Considering Anisotropic Behaviour and Process Induced Weaknesses in Fibre Reinforced Polymers in CAE A comparison of material models for fibre reinforced materials in LS-DYNA Master’s thesis in Materials Engineering GUSTAV HINDÉR DEPARTMENT OF INDUSTRIAL AND MATERIALS SCIENCE CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden 2021 www.chalmers.se www.chalmers.se Master’s thesis 2021 Considering Anisotropic Behaviour and Process Induced Weaknesses in Fibre Reinforced Polymers in CAE A comparison of material models for fibre reinforced materials in LS-DYNA GUSTAV HINDÉR Department of Industrial and Materials Science Chalmers University of Technology Gothenburg, Sweden 2021 Considering Anisotropic Behaviour and Process Induced Weaknesses in Fibre Rein- forced Polymers in CAE A comparison of material models for fibre reinforced materials in LS-DYNA GUSATV HINDÉR © GUSTAV HINDÉR, 2021. Supervisor: Henrik Alm, Thule Supervisor: Antal Boldizar, Department of Industrial and Materials Science Examiner: Antal Boldizar, Department of Industrial and Materials Science Master’s Thesis 2021 Department of Industrial and Materials Science Chalmers University of Technology SE-412 96 Gothenburg Telephone +46 31 772 1000 Cover: Typeset in LATEX, template by Magnus Gustaver Printed by Chalmers Reproservice Gothenburg, Sweden 2021 iv Considering Anisotropic Behaviour and Process Induced Weaknesses in Fibre Rein- forced Polymers in CAE A Comparison of material models for fibre reinforced materials in LS-DYNA GUSTAV HINDÉR Department of Industrial and Materials Science Chalmers University of Technology Abstract Computer Aided Engineering (CAE) is widely used for developing new products nowadays. Through advanced software, it is possible to simulate the reality in the computer to save time and money when less component testing is needed. Two examples of CAE are Finite Element Analysis (FEA) and Mould Fill Simulation (MFS). MFS can be used to simulates the melt flow in the mould of an injection moulding process and FEA can be used to structurally analyse components when subjected to various loads. This thesis work was conducted at Thule to investigate the possibility of consider the anisotropic behaviour and process induced weaknesses of short fiber reinforced polymers (SFRP) through MFS in Moldex3D with a sub- sequent FEA in LS-DYNA. The MFS results was implemented in the FEA through the usage of material models Mat_157 and Mat_215 which are designed for fibre reinforced materials. A tensile test using Polyamide 6 reinforced with 30 wt% short glass fibres (PA6 GF30) specimens was performed and compared with results from the corresponding MFS and FEA. A subsequent Case Study on Thule’s Outway Hanging Bike Rack was performed, which also included physical testing, MFS and FEA. Results indicate that it is possible to capture the anisotropic behaviour of SFRP by obtaining the fibre orientation through MFS. Also, some process induced weaknesses, especially weld lines and air traps can be obtained from MFS. In the FEA, the comparison of material models shows that the implementation of fibre orientation can increase the reliability of the analysis, but there is a need for ma- terial testing with combined calibration of the material models before they can be implemented in the daily calculations at Thule. Keywords: Polyamide 6, short glass fiber reinforced polymers, anisotropy, weld lines, air traps, structural analysis, FEM, material models, mould fill simulation. v Acknowledgements I would like to take this opportunity to thank Thule for giving me the opportunity to conduct an interesting master’s thesis with the structural analysis division at the company. It has given me a broader spectrum of the development process and a closer understanding of the relation between materials and CAE. A special thanks to my supervisor at Thule, Henrik Alm, who has contributed the work with extensive knowledge and performed the conducted simulations which has made this work possible. Henrik has also been a great source for guidance and discussion of all the results we obtained during the project. I would also like to thank my supervisor at Chalmers University of Technology, Antal Boldizar for the valuable input regrading the academic aspects of the work. Gustav Hindér, Gothenburg, June 2021 vii Contents List of Figures xi List of Tables xv 1 Introduction 1 1.1 The Company - Thule . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 Purpose and Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.4 Delimitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.5 Ethics and Social Aspects . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Polymer Materials 5 2.1 Molecules and Microstructures . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Properties of Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.1 Temperature Dependency . . . . . . . . . . . . . . . . . . . . 7 2.2.2 Viscoelasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.3 Yielding and Fracture . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Fiber Reinforced Polymers . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3.1 Reinforcement Materials . . . . . . . . . . . . . . . . . . . . . 12 2.3.2 Polymer Matrix Materials . . . . . . . . . . . . . . . . . . . . 13 2.3.3 Fibre/Matrix Interface . . . . . . . . . . . . . . . . . . . . . . 14 2.3.4 Micro-mechanics of GFRP . . . . . . . . . . . . . . . . . . . . 15 2.3.5 Macro-mechanics of GFRP . . . . . . . . . . . . . . . . . . . . 18 2.3.6 Strength and Fracture of GFRP . . . . . . . . . . . . . . . . . 21 2.4 Polyamide 6 GF30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.5 Injection Molding of SFRP . . . . . . . . . . . . . . . . . . . . . . . . 28 2.6 Defects in Injection Molding . . . . . . . . . . . . . . . . . . . . . . . 30 2.6.1 Flow Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.6.2 Weld Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.6.3 Vacuum voids . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.6.4 Surface Delamination . . . . . . . . . . . . . . . . . . . . . . . 31 2.6.5 Sink Marks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.6.6 Warping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.6.7 Jetting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.6.8 Flash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.6.9 Short Shots . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 ix Contents 2.7 Anisotropy in Short Glass Fibre Reinforced Thermoplastics . . . . . . 32 3 CAE - Predicting and Preventing in use Failure 35 3.1 Finite Element Analysis - LS-DYNA . . . . . . . . . . . . . . . . . . 35 3.2 Material Models - LS-DYNA . . . . . . . . . . . . . . . . . . . . . . . 37 3.2.1 Mat_24 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.2.2 Mat_157 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.2.3 Mat_215 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.3 Mold Flow Analysis - moldex3D . . . . . . . . . . . . . . . . . . . . . 