Materials Science Forum Vols. 638-642

Abstract: In this paper, the precipitation behaviour of  (Ni3(Nb,Al)) and ’ (Ni3(Al,Ti,Nb)) phases in the nickel-base superalloy ATI Allvac® 718PlusTM, as well as their kinetic interactions are discussed. Important parameters such as volume fraction, mean radius and number density of precipitates are experimentally determined and numerically simulated as a function of the heat treatment parameters time and temperature. To match the experimentally observed kinetics, the predicted interfacial energy of the precipitates, as calculated for a sharp, planar phase boundary, is adjusted to take into account the interfacial curvature and entropic effects of a diffuse interface. Correction functions for the interfacial energies of  as well as ’ precipitates are presented. Using these modified interfacial energies, the calculated results show excellent agreement with the experimental measurements.

Abstract: Formerly based on empirical knowledge, casting is now inseparable from a scientific approach. Numerical simulation is commonly used to predict and understand the behaviour of alloys and moulds. Even if models used in software are accurate, one of the main difficulties in obtaining good results is the lack of databases. Among the needed data, the knowledge of interfacial thermal properties is one of the most significant in permanent moulding. Indeed, the cooling and solidification of the alloy are controlled by the interfacial behaviour with the mould and impact directly on the microstructure and on the formation of defects (shrinkage…). In die casting thermal conductivity at the interface is controlled by the use of different kinds and thicknesses of coatings. The fact that coatings are used in thin layers and the existence of bonding resistance increase the lack of accuracy of the data. So it appears necessary to be able to determine quickly and easily the HTC for different materials, thicknesses and process parameters. In industrial conditions it is difficult to control and reproduce the coatings. It is also important to be able to measure the HTC directly in the workshop. Many results concerning these problems are available in the literature, but very few able to quickly lead to reliable results. The experimental device which is proposed in the present study allows the determination of the HTC. The design of the software was done to allow the full automation of measurements and calculations in the experiment. Analytical calculation of the HTC is not sufficient to give relevant results due to the phase transformations, so an indirect numerical solution based on Beck’s method has been introduced with the development of a finite difference thermal solver. The three dimensional solver was designed to take into account the heat loss (radiation and convection) and the nonlinearity of thermal equations. Calculations performed from the results of experimental casting temperatures show good match and stability.

Abstract: Thermodynamic stability of Grain boundary in materials under severe plastic deformation was simulated by the Monte Carlo and the phase field methods. Computer simulations were performed on 3-dimensional textured materials. The Monte Carlo simulation results were qualitatively in good agreement with those by the phase field model. The classification of the solution of differential equations based on the mean-field Hillert model describing temporal evolution of the scaled grain size distribution function was in good agreement with those given by the Computer simulations. The ARB experiments were performed for pure Al and Al alloys-sheets in order to validate the computer simulation results concerning the grain boundary stability of textured materials. With use of the Monte Carlo and the phase field methods. Effect of grain boundary mobilises and interface energy given by the computer simulations.

Abstract: Interfacial energies are essential in modelling nucleation, growth and coarsening processes in solid materials; especially nucleation rates respond very sensitively to small changes of this quantity. Thus, the prediction of interfacial energies has attracted the interest of many researchers since many years. In this work, a simple concept for the calculation of energies of coherent interfaces in multicomponent systems is presented. The model advances the classical nearest-neighbor-broken-bond concept for arbitrary interface orientations and interface curvature. The obtained result is simple enough to be expressed in a single, closed equation. Consequently, it can be easily implemented in the framework of classical nucleation theory, or in complex simulation tools for precipitate evolution based on Kampmann-Wagner type models. In this paper, the theoretical background of the model is discussed, and the results are compared to experimental data. Furthermore, a size correction function for small precipitates is presented and applied to the prediction of nucleation rates. Despite the simplicity of the model, the predictions of the model are found to be in satisfactory agreement with experimental evidence.

