Determination of Deformation of Glass Epoxy Plate under Uniformly Distributed Loading Condition

Transcription

1 International Conference on Multidisciplinary Research & Practice P a g e 482 Determination of Deformation of Glass Epoxy Plate under Uniformly Distributed Loading Condition Vivek Patel 1, Dhaval B. Shah 2, Shashikant J. Joshi 3 1 PG Student, Mechanical Engineering Department, Institute of Technology, Nirma University, Ahmedabad, India 2 Asst. Prof., Mechanical Engineering Department, Institute of Technology, Nirma University, Ahmedabad, India 3 Asso. Prof., Mechanical Engineering Department, Institute of Technology, Nirma University, Ahmedabad, India Abstract Specific strength and specific modulus of composite materials is very high as compared to metallic counterparts. This is the reason that last two decades have witnessed large increase in the use of composite materials. Determination of deformations of laminates is important to limit its value within permissible limit. An attempt is made in the present paper to determine the deformations of 4-ply glass epoxy laminate with [0 90] s and [90 90] s orientation under uniformly distributed load for simply supported boundary condition. Three approaches viz. experimental, finite element and analytical were adopted for this. Specimen were manufactured using hand layup method to perform experiments and in house set up was developed. Finite element analysis was carried out using ANSYS and HyperWorks software. A code has been developed using SCILAB for calculation of deformation of the plate using classical lamination theory. The results of three methods were found in good agreement with one another. Fiberglass refers to a group of products developed from individual glass fibers combined into a variety of forms. Glass fibers can be divided into two major groups according to their geometry i.e. continuous fibers, and discontinuous (short) fibers. They are commonly found in ship and submarine, bulkheads and hulls, automobile engine compartments and body panel lines, furnaces and air conditioning units, etc. Composites are popular for producing prototype parts because of extensive change of bodies can be produced rapidly and inexpensively. It is commanded solely to configure a bed of fibers in the desired form, and then saturate them with a curable thermosetting polymer. The procedure for the same has been illustrated as shown in figure 2 simply by placing a woven fabric on a mould. Keywords- Composite plate, Classical lamination theory, FE analysis, experimental analysis. F I. INTRODUCTION iber-reinforced polymer (FRP), also fiber-reinforced plastic, is a composite material formed of a polymer matrix reinforced with fibers. The Fibers are usually glass, carbon, etc. The polymer is usually an epoxy, vinyl ester or polyester thermosetting plastic, and phenol formaldehyde resins are still in employment. Applications for the same are in aerospace industry, sporting goods industry, automotive industry, and home appliance industry. The composite plate has multiple layers as shown in figure 1, called as laminates. Laminate stacks are denoted by the fiber orientation in a sequence. Here, "2" outside of the small bracket shows that the same kind of sequence is used twice whereas "s" stays for symmetrical sequence from the mid-ply. Fig. 2. Wet-hand lay-up process II. ANALYTICAL METHODOLOGY Fig. 1. Example of Layer stacking sequence Classical lamination theory has been used to calculate deformation of composite plate for analytical method. A code has been developed for classical lamination theory to reduce calculation time and error using SCILAB tool. The deflection of the simply supported composite plate under uniformly

2 International Conference on Multidisciplinary Research & Practice P a g e 483 distributed load boundary condition has been determined using programing code. The governing equations consist of the behaviour of the plate internally as well as the behaviour of the boundary conditions. The governing equations i.e. ABD matrix have been derived using the Newtonian approach, where summing the forces and moments on the plate is used to develop the differential equations. Material properties for the composite plate have been described in table I. Plate dimensions has been taken as 100 mm x 100 mm x 10 mm having 4 layers with 2.5mm each thickness. supported boundary conditions at all four sides of plate and uniformly distributed loading condition analysis have been carried out and deformation results are obtained. Meshing of model has been carried out using SHELL181 element available in software which contains 4 nodes with 6-degree of freedom at each node. SHELL181 element is used as it has the capacity to analyse up to 255 layers of the composite material. The geometry for the same element is as shown in figure 3 [4]. TABLE I MATERIAL PROPERTIES Material Properties Value Unit Young's Modulus in x-direction (Ex) 25*10 6 N/mm 2 Young's Modulus in y-direction (Ey) 1*10 6 N/mm 2 Shear Modulus in xy-plane (Gxy) 5*10 5 N/mm 2 Major Poisson's Ratio 0.25 Fig.3: SHELL181 geometry The deformation for 4-ply composite plate with layer orientation [0 90]s and [90 90]s with prescribed boundary condition has been determined using code and results for the same have been given in table 2. Material properties have been taken same as analytical method to compare deformation results. Figure 4 and 5 shows material properties for 4-ply composite plate inserted in ANSYS and HyperWorks software respectively. TABLE II RESULTS OF ANALYTICAL METHOD Layer Orientation Deflection of composite plate(m) [0 90]s [90 90]s III. NUMERICAL METHODOLOGY Here, in numerical methodology two different software packages have been used to analyse composite plate. 3D model has been generated for 4-ply composite plate using ANSYS and HyperWorks software. Also, finite element analysis have been carried out using same software package. For simply Fig.4 Material Properties in ANSYS

