Prediction of constant amplitude fatigue crack growth life of 2024 T3 Al alloy with R-ratio effect by GP
Graphical abstract
Introduction
Load bearing components and structures contain defects/imperfections either at the time of manufacturing or during service. These defects ultimately lead to cracks under fatigue loading which grow to a critical size leading to catastrophic failure. Therefore, the growth of these cracks should be predictable to provide guidelines for suitable inspection intervals, which ensure that cracks will never propagate and fail prior to detection. In predicting fatigue crack growth life, stress intensity factor range (ΔK) is generally utilized as a crack driving force. However, the apparent effectiveness of ΔK is known to be affected by the load ratio R (minimum load/maximum load), crack closure, overload, crack size, environment, microstructure, geometry, temperature, etc. [1]. The primary loading parameter affecting the fatigue crack growth is the load ratio R, which quantifies the influence of mean load. It is well known that the growth rate either increases or decreases by increasing the value of load ratio under different loading conditions [2], [3], [4]. Therefore, the ability to correlate and predict the fatigue crack growth rate for different load ratios is of significant importance.
Problems associated with fatigue are difficult to solve using conventional mathematical models because of non-linearity, noise, cost, time constraint and above all the associated micro-mechanisms. Soft-computing is a good alternative for handling those complex problems as it is tolerant of imprecision, uncertainty and partial truth. Till date various soft-computing methods e.g. artificial neural network (ANN) [5], [6], [7], fuzzy logic [8] and adaptive neuro-fuzzy inference system (ANFIS) [9], [10] have been used in the field of fatigue. However, prediction of fatigue life using genetic programming (GP) is lacking. In the present work an attempt has been made to predict fatigue life of 2024 T3 aluminum alloy under the influence of load ratio by applying genetic programming. The predicted result has been compared with experimental results as well as the results obtained from one of the authors’ previously proposed [11] artificial neural network model. The results show that GP gives better prediction than ANN.
Section snippets
Genetic programming: Theoretical background
Genetic programming (GP) is a domain-independent problem-solving technique in which computer programs are evolved to solve, or approximately solve, the problems. This technique is based on the Darwinian principle of reproduction and survival of the fittest. Genetic programming addresses one of the central goals of computer science, namely automatic programming; which is to create a computer program that enables a computer to solve a problem.
In genetic programming, first the initial population
Data preparation
In this research, the experimental set up and database created from the fatigue tests are based on the previous work of one of the present author [12]. In that work, material was 7020 T7 aluminum alloy and the crack growth rate prediction was done by analytical method i.e. “Exponential model”. In the present study, 2024 T3 aluminum alloy which is suitable for air-craft structure, has been selected and GP tool has been adopted to predict the crack growth rate. The chemical composition and
GP model development for crack growth rate determination
The main aim of the present investigation was to employ genetic programming technique to predict crack growth rate of 2024 T3 Al alloy under constant amplitude loading with load ratio effect. To reach the stated goal, the whole experimental data consisting of six sets having different load ratios (R = 0, 0.2, 0.4, 0.5, 0.6, and 0.8) were divided into training and validation sets. The training set was constructed with five sets with R = 0, 0.2, 0.4, 0.6, and 0.8 while the remaining one set with R =
Results and discussion
The simulated results from GP model are compared with experimental results and the results obtained from ANN model [11]. The performances of the results are analyzed in details below.
Conclusion
It is well known that prediction of fatigue crack growth life (residual life) of machine components or structures are essential so that they can be timely inspected and repaired before failure. Therefore, fatigue crack growth tests are highly essential which are costly and time consuming. Earlier, several analytical and empirical models have been proposed by different investigators in order to predict fatigue crack growth life under various cyclic loading conditions. Most of the models relate
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