Abstract: The metallurgical equations have been implemented into the finite difference model to predict the microstructure evolution at different locations in the plate cross-section. Recrystallization kinetics and grain size distributions instead of average grain size values were computed for different rolling schedules. For 20mm plate, the austenite grain sizes at the surface are smaller than at the center, with the exception of the conner where there are the largest grain sizes in throughout cross-section, and the smallest grain sizes can be found near the end of the horizontal central line. The fine austenite grain size and relatively high retained strain could be obtained by modifying rolling practice, such as changing the temperature and thickness at the entrance of finishing rolling and adopting intermediate water cooling. The ferrite grain size and its distribution have a good agreement with the measurements.

Abstract: Two-phase ceramic composite materials, (CMC, e.g. Al2O3/ZrO2), have a non-linear and complex overall response to applied loads due to: different phases, existence of an inital porosity, development of limited plasticity and internal microdefects. All microdefects act as stress concentrators and locally change the state of stress, leading to the development of mesocracks and finally macrocracks. Experimental results show that defects develop mainly inter-granular and cause inhomogeneity and induced anisotropy of the solid. Modelling of such material response is possible by multiscale approach describing different phenomena occuring at different scales: micro- meso- and macro- ones. The paper presents uniaxial tension process of the Al2O3/ZrO2 composite with the gradual degradation of the material properties due to different defects development.

Abstract: A non-simple continuum model is adopted to grossly describe the behaviour of elastic microcracked bodies. The constitutive relations, obtained using a multiscale modelling based on the hypotheses of the classical molecular theory of elasticity, allow taking into account the microscopic features of the material. Referring to a one-dimensional microcracked bar, the possibility of the continuum to reveal the presence of internal heterogeneities is investigated.

Abstract: The importance of a multiscale modeling to describe the behavior of materials with microstructure is commonly recognized. In general, at the different scales the material may be described by means of different models. In this paper we focus on a specific class of materials for which it is possible to identify (at the least) two relevant scales: a macroscopic scale, where continuum mechanics applies; and a microscale, where a discrete model is adopted. The conceptual framework and the theoretical model were discussed in previous work. This approach is well suited to study multifield and multiphysics problems. We present here the multiscale algorithm and the computer code that we developed to implement this strategy. The solution of the problem is searched for at the macroscale using nonlinear FEM. During the construction of the FE solution, the material behavior needs to be described at Gauss points. This step is performed numerically, formulating an equivalent problem at the microscale where the inner structure of the material is described through a lattice-like model. The two scales are conceptually independent and bridged together by means of a suitable localization-homogenization procedure. We show how different macroscopic models (e.g. Cauchy vs. Cosserat continuum) can be easily recovered starting from the same discrete system but using different bridges. The interest of this approach is shown discussing its application to few examples of engineering interest (composite materials, masonry structures, bone tissue).

Abstract: A hybrid numerical-experimental approach is used to characterize the macroscopic mechanical behaviour of polymer foams. The method is based on characterization of foams with X-ray Computed Tomography and conversion of the data to Finite Element (FE) models. Results of FE analyses revealed that plasticity has a large influence on the mechanical response of these structures.

Abstract: The homogenization of elastic periodic plates is as follows: The 3D heterogeneous body is replaced by a homogeneous Love-Kirchhoff plate whose stiffness constants are computed by solving an auxiliary boundary problem on a 3D unit cell that generates the plate by periodicity in the in-plane directions. In the present study, a generalization of the above mentioned approach is presented for the random case. The homogenized bending stiffness and the moduli for in-plane deformation of a plate cut from a block of composite material, considered to be a statistically uniform random material in the in-plane directions, are defined in three equivalent manners: a) the first definition considers statistically invariant stress and strain fields in the infinite plate. In the second and third definitions, a finite representative volume element of the plate is submitted to suitable b) kinematically uniform boundary conditions and c) statically uniform boundary conditions. The relationships between these three definitions are studied and bounds are derived.