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Large elastoplastic deformation generally occurs in sheet-metal forming processes during stretching, blanking, punching, stamping, bending, bending-unbending, reverse bending and deep drawing. In today’s world, due to very high competition and swift development of products in metal forming industries, there is a growing demand in high precision end products to be manufactured in short duration. It is very essential and important to have a knowledge of an in-depth understanding of material behaviour in all these metal forming steps. Therefore, to predict material behaviour, an accurate material modelling is required by considering the simultaneous effects of strain and strain rate. Classical flow rules are generally used to predict the material behaviour in the post yield range. Overall material deformation can be represented as the change in size, change in shape and their rates. A new generalised relation is developed to represent the material behaviour from elastic range to failure. This relation involves eight material parameters which includes two classical material constants like bulk modulus and shear modulus, two material viscosity terms and four in the form rule which relates elastic strain rate to plastic strain rate. All these material parameters can be obtained from uniaxial tension experiments. The material deformation is 3-D in nature and therefore classical yield criteria is avoided while formulating the relation. Instead, concept of activation energy is used. In the present work, experimental observations and data analysis on the commercial grade aluminium (6082T6) was discussed. The material behavior in the post yield region with new understanding of the material model was presented here for uni-axial loading case. Based on the experimental observations and the results obtained it was found that the both the elastic moduli and the viscosities remain constant throughout the large deformation.

In metallurgy, the microstructure study is very important to evaluate the properties and performances of a material. The Monte Carlo method is applied in so many fields of Engineering Science and it is a very effective method to examine the topology of the computer-simulated structures and exactly resembles the static behavior of the atoms. The effective 2D simulation was performed to understand the grain growth kinetics, under the influence of second phase particles (impurities) is a base to control the microstructure. The matrix size and [Formula: see text]-states are optimized. The grain growth exponent was investigated in a polycrystalline material using the [Formula: see text]-state Potts model under the Monte Carlo simulation. The effect of particles present within the belly of grains and pinning on the grain boundaries are observed. The mean grain size under second phase particles obeys the square root dependency.

Al 7075 is an aluminium alloy with zinc as major element. Al 7075 is commonly used in aircraft components, especially for critical parts like wing and fuselage components. In present investigation Al 7075 has been selected subjected to annealing, cryogenic treatment and the combination of annealing and cryogenic treatment for the study of fatigue crack growth subjected to fatigue load at constant amplitude. Specimens were subjected to fatigue crack growth as per ASTM E-647 standards and the results of fatigue crack growth were compared. NASGRO software was used to predict the fatigue crack growth (FCG) and the results are validated using experimental results. Microstructure analysis of metallic specimens was also carried out to study the micro structural changes in specimens undergoing heat treatment and cryotreatment. From the present investigation it has been observed that cryogenic treatment and heat treatments plays vital role in improving fatigue life of Al 7075 components.

The Monte Carlo simulation method is now widely applied to materials science and engineering to the study of the kinetics of grain growth in two dimensions. This review Survey includes the grain growth kinetics, Grain Size and Grain Distribution by Monte Carlo simulation method. The initial distribution of orientations is chosen at random and the system evolves so as to reduce the number of nearest neighbor pairs of unlike crystallographic orientation. The temporal evolution of the microstructure is monitored to yield the time dependence of the size and shapes of the grains. A procedure incorporating the Metropolis algorithm which helps in developing the code for computer simulation is given as examples, two codes written using MATLAB software to simulate microstructure evolution using 2D ISING and POTTS Q-States Model would be demonstrated.The Monte Carlo simulation method is now widely applied to materials science and engineering to the study of the kinetics of grain growth in two dimensions. This review Survey includes the grain growth kinetics, Grain Size and Grain Distribution by Monte Carlo simulation method. The initial distribution of orientations is chosen at random and the system evolves so as to reduce the number of nearest neighbor pairs of unlike crystallographic orientation. The temporal evolution of the microstructure is monitored to yield the time dependence of the size and shapes of the grains. A procedure incorporating the Metropolis algorithm which helps in developing the code for computer simulation is given as examples, two codes written using MATLAB software to simulate microstructure evolution using 2D ISING and POTTS Q-States Model would be demonstrated.

