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stimation of flow stress behavior of AA5083 using artificialeural networks with regard to dynamic strain ageing effect

. Sheikh, S. Serajzadeh ∗

epartment of Materials Science and Engineering, Sharif University of Technology, Azadi Ave., P.O. Box 11365-9466, Tehran, Iran

r t i c l e i n f o

rticle history:

eceived 4 September 2006

eceived in revised form

1 April 2007

ccepted 12 May 2007

a b s t r a c t

In this work, neural networks are used for estimation of flow stress of AA5083 with regard

to dynamic strain ageing that occurs in certain deformation conditions and varies flow

stress behavior of the metal being deformed. The input variables are selected to be strain

rate, temperature and strain and the output value is the flow stress. In the first stage, the

appearance and terminal of dynamic strain aging are determined with the aid of tensile

testing at various temperatures and strain rates and subsequently for the serrated flow

and the smooth yielding domains different neural networks are constructed based on the

eywords:

athematical modelling

eural network

low stress

achieved results. While a feed-forward backpropagation algorithm is employed to train the

neural networks. Stress–strain curves in both regions are calculated by the employed model

and compared with the experimental data. The comparison between the two sets of results

indicates the reliability of the predictions.

it alters the flow stress behavior of the metal and even it may

luminum alloy

. Introduction

rediction of materials behavior during metal working oper-tions is important for scientist and engineers. However, dueo the complex interconnections among process parametersnd materials properties, mathematical models are some-imes very complex to handle by the numerical techniquess well as by the experimental methods. In recent years, neu-al network models are widely used in different metallurgicalperations. The neural networks are a relatively new artificial

ntelligence technique that emulates the behavior of biologi-al neural systems in digital software or hardware. In previousorks, efforts have been done to use this technique for solv-

ng a large variety of metallurgical problems. For example.arayan et al. (Narayan et al., 1999) estimated hot torsion

tress–strain curves in iron alloys using appropriate neural

etwork pattern and in another research, Jung and Ghaboussi

Jung and Ghaboussi, 2006) have used a neural network modelo assess flow stress for the rate-sensitive materials. They

∗ Corresponding author.E-mail address: serajzadeh@sharif.edu (S. Serajzadeh).

924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.jmatprotec.2007.05.027

© 2007 Elsevier B.V. All rights reserved.

have used the model for analyzing time-dependent behaviorof concrete and acceptable results have been achieved. Thedeformation behavior of a Zr-alloy has been investigated byKapoor et al. (Kapoor et al., 2005). In this work, a feed-forwardscheme with two hidden layers was used to train the network.The results show that the model can predict the flow stresseven better that the well-known “sine-hyperbolic” constitutiveequation. Bhadeshia employed this technique to determineweld seam tracking and charpy toughness of steel weld met-als (Bhadeshia, 1999). Guo and Sha modeled the correlationbetween processing parameters and properties of alloy steelsusing artificial neural network (Guo and Sha, 2004).

One of the metallurgical events that usually occurs duringwarm or cold working regions, is dynamic strain ageing. Thisphenomenon occurs in a large number of metal and alloys and

cause the formation of flow-localized regions during defor-mation due to the negative strain rate sensitivity (Klose andZiegenbein, 2004; Pink and Kumar, 2000). Therefore, prediction

116 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 1 9 6 ( 2 0 0 8 ) 115–119

Table 1 – Chemical composition of the material used inthis work (wt%)

Element

Mg Mn Fe Si Cr Cu

4.5 0.71 0.33 0.19 0.058 0.037

of flow stress behavior is important in such metals and alloys.In this work, a neural network algorithm is employed to assessflow stress of AA5083 in both regions of the serrated flow andthe smooth yielding. The input parameters are selected to beas temperature, strain and strain rate and the output is theflow stress. In order to construct the networks, tensile testingunder different temperatures and strain rates are conductedand then the region of serrated flow is determined. In the nextstep, the achieved flow stresses are used for training two differ-ent neural networks where one of the networks is trained forthe serrated flow and the other one is trained in the smoothyielding region. A good agreement is observed between thepredicted results and the experimental data for both regionsthat shows the reliability of the employed model.

2. Experimental procedure and database

The AA5083 slab with the initial thickness of 25 mm was usedin this investigation. The composition of the employed mate-rial is given in Table 1. The as-received material was firstannealed at 430 ◦C for 2 h and afterward air cooled and thenthe samples were machined out of the raw material accordingto ASTM E8 and E21 standards. Laboratory tensile tests werecarried out to assess the flow stress behavior as well as to studythe dynamic strain ageing phenomenon. The tensile testswere performed using an Instron machine. It is worth notingthat the crosshead speed during each experiment was keptconstant therefore the true strain rate was being decreasedslightly. Different average true strain rates were used rangingbetween 10−4 and 10−1 (s−1) and various temperatures fromroom temperature to 233 ◦C Table 2 shows the strain rates andtemperatures employed in this research. A computer controlsystem is used to record the load versus displacement, whichwere converted into true stress versus true strain curves forpreparing initial data for neural networks as database. Then,calculated flow stresses are used for the neural network anal-

ysis. For this purpose, the experimental data is divided intotwo sets, a set is allocated for training data sets and the otherone is for testing the designed networks. It should be notedthat the experimental flow stress that used in construction the

Table 2 – Temperatures and strain rates used for thetensile tests

Strain rate (s−1) Temperature (◦C)

0.0001 250.001 680.01 1100.04 1690.1 233

Fig. 1 – Schematic illustration of the neural networkstructure.

network were chosen under various deformation conditionsincluding strain rates of 0.0001, 0.001, 0.01 and 0.1 and differ-ent temperatures mentioned in Table 2, and at true strainsof 0.04, 0.08, 0.12, 0.16 and 0.2. Obviously, the flow stressesunder the other deformations conditions were noted as non-sampled data.

3. The neural network models

Strain rate, temperature and strain are considered as the inputvariables, which they are extracted from the stress–straincurves. The measured true stress is selected to be as the out-put level. While all variable were normalized within range “0”to “1” as follows:

xN = x

xmax(1)

where xN and xmax are the normalized value and the maxi-mum value of variable, respectively. Normalization operationpermits comparison of the relative importance of individualinputs in the analysis. The patterns of the neural networkmodels for serrated flow and smooth yielding conditionsare shown in Fig. 1. The inputs and the outputs levelsare connected through a hidden layer hi where the inputsxj are operated by a transfer function as follows (Golden,1996):

hi = f

(∑w

(1)ij

xj + �(1)ij

)(2)

where �(1)ij

is defined as the bias, analogous to the constant that

appears in the linear regression method, w(1)ij

are defined as theweights that determine the strength of the transfer function.The following sigmoidal function is employed to construct thehidden layer.

f (n) = 21 + exp(−2n)

− 1 (3)

All the hidden units contribute to the out put as follows:

y = g

(∑i

w(2)ij

hi + �(2)

)(4)

t e c h n o l o g y 1 9 6 ( 2 0 0 8 ) 115–119 117

wg

g

dps

M

watrtiasdmfin

Fd

j o u r n a l o f m a t e r i a l s p r o c e s s i n g

here �ij and �(2) are a second set of weights and a bias and(n) is a linear function as below:

(n) = n (5)

The weights and biases are unknowns and they areetermined through training by the aid of a feed-forward back-ropagation scheme, which involves minimization of meanquare error (Eq. (6)) in each iteration.

SE = 1Q

Q∑k=1

e(k)2 = 1Q

Q∑k=1

(t(k) − a(k))2 (6)

here t(k), a(k) and Q are the target value, the output valuend the number of target data, respectively. Backpropaga-ion was created by generalizing the Widrow–Hoff learningule to multiple-layer networks and nonlinear differentiableransfer functions. The input vectors and the correspond-ng target vectors are used to train a network until it canpproximate a function, associating the input vectors withpecific output vectors. Standard backpropagation is a gra-ient descent algorithm, in which the network weights are

oved along the negative of the gradient of the performance

unction. The term backpropagation refers to the mannern which the gradient is computed for nonlinear multilayeretworks.

ig. 2 – True stress vs. true strain curves achieved underifferent working conditions, (a) at 25 ◦C and (b) at 145 ◦C.

Fig. 3 – Domains of serrated flow and smooth yielding.

Properly trained backpropagation networks tend to givereasonable answers when presented with fresh inputs. Thisgeneralization property makes it possible to train a network ona representative set of input/target pairs and get good resultswithout training the network on all possible input/outputpairs.

4. Results and discussion

Fig. 2 shows stress–strain curves under different working con-ditions. According to the previous researches (Clausen andBorvik, 2004) the typical temperature range of DSA has beenreported ranging between −80 and 120 ◦C. As it is observed,dynamic strain ageing occurs in certain deformation condi-tions and alters the flow stress of the metal. Based on the

achieved stress–strain curves and using the Arrhenius-typeequation as below, appearance and terminal of serrated flowwere determined as presented in Fig. 3 where the flow stresses

Fig. 4 – Predicted flow stress vs. measured flow stress inserrated conditions for the sampled data.

n g t

118 j o u r n a l o f m a t e r i a l s p r o c e s s i

vary between 210 and 320 MPa.

ε̇ = A exp(

− Q

RT

)(7)

here ε̇ is the applied strain rate, A a frequency factor, T the

absolute temperature, R the gas constant and Q is the activa-tion energy.

In this work, for estimation of the flow stress, the number oftraining iterations are determined on the best accuracy. Then,

Fig. 5 – Comparsion between the experimental data andthe predicted results for the non-sampled results, (a) 25 ◦Cand (b) 145 ◦C.

e c h n o l o g y 1 9 6 ( 2 0 0 8 ) 115–119

a strain–stress curve in both regions are predicted with biasesand weights matrixes of trained neural network and com-pared with the non-sampled stress–strain curves to ensureof accuracy of the proposed model. It is worth noting that theneural network models for the serrated and the smooth yield-ing domains contain a hidden layer and a linear output layerbut numbers of levels in hidden layer are selected as 10 and 8,respectively, to achieve the highest accuracy.

Fig. 4 shows the predicted flow stresses versus the mea-sured values for the sampled data in different temperaturesand strain rates. The angle of passing line through the data isexactly 45◦ that illustrates that the neural networks have beentrained properly.

Fig. 5 indicates both experimental and predicted truestrain–stress curves in serrated-flow region. Under these con-ditions, the flow stress is reduced by increasing in the strainrate as shown in this figure.

Therefore, the predictions show that there is a negativestrain rate sensitivity in this domain. It has been establishedthat the magnesium atoms that are responsible for happeningof dynamic strain ageing in AA5083, diffuse to the dislocationcores and create clusters and reduce the dislocations mobil-ity. However, by increasing the applied strain rate, creation ofcluster around the core of dislocation is prevented due to thehigh speed of the mobile dislocation (Picu and Zhang, 2004).This phenomenon causes a negative strain rate behavior inthe region of serrated flow. As it is observed, the predictionsalso show the same behavior that it illustrates the accuracy ofthe employed model.

The predicted strain versus measured stress in smoothyielding domain are shown in Fig. 6. This figure indicates thatthe utilized model can predict the flow stress with a good

Fig. 6 – Predicted flow stress vs. measured flow stress forthe sampled data.

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c

Fc1

awc

5

Ib

r

alloys using a neural network analysis. ISIJ Int. 39, 999–1005.

ig. 7 – Comparison between non-sampled stress–strainurve with the experimental values in the temperature of10 ◦C and the strain rate of 0.1 s−1.

ccuracy. The non-sampled stress–strain curve is comparedith the experimental data in Fig. 7. It is observed that a good

onsistency still exists between the two sets of results.

. Conclusion

n this work, the neural networks models with a feed-forwardackpropagation method have been coupled to predict flow

h n o l o g y 1 9 6 ( 2 0 0 8 ) 115–119 119

stress in AA5083. The input levels are strain rate, temperatureand strain and the output level is the flow stress. To improvethe accuracy of the predictions two separate neural networkshave been constructed, one for the serrated-flow region andthe other one for the smooth yielding conditions. The pre-dicted results are in a good agreement with the experimentaldata in both regions which illustrates the capability of themodel as a tool for accurate estimation of flow stress in warmand cold working conditions.

e f e r e n c e s

Bhadeshia, H.K.D.H., 1999. Neural networks in materials science.ISIJ Int. 39 (10), 966–979.

Clausen, A.H., Borvik, T., 2004. Flow and fracture characteristicsof aluminum alloy AA5083-H116 as function of strain rate,temperature and triaxility. Mater. Sci Eng. A 364, 260–272.

Golden, R.M., 1996. Mathematical Methods for Neural NetworkAnalysis and Design. The MIT Press, Cambridge,Massachusetts (Chapter 2).

Guo, Z., Sha, W., 2004. Modelling the correlation betweenprocessing parameters and properties of maraging steelsusing artificial neural network. Comput. Mater. Sci. 29, 12–28.

Jung, S., Ghaboussi, J., 2006. Neural network constitutive modelfor rate-dependent materials. Comput. Struct. 84, 955–963.

Kapoor, R., Pal, D., Chkaravartty, J.K., 2005. Use of artificialnetworks to predict the deformation behavior ofZr–2.5Nb–0.5Cu. J. Mater. Proc. Tech. 169, 199–205.

Klose, F.B., Ziegenbein, A., 2004. Analysis of Portevin-Le Chatelierserrations of type Bin Al–Mg. Mater. Sci. Eng. A 369, 76–81.

Narayan, V., Abad, R., Lopez, B., Bhadesia, H.K.D.H., Mackay, D.J.C.,1999. Estimation of hot torsion stress strain curves in iron

Picu, R.C., Zhang, D., 2004. Atomistic study of pipe diffusion inAl-Mg alloys. Acta Mater. 52, 161–171.

Pink, E., Kumar, S., 2000. Serrated flow of aluminum alloysinfluenced by precipitates. Mater. Sci. Eng. A 280, 17–24.