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A model for Stress Generation, Crack Growth and Fracture Toughness Estimation in TPO Based Nanocomposites using Finite Element and Single Edge Precracked Method

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A three dimensional Finite Element Model (FEM) using damage initiation mechanisms was carried out to investigate the effect of crack propagation on the developed composite material made of Thermoplastic Polyolefin elastomer(TPO) blend nanocomposites
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  International Journal of Futuristic Trends in Engineering and Technology ISSN: 2348-5264 (Print), ISSN: 2348-4071 (Online) Vol. 1 (08), 2014 Akshar Publication © 2014 http://www.ijftet.wix.com/research 50 A model for Stress Generation, Crack Growth and Fracture Toughness Estimation in TPO Based Nanocomposites using Finite Element and Single Edge Precracked Method (Paper ID: 08ET30092014012) Prof. Dr. Sanjay. K. Nayak Bishnu P. Panda Smita Mohanty Sushovit Mohanty  Laboratory for Advanced Research in Polymeric Materials (LARPM)  Laboratory for Advanced  Research in Polymeric  Materials (LARPM)  Laboratory for Advanced  Research in Polymeric  Materials (LARPM)  Laboratory for Advanced  Research in Polymeric  Materials (LARPM) Central Institute of Plastics  Engineering and Technology, Central Institute of Plastics  Engineering and Technology, Central Institute of Plastics  Engineering and Technology, Central Institute of Plastics  Engineering and Technology,  Bhubaneswar. Orissa, India.  Bhubaneswar. Orissa,  India.  Bhubaneswar. Orissa,  India.  Bhubaneswar. Orissa,  India. larpmcipet@gmail.com  Abstract:   A three dimensional Finite Element Model (FEM) using damage initiation mechanisms was carried out to investigate the effect of crack propagation on the developed composite material made of Thermoplastic Polyolefin elastomer(TPO) blend nanocomposites and compared with the existing product material. A specific rear bumper protector was selected and corner crack made to investigate the fracture using linear elastic fracture mechanics (LEFM). Distribution of analysis parameters such as Von Misses stress, deformation and fracture toughness properties were carried out to study the design parameters of the protector. The Von Misses stress of the product compared against to the yield strength of the developed composite material. The Mode I stress-intensity factor is compared against the material’s fracture toughness. Deformation and Von Misses stress behavior obtained from the simulations performed was found to be non-symmetric. Variation of stress intensity as a function of notch tip radius with respect to different crack length evaluated to understand crack propagation behavior. Increased crack tip displacement observed with an increase of load from 250N to 1500N for all composites whereas the value of maximum stress intensity decreased with an increase in the notch radius. Relation  between energy with crack displacement is non linear from a small crack to large crack. Continuous increment of energy observed with crack displacement.  Keywords: Crack Propagation, Stress Intensity, Fracture, Toughness, FEA, Static Structural. I.   I  NTRODUCTION  Cracks are the main reason for failure of engineering structures which depends on the operating condition and design of the product. Growth of a crack leads decrease of structural strength. Fracture takes place rapidly and proceeds  by crack growth, which has been developed during normal service conditions. Fracture mechanics have been developed to predict the strength and life of cracked structure. LEFM  principle can be used to measure of the crack propagation and damage tolerance to describe behavior of crack. Crack  propagation behavior solely depends on the stress intensity factor with the area function of the applied load and geometry of the material. FEM is commonly used to estimate the stress intensity factor numerically to estimate crack propagation. Using singular elements around the crack tip, singularity  behavior can be achieved and the stress intensity can be calculated numerically. It is of particular interest to investigate crack propagation associated with rubber-rich TPO blends reinforced with rigid nanofillers. The effect of nanoclay additions on the structure and property of rubber-rich TPO blends have been investigated by Mishra et al. [1] and Tjong and Ruan [2] more recently. Panda et al. [3] prepared the TPO/clay nanocomposites where the TPO contains PP and EPDM with the ratio of 70:30 by weight. They reported that the blend nanocomposites exhibited remarkable improvement of tensile and storage modules over their pristine TPO blend. Tjong and Ruan [2] reported that TPO-based nanocomposites reinforced with 0.1–1.5wt% organically modified clay exhibits enhanced stiffness and tensile strength. Moreover, the fracture toughness of TPO/clay blend nanocompsites increases with the increasing clay content. Chaari et al.