FINITE ELEMENT AND MICROMECHANICAL MODELING FOR INVESTIGATING EFFECTIVE MATERIAL PROPERTIES OF POLYM

International Journal of Mechanical and Production Engineering Research and Development (IJMPERD) ISSN (P): 2249–6890; ISSN (E): 2249–8001 Vol. 10, Issue 3, Jun 2020, 71–86 © TJPRC Pvt. Ltd.

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FINITE ELEMENT AND MICROMECHANICAL MODELING FOR INVESTIGATING EFFECTIVE MATERIAL PROPERTIES OF POLYMER–MATRIX COMPOSITE AND GENERATION OF WATER ABSORPTION PROFILE EXPERIMENTALLY NARENDRA KUMAR JHA1 & SANTOSH KUMAR2 1

Research Scholar, Department of Mechanical Engineering, Indian Institute of Technology (BHU), Varanasi, India 2

Professor, Department of Mechanical Engineering, Indian Institute of Technology (BHU), Varanasi, India

ABSTRACT The present investigation consists of two parts where the first part contains the investigation of the elastic property of polymer composite which is helpful in structural design and then application of this composite as in case of boat hulls and also in case of other automotive parts and aerospace industry, which generally face different water conditions during operation. In the backdrop of this, I have considered three water situations: seawater, acidic water, and distilled water.

The effect of varying diameter and volume fraction on the property of composite have been presented using diameter and volume fraction. The main aim of this article is to relate the value of the analytical method with the computational results to obtain the best property. It seems that GFRP composite is the most effective if the load acts along the direction of fiber. There is a good agreement between FEA and Analytical results. Nielsen elastic model showed large variation after 60% volume fraction.

The water absorption effect on composites is studied. Different water conditions are as follows: seawater, acidic

Original Article

FEA(Abaqus) and Analytical methods which results in an improvement of the property by increasing the value of

water, and distilled water. This test is done on room temperature and elevated temperature during the different time intervals. From the results, it was observed that the pattern of water absorption resembles non-Fickian. Maximum moisture content value (Mm) values are 11.855. Mostly, the application of this research is in the case of Boat hulls (flat, round, multi, vee, etc.) which generally faces these types of water. So, the design of Boat hulls, automotive parts, aerospace vehicle parts etc., should be based on acidic water.

KEYWORDS: Fibers, Glass Fibre Reinforced Polymer Composites, Environmental Degradation & Representative Elementary Volume (RVE)

Received: Feb 06, 2020; Accepted: Feb 26, 2020; Published: Apr 23, 2020; Paper Id.: IJMPERDJUN20207

1. INTRODUCTION The application of polymer composite in mechanical, electrical, medical and many more applications is undeniable [1].

Investigating the properties of composite with the help of an experiment is difficult and costly. So, with the help of various analytical models and methods developed by various researchers, the properties can be calculated. The wellknown models that have been propounded are Voigt, also called as the rule of mixture [2] and Reussalso called inverse rule of mixture [3] and these models are used for the calculation of properties of unidirectional composite. The HalpinTsai [4] model tends to correct longitudinal shear modulus and the transversal Young’s modulus. The Chamis micromechanical [5] model is the most used and trusted model which gives a formulation for all five independent elastic properties. Nielsen Elastic [6] Model is obtained by simply introducing maximum packing fraction ϕmax and its

