Erosion Studies of Short Glass Fiber-reinforced Thermoplastic Composites and Prediction of Erosion Rate Using ANNs ARJULA SURESH Department of Mechanical Engineering, Sreenidhi Institute of Science and Technology Yamnampet, Ghatkesar, Hyderabad 501 301, India A. P. HARSHA* AND M. K. GHOSH Department of Mechanical Engineering, Institute of Technology, Banaras Hindu University Varanasi 221005, India ABSTRACT: Erosion behavior of polyetherketone (PEK) reinforced by short glass fibers with varying fiber content (0–30 wt%) has been studied. Steady-state erosion rates have been evaluated at different impact angles (158–908) and impact velocities (25–66 m/s) using silica sand particles as an erodent. PEK and its composites exhibited maximum erosion rate at 308 impact angle indicating ductile erosion behavior. The erosion rates of PEK composites increased with increase in amount of glass fiber. Also, artificial neural networks technique has been used to predict the erosion rate based on the experimentally measured database of PEK composites. The effect of various learning algorithms on the training performance of the neural networks was investigated. The results show that the predicted erosion rates agreed well when compared with the experimentally measured values. It shows that a well-trained neural network will help to analyze the dependency of erosive wear on material composition and testing conditions making use of relatively small experimental databases. KEY WORDS: thermoplastic, erosive wear, polymer composites, artificial neural networks.
INTRODUCTION their composites are used as tribo- and structural materials in various automotive and aerospace applications due to their high strength, high modulus, enhanced toughness, and recyclability. The most important advantage of thermoplastics is design flexibility and ease of manufacturing into complicated parts by injection molding or extrusion process. In certain structural applications erosive wear has become a serious problem as it results in failure of the components. The erosion resistance of polymer composites is strongly influenced by the type of polymer matrix and type, amount, and arrangement of fiber used for reinforcement [1]. Erosion tests have been performed under various experimental conditions on different polymers and their composites. It has been concluded that composite materials present a rather poor erosion
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HERMOPLASTIC POLYMERS AND
*Author to whom correspondence should be addressed. E-mail:
[email protected]
Journal of REINFORCED PLASTICS
AND
COMPOSITES, Vol. 29, No. 11/2010
0731-6844/10/11 1641–12 $10.00/0 DOI: 10.1177/0731684409338632 ß The Author(s), 2010. Reprints and permissions: http://www.sagepub.co.uk/journalsPermissions.nav
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resistance [2,3]. A crucial parameter for the design with composites is the fiber-form, type, and content, as it controls the mechanical and thermomechanical responses [4]. The erosive wear behavior of short fiber-reinforced polymer composites as a function of fiber content has been studied in the past [5–9]. It was concluded that the inclusion of brittle fibers in polymer matrices leads to poor erosion resistance of polymer composites. Harsha et al. [8] studied the erosion behavior of various polyaryletherketones (PAEKs) matrix and composites reinforced with short glass or carbon fiber. Neat polyetheretherketone (PEEK) and 20% glass fiber reinforced PEEK showed peak erosion at 308 impingement angle whereas other PAEK (i.e., PEK and polyetherketoneketone) matrix and their composites showed peak erosion at 608 impingement angle indicating semi-ductile erosion behavior. There have been several attempts to correlate erosion resistance with various mechanical properties of polymers and composites [10–17]. The dependence of erosion rate on mechanical properties is complicated because the deformation caused by erosive particles is associated with high strain rates about 105–106 s1 and the stress state is complex [10]. Also, the effect of fiber and/or filler on abrasion/erosion of polymer composites is a complex and unpredictable phenomenon [18]. Hence, the dependence of erosive wear rate on the experimental parameters is difficult to model. Physical effects such as fiber fragmentation, debonding, pullout, etc. affect the behavior of polymer composites subjected to the erosive wear process. It is difficult to predict their relative contribution because various other mechanisms influence the erosion process. Meng and Ludema [19] reviewed the information about the existing wear models and equations for predicting the erosion rates of various types of materials. Their main conclusion was that there is no universal model/predictive equation exists. For this reason, artificial neural networks (ANNs) have been recently introduced for the prediction of wear data in various tribological tests [20–25]. Velten et al. [21] and Zhang et al. [22] were among the earliest pioneers to explore this approach to predict the wear volume of short-fiber/particle reinforced thermoplastics. In further work, Zhang et al. [23] applied this approach to predict the erosion rate of three polymers, i.e., polyethylene, polyurethane, and an epoxy modified by hygrothermally decomposed polyurethane. Objective of the present work was to conduct erosion experiments on PEK and its composites under a particular set of experimental conditions and prediction of the erosion rate using ANNs. EXPERIMENTAL DETAILS Materials PEK and its glass (short E-glass) fiber-reinforced composites were supplied by Victrex Plastics, USA in the form of molded plaques. The details of PEK and its composites selected for the present study and its designation, fiber content, physical, and mechanical properties are listed in Table 1. Erosive Wear Testing A schematic diagram of the solid particle erosion test rig used in the present study was given elsewhere [17]. The rig consists of an air compressor, a particle feeder, an air particle mixing, and accelerating chamber. Dry compressed air is mixed with the particles, which are fed at a constant rate from a conveyor belt type feeder into the mixing chamber and then accelerated by passing the mixture through a tungsten carbide converging nozzle of
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Erosion Studies of Short Glass Fiber-reinforced Thermoplastic Composites Table 1. Properties of short glass fiber-reinforced PEK composites. Property
PEK
PEK10
PEK20
PEK30
Fiber weight fraction (wt%) Fiber volume fraction (vol.%) Density (kg/m3) Tensile strength (MPa) Tensile elongation at break (%) Vickers hardness (HV) Izod impact, notched (J/m)
– – 1300 110 20 34 55
10 5.3 1380 140 6.03 35 60
20 11.3 1440 155 4.14 39 70
30 18 1530 165 3.88 44 80
Table 2. Erosion test conditions. Test parameters Erodent Erodent size (mm) Erodent shape Impact angle ( ) Impact velocity (m/s) Erodent feed rate (g/min) Test temperature Nozzle to sample distance (mm)
Silica sand 150–250 Angular 158, 308, 608, 908 25, 37, 50, 66 (5) 3.6 0.3 RT 10
4 mm diameter. These accelerated particles impact the specimen, which could be held at various angles with respect to the impacting particles using an adjustable sample holder. The feed rate of the particles can be controlled by monitoring the distance between the particle feeding hopper and belt drive carrying the particles to mixing chamber. The impact velocity of the particles can be varied by varying the pressure of the compressed air. The velocity of the eroding particles is determined using a rotating disc method [26]. Square samples of size 30 mm 30 mm 4 mm were cut from the plaques for erosion tests. The conditions under which the erosion tests were carried out are listed in Table 2. A standard test procedure was employed for each erosion test. The samples were weighed to an accuracy of 0.1 mg using an electronic balance, eroded in the test rig for 5 min and then weighed again to determine the weight loss. The ratio of weight loss to the weight of the eroding particles causing loss (i.e., testing time particle feed rate) is then computed as the dimensionless incremental erosion rate. This procedure was repeated till the erosion rate attained a constant steady-state value. The characterization of eroded surfaces was done using JOEL JSM-840 scanning electron microscope. The samples were gold sputtered in order to reduce the effect of charging on the surface. RESULTS AND DISCUSSION The variation in incremental erosion rate of PEK and its composites as a function of cumulative weight of erodent at different impact angles for an impact velocity of 66 m/s is shown in Figure 1. These plots were obtained for determining the steady-state erosion rate. In general, polymers and short fiber-reinforced composites exhibit different stages like
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Figure 1. Variation of erosion rate of PEK and its composites with cumulative weight of erodent at different impact angles for an impact velocity of 66 m/s.
incubation, acceleration, peak erosion rate, and deceleration before they achieve a steadystate value [9]. The incubation or induction period is the period of little or no weight loss some times weight gain is observed. The acceleration period is the period of cumulative mass of erodent during which the erosion rate increases rapidly to a peak value called peak erosion rate. The steady-state period is the period of cumulative mass of the impinging particle during which the erosion rate is almost constant. The deceleration period is the period of cumulative weight of the impinging particle during which the erosion rate decreases rapidly from peak or steady-state value. It can be seen from the curves in Figure 1 that the erosion rate either initially increases from a low value to a high value and then decreases to a constant value (i.e., acceleration, peak erosion rate, deceleration, and steady-state value) or initially increases from a low value to a constant value (i.e., acceleration and steady-state period). Such transients before establishment of steady-state are very common for polymers/composites. Steady-state erosion rates of PEK and its composites as a function of impact angle are plotted in Figure 2. PEK and its composites exhibited maximum erosion rate at 308 and minimum at 908 impact angle. The erosion rate of short glass fiber-reinforced composites
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Erosion Studies of Short Glass Fiber-reinforced Thermoplastic Composites
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Figure 2. Influence of impact angle on the steady-state erosion rate of PEK and its composites.
is higher than that of the neat PEK. The shape of the curves is similar at different impact velocities (Figure 2). The erosion rate increased to about one order of magnitude when the impact velocity increased from 25 to 66 m/s. The erosion behavior of materials is broadly classified in the literature as ductile and brittle depending on the variation of erosion rate with impact angle. However, this grouping is not definitive; as the erosive wear behavior depends on many interrelated factors that include experimental conditions and the composition and properties of the target material [1]. Ductile behavior is characterized by maximum erosion at low impact angles in the range of 10–308. On the other hand, if maximum erosion occurs at ¼ 908, then the behavior is said to be brittle. Following the above classification, PEK and its composites exhibited ductile behavior. The erosion rates of PEK composites are higher than that of neat resin at all impact angles (Figure 2). It can also be seen that the erosion rate increased almost linearly with increase in fiber content at all impact angles. The influence of fiber content is less at an impact angle of 908 than the other impact angles. The ability of a composite to absorb the energy elastically depends more on its fiber content. It was also reported in the literature that inclusion of brittle fibers in thermoplastic matrices lowers the erosion resistance of composites [6–9]. The impact velocity of particle has a strong effect on erosive wear. For any material, once steady-state conditions have been reached, the erosion rate (E) can be expressed as a simple power function of impact velocity (v) [2]: E ¼ kvn
ð1Þ
where k is the constant of proportionality includes the effects of all the other variables. The value of n, the velocity exponent, is typically between 2 and 3, although much higher exponent is seen under some circumstances [15]. A value of approximately 2.3 is commonly seen for the erosion of ductile materials [2]. According to Pool et al. [3] for polymeric materials behaving in ductile manner, the velocity exponent n varies in the range 2–3 while for polymer composites behaving in a brittle fashion the value of n should be in the range of 3–5. Figure 3 shows variation of steady-state erosion of PEK and its composites
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a = 30° PEK PEK 10 PEK 20 0.0001
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0.00001 10
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Figure 3. Variation of steady-state erosion rate of PEK and its composites as a function of impact velocity.
with impact velocity at impact angles of 308 and 908. The least-square fits to the data points were obtained by using the power law. The velocity exponents are in the range of 2.0–2.5. Thus, PEK and its composites exhibited ductile erosion behavior, the velocity exponents are in conformity with Pool et al. [3]. ANN PREDICTION OF EROSION RATE Configuration of ANNs ANNs are revolutionary computing paradigms that try to mimic biological brains. These ANNs are modeling techniques that are especially useful to find solutions for rather complex, non-linear, multi-dimensional functional relationships. ANNs have the ability to learn by examples. Patterns in a series of input and output values of example cases are recognized. This acquired ‘knowledge’ can then be used by ANNs to predict unknown output values for a given set of input values. The backpropagation (BP) neural networks, also referred to as multi-layer feed forward networks, are the ones most widely applied for research in material science [27,28]. A BP network is commonly divided into three parts: input layer, hidden layer, and output layer. The nodes (the basic processing units, also called neurons) are connected by weighted inter-connections, which resemble the intensity of the bioelectricity transferring among the neuron cells in a real neural network. The learned knowledge can be memorized in terms of the state of these weights as well as the biases. The number of neurons in the input and the output layer are fixed to be equal to that of input and output variables, whereas the hidden layer can contain more than one layer, and in each layer the number of neurons is flexible. Adjusting the structure of a network, namely the number of hidden layers and neurons, is one of the main ways to improve its performance. The structure of a network can be expressed as: m ½h1 h2 hl l q,
ð2Þ
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where m and q refer to the number of input and output nodes equal to the corresponding variables, respectively. Subscript l denotes the number of hidden layers, h1, h2, and hl are the numbers of neurons in each hidden layer. The network accepts the information from the input layer, processes the data in the hidden layers, and then exports the results via the output layer. In each hidden layer and output layer, the neurons take the output of the neurons in the preceding layer as the input. The data are modulated by a transfer function with weights and bias in the neurons to compute the output, as described by: Xðj nÞ
¼f
X
! WðjinÞ Xði n1Þ
þ
bðnÞ j
ð3Þ
i ðnÞ where XðnÞ j is the output of node j in the n-th layer Wji is the weight from node i in the ðnÞ (n1)-th layer to node j in the n-th layer, and bj is the bias of node j in the n-th layer. A BP algorithm is an iterative gradient descent technique, which is one of the most widely used training algorithms for multi-layer networks, to minimize the mean squared error e between the predicted and desired values:
e¼
L 1 X ½dðpÞ tðpÞ2 2L p¼1
ð4Þ
where L refers to the number of training patterns, dðpÞ is the desired output value (measured), and tðpÞ is the target output value predicted by the ANN for the p-th pattern. During the training procedure, the network is presented with the data for hundreds of cycles, the weights and biases are adjusted until the expected error level is achieved or the maximum iteration is reached. Further details about the mathematical theory can be found in the textbooks, e.g., Haykin [29]. Evaluation and Optimization of ANN A database containing 64 independent measurements obtained from the erosive wear tests on PEK composites was divided into training and test datasets. A non-linear tan-sigmoid transfer function was employed in the hidden layers and a linear transfer function in the output layer was used to avoid limiting the output value to a small range. Impact angle, impact velocity (testing variables), and fiber content (material composition) were selected as input variables and the erosion rate was chosen as output parameter. The network performance was evaluated on the test dataset, using the mean relative error (R) [24]: R¼
M N jOp ðiÞ OðiÞj 1 X 1X M j¼1 N i¼1 OðiÞ
ð5Þ
where Op ðiÞ and OðiÞ are the i-th predicted and measures value, respectively. Oavg is average value of OðiÞ. M is the number of repeated times, and N is the number of test data. Obviously, the lower R becomes, the better is the performance of the network. During the evaluation, 52 datasets were randomly selected from the experimental database as training
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sets and the remaining 12 were used to test the neural network. For all networks, the training and testing process was repeated 100 times independently to avoid random error. There are many learning algorithms using various strategies to optimize the performance of neural networks, namely to minimize error (e). However, different algorithms are applied to different problems. It is therefore necessary to choose an appropriate one [24,30]. In this article, five learning algorithms (i.e., scaled conjugate gradient algorithm, adaptive learning rate algorithm, Powell–Beale conjugate gradient algorithm (CGB), Levenberg–Marquardt algorithm, and Bayesian regularization) that are provided in neural network toolbox of MATLAB [31] were studied for prediction accuracy. Three ANN structures with varying number of hidden layers, 3-[5]1-1, 3-[3-2]2-1, and 3-[4-3-2]3-1, were used to compare the performance of the algorithms. The CGB algorithm gave highest prediction accuracy among the five algorithms with the least R-value for all the three network structures used. Therefore, the CGB algorithm was used in the following work. The performance of the neural network depends on the number of hidden layers and number of neurons in these hidden layers. However, there are no defined rules to design an optimum network structure and it has to be done by trial and error method [18]. Therefore many attempts should be carried out in choosing the optimal structure of the neural
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network, by changing the number of hidden layers as well as the number of neurons in each of these hidden layers. Therefore, various ANN structures in the range from single layer to three hidden layers were tested. An ANN structure, 3-[5-4]2-1 exhibited relatively good performance, with the least R-value, for this case. Prediction and Analysis Figures 4–6 show the prediction results of erosion rate as a function of various combinations of input parameters. In order to get the best prediction quality the neural network was trained with the whole experimental database. New input datasets constructed within the range of training database were provided to the well-trained network for the prediction of erosion rate. The experimental data points were plotted as black dots in Figures 4–6. Figure 4 shows the prediction results of erosion rate for PEK and its composites as a function of impact angle and impact velocity in the form of a 3 D mesh. It is clear from the Figure 4 that the erosion rate increases significantly with increase in impact velocity. Figure 5 shows the prediction results of erosion rate as a function of impact angle and fiber content at different impact velocities in the form of a 3 D mesh. It is
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Figure 5. Prediction results of erosion rate (steady-state) as a function of impact velocity and fiber content at impact velocities of: (a) 25, (b) 37, (c) 50, and (d) 66 m/s.
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Figure 6. 3D profiles of erosion rate (steady state) as a function of impact velocity and fiber content at impact angles of: (a) 158, (b) 308, (c) 608, and (d) 908.
clear that the erosion rate increases almost linearly with fiber content. The predicted results of erosion rate as a function of impact velocity, fiber content at different impact angles are displayed in the form of a 3 D mesh as shown in Figure 6. It can be seen that the erosion rate increases with increase in impact velocity and fiber content for all impact angles. It is also clear from the above three figures that the predicted profiles show good agreement with experimental data points. Thus, a well-trained ANN is expected to be very helpful for prediction of wear data for systematic parameter studies with the help of relatively small experimental databases. CONCLUSIONS (1) PEK and its composites exhibited maximum erosion rate at 308 impact angle indicating ductile behavior. The erosion rate of PEK composites increased with increase in fiber content. (2) The impact velocity has a pronounced effect on the erosive wear of the composites. The velocity exponents (n) of PEK composites were in the range of 2.0–2.5 at 308 and 908 impact angles.
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(3) The neural network technique was applied to predict the erosion rate of PEK and its composites. The results show that the predicted data were well agreed with the measured values. The predicted results of erosion rate as a function of fiber content and testing conditions proved a remarkable capability of well-trained neural networks for modeling erosion. Thus, an ANN will help to analyze the dependency of erosion behavior on different compositions and testing variables making use of relatively small experimental databases. REFERENCES 1. Barkoula, N. M. and Karger-Kocsis, J. (2002). Review – Processes and Influencing Parameters of the Solid Particle Erosion of Polymers and Their Composites, J. Mater. Sci., 37: 3807–3820. 2. Tilly, G. P. and Sage, W. (1970). The Interaction of Particle and Material Behavior in Erosion Processes, Wear, 16: 447–465. 3. Pool, K. V., Dharan, C. K. H. and Finnie, I. (1986). Erosive Wear of Composite Materials, Wear, 107: 1–12. 4. Barkoula, N. M. and Karger-Kocsis, J. (2002). Effect of Fiber Content and Relative Fiber Orientation on the Solid Particle Erosion of GF/PP Composites, Wear, 252: 80–87. 5. Lhymn, C. and Lhymn, Y. O. (1989). Erosive Wear of Fibrous PEEK Composites, In: Proceedings of the 21st International SAMPE Technical Conference, 25–28 September, Eric, PA, USA, pp. 720–729. 6. Miyazaki, N., Takeda, N. (1993). Solid Particle Erosion of Fiber Reinforced Plastics, J. Compos. Mater., 27: 21–31. 7. Miyazaki, N., Hamao, T. (1994). Solid Particle Erosion of Thermoplastic Resins Reinforced by Short Fibers, J. Compos. Mater., 28: 871–883. 8. Harsha, A. P., Tewari, U. S. and Venkatraman, B. (2003). Solid Particle Erosion Behavior of Various Polyaryletherketone Composites, Wear, 254: 693–712. 9. Harsha, A. P. and Thakre, A. A. (2007). Investigation on Solid Particle Erosion Behavior of Polyetherimide and Its Composites, Wear, 262: 807–818. 10. Walley, S. M., Field, J. E. and Greengrass, M. (1987). An Impact and Erosion Study of Polyetheretherketone, Wear, 114: 59–71. 11. Walley, S. M., Field, J. E., Scullion, I. M., Heukensfeldt Jansen, F. P. M. and Bell, D. (1984). Dynamic Strength Properties and Solid Particle Erosion Behavior of a Range of Polymers, In: Field, J. E. and Dear, J. P. (eds), Proceedings of Seventh International Conference on Liquid and Solid Impact, Cavendish Laboratory, Cambridge, pp. 58–63. 12. Rao, P. V. and Buckley, D. H. (1985). Angular Particle Impingement Studies of Thermoplastic Materials at Normal Incidence, ASLE Trans., 29: 283–298. 13. Friedrich, K. (1986). Erosive Wear of Polymer Surfaces by Steel Blasting, J. Mater. Sci., 21: 3317–3332. 14. Hutchings, I. M., Deuchar, D. W. T. and Muhr, A. H. (1987). Erosion of Unfilled Elastomers by Solid Particle Impact, J. Mater. Sci., 22: 4071–4076. 15. Roy, M., Vishwanathan, B. and Sundararajan, G. (1994). The Solid Particle Erosion of Polymer Matrix Composites, Wear, 171: 149–161. 16. Rajesh, J. J., Bijwe, J., Tewari, U. S. and Venkataraman, B. (2001). Erosive Wear Behavior of Various Polyamides, Wear, 249: 702–714. 17. Arjula, S., Harsha, A. P. and Ghosh, M. K. (2008). Solid-particle Erosion Behavior of High-performance Thermoplastic Polymers, J. Mater. Sci., 43: 1757–1768. 18. Harsha, A. P. and Nagesh, D. S. (2007). Prediction of Weight Loss of Various Polyaryletheretherketones and Their Composites in Three-body Abrasive Wear Situation Using Artificial Neural Networks, J. Reinf. Plast. Compos., 26(13): 1367–1377. 19. Meng, H. C. and Ludema, K. C. (1995). Wear Models and Predictive Equations: Their Form and Content, Wear, 181–183: 443–457. 20. Jones, S. P., Jansen, R. and Fusaro, R. L. (1997). Preliminary Investigations of Neural Network Techniques to Predict Tribological Properties, Tribol. Trans., 40(2): 312–320. 21. Velten, K., Reinicke, R., Friedrich, K. (2000). Wear Volume Prediction with Artificial Neural Networks, Tribol. Int., 33: 731–736. 22. Zhang, Z., Friedrich, K. and Velten, K. (2002). Prediction on Tribological Properties of Short Fiber Composites Using Artificial Neural Networks, Wear, 252: 668–675.
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