[4] demonstrated crack  propagation path analysis using FEM and its application in spur gear. Mubashir Gulzar has studied linear and nonlinear analysis of central crack propagation in polyurethane material [5].Priscilla L. Chin has studied stress analysis, crack  propagation and stress intensity factor computation of a Ti-6Al-4V Aerospace Bracket using ANSYS and FRANC3D [6]. Joes et al. [7] carried out (FEM) to predict the laminated fracture toughness and compared the data’s obtained by ASTM standard E399 . Energy release rate is the amount of work associated with a crack opening or closure. The evaluation of the stress field around the crack tip shows the  pure opening mode and in the limit of linear elastic fracture mechanics with vanishing small fields. For any type of  International Journal of Futuristic Trends in Engineering and Technology ISSN: 2348-5264 (Print), ISSN: 2348-4071 (Online) Vol. 1 (08), 2014 Akshar Publication © 2014 http://www.ijftet.wix.com/research 51 loading, geometry or structure, size, a critical value K  C  must exist so that when the actual stress intensity K  I , is lower, no crack growth can take place. This reasoning may be extended to other fracture mode to obtain fracture criteria. The main objective of the present work is to investigate the effect of crack propagation developed due to notch tip radius and to make a comparative study of developing TPO blend nanocomposite vis-à-vis with existing product material using FEM. Different numerical FE models are used for better understanding of the whole damage process and to get a better control over the damage parameters. In the present work, crack propagation path has been studied through a special element called a deformation probe, placing over the crack tip, which will create the stress singularity at the crack tip. Then for different loadings the propagation of the crack tip is being measured in any of the X, Y and Z directions. The entire analysis is carried out in ANSYS13 using a set of boundary and loading conditions. Damage Tolerance (DT) assessment has been conducted for generating the following information upon which fracture control decision can be made: Relation  between Von Mises stress with strain, the effect of cracks on the structural residual strength, crack growth as a function of time, Stress intensity Vs. Crack length, Relation between strain energy with displacement.   Linear elastic fracture mechanics (LEFM) By using linear elastic theory, crack propagation phenomenon at any point of the crack tip can be derived [1].The general equation used in LEFM is given as: σ  =    √   ∗ f   ( θ )  (1) Where K  = Mode I stress intensity factor  = distance from the crack tip f   ( θ ) =function represents stress dependence θ  Assumptions Application of LEFM associated to the elasticity of the body contains cracks. During crack propagation, crack distance d from the crack tip tends towards zero and stresses goes to infinity. With exceed of yield stress, deformation of material undergoes plastically and a plastic zone formed ahead of the crack tip. The basis of LEFM valid, if plasticity remains small compared to overall dimension of the cracked body. Stress Intensity Factors (SIF) Stress intensity factor, K   is related to the nominal stress level (σ) in the structural member and the size of the crack (a). In general, the relation is represented by: K  =  √         (2) Where    a geometrical parameter is depends on the structural member and crack. The stress field near crack tips can be categorized as Mode I: opening mode related to local displacement in which the crack surfaces move directly apart (symmetric with respect to the x-y and x-z planes).  