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value depends on model geometry. The Micro-mechanical model [7] Eight (8) models are applied to calculate the elastic property of composite, which was then compared with experimental results and FEA. There are lots of options to enhance the property of composite such as varying fiber orientation, varying volume fraction and thickness of composite [8-11]. RVE or unit cell is being considered as a statistical sample used for the calculation of properties. The desired thickness of composite material is obtained by an infinite number of these unit cells. RVE will finally give the stress and corresponding strain real value of material and gives a better idea about the elastic property. This method was used to show the mechanical behavior of material along with circular inclusion [12]. They found that property was varying with the orientation of inclusion and shape of inclusion. Moreover, they got this by increasing inter phase thickness which led to an improvement in the modulus. In this article (a) The Effective Elastic Moduli of polymer composite is being investigated using FEM methodology. Here, the main aim is to relate the value of FEA with the value of the analytical solution to find the best property of composite. There is a good comparison between FEA and Analytical results observed. Finally, it seems that almost all methods had shown good agreement up to 50% and thereafter deviation tend to increase. Further, it can be concluded that Nielsen elastic method showed large and maximum deviation after 50%. The results showed that the analytical model gave the effects of varying diameter and volume fraction of fiber on longitudinal Modulus, but there was a slight variation in transverse modulus of elasticity, modulus of rigidity and Poisson’s ratio. Water absorption profile of Natural fibers like bamboo fiber, jute fiber, shows poor wettability characteristics, and poor adhesion between matrix and untreated fiber results in debonding with the lapse of time [13,14]. The water absorption by the thermosetting polymer composite leads to degradation in property and so it will affect its performance. The mechanism including swelling of fiber results in a decrement in property [15]. Swelling in natural composite results in a decrement in tensile property, flexural property value and another mechanical parameter [1518]. Moisture diffusion in polymer composites is governed by three (3) mechanisms. Firstly, there is a dispersion of water inside the polymer, next due to capillary action, there will be a gap and flaw between fiber and matrix. Lastly, there is a microcrack inside the matrix due to swell fiber, especially happens for natural composite [15-18]. (b) Samples of GFRP composites are successfully produced using Hand Lay-up method. The material is used to investigate its behavior under different aqueous environments such as distilled water, acidic water, and seawater respectively. This test is done in room temperature and elevated temperature during the different time intervals. Water absorption tests were performed by immersing composite specimens into three different aqueous environments, namely: an acidic solution (pH-3), seawater (pH-8), and distilled water (pH-7) which were at room temperature and elevated temperature. From the results, it was observed that the pattern of water absorption resembles non-Fickian. The maximum moisture content value (Mm) and the highest diffusion coefficient (D) value were recorded.

2. PROBLEM DESCRIPTION The effect of varying diameter and volume fraction on the property of composite is presented with the help of RVE model.

As an initial assumption, the model used is (a) cube of size 21.1µm and the volume fraction ranging from 10 to 75%. The fiber diameter is obtained with the help of volume fraction. The property of matrix and fiber is shown in Table 1, 2 (supplied by hindoostan composite solution).

3. MICROMECHANICAL MODELING The main aim of this paper is to calculate the mechanical properties of GFRP composite. Hence, micromechanical models are used to calculate their properties. The used models are Voigt model, Tsai Hahn’s Equation, Halpin-Tsai, Micromechanics Model, Nielsen model, and Chamis method.

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Rule of Mixture: This model is developed by Voigt and ruess [2,3]. Here, the considered material is a fiber of continuous type and matrix.

Longitudinal properties, E1  E f V f  Em (1  V f ) v12  v f V f  vmVm

(1) (2)

Where, V f andVm are volume fractions.

Transverse properties, E2 

Em E f EmV f  E f Vm

v21 

v12 E2 E1

(3) (4)

Shear properties, E 2(1  v ) G f Gm  GmV f  G f (1  V f )

G G12

 5 (6)

It is one of the easiest methods to calculate the elastic properties of a unidirectional composite [1, 2]. It represents a simple linear variation of Young's modulus E1 from Em to Ef as Vf goes from 0 to 1.

The Halpin-Tsai [4] model tends to correct longitudinal shear modulus and the transversal Young’s modulus.

Nielsen Elastic [6] Model is obtained by simply introducing maximum packing fraction ϕmax and its value depends on model geometry. ϕmax= 0.785 and 0.907 used in a square and hexagonal array of fibers.

The Chamis micromechanical [5] model is the most used and trusted model which gives a formulation for all five independent elastic properties.

4. FINITE ELEMENT ANALYSIS USING ABAQUS This method is employed to calculate the property of GFRP composite material. It contains the E11 , E22 , µ12, µ21, G12 . The RVE is observed as a clamped free arrangement and the load is axial displacement =1µm. And it is applied on the free edge, as given in figure 1.