39 4 Tensile Test of PA6 GF30 41 4.1 Mechanical Tensile Test . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.1.1 Setup - Mechanical Tensile Test . . . . . . . . . . . . . . . . . 41 4.1.2 Results - Mechanical Tensile Test . . . . . . . . . . . . . . . . 42 4.2 Simulation of Tensile Test . . . . . . . . . . . . . . . . . . . . . . . . 44 4.2.1 Setup - Simulation in Moldex3D . . . . . . . . . . . . . . . . . 44 4.2.2 Result - Simulation in Moldex3D . . . . . . . . . . . . . . . . 44 4.2.3 Setup - Simulation of Tensile Test . . . . . . . . . . . . . . . . 45 4.2.4 Results - Simulation of Tensile Test . . . . . . . . . . . . . . . 45 4.3 Discussion - Tensile Test of PA6 GF30 . . . . . . . . . . . . . . . . . 46 5 Case Study - Thule OutWay Hanging Bike Rack 49 5.1 The component - Thule OutWay Hanging Bike Rack . . . . . . . . . 49 5.2 Mechanical testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.2.1 Setup - Mechanical Testing . . . . . . . . . . . . . . . . . . . . 50 5.2.2 Result - Mechanical Testing . . . . . . . . . . . . . . . . . . . 50 5.3 Simulation with Moldex3D . . . . . . . . . . . . . . . . . . . . . . . . 52 5.3.1 Setup - Moldex3D . . . . . . . . . . . . . . . . . . . . . . . . 52 5.3.2 Results - Moldex3D . . . . . . . . . . . . . . . . . . . . . . . . 53 5.4 Simulation with LS-DYNA . . . . . . . . . . . . . . . . . . . . . . . . 55 5.4.1 Setup - LS-DYNA . . . . . . . . . . . . . . . . . . . . . . . . 55 5.4.2 Results - LS-DYNA . . . . . . . . . . . . . . . . . . . . . . . . 56 5.5 Discussion - Case Study . . . . . . . . . . . . . . . . . . . . . . . . . 58 6 Conclusion 61 7 Future Work and Recommendations 63 References 65 A Appendix 1 - Theory of Material Models I B Appendix 2 - Material Models in Simulations V x List of Figures 1.1 Thule OutWay Hanging bike rack. . . . . . . . . . . . . . . . . . . . . 2 2.1 Molecular structure of polyethylene. . . . . . . . . . . . . . . . . . . . 5 2.2 Illustration of Linear, Branched, and Cross-linked polymer [1]. . . . . 6 2.3 Illustration of Random, Block, and Graft copolymer [1]. . . . . . . . . 6 2.4 Young’s modulus versus temperature of an amorphous and a semi- crystalline polymer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 Creep visualized as increasing strain at constant stress. . . . . . . . . 8 2.6 Stress relaxation visualized as decreasing stress at constant strain. . . 8 2.7 Stress versus strain curve from tensile test of PS and PE at room temperature [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.8 Stress and strain curves versus time as recorded from tensile test at room temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.9 Tresca and von Mises yield criterion. . . . . . . . . . . . . . . . . . . 10 2.10 (a) Parabolic prediction of von Mises yield criterian at m = 1.30 toghether with experimental results of PVC, PC, PS, and PMMA, and (b) tension and compression test of PA6 [3]. . . . . . . . . . . . . 11 2.11 A polymer matrix: (a) reinforced with short fibre in undeformed and (b) deformed state, and (c) an unreinforced matrix in deformed state [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.12 Comparison of tensile strength of PA6, PA6/MMT5, and PA6/GF25 [4]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.13 Chemical bridge between matrix and fibre using organosilane coupling agent [6]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.14 Young’s modulus of a glass-fibre reinforced polymer predicted by rule of mixture [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.15 Microscopic image of the skin-core-skin structure. The white arrow denotes the MFD [5]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.16 Visualization of Eshelby’s inclusion model. . . . . . . . . . . . . . . . 18 2.17 A three dimensional cube with stress components when exposed to a normal force. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.18 Variation of elastic constants (a) Young’s modulus, (b) Shear mod- ulus, and (c) Poisson’s ratio depending on fibre orientation in a 50 wt% carbon fibre reinforced epoxy . . . . . . . . . . . . . . . . . . . . 20 2.19 Illustration of failure from (a) axial tensile stress σ1u, (b) transverse tensile stress σ2u, and (c) shear stress τ12u [9]. . . . . . . . . . . . . . 21 xi List of Figures 2.20 Strength of a composite versus the fibre volume fraction of a compos- ite with fibres having lower fracture strain than the matrix [6]. . . . . 22 2.21 Fibre pullout and debonding at a crack [6]. . . . . . . . . . . . . . . . 22 2.22 Tensile (σF ) and shear stress (τ) distribution along the length (l) and critical length (lc) of a short fibre in an (a) linearly elastic and an (b) elastic-plastic matrix [5]. . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.23 Prediction of failure of a lamina with 50 % GF according to maximum stress criteria [9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.24 Comparison of the four described failure criteria [10]. . . . . . . . . . 26 2.25 Ring opening of Caprolactam to form PA 6. . . . . . . . . . . . . . . 27 2.26 Interaction between water molecules and a PA 66. . . . . . . . . . . . 27 2.27 Experimental results of (A) moisture content, (B) ultimate tensile strength, (C) modulus of elasticity, (D) elongation, (E) yield strength, and (F) flexural strength versus immersed time in distilled water [13]. 28 2.28 Illustration of the injection molding process [16]. . . . . . . . . . . . . 29 2.29 Illustration of (a) a SFP and (b) a LFP [16]. . . . . . . . . . . . . . . 29 2.30 (a) Visual simulation of the skin-core-skin structure together with (b) probability density of the fibre angle (α) from MFD (x) [15]. . . . . . 33 4.1 Experimental setup for tensile tests. . . . . . . . . . . . . . . . . . . . 41 4.2 Dimension of tensile test specimens scaled from ISO 527 1AB. . . . . 42 4.3 Stress strain curves from one tensile test per angle. . . . . . . . . . . 43 4.4 Fracture of all specimens at different angles. . . . . . . . . . . . . . . 43 4.5 Plate in Moldex3D with finite element mesh and inlet marked in red. 44 4.6 Degree of fibre orientation in the skin layer of the injection moulded plate. The colour scale denotes the degree of orientation; red denotes highly oriented fibres, whereas blue denotes randomly oriented fibres. 44 4.7 Degree of fibre orientation in the two cross-sections of the injection moulded plate. The colour scale denotes the degree of orientation; red denotes highly oriented fibres, whereas blue denotes randomly oriented fibres. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.8 Setup of the tensile test simulation. The red cross indicates the fixed boundary condition and the red arrow indicates the displacement. . 