Relation of Energy with crack displacement Energy supplied at the crack tip to propagate crack elastically and dissipated as heat, sound and surface energy. Energy dissipated by fracture per unit area(s) replaced by new fracture surface area (  ) .Strain energy (G) considered as function of applied displacement (d) and crack surface can be explained as:  =   (  ,  )  If crack propagated to new fracture surface area  ,  change in strain energy as follows:  =   ∗ +    ∗  (3) As crack grows, displacement  =0,  so  =   ∗  Energy release rate G, defined as  =  −    (4) Change in total strain energy for increment of    is  = −  (5) For LEFM, specimen deformation totally elastic manner so that compliance, C,is a function of crack length and geometry. Thus, for an applied load P resulting deflection x, can be written as  =   (  )  (6) Where d is the crack length. As the deflection is entirely elastic thus, so energy absorbed displacement per unit force in terms of compliance can be written as  =    =         (7) II.   E XPERIMENTAL P ROCEDURE    A)    Material Two developed TPO blend nanocomposite materials containing composition of PP/EPDM/Cl 30B and PP/EOC/ATP blend nanocomposite used as bumper protector material. The composition detail of the developed material is shown in Table 1. Polypropylene (PP) material used in the composition are procured from Reliance Petrochemical under the trade name Repol B120MA of density 0.96 and melt flow index 12g/10min (230 ˚C/2.16 kg, ASTM D 1238).E thylene Octane copolymer (EOC) and Ethylene Propylene diene monomer (EPDM) elastomers used for the preparation of  blend are procured from Dow elastomers under the trade name Engage 8150 and Nordel IP 4770 respectively. Attapulgite (ATP) nano-fibrillar clay with average diameter of 20nm (purity 99.5%, 200-mesh sieve, specific surface area 150 m 2 /g) was provided by M/S 20 Micron Limited. Cloisite 30B (MMT-TMDA onium ion-modified montmorillonite clay) which was modified with methyl tallw- bis-2-hydroxyethyl quaternary ammonium (TMDA) with interlayer distance 1.85mm supplied by M/s Southern Clay Products, USA. The details of the anionic polymerization of dib lock polymers have been presented previously [3]. The properties of the three  International Journal of Futuristic Trends in Engineering and Technology ISSN: 2348-5264 (Print), ISSN: 2348-4071 (Online) Vol. 1 (08), 2014 Akshar Publication © 2014 http://www.ijftet.wix.com/research 52 materials evaluated experimentally have been summarized in Table 2.  B)    Process Modeling through FEA a)   Geometric model    The model with notches of different dimensions for FEA analysis is created with all the Actual dimensions measured in mm using CATIA-V5 for simulation. Main features of the geometric model of the protector with notches were demonstrated in Fig.1 showing detailed engineering drawing including dimension of all the parts. Notches having different size inserted onto the product to initiate the crack for study of the rate of propagation. Five different notch radii are taken to  judge its impact on crack propagation with radius 0.1mm, 0.3mm, 0.5mm, 0.7mm and 0.9 mm respectively. 2.2.2    Boundary conditions For the analysis purpose, certain set of boundary conditions is defined to simplify the model without losing a realistic approximation. The set of the boundary conditions used in this    project is demonstrated in Fig. 2. The boundary has been fixed and relative displacements in all degrees of freedom (DOF) are fixed. Equivalent load ranging from 500N to 4000N in the  positive X direction applied along with a set of boundary conditions. b)    Meshing The FE model is meshed in ANSYS using SHELL93 elements [8]. The SHELL93 elements are particularly well suited for model curved structures. The thickness of the shell elements is a defined parameter and therefore do not have any elements in that direction. The thickness and other cross-sectional  properties are incorporated into the element stiffness matrix and input as "real constants" in ANSYS. The meshed product is shown in Fig.3. c)   Crack Propagation A computational technique for calculation of fracture  parameter such as crack propagation is evaluated by the use of a “Special element” which must possess the ability to incorporate the stress singularity near the crack tip using the FEA model. The direct linear equation solver is used in almost all cases to find propagation rate. To judge the crack  propagation, special element called deformation probe has  been incorporated at the tip of the crack which will be singularized at the crack tip. Tip of the crack is assigned as the srcin with local coordinate system as shown in Fig.4 and stress intensity is obtained according to different loading conditions. d)    Energy calculation The area under the force-displacement curve is classically termed as strain energy. For each radius of the notch, a 500N ramp load was applied along the 1 s step time. Step time  parameter ranged from 0 to 1 allows determining increment for each applied load. Whole force-displacement curve was deduced (discredited using the step-time parameter) [9], for one single load case, by using the results for each increment. An integration of the force-displacement curve was  performed, giving a strain energy–displacement curve.  