**5. TWB formability prediction using ANNs**

The set of tensile and deep drawing characteristics of TWB from the simulation trials are used for ANN modelling and expert system development. The ANN is trained to learn arbitrary nonlinear relationships between input and output parameters of TWB. The ANNs are inspired by biological neurons and have shown credible results in learning the arbitrary and complex relationships between the inputs that govern the outputs of an system. ANN consists of several layers of highly interconnected neurons which are the basic computing. The various architectural parameters of an ANN are number of hidden layers, neurons, and transfer functions which are optimized based on many trials to predict the outputs within certain errors that can be tolerated in an given application. In the present study a normalized error limit of 10-4 is taken. Using the simulation data obtained ANN with various network structures with one and two hidden layers with varying number of neurons in each layer and different transfer functions were examined. Optimized ANN

Prediction of Tensile and Deep Drawing Behaviour of Aluminium Tailor-Welded Blanks 107

Intermediate Intermediate

True Stress (MPa)

True Strain True Strain

Fig. 20. Validating the true stress - strain behaviour predicted by ANN with FE simulation

The TWB tensile properties from FE simulations and ANN modelling for chosen two intermediate trials were compared to validate the accuracy of ANN prediction. Table 3 summarizes the average error statistics pertaining to ANN prediction for training and testing with two intermediate test data not used for training. In the industrial application error range of 10-12% is considered acceptable and the same has been taken as a bench mark. It can be seen that almost all the output parameters are predicted within acceptable error limits. It is seen that only strain-hardening exponent (*n*) value of aluminium alloy TWB shows unacceptable error percentage (14.35%). This is possibly due to the smaller values of strain-hardening exponent which gives large percentage difference even if varied within small range (Veerababu et al., 2009). Similarly, the second set of tensile simulation with notched sample was used to train an ANN in a similar way. The limit strain (major and minor strain), failure location, minimum thickness, strain path were predicted using the trained ANN and validated with FE simulation results for two intermediate input levels. The prediction of failure location showed a higher level of prediction error (6.52 %) (Table 4). All other parameters show better prediction level with acceptable error range (Abhishek

**Output Training Testing** 

Yield strength (MPa) 0.18 7.08 11.91 50.04 Ultimate tensile strength (MPa) 0.05 13.71 5.03 35.63 Uniform elongation (mm) 0.09 0.10 4.45 1.41 Strain-hardening exponent '*n*' 0.01 0.01 *14.35* 0.01 Strength coefficient '*K*' (MPa) 0.01 13.01 10.49 36.04

Table 3. Validation of ANN model for tensile test simulation within safe progression limits

0 0.05 0.1 0.15 0.2

**% error SD in error % error SD in error** 

ANN prediction Simulation prediction

ANN prediction Simulation prediction

0 0.05 0.1 0.15 0.2 0.25

for two test data (Veerababu et al., 2009)

600

500

400

300

True Stress (MPa)

200

100

0

et al., 2011).

architecture are found to model the tensile behaviour from the two sets of tensile simulation as well as the deep drawing behaviour. In all these cases, the ANN architecture consists of input layer with 6 input neurons (corresponding to 6 factors), and one / two hidden layers and output neurons corresponding to the number of outputs to be predicted. A feed forward back propagation algorithm is selected to train the network in Matlab® programming environment (Mathworks Inc., 2008). Here the scaled conjugate gradient algorithm (Mathworks Inc., 2008) is used to minimize the error. For each of the simulation trials based on the L27 orthogonal design of experiments, 27 data sets were used to train and two intermediate data sets were utilized for testing. The TWB tensile behaviour or deep drawing behaviour from FE simulations and ANN modelling for chosen two intermediate test sets or trials are compared to validate the accuracy of ANN predictions in each case. As an example, the ANN architecture used to predict the tensile behaviour without pre-existing defect based on the first set of tensile simulation data is shown in Fig. 19. Similar ANNs were trained for the other tensile simulation test for limit strain prediction as well as deep drawing simulation. The salient observations on the prediction of TWB tensile and deep drawing behaviour are described further.

Fig. 19. Neural network architecture for TWB tensile behaviour prediction in safe region

The first set of 27 tensile simulation data (for the safe region of progression) was used to train an ANN and true stress-strain response, yield strength, ultimate tensile strength, uniform elongation, strain-hardening exponent and strength coefficient of welded blanks were predicted and validated with FE simulation results for two intermediate input levels. The comparison between ANN predicted true stress-strain behaviour and simulation results are shown in Fig. 20. The strain-hardening exponent (*n*) and strength coefficient (*K*) values obtained from ANN models were incorporated into Hollomon's equation (*σ* = *K εn*) for TWB made aluminium alloy base materials and true stress-strain curves were obtained. It should be noted that even though Hollomon's strain-hardening law is not accurate to predict the tensile behaviour of aluminium alloy base material, ANN predictions are quite accurate in predicting the same.

architecture are found to model the tensile behaviour from the two sets of tensile simulation as well as the deep drawing behaviour. In all these cases, the ANN architecture consists of input layer with 6 input neurons (corresponding to 6 factors), and one / two hidden layers and output neurons corresponding to the number of outputs to be predicted. A feed forward back propagation algorithm is selected to train the network in Matlab® programming environment (Mathworks Inc., 2008). Here the scaled conjugate gradient algorithm (Mathworks Inc., 2008) is used to minimize the error. For each of the simulation trials based on the L27 orthogonal design of experiments, 27 data sets were used to train and two intermediate data sets were utilized for testing. The TWB tensile behaviour or deep drawing behaviour from FE simulations and ANN modelling for chosen two intermediate test sets or trials are compared to validate the accuracy of ANN predictions in each case. As an example, the ANN architecture used to predict the tensile behaviour without pre-existing defect based on the first set of tensile simulation data is shown in Fig. 19. Similar ANNs were trained for the other tensile simulation test for limit strain prediction as well as deep drawing simulation. The salient observations on the prediction of TWB tensile and deep

Fig. 19. Neural network architecture for TWB tensile behaviour prediction in safe region

The first set of 27 tensile simulation data (for the safe region of progression) was used to train an ANN and true stress-strain response, yield strength, ultimate tensile strength, uniform elongation, strain-hardening exponent and strength coefficient of welded blanks were predicted and validated with FE simulation results for two intermediate input levels. The comparison between ANN predicted true stress-strain behaviour and simulation results are shown in Fig. 20. The strain-hardening exponent (*n*) and strength coefficient (*K*) values obtained from ANN models were incorporated into Hollomon's equation (*σ* = *K εn*) for TWB made aluminium alloy base materials and true stress-strain curves were obtained. It should be noted that even though Hollomon's strain-hardening law is not accurate to predict the tensile behaviour of aluminium alloy base material, ANN predictions are quite accurate in

drawing behaviour are described further.

predicting the same.

Fig. 20. Validating the true stress - strain behaviour predicted by ANN with FE simulation for two test data (Veerababu et al., 2009)

The TWB tensile properties from FE simulations and ANN modelling for chosen two intermediate trials were compared to validate the accuracy of ANN prediction. Table 3 summarizes the average error statistics pertaining to ANN prediction for training and testing with two intermediate test data not used for training. In the industrial application error range of 10-12% is considered acceptable and the same has been taken as a bench mark. It can be seen that almost all the output parameters are predicted within acceptable error limits. It is seen that only strain-hardening exponent (*n*) value of aluminium alloy TWB shows unacceptable error percentage (14.35%). This is possibly due to the smaller values of strain-hardening exponent which gives large percentage difference even if varied within small range (Veerababu et al., 2009). Similarly, the second set of tensile simulation with notched sample was used to train an ANN in a similar way. The limit strain (major and minor strain), failure location, minimum thickness, strain path were predicted using the trained ANN and validated with FE simulation results for two intermediate input levels. The prediction of failure location showed a higher level of prediction error (6.52 %) (Table 4). All other parameters show better prediction level with acceptable error range (Abhishek et al., 2011).


Table 3. Validation of ANN model for tensile test simulation within safe progression limits

Prediction of Tensile and Deep Drawing Behaviour of Aluminium Tailor-Welded Blanks 109

**Parameters Test Data 1 Test Data 2** 

Table 5. Input properties for validating the ANN deep drawing behaviour prediction of TWB

This chapter presented some studies on tensile and deep drawing behaviour of aluminium tailor-welded blanks. A finite element based numerical simulation method is used to understand the behaviour. The presence of thickness, strength heterogeneities and weld region deteriorates the formability of aluminium welded blanks in most of the cases. Designing TWB for a typical application will be successful only by knowing the appropriate thickness, strength combinations, weld line location and profile, number of welds, weld orientation and weld zone properties. Predicting these TWB parameters in advance will be helpful in determining the formability of TWB part in comparison to that of un-welded base materials. In order to fulfil this requirement, one has to perform lot of simulation trials separately for each of the cases which is time consuming and resource intensive. Automotive sheet forming designers will be greatly benefited if an 'expert system' is available for TWBs that can deliver its forming behaviour for varied weld and blank conditions. A artificial neural network based expert system is described which is being developed by the authors. The expert system is envisaged to be expanded with industrial applications also. For example, a sheet forming engineer who wants to develop expert system for some industrial TWB sheet part can just make it as part of existing system framework in the same line of thought, without introducing new rules and conditions. The relations between TWB inputs and outputs are non-linear in nature and hence it is complex to explicitly state rules for making expert system. But these complex relationships can be captured by artificial neural networks. The expert system proposed is a continuous learning system as the field problems solved by the system can also become a part of training sample. Though the expert system can not reason out the decisions/results unlike rule based systems, one can interpret the results by comparing the outputs of two different input

Thickness ratio (*T*1*/T*2), *T*1 mm 0.6, 0.9 0.7, 1.05 Strength ratio (*YS*1*/YS*2), *YS*1 MPa 0.7, 210 0.6, 180

Weld orientation (º) 35 55 Weld location, mm 14 7 Weld yield strength *(YSW)*, MPa, 250 325

conditions quantitatively with minimum knowledge in TWB forming behaviour.

Ahmetoglu, M. A., Brouwers, D., Shulkin, L., Taupin, L., Kinzel, G. L. & Altan, T. (1995).

*Processing Technology*, Vol. 53, No. 3-4 , (September 1995), pp. 684-694 ASTM, (2000). Test Methods for Tensile Strain-hardening Exponents (*n*-values) of Metallic

Deep Drawing of Round Cups from Tailor-welded Blanks, *Journal of Material* 

Sheet Materials. *Annual book of ASTM standards 2000 (E 646-98)*, Section 3, Vol.

**6. Conclusion** 

**7. References** 

03.01.


Table 4. Validation of prediction by ANN for tensile simulation with necking induced failure

The deep drawing simulation data was used to train ANN to predict global TWB deep drawing behaviour viz., maximum weld line movement, draw depth, maximum punch force, draw-in profile for the chosen range of thickness and strength combinations, weld properties, orientation, and location. Two intermediate level data were taken for testing and validating the results as shown in Table 5. Fig. 21 presents the comparison between ANN and simulation results of draw-in profile of deep drawn cup. At different TWB conditions, the draw-in profile predicted by ANN model is well matched with the simulation results. All output parameters are predicted within acceptable error limits, except maximum weld line movement. Average error in this case is approximately 15% which is unacceptable. This possibly can be improved by using different strain-hardening laws and yield theories more suitable for aluminium alloy base materials. It is observed from Fig. 21a that the draw-in profiles are un-symmetric in shape. Minimum draw-in is seen along the angular weld region and in thicker material side, while thinner material shows maximum draw-in.

a) Test sample-1 b) Test sample-2

Fig. 21. Comparison of draw-in profile between ANN prediction and FE simulation for two deep drawing test simulation of aluminium alloy TWB


Table 5. Input properties for validating the ANN deep drawing behaviour prediction of TWB