3 International Conference on Multidisciplinary Research & Practice P a g e 484 Fig.5 Material Properties in HyperWorks The meshed model of composite plate in ANSYS and HyperWorks software as shown in figure 6. Fig.6: Effect of change in layer orientation on deformation for composite plate using ANSYS Fig. 6 ANSYS and HyperWorks plate meshed model The response of a symmetric 4-ply plate with a lay-up of [0 90]s and [90 90]s have been performed using ANSYS to compare results with analytical method. The effect of change in fiber orientations on deformation of plate have been investigated for the prescribed boundary and loading conditions. The results for the same are given in table III and same as represented in graphical form as shown in figure 6. Figure 7 shows deformation plot for [0 90]s plate in ANSYS. TABLE III ANSYS RESULTS FOR DIFFERENT LAYER ORIENTATION Layer Orientation Deformation of plate in ANSYS (m) [0 90]S [90 90]S [10 90]S [20 90]S [30 90]S [40 90]S [50 90]S [60 90]S [70 90]S [80 90]S Fig.7: Deformation plot for [0 90]s plate in ANSYS The response of a symmetric 4-ply plate with a lay-up of [0 90]s and [90 90]s have been performed using HyperWorks to compare results with analytical method. The effect of change in fiber orientation on deformation of plate have been investigated for the prescribed boundary and loading conditions. The results for the same are given in table IV and same as represented in graphical form as shown in figure 8. Figure 9 shows deformation plot for [0 90]s plate in HyperWorks.

4 International Conference on Multidisciplinary Research & Practice P a g e 485 TABLE IV HYPERWORKS RESULTS FOR DIFFERENT LAYER ORIENTATION Layer Orientation Deformation of plate in HyperWorks (m) [0 90]S [10 90]S [20 90]S [30 90]S [40 90]S [50 90]S [60 90]S [70 90]S [80 90]S [90 90]S boundary condition and uniformly distributed loading condition have been carried out using two different software analysis results. The same results have been given in table V with percentage variation in them. Figure 10 shows graphical representation of comparison for these results. TABLE V RESULTS OF DEFORMATION FOR DIFFERENT LAYER ORIENTATION USING ANSYS AND HYPERWORKS SOFTWARE LAYER ORIENTATION DEFLECTION OF PLATE IN ANSYS (M) DEFLECTION OF PLATE IN HYPER MESH (M) % DIFFERENCE [0 90]S [90 90]S [10 90]S [20 90]S [30 90]S [40 90]S [50 90]S [60 90]S [70 90]S [80 90]S Fig. 8: Effect of change in layer orientation on deformation for composite plate using HyperWorks Fig.10: Comparison of layer orientation for 4-ply composite plate Fig.9: Deformation plot for [0 90]s plate in HyperWorks The comparison for deformation under different layer orientation of 4-ply composite plate with simply supported IV. EXPERIMENTAL METHOD The composite plate with same size has been manufactured using manual lay-up technique. Here, for manufacturing of fiberglass / epoxy composite plate, fiberglass 2400 tex, epoxy resin and its harder, plastic cups, syringe, wooden plate, gum tape, grease, brush and roller, surgical gloves and nose protection cover have been used. In manual lay-up process of composite manufacture, first grease layer has been spread on wooden plate mould with very small thickness. Mixture of epoxy resin to hardener ratio 10:1 has been prepared to make first layer of composite plate. Similarly other layers of fiberglass string at required angle have been arranged

