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FEM and ANN investigation of A356 composites reinforced with B4C particulates
Journal of King Saud University – Engineering Sciences (2012) 24, 107–113
King Saud University
Journal of King Saud University – Engineering Sciences www.ksu.edu.sa www.sciencedirect.com
ORIGINAL ARTICLE
FEM and ANN investigation of A356 composites reinforced with B4C particulates Mohsen Ostad Shabani, Ali Mazahery, Mohammad Reza Rahimipour *, Mansour Razavi Materials and Energy Research Center (MERC), Tehran, Iran Received 15 February 2011; accepted 25 May 2011 Available online 17 August 2011
KEYWORDS A356 matrix; Boron carbide; Finite element technique; Artificial neural network
Abstract In this research, the mechanical properties of A356 matrix reinforced with B4C particulates were first experimentally investigated and then a combination of artificial neural network (ANN) and finite element technique was implemented in order to model the mechanical properties including yield stress, UTS, hardness and elongation percentage. Microstructural characterization revealed that the B4C particles were distributed between the dendrite branches. The strain-hardening behavior and elongation to fracture of the composite materials appeared very different from that of un-reinforced Al alloy. It was noted that the elastic constant, strain hardening and UTS of the MMCs is higher than that of the un-reinforced Al alloy and increase with increasing of B4C content. It is also revealed that predictions of ANN are consistent with experimental measurements for A356 composite and considerable savings in terms of cost and time could be obtained by using neural network model. The results of this research were used for solidification codes of SUT CAST software. ª 2011 King Saud University. Production and hosting by Elsevier B.V. All rights reserved.
1. Introduction
* Corresponding author. Tel.: +98 912 563 6709; fax: +98 261 620 1888. E-mail address: [email protected] (M.R. Rahimipour). 1018-3639 ª 2011 King Saud University. Production and hosting by Elsevier B.V. All rights reserved. Peer review under responsibility of King Saud University. doi:10.1016/j.jksues.2011.05.001
Production and hosting by Elsevier
Cast A356 aluminum alloy, which is commonly used as cylinder head and engine block material, has widespread applications for structural components in the automotive, aerospace, and general engineering industries because of its excellent castability, corrosion resistance and particularly high strengthto-weight ratio (Barresi et al., 2000; Hetke and Gundlach, 1994; Caceres and Wang, 1996; Paray and Gruzleski, 1994; Kashyap et al., 1993; Shabestari and Moemeni, 2004). The addition of high modulus refractory particles to a ductile metal matrix produces a material whose mechanical properties are intermediate between the matrix alloy and ceramic reinforcement. Composite mechanical property enhancement is a function of cooling rate, the volume fraction, size, shape, spatial distribution of the reinforcement and also dependent
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upon how well the externally applied load is transferred to the reinforcing phase. Stronger adhesion at the particle/matrix interface improves load transfer, increasing the yield strength and stiffness, and delays the onsets of particle/matrix de-cohesion (Evans et al., 2003). ANN is a non-linear statistical analysis technique and is especially suitable for simulation of systems which are hard to be described by physical models. It provides a way of linking input data to output data using a set of non-linear functions. Choosing the optimum architecture of the network is one of the challenging steps in neural network modeling. The term ‘architecture’ refers to the number of layers in the network and number of neurons in each layer. Unfortunately this step is usually a trial and error procedure and various situations are required to be attempted (Karimzadeh et al., 2006; Altinkok and Koker, 2004; Hassan et al., 2009; Singh et al., 2010; Lisboa and Taktak, 2006). The description of the mechanical properties requires parameters such as cooling rate, temperature gradient, volume percentage of B4C, amount of porosities, yield stress, ultimate tensile strength and elongation percentage. In this paper, the mechanical properties of A356 composite reinforced with B4C particulates were first experimentally investigated and then the combination of finite element method with artificial neural network is implemented for modeling of these properties which can be incorporated in academic software for prediction of mechanical properties in the shape castings. 2. Experimental procedure In this study, a commercial casting-grade aluminum alloy (A356) [(wt%): 7.5 Si, 0.38 Mg, 0.02 Zn, 0.001 Cu, 0.106 Fe, and Al (balance)] was employed as the matrix material while the B4C particles with particle size ranged from 1 to 5 lm were used as the reinforcements. For manufacturing of the MMCs, 1, 2, 3, . . . , 14 and 15 vol% B4C particles were used. The melt-particle slurry has been produced by mechanical stirrer. Approximately, 5 kg of A356 alloy was charged into the graphite crucible and heated up to a temperature above the alloy’s melting point (750 C). The graphite stirrer fixed on the mandrel of the drilling machine was intro-
Figure 1
duced into the melt and positioned just below the surface of the melt. Reinforcement was inserted into an aluminum foil by forming a packet. The packets were added into molten metal of crucible when the vortex was formed at every 10 s. The packet of mixture melted and the particles started to distribute around the alloy sample. It was stirred at approximately 600 rev/min speed and then the step casting was poured into the CO2-sand mould. Fig. 1 shows scale drawing for step casting. The casting was gated from the side of the riser. It was then sectioned and samples were extracted from steps 1 to 5. Argon gas was also blown into the crucible during the operation. For microstructure study, specimens were prepared by grinding through 120, 400, 600, 800 grit papers followed by polishing with 6 lm diamond paste and etched with Keller’s reagent (2 ml HF (48%), 3 ml HCl (conc.), 5 ml HNO3 (conc.) and 190 ml water). The experimental density of the composites was obtained by the Archimedian method of weighing small pieces cut from the composite cylinder first in air and then in water, while the theoretical density was calculated using the mixture rule according to the weight fraction of the B4C particles. The porosities of the produced composites were evaluated from the difference between the expected and the observed density of each sample. To study the hardness, the Brinell hardness values of the samples were measured on the polished samples using an indenter ball with 2.5 mm diameter at a load of 31.25 kg. For each sample, 5 hardness readings on randomly selected regions were taken in order to eliminate possible segregation effects and get a representative value of the matrix material hardness. During hardness measurement, precaution was taken to make indentation at a distance of at least twice the diagonal length of the previous indention. The tensile tests were conducted using a Universal Testing Machine (Schimadzu) at a strain rate of 101. The composite and matrix alloy rods were machined to tensile specimens according to ASTM.B 557 standard. The load displacement diagram and the load displacement data were recorded from the digital display attached with the equipment. These load and displacement data were transformed to true stress and true strain data using the standard methodology, and ultimate tensile strength values were obtained.
