A new constitutive relationship for alloy TC11
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A New Constitutive Relationship for Alloy TC11 O. Liu, Z. Fu, S. Wu, and H. Yang Engineers need constitutive relationships for planning engineering of high quality forgings. Accordingly, accurately describing the mechanical performance of material deformation is of decisive importance. In this paper, a new method is presented, in which a four-layer backpropagation neural network is built to acquire the constitutive relationship of the T C l l alloy based on the homogeneous compression test. Temperature, effective strain, and effective strain rate are used as the input vectors of the neural network, and the output of the neural network is the flow stress. After the network is trained with experimental data, it correctly reproduces the flow stress in the sampled data. Furthermore, when the network is presented with nonsampled data, it also correctly predicts the flow stress.
Keywords
flow stress, mechanical properties, neural network analysis, Ti-6.SAI-3.5Mo-2Zr-0.3Si, titanium alloy
1. Introduction The nominal composition of the titanium TC 11 alloy, a two phase titanium alloy, is Ti-6.5AI-3.SMo-2Zr-0.3S i. It is commonly used with two different microstructures (Ref 1, 2). The first ((x + 13) microstructure consists of the equiaxial ct phase in the matrix of the transformed 13phase. This is obtained by forging and annealing the alloy at temperatures below the [3 transus (Tf,) followed by a relatively rapid cooling. The second microstructure is the [3 or basketweave microstructure, which is obtained by forging and annealing the alloy above Tli, followed by a relatively rapid cooling. The acicular 13structure is transformed into the metastable equiaxial (ct + [3) structure with heating and deforming of the alloy under the phase transus temperature. The nature and extent of this transus are dependent on deformation temperature and strain. Accordingly, it is practical to control the final structure and its distribution by controlling hot-working parameters. Conversely, because of the sensitivity to temperature and strain rate, low conductivity, and extensive deformation softness phenomenon, the T C l l alloy becomes more nonuniform during forging processes. Therefore, accurately describing the mechanical performance of deformation is very important. During plastic deformation of the TC11 alloy, the variation of the structure is very complex, and the constitutive model is highly nonlinear and requires complex mapping. It is difficult to find the constitutive model of the TC11 alloy in a theoretic method, thus most researchers investigate the constitutive relationship using a large quantity of experiments. Then, a sophisticated mathematical model is postulated to explain the observed behavior, and the material parameters are determined (Ref 3-5). The mathematical formulation and the identification of parameters have an important effect on the constitutive relationship of the TC11 alloy. Artificial neural networks can simulate biological neural systems and are referred to as parallel distributed proces
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