Acta Metall Research Articles

Kinetics of crystallization of amorphous Cu50Ti50 alloy

The kinetics of crystallization of amorphous Cu50Ti50 alloy has been studied with the help of non-isothermal scanning experiments in a differential scanning calorimeter. The thermograms at different scanning rates show a sharp crystallization peak followed by a broad, diffuse exothermic event. The method suggested [K. Matusita, S. Sakka, Phys. Chem. Glasses 20 (1979) 77] and the peak shift method given by Kissinger have been utilized to derive important kinetics parameters namely activation energy of crystallization Ec, Avrami exponent, n; and dimensionality of growth m. The derived value of Ec=303±83kJ/mol, obtained via the modified Kissinger equation, is in fair agreement with the reported value 280kJ/mol for Cu50Ti50 [K.H.J. Buschow, Acta Metall. 31 (1983) 155; Scripta Metall. 17 (1983) 1135] and 261.2kJ/mol for Cu40Ti60 glass reported by Miao et al. The results indicate bulk crystallization in the present amorphous alloy. The dimensionality of growth has been found to decrease with an increase in the heating rate.

Grain size dependence of the activation parameters for plastic deformation: Influence of crystal structure, slip system, and rate-controlling dislocation mechanism

A critical review of available results on the dependence of grain size on the activation parameters for deformation, specifically, the activation volume, V*, and the thermal component of flow stress, σ*, has been carried out with a view to verifying the Armstrong prediction that identifies the Hall-Petch (H-P) intercept with the easy slip system and the H-P slope with the most difficult system in polycrystals. The influence of slip system choice is demonstrated using results on Cd and Zr. The Armstrong prediction is valid for basal slip hcp metals, such as Cd and Zn, with V* and σ* determined by the difficult pyramidal slip. For the prism slip metals such as Zr and Ti, V* and σ* are controlled by interstitial solutes and are independent of grain size. The results on Zr are used to highlight the influence of dynamic strain aging on the H-P parameters. In bcc metals, in which the Peierls-Nabarro barrier is the rate-controlling obstacle, V* and σ* are again independent of grain size. For fcc metals, correlation of the H-P slope with the cross-slip stress, predicted by the Armstrong model, has been demonstrated for a few cases. The variation of V* with grain size in Ni as reported by Narutani and Takamura (Acta Metall. Mater., 1991, vol. 227, pp. 2037–49) is newly interpreted in terms of the Armstrong model that associates the H-P intercept in fcc metals with dislocation intersections and the H-P slope with cross-slip, and provides realistic results for the activation volumes for the two processes.

Strain localization phenomena associated with static and dynamic strain ageing in notched specimens: experiments and finite element simulations

The aim of the present work is to use an available constitutive model for the description of the Portevin–Le Châtelier effect to simulate the deformation of notched specimens in tension (smooth and sharp U-notched specimens). This model can be used to account for dynamic strain ageing as suggested by Estrin et al. [Acta Mater. 49 (2000) 1087] but also static strain ageing as suggested by Kubin et al. [Acta Metall. Mater. 40 (1992) 1037]. The experimental material studied is an Al–Cu alloy, displaying dynamic strain ageing at room temperature. Regarding Lüders band propagation, the experimental material studied is a mild steel. This work shows that the PLC serrations disappear progressively on the macroscopic curve when the notch radius decreases. However, strain localization still takes place in the deformed notched zone, and can escape from the notched zone. Regarding the Lüders behavior, the computed spreading of deformation bands is in agreement with experimental observations.

Linear morphological stability analysis of the solid-liquid interface in rapid solidification of a binary system.