Scale drawing for step casting.
FEM and ANN investigation of A356 composites reinforced with B4C particulates
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3. FEM and artificial neural network In this research, mechanical properties are considered to be related to cooling rate, temperature gradient and volume percentage of B4C. The method couples thermal and solute diffusion with the governing equations for modeling of heat transfer during solidification as follow (Peres et al., 2004): @Tðx; tÞ ¼ Kr2 Tðx; tÞ @t 8 T > TL > < CPðLÞ L fs CP ¼ CPðSLÞ þ TL TS TS T TL > : CPðSLÞ T < TS
qCp
CPðSLÞ ¼ CPðSÞ fS þ CPðLÞ fL fS ¼ 1
TL T TL TS
ð1Þ
ð2Þ
ð3Þ
1=ðk0 1Þ ð4Þ
The evolution of solid fraction (fS) is given by the Scheil equation based on the above transient temperature model, the FEM method is used for discretization and to calculate the transient temperature field of quenching. Since it is almost at T = TS + 0.1(TL TS) that final structure and latent heat are obtained, the cooling rate and temperature gradient in dendrite tip are required. R ¼ Tði; j; k; tÞ Tði; j; k; t þ 1Þ
ð5Þ
G ¼ jðTði þ 1; j; k; tÞ Tði; j; k; tÞÞj
ð6Þ
where q is density, C heat capacity, k0 solute partition coefficient, K heat diffusion coefficient, L latent heat, R cooling rate and G temperature gradient. The method to judge the convergence was to monitor the magnitude of scaled residuals. Residuals are defined as the imbalance in each conservation equation following each iteration. Setting the convergence criteria solve the governing equations iteratively until at all nodes in the computational domain the relative changes in components between two successive iterations become less than 103 (residual monitors). The numbers of hidden neurons are fixed for each model based on mean square error (MSE). MSE was computed according to the following equation (Rashidi et al., 2009): ! Q N 1 XX 2 MSE ¼ jdn ðmÞ yn ðmÞj ð7Þ NQ m¼1 n¼1 where N is the number of output, Q the number of training sets, d the desired output, and y the network output. In order to design a neural network for a problem solution, a training algorithm is required. It is necessary to prepare a set of examples, which represents the problem in the forms of system inputs and outputs. During the training process, the weights and biases in the network are adjusted to minimize the error and obtain a high-performance in the solution. At the end of the training and during the training error, MSE is computed between desired outputs and target outputs. The ANN was trained and implemented using fully developed feed forward back propagation neural network. The number of neurons in the input and the output layers are determined by the number of input and output variables, respectively. In order to find an optimal architecture, different
Figure 2 Schematic representation of the neural network architecture.
number of neurons in the hidden layer was considered and MSE error for each network was calculated (Mousavi Anijdan et al., 2006; Hwang et al., 2010; Fratini et al., 2009; Hamzaoui et al., 2009; Reddy et al., 2005). For the training problem, the following parameters were found to give good performance and rapid convergence: three input nodes that obtained from FEM method namely cooling rate (K/s), temperature gradient (K/m) and volume percentage of B4C and five output neurons which are hardness, amount of porosities, yield stress, ultimate tensile strength (UTS), and fracture strain. Sigmoid activation function was selected to be the transfer function between all layers. The ANN architecture is shown in Fig. 2. A total dataset of 30 samples was used to learn the proposed ANN. This dataset was obtained from step casting process. Among them, 23 of these points are used in training process and seven used in validation process. 4. Results and discussion Microscopic examinations of the composites and matrix alloy were carried out using an optical microscope. Fig. 3 shows microstructure of the metal matrix composite. Because of the casting process, the B4C particles were distributed between the dendrite branches and were frequently clustered together, leaving the dendrite branches as particle-free regions in the material. Fig. 4 indicates that increasing amount of porosity is observed with increasing the volume fraction of composites. This is ascribed to increasing sites for heterogeneous pore nucleation (increasing surface gas layers surrounding particles) and the hindered liquid metal flow due to more particle clustering (improper filling of the gaps between adjacent particles) (Zamzam et al., 1994; Kok, 1999; Zhou and Xu, 1997; Ray, 1988; Lloyd and Chamberian, 1988). Fig. 5 shows that the hardness of the MMCs increases with the volume fraction of particulates in the alloy matrix. The dispersion of particles enhances the hardness, as B4C particles act as obstacles to the motion of dislocation. It is reported that B4C particles are harder than Al alloy and render their
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Volume % Porosity
2.5
2
1.5
1
0.5
0 0
3
6
9
12
15
Volume % B4C Figure 4 Variations of porosity as a function of B4C content (extracted from step 3, R = 0.1 C/s).