By applying Hook’s law on the RVE, following value is obtained:

l 

PL PL E A l AE

(1)

Figure 1: 3D RVE Loading and Boundary Condition. www.tjprc.org

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Where L =Preliminary length of RVE, E =Modulus of elasticity in the direction of displacement, A =Crosssection area, and F= force created at the nodes of section and can be evaluated by using this software. So E can be calculated in that particular direction. Similarly E22, E33 value is obtained. The Poisson’s ratio can be calculated as:

 

 transverse  longitudinal

(2)

The shape and size of the mesh will affect the results. An improvement in results is observed as we are decreasing the mesh size. By decreasing the mesh size, the chances of getting an error has increased and hence the calculation time has also increased. So, the resultant shape is reliant on geometry. The best shape is selected as per geometry. The most suitable mesh size is obtained using the Trial and error technique. Let us take a starting mesh size and FEA will calculate the result.

The results will be recalculated based on the selected smaller mesh. This process is going to be continued up until the results are optimum. The meshes are triangular, square and many other shapes, while the triangular and square meshes are foremost common.

In this Investigation, because of the Cube-shape geometry, the most suitable meshes are Hex-dominated meshing.

Here, after performing trial and error practice so many times, the optimal mesh size obtained is 1 and the calculated values are converged (Figure 2).

Figure 2: The Final Mesh of 3D RVE of Neat Composite.

5. COMPUTATIONAL RESULTS AND DISCUSSIONS The calculated results such as various modulus and poisons ratio for various volume fraction with the help of RVE where the volume fraction range =10 to 75% is considered. The results are presented in the form of the chart, as shown in figure 3 to 7. The FEA results and analytical results are compared. Analytical models used are Micromechanics Model, Tsai Hahn’s equation, Nielsen method, etc. which properly predict the effects of varying diameter and volume fraction on E11 , E22 , µ12 , µ21 , G12 of composites. As Vf increases E11 increases linearly, as shown in figure3. The FEA values and analytical model give very good predictions in the case of E 11 but there is a slight variation in E 22 , µ12 , µ21 , G12 of the composite.

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Figure 3: Variation of Longitudinal Modulus of Elasticity Versus Fiber volume Fraction.

Figure 4: Variation of Transverse Modulus of Elasticity Versus Fiber Volume Fraction.

In the composite system, a portion of the matrix is substituted by a fiber. As a result, fiber content increases which make composite stiffer and stiffer and give the higher value of modulus of elasticity. FEM also presents that behavior.

With the help of contour results against Vf, a graph is generated and there is a non-linear plot between Vf and modulus of elasticity E2 as shown in figure.4. Halpin-Tsai and Chamis model overvalue the FEA results, while Voigt model gives good prediction with FEA value.

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Figure 5: Shear Modulus versus volume Percent of Fiber.

Figure 6: Poisson’s Ratio versus Volume Percent of Fiber.

There is large variation in result after 50% volume fraction. However, the Nielsen method also shows good prediction. The fiber percentage up to 40% approximately has shown very less effect on the E2. With the help of contour results against Vf, a graph is generated and there is a non-linear plot between Vf and modulus of elasticity G12, as shown in figure 5. There is a non-linear behaviour between G12 and Vf. By varying Vf the G12 value will tend to increase. HalpinTsai method and Chamis method overestimated the FEA result. The shear modulus increases gradually by increasing the fiber percentage. Hence there is a maximum contribution of fiber to achieve best result for composite, if the applied load is shear. The best result is obtained for highest value of Vf.

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Figure 7: Poissons Ratio Variation against Volume Fraction of Fiber.

6. EXPERIMENTAL DETAILS 6.1 Materials and Fabrication of Composite The GFRP composite is fabricated with the help of a hand layup method. According to the requirement, of total number of specimens required for characterization of composite, a composite plate is being manufactured having dimension of 275mm x 190 mm x 2.5 mm and having ply orientation of 0 degree and 90 degree respectively. Firstly, the required amount of Hinpreg®A45 epoxy resin and hardener are mixed in an appropriate ratio of 10:3. After mixing resin and hardener in proper ratio, mixture was stirred using magnetic stirre for half an hour to obtain a uniform solution. As the mixture gets warmed up, laminated composites are laid using layer deposition method to counter epoxy accumulation and to avoid dry patches, a pressure of 10KPa is applied on the top surface. The perfect curing of composites occurs approximately after 22 hours. After complete curing, composites are cut into required sample dimensions for experimental testing.

