Extraction of Creep Parameters from Indentation Creep Experiment: An Artificial Neural Network- Based Approach

Abstract

Conventional methods for extracting creep properties require conducting several uniaxial tests at different loads, which consumes an intensive amount of material and time. Indentation may minimize the material volume requirement; however, interpretation of indentation creep data in terms of uniaxial creep response, which is the standard practice, is quite challenging. Artificial neural network (ANN) may be used to obtain uniaxial creep parameters from indentation creep experiments; however, it has never been attempted. Here, we use fully connected sequential multi-layered ANN, trained using finite element (FE) indentation creep simulations, to map the observables (displacement, time) of indentation creep experiments to the corresponding uniaxial creep parameters. A constitutive law that relates the creep strain, 𝜖𝑐𝑟𝑒𝑒𝑝 to stress, 𝜎, and time, t, in form of a power-law (e.g., 𝜖𝑐𝑟𝑒𝑒𝑝 = 𝐴 𝜎𝑛𝑡𝛼) is used. Subsequently, multitude of indentation displacement-time curves are generated by conducting FE simulations with varying creep parameters (i.e., A, n and a) used in the constitutive relationship, while keeping the elastic and plastic properties of the material fixed. An indentation displacement-time (𝑑𝑐𝑟𝑒𝑒𝑝-t) curve obtained through FE simulations is fitted using a relationship comprising power-law and exponential terms in time (e.g., 𝑑𝑐𝑟𝑒𝑒𝑝 = 𝑑0 + 𝑚 𝑡𝑏 + 𝑝 𝑒−𝑐𝑡). The pre- processed fitting parameters, thus obtained, are provided as inputs to the ANN. ANN is trained using a back-propagation algorithm based on a batch gradient descent to map these inputs (i.e., 𝑑0, m, b, p and c) to the corresponding creep parameters (i.e., A, n and 𝛼) used in the FE simulations. Performance of the ANN is improved by optimizing its architecture using the Bayesian optimization approach and varying the fitting function, the parameters of which are the inputs to the ANN. The performance of ANN is evaluated based on its prediction on the validation set (size - 10% of the training set) and the learning is continued till the mean squared error of the prediction becomes ~10−3. Finally, the trained ANN is tested on the indentation creep data obtained by testing commercial purity Pb and its prediction is compared with the uniaxial creep parameters. A decent match between the experimental data and the ANN prediction for stress exponent (i.e., n) and time exponent (i.e., 𝛼) is noted.