100
Hardness (BHN)
80
60
40
20
0 0
5
10
15
Vol. % B4C Figure 5 Variations of hardness value of the samples as a function of B4C content (extracted from step 1, R = 10 C/s).
Figure 3 Typical optical micrographs (extracted from step 1, R = 10 C/s): (a) the composite with 2 vol% B4C, (b) the composite with 10 vol% B4C, (c) the composite with 15 vol% B4C.
inherent property of hardness to the soft matrix (Hosking et al., 1982; Roy et al., 1992; Chung and Hwang, 1994; Skolianos and Kattamis, 1993; Bindumadhavan et al., 2001). Fig. 6 shows the typical true stress–true strain curves obtained from uniaxial tension tests. The yield strength and UTS of the materials were found to increase with increasing of B4C content. The great enhancement in values observed in these composites in comparison to monolithic aluminum is due to grain refinement, the strong multidirectional thermal stress at the Al/B4C interface, small particle size and good distribution of the B4C particles and low degree of porosity which leads to effective transfer of applied tensile load to the uniformly distributed strong B4C particulates (Needleman and Suresh, 1989; Suresh et al., 2003; Reddy, 2003).
Figure 6 Stress–strain curves for un-reinforced Al alloy (A), Al/ 3 vol% B4C (M), Al/7 vol% B4C (B), Al/10 vol% B4C (N), Al/ 12 vol% B4C (C) and Al/15 vol% B4C (D) (extracted from step 4, R = 0.01 C/s).
FEM and ANN investigation of A356 composites reinforced with B4C particulates It is assumed that the non-linear part of the true stress–true strain curves followed Zener–Hollomon relationship (Kashyap et al., 2000):
12.00
ð8Þ
from the above relationship, the work hardening rate (dr/de) was calculated at different strain values. Fig. 7 shows the curves of dr/de versus true strain (e) for various alloys. The considerable increase of strain hardening observed during plastic deformation of composites is rationalized by resistance of the hard reinforcing particles to slip behavior of the Al matrix. Dendrite branches of the Al matrix is surrounded by the B4C particles and these particles along the dendrite boundaries act as barriers to the slip behavior of the matrix and, hence, strengthen the composite material. It is also expected that due to the thermal mismatch stress, there is a possibility of increased dislocation density within the matrix which might lead to making local stress and also increase in strength of the matrix, and thus to the composite. The difference between the coefficient of thermal expansion (CTE) values of matrix and ceramic particles generates thermally induced residual stresses and increase dislocations density upon rapid Solidification during the fabrication process. This type of internal stress would resist the slip behavior in the metal matrix, and hence, the strain-hardening rate would increase. The elongation to fracture of the composite materials was found very low, and no necking phenomenon was observed before fracture. The microscopic nonuniformity of the particle distribution, created by dendrite structure formation and usually in the form of clustering, is considered as the reason for internal stresses and also stress triaxiality, which are responsible not only for the special hardening behavior, but also for the early appearance of particle cracking, particle interface debonding, and void formation
4.00
0.00
3
4
5
6
7
8
9
10
11
12
13
Number of neurons in the hidden layer MSE error values for various neurons in the hidden
Figure 8 layer.
a
100
Experimental Hardness
ð9Þ
8.00
80
60
40
20
0 0
20
40
60
80
100
Predicted Hardness
b
3
Experimental Porosity %
where r is the true stress, e the true plastic strain, n the strainhardening exponent and k a constant. From the slope of the log (true stress) versus log (true strain) plots, the strain-hardening exponents were calculated. dr nr ¼ de e
16.00
MSE
r ¼ ken
111
2
1
0 0
1
2
3
Predicted Porosity% Figure 9 Comparison between the experimental and predicted values: (a) hardness and (b) porosity.
Figure 7 dr=de-strain curves for un-reinforced Al alloy (A), Al/ 3 vol% B4C (M), Al/7 vol% B4C (B), Al/10 vol% B4C (N), Al/ 12 vol% B4C (C) and Al/15 vol% B4C (D) (extracted from step 3, R = 0.1 C/s).
in the matrix. It can be speculated that the low ductility of the studied MMC is due to early coalescence of the microdamages. On the other hand, the elongation to fracture of the un-reinforced Al alloy was about 15 percentages, while it is 1.5 for Al/7 vol% B4C (Needleman and Suresh, 1989; Suresh et al., 2003; Reddy, 2003; Kashyap et al., 2000; Kang and Chan, 2004; Zhao et al., 2008). Fig. 2 shows a schematic representation of the neural network architecture employed in this study. Since the use of these training algorithms is indeed very time consuming process, it is
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M.O. Shabani et al. The mechanical properties of A356 composite reinforced with B4C particulates were experimentally investigated. The results show the great enhancement in values of hardness, elastic constant and UTS in composites relative to monolithic aluminum. 2- The mechanical properties modeling were developed to predict the hardness, yield stress, ultimate tensile strength and elongation percentage. The prediction of ANN model was found to be in good agreement with experimental data. 3- It is concluded that considerable savings in terms of cost and time could be obtained by using neural network model and ANN is a successful analytical tool provided it is properly used. References
Figure 10 Effect of cooling rate on hardness (a) and UTS (b) of the composite.