Assumption and approach a)   All the 13 positions at the strain tensors are rigidly fixed.  b)   The entire product is considered as the RVE (Representative Volume Element) for the testing. c)   The RVE is considered as the single solid body. d)   A set of ramped load ranging from 250N to 900N is applied for the notched specimen. e)   The load is applied on the product in positive X direction. III.   R  ESULT AND DISCUSSION    A)   3.1 Static Structural Results Fig. 5(a) shows relation between Von Mises strain vs. Von Mises stress for three different materials for a 500N ramped load. Maximum Von Misses stress of PP/EOC/ATP blend nanocomposite and product material is 27.67 Mpa and 38.15 Mpa respectively which is above the yield stress of the material suggested yielding of the material. Von-Misses stress value for PP/EPDM/Cl 30B blend nanocomposite is slightly less in comparison to other compositions suggested less deformation. Both Von Misses stress and strain shows a linear relationship consistent with Hooke’s law. Variation of stiffness with displacement is plotted in Fig.5 (b).It has been observed that influence of crack displacement on stiffness is high and the value increases with displacement. Higher value of stiffness observed for PP/EPDM/Cl 30B blend nanocomposite. The stress distribution results are obtained in the form of Von-Misses stresses from ANSYS as shown in fig. 6(a) is non-symmetric and the maximum stresses are found around the tensors. Another important fact about the stress distribution is that there is not much variation of stresses in the internal geometries. These results showed that there are no significant effects of these internal geometries on the simulation results. The deformations in the model are analyzed in order to understand the behavior of the FE model under the applied conditions. The deformation behaviors obtained from FE analysis for a 500N ramped load is compared for the three reference materials as shown in Fig.6. Non-symmetric structural deformation observed around the surface. The values obtained are in good acceptable range for structural application with maximum at 13.28mm for the product material as shown in fig. 6(b) and the minimum at 6.79mm for the PP/EPDM/ATP blend nanocomposite(Fig.6(d)). It has  been found, that the structural deformation behavior is non-symmetric.  B)   Crack propagation Fig.7(a) demonstrates the variation of stress intensity as function of notch tip radius with respect to different crack length to understand crack propagation behavior.The stress intensity increases as the crack length increases. Results of  International Journal of Futuristic Trends in Engineering and Technology ISSN: 2348-5264 (Print), ISSN: 2348-4071 (Online) Vol. 1 (08), 2014 Akshar Publication © 2014 http://www.ijftet.wix.com/research 53 crack tip blunting corresponding to initial SIF (K  C )  about  0.28, 0.42 and 0.38 MPa √ m respectively for PP/EPDM/Cl30B,PP/EOC/ATP and product material. Result has been compared with previous experimental results cited in the literature by A. Ramjaroop et al.[10], Zabarjad et al.[11] and Keledi et al[12]. In principle, SIF predicted by this study agrees well with experimental results. Simulation result showed that applied stresses are main responsible for the crack  propagation because of loading condition. It has been found that K  I govern the crack propagation behaviour with maximum at 2.18 Mpa. √m  at 2.08 mm crack length for PP/EPDM/Cl 30B nanocomposite and 2.9 Mpa. √m  at 2.24 mm crack length for PP/EOC/ATP nanocomposite respectively. Maximum crack length growth for product material is 2.08 mm corresponding to stress intensity 4.43 Mpa. √m , which is higher in comparison with developed composites. Minimum value found for all composites are almost negligible compared to maximum values as shown in Fig.7(a) which governs the crack propagation behaviour. SIF value for all composite is  below the material fracture toughness which indicated that  protector can tolerate small corner cracks in the structure. Based on the prediction of Zebarjad et al.