Constitutive modelling of carbon and alloy steels

Semi-empirical models for the constitutive behaviour of steels often fail to predict the flow stress with sufficient accuracy. A simple neural network structure 3:4: 1 is able to model flow behaviour better than other models available in the literature. It has been developed for four carbon steels, two microalloyed steels, an austenitic stainless steel and a high speed steel

Constitutive model for vanadium microalloyed steel under hot working conditions

Hot compression tests were carried out in the temperature range $850-1150^oC$ at $0.1-60 s^-1$ strain rates. The hyperbolic sine equation and neural networks were used to model the constitutive behaviour. Evaluating constitutive parameters n, Q and A using the usual log – log plots does not yield constant values. The n, Q and A values were determined simultaneously using a non-linear optimisation procedure and were fitted as functions of strain. These relations, in conjunction with the hyperbolic sine equation, describe the constitutive behaviour of the steel. A 3 : 4 : 1 neural network is trained using 75% of the stress – strain data. The network predicts flow stresses and peak strains with good accuracy. Vanadium increases the peak strain, peak stress, and mean flow stress of austenite significantly

Constitutive equation for elevated temperature flow behavior of plain carbon steels using dimensional analysis

Dimensional analysis using π-theorem is applied to the variables associated with plastic deformation. The dimensionless groups thus obtained are then related and rewritten to obtain the constitutive equation. The constants in the constitutive equation are obtained using published flow stress data for carbon steels. The validity of the constitutive equation is tested for steels with up to 1.54 wt%C at temperatures: 850–1200 °C and strain rates: 6 × 10−6–2 × 10−2 s−1. The calculated flow stress agrees favorably with experimental data

Grain-size distribution effects in plastic flow and failure

There has been considerable success over the past five decades in developing a phenomenological and micromechanism-based understanding of plastic flow, creep and superplasticity. Although it is widely known that grain sizes have a distribution in polycrystals and nanocrystals, this factor is usually not included in most analysis of deformation and failure. Experimental observations relating to the influence of grain size distributions are discussed briefly, and an analysis is developed to consider the influence of this factor on the transition from grain boundary strengthening to grain boundary weakening in nanocrystalline materials. The transition from grain boundary strengthening to weakening becomes broader with an increase in the standard deviation of the grain size distribution. It is demonstrated that the observed standard deviations for grain size distributions and nominal errors in grain size measurements can lead to substantially different experimental observations under nominally identical conditions