The interface stability against small perturbations of the planar solid-liquid interface is considered analytically in linear approximation. Following the analytical procedure of Trivedi and Kurz [Acta Metall. 34, 1663 (1986)]], which is advancing the original treatment of morphological stability by Mullins and Sekerka [J. Appl. Phys. 35, 444 (1964)]] to the case of rapid solidification, we extend the model by introducing the local nonequilibrium in the solute diffusion field around the interface. A solution to the heat- and mass-transport problem around the perturbed interface is given in the presence of the local nonequilibrium solute diffusion. Using the developing local nonequilibrium model of solidification, the self-consistent analysis of linear morphological stability is presented with the attribution to the marginal (neutral) and absolute morphological stability of a rapidly moving interface. Special consideration of the interface stability for the cases of solidification in negative and positive thermal gradients is given. A quantitative comparison of the model predictions for the absolute morphological stability is presented with regard to experimental results of Hoglund and Aziz [D. E. Hoglund and M. J. Aziz, in Kinetics of Phase Transformations, edited by M.O. Thompson, M. J. Aziz, and G. B. Stephenson, MRS Symposia Proceedings No. 205 (Materials Research Society, Pittsburgh, 1991), p. 325] on critical solute concentration for the interface breakdown during rapid solidification of Si-Sn alloys.

A constitutive model for fcc single crystals based on dislocation densities and its application to uniaxial compression of aluminium single crystals

A new dislocation density based constitutive model for fcc single crystals at elevated temperatures is developed. In addition to former composite models [Acta Mater 48 (2000) 4181; J Mater Proc Technol 123 (2002) 155; Acta Metall Mater 41 (1993) 589; Acta Metal 31 (1983) 1367] it distinguishes the individual slip systems and thus directly accounts for latent hardening. This distinction is an essential prerequisite for a later implementation into crystal plasticity finite element models. The model is applied to hot compression tests of aluminium single crystals with their 〈1 1 0〉 axis parallel to the compression axis. The predicted stress strain curves fit the experimental observations very well for a strain rate range from 1×10 −5 to 1×10 −1 s −1 and a temperature range from 623 to 723 K using a single set of parameters.

Sintering kinetics by structural transition at grain boundaries in barium titanate

For its analysis and understanding, sintering has been conventionally assumed to occur in proportion to driving force [J. Appl. Phys. 36 (1955) 1205; Acta Metall. 13 (1965) 227; Mater. Sci. Eng. 48 (1981) 53; Ceramic Processing and Sintering, Marcel Dekker, New York, 2003, p. 470]. This investigation, however, shows for the first time that the conventional assumption does not apply to faceted boundaries and that the microstructure can be frozen for faceted boundaries. A structural transition from rough to faceted was induced in BaTiO 3, by changing oxygen partial pressure. As long as the boundary was rough, continuous grain growth and densification occurred with sintering time, in agreement with the conventional assumption. With the onset of the structural transition from rough to faceted, however, grain growth and densification rates were reduced and became zero at the completion of the transition. This result demonstrates that critical driving forces are present for grain growth and densification for faceted boundaries, unlike the conventional understanding. The result also suggests that the formation or maintenance of faceted boundaries is crucial to inhibit grain growth and thus to produce ultrafine-structured materials.

Anisotropic elasto-plastic finite element analysis using a stress–strain interpolation method based on a polycrystalline model

This paper describes a stress–strain interpolation method to model the macroscopic anisotropic elasto-plastic behavior of polycrystalline materials. Accurate analytical descriptions of yield loci derived from crystallographic texture [Int. J. Plasticity 19 (2003) 647; J. Phys. IV France 105 (2003) 39] are an interesting alternative to finite element models, where the macroscopic stress is provided by an averaging of microscopic stresses computed on a set of representative crystallites [Acta Metal 22 (1985) 923; Int. J. Plasticity 5 (1989) 67]. The parameters of the analytical functions modeling the yield locus are identified by comparison with a high number of stress tensors computed, for instance, by the well-known Taylor model [J. Inst. Metal 62 (1938) 307]. This identification method depends on the crystallographic texture and should be applied each time that the plastic strain has induced a significant texture evolution. The stress–strain interpolation method accurately describes the anisotropic material behavior in a narrow stress direction defined by only five stress points. The cost of texture updating is then greatly reduced compared to a full analytical function of the yield locus. After the mathematical description of the stress–strain interpolation method, its validity is demonstrated on two non-radial strain paths. The simulations of a deep drawing experiment allow comparing model predictions and measurements. Accuracy and CPU time of the interpolation stress–strain method are judged against two other models, respectively based on a complete analytical yield locus and on the averaging of crystallite stresses.