5 International Conference on Multidisciplinary Research & Practice P a g e 486 as per sequence of composite plate. To make hard solid plate, manufactured composite plate has been dried up to 4-5 hours depends of resin to hardener ratio, resin type and surrounding temperature. Here, two different composite plates [0 90]s and [90 90]s with required size have been prepared for the further experimental process and same is shown in figure 11 and figure 12 respectively. (a) (b) Fig. 13: Experimental setup (a) with simply supported boundary condition (b) with uniformly distributed loading condition on composite plate Fig.11: [0 90]s manufactured plate Vernier calliper instrument has been used to measure deformation of composite plate. The reading of vernier calliper have been marked before and after uniformly distributed loading on plate. The difference between these two readings have been taken as deformation value for composite plate. This procedure have been performed for both plates i.e. [0 90]s and [90 90]s. the values for reading of vernier calliper and deformation have been given in table VI. EXPERIMENTAL RESULTS TABLE VI PLATE LAYER ORIENTATION INITIAL READING OF VERNIER (MM) AFTER LOADING READING OF VERNIER (MM) DIFFERENCE BETWEEN TWO READINGS (MM) [0 90]S [90 90]S V. COMPARISON RESULTS Fig.12: [90 90]s manufactured plate Wooden set up have been prepared to apply required loading and boundary conditions on composite plate. For simply supported boundary condition, the composite plate is freely supported at four sides on wooden strips whereas for uniformly distributed loading condition, wooden block of required weight has been kept on composite plate. The experimental setup with simply supported boundary condition and uniformly distributed loading condition have been shown in figure 13 (a) and (b) respectively. Four ply composite plate with layer orientation [0 90]s and [90 90]s have been taken as study of deformation with uniformly distributed loading with simply supported boundary condition. The comparison has been made for analytical methodology, numerical methodology using ANSYS and HyperWorks software and experimental methodology. The results of deformation for all methodology have been described in table VII. TABLE VII COMPARISON BETWEEN ANALYTICAL, NUMERICAL AND EXPERIMENTAL METHODOLOGY FOR DEFORMATION OF PLATE ANALYTICAL PLATE LAYER RESULTS ORIENTATION (MM) NUMERICAL RESULTS (MM) EXPERIMENTAL RESULTS (MM) ANSYS HYPERWORKS [0 90]S [90 90]S

6 International Conference on Multidisciplinary Research & Practice P a g e 487 VI. CONCLUSIONS Four ply fiberglass composite plate has been taken to determine deformation with different fiber orientation and simply supported boundary condition under uniformly distributed loading in this research. From the observation, it has been found that minimum deformation occurs at layer sequence [90 90]s, whereas maximum deformation occurs when outer layer at 60. To verify the results for deformation under prescribed boundary condition, analytical method using SCILAB programming, numerical method using FE software like ANSYS and HyperWorks and experimental methods have been used. Comparison for all these methods have been carried out to validate results and difference between them have been found within 2-5 %. From this comparison one can predict or rely any one of the method for other boundary and loading condition to get deformation value. Here, for layer orientations [0 90]s and [90 90]s results were compared for all different methodology whereas for remaining layer orientations only numerical results were compared using two different software. REFERENCES [1] Venkateswarlu M., Rao S. Rama, "Bending of composite material", Def Science J, Vol , pp [2] M.R. Khalili a, K. Malekzadeh b, R.K. Mittal c,." A new approach to static and dynamic analysis of composite plates with different boundary conditions ", Composite Structures, Vol. 69 (2005), pp [3] Khashaba U A,Seif M. A, "Effect of different loading conditions on the mechanical behaviour of [0/±45/90]s woven composites",composite structure, Vol. 74, 2006, pp [4] Mer Arnel Manahan, "A Finite Element Study of the Deflection of Simply Supported Composite Plates Subject to Uniform Load", Dec [5] J.M. Whitney and A. W. Leissa "Analysis of heterogeneous Anisotropic plates", Journal of applied mechanics, june 1969, pp [6] J.N. Reddy,"A generation of two-dimention theories 0f laminated composite plates", Applied numarical methods, vol. 3, pp (1987) [7] J.N. Reddy, D.H. Robbins Jr."Theories and computational models for composite laminates" ApplMech Rev, 47 (1994), pp