Indian Journal of Engineering & Materials Sciences Vol. 12, October 2005, pp. 443-450 Influence of fibre proportion and position on the machinability of GFRP composites- An FEA model D Abdul Budan* Department of Mechanical Engineering, PSG College of Technology, Coimbatore 641 004, India Received 19 July 2004; accepted 31 May 2005 More commonly considered criteria for judging the machinibility are the cutting forces on the tool and power consumption. A classical Merchant s model is widely used to predict the cutting forces while machining isotropic material. However, no such model exists to predict the cutting forces while machining orthotropic materials. In this paper, an effort is made to modify the Merchant s formula by incorporating the K-factor to evaluate the shear strength, the fibre orientation as shear angle and a constant coefficient of friction. The cutting forces evaluated by modified Merchant s model on unidirectional GFRP composite material has been compared with the results predicted by two-dimensional FEA model. In FEA model both maximum stress and Tsai-Hill failure criteria were used to simulate the chip separation. The influence of composite design, in particular the fibre proportion and orientation on cutting forces has been investigated. The higher fibre proportion in the composite caused an increase in cutting force values. Fibre orientations 45 and 60 have shown favorable results. The FEA predicted results have shown good agreement with the results evaluated by modified Merchant s model. IPC Code: G01N3/58, C08B A large range of components made from polymer matrix composite (PMC) are fabricated, but for small production or for extremely complex or accurate shapes, machining of PMC is very much essential. More efficient technique for machining is possible provided the peculiarity in behaviour of this material is taken in to consideration. In recent years much attention has been focused on the problems arising from the machining of PMC by conventional means. Due to heterogeneity of PMC some problems like delamination, short tool life, fibre pull out and matrix de-bonding occur during machining. Also high abrasive nature of glass and graphite fibres leads to rapid tool wear. In industry, much of the data available on tooling and cutting parameter for PMC are based on metal cutting. Sufficient literature on various aspects of machining of conventional material are available but only a few literature exists on the machining of PMCs. In one of the investigation a scheme of twin node processing and concept of loading/unloading were presented for the chip formation and a coupled finite model of thermo-elastic-plastic large deformation for orthogonal cutting was developed. It is reported that *Present address: Department of Mechanical Engineering, University BDT College of Engineering, Davangere 577 004, India (E-mail: abdul_budan@rediffmail.com) the FEA results have shown good agreement with experimental values 1. An experimental study reported that on both unidirectional and multidirectional graphite/epoxy composites similar type of chips were observed and the distinct surface profiles were observed on different fibre orientation 2,3. A study on fibre orientation has revealed that the cutting forces also depend on fibre orientation. Maximum fibre debonding was observed at 135 fibre orientation 4. An investigation to evaluate the effect of tool wear on cutting forces on UGFRP composite laminate revealed that under selected operating condition rapid tool nose wear was observed. A strict correlation is found between the flank wear and the vertical force variation 5-7. The predictions from the numerical simulation verified with the experimental results for graphite/epoxy laminates. It is reported that FEA method is a valid approach for modeling orthogonal cutting of FRP material 8. A study on the influence of fibre volume on mechanical property during the machining of GFRP composites revealed that, increased fibre content increases the tensile and flexural modulus incrementally. However, there is a drop of reinforcing efficiency of the composite due to higher void content 9,10. This work motivated the author to consider the fibre proportion as one of the major influencing parameter on the machining performance for the present investigation.
444 INDIAN J. ENG. MATER. SCI., OCTOBER 2005 In the present work, few experiments on glass/epoxy specimens with fibre proportion ranging from 30 to 70% by weight have been conducted to evaluate the obliquity in tensile failure. Based on the angle of obliquity an equivalent factor (K) to evaluate shear strength of the specimen has been derived using strength of material approach 11. The value of K-factor, shear angle equal to fibre orientation and the friction angle for a constant coefficient of friction have been incorporated in the existing Merchant s equation to apply on unidirectional glass fibre reinforced polymer (UGFRP) composite material. Secondly an FEA model to predict the cutting forces during the machining of UGFRP composite has been developed. Maximum stress and Tsai-Hill failure criteria were adapted to simulate the chip separation. Variation of mechanical properties with respect to fibre proportion has been considered in the finite element analysis 12, all aspects of tool and cutting parameters have considered. In most of the previous works, research was carried out on specimens with a specific fibre percentage. However, the investigation on the influence of fibre proportion on machining performance is insufficient. The present investigation considers the fibre proportion as one of the major parameter influencing on machining performance. In this analysis the influence of fibre volume has been compared with the other parameters, viz., fibre orientation, tool rake angle and depth of cut on the machinability of UGFRP composite materials. Results revealed that the higher fibre proportion of the composite results in increased cutting forces. Fibre angles 45 and 60 have shown favorable results. The predicted principal cutting forces by FEA agree well with the results evaluated by modified Merchant s model. Merchants Model Modification Variation of stresses with aspect of cross section 11 Visualising the prismatic bar subjected to axial tension as made up of a bundle of longitudinal fibres, each of which carries its fair share of the load, the distribution of forces over the cross-section will be uniform. It is seen that the resultant of this uniform distribution of internal forces must be equal to the external load P. Thus, if A is the cross-sectional area and σ t the force per unit area, we have. P = σ t A or σ t = P/A (1) Consider the state of stress on an oblique crosssection pq cutting the bar at an angle φ ' with the normal cross-section mn as illustrated in Fig. 1a. First we isolate that portion of the bar to the left of the oblique section pq as a free body and represent the action of the removed portion on this free body by the resultant stress S as shown in Fig. 1b. From the equilibrium condition, this internal force S must be equal, opposite, and collinear with the external force P. Resolving the force S in to two components to the plane pq, we find N = P cosφ ' and Q = P sinφ ' Corresponding stresses are : Normal stress σ n =N/A = (P/A)cos 2 φ ' Shear stress τ s =Q/A = (P sinφ ' ) / (A/cosφ ' ) = ½.(P/A)sin2φ ' where A =Area of the oblique section pq = A/cosφ ' Substituting (P/A ) in the above equation from (1) we get τ s = ½.(σ t ) sin2φ ' = K σ t (2) where K = ½ sin2φ ' Shear stress acting on the oblique plane is approximately equal to K times that of tensile stress. The tensile failure tests conducted on FRP specimens revealed that the rupture takes place at certain obliquity. The obliquity ranges from 0 to 45 with respect to fibre proportion. The average obliquity of 22.5 has been considered in the present analysis. The K factor calculated based on average obliquity is 0.354. On substituting this value in Eq. (2) we get. τ s = 0.354 σ t (3) Now the Merchant s equations used for conventional materials are given by Fig. 1 Obliquity (φ ) in axial tension of FRP material
BUDAN: INFLUENCE OF FIBRE PROPORTION AND POSITION ON THE MACHINABILITY OF GFRP COMPOSITES 445 Cutting force F c = { t 1 b 1 τ s cos(β - α) / sinφ cos (φ + β - α)} (4) Feed force F t = { t 1 b 1 τ s sin(β - α) / sinφ cos (φ + β - α)} (5) In the present work a 2-dimensional FEA model has been constructed per mm basis, hence the width of cut (b 1 ) is assumed as 1# mm. Considering the work to be ductile, with a constant coefficient of friction 0.3 the corresponding friction angle (β) is 17. Literature revealed that the shear in FRP usually occur along fibre orientation, considering φ as θ and substituting φ, β and τ s equal to θ, 17 and 0.354σ t respectively in Eqs (4) and (5), we get Cutting force F c = { 0.354σ t t 1 cos(17 - α) / sinθ cos (17+θ - α)} (6) rake angle, relief angle and nose radius. Only a portion of the specimen is modelled. Condense of the model is necessary to reduce the computational time. Work-piece and chip portion are modelled separately and the coincident nodes are coupled along both x and y direction, so that the work piece and chip behave as a single object before fracture. Contact elements are generated between the tool and work piece. Appropriate boundary condition included x- symmetric along the work piece boundary and fully pinned at the bottom associated with vice constraint. Fig. 3a illustrates the tool geometry, boundary conditions and cutting forces. Fig. 3b illustrates the finite element model of work tool interface. The following assumptions were made in the construction of present FEA model 8 : (i) The incremental plastic, visco-elastic and thermal strains are negligible with Feed force F t = { 0.354σ t t 1 sin(17 - α) / sinθ cos (17+θ - α)} (7) The σ t values for glass/epoxy composite for various fibre percentages have been obtained from the engineers guide to composite materials 12. Finite Element Analysis Material property evaluation The material considered in the present investigation is a unidirectional GFRP composite. E-glass fibre reinforced with epoxy resin. Since the pattern of cutting up to 30 and beyond 75 is quite different, only fibre orientations 30, 45, 60 and 75 have been considered. FEA models were developed on five specimens with fibre percentages 30, 40, 50, 60 and 70% by weight. Based on the individual properties of fibre and matrix, the composite properties have been evaluated along different fibre orientation. The empirical equations developed by Halpin Tsai were used to evaluate the mechanical properties of the composite materials. The composite properties thus evaluated are illustrated in Fig. 2(a-c). The Young s modulus and the density of the tool material are E = 2.12 10 3 N/mm 2 and ρ = 0.078 10-4 kg/mm 3 respectively. FEA model and Methodology An FEA model for orthogonal cutting of UGFRP composite has been constructed using ANSYS 5.4 a commercially available FEA package. The tool was defined as a rigid body with the geometry defined by Fig. 2 Stiffness properties evaluated by Halpin Tsai equations
446 INDIAN J. ENG. MATER. SCI., OCTOBER 2005 respect to the elastic component, this assumption is true for lower range of cutting speeds usually adopted for machining FRP composite. (ii) Heat flux generated on the rake face through friction is minimal and may be neglected. (iii) The composite material is assumed to be orthotropic and locally homogeneous there by allowing incremental linear stress-strain relation in cutting FRP material. (iv) The cutting process is quasi-static. This assumption is supported by the fact that FRP materials show minimal strain rate dependence due to the brittle fibre dominance. (v) As the temperature generated on the tool flank through friction is well below the matrix disintegration temperature, a constant coefficient of friction 0.3 was used to specify friction for all constants. Tool displacement and chip separation criteria In FRP machining the chip separation can be defined by using a stress criteria approach for both primary and secondary fracture. In primary fracture the chip formation was achieved by nodal de-bonding criterion. Secondary fracture and subsequent chip release transpired when the stresses at the free edge reaches the critical values promoting global failure by either the maximum stress or Tsai-Hill criteria. An iterative approach was used to satisfy the failure criterion in each fibre orientation. The tool displacement was extended till the failure criterion for secondary fracture was satisfied. Chip release was defined when the global failure envelope approached a distance ahead of the cutting tool on the free edge, which is consistent with the distance of node separation during primary fracture. Material removal occurs through a combination of compression and shear failure at the tool nose. Thus the condition required to satisfy for primary fracture is given as. σ y = σ mu cosec 2 ϕ where σ mu = matrix ultimate strength. = 82.8 MPa and ϕ = (90 - θ) where θ is the fibre orientation. Two theories, viz., maximum stress/strain theory and Tsai-Hill criterion were used. The Tsai-Hill criteria accounts for stress component interaction, where as maximum stress criteria accounts for no interaction. Maximum stress criteria: Maximum strain criteria: σ x = S / (sinθ.cosθ) ε x = S / ( G xy sinθ.cosθ) where S and G xy are shear strength and modulus of the composite. Fig. 3a Tool geometry, boundary conditions and cutting forces Fig. 3b Finite element model of work tool interface Tsai-Hill criteria cos 4 θ/x 2 + {1/S 2 1/X 2 } cos 2 θ / sin 2 θ + sin 4 θ/y 2 = 1/σ 2 x where, X and Y are tensile and compressive strength respectively. Chip release was believed to occur when the criteria for both primary and secondary fracture were satisfied. The nodes coupled at the chip and work piece interface are de-bonded by deleting the corresponding coupled set. This process is repeated until the free edge reaches the fracture stress. Results and Discussion Effect of fibre orientation The cutting and feed forces for fibre orientations 30, 45, 60 and 75 have been evaluated using FEA model keeping the other parameters constant. Since the cutting pattern up to 30 and beyond 75 is quite different only orientations 30 to 75 have been
BUDAN: INFLUENCE OF FIBRE PROPORTION AND POSITION ON THE MACHINABILITY OF GFRP COMPOSITES 447 considered. FEA results revealed that the tool requires high cutting and feed forces at 30 -fibre orientation. Larger chip thickness at this fibre angle is the reason for higher cutting forces. Minimum tool forces were observed at 45 and 60 fibre orientation. Figs 4a and 4b illustrate the comparison of FEA and Merchant s equation results. Comparison of results of previous work 8 with the results of FEA and Merchant s model are illustrated in Fig. 6a. Except at 30 fibre orientation all the FEA results have shown good agreement with the Merchant s model. Though slight variation in cutting force results of two models was observed at 75 -fibre orientation, the feed force values from 45 to 75 are well matching. Fibre orientations 45 and 60 have shown favourable results. Effect of tool rake angles Four tool rake angles 0, 5, 10 and 15 were selected to analyse its effect on cutting forces keeping the other parameters remain constant. Figs 5a and 5b illustrate the comparison of cutting and feed forces evaluated by FEA and modified Merchant s equation respectively with the tool rake angle. Results revealed that, the rake angle has a strong influence on cutting forces. As illustrated in Fig. 5a for a given depth of cut, the cutting force tends to decay with the increase of rake angle. The same effect is noted on the feed force, which is also largely reduced for higher rake angle values. The above observations conform to the conclusion made in the previous work 7. The results revealed that the extent of the effect of tool rake angle is less when compared to the effect of fibre orientation and fibre percentage. However, since the small tool rake angles (0-5 ) expose the tool face to wear early (Crater wear) and weakens the tool due to smaller cross section of the tool head, an average tool rake angle between 5 and 10 is preferable. Cutting force results of Merchant s model are almost matching with the FEA results. The 10 -tool rake angle has shown favourable results. Effect of depth of cut Three depths of cuts 0.12, 0.25 and 0.5 mm has been chosen keeping the other parameters constant. Results revealed that the cutting and feed force values increased with the increase of depth of cut. The range of cutting force and feed force values are 55.4 to 220.15 N s and 4.7 to 37.8 N s respectively. These results indicate that the effect of depth of cut on tool forces is comparatively high. Figs 6a and 6b illustrate the relation between FEA and Merchants model on the cutting and feed force values versus depth of cuts. From the best-fit straight line in the above figure it Fig. 4 Effect of fibre orientation on (a) cutting force and (b) feed force Fig. 5 Effect of tool rake angle on (a) cutting force and (b) feed force
448 INDIAN J. ENG. MATER. SCI., OCTOBER 2005 observed that the cutting forces undergo a sensibly linear increase with increasing the depth of cut, this observation conform to the conclusion reported in previous study 5. Most of the results evaluated by Merchant s model have shown good agreement with FEA model. Higher depth of cuts result poor surface quality and smaller depth of cuts slows down the productivity. Hence, an optimum depth of cut which can overcome both the limitations is essential. Effect of fibre percentage Five specimens with fibre percentage ranging from 30 to 70 by weight were selected with the other parameters remain constant. Figs 7a and 7b illustrate the effect fibre percentage on cutting and feed forces. Results revealed that the increase of fibre content increased the cutting and feed force values. As the matrix is soft, it gets deformed easily even with small cutting forces, however the tool require higher cutting forces to shear the brittle fibre material. It is observed from the results that the minimum to maximum values of the cutting and feed forces were 127.7 to 308.8 N s and 15.4 to 38.8 N s respectively. This range indicated that the effect of fibre percentage on tool force values is very high compare to all the other parameters. Most of the results of Merchant s model have shown good agreement with FEA results. Specimens with higher fibre percentages are strong enough, but they require higher cutting forces and they face limitations like fuzzy and poor surface quality, delamination and fibre pullout. An optimum fibre proportion based on the strength and surface quality requirement is recommendable. Specimens with 40 and 50 fibre percentage by weight have shown favourable results in the present cutting condition. The strain distribution with respect to fibre percentage and tool displacement on specimens with 30, 50 and 70% by weight are illustrated in Figs 8a, 8b and 8c respectively. These models revealed that the specimens with higher fibre proportion strained more. Conclusions The following conclusions may be drawn from this study: (i) Results revealed that the tool requires higher cutting forces at 30 fibre orientation, as the chip thickness at this fibre orientation is high. At 45 orientation the cutting force and feed force values are 127.7 and 15.4 N s respectively. At 60 orientation the cutting force and feed force values are 185.4 and 20.1 N s respectively. These two orientations have Fig. 6 Effect of depth of cut on (a) cutting force and (b) feed force Fig. 7 Effect of fibre percentage on (a) cutting force and (b) Feed Force
BUDAN: INFLUENCE OF FIBRE PROPORTION AND POSITION ON THE MACHINABILITY OF GFRP COMPOSITES 449 Fig. 8a Strain distribution on specimen with 30% fibre content Fig. 8b Strain distribution on specimen with 50% fibre content Fig. 8c Strain distribution on specimen with 70% fibre content shown favourable results when compared to 30 and 75 fibre orientations. (ii) The cutting and feed forces tend to decay when the rake angle increases. The extent of the effect of tool rake angle on tool forces is less compared to fibre orientation and percentage. However since the small rake angles (0-5 ) cause the tool to wear early and high rake angles ( 15 ) weakens the tool strength an average angle between 5-10 tool rake is preferable. (iii) The higher depth of cut leads to increase the cutting forces. The cutting and feed force values on 0.12# mm depth of cut are 55.4 and 4.7N s respectively. On 0.5# mm depth of cut, they are 220.15 and 37.8 N s respectively. This reveals that the extent of the effect of depth of cut on tool forces is comparatively higher than the tool rake angle. (iv) The cutting and feed force values on 30% fibre weight are 127.7 and 15.4 N s where as on 70% fibre weight they are 308.8 and to 38.8 N s respectively. This revealed that Increase in fibre percentage have increased the tool force values. Composites with higher fibre content are strong, but require higher cutting forces, produce fuzzy and poor surface quality. An optimum fibre proportion based on the strength and surface quality requirement is preferable. Specimens with 30 to 40% fibre weight have shown good machinability. (v) The modified Merchant s formula has been utilised successfully to validate the FEA predicted results. Most of the FEA results have shown good agreement with the Merchant s model. The model can be used to select the optimised tool, cutting and design parameters. (vi) As the preparation of specimens for various fibre proportion and position is tedious and highly expensive. The model saves the time, expenses and risk involved in preparation and machining of FRP specimens. Nomenclature E 11, E 22 = Young s modulus of composite along and transverse to fibre orientation respectively. ν 12 = Poisons ratio of composite, G 12 = Shear modulus of composite, V m, V f = Volume fraction of matrix & fibre respectively, Ex and Ey = Young s modulus along x and y direction, ν xy = Poisson s ratio G xy = shear modulus. σ mu = Matrix Ultimate Strength. θ = fibre orientation φ = shear angle σ t = tensile strength of composite φ ' = obliquity of tensile failure.. S = shear strength of the composite. = Shear modulus of composite. G xy
450 INDIAN J. ENG. MATER. SCI., OCTOBER 2005 X Y S t 1 b 1 β σ n τ t α Fc Ft K W f = tensile strength = compressive strength = shear strength = un-deformed chip thickness or depth of cut. = width of cut = friction angle = normal stress = Shear stress = tool rake angle = principal cutting force = feed force (thrust force) = shear strength equivalent factor. = fibre percentage by weight. References 1 Lin Z C & Lin S Y, Trans ASME J Eng Mater Technol, 114 (1992) 218-226. 2 Wang D H, Ramulu M & Arola D, Int J Mach Tools Manufact, 35 (1995) 1623-1638. 3 Wang D H, Ramulu M & Arola D, Int J Mach Tools Manufact, 35 (1995) 1639-1648. 4 Wern C W, Ramulu M & Shukla A, Exp Mech, (1995) 33-41. 5 Caprino G, De lorio I, Nele L & Santo L, Composites, 27A (1996) 409-415. 6 Caprino G, Nele L & Santo L, Composites, 29A (1998) 887-891 7 Caprino G, Nele L & Santo L, Composites, 29A (1998) 892-897 8 Arola D & Ramulu M, Int J Mach Tools Manufact, 39 (1997) 597-613. 9 Joshi S S, Ramakrishnan N, Sarathy D & Ramakrishnan P, (1998) 17 th AIMTDR.85-87. 10 Nam-Jeong Lee & Jyongsik Jang, Composites, 30A (1999) 815-822. 11 Timoshenko S P & Young D H, Elem Strength Mater, (1978) 26-27. 12 John W Weeton, Dean M Peter & Karyan L Thomas, Engineers guide to Composite materials (ASTM), Property Data: PMC (1987) Sec.6-56.