On precipitate induced hardening in crystal plasticity: algorithms and simulations

A crystal elasto-plastic setting was suggested by the authors in Han et al. [Int. J. Plasticity (in press)] to account for precipitate shapes and structure in the kinematic hardening description. In this article, the corresponding elastic–plastic rate independent algorithmic treatment is derived and numerical simulations performed. For the convenience of the computational derivation and implementation, the material formulation is formulated in the unrotated intermediate configuration mapped by the plastic part of the deformation gradient. Several descriptions for the evolution equations, based on the elastic inclusion model [Acta Metal. 29 (1981) 1797] of the kinematic hardening, are suggested and discussed. Finally, some numerical examples are presented to assess the performance of the suggested model and its rate-independent algorithmic treatment.

The local internal stress in ferromagnetic alloys. Dislocation–solute interaction model for local internal stress source

In order to elucidate the Raleigh and Left Shift phenomena encountered in the investigations into damping capacity (internal friction) of ferromagnetic alloys (Acta Metall Sin 34 (1998) 1039; Trans Jpn Inst Met 25 (1984) 891; Trans Jpn Inst Met 20 (1979) 409; Mater Sci Forum 119–121 (1993) 415; Metall Mater Trans A 25 (1994) 111), the solute atom model (Mater Design (in press)) for the local internal stress source is modified and replaced by the dislocation–solute interaction model proposed by the authors. The coercive force as well as crystal lattice parameter of FeCrAl and FeCrAlSi alloys was measured and the local internal stress of these alloys was discussed. It is pointed out that only when the alloy is fully re-crystallized, the potential of damping capacity could be fully developed, and at the pre-requisite of which do not lower the energy density of domain walls (Mater Design 21 (2000) 541), to choose those alloying element that distort crystal lattice slightly is benefit to improve the damping capacity of ferromagnetic alloys.

Grain boundary pinning by Al 6Mn precipitates in an Al–1wt%Mn alloy

The grain boundary area per unit of volume, S V, and the interface area per unit of volume of Al 6Mn precipitates, S VP, were measured in a high purity Al–1wt%Mn alloy for an annealing time of 3600 s at temperatures ranging from 500 to 620 °C. The experimental results show very good agreement with the expression proposed by Rios [Acta Metall. 35 (1987) 2805]: S VL=3 S VP where S VL is the limiting grain boundary area per unit of volume. This expression is easier to verify experimentally than its equivalent form: R L= r/6 f, where r is the particle radius, f is the volume fraction of the particles and R L is the limiting grain radius.

A pressure-sensitive yield criterion under a non-associated flow rule for sheet metal forming

Spitzig and Richmond [Acta Metall. 32 (1984) 457] proposed that plastic yielding of both polycrystalline and single crystals of steel and aluminum alloys shows a significant sensitivity to hydrostatic pressure. They further showed that under the associated flow rule, this pressure sensitivity leads to a plastic dilatancy, i.e. permanent volume change, that is at least an order of magnitude larger than observed. Indeed, the plastic dilatancy for most materials is on the order of the measurement error and must be zero in the absence of phase change and significant void nucleation during plastic deformation. A non-associated flow rule based on a pressure sensitive yield criterion with isotropic hardening is proposed in this paper that is consistent with the Spitzig and Richmond data and analysis. The significance of this work is that the model distorts the shape of the yield function in tension and compression, fully accounting for the strength differential effect (SDE). This capability is important because the SDE is sometimes described through kinematic hardening models using only pressure insensitive yield criteria.

