Elsevier

Ceramics International

Volume 39, Issue 2, March 2013, Pages 1991-2002
Ceramics International

Modeling Charpy impact behavior of Al6061/SiCp laminated nanocomposites by genetic programming

https://doi.org/10.1016/j.ceramint.2012.08.051Get rights and content

Abstract

In this work, 4 different gene expression programming models were conducted to predict Charpy impact energy of Al6061-SiCP laminated nanocomposites produced by mechanical alloying. The differences between the models were in their number of genes, head size and chromosomes as well as their linking function. To build the models, 171 pair input-target data were gathered from the literature, randomly divided into 133 and 38 data sets and then were respectively trained and tested by the proposed models. The thickness of layers, the number of layers, the adhesive type, the crack tip configuration, the content of SiC nanoparticles and the test trial number were 6 independent input parameters. The output parameter was Charpy impact energy of the laminated nanocomposites. Although the entire models proposed high performance outcomes, the best performance model had the absolute fraction of variance, the mean absolute percentage error and the root mean square error of 0.9826, 10.217 and 12.432, respectively. All of the training and testing results in the models showed an appropriate performance for predicting Charpy impact energy of Al6061/SiCp laminated nanocomposites in the considered range.

Introduction

Unsuitable impact behavior of Al/SiCP composites make their use limited in applications with appropriate energy requirement. The conducted works on impact energy of these materials are confined which may be as a result of the specified low impact energy. Zahedi et al. [1], [2] investigated Charpy impact energy of Al/SiCP composites and reported relatively low energies for the specimens produced in different conditions and by different methods. This has been reported in Ortega-Celaya et al. [3] work in which Al/SiCP composites were fabricated by pressureless infiltration with different types of SiCP.

One of the best methods to increase impact energy of engineering materials is producing laminated nanocomposites. Laminated composites are alternately separated by discrete interfaces, because of their capability of arresting propagating cracks under impact loading conditions are interesting. This effect is related to the interfaces delaminated under dynamic conditions and is responsible of the high fracture resistance of the composites, much better than the constitutive material components individualy [4]. In the previous work [5], the effect of lamination on different types of Al/SiCP nanocomposites was studied. It was reported that lamination of the suggested compositions could produce specimens with impact energy even 4 times greater.

Soft computing techniques such as artificial neural networks (AANs), adaptive neuro-fuzzy interfacial systems (ANFIS), fuzzy logic (FL) and genetic programming (GP) and its extension, gene expression programming (GEP) are common models used especially when the number of the accessable data are appropriate. In the previous study [5], ANNs were employed to predict Charpy impact energy of laminated Al/SiCP nanocomposites. In the present work GEP has been utilized to evaluate this property. Application of GP and GEP in different engineering problems are reported. For instance, Cevik and Guzelbey [6] predicted the ultimate strength of metal plates in compression by GEP. They conducted a simple model with 3 genes, different linking functions and head sizes and obtained results with suitable performance. In the other work, Cevik [7] proposed a GP-based modeling for the formulation of web crippling strength of cold-formed steel decks for various loading cases. Eskil and Kanca [8] developed GP for the formulation of martensite start temperature (Ms) of Fe–Mn–Si shape memory alloys for various compositions and heat treatments.

In the present study, GEP was selected for predicting and presenting suitable formulation of Charpy impact energy of laminated Al/SiCP nanocomposites. In the previous work [5], ANNs were employed to predict this property. The superiority of GEP model proposed here with respect to the previously ANN-based model is the GEP capability to provide straightforward equations for predicting Charpy impact energy of the considered laminated nanocomposites by means of the input parameters. Hundred and seventy one pairs of input-target data were gathered from the previous work [5], randomly divided into 133 and 38 data sets and then were respectively trained and tested by the proposed models. Such as that work [5], the thickness of layers, the number of layers, the adhesive type, the crack tip configuration, the content of SiC nanoparticles and the test trial number were considered as 6 independent input parameters.

Section snippets

Data collection

The required data were collected from the previous work [5]. Al6061 powder with the average particles size of 75 μm produced by nitrogen gas atomization were mixed by SiC nanoparticles with the particle sizes less than 100 nm and then ball-milled under argon atmosphere. Specimens with 2, 3 and 5 vol% of SiC nanoparticles were prepared in this stage. Aluminum cans with the specific dimensions were stored in a steel mold, filled by the produced powder in several layers and finally cold-pressed under

Gene expression programming structure

An extension to genetic algorithms, genetic programming (GP) was first proposed by Koza [9]. “GP is a domain of independent problem solving approach in which computer programs are evolved to solve, or approximately solve, problems based on the Darwinian principle of reproduction and analogs of naturally occurring genetic operations such as reproduction, crossover and mutation”. The complete theory of GP could be achieved from [10].

Gene expression programming (GEP), a population-based

Predicted results and discussion

The related equations of GEP1 to GEP4 models obtained from Fig. 2, Fig. 3, Fig. 4, Fig. 5 are in accordance to Eqs. (3), (4), (5), (6), respectively;JCVN(GEP1)=S2(C3cos3(CS4.56))1.5+(2.268.59sin2(S))(S2S+N)+(CSExp(sin2(S)))5.73NATS+ln(K)13.9TTsin(S6.71)+S65sin3(C)143.8N+C3+C3JCVN(GEP2)=sin(CS)(S2+N3.83)+CSsin(S)S+Exp(C)0.45cos(A2+cos(T))Arctan9(S)+Ccos(T)+ln(T)+TNsin(S)+T7.16K+(sin(1.38AC3+N)N)2+cos(TS)TC+73.5C+sin(A)+Csincos(N)+S3+AT0.5ln(T)3JCVN(GEP3)=1.63C3(C+29.5Exp2(T+N

Conclusions

Four different GEP models were proposed for predicting Charpy impact energy values of the considered Al/SiCP laminated nanocomposites. In GEP1 and GEP2 models, addition was set as linking function, 30 chromosomes and the head size of 12 was used and 6 and 7 genes were utilized, respectively. On the other hand, multiplication as linking function, 40 chromosomes and head size of 14 were used in GEP3 and GEP4 models together with 6 and 7 genes, respectively. The acquired results indicated that GEP

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