Mechanical characterization and modeling of polymerclay nanocomposites

MECHANICAL CHARACTERIZATION AND MODELING OF POLYMER/CLAY NANOCOMPOSITES SONG SHAONING NATIONAL UNIVERSITY OF SINGAPORE 2014 MECHANICAL CHARACTERIZATION AND MODELING OF POLYMER/CLAY NANOCOMPOSITES SONG SHAONING (B.ENG) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2014 Declaration Declaration I hereby declare that this thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. ______________________________ Song Shaoning Date: 28/04/2014 i Acknowledgement Acknowledgement The author would like to express his sincere gratitude to all of the kind hearted individuals for their precious advice, guidance, encouragement and support, without which the successful completion of this thesis would not have been possible. Special thanks to the author’s supervisors A/Prof. Vincent Tan Beng Chye and A/Prof. Quan Chenggen, whom the author has the utmost privilege and honor to work with. Their profound knowledge on mechanics and strict attitude towards academic research will benefit the author’s whole life. The author would also like to thank Dr Chen Yu, Dr Su Zhoucheng, Dr Ren Yunxia, Mr Joe Low Chee Wah, Dr Sun Xiushan, Dr Muhammad Ridha and Dr Tan Longbin for their invaluable help. Many thanks to his friends Dr Andi Haris, Dr Jiang Yong, Dr Chen Boyang, Dr Li Sixuan, and Mr Umeyr Kureemun for making the research environment a lively place. Last but not least, the author expresses his utmost love and gratitude to his wife, Gao Yuan, for her understanding and support throughout his research. ii Table of Contents Table of Contents Declaration i Acknowledgement .ii Table of Contents . iii Summary v List of Tables . viii List of Figures . ix Nomenclature xiv Chapter Introduction and Literature Review . 1.1 Introduction 1.2 Review of Studies on Mechanical Properties of PCNs 1.2.1 Experimental Work on PCNs 1.2.2 Analytical Studies of PCNs 1.2.3 Numerical Models of PCNs 15 1.3 Review of Studies on Fiber Reinforced Polymer/clay Nanocomposites (FRPCNs) . 24 1.4 Objectives and Significance of the Study 26 Chapter 31 Representative Volume Element (RVE) Model for Polymer/clay Nanocomposites . 31 2.1 Finite Element Clay Model and RVE Model . 32 2.1.1 Finite Element Clay Model . 32 2.1.2 RVE Model . 34 2.2 Boundary Conditions . 37 2.3 Dynamic Explicit Formulation 42 2.4 Summary 45 Chapter 47 Mechanical Characterization and Modeling of Epoxy/clay Nanocomposites . 47 3.1 Finite Element Clay Model for Epoxy/clay Nanocomposites . 48 3.2 Traction-Separation Law . 49 3.3 Brittle Cracking Criterion 53 3.4 Results and Discussion 55 3.4.1 RVE Size . 57 3.4.2 Parametric Study . 58 iii Table of Contents 3.4.3 Damage Analysis 61 3.4.4 Effect of the Gallery Strength . 64 3.4.5 Effect of Nano-clay/matrix Interphase 65 3.5 Conclusions 67 Chapter 69 Mechanical Characterization and Modeling of Nylon 6/clay Nanocomposites 69 4.1 Finite Element Clay Model for Nylon 6/clay Nanocomposites . 70 4.2 Traction-Separation Law . 71 4.3 Damage Models for Nylon 75 4.3.1 Progressive Ductile Damage Criterion for Nylon 77 4.3.2 GTN model . 82 4.4 Results and Discussion 84 4.4.1 Parametric Study . 85 4.4.2 Effect of Particle Size . 85 4.4.3 Effect of Number of Silicate Layers . 88 4.4.4 Damage Analysis 89 4.4.5 Effect of Interface Strength . 91 4.4.6 Effect of Initial Stress Triaxiality on NCNs . 93 4.5 Conclusions 96 Chapter 98 Mechanical Characterization of Fiber Reinforced Polymer/clay Nanocomposites . 98 5.1 Effective Clay Models . 99 5.1.1 Quasi-Traction-Separation Law 101 5.1.2 Validation of Effective Clay Model 106 5.1.3 Damage Analysis 111 5.2 Mechanical Characterization of Fiber Reinforced Polymer/clay Nanocomposites . 115 5.2.1 Elastic Properties of FRECNs . 119 5.2.2 Damage Analysis of FRECNs 120 5.3 Conclusions 123 Chapter 125 Conclusions and Recommendations 125 6.1 Conclusions 125 6.2 Recommendations for Future Work . 130 References 132 iv Summary Summary Polymer/clay nanocomposites (PCNs) have drawn great attention both from industry and academia due to their remarkable enhancement of mechanical, thermal and barrier properties compared to traditional polymers. Although the elastic properties of PCNs have been extensively studied and well documented, their damage behavior has not yet been completely addressed. In this thesis, the damage behavior of two typical PCNs systems, namely epoxy/clay nanocomposites (ECNs) and nylon 6/clay nanocomposites (NCNs) were characterized by a 3D representative volume element (RVE) model implemented with a computational homogenization approach. Despite all the advances in polymer nanocomposites, as