45 4.9 Stress-strain curves from simulation of tensile test of 0°and 90°specimens with material model Mat_24, Mat_157, Mat_215 and result from mechanical tensile test. . . . . . . . . . . . . . . . . . . . . . . . . . . 46 5.1 (a) Thule Outway Haning Bike Rack and (b) the investigated console with aluminium beam and profile. . . . . . . . . . . . . . . . . . . . . 49 5.2 Experimental setup for mechanical testing of console. . . . . . . . . . 50 5.3 Load versus displacement curves for the mechanical testing of four consoles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5.4 Fracture of console test 1 (a) and (b, c, d) close up of the fracture in at different directions. . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5.5 Fracture of console test 4 (a) and (b) close up of the fracture. . . . . 51 5.6 Setup of the simulation in Moldex3D visulised in (a) 2D and (b) 3D [36]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 xii List of Figures 5.7 Cross section of the model to visualise element size in the thickness [36]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 5.8 Simulated mould fill at (a) 15%, (b) 35%, (c) 55%, (d) 75%, and (e) 100% volume filled. The colour scale denotes the melt movement over time; blue denotes the most recent changes, whereas red denotes the first. The red lines and the blue spheres marks the arising weld lines and air traps respectively. . . . . . . . . . . . . . . . . . . . . . . . . 53 5.9 Zoom in of air trap. The blue spheres marks the arising air traps. . . 53 5.10 Simulated degree of fibre orientation in (a) the whole console and the amount of oriented fibres in the (b) x-, (c) y-, and (d) z-direction. The colour scale denotes the (a) degree of orientation and the (b, c, d) amount of fibres oriented in the respective direction. Red denotes (a) highly oriented fibres and (b, c, d) many oriented fibres, whereas blue denotes (a) randomly oriented fibres and (b, c, d) few oriented fibers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.11 Degree of fibre orientation, weld lines and air traps at a cross-section of the lower wholes on each side. . . . . . . . . . . . . . . . . . . . . . 54 5.12 The imported console alone (a) and with beam and profile (b) for simulation in LS-DYNA. . . . . . . . . . . . . . . . . . . . . . . . . . 55 5.13 Boundary conditions (a) and applied load (b) for simulation in LS- DYNA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5.14 Visual representation of mapping fibre properties from moldex3D to LS-DYNA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.15 Load versus displacement curves for the mechanical testing of four consoles and simulations using Mat_24, Mat_157, and Mat_215. . . 57 5.16 Visual comparison of FEA results using Mat_157 (a) and Mat_215 (b) including P1, P2, and P3. The colouring denotes the level of strain, where red is high strains and blue is low strains. . . . . . . . . 57 5.17 Von Mises stress-strain curve at P1, P2, and P3. . . . . . . . . . . . . 58 5.18 Zoom in on an (a) air trap and (b) P1 from a different angle. The colouring denotes the level of strain, where red is high strains and blue is low strains. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 A.1 Material card with parameters for Mat_24 [34]. . . . . . . . . . . . . I A.2 Material card with variables for Mat_157 [34]. . . . . . . . . . . . . II A.3 Material card with variables for Mat_215 [34]. . . . . . . . . . . . . . II B.1 Mat_24 material card. . . . . . . . . . . . . . . . . . . . . . . . . . . V B.2 Mat_24 material curve for PA6 GF30. . . . . . . . . . . . . . . . . . V B.3 Mat_157 material card. . . . . . . . . . . . . . . . . . . . . . . . . . VI B.4 Mat_157 material curve for PA6 GF30. . . . . . . . . . . . . . . . . . VI B.5 Mat_215 material card. . . . . . . . . . . . . . . . . . . . . . . . . . VII B.6 Mat_215 material curve for PA6. . . . . . . . . . . . . . . . . . . . . VII xiii List of Figures xiv List of Tables 2.1 Density, Elongation, Tensile strength and Young’s modulus of some fibre materials [7] [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Comparison of weld line impact on tensile strength from tests per- formed by Zhou and Mallick [24], Ozelik et. al. [25], Demirer and Deniz [26], and [27] . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.3 Comparison the impact of specimen angle relative to MFD on ten- sile properties from the tests performed by Holmstrom et. al. [15], Mortazavian and Fatemi [30], Monte et. al. [31], and Appelsved [32]. 34 3.1 Material model attributes of the three evaluated materials [34]. . . . . 38 4.1 Test results from tensile tests of PA6 GF30 specimen at different angles. 43 6.1 Description of the sequence when using simulation software. . . . . . 62 A.1 Definition of parameters in Mat_24 material card [34]. . . . . . . . . I A.2 Definition of variables in Mat_157 material card [34]. . . . . . . . . . II A.3 Definition of parameters in Mat_215 material card [34]. . . . . . . . . III xv List of Tables xvi 1 Introduction Computer Aided Engineering (CAE) is a tool widely used in the industry to improve productivity and lower the cost of development of new products. By using advanced computational software for Finite Element Analysis (FEA), it is possible to foresee the strengths and weaknesses of products before physical testing of them. However, as the development of materials moves on and they become more advanced it gets more difficult to capture the characteristics of them. If a correct material model is used in the FEM analysis, the risk of discovering costly problems in the end of the development process will be minimized. This Master’s thesis will investigate how the anisotropic behaviour and process-induced weaknesses can be predicted and included in the material models for CAE. 1.1 The Company - Thule Thule was founded in 1942 in Hillerstorp, Småland, where the development and test center is located today. Thule has around 2300 employees around the world. The main focus of Thule is to provide products making it easy for the customers to bring whatever equipment is needed on an adventurous trip. Included in the range of products are bike racks, roof cargo carriers, strollers, backpacks and much more. 1.2 Problem Description At the global development centre of Thule Group in Hillerstorp Sweden, all the major product categories of the Thule brand are developed and tested. Due to high demands on the structural integrity of the products, simulations are a vital tool that is used throughout the development process. The accuracy of the FEA is highly dependent on the accuracy of the material models used in the simulations. For critical components, it is vital to be able to consider the anisotropic behaviour and process-induced weaknesses early in the product development process. Current material models used in the simulations