[11], crack arrest length via the present method is nearly identical with reference to experimental study corresponds to this study. Fig. 7(b) shows the results for the crack length vs. time obtained based on the material properties separately. The results obtained are nearly similar to the predictions used to the static elastic  properties. For all composites, crack length increases linearly with time on application of 500N load. The crack continues to grow from 0.18mm to 2.24 mm for PP/EPDM/Cl 30B and 0.24mm to 2.24 mm for PP/EOC/ATP nanocomposite. At the  points in the vicinity of final fracture zone, the crack size  becomes large enough to raise the SIF K  I   at crack tip to the level of the material’s fracture toughness K  C   and sudden failure occurs instantaneously. In order to study the influence of notch size on the crack  propagation with load component, three FE models are created with of radius 0.1, 0.3, 0.5,0.7 and 0.9mm respectively. The other features including material properties, meshing and loading conditions are same in all models as discussed. Equivalent load ranging from 250N to 900N applied in  positive X direction applied along with a set of boundary conditions. Fig. 8 demonstrates the effect of notch radius load effect on crack tip displacement for all composites. Table 2 summarizes effect of notch radius on stress intensity for all materials. As expected, it has been found that the value of crack tip displacement increases with an increase of load from 500N to 2000N for all composites whereas the value of maximum stress intensity decreases with an increase in the notch radius. In order to understand the effect of notch size on the crack growth, simulations are performed until the notch radius reaches a value of 0.9 mm in all three cases. The maximum stress intensity of 44.1 Mpa is found in the FE model with notch radius of 0.1 mm for the srcinal product material. The simulation results showed that the value of maximum stress intensity and the crack growth rate both decreases with an increase in the notch. Hence, the crack growth rate increases with the sharper notch as expected. C)    Energy displacement The area under the force-displacement curve is classically termed as strain energy. For each radius of the notch, a 500N ramp load was applied along the 1 s step time. This means that the step time parameter (ranging from 0 to 1) allows determining for each increment of the applied load. An integration of the force-displacement curve was performed, giving a strain energy–displacement curve as shown in Fig. 9[13-14].It is indicated that the relation between energy with crack displacement is non linear from small crack to large crack. Continuous increment of energy observed with crack displacement. As per G theta Maximum theory, crack  propagates in the direction of maximum energy release rate when critical energy rate achieved [15].From FE analysis of Fig.9, it is shown that smaller value of notch size gives higher strain energy value. Also displacement-energy curve exhibited a second order polynomial shape. The interfacial deformation modes are governed by energy release rate described as driving force for crack propagation. From the analysis, it is observed that smaller value of notch size gives higher strain energy value. IV.   C ONCLUSION This project investigated the process of crack propagation and the resulting stress distribution in a typical Protector using ANSYS. The first step of the analysis consisted of using ANSYS to perform static structural analysis on an existing notched protector to identify the high stress regions. the results show that the Von Mises elastic static stress is below the yield strength for the PP/EPDM/Cl 30B and PP/EOC/ATP composite suggested capability of the product to withstand the applied load and above for product material confirmed yielding and deformation. The deformation and Von Mises stress behavior obtained from simulations performed was found to be non-symmetric with maximum at 13.28mm for the srcinal material and the minimum at 6.79 mm for the material PP/EPDM/ATP blend nanocomposite. The Mode I stress intensity factors for the developed composites are below the material’s fracture toughness suggested that protector can tolerate small corner cracks in the structure. From the strain energy and displacement approach, from the analysis, it is observed that smaller value of notch size gives higher strain energy value. Relation between energy with crack displacement is non linear from small crack to large crack. Continuous increment of energy observed with crack displacement. The simulation results obtained from the FE analysis performed with ANSYS showed good agreement with the experimental findings. It can also be deduced that the distributions of analysis parameters such as strain energy density and Von Mises stress given by the FE analysis are acceptable and can be used to improve the design of Protector.  