discontinuous reinforcement, nanoparticle filled polymer composites cannot achieve the strength and the modulus comparable to that of the continuous fiber reinforced polymers (FRPs). Fiber reinforced polymer/clay nanocomposites (FRPCNs) are developed to harness both the advantages of the PCNs and FRPs. The damage behavior of FRPCNs under transverse tensile loading was also studied to highlight the application of PCNs. For the PCNs systems, a 3D RVE model, which consists of the polymer matrix, the clay platelets, the gallery layer and the interphase layer, was developed to mimic the microstructure of actual PCNs. Different appropriate damage criteria were used to describe the material behavior of these constituents. The brittle cracking model was applied to epoxy, while v Summary deformation of nylon was mimicked by the progressive ductile damage (PDD) criterion or the Gurson-Tvergaard-Needleman (GTN) model. The traction-separation law was used for the gallery layer and interphase layer. Effects of parameters of constituents, such as structural parameters of the clay particle, the strength of the interphase layer and the gallery layer, on the constitutive relationship and the damage behavior of the PCNs were studied by a computational homogenization approach implemented with explicit finite element method (FEM). It was found that for both the ECNs model and the NCNs model, the predicted constitutive relationship and fracture patterns are close to the experimental data. Moreover, the clay particles with less number of silicate layers or larger particle size could lead to an increase in elastic stiffness and stress at engineering strain 0.1 for the NCNs model but a decrease in tensile strength for the ECNs model. In addition, the damage mechanisms of PCNs were found to be related to the strength of the gallery layer and the interphase layer. A lower strength of the gallery layer or the interphase layer could respectively cause damage to initiate as splitting of the gallery layer or debonding of the interphase layer, leading to reduction in the strength of PCNs. These results could be used as guidelines for manufacturing PCNs with interfaces having high quality. For the fiber reinforced PCNs (FRPCNs), an effective clay model was proposed to reduce the computational time in explicit FEM. A corresponding user defined material subroutine (VUMAT) was developed to describe the material behavior of the effective clay in the commercial FEM software vi Summary (Abaqus). The damage analysis of the FRPCNs under transverse tensile loading was also conducted by computational homogenization. Results indicate the interphase between the fiber and matrix is the key factor which dominates the strength of the FRPCNs. The effect of adding nano-clay to FRPs in order to increase interfacial strength, however, needs to be further studied. Overall, this study suggests the 3D RVE model implemented with computational homogenization method and appropriate damage criteria could successfully replicate the properties of ECNs/NCNs. To the best knowledge of the author, this is the first 3D RVE model which takes into account the damage behavior for both the interfacial layers and the polymer matrix in polymer/clay nanocomposites. This method could be applied to other PCNs provided material properties of their constituents are well characterized. vii List of Tables List of Tables Table 3.1 Cohesive law for gallery. Table 3.2 Material properties in epoxy/clay nanocomposites. Table 4.1 Stretches to generate different initial triaxiality. Table 5.1 Boundary conditions to obtain the elastic constants of effective clay. Table 5.2 Elastic properties nanocomposites. Table 5.3 Elastic properties nanocomposites. Table 5.4 Material properties of fiber. of of viii effective effective clay clay in in epoxy/clay nylon 6/clay Chapter Conclusions and Recommendations Chapter Conclusions and Recommendations Conclusions on two main objectives, namely, developing a 3D representative volume element model to perform damage analysis of polymer/clay nanocomposites and analyzing the effect of polymer/clay nanocomposites on bulk behavior of unidirectional fiber reinforced polymer/clay nanocomposites under transverse tensile loading, will be addressed separately. Limitations will be discussed followed by recommendations. 