of injection molded components in short glass fiber reinforced polymers at Thule consider the material to be homoge- neous and isotropic without any defects. Nevertheless, defects induced during the injection molding process are not uncommon and should be considered along with 1 1. Introduction the anisotropic behaviour caused by the reinforcement to obtain a more accurate result in the FEA. 1.3 Purpose and Goals The purpose of this master’s thesis is to investigate how the anisotropic behaviour and process-induced defects from injection molding of Polyamide 6 with reinforce- ment of 30 wt% short glass fibers (PA6 GF30) can be predicted and included in the material models for CAE. This will be done through the answering of the following questions. • What are the defects occurring during the injection molding process (especially when using PA6 GF30 as material)? • What impact do anisotropy and process-induced weaknesses have on material properties? • How can anisotropy and process-induced weaknesses be included in material models used for FEA? Material testing of PA6 GF30 will be performed to capture the anisotropic behaviour of the material. Furthermore, a case study will be performed on the Thule OutWay Hanging bike rack seen in figure 1.1. The two red circles in the figure shows two load bearing consoles produced in PA6 GF30 which is the investigated component. The case study will include component testing, mould fill simulation in Moldex3D, and implementation of material models Mat_157 and Mat_215, which consider fibre orientation, for structural FEA in LS-DYNA. Figure 1.1: Thule OutWay Hanging bike rack. 2 1. Introduction 1.4 Delimitation • FEA and MFS will be carried out by personnel at Thule. • The influences on the mechanical properties will be limited to weld lines, air traps and fibre direction. • The adaption of production parameters of injection molding to minimize cer- tain defects and obtain wanted fibre direction will not be investigated. 1.5 Ethics and Social Aspects There are two main aspects to consider regarding ethics and sustainability in this master thesis. The first one is the environmental impact that is caused by the materials used in the products investigated. Are there better alternatives to lower the environmental impact? Since this is not part of the thesis this should not be given much thought. The second, and more important aspect regarding ethics is that the part which will be investigated in the case study is a load bearing part. If this part would break during use, there is a high risk that there would be an accident. Therefore it is of high importance that the material properties and design is chosen correctly. 3 1. Introduction 4 2 Polymer Materials Polymer materials are usually divided into thermoplastics and thermosets. When a thermoplastic polymer is heated, it melt into a highly viscous liquid and solidifies when cooled again. This process can be repeated multiple times without a dramatic impact on the properties. In contrary, when a thermoset is heated or mixed with a curing agent, it flows like viscous fluid before chemical cross-linking of the molecules occur. This causes the material to solidify into an infusible mass. Thermoplastics polymers cover around 80 % of the market and are the type that will be investigated further in this master’s thesis [1]. 2.1 Molecules and Microstructures Polymers are made up of several smaller units called monomers connected with covalent bonds to form a long single molecule. The majority of all thermoplastic polymers have a carbon chain structure, often with side groups of hydrogen and other organic elements. These polymers are known as hydrocarbon polymers. The simplest variant is called Polyethylene which has a chain of two hydrogen atoms connected to a carbon atom seen in figure 2.1. Figure 2.1: Molecular structure of polyethylene. φ1 and φ2 are the small end groups that do not impact the properties significantly and the n is the number of ethylene monomers the molecule is built from, usually in the order of 104. Polymers are formed in a process called polymerization. There are multiple methods of polymerization, but the resulting polymers fall into two different categories, ad- dition polymers or condensation polymers. Addition polymers are formed through the addition of unsaturated monomers to the end of the growing molecule chain. At the growing end, there is an unpaired electron that attracts the loose monomer. The monomer is attached and the unpaired electron moves to the new end. This process continues until a chain termination reaction occurs which forms a stable 5 2. Polymer Materials φ2 end group. Condensation polymers are formed through the combination of two often more complex molecules which leaves a residue of a small molecule besides the desired one. This also continues to form a long molecule until the process is stopped [1]. The general idea is that the molecule formed in the polymerization is a long contin- uous formation. In this case, it is said to be linear. However, it is possible that the chain backbites during polymerization to form a side-branched polymer. Another formation of polymers is called cross-linked polymers. Instead of having a long chain, the monomers in this type connects to multiple other monomers to form a web-like pattern [1]. What type of polymer is formed depends on the process parameters such as monomer type, temperature, pressure, etc. An illustration of the different formations can be seen in figure 2.2. Figure 2.2: Illustration of Linear, Branched, and Cross-linked polymer [1]. If the polymer is composed of two or more different monomers, it is called a copoly- mer. There are many types of copolymers, such as random, block or graft polymer depending on the order of the different monomers. Generally, the formation of the monomers is random, but when put in order in a linear sequence they are called block copolymer and when one monomer are put in branches it is called graft copolymer. The three types of copolymers are illustrated in figure 2.3. Figure 2.3: Illustration of Random, Block, and Graft copolymer [1]. When the polymers are formed and the temperature is lowered below the melt tem- perature the melt will start to solidify and form either a crystalline or an amorphous solid. The molecules in an amorphous polymer have a random conformation and are 6 2. Polymer Materials considered to have no long-range order. Interesting amorphous polymers are consid- ered to be either glasses or elastomers. For a crystalline material, the solidification is known as crystallization which is initiated at nuclei in the melt. Spherulites start to form where the polymer chains fall into an ordered structure. However, between the crystals, amorphous regions are formed which makes crystalline materials also known as semi-crystalline. The proportion of the solid which is crystalline is known as its crystallinity. The bonds between the polymer chains differs a lot between different polymers. In the amorphous state, the chains can be both chemically cross-linked with covalent or valence bonds or physically through entanglement or being pinned by crystals. In a crystalline state, the chains are bonded together through weaker van der Waals or hydrogen bonds. 