6.2 Sample Preparation The prepared samples as per the required dimension are used for the water absorption test. The process of polishing samples is performed using different grades. Grades of the emery used include 50,200 and 600 numbers for obtaining proper geometry and perfect surface finish. The epoxy resin and E- glass fiber is shown in Figure 15 (a) and 15 (b). For water absorption investigation, square samples were prepared having dimension 1cm×1cm from the composite plate as per condition h/l<1, h/n<1. Table 1 provides an idea about the properties of Glass fibers and the matrix properties are presented in Table 2.

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Figure 15: (a) Woven E-glass.

Figure 15: (b) Final Composite plate.

Figure 16: Geometry of the Test Specimen[19].

Table 1: Properties of the Glass Fiber (E-Glass) Properties Value Unit E-modulus 80 Poisson's ratio 0.25 Volume fraction 0.5 Density 2.62 Shear-modulus 32

Table 2: Properties of the Matrix (Epoxy resin) Properties Value Unit E-modulus 2.915 Poisson's ratio 0.3 Volume fraction 0.5 Density 1.15 Shear-modulus 1.121

6.3 Material Characterization The water absorption effect on composites is studied. Different water conditions are as follows: seawater, acidic water, and distilled water. This test is done on room temperature and elevated temperature during a different time intervals. During the measurement of water absorption, the composite specimen are withdrawn during a different span of the time interval from the solution, and surface moisture are removed with the help of tissue paper, and then weighted with the help of an electronic balance to monitor the weight gained.

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Figure 17: The Flask Containing Acidic Water Distilled Water and Sea Water.

Figure 18: Schematic diagram of Moisture Content of FRP Composite [shodhganga.inflibnet.ac.in].

The water absorption process of FRP composites is given in figure 18. At the start, water absorption takes place linearly inside the polymer as per Fick’s law and thereafter, it nearly saturated and finally stopped. Furthermore, it increases due to capillary action and digression of epoxy polymer and there is a penetration of water through micro-cracks.

With the help of equation (1) the moistness content M (%) of the composite is calculated (ASTM D5229): (1) Where, M(%) = moisture content (%); M1(g) = wet sample weight at a particular time, andM0(g) =initial weight.

Next to water absorption behavior is being analyzed by calculating diffusion coefficient (D) and to achieve these GFRP composite samples are dipped in different solutions. Diffusion coefficient (D) can be calculated as:

 kh  D   4M m 

2

(2)

Where, Mm (%) = maximum weight gain (%); h (mm) = thickness of specimen; and k = initial slope can be calculated as:

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 M  M1 k  2  T  T 1  2

   

2

(3)

Figure 19: Neat Composite having 90 Degree Ply Orientation.

Figure 20: Neat Composite having 0 Degree ply Orientation.

The first reading was taken before loading and the next after the loading of the water absorption process.

Therefore, the difference in weight can be easily visible and recorded and this change took place linearly with root time, √𝑡=√𝑠. The resultant values are shown in Table 4.

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Table 4: The outcome of Absorption Environments on the Maximum Moisture content, Mm (%) of GFRP Composite.

Sample Maximum moisture content, Mm(%) Zero degree Ph-3 11.21 Ninty degree Ph-3 11.855 Zero degree Ph-7 2.87 Ninty degree Ph-7 3.33 Zero degree Ph-8 2.18 Ninty degree Ph-8 0.038

6.4 Energy-Dispersive X-ray Spectroscopy (EDS)

EDS is a chemical microanalysis method used in combination with scanning electron microscopy. It identifies xrays emitted from the sample during bombardment by an electron beam to characterize the elemental composition of the analyzed volume. EDS analysis is being carried out on the composite face and adhesion of carbon is confirmed and it is due to the charred epoxy. The analysis is shown in Figure 21.

Figure 21: EDS Analysis of Neat Composite.

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6.5 Microscopic Examination

Figure 22: Cross Sectional Identical Distribution of Glass Fibers inside the Epoxy Matrix

Figure 23: Longitudinal Identical Distribution of Glass Fibers inside the Epoxy Matrix