Large scale Potts model Monte Carlo simulation was carried on 3-dimensional square lattices of 1003 and 2003 sizes using the Metropolis algorithm to study grain growth behavior. Simulations were carried out to investigate both growth kinetics as well as the Zener limit in two-phase polycrystals inhibited in growth by second phase particles of single-voxel size. Initially the matrices were run to 10,000 Monte Carlo steps (MCS) to check the growth kinetics in both single phase and two-phase poly-crystals. Grain growth exponent values obtained as a result have shown to be highest (~ 0.4) for mono-phase materials while the value decreases with addition of second phase particles. Subsequently the matrices were run to stagnation in the presence of second phase particles of volume fractions ranging from 0.001to 0.1. Results obtained have shown a cube root dependence of the limiting grain size over the particle volume fraction thus reinforcing earlier 3D simulation efforts. It was observed that there was not much difference in the values of either growth kinetics or the Zener limit between 1003 and 2003 sized matrices, although the results improved mildly with size.

Monte Carlo Potts model simulation was carried out on a 2D square lattice for various surface fractions of second phase particles for over 50,000 iterations. The observations are in good agreement with known theoretical and experimental results with respect to both growth kinetics as well as grain size distribution. Further, the average grain size and the largest grain size were computed for various surface fractions which have indicated normal grain growth and microstructure homogeneity. The surface fraction of the second phase particles interacting with the grain boundaries (Φ), hitherto not computed through the simulation route, is shown to vary inversely as the average grain size due to Zener pinning.

2D Potts model Monte Carlo simulation was carried out on a square lattice to investigate the effects of varying the size of second phase particles on the Zener limit of grain growth, in two-phase polycrystals. Simulations were carried out on a 1000^2 size matrix with Q-state of 64, dispersed with second phase particles of various sizes and surface fractions, and run to stagnation. Different grain growth parameters such as mean grain size, largest grain size, fraction of second phase particles lying on grain boundaries, etc., were computed for the pinned microstructures. The pinned average grain size or the Zener limit increased with increase in particle size, as per the classic Smith-Zener equation. The Zener limit scaled inversely with the square root of the particle fraction for all particle sizes, while it scaled exponentially with the fraction of second phase particles lying on the grain boundaries (ϕ), for all particle sizes tested.

Extensive 2D Monte Carlo simulations were carried out on a square lattice to verify the Zener limit in the presence of inert second phase particles. Matrices of various sizes (from 100 to 10,000) were first run to stagnation to investigate the effect of matrix size on the limiting grain size, scaling constant and the fraction of second phase particles interacting with the grain boundaries (ϕ). The optimum matrix size selected was then run to stagnation for a wide range of particle fractions, at different Q-States, to arrive at limiting grain size and other parameters. Larger matrices (⩾1000) were found to be more suitable than smaller matrices to carry out simulation studies, while there was negligible effect on limiting grain size upon any variation in the Q-States. Based on our studies of particle-pinned regimes, a new relationship between the Zener limit and the fraction of second phase particles lying on the grain boundaries, i.e. R ( lim ) ∝ 1 / exp ( ϕ ) , is proposed, while the limiting grain size observed obeys a square root dependence on the particle fraction, agreeing largely with the earlier simulation results in 2D.

For more than three decades now simulation of recrystallization and grain growth phenomena in annealed metals have been studied through a variety of computer modeling techniques including that of Monte Carlo (MC) simulation. In this study, we have been able to show the efficiency of the MC technique by evolving simulated microstructures comparable very closely to real microstructures. The real microstructures were generated in about a 50% cold-worked alloy of Al-4% Cu (Duralumin) annealed to various degrees. The digital microstructures were evolved through a 2D simulation of a square lattice using Potts model Monte Carlo simulation technique based on the Metropolis algorithm. Through our work we have been able to show the close similarity between microstructures of real metals and microstructures digitally evolved through simulation, perhaps for the first time, thereby validating the MC technique as an efficient computer simulation tool for grain growth studies.