important to be convinced that the obtained solutions are the optimum ones. Therefore, the error behavior of the neural network has to be observed to find the results with minimum errors. There is no known concept about selection of the number of neurons in the hidden layer. The neuron number in the hidden layer can be found experimentally. Finding the minimum number of neurons and the hidden layer to obtain the results with minimum errors takes too much time because of the heavy computations for each different neuron number in the hidden layer. In Fig. 8, MSE error values are computed and given at the end of training process for various neurons in the hidden layer. According to this figure, the ANN with eight neurons in hidden layer has the smallest error. Therefore, a model was used with the mentioned properties. Random weightings are assigned to each processing element as an arbitrary starting point in the training process and the weightings are progressively altered on exposure to numerous repetitions of training examples. The model is verified against the cases in the test data file, which are independent of the cases in the train data file. The predicted results are plotted versus the experimental results. Although the use of this model may result in a higher performance error for the training datasets, the error for the test datasets are reduced which is an indication of higher ability of the network to predict more precise results from unseen patterns. Comparison between the experimental and predicted values of amount of porosities and hardness is displayed in Fig. 9. The higher consistency of this model with experimental measurement can be easily observed. The remarkable agreement between the experimental and predicted values implies that the ANN model can be used to predict the mechanical properties. In order to exhibit some results of A356 composites, the distribution of hardness and UTS in this model is displayed in Fig. 10. 5. Conclusion 1- Microstructural observations revealed a reasonably uniform distribution of B4C particles in the matrix. These particles decreased the coefficient of thermal expansion.
Altinkok, N., Koker, R., 2004. Neural network approach to prediction of bending strength and hardening behaviour of particulate reinforced (Al–Si–Mg)-aluminium matrix composites. Mater. Des. 25, 595–602. Barresi, J., Kerr, M.J., Wang, H., Couper, M.J., 2000. Effect of magnesium, iron and cooling rate on mechanical properties of Al– 7Si–Mg foundry alloys. AFS Trans. 114, 563–570. Bindumadhavan, P.N., Wah, H.K., Prabhakar, O., 2001. Dual particle size (DSP) composites: effect on wear and mechanical properties of particulate metal matrix composites. Wear 248, 112–120. Caceres, C.H., Wang, Q.G., 1996. Solidification conditions heat treatment and tensile ductility of Al–7Si–0.4Mg casting alloys. AFS Trans. 104, 1039–1043. Chung, S., Hwang, B.H., 1994. A microstructural study of the wear behavior of SiCp/Al composites. Tribol. Int. 27 (5), 307–314. Evans, A., Marchi, C.S., Mortensen, A., 2003. Metal Matrix Composites in Industry: An Introduction and a Survey, first ed. Kluwer Academic Publishers, Dordrecht, Netherlands. Fratini, L., Buffa, G., Palmeri, D., 2009. Using a neural network for predicting the average grain size in friction stir welding processes. Comput. Struct. 87, 1166–1174. Hamzaoui, R., Cherigui, M., Guessasm, S., ElKedim, O., Fenineche, N., 2009. Artificial neural network methodology: application to predict magnetic properties of nanocrystalline alloys. MSE B 163, 17–21. Hassan, A.M., Alrashdan, A., Hayajneh, M.T., Mayyas, A.T., 2009. Prediction of density, porosity and hardness in aluminum–copperbased composite materials using artificial neural network. J. Mater. Process. Technol. 209, 894–899. Hetke, A., Gundlach, R.B., 1994. Aluminum casting quality in alloy 356, engine components. AFS Trans. 102, 367–380. Hosking, F.M., Folgar Portillo, F., Wunderlin, R., Mehrabian, R., 1982. Composites of aluminium alloys: fabrication and wear behaviour. J. Mater. Sci. 17, 477–498. Hwang, R., Chen, Y., Huang, H., 2010. Artificial intelligent analyzer for mechanical properties of rolled steel bar by using neural networks. Expert Syst. Appl. 37, 3136–3139. Kang, Y.C., Chan, S.L.I., 2004. Tensile properties of nanometric Al2O3 particulate-reinforced aluminum matrix composites. Mater. Chem. Phys. 85 (2–3), 438–443. Karimzadeh, F., Ebnonnasir, A., Foroughi, A., 2006. Artificial neural network modeling for evaluating of epitaxial growth of Ti6Al4V weldment. MSE A 432, 184–190. Kashyap, K.T., Murali, S., Murthy, K.S.S., 1993. Casting and heat treatment variables of Al–7Si–Mg alloy. Mater. Sci. Technol. 9, 189–203. Kashyap, K.T., Ramachandra, C., Chatterji, B., 2000. Role of work hardening characteristics of matrix alloys in the strengthening of metal matrix composites. Bull. Mater. Sci. 23, 47–49.
FEM and ANN investigation of A356 composites reinforced with B4C particulates Kok, M., 1999. Preparation and some properties of SiC particle reinforced Al matrix. Ph.D. Thesis, The Institute of Science and Technology of Elazig University, Turkey. Lisboa, P.J., Taktak, A.F.G., 2006. The use of artificial neural networks in decision support in cancer: a systematic review. Neural Netw. 19, 408–415. Lloyd, D.J., Chamberian, B., 1988. Properties of shape cast Al–SiCp metal matrix composites. In: Proceedings of the International Symposium on Advances in Cast Reinforced Metal Composites, ASM, Illinois, USA, pp. 263–269. Mousavi Anijdan, S.H., Bahrami, A., Madaah Hosseini, H.R., Shafyei, A., 2006. Using genetic algorithm and artificial neural network analyses to design an Al–Si casting alloy of minimum porosity. Mater. Des. 27, 605–609. Needleman, A., Suresh, S., 1989. Experimental and numerical study of deformation in metal–ceramic composites. Acta Metall. 37, 3029– 3050. Paray, F., Gruzleski, J.E., 1994. Microstructure–mechanical property relationships in a 356 alloy: part 2: mechanical properties. Cast Met. 7, 153–163. Peres, M.D., Siqueira, C.A., Garcia, A., 2004. Macrostructural and microstructural development in Al–Si alloys directionally solidified under unsteady-state conditions. J. Alloys Compd. 381, 168–181. Rashidi, A.M., Eivani, A.R., Amadeh, A., 2009. Application of artificial neural networks to predict the grain size of nanocrystalline nickel coatings. Comput. Mater. Sci. 45, 499–504. Ray, S., 1988. Porosity in foundry composites prepared by vortex method. In: Fishman, S.G., Dhingra, A.K. (Eds.), Proceedings of the Survey on Fabrication Methods of Cast Reinforced Metal Composites, ASM/TMS, Chicago, USA, pp. 77–80.
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Reddy, R.G., 2003. Processing of nanoscale materials. Rev. Adv. Mater. Sci. 5, 121–133. Reddy, N.S., Prasada Rao, A.K., Chakraborty, M., Murty, B.S., 2005. Prediction of grain size of Al–7Si Alloy by neural networks. MSE A 391, 131–140. Roy, M., Venkataraman, B., Bhanuprasad, V.V., Mahajan, Y.R., Sundararajan, G., 1992. The effects of particulate reinforcement on the sliding wear behavior of aluminum matrix composites. Metall. Trans. A 23, 2833–2846. Shabestari, S.G., Moemeni, H., 2004. Effect of copper and solidification conditions on the microstructure and mechanical properties of Al–Si–Mg alloys. Mater. Process. Technol. 153–154, 193–198. Singh, S.K., Mahesh, K., Gupta, A.K., 2010. Prediction of mechanical properties of extra deep drawn steel in blue brittle region using artificial neural network. Mater. Des. 31, 2288–2295. Skolianos, S., Kattamis, T.Z., 1993. Tribological properties of SiC reinforced Al–4.5% Cu–1.5% Mg alloy composites. Mater. Sci. Eng. A 163, 107–113. Suresh, K.R., Niranjan, H.B., Martin Jebaraj, P., Chowdiah, M.P., 2003. Tensile and wear properties of aluminum composites. In: 14th International Conference on Wear of Materials, August– September, p. 638. Zamzam, M., Ros, D., Grosch, J., 1994. On the microstructure and mechanical properties of squeeze-cast Al-7 wt% Si alloy. J. Mater. Process. Technol. 40, 73–85. Zhao, Y.T., Zhang, S.L., Chen, G., Cheng, X.N., Wang, C.Q., 2008. In situ(Al2O3 + Al3Zr)np/Al nanocomposites synthesized by magneto-chemical melt reaction. Compos. Sci. Technol. 68, 1463–1470. Zhou, W., Xu, Z.M., 1997. Casting of SiC reinforced metal matrix composites. J. Mater. Process. Technol. 63, 358–363.
King Saud University
Journal of King Saud University – Engineering Sciences www.ksu.edu.sa www.sciencedirect.com
ORIGINAL ARTICLE
FEM and ANN investigation of A356 composites reinforced with B4C particulates Mohsen Ostad Shabani, Ali Mazahery, Mohammad Reza Rahimipour *, Mansour Razavi Materials and Energy Research Center (MERC), Tehran, Iran Received 15 February 2011; accepted 25 May 2011 Available online 17 August 2011
KEYWORDS A356 matrix; Boron carbide; Finite element technique; Artificial neural network
Abstract In this research, the mechanical properties of A356 matrix reinforced with B4C particulates were first experimentally investigated and then a combination of artificial neural network (ANN) and finite element technique was implemented in order to model the mechanical properties including yield stress, UTS, hardness and elongation percentage. Microstructural characterization revealed that the B4C particles were distributed between the dendrite branches. The strain-hardening behavior and elongation to fracture of the composite materials appeared very different from that of un-reinforced Al alloy. It was noted that the elastic constant, strain hardening and UTS of the MMCs is higher than that of the un-reinforced Al alloy and increase with increasing of B4C content. It is also revealed that predictions of ANN are consistent with experimental measurements for A356 composite and considerable savings in terms of cost and time could be obtained by using neural network model. The results of this research were used for solidification codes of SUT CAST software. ª 2011 King Saud University. Production and hosting by Elsevier B.V. All rights reserved.
1. Introduction
* Corresponding author. Tel.: +98 912 563 6709; fax: +98 261 620 1888. E-mail address: [email protected] (M.R. Rahimipour). 1018-3639 ª 2011 King Saud University. Production and hosting by Elsevier B.V. All rights reserved. Peer review under responsibility of King Saud University. doi:10.1016/j.jksues.2011.05.001
Production and hosting by Elsevier
Cast A356 aluminum alloy, which is commonly used as cylinder head and engine block material, has widespread applications for structural components in the automotive, aerospace, and general engineering industries because of its excellent castability, corrosion resistance and particularly high strengthto-weight ratio (Barresi et al., 2000; Hetke and Gundlach, 1994; Caceres and Wang, 1996; Paray and Gruzleski, 1994; Kashyap et al., 1993; Shabestari and Moemeni, 2004). The addition of high modulus refractory particles to a ductile metal matrix produces a material whose mechanical properties are intermediate between the matrix alloy and ceramic reinforcement. Composite mechanical property enhancement is a function of cooling rate, the volume fraction, size, shape, spatial distribution of the reinforcement and also dependent
108
M.O. Shabani et al.
upon how well the externally applied load is transferred to the reinforcing phase. Stronger adhesion at the particle/matrix interface improves load transfer, increasing the yield strength and stiffness, and delays the onsets of particle/matrix de-cohesion (Evans et al., 2003). ANN is a non-linear statistical analysis technique and is especially suitable for simulation of systems which are hard to be described by physical models. It provides a way of linking input data to output data using a set of non-linear functions. Choosing the optimum architecture of the network is one of the challenging steps in neural network modeling. The term ‘architecture’ refers to the number of layers in the network and number of neurons in each layer. Unfortunately this step is usually a trial and error procedure and various situations are required to be attempted (Karimzadeh et al., 2006; Altinkok and Koker, 2004; Hassan et al., 2009; Singh et al., 2010; Lisboa and Taktak, 2006). The description of the mechanical properties requires parameters such as cooling rate, temperature gradient, volume percentage of B4C, amount of porosities, yield stress, ultimate tensile strength and elongation percentage. In this paper, the mechanical properties of A356 composite reinforced with B4C particulates were first experimentally investigated and then the combination of finite element method with artificial neural network is implemented for modeling of these properties which can be incorporated in academic software for prediction of mechanical properties in the shape castings. 2. Experimental procedure In this study, a commercial casting-grade aluminum alloy (A356) [(wt%): 7.5 Si, 0.38 Mg, 0.02 Zn, 0.001 Cu, 0.106 Fe, and Al (balance)] was employed as the matrix material while the B4C particles with particle size ranged from 1 to 5 lm were used as the reinforcements. For manufacturing of the MMCs, 1, 2, 3, . . . , 14 and 15 vol% B4C particles were used. The melt-particle slurry has been produced by mechanical stirrer. Approximately, 5 kg of A356 alloy was charged into the graphite crucible and heated up to a temperature above the alloy’s melting point (750 C). The graphite stirrer fixed on the mandrel of the drilling machine was intro-
Figure 1
duced into the melt and positioned just below the surface of the melt. Reinforcement was inserted into an aluminum foil by forming a packet. The packets were added into molten metal of crucible when the vortex was formed at every 10 s. The packet of mixture melted and the particles started to distribute around the alloy sample. It was stirred at approximately 600 rev/min speed and then the step casting was poured into the CO2-sand mould. Fig. 1 shows scale drawing for step casting. The casting was gated from the side of the riser. It was then sectioned and samples were extracted from steps 1 to 5. Argon gas was also blown into the crucible during the operation. For microstructure study, specimens were prepared by grinding through 120, 400, 600, 800 grit papers followed by polishing with 6 lm diamond paste and etched with Keller’s reagent (2 ml HF (48%), 3 ml HCl (conc.), 5 ml HNO3 (conc.) and 190 ml water). The experimental density of the composites was obtained by the Archimedian method of weighing small pieces cut from the composite cylinder first in air and then in water, while the theoretical density was calculated using the mixture rule according to the weight fraction of the B4C particles. The porosities of the produced composites were evaluated from the difference between the expected and the observed density of each sample. To study the hardness, the Brinell hardness values of the samples were measured on the polished samples using an indenter ball with 2.5 mm diameter at a load of 31.25 kg. For each sample, 5 hardness readings on randomly selected regions were taken in order to eliminate possible segregation effects and get a representative value of the matrix material hardness. During hardness measurement, precaution was taken to make indentation at a distance of at least twice the diagonal length of the previous indention. The tensile tests were conducted using a Universal Testing Machine (Schimadzu) at a strain rate of 101. The composite and matrix alloy rods were machined to tensile specimens according to ASTM.B 557 standard. The load displacement diagram and the load displacement data were recorded from the digital display attached with the equipment. These load and displacement data were transformed to true stress and true strain data using the standard methodology, and ultimate tensile strength values were obtained.
Scale drawing for step casting.
FEM and ANN investigation of A356 composites reinforced with B4C particulates
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3. FEM and artificial neural network In this research, mechanical properties are considered to be related to cooling rate, temperature gradient and volume percentage of B4C. The method couples thermal and solute diffusion with the governing equations for modeling of heat transfer during solidification as follow (Peres et al., 2004): @Tðx; tÞ ¼ Kr2 Tðx; tÞ @t 8 T > TL > < CPðLÞ L fs CP ¼ CPðSLÞ þ TL TS TS T TL > : CPðSLÞ T < TS
qCp
CPðSLÞ ¼ CPðSÞ fS þ CPðLÞ fL fS ¼ 1
TL T TL TS
ð1Þ
ð2Þ
ð3Þ
1=ðk0 1Þ ð4Þ
The evolution of solid fraction (fS) is given by the Scheil equation based on the above transient temperature model, the FEM method is used for discretization and to calculate the transient temperature field of quenching. Since it is almost at T = TS + 0.1(TL TS) that final structure and latent heat are obtained, the cooling rate and temperature gradient in dendrite tip are required. R ¼ Tði; j; k; tÞ Tði; j; k; t þ 1Þ
ð5Þ
G ¼ jðTði þ 1; j; k; tÞ Tði; j; k; tÞÞj
ð6Þ
where q is density, C heat capacity, k0 solute partition coefficient, K heat diffusion coefficient, L latent heat, R cooling rate and G temperature gradient. The method to judge the convergence was to monitor the magnitude of scaled residuals. Residuals are defined as the imbalance in each conservation equation following each iteration. Setting the convergence criteria solve the governing equations iteratively until at all nodes in the computational domain the relative changes in components between two successive iterations become less than 103 (residual monitors). The numbers of hidden neurons are fixed for each model based on mean square error (MSE). MSE was computed according to the following equation (Rashidi et al., 2009): ! Q N 1 XX 2 MSE ¼ jdn ðmÞ yn ðmÞj ð7Þ NQ m¼1 n¼1 where N is the number of output, Q the number of training sets, d the desired output, and y the network output. In order to design a neural network for a problem solution, a training algorithm is required. It is necessary to prepare a set of examples, which represents the problem in the forms of system inputs and outputs. During the training process, the weights and biases in the network are adjusted to minimize the error and obtain a high-performance in the solution. At the end of the training and during the training error, MSE is computed between desired outputs and target outputs. The ANN was trained and implemented using fully developed feed forward back propagation neural network. The number of neurons in the input and the output layers are determined by the number of input and output variables, respectively. In order to find an optimal architecture, different
Figure 2 Schematic representation of the neural network architecture.
number of neurons in the hidden layer was considered and MSE error for each network was calculated (Mousavi Anijdan et al., 2006; Hwang et al., 2010; Fratini et al., 2009; Hamzaoui et al., 2009; Reddy et al., 2005). For the training problem, the following parameters were found to give good performance and rapid convergence: three input nodes that obtained from FEM method namely cooling rate (K/s), temperature gradient (K/m) and volume percentage of B4C and five output neurons which are hardness, amount of porosities, yield stress, ultimate tensile strength (UTS), and fracture strain. Sigmoid activation function was selected to be the transfer function between all layers. The ANN architecture is shown in Fig. 2. A total dataset of 30 samples was used to learn the proposed ANN. This dataset was obtained from step casting process. Among them, 23 of these points are used in training process and seven used in validation process. 4. Results and discussion Microscopic examinations of the composites and matrix alloy were carried out using an optical microscope. Fig. 3 shows microstructure of the metal matrix composite. Because of the casting process, the B4C particles were distributed between the dendrite branches and were frequently clustered together, leaving the dendrite branches as particle-free regions in the material. Fig. 4 indicates that increasing amount of porosity is observed with increasing the volume fraction of composites. This is ascribed to increasing sites for heterogeneous pore nucleation (increasing surface gas layers surrounding particles) and the hindered liquid metal flow due to more particle clustering (improper filling of the gaps between adjacent particles) (Zamzam et al., 1994; Kok, 1999; Zhou and Xu, 1997; Ray, 1988; Lloyd and Chamberian, 1988). Fig. 5 shows that the hardness of the MMCs increases with the volume fraction of particulates in the alloy matrix. The dispersion of particles enhances the hardness, as B4C particles act as obstacles to the motion of dislocation. It is reported that B4C particles are harder than Al alloy and render their
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Volume % Porosity
2.5
2
1.5
1
0.5
0 0
3
6
9
12
15
Volume % B4C Figure 4 Variations of porosity as a function of B4C content (extracted from step 3, R = 0.1 C/s).
100
Hardness (BHN)
80
60
40
20
0 0
5
10
15
Vol. % B4C Figure 5 Variations of hardness value of the samples as a function of B4C content (extracted from step 1, R = 10 C/s).
Figure 3 Typical optical micrographs (extracted from step 1, R = 10 C/s): (a) the composite with 2 vol% B4C, (b) the composite with 10 vol% B4C, (c) the composite with 15 vol% B4C.
inherent property of hardness to the soft matrix (Hosking et al., 1982; Roy et al., 1992; Chung and Hwang, 1994; Skolianos and Kattamis, 1993; Bindumadhavan et al., 2001). Fig. 6 shows the typical true stress–true strain curves obtained from uniaxial tension tests. The yield strength and UTS of the materials were found to increase with increasing of B4C content. The great enhancement in values observed in these composites in comparison to monolithic aluminum is due to grain refinement, the strong multidirectional thermal stress at the Al/B4C interface, small particle size and good distribution of the B4C particles and low degree of porosity which leads to effective transfer of applied tensile load to the uniformly distributed strong B4C particulates (Needleman and Suresh, 1989; Suresh et al., 2003; Reddy, 2003).
Figure 6 Stress–strain curves for un-reinforced Al alloy (A), Al/ 3 vol% B4C (M), Al/7 vol% B4C (B), Al/10 vol% B4C (N), Al/ 12 vol% B4C (C) and Al/15 vol% B4C (D) (extracted from step 4, R = 0.01 C/s).
FEM and ANN investigation of A356 composites reinforced with B4C particulates It is assumed that the non-linear part of the true stress–true strain curves followed Zener–Hollomon relationship (Kashyap et al., 2000):
12.00
ð8Þ
from the above relationship, the work hardening rate (dr/de) was calculated at different strain values. Fig. 7 shows the curves of dr/de versus true strain (e) for various alloys. The considerable increase of strain hardening observed during plastic deformation of composites is rationalized by resistance of the hard reinforcing particles to slip behavior of the Al matrix. Dendrite branches of the Al matrix is surrounded by the B4C particles and these particles along the dendrite boundaries act as barriers to the slip behavior of the matrix and, hence, strengthen the composite material. It is also expected that due to the thermal mismatch stress, there is a possibility of increased dislocation density within the matrix which might lead to making local stress and also increase in strength of the matrix, and thus to the composite. The difference between the coefficient of thermal expansion (CTE) values of matrix and ceramic particles generates thermally induced residual stresses and increase dislocations density upon rapid Solidification during the fabrication process. This type of internal stress would resist the slip behavior in the metal matrix, and hence, the strain-hardening rate would increase. The elongation to fracture of the composite materials was found very low, and no necking phenomenon was observed before fracture. The microscopic nonuniformity of the particle distribution, created by dendrite structure formation and usually in the form of clustering, is considered as the reason for internal stresses and also stress triaxiality, which are responsible not only for the special hardening behavior, but also for the early appearance of particle cracking, particle interface debonding, and void formation
4.00
0.00
3
4
5
6
7
8
9
10
11
12
13
Number of neurons in the hidden layer MSE error values for various neurons in the hidden
Figure 8 layer.
a
100
Experimental Hardness
ð9Þ
8.00
80
60
40
20
0 0
20
40
60
80
100
Predicted Hardness
b
3
Experimental Porosity %
where r is the true stress, e the true plastic strain, n the strainhardening exponent and k a constant. From the slope of the log (true stress) versus log (true strain) plots, the strain-hardening exponents were calculated. dr nr ¼ de e
16.00
MSE
r ¼ ken
111
2
1
0 0
1
2
3
Predicted Porosity% Figure 9 Comparison between the experimental and predicted values: (a) hardness and (b) porosity.
Figure 7 dr=de-strain curves for un-reinforced Al alloy (A), Al/ 3 vol% B4C (M), Al/7 vol% B4C (B), Al/10 vol% B4C (N), Al/ 12 vol% B4C (C) and Al/15 vol% B4C (D) (extracted from step 3, R = 0.1 C/s).
in the matrix. It can be speculated that the low ductility of the studied MMC is due to early coalescence of the microdamages. On the other hand, the elongation to fracture of the un-reinforced Al alloy was about 15 percentages, while it is 1.5 for Al/7 vol% B4C (Needleman and Suresh, 1989; Suresh et al., 2003; Reddy, 2003; Kashyap et al., 2000; Kang and Chan, 2004; Zhao et al., 2008). Fig. 2 shows a schematic representation of the neural network architecture employed in this study. Since the use of these training algorithms is indeed very time consuming process, it is
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M.O. Shabani et al. The mechanical properties of A356 composite reinforced with B4C particulates were experimentally investigated. The results show the great enhancement in values of hardness, elastic constant and UTS in composites relative to monolithic aluminum. 2- The mechanical properties modeling were developed to predict the hardness, yield stress, ultimate tensile strength and elongation percentage. The prediction of ANN model was found to be in good agreement with experimental data. 3- It is concluded that considerable savings in terms of cost and time could be obtained by using neural network model and ANN is a successful analytical tool provided it is properly used. References
Figure 10 Effect of cooling rate on hardness (a) and UTS (b) of the composite.
important to be convinced that the obtained solutions are the optimum ones. Therefore, the error behavior of the neural network has to be observed to find the results with minimum errors. There is no known concept about selection of the number of neurons in the hidden layer. The neuron number in the hidden layer can be found experimentally. Finding the minimum number of neurons and the hidden layer to obtain the results with minimum errors takes too much time because of the heavy computations for each different neuron number in the hidden layer. In Fig. 8, MSE error values are computed and given at the end of training process for various neurons in the hidden layer. According to this figure, the ANN with eight neurons in hidden layer has the smallest error. Therefore, a model was used with the mentioned properties. Random weightings are assigned to each processing element as an arbitrary starting point in the training process and the weightings are progressively altered on exposure to numerous repetitions of training examples. The model is verified against the cases in the test data file, which are independent of the cases in the train data file. The predicted results are plotted versus the experimental results. Although the use of this model may result in a higher performance error for the training datasets, the error for the test datasets are reduced which is an indication of higher ability of the network to predict more precise results from unseen patterns. Comparison between the experimental and predicted values of amount of porosities and hardness is displayed in Fig. 9. The higher consistency of this model with experimental measurement can be easily observed. The remarkable agreement between the experimental and predicted values implies that the ANN model can be used to predict the mechanical properties. In order to exhibit some results of A356 composites, the distribution of hardness and UTS in this model is displayed in Fig. 10. 5. Conclusion 1- Microstructural observations revealed a reasonably uniform distribution of B4C particles in the matrix. These particles decreased the coefficient of thermal expansion.
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