensite formation, but is only occasionally so during diffusional growth, where only the terrace plane is generally useful. This article is based on a presentation in the symposium “Interfacial Dislocations: Symposium in Honor of J.H. van der Merwe on the 50th Anniversary of His Discovery,” as part of the 2000 TMS Fall Meeting, October 11–12, 2000, in St. Louis, Missouri, sponsored under the auspices of ASM International, Materials Science Critical Technology Sector, Structures.     

Autocatalysis: The self-induced growth of martensitic phase transformations in ceramics

The phenomenon of autocatalysis, wherein a region of elastic phase transformation creates stresses sufficient to drive alone further transformations, is studied for two specific configurations: a rectangular strip and an infinite row of equally spaced circular spots. The phenomenon is associated, not exclusively, with dilatational strains triggered by critical levels of maximum in-plane shear stress. The analysis predicts that there may be a minimum critical transformation stress level below which spontaneous transformation occurs.