2.2 Properties of Polymers Several properties have to be understood when using polymer material for a compo- nent. Using an inappropriate polymer in bad conditions can cause drastic failures. 2.2.1 Temperature Dependency The properties of thermoplastics are strongly temperature dependent. Depending on if the material is semi-crystalline or amorphous the behaviour differs slightly. There are two temperatures where the behaviour of a polymer material shift drastically, melt temperature Tm and glass transition temperature Tg. The Tg is usually within a span of temperature where the amorphous parts of the material change behaviour. Below the Tg it is in the hard and brittle glassy state. The polymer chains are locked in position by strong bonds which result in high stiffness. When the temperature increases above the Tg the bonds between the chains decreases in strength which makes it possible for them to move relative to one another at applied stress. This is represented by a drop in stiffness. The stiffness relative to the temperature of an amorphous and semi-crystalline material can be seen in figure 2.4. Figure 2.4: Young’s modulus versus temperature of an amorphous and a semi- crystalline polymer. 7 2. Polymer Materials When the temperature reaches Tm the behaviour differs as well. A chemically cross- linked amorphous material will burn, unlike a semi-crystalline material which will melt. 2.2.2 Viscoelasticity Thermoplastic polymers generally exhibit viscoelastic behaviour meaning that when a force is applied to it, both elastic, plastic and viscous deformation occurs. This behaviour is linked to the movement of the polymer chains relative to each other at an applied load. The viscoelastic response of thermoplastic, when subjected to stress, is caught by two tendencies, creep and stress relaxation. Creep is what happens when a thermoplastic is subjected to constant stress, but the strain increases with time, which is visualized in figure 2.5. Even if the stress is below the yielding point of the material, plastic deformation occurs due to molecular rearrangement. Figure 2.5: Creep visualized as increasing strain at constant stress. In contrast to creep, stress relaxation occurs when a thermoplastic is subjected to stress to keep the strain constant. Due to the same molecular rearrangement as in creep, the stress to keep the strain is decreasing with time. This is visualized in figure 2.6. Creep and stress relaxation increases with temperature. Figure 2.6: Stress relaxation visualized as decreasing stress at constant strain. Another important factor considering the viscoelastic behaviour of thermoplastics is the reaction to dynamic loading. If a sinusoidal oscillatory strain is applied the stress response of the material will be phase shifted, trailing slightly behind the strain level. This can be described as mechanical damping and is useful to lower vibrations from natural frequencies in construction, in comparison to metals which has non or very low damping effects [1]. 2.2.3 Yielding and Fracture Deformation in polymers differs a lot from metallic materials where plastic deforma- tion is a consequence of dislocation movement. Instead, the deformation in thermo- 8 2. Polymer Materials plastics is explained by the movement of the molecule chains, such as chain stretch, rotation, slide, and disentanglement [2]. Two typical tensile test curves of a brittle Polystyrene (PS) and a ductile Polyethylene (PE) polymer is shown in figure 2.7. How the material behaves depends on its resistance to yield and to crazing and crack propagation. These mechanisms are affected by surrounding conditions such as temperature, strain rate, type of loading, pressure etc. Figure 2.7: Stress versus strain curve from tensile test of PS and PE at room temperature [1]. A, B, C, and D notes four different stages in the deformation process of the ductile thermoplastic PE. During the elastic deformation in step A, the material is stretched without permanent deformation. When the stress reaches the materials yielding point at step B, significant deformation occurs. First, the molecules start to move relative to each other and later the molecules themselves are straightened. The test bars B and C in figure 2.7 visualizes the behaviour of a neck which occurs at yielding and is extended along with the detangle and extension of the molecules. In step D the molecules are fully extended and the stress increases until a macroscopic fracture occurs. The brittle polymer PS will fracture without significant deviation from the linear- elastic curve. When PS is exposed to high loads crazes are formed from micro-cracks, rendering free surfaces or voids within the material. Craze fibrils are drawn out from the solid part of the polymer until the fracture is reached. The behaviour of thermoplastic polymers is also highly strain rate dependent ac- cording to Eyring’s model of solid flow. When a strain is applied, the rate at which it is applied influences the behaviour of the material. A higher strain rate ε̇n results in both higher modulus and higher yield stress, but lower total strain due to the shorter time for the molecules to rearrange [1]. This is visualized in figure 2.8. 9 2. Polymer Materials Figure 2.8: Stress and strain curves versus time as recorded from tensile test at room temperature. In metals, the transition from elasticity to plastic deformation from applied stress is described by mathematical expressions called yielding criterion. The two most common are known as von Mises and Tresca. The yielding of a material is driven by local shear stress whereas fracture is driven by normal stresses. For the Tresca criteria, yielding starts when the maximum shear stress in the material equals the maximum shear stress the material reaches in a regular tensile test. Similarly, for von Mises criteria, yielding starts when the maximum shear energy in the material equals the maximum shear energy the material reaches in a regular tensile test. These assumptions result in two general forms of equations for the Tresca and von Mises criteria respectively. σmax − σmin = σy (2.1) 1/ √ 2[(σxx − σyy)2 + (σyy − σzz)2 + (σzz − σxx)2 + 6(τ 2 xy − τ 2 yz − τ 2 zx)]1/2 = σy (2.2) This can be visualized as in figure 2.9. Figure 2.9: Tresca and von Mises yield criterion. 10 2. Polymer Materials As seen in figure 2.9, the Tresca criteria has a more conservative estimate and will always be less than or equal to von Mises which on the other hand is said to be more accurate [källa]. One thing that is not included in these criteria is the influenced by the hydrostatic component of the stress state. Unlike metals, where this does not need to be in- cluded, polymers have shown dependency on hydrostatic pressure. The reason for this is the chain arrangement and deformation micromechanisms of polymers [3] in- cluding that it suppresses crazing [1]. Donato and Bianchi [3] have investigated this phenomenon and using one conic and one parabolic modification of the von Mises yield criterion with the introduction of a variable m to account for the unevenness in the tensile and compressive yield strength. The shift towards the negative quadrant seen in figure 2.10 (a) indicates higher yield strength in compressive stress, which is confirmed by results from a tensile and compressive test of PA6 seen in figure 2.10 (b). Figure 2.10: (a) Parabolic prediction of von Mises yield criterian at m = 1.30 toghether with experimental results of PVC, PC, PS, and PMMA, and (b) tension and compression test of PA6 [3]. 2.3 Fiber Reinforced Polymers Most polymers have a lower density than metals, and strength and stiffness are often not enough for structural load bearing components. By adding reinforcement to a polymer matrix, a light and strong composite material can be obtained. Various types of matrices and reinforcement can be combined to form a composite with the wanted mechanical properties while still preserve the desirable qualities of polymer materials. The general idea of a fibre reinforced composite is for the polymer matrix to keep the fibres in place and transfer the load between the much stronger and stiffer fibres [1]. In figure 2.11 (a) a polymer matrix reinforced with a single short fibre with length l and diameter d is shown. Figure 2.11 (b) and (c) shows the behaviour of the reinforced matrix and a non reinforced polymer when subjected to a tensile load. The fibre in (b) is stiffer than the matrix causing it to deform less which reduces 11 2. Polymer Materials the overall strain in comparison to the unreinforced matrix in (c). The strain is visualized by the horizontal lines. Figure 2.11: A polymer matrix: (a) reinforced with short fibre in undeformed and (b) deformed state, and (c) an unreinforced matrix in deformed state [1]. When adding a sufficient amount of reinforcement the properties of a material changes a lot. As an example, figure 2.12 shows the difference in tensile strength be- tween plain Polyamide 6 (PA6), PA6 reinforced with 5 % montmorillonite platelets (PA6/MMT5), and PA6 reinforced with 25 wt% short glass fibres (PA6/GF25). Figure 2.12: Comparison of tensile strength of PA6, PA6/MMT5, and PA6/GF25 [4]. The mechanical performance of short fibre reinforced polymers is affected by several factors. These include fibre and matrix properties, interface characteristics, fibre length distribution, fibre orientation distribution and fibre volume fraction [5], which will be discussed further in the following section. 2.3.1 Reinforcement Materials As mentioned, there are several types of reinforcement materials, including particles, flakes, whiskers, short fibres, continuous fibers and sheets, where the last three mentioned are most common in combination with a polymer matrix [6]. Concerning 12 2. Polymer Materials fibres, there are many natural, such as cotton, jute, hemp, sisal and ramie. However, industrial fibers with higher strength and stiffness have been developed for high demand applications. This includes glass fibres, carbon fibres, aramid fibres and other polymeric fibres. The properties of some fibres are shown in table 2.1. Table 2.1: Density, Elongation, Tensile strength and Young’s modulus of some fibre materials [7] [1]. Fibre Density Elongation Tensile Strength Young’s Modulus (g/cm3) (%) (MPa) (GPa) Carbon 1.66-2.25 2500-4500 230-340 Aramid 1.4 3.3–3.7 3000–3150 63–67 Glass 2.5 2.5–3 2000–4570 70-86 Cotton 1.5–1.6 3–10 287–597 5.5–12.6 Hemp 1.48 1.6 550–900 70 Jute 1.3–1.46 1.5–1.8 393–800 10–30 Ramie 1.5 2–3.8 220–938 44 Sisal 1.33–1.5 2–14 400–700 9–38 Glass fibres are further divided depending on the chemical composition and specific usage. Most glass fibres are silica-based with around 60 wt.% SiO2, in a combination of other oxides from aluminium, calcium, magnesium, sodium, potassium, and boron for example. Three common glass fibres are E glass, C glass and S glass, named after their specific characteristics. E glass is a good electrical insulator, C glass has good corrosion resistance and S contains a lot of silica which make it withstand high temperatures. E glass also has relatively high strength and stiffness making it the most used glass fibre [6]. One conventional way of producing E glass is to put the wanted mix of raw materials in a hopper where it is melted. The molten glass is fed into bushings or crucibles each containing about 200 wholes which the molten glass flow through to form continuous filaments. The filaments are gathered into a strand which is wound on a drum [6]. 2.3.2 Polymer Matrix Materials Polymer matrices can be divided into the two categories mentioned in the previous chapter, thermoset and thermoplastic. Thermoset resins are often used together with sheet laminates and long fibres for small batches using production methods such as hand lay-up, bag moulding, pultrusion or filament winding [6]. This can include the production of boat hulls, kayaks, rods, wind turbine blades and other components of similar shape. On the other hand, thermoplastic matrices are more often used in various moulding techniques, especially injection moulding usually using short fibre reinforcement for larger batches. Some common thermoplastics used as a matrix in composites are Polyamide (PA), Polypropylene (PP), Polyethylene (PE), Polyethylene terephthalate (PET), Poly- lactic acid (PLA), Polyurethane (PU), Polyethersulfone (PES), Polycaprolactone (PCL) [7][1]. 13 2. Polymer Materials 2.3.3 Fibre/Matrix Interface When designing composite materials it is important to consider not only the rein- forcement and matrix material individually but also the interaction between their surfaces. This is called the interface. Even if the reinforcement is usually very small in dimensions the high content results in a large internal surface area which means that the properties of the interface region are extremely important. The two most important factors to consider in fibre reinforced polymers are wettability and the type of bonding. Furthermore, it is also important to consider the impact of factors such as temperature, diffusion, residual stresses, and so on. Wettability is described as the ability of a liquid to spread on a solid surface. Usually described by a drop placed on a solid surface where the contact angle is measured, or calculated from specific surface energies. This concept assumes a perfectly smooth surface of the solid which of course is not true in practice. The interface between fibre and matrix is rather rough which means that the matrix must have a good wettability to form an intimate contact. However, good wettability does not necessarily result in a strong bond at the interface. Bonding at the interface can be classified as mechanical, physical or chemical. Me- chanical bonding can be described as keying or interlocking generating friction be- tween the two surfaces. Physical bonding includes week, secondary and van der Waals forces, dipolar interactions and hydrogen bonding. Chemical bonding is achieved when there is a diffusion process of atomic or molecular transport oc- curring. This can include the formation of a solid solution resulting in a thickness of the interface region. To achieve a good interface in glass fiber reinforced polymers (GFRP), the fibres are the first surface treated with a so called size after production to protect them from inducing surface defects. Before the fibres are combined with the polymer matrix, the size is removed and a coupling agent is added to enhance bonding at the interface. Usually, an organosilane compound is used which includes a silicon base with one side group compatible with the matrix and another compatible with the fibre [6]. This has been described as a chemical bridge and can be visualized as in figure 2.13, where R is the matrix compatible group and M is the fibre compatible group. Figure 2.13: Chemical bridge between matrix and fibre using organosilane coupling agent [6]. 14 2. Polymer Materials This chemical generates a strong bond at the interface. However, if the interface is too strong it will generate a material with low toughness due to the initiation of cracks at the interface region. In contrary, a week interface will behave like a fibre bundle relying only on inter-fibre friction resulting in lower strength. An optimum interface will generate a both strong and tough composite with multiple failure sites spread over the whole interfacial area. 2.3.4 Micro-mechanics of GFRP The micro-mechanical approach of composites includes the analysis of the con- stituents individually. Hence, there has to be a knowledge about the geometrical arrangement of the fibres. Generally, the properties of a fibre reinforced polymer can be described by the rule of mixture, first described by Voigt. This combines the properties of the matrix (the viscoelasticity is neglected) and the reinforcement in an isostrain or action-in-parallel situation. Pc = fPf + (1− f)Pm (2.3) P is the investigated property of the composite (c), the fibre (f), and the matrix (m), and f is the volume fraction of fibres. Note that fibre fraction often is measured in weight as well. The rule of mixture generally works for properties such as Young’s modulus, Tensile strength, density and so on. This assumes a matrix reinforced with uniaxially aligned continuous fibres which are perfectly adhered to the matrix and having the same Poisson’s ratio, causing them to undergo the same elongation. For loads in the transverse direction, there is a situation called isostress or action-in series instead, where a similar model developed by Reuss (1929) is used [6]. 1/(Pc) = f/(Pf ) + (1− f)/(Pm) (2.4) The longitudinal (E1) and transverse (E2) Young’s modulus of a composite can then be plotted against the volume fraction of fibres according to figure 2.14. Figure 2.14: Young’s modulus of a glass-fibre reinforced polymer predicted by rule of mixture [1]. 15 2. Polymer Materials As seen, E1 is mainly dependent och the fibre modulus and the polymer matrix mainly works as a glue to keep the fibres together whereas E2 is mainly dependent on the polymer matrix. This type of composite is known as unidirectional, which is good when the load needs to be carried in only one direction. Commonly, multiple layers of unidirectional fibre composites at different angles are used to get a stiffer and stronger material in multiple directions, but due to manufacturing factors, this is not always possible. Therefore short fibre reinforced polymers are often used, but then a modified rule of mixture needs to be used [5]. Pc = XfPf + (1− f)Pm (2.5) X is a coefficient including factors such as the fibre aspect ratio, fibre orientation, and fibre-matrix adhesion depending on which property is included [5]. The fibre aspect ratio (AR) is simply AR = l/d (2.6) l is the fibre length and d is the fibre diameter. The fibre length in a short fibre reinforced polymer (SFRP) is highly dependent on the production method. In the process of injection moulding, the fibres will break due to shear stresses exerted by the screw. This will cause a distribution of fibre lengths depending on the process parameters and matrix viscosity. The injection moulding process will be further discussed later. There is a critical aspect ratio where the critical fibre length lc notes the length of a fibre where it no longer can carry full load. Similarly, the fibre orientation distribution is highly dependent on the processing parameters, but also mould geometries. When a large mould is filled, the fibres tend to orient themselves creating a skin-core-skin structure [5]. As seen in figure 2.15 the fibres in the core layer are mainly oriented transverse to the melt flow direction (MFD), whereas the fibres in the skin layers are mainly oriented along the MFD. On the contrary, in a thin specimen, the fibres will mainly be aligned along the MFD [5]. Figure 2.15: Microscopic image of the skin-core-skin structure. The white arrow denotes the MFD [5]. The recently mentioned rules of mixtures do not really capture the complexity of fibre reinforced materials. Therefore the mechanical behaviour of composites has 16 2. Polymer Materials been described further. The state of stress and strain can be described by six inde- pendent components. These include three tensile and three shear components. To describe the stress and strain relation of an anisotropic body with no symmetry, 21 independent elastic components is required. On the contrary, an elastically isotropic body only need two independent elastic constants [6]. It can be understood that the symmetry of the material determines the number of elastic constants needed for a material. However, there are more accurate ways of obtaining these constants including the consideration of the inevitable scatter of fibre distribution. If there the fibres are short and aligned in the loading direction, there are numerical equations, called Halpin-Tsai equations, that can be used to predict the elastic constants [6]. A general form of the equations are p/pc = (1 + ξηVf )/(1− ηVf ) (2.7) where η = (pf/pm − 1)/(pf/pm + ξ) (2.8) p represent one of the investigated moduli, pf and pm are the corresponding moduli of the fibre and matrix, Vf is the volume fraction of fibres, and ξ is a measure of the reinforcement that depends on fibre geometry, fibre distribution, and loading conditions. Mori and Tanaka developed a method known as the Mori-Tanaka model to determine the effective stiffness of composite materials [8]. A simplified derivation of the model can be described as C̄ = Cm + Vf [Cf − Cm]B (2.9) B = T (VmI + VfT )−1 (2.10) T = [I − PCm−1(Cm − Cf )]−1 (2.11) C̄ is the effective stiffness tensor of the composite, Cm and Cf is the related stiffness tensors of the matrix and the fibre. B is the strain concentration tensor that relates the homogenized strain in the fibre to strain due to remote stress. T relates the elastic properties of the fibre and the matrix according to Eshelby inclusion model, where P is Eshelby’s tensor which relates eigenstrain with strain [8]. The final form of the Mori-Tanaka model-based homogenized elastic tensor C̄ can then be presented as C̄ = Cm + Vf [Cf − Cm][I − PCm−1(Cm − Cf )]−1(VmI + VfT )−1 (2.12) 17 2. Polymer Materials Eshelby’s inclusion model is based on an ellipsoidal inclusion in an infinite matrix visualized in figure 2.16. This model is as mentioned used to calculate the stress and strain fields around the inclusion [5]. Figure 2.16: Visualization of Eshelby’s inclusion model. 2.3.5 Macro-mechanics of GFRP As mentioned in the previous section composites are often laminates bonded together and oriented such as mechanical and physical properties are different in different directions, known as an anisotropic material. For a macro-mechanical analysis of a composite lamina, information from the micro-mechanical analysis is used as input. When this is done, it is possible to treat the material as homogeneous, orthotropic sheets. It is then possible to use the well-established theory of laminated plates to analyze the composite [6]. This is to some extent also valid for SFRP since they can be simulated as various laminates with different fibre angle orientations [5]. When a cube is exposed to a load, the stresses in the cube can be described three normal and six shear components, σij (where i, j=1, 2, 3), acting on the faces of the cube. This stress cube is visualized in figure 2.17. The subscript i refers to the outward direction normal to the face at which the stress acts, and j refers to which direction the stress acts. Figure 2.17: A three dimensional cube with stress components when exposed to a normal force. 18 2. Polymer Materials Each stress component has a corresponding strain εij which together with a stiffness forms the generalised Hooke’s law for anisotropic materials. σij = Cijklεkl i, j, k, l = 1, 2, 3 (2.13) σij is the stress tensor, εkl the strain tensor, and Cijkl is the stiffness tensor. This equation represents nine equations where the stiffness tensor has 9x9 elements.  σ11 σ22 σ33 σ23 σ31 σ12 σ32 σ13 σ21  =  C1111 C1122 C1133 C1123 C1131 C1112 C1132 C1113 C1121 C2211 C2222 C2233 C2223 C2231 C2212 C2232 C2213 C2221 C3311 C3322 C3333 C3323 C3331 C3312 C3332 C3313 C3321 C2111 C2122 C2133 C2123 C2131 C2112 C2132 C2113 C2121   ε11 ε22 ε33 ε23 ε31 ε12 ε32 ε13 ε21  (2.14) Note that the shear stresses and strains (i 6= j) often are written as τij and γij. A contracted notation can be used to reduce the number of subscripts. Thus, the stress-strain relationship can be written as. σi = Cijεj i, j = 1, 2, 3..., 6 (2.15) with the following matrix notation.  σ1 σ2 σ3 σ4 σ5 σ6  =  C11 C12 C13 C14 C15 C16 C22 C23 C24 C25 C26 C33 C34 C35 C36 C44 C45 C46 C55 C56 C66   ε1 ε2 ε3 ε4 ε5 ε6  (2.16) By doing this the stiffness constants can be reduced from 81 to 36 elastic constant. Furthermore, the symmetry along the diagonal results in the 21 independent elastic constants mentioned in the previous section about micro-mechanics. Usually, a converse notation is used including a compliance matrix Sij, which is the inverse of the stiffness matrix. εi = Sijσj (2.17) 19 2. Polymer Materials For most materials, the elastic constants can be reduced further through the con- sideration of symmetry. As mentioned, a fully isotropic material where the elastic properties are independent of direction, only C11 and C12 are independent. This is because Young’s modulus E, Poisson’s ratio v, shear modulus G, and bulk modulus K are all interrelated. E = 2G(1 + v) and K = E/(3(1− 2v) (2.18) This results in the following equation using the compliance matrix.  ε1 ε2 ε3 ε4 ε5 ε6  =  S11 S12 S12 0 0 0 S11 S12 0 0 0 S11 0 0 0 2(S11 − S12) 0 0 2(S11 − S12) 0 2(S11 − S12)   σ1 σ2 σ3 σ4 σ5 σ6  (2.19) Looking at a laminated composite the situation is different. Here a plane stress condition is assumed, causing the through-thickness stress components to be zero. This results in a reduced class of anisotropy called orthotrophy. Due to the symme- try, the number of elastic constants is reduced in comparison to a fully anisotropic material. Hence, for an orthotropic material, the compliance matrix is written as. [ Sij ] =  S11 S12 S13 0 0 0 S22 S23 0 0 0 S33 0 0 0 S44 0 0 S55 0 S66  (2.20) For example, the elastic constants of a 50 wt% carbon fibre reinforced epoxy vary with the fibre directions according to figure 2.18. Figure 2.18: Variation of elastic constants (a) Young’s modulus, (b) Shear modu- lus, and (c) Poisson’s ratio depending on fibre orientation in a 50 wt% carbon fibre reinforced epoxy . 20 2. Polymer Materials 2.3.6 Strength and Fracture of GFRP Similarly to the elastic properties of fibre reinforced composites, the strength can be described in multiple ways. When the ultimate stress is reached in a unidirectional lamina, there are typically three ways in which the failure occurs. Those are by axial tensile stress, transverse tensile stress, and shear stress, illustrated in figure 2.19. Figure 2.19: Illustration of failure from (a) axial tensile stress σ1u, (b) transverse tensile stress σ2u, and (c) shear stress τ12u [9]. Furthermore, for axial tensile failure, several modes are describing how failure occurs, mainly depending on the loading conditions, fibre and matrix, and the interface between them. For a fibre reinforced polymer, the matrix material usually has a higher strain at fracture than the fibre [6]. If the following condition is met, the composite will show a single fracture since the matrix will not be able to carry additional load as the fibres are breaking. σfuVf > σmuVm − σ′mVm (2.21) σ′m is the matrix stress corresponding to the fibre fracture strain and σfu and σmu are the ultimate tensile stresses of the fibre and the matrix respectively. Vf and Vm is the fibre and matrix volume fraction respectively. If the following condition is met instead, the fibres will break in multiple places until the matrix fractures. σfuVf < σmuVm − σ′mVm (2.22) These conditions are plