Failure load prediction of adhesively bonded GFRP composite joints using artificial neural networks

There are different process parameters of bonding joints in the literature. The main objective of the paper was to investigate the effects of bonding angle, composite lay-up sequences and adherend thickness on failure load of adhesively bonded joints under tensile load. For this aim, the joint has four types of the bonding angles 30°, 45°, 60° and 75°. Composite materials have three different lay-up sequences and various thicknesses. The bonding angle, adherend thickness and composite lay-up sequences lead to an increase of the failure load. Moreover, artificial neural network that utilized Levenberg-Marquardt algorithm model was used to predict failure load of bonding joints. Mean square error was put into account to evaluate productivity of ANN estimation model. Experimental results have been consistent with the predicted results obtained with ANN for training, validation and testing data set at a rate of 0.998, 0.997 and 0.998 respectively.


Introduction
Joint strength is important for aerospace, aviation and automotive industries [1]. Therefore, researchers require increasing joint strength. Bonding geometry, adhesive area and sample thickness have significant effect on the joint strength [2]. To improve the joint strength, one of the leading methods is increasing failure load. ANNs (artificial neural network) are robust computing technique that are widely used in solving many complex and poorly defined problem. Lately, studying artificial neural networks for anticipating has caused remarkable advance in engineering areas [3,4]. Tosun and Çalık [5] figured out that failure load in single lap bonding joints was exposed to axial tensile load. Various bonding length and bonding area in single lap joint were used to find failure load. Levenberg-Marquardt model was applied to estimate relationship between failure load and input data. The mean error was found 0.997 % and 0.992 %. They demonstrated that ANN had a perfect approximation for bonding joints. Balcıoğlu et al. [6] analyzed the effects of single-sided and double-sided of bonding angle, patch structure and patch type for composite materials of bonded joints on failure load. Because of this five different bonding types and angles were exposed to axial tensile load. According to experimental results failure loads were predicted by ANN. The mean absolute error was found 1.03 %. Rangaswamy et al. [7] investigated glass fiber reinforced epoxy composites for single lap adhesive joints. The effects of bonding area and adhesive thickness on failure load were studied experimentally. The bonding area was a profound impact on the joint strength. Moreover, artificial neural networks were used for the prediction of failure load. The values of training and validation for the ANN model were 0.99997 and 0.99998 respectively. Neto et al. [8] examined the experimental study on the joint strength of composite materials. They proposed a joint geometry for single lap adhesive joint with different bonding areas. They demonstrated that failure load increased with the increase of the bonding area. Silva et al. [9] studied the effect of the joint strength of single lap joints for various geometry and materials. They showed that failure load increased with the increase of the bonding area. They determined that failure load also in-creased with the increase of the adherend thickness. As a result, the bonding area had a great impact on the joint strength. Altan and Topçu [10] developed butterfly shape geometry made of glass-fiber composites to specified failure load. Different geometry parameters of this shape were analyzed to take maximum load. Furthermore the finite-elements method was used to predict of failure load by using experimental results. Experimental results were confirmed with numerical method. Sun et al. [11] presented failure prediction of scarf joints of composite material. Tensile experiments were applied with different scarf angles and finite element models were established to presume failure. A cohesive model was defined to predict the failure load of bonding joints. This model was compared with experimental results to validate the accuracy of the cohesive model. Besides, the influence of composite stacking sequence on the bonding joints was discussed. Various stacking sequence has remarkable difference on the failure load. Matta and Ramji [12] performed mechanical estimation of adhesively bonded CFRP scarf joint. Tensile tests were applied with different scarf angles using digital image correlation to predict failure load. Various composite stacking sequences on the bonding joints were discussed. Moreover, DIC technique was preferred to estimate values compared with test data for validation. DIC technique could be recommended for examining mechanical behavior of CFRP scarf joints. Wu et al. [13] compared the damage tolerance of stepped-lap and scarf joints under tensile loading. 3D finite element models were installed for both joint types. Other parameters, which may affect stacking sequence of laminate were considered. The stacking sequence had highly effect on peel stresses along bonding length. With the increase of the length of adherend, joint strength decreased. Scarf joint has higher strength than the other type of joint. Bardak [17] said that experimental studies were costly usually complex and even time consuming. To prevent this situation, lots of techniques were used. ANN was the most usable one. The principles of ANN were neurons which are subjected to each other with weight. Researches can be trained to develop a special function by arranging the rates of these weights. ANN was used most of researchers due to powerful prediction. Bardak et al. [18] made use of ANN to predict bonding strength of wood joints under load. They stated that ANN estimated bonding strength of joints with high accuracy. Tiryaki and Hamzacebi [19] made use of ANN to anticipate modulus of elasticity and modulus of rupture of heat treated woods. They checked the experimental values of modulus of elasticity and rupture with outputs of ANN. They stated that ANN estimated these parameters with high accuracy. Kim et al. [20] described prediction of failure behavior of adhesively bonded composite joints. They also researched into strength of single lap bonded composite joints with using experimental and numerical method. Tsai and Morton [21] presented mechanical behavior of double lap bonded composite joints subjected to tensile load. They also investigated stress distributions and deformation for the bonded joints by using linear elastic finite element model. Mahdi and Kadi [22] studied energy absorption and crushing behavior of elliptical glass fiber composite tubes. They also used ANN to compare predicted data with real experimental one. Hence, they stated that ANN estimated the response of composite energy absorption with high accuracy and could be used efficiently. Ramasamy and Sampathkumar [23] studied impact damage tolerance of glass fiber reinforced composites by using ANN. They also used acoustic emission method. They decided that signal strength which is related to one of acoustic emission major parameters to train ANN. They stated that ANN predicted the impact damage tolerance with high accuracy and very efficiently. Varol et al. [24] worked reinforcement effects on mechanical and physical properties of composites. They also used ANN to compare experimental values which are tensile strength, density and hardness. They showed that well-trained ANN model could be used effectively and powerful to predict reinforcement effects on composites. Bezerra et al. [25] researched stress-strain behavior of CFRP and GFRP composites. They also used a multilayered ANN technique. Analyses results showed that ANN has powerful effect to estimate stress-strain behavior for both composite types. Dominczuka and Kaczmarzewski [26] investigated ANN for processing of experimental data associated with strength of bonding joints. They checked ability of ANN with capacity of typical statistical analysis methods like polynomial and linear regression. Zghoul [27] utilized ANN in single lap adhesive joints for rating dependent output of adhesives. ANN model obtained information about experimental data. Kovan and Sekercioglu [28] presented a model by using ANN to anticipate fatigue life and shear force of bonded cylindrical joints. The outcome indicated related model was viable for fatigue life and shear force of bonded joints. Tiryaki and Aydın [29] proposed ANN model. They took multiple linear regressions for heat treated wood material to estimate ideal bonding joint strength. Kalhor et al. [30] considered effects of FRP thickness and laminate stacking order. They received response of FRP square pipes exposed to axial load. ANN model has been used to see the effect of impact velocity on composite plates. Fernandez et al. [31] used ANN to practice ballistic effect of composite materials that analyze impact orbit. ANN was an effective way for estimating effect of laminates as exposed to low velocity impact load. Turgut and Birecikli [32] studied experimental and numerical analysis of bonding joint. They showed that mechanical behaviors especially failure load vary depending on geometry of bonding joint, composite stacking sequence and type of adhesive. Geleta et al. [33] prepared thick adhesive inclined joints to predict the effect of defect types and locations on the joint strength. Specimens with two different geometries were prepared. Experimental tensile test results were compared finite element analysis. The predicted results were confirmed with experimental results. Kumar et al. [34] studied carbon epoxy composite laminates to evaluate the failure loads of pin joints by using experimental and numerical methods. Various types of geometric ratios were used to analyze the joints. Experimental tests were validated with numerical analysis. The numerical results were found to be consistent with the experimental results.
Artificial neural networks (ANN) are inspired from biological neural networks in our brain. Brain of human consists of about 100 billion neurons which have about 100 trillion interconnections among them. Every neuron for input is given either closed or open on state. Interconnections work on the notion of positive empowerment, a number of inputs pave the way for an exact output; and by this way, the "brain" remembers this way accurately and "learns" which way to relate [35].
Many engineering problems can be solved easily by using ANN instead of complex mathematical rules [36].
There are many different types of joint geometries in previous works. The effects of various variables on the joint strength have been discussed so far. Also using the methods of the artificial neural network have not very common on the joint strength. The advantage of the present research was to determine the effects of new variables on the joint strength. In this paper, a new type of joint geometry was presented. Also, the joint strength was investigated both experimentally and predicted by using artificial neural networks. The major point for using of ANN is the ability to predict many variables simultaneously. The flowchart of this study was drawn in Fig. 1.

Materials and methods
The effects of the various variables on the joint strength were investigated in the relevant literature. For this purpose, different joint geometries were designed on the bonding joint by researchers. Furthermore, less information was available on predicting the effects of variables on the joint strength by using ANN. In the present work, a new type of joint geometry was handled and more detailed strength analysis was aimed unlike previous studies. The joint strength was investigated experimentally and predicted by using artificial neural networks.

Experimental detail
Ductile type adhesive, DP460 made by 3M firm, was used for bonding joints. Glass fibers reinforced composite materials (Sigratex Prepreg GE 8903-280-37S, Resin system: E201), were manufactured by Odak Composite Technology in Ankara, Turkey. The composite materials were made of glass/epoxy prepregs (by autoclave curing process) with the layup se- Properties for adhesive (DP460) and adherend (glass fiber composite materials) are listed in Table 1. The mechanical properties of materials were obtained by the producer firm Odak Composite Technology in Ankara, Turkey [37].
Bonding geometry have four types of angles (30°, 45°, 60°, 75°) as seen in Fig. 2. Dimension parameters for test samples  are given in Table 2. Bonding length has 20 mm for each side and resulting in a total length of 60 mm (2a+b = (2x20) + 20 = 60 mm). Bonding length was held constant for each joint because of determining the influence of bonding angle.
Sharp corners are avoided to prevent stress concentration in design. Because of this, bonding angles with sharp corners were rounded in radius of 2 mm as displayed in Fig. 3.
Adhesive thickness was held constant to be 0.20 mm. The length of each test sample is 250 mm and resulting in a total length of 250.2 mm include in the adhesive thickness. For the accuracy of the test results, three samples of the same bonding joint were produced and the experiment was repeated in Fig. 4.
Experiments were performed by Shimadzu AG-X model tensile test machine at Dokuz Eylul University Composite Research and Testing Laboratory as shown in Fig. 5. Lower grip of test machine is fixed and upper grip is moving. The grip allowance was left at both ends of the samples. The calibration of the test machine was done. It is assumed that the humidity of the surroundings does not affect the material properties. The tensile test was performed according to ASTM D3039-76 standard method [38]. Total capacity of the machine is 100 kN.
The sample was connected to the test machine according to boundary conditions as illustrated in Fig. 5. It is given pre-load of 0.10 MPa and crosshead speed of 1 mm/min. at constant room temperature 22 °C with relative humidity 51 % [39].

Artificial neural network
ANN is consisting of 3 components that are input, output and hidden layer. Link between all layers is provided by weights as can be seen in Fig. 6. Experimental data received from the     input layer are multiplied by the link weights between the input layer and the hidden layer and transmitted to the hidden layer.
The inputs coming to the neurons in the hidden layer are collected and transmitted to the output layer by multiplying them with the link weights between the hidden layer and the output layer. The neurons in the output layer also collect these inputs coming to them. Activation functions process them and produce more accurate output. The weight values of the links are determined during the learning process. The first step of learning can be described as activation. Does the sum of signals entering the nerve cell does it have a value that can activate the cell or not? The answer is as follows: if the total signal is high enough to ignite the cell and exceed the threshold value, then it is the cell active (y = 1); otherwise, the cell is passive (y = 0). ANN has several activation functions. The most widely used is "multi-layer perceptron" model and in present day, "Sigmoid function" is generally used as the activation function. The sigmoid activation function is a continuous and derivable function. This function generates a value between 0 and 1 for each input value. It is defined by Eq.
In biological systems, learning occurs through synaptic connections between neurons. In other words, people start learning process by living from their birth. In this process, the brain continuously develops. As experience increases, synaptic connections are established and even new connections occur. In this way, learning occurs and this also applied to ANN. Learning happens by using examples through training. In other words, by processing the input / output data, that is, by using these data, the training algorithm repeatedly adjusts the weights of the synapses until a convergence is achieved. The selected training algorithm is important to get a good result. A large number of training algorithms exist in the literature. With regard to the training algorithm put account, the error among the network output and the wanted output is propagated backwards to alter the weights of the network until the error is decreased. A neuron can be defined by Eq. (2): where w and x define weights and inputs. Where b is bias. The intention of bias entries is to balance the origin of the activation function to provide better learning [40]. Transfer function can be described by Eq. (3): In this study, we use an input layer with 4 neurons, an output layer with one neuron and a hidden layer with 10 neurons. Bonding angle (°), adherend thickness (mm), composite lay-up sequence and bonding area (mm 2 ) are used as the input variables. Failure load (N) is used as the output variable in our ANN model.
The Levenberg -Marquardt algorithm, which is a kind of back propagation algorithm, is used to train the modeled network.
Experimental data is divided into three parts: training, validation and testing. MATLAB -Neural Network Toolbox is used for design, train and simulate for our network. The network is trained and tested using 48 different samples.
The data used in neural network model were composed in a format of four input parameters that include bonding angle, adherend thickness, composite lay-up sequence and bonding area. A neural model consists of 4 input layers and an output, was analyzed as demonstrated in Fig. 7.

Results and discussions
In this section, samples of bonding joint were exposed to tensile load until rupture and maximum failure load were determined by test machine.
There are three considerable points here; the first one is that influence of bonding angles on failure load. The second one is that influence of composite lay-up sequence on failure load. The latter one is that influence of adherend thickness on failure load.

Influence of composite lay-up sequence on failure load
The load-thickness plot for the bonding joint samples which are obtained experimentally is shown in Fig. 8. Test results for bonding angle 30° is indicated in Fig. 8(a). The other test results for bonding angle 45°, 60° and 75° are indicated in Figs.

8(b)-(d).
Failure load greatly increased as adherend thickness increase. It carries more load due to bonding area is enlarging. Failure load also increased with the use of various composite lay-up sequences in the same thickness. It is designated that changing composite lay-up sequences has a profound effect on failure load. Bonding angle for 75° has the highest failure load as seen in Fig. 8(d).
In addition to these, multi-directional fabric of [0/90/45/-45] was used, the failure load increased considerably. The important point is that multi-directional fabric carried more load than one directional fabric.

Influence of bonding angle on failure load
The load-area plot for all bonding angles which are obtained experimentally is shown in Fig. 9. The test results for angles (30°, 45°, 60° and 75°) by using composite lay-up sequence of [0/90] are shown in Fig. 9(a) The results of the experiments demonstrated that bonding angles effect the failure load. It can be said that the load was directly increased by raising angle on the same bonding area. The minimum failure load is determined for bonding angle 45°. It is thought to have occurred glass fibers are ineffective on tensile load.
The load-angle plot for all composite lay-up sequences which are obtained experimentally in only one bonding area (180 mm 2 ) is compared in Fig. 10. In this graph the influence of composite lay-up sequence on the failure load was indicated at different angles. The essential point is that composite lay-up sequence of [0/90/45/-45] carried more load than the others.

Influence of composite adherend thickness on failure load
The load-angle plot for all adherend thicknesses which are obtained experimentally is shown in Fig. 11.
The test results for thicknesses (3, 5, 7 and 9 mm) by using composite lay-up sequence of [0/90] are shown in Fig. 11 The results of the experiments demonstrated that adherend thickness affected the failure load. It can be said that the load was directly increased by raising thickness valid for all angles.
The major point is that thickness of 9 mm carried more load than the others due to increasing bonding area. The minimum failure load is determined thickness of 3 mm. The bonding area can be changeable with different adherend thickness.

Prediction of failure load by using ANN
In this study, 34 of the 48 values were used for training. 7 values were used for validation and testing respectively. The mean square error (MSE) was put into account to evaluate the productivity of ANN estimation model. MSE is defined as the average of squares of "errors". The mean square error was calculated by Eq. (4): where t i is the measured value of the experiment, td i is the estimated value, and N is the total number of samples. The mean square error depending on iteration of the ANN is shown in Fig. 12. The training of the ANN was turned off after 10 epochs due to the targeted MSE value was achieved in 1000 iterations.
·Artificial neural networks using the Levenberg-Marquardt algorithm predicted the failure load. ·The error percentage rates for validation, testing and training calculated by ANN. ·The first 34 values were used for training. ·The next 7 values were used for validation. ·The last 7 values were used for testing. ·The predicted values obtained by ANN were found with very low percentage errors. ·The correlation values of R 2 for training data set, validation data set and testing data set in the prediction of failure load by ANN were 0.9988, 0.9979 and 0.9981 respectively as shown in Fig. 13. ·The overall correlation value of R 2 was calculated 0.9987, ·The marvelous results have been obtained effectively with the use of ANN method. ·This result shows that the ANN has a very high reliability in estimating the failure load.
The comparison of ANN (artificial neural network) and experimental results were represented as a bar graph in Fig. 14.
The results of this bar graph were occurred for the adherend thickness of 3 mm. Finally, the predicted results of ANN were consistent with the experimental data in the end.

Conclusions
This experimental study was carried out to investigate the effects of the bonding angle, composite lay-up sequence and adherend thickness on the joint strength. To improve the joint strength, one of the leading methods is increasing failure load. Furthermore ANN trained algorithm was performed by using experimental test data in order to predict the failure load of the adhesively bonded composite joints.
The following results were obtained: ·The failure load of the bonding joint increased with the increase of the bonding angle. The maximum experimental failure load was obtained as 52950 N for bonding angle θ = 75°. ·Then, the minimum experimental failure load was obtained as 31446 N for bonding angle θ = 45° on the same bonding area. Due to the increase in bonding angle, the failure load raised approximately by 68.40 %. ·The failure load of the bonding joint also increased with the increase of the adherend thickness. Failure load was enhanced up changing adherend thickness from 3 mm to 9 mm for samples on the same bonding angle. ·Composite lay-up sequences caused a significant change on the failure load with Refs. [11][12][13].    ·The correlation values of R 2 for training data set, validation data set and testing data set in the prediction of the failure load by ANN were 0.998, 0.997 and 0.998 respectively. These results have been consistent with Refs. [5][6][7]. ·The values estimated by ANN indicated that the errors were in acceptable limits. ·The results of analysis described that ANN model could be used effectively and powerful to predict the failure load. ·ANN reduced time loss and it can be used to support the experimental results. ·Thus, the model of ANN will help researchers to determine correct variables on the joint strength.