International Journal of Futuristic Trends in Engineering and Technology ISSN: 2348-5264 (Print), ISSN: 2348-4071 (Online) Vol. 1 (08), 2014 Akshar Publication © 2014 http://www.ijftet.wix.com/research 54 R  EFERENCES   [1]   J. K. Mishra, K.J. Hwang, and C.S. Ha, “Preparation, mechanical and rheological properties of a thermoplastic polyolefin (TPO)/organoclay nanocomposite with reference to the effect of maleic anhydride modified polypropylene as a compatibilizer,”  Polymer  , vol. 46, no. 6, pp. 1995–2002, 2005. [2]   S.C. Tjong and Y.H. Ruan, “Fracture behavior of thermoplastic  polyolefin/clay nanocomposites”,  Journal of Applied     Polymer Science , vol. 110, no. 2, pp. 864–871, 2008. [3]   B. P. Panda, S. Mohanty, S. K. Nayak, and S. Pandit, “Fracture study of modified TiO2 reinforced PP/EPDM composite: mechanical behavior and effect of compatibilization”.  International Journal of Plastics Technology , 16  (1), 89-100, 2012. [4]   F. Chaari, T. Fakhfakh, and M. Haddar, “Analytical modelling of spur gear tooth crack and influence on gear mesh stiffness”.  European Journal of Mechanics-A/Solids , 28 (3), 461-468, 2009. [5]   M. Gulzar, “Linear and Non Linear Analysis of Central Crack Propagation in Polyurethane Material-A Comparison”. In  Proceedings of the World Congress on Engineering   ,Vol. 3,2012. [6]   P. L. Chin, “ Stress Analysis, Crack Propagation and Stress  Intensity Factor Computation of a Ti-6Al-4V Aerospace Bracket using ANSYS and FRANC3D”  (Doctoral dissertation, Rensselaer Polytechnic Institute). 2011. [7]   S. Jose, R. K. Kuma, M. K. Jana and G. V. Rae, “Intralaminar fracture toughness of a cross-ply laminate and its constituent sub-laminates”, Composites Science and Technology, 61 (8),1115– 1122, 2001. [8]   A. Horbanpour, R.Rahmani, and A. Arefmanesh, “Elastic  buckling analysis of single-walled carbon nanotube under combined loading by using the ANSYS software”.  Physical E:  Low-dimensional Systems and Nanostructures ,40(7), 2390-2395,2008. [9]   T. S. Botelho, and E. Bayraktar, “Experimental and numerical study of damage initiation mechanism in elastomeric composites”.  Journal of Achievements in Materials and  Manufacturing Engineering  , 36  (1), 65-70, 2009. [10]   A. Ramsaroop, K. Kanny, and T. P. Mohan, “Fracture Toughness Studies of Polypropylene-Clay Nanocomposites and Glass Fiber Reinforced Polypropylene Composites”.  Materials Sciences and  Applications , 1 (5), 301-309, 2010. [11]   S. M. Zebarjad, A. Lazzeri, R. Bagheri, S.M.S. Reihani, and Frounchi, “Fracture mechanism under dynamic loading of elastomer-modified polypropylene”.  Materials Letters , 57  (18), 2733-2741, 2003. [12]   G. Keledi, A. Sudár, C. Burgstaller, K. Renner, J. Móczó, and B. Pukánszky, “Tensile and impact properties of three-component PP/wood/elastomer composites”  Express Polym Lett  , 6  , 224-236, 2012 [13]   J.R. Cho, J.I. Song, K.T. Noh and D.H. Jeon, “Nonlinear finite element analysis of swaging process for automobile power steering hose”  Journal of Materials Processing Technology , 170/1-2,50-57, 2005. [14]   S. Jerrams, K. Sanders, K.B. Goo, “Realistic modelling of earthquake-isolation bearings”  Journal of Materials Processing Technology,  118/1-3,158-164, 2001. [15]   P. Husain, and Underwood, “Strain energy release rate for a crack under combined mode I and II,”  Fracture Analysis , ASTM STP 560, pp. 2-28, 1974.  List of Figures and Tables  Figure 1   Geometric model of protector with notch including all dimensions in mm  Figure 2    protector showing applied load and fixed supports  Figure 3   generation of meshing of the Protector model  Figure 4  Assignment of probe with local coordinate system  Figure 5  (a) Von Mises stress vs. Von Mises strain curve (b) Stiffness energy vs. displacement curve  Figure 6   (a) Von Mises stress distribution of PP/EPDM/Cl 30B composite and deformation Pattern of (b) Product material (c) PP/EOC/ATP Composite (d) PP/EPDM/Cl 30B composite  Figure 7   (a) Crack Length Vs Stress Intensity (b) Time Vs Crack Length  Figure 8  Force Vs crack tip displacement due to effect of notch tip radius of (a) PP/EPDM/CL 30B (b) PP/EOC/ATP (c) Product material  Figure 9  Energy Vs. displacement for (a)PP/EPDM/Cl 30B (b) PP/EOC/ATP (c) Product material Table1  Composition of developed blend nanocomposites Table 2  Experimental properties of materials Table 3  Effect of notch radius on stress intensity (KI)
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