6.1 Conclusions The primary objective of this study was to characterize the damage behavior of two polymer/clay nanocomposites (PCNs) systems, namely the nylon 6/clay 125 Chapter Conclusions and Recommendations nanocomposites and the epoxy/clay nanocomposites. Although the polymer matrices used in these two systems are different, their microstructures are almost the same. A 3D representative volume element (RVE) model which consist of the polymer matrix, the clay platelet, the gallery layer and the interphase layer was developed to mimic the microstructure of the actual polymer/clay nanocomposites. Appropriate damage criteria were used to describe the material behavior of these constituents. Effects of structural parameters of clay particles, such as the clay particle size and the number of silicate layers, on the constitutive relationship and damage behavior of the PCNs were studied. Computational hierarchical multiscale homogenization models of the PCNs were constructed and analyzed using the explicit finite element method. The material properties of the gallery layer and the interphase layer used in the FEM model were obtained from MD simulations. The main findings for the ECNs model and NCNs model are as follows. For the epoxy/clay nanocomposites models, it was found that the predicted constitutive relationship and fracture patterns are close to experimental data reported in literature [11, 13]. The damage of epoxy/clay nanocomposites could be caused by several factors, such as splitting of the gallery layer, debonding of the interphase layer or stress concentration around the clay particle. All of these three types of damage mechanisms were observed in reported experimental studies [11, 13]. Moreover, not all parameters of the clay particles significantly affect the elastic stiffness or the tensile strength of epoxy/clay nanocomposites, e.g., particle size, number of silicate layers in per particle. However, the galley strength will significantly affect the strength of 126 Chapter Conclusions and Recommendations the epoxy/clay nanocomposites, which could explain why the tensile strength of nanocomposites often shows a much larger variation in experiments than elastic properties. For the nylon 6/clay nanocomposites model, the predicted results of the stressstrain response was also shown to be in agreement with experimental data reported in literature [18]. The damage of nylon 6/clay nanocomposites was found to be mainly caused by debonding of the interphase layer. It was also experimentally reported that the clay particles can better exfoliate in the nylon 6/clay nanocomposites model than in the epoxy/clay nanocomposites model, which leads the number of formed gallery layers to be quite small [18]. However, it was found that the damage still results from the debonding of interphase even when the gallery layer was added into the numerical model. The possible reason is the strength of the gallery layer is higher than that of the interphase layer in the nylon 6/clay nanocomposites model. Moreover, the structural parameters of the clay particles may not significantly affect the elastic stiffness. The stress at engineering strain 0.1 could increase when nylon 6/clay nanocomposites model are reinforced with larger clay particles or particles with lower number of silicate layers. This is because particles with larger size (aspect ratio) could more effectively transfer load. A higher degree of exfoliation also increases the aspect ratio of the clay platelets and the interphase region to enhance stress transfer. When the interphase layer has a relatively higher strength, the damage initiates from the polymer matrix outside of the interphase layer. This may be due to the inherent weak adhesion strength between the polymer chains. 127 Chapter Conclusions and Recommendations In summary, 3D RVE model was developed and it could accurately simulate actual polymer/clay nanocomposites. To the best knowledge of the author, this is the first 3D RVE model which takes into account the damage behavior for both the interfacial layers and the polymer matrix in polymer/clay nanocomposites. Based on the study of both epoxy/clay nanocomposites and nylon 6/clay nanocomposites, it was found that different damage mechanisms are present in epoxy/clay nanocomposites and nylon 6/clay nanocomposites. This is mainly due to the different material behavior of their constituents, especially the polymer matrix. However, this study suggests the hierarchical multiscale modeling method implemented with 3D RVE model and appropriate damage criteria can be used to study some aspects of nano-clay reinforced epoxy and nylon nanocomposites. This method could be applied to other polymer/clay nanocomposites provided material properties of their constituents are well characterized. Undoubtedly, the strength of the interphase layer and the gallery layer will significantly affect the strength of the polymer/clay nanocomposites. This emphasizes the importance of manufacturing polymer/clay nanocomposites with interfaces having high quality. Furthermore, the hierarchical multiscale approach could also be used to study the damage behavior of structural problems which is quite expensive and difficult to be characterized experimentally. For the fiber reinforced polymer/clay nanocomposites, an effective clay model was proposed to reduce computational time in explicit finite element analysis. A user defined material model (VUMAT) was developed in Abaqus to describe a quasi-traction-separation law for the effective clay. This effective 128 Chapter Conclusions and Recommendations clay model was verified by comparing it with the explicit clay models. It is found that the effective clay model gives more conservative predictions of tensile strength compared with the explicit clay model. Finally, the damage behavior of FRPCNs under transverse tension was studied. It was found that the addition of nano-clay into fiber reinforced composites could increase the transverse elastic modulus. It is also shown that the transverse tensile strength of FRPCNs is determined mainly by the strength of the interface between the fiber and the matrix rather than the strength of the effective clay. There are admittedly some limitations that need further attention. For polymer/clay nanocomposites, a concurrent multiscale modeling method could be more accurate because of the strong coupling of events at different length scales throughout the entire damage evolution. However, in this study the hierarchical multiscale modeling strategy rather than the concurrent multiscale modeling method was adopted because the computational cost could be unreasonably high for damage problems with complex microstructures using the concurrent multiscale modeling method. Secondly, periodic boundary conditions (PBCs) could not be prescribed exactly using the constrained equations in the commercial FEM software, ABAQUS. The simulation time was also prohibitively large when the number of constrained equations exceeds 1000 in explicit FEM. The lack of information on the interface between the fibers and the matrix is the main obstacle to accurately characterize the damage behavior of fiber reinforced polymer/clay nanocomposites. 129 Chapter Conclusions and Recommendations 6.2 Recommendations for Future Work The following possible directions for future work are proposed: (1) The damage behavior of other types of nanometer-sized fillers reinforced polymer nanocomposites could be characterized, such as polymer/nanotube nanocomposites or polymer/silica nanocomposites. It can be expected the properties of the interphase between the nano-fillers and polymer matrix still play a critical role in determining the macroscopic performance of such nanocomposites systems. (2) The nano-clay effect on the strength of interface between the fiber and matrix in the FRPCNs system needs be investigated by using the molecular mechanics analysis. This could help understand the effects of PCNs when they are used as the matrix system in traditional fiber reinforced composites. (3) Only unidirectional fiber reinforced polymer/clay nanocomposites subjected to transverse tension was studied. A possible extension of this work is to study structural problems. By incorporating the multiscale modeling method, the simulations on macroscopic flexural test may be performed. Rather than the unidirectional fiber more complex type of fiber reinforcements, i.e., woven fiber reinforced polymer/clay nanocomposites could also be studied. (4) Another possible extension of the work is to model crack propagation in nanocomposites with the extended finite element method (X-FEM). 130 Chapter Conclusions and Recommendations Computational models for damage analyses are commonly based on traditional FEM. Examples including the brittle cracking model, progressive ductile damage model, GTN model and cohesive zone model have been used in this study. In these kinds of computational models, elements will be removed when a damage criterion is reached. In contrast to traditional FEM, the X-FEM can explicitly simulate the crack with strong displacement discontinuity which is achieved by nodal enrichments [117, 118]. Typically, a jump function and a crack-tip function with partition of unity are used to model the discontinuous crack surfaces. This method provides an accurate and robust model in analyzing crack problems. 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International Journal for Numerical Methods in Engineering. 2009;77(2):214-239. 140 [...]... properties of the epoxy/clay nanocomposites and the nylon 6/clay nanocomposites as a function of clay content (a) elastic stiffness of epoxy/clay nanocomposites (b) elastic stiffness of nylon 6/clay nanocomposites (c) tensile strength of epoxy/clay nanocomposites (d) maximum strength and strain at maximum strength of nylon 6/clay nanocomposites (e) Model I critical strain energy release rate of epoxy/clay nanocomposites. .. strength of epoxy/clay nanocomposites; Effect of number of silicate layers on (c) elastic modulus and (d) tensile strength of epoxy/clay nanocomposites Figure 3.7 Comparison of internal and kinetic energy during loading increases Figure 3.8 Stress-strain curve of epoxy/clay nanocomposites with 3% weight fraction of nano-clay Figure 3.9 Numerical prediction of damage sequence of epoxy/clay nanocomposites. ..List of Figures List of Figures Figure 1.1 Schematic illustration of polymer/clay nanocomposites morphologies (a) Microcomposite (b) Intercalated nanocomposites and (c) Exfoliated nanocomposites Figure 1.2 Schematic illustration of crack initiation and propagation in the epoxy/clay nanocomposites Figure 1.3 Mechanical properties of the epoxy/S-clays and the nylon 6/clay nanocomposites as a function of. .. chains of nylon 6 not far from the nano-clay Figure 1.2 Schematic illustration of crack initiation and propagation in the epoxy/clay nanocomposites, reprinted from [11] In order to understand the different mechanical performances between thermoset/clay nanocomposites and thermoplastic/clay nanocomposites, the comparison of mechanical properties between the epoxy/clay nanocomposites and the nylon 6/clay nanocomposites. .. of nano-clay Figure 3.10 Stress-strain curves of epoxy/clay nanocomposites with 3% weight fraction of nano-clay and different gallery strength Figure 3.11 Combined effects of gallery layer and interphase on tensile strength of epoxy/clay nanocomposites with 3% weight fraction of nano-clay Figure 4.1 (a) Illustration of clay platelet in nylon 6/clay nanocomposites (b) FE model of the clay particle and. .. morphologies (a) Microcomposite (b) Intercalated nanocomposites and (c) Exfoliated nanocomposites, reprinted from [6] 4 Chapter 1 Introduction and Literature Review 1.2 Review of Studies on Mechanical Properties of PCNs Experimental work, analytical modeling and numerical modeling method are widely used in material science to understand and explain microstructure versus mechanical properties relationship In this... in FE simulations with randomly distributed and oriented particles at different clay volume fractions Figure 1.9 Scenario of mechanical properties improvement of CFRP by incorporation of nano-fillers Figure 2.1 (a) Illustration of clay platelet in polymer/clay nanocomposites and (b) FE model of the clay particle Figure 2.2 Schematic illustration of translation and rotation of a newly generated clay... number of silicate layers, (for the NCNs model) Figure 5.3 (a) The explicit RVE and (b) the effective RVE Figure 5.4 Dependency of elastic modulus of explicit RVE and effective RVE on the number of silicate layers, (for ECNs) xi List of Figures Figure 5.5 Dependency of elastic modulus of explicit RVE and effective RVE on diameter of clay particle, (for ECNs) Figure 5.6 Dependency of elastic modulus of. .. tensile strength of glass fiber/epoxy nanocomposites with various organoclay loadings Figure 5.21 SEM micrographics of glass fiber/epoxy nanocomposites samples (a) pure epoxy and (b) 5% weight fraction of organoclay xii List of Figures Figure 5.22 Effect of strength of interface on the transverse tensile strength of FRECNs Figure 5.23 Damage patterns of FRECNs with (a) weak interface and (b) strong interface... polymer/clay nanocomposites and obtained: ' ' ' Ec 1   p  p  ' Em 1  ' p (1-9) and '  ' Ep 1 (1-10) ' ' Ep   p ' ' where, E p the ratio of modulus of platelet stack to that of the matrix,  p the ' shape parameter of the platelet stack and  p the volume fraction of the platelet stacks in the matrix In each platelet stack, there are N layers of platelets Using t for the thickness of the platelet and . MECHANICAL CHARACTERIZATION AND MODELING OF POLYMER/CLAY NANOCOMPOSITES SONG SHAONING NATIONAL UNIVERSITY OF SINGAPORE 2014 MECHANICAL CHARACTERIZATION AND MODELING. dependency of elastic modulus on the number of clay particles. Figure 3.6 Effect of particle size on (a) elastic modulus and (b) tensile strength of epoxy/clay nanocomposites; Effect of number of. of elastic modulus of explicit RVE and effective RVE on the number of silicate layer, (for NCNs). Figure 5.7 Dependency of elastic modulus of explicit RVE and effective RVE on diameter of