A mechanistic approach to damage in short-fiber composites based on micromechanical and continuum damage mechanics descriptions

A micro-macro mechanistic approach to matrix cracking in randomly oriented short-fiber composites is developed in this paper. At the micro-scale, the virgin and reduced elastic properties of the reference aligned fiber composite are determined using micromechanical models [Proc. Roy Soc. Lond. A241 (1957) 376; Acta Metall. 21 (1973) 571; Mech. Mater. 2 (1983) 123], and are then distributed over all possible orientations in order to compute the stiffness of the random fiber composite containing random matrix microcracks. After that the macroscopic response is obtained by means of a continuum damage mechanics formulation, which extends the thermodynamics based approach in [Comp. Sci. Technol. 46 (1993) 29] to randomly oriented short-fiber composites. Damage accumulations leading to initiation and propagation of a macroscopic crack are modeled using a vanishing element technique. The model is validated against the published experimental data and results [Comp. Sci. Technol 55 (1995) 171]. Finally, its practical application is illustrated through the damage analysis of a random glass/epoxy composite plate containing a central hole and under tensile loading.

A selfconsistent formulation for the prediction of the anisotropic behavior of viscoplastic polycrystals with voids

In this work we consider the presence of ellipsoidal voids inside polycrystals subjected to large strain deformation. For this purpose, the originally incompressible viscoplastic selfconsistent (VPSC) formulation of Lebensohn and Tomé (Acta Metall. Mater. 41 (1993) 2611) has been extended to deal with compressible polycrystals. In doing this, both the deviatoric and the spherical components of strain-rate and stress are accounted for. Such an extended model allows us to account for the void and for porosity evolution, while preserving the anisotropy and crystallographic capabilities of the VPSC model. The formulation can be adjusted to match the Gurson model, in the limit of rate-independent isotropic media and spherical voids. We present several applications of this extended VPSC model, which address the coupling between texture, plastic anisotropy, void shape, triaxiality, and porosity evolution.

On precipitate induced hardening in crystal plasticity: theory

A material description for the elasto-plastic deformation of crystals with non-shearable precipitates at finite strains is presented in this article. On the basis of the elastic inclusion model of Bate et al., [Acta Metall. 29 (1981), 1797–1814] the constitutive equations are formulated in a crystal plasticity setting. The anisotropic kinematic hardening for the actual yield condition of the slip systems is described by the averaged accommodation tensor over all precipitates of an aggregate. For needle and disk-like shaped precipitates the incorporation of precipitate rotations is suggested to describe the evolution of back stress terms in the deformation process. The dependencies of the kinematic hardening description on shape, size, and orientation of the precipitates within the deformation process are discussed.

A micromechanical method for particulate composites with finite particle concentration

Many micromechanical models can be obtained by embedding one single ellipsoidal pattern into matrix material to derive localization relation, the direct influence of the other patterns is neglected. An extension of Ponte Castaneda and Willis model (PCW) [J. Mech. Phys. Solids 43 (1995) 1919] to many patterns interaction is proposed for particulate composites with an ellipsoidal distribution of particles. Compared to the models based on one single spherical pattern (Mori–Tanaka model [Acta Metall. 21 (1973) 571] for an isotropic composite) or based on one single ellipsoidal pattern (PCW model for an transverse isotropic composite due to ellipsoidal distribution of particles), the proposed method gives better prediction on the overall elastic properties for particulate composites with finite particle concentration. The extension of the elastic results directly to plasticity are performed with the help of secant moduli method based on second-order stress moment, the prediction on the overall elastic and plastic properties for particulate composites agrees well with the experimental results in literature.

The anomalous contraction on disordering Ni 3Si

Zhou and Bakker (Acta Metall Mater 1994; 42:3009) reported the formation of progressively disordered L1 2 and also a distinct disordered fcc solid solution on ball-milling Ni 3Si with the ordered L1 2 structure. The formation of disordered phases was accompanied by a decrease in lattice parameter, 0.53% for partially disordered L1 2 at a 1ro parameter of ∼0.56, and as much as 2.44% for the disordered fcc. These contractions were attributed to antisite defects. This behaviour is at variance with the generally observed small expansion on such disordering. Further, of the several L1 2 structures disordered by mechanical means, this is the only observation of the co-existence of a disordered L1 2 and a distinct disordered fcc phase. These results have been re-interpreted to show that the diffraction peak identified by them as characteristic of fcc in fact belongs to hexagonal Ni 31Si 12 phase, thus accounting for the major anomaly. The small decrease on partially disordering L1 2 is possibly due to an increase in the valence of Si.

Validation of the tangent formulation for the solution of the non-linear Eshelby inclusion problem

An extension of the Eshelby problem for non-linear viscous materials is considered. An ellipsoidal heterogeneity is embedded in an infinite matrix. The material properties are assumed to be uniform within the ellipsoid and in the matrix. The problem of determining the average strain rate in the ellipsoid in terms of the overall applied strain rate is solved in an approximate way. The method is based on the non-incremental tangent formulation of the non-linear matrix behavior [Acta Metall. 35 (1987) 2983]. In the present work this approximate solution is verified with a good agreement by comparing to finite element calculations for various inclusion shapes and loading conditions.

Kinetics of atomic rearrangement in the processes of crystal growth into undercooled melts

Dendrite crystal growth is one of the examples of crystal growth in undercooled liquids. In spite of a number of attempts to improve the widely quoted model of dendritic crystal growth from undercooled melts (Acta Metall. 35 (1987) 957) the agreement between the theory and the experiment, especially at high undercooling, is still poor. In this study, we show that the temperature of crystal/melt interface of a growing crystal into a deeply undercooled liquid can differ considerably from the melting temperature, thus making the kinetic attachment coefficient to depend on the undercooling temperature, a fact ignored by previous models. For deeply undercooled liquids we propose a new fluctuation model of atomic mobility, viscosity and diffusion, and on its basis a phenomenological model for the temperature dependence of the kinetic coefficient is developed. Analysis of the model and the experimental data shows that the slowed attachment kinetics in deeply undercooled liquids considerably decreases the velocity of crystal growth, and can even lead to glass transition.

A traveling wave solution for coupled surface and grain boundary motion

We study the coupled motion of a grain boundary in a bicrystal which is attached at a “groove root” to an exterior surface which evolves according to surface diffusion in a “quarter loop” geometry (Dunn et al., Trans. Am. Inst. Min. Engrs. 185 (1949) 708), and prove the existence of a unique traveling wave solution for various partially linearized formulations. Our results complement and complete the earlier analysis by Mullins (Acta metall. 6 (1958) 414) where the groove root and the velocity as a function of groove depth were determined. We demonstrate that the net effect of the coupling to the exterior surface is to reduce the overall velocity relative to a freely moving grain boundary by a factor which is small (≈3.5%) for typical parameter values. For extreme values of the parameters, the coupling may cause an increase in the overall grain boundary velocity. No “jerky” or “stop and go” motion is predicted by our solution, and we conjecture why this is so.

Annihilation mechanisms in thin film grain growth

Grain growth in succinonitrile thin films is dominated by topological effects [ Scripta Metall. Mater. 30 (1994) 633; Metall. Mater. Trans. A 26 (1995) 1061; Philos. Mag. 79(4) (1999) 763]. The topological transformations are effected by the shortened length of the grain boundaries [ R.T. De Hoff, in: H. Weiland, B.L. Adams, A.D. Rollet, Grain Growth in Polycrystalline Materials III, TMS, 1998, p. 225; Acta Mater. 48 (1998) 5175]. To explain how these events occur in three dimensions each face of a grain is assumed to behave as predicted by Smith [ Metal Interf. 3 (1952) 65; Contemporary Phys. 25 (1984) 59], and placed in the context of work by Fortes and Ferro [ Acta Metall. 33 (1985) 1697; 1683].