Elsevier

Materials & Design

Volume 25, Issue 7, October 2004, Pages 547-554
Materials & Design

Prediction of elevated temperature fatigue crack growth rates in TI-6AL-4V alloy – neural network approach

https://doi.org/10.1016/j.matdes.2004.03.003Get rights and content

Abstract

The results obtained from two experimental test programs (TP-1 and TP-2) were used to train neural networks to predict elevated temperature, fatigue crack growth rates in Ti-6Al-4V alloy. Two programs, TP-1 and TP-2, were conducted at room and elevated temperatures under high humidity and laboratory air environments, respectively. While elevated temperature effects were investigated in TP-2, stress ratio effects were studied in TP-1 using several stress ratios. Networks were trained using the elevated temperature data to predict the crack growth rates at a given stress intensity under different temperatures. The experimental and predicted fatigue crack growth rates showed a least squared error of 0.03. Thus, this approach was found to predict fatigue crack growth rates in Ti-6Al-4V alloy at elevated temperatures.

Introduction

Artificial neural networks (ANNs) approach has been used in fatigue to predict the low cycle fatigue, environmentally assisted cracking and other cracking behaviors. Since the networks use the experimental data, estimates of life are based on data and not preconceived trend or a curve that predicts life. The ANN is an information processing system, its structure is modeled on the biological neural structure. Fig. 1 illustrates a biological neuron and its three parts namely soma, axon, and dendrite, respectively. Each neuron in ANN receives input from several others. The signals generated in soma are transmitted to other neurons through an extension on the cell body called axon or nerve fibers. Another kind of extensions around the cell body is the dendrites, which are responsible for receiving the incoming signals generated by other neurons. As seen in figure, two neurons connect at the end of axon and generate a dendrite, which is also called synapse. The ANN format is a model that is comprised of simple processors, called neurons or nodes and numerous connections between them. Each connection is associated with some numerical value called a weight. Each neuron unit is stimulated by the sum of incoming weighted signals and transmits the activated response to other connected neurons. Such a network represents an efficient and parallel computational entity and compares the input with the target data to predict crack growth rates.

The type of ANN used here is known as a back-propagation network. Back-propagation describes the learning algorithm and not the network structure. Fig. 2 shows the typical architecture of a back-propagation artificial neural network that consists of one input layer, one hidden layer and one output layer. The typical architecture is fully interconnected. Unlike the hidden and output layers, the input layer does not have any processing units and receives the input patterns and transmits the signals to the next layer. The back propagation layers can learn when presented with input and target output pairs and a learning rule. Learning or training involves modifying the connection weights until the network is capable of reproducing the target output within some specified error margin, Fig. 3. The connection weights are adjusted such that a mean squared error is minimized. This is done by continually changing the values of the weights in the direction of the steepest descent with respect to the error. Training takes place in an iterative fashion. Each iteration cycle involves a forward step followed by a back-propagation step to update the connection weights. The network was considered trained for each step when the least squared error for back propagation was less than 0.01–0.1 depending on a particular scenario. The artificial neuron has a transfer function just like the soma in typical neuron. The output of artificial neuron is the same as axon that connects to the next neuron as input or in the last layer as output of the network as shown in Fig. 4 [1].

Section snippets

Training fundamentals

An artificial neuron can be trained as follows:

Each input of neuron (pj) is multiplied by related weight (wj). For all inputs, Fig. 2, the bias (b) is added to the sum of these multiplies (∑j=1Npjwj) and the argument of transfer function, a, is performed as shown by Eq. (1)n=∑j=1Npjwj+b,where p is input of network, w is weight of each input, b is bias and N is the number of inputs. The network can be calculated with substituting an argument in transfer function Eq. (2). Either a sigmoid Eq. (3)

Training network

Results obtained from two experimental test programs (TP-1 and TP-2) published elsewhere [3], [4] were utilized to train the networks. These experimental programs were conducted to investigate the transition from Regime I to Regime II fatigue crack growth behavior in a room temperature high humidity environment (TP-1) and elevated temperature fatigue crack growth behavior of Ti-6Al-4V alloy (TP-2), respectively [3]. Constant amplitude tests were conducted for both the programs. While TP-1

Results and discussion

One of the objectives of this paper is to develop a trend curve of da/dN versus ΔK at 290 °C. A range of ΔK from 10.69 to 66.31 MPa m1/2 was selected together with test temperature of 290 °C. The results generated by the program are illustrated in Fig. 9(a). No experimental data for 290 °C were used either to train the networks or to generate a tentative curve up to this stage. Once the results were obtained from the ANNs analysis, the crack growth rates predicted were superimposed with the

Conclusions

The ANN approach is found applicable to predict the fatigue crack growth rates at elevated temperatures. The framework used in this study to train the networks with the combination of standard error, correlation coefficient, and experimental data was able to predict the fatigue crack growth rates in Ti-6Al-4V at elevated temperatures. Thus, the architecture used together with the transformation functions were applicable in this case and may be extended to predict the influence of other

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