A Phase-field Model for Computer Simulation of Lamellar Structure Formation in y-TiAI

In the present paper, a phase-field model is developed to simulate the formation and evolution of lamellar microstructure in γ-TiAl alloys. The mechanism of formation of TiAl lamellae proposed by Denquin and Naka is incorporated into the model. The model describes the formation and evolution of the face-centered cubic (fcc) stacking lamellar zone followed by the subsequent appearance and growth of the γ-phase, involving both the chemical composition change by atom transfer and the ordering of the fcc lattice. The thermodynamics of the model system and the interaction between the displacive and diffusional transformations are described by a non-equilibrium free energy formulated as a function of concentration and structural order parameter fields. The long-range elastic interactions, arising from the lattice misfit between the α, fcc (A1) and the various orientation variants of the γ-phase are taken into account by incorporating of the elastic strain energy into the total free energy. Simulation studies based on the model successfully predicted some essential features of the lamellar structure. It is found that the formation and evolution of the lamellar structure are predominantly controlled by the minimization of the elastic energy of the interfaces between the different fcc stacking groups, low-symmetry product phase γ and the high-symmetry α-phase, as well as between the various orientation variants of the product phase.

A simple model of atomic interactions in noble metals based explicitly on electronic structure

A total energy tight-binding model with a basis of just one s state per atom is introduced. It is argued that this simplest of all tight-binding models provides a surprisingly good description of the structural stability and elastic constants of noble metals. By assuming inverse power scaling laws for the hopping integrals and the repulsive pair potential, it is shown that the density matrix in a perfect primitive crystal is independent of volume, and structural energy differences and equations of state are then derived analytically. The model is most likely to be of use when one wishes to consider explicitly and self-consistently the electronic and atomic structures of a generic metallic system, with the minium of computation expense. The relationship to the free-electron jellium model is described. The applicability of the model to other metals is also considered briefly.

Constitutive model for localized Lüders-like stress-induced martensitic transformation and super-elastic behaviors of laser-welded NiTi wires

The application of the shape memory alloy NiTi in micro-electro-mechanical-systems (MEMSs) is extensive nowadays. In MEMS, complex while precise motion control is always vital. This makes the degradation of the functional properties of NiTi during cycling loading such as the appearance of residual strain become a serious problem to study, in particular for laser micro-welded NiTi in real applications. Although many experimental efforts have been put to study the mechanical properties of laser welded NiTi, surprisingly, up to the best of our understanding, there has not been attempts to quantitatively model the laser-welded NiTi under mechanical cycling in spite of the accurate prediction required in applications and the large number of constitutive models to quantify the thermo-mechanical behavior of shape memory alloys. As the first attempt to fill the gap, we employ a recent constitutive model, which describes the localized SIMT in NiTi under cyclic deformation; with suitable modifications to model the mechanical behavior of the laser welded NiTi under cyclic tension. The simulation of the model on a range of tensile cyclic deformation is consistent with the results of a series of experiments. From this, we conclude that the plastic deformation localized in the welded regions (WZ and HAZs) of the NiTi weldment can explain most of the extra amount of residual strain appearing in welded NiTi compared to the bare one. Meanwhile, contrary to common belief, we find that the ability of the weldment to memorize its transformation history, sometimes known as ‘return point memory’, still remains unchanged basically though the effective working limit of this ability reduces to within 6% deformation.

1-D constitutive model for evolution of stress-induced R-phase and localized Lüders-like stress-induced martensitic transformation of super-elastic NiTi wires