7. RESULTS AND DISCUSSIONS Water absorption behavior of GFRP composites samples were immersed into three different aqueous environments, namely: an acidic solution (pH-3), seawater (pH-8), and distilled water (pH-7) which were at room temperature and at elevated temperature, for a period of 9 days, 12 days under room temperature and then 2 more days, 16 hours and then 7 hours under elevated temperature. These solutions are chosen because these solutions represent real-life situation and the solutions are applied on those samples. Those three (3) solutions were also applied by the earlier researcher [20, 13]. Water absorption profile, for 00 ply orientation composite specimen and 900 ply orientation composite specimens, as given in figure1(a), figure 1(b). From the water absorption curves, it is clear that with an increasing immersion time, the absorbed water content increased. These findings were published earlier regarding the GFRP composites [20, 22, 13, 23]. The pattern of water absorption resembles non-Fickian and showed increasing tendency and never attained equilibrium after the start. Similar findings were previously reported [20, 13]. The moisture uptake never reaches equilibrium, and follows nonFickian behavior. The maximum moisture content, Mm for GFRP composite are represented in Tables 5 and 6. The highest value of moisture content are immersed in acidic solution followed by a distilled water and seawater. Further, the diffusion coefficient is calculated with the help of Equation (2). Based on the diffusion coefficient value, diffusion of water GFRP Impact Factor (JCC): 8.8746

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composite is more suitable in case of distilled water than acidic water and lastly sea water due to the presence of huge salt molecules within the seawater, it slows down the diffusion technique inside the matrix of a composite material which results to lesser absorption kinetic factors22. It is similar to the hydrolysis technique of cellulose inside the fiber.

The hydrolysis is more noticeable in acidic water compared to distilled water and lastly sea water.

8. CONCLUSIONS The present investigation consists of two parts where the first part contains the investigation of the elastic property of polymer composite which is helpful in structural design and then application of this composite as in case of boat hulls and also in case of other automotive parts and aerospace industry which generally faces different water conditions during operation. Hence, here, I have considered three water situations: seawater, acidic water, and distilled water.

The Effective Elastic Moduli of polymer composite is being investigated using FEM methodology. There is a good agreement between FEA and Analytical results. There is a linear increment of E11 value whereas in case of E22 value there is non-linear increment as the Vf is going to increase from 0 to 75%. The µ12 and µ21 value given by FEA are closely agreed with the value given by the Analytical solution. There is a linear decrement in the value of µ12 and has a good agreement with Analytical value. On the other hand, there is a decrement in value of µ21 until it reaches minimum value and then again there is an increment in value as Vf increases. Almost all methods showed good agreement upto 50% volume fraction and thereafter deviation tend to increase. Nielsen elastic method showed large variation after 50% volume fraction. There is an increment in the value of modulus of rigidity G12 by increasing Vf. Almost all methods showed good agreement. Further, it can be concluded that the rule of mixture showed negligible variation, but Nielsen elastic method showed large and maximum deviation after 50%. Nielsen elastic model showed large variation after 50% volume fraction.

The water absorption effect on composites is studied. Different water conditions are as follows: seawater, acidic water, and distilled water. This test is done on room temperature and elevated temperature during a different time intervals.

From the results, it is observed that the pattern of water absorption resembles non-Fickian. Maximum moisture content value (Mm) and the highest diffusion coefficient (D) value is recorded. Also, it is found that the specimen absorbes maximum acidic water than distilled water and lastly, the seawater. Mostly, the application of this research is in the case of Boat hulls (flat, round, multi, vee, etc.) which generally faces these types of water. So, the designer should consider acidic water as a criterion during the design of Boat hulls, automotive parts, aerospace vehicle parts.

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AUTHORS PROFILE

Narendra Kumar Jha is currently doing research on Nano composite material (FRP) in the Mechanical Engineering Department, with Machine Design as specialisation at IIT BHU. He has done M.Tech. from NIT. He has completed my M.Tech last year dissertation work at Indira Gandhi Centre for Atomic Research centre, Kalpakkam. His topic was “Effect of notch on low cycle fatigue behaviour of Gr. 91 steel and constitutive modeling towards fatigue life prediction”. He did BE from State Govt. Engg. College.

Dr. Santosh Kumar is a Professor in Department of Mechanical Engineering, IIT (BHU). He is a Fellow IE (India) and presently serving as Chairman & Coordinator of Teaching-Learning Cell at IIT (BHU). He has graduated (Production Engineering) from NIT Allahabad in 1986. He did his ME in 1988 from the same institution. He did his Ph.D. work at IIT Kanpur (1999) under guidance of Prof. G. K. Lal and Prof. Kripa Shanker. He has Industry experience working in R&D of Ispat Industries Dolvi (Mumbai).

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