NiTi alloys have been widely used in the applications for micro-electro-mechanical-systems (MEMS), which often involve some precise and complex motion control. However, when using the NiTi alloys in MEMS application, the main problem to be considered is the degradation of functional property during cycling loading. This also stresses the importance of accurate prediction of the functional behavior of NiTi alloys. In the last two decades, a large number of constitutive models have been proposed to achieve the task. A portion of them focused on the deformation behavior of NiTi alloys under cyclic loading, which is a practical and non-negligible situation. Despite of the scale of modeling studies of the field in NiTi alloys, two experimental observations under uniaxial tension loading have not received proper attentions. First, a deviation from linearity well before the stress-induced martensitic transformation (SIMT) has not been modeled. Recent experiments confirmed that it is caused by the formation of stress-induced R phase. Second, the influence of the well-known localized Lüders-like SIMT on the macroscopic behavior of NiTi alloys, in particular the residual strain during cyclic loading, has not been addressed. In response, we develop a 1-D phenomenological constitutive model for NiTi alloys with two novel features: the formation of stress-induced R phase and the explicit modeling of the localized Lüders-like SIMT. The derived constitutive relations are simple and at the same time sufficient to describe the behavior of NiTi alloys. The accumulation of residual strain caused by R phase under different loading schemes is accurately described by the proposed model. Also, the residual strain caused by irreversible SIMT at different maximum loading strain under cyclic tension loading in individual samples can be explained by and fitted into a single equation in the proposed model. These results show that the proposed model successfully captures the behavior of R phase and the essence of localized SIMT.

Modelling and characterization of ultrasonic consolidation process of Aluminium alloys

Ultrasonic consolidation process is a rapid manufacturing process used to join thin layers of metal at low temperatures and low energy consumption. In this work, finite element method has been used to simulate the ultrasonic consolidation of Aluminium alloys 6061 (AA-6061) and 3003 (AA-3003). A thermomechanical material model has been developed in the framework of continuum cyclic plasticity theory which takes into account both volume (acoustic softening) and surface (thermal softening due to friction) effects. A friction model based on experimental studies has been developed, which takes into account the dependence of coefficient of friction upon contact pressure, amount of slip, temperature and number of cycles. Using the developed material and friction model ultrasonic consolidation (UC) process has been simulated for various combinations of process parameters involved. Experimental observations are explained on the basis of the results obtained in the present study. The current research provides the opportunity to explain the differences of the behaviour of AA-6061 and AA-3003 during the ultrasonic consolidation process. Finally, trends of the experimentally measured fracture energies of the bonded specimen are compared to the predicted friction work at the weld interface resulted from the simulation at similar process condition. Similarity of the trends indicates the validity of the developed model in its predictive capability of the process. © 2008 Materials Research Society.

FE Simulation of Viscoplastic Consistency Model

Finite element (FE) simulations provides an inexpensive alternative for material testingof new metal alloys. Carrying out experimental testing is expensive. Nanoindentation is particularly costly due to the equipment needed to work on such a scale. FE simulations provide an inexpensive means of material testing if accurately carried out. This paper will demonstrate the applicability and accuracy of using FE modelling for basic material tests and will propose that the viscoplastic model may be used for nanoindentation testing. The simulations will test the Young’s modulus of materials during analysis when an Abaqus VUMAT is used. The viscoplastic model is incorporated into a subroutine and is tested at the macroscopic scale against previous published results.

Modeling of titanium alloys by using artificial neural networks

Titanium alloy exhibits an excellent combination of bio-compatibility, corrosion resistance, strength and toughness. The microstructure of an alloy influences the properties. The microstructures depend mainly on alloying elements, method of production, mechanical, and thermal treatments. The relationships between these variables and final properties of the alloy are complex, non-linear in nature, which is the biggest hurdle in developing proper correlations between them by conventional methods. So, we developed artificial neural networks (ANN) models for solving these complex phenomena in titanium alloys.

In the present work, ANN models were used for the analysis and prediction of the correlation between the process parameters, the alloying elements, microstructural features, beta transus temperature and mechanical properties in titanium alloys. Sensitivity analysis of trained neural network models were studied which resulted a better understanding of relationships between inputs and outputs. The model predictions and the analysis are well in agreement with the experimental results. The simulation results show that the average output-prediction error by models are less than 5% of the prediction range in more than 95% of the cases, which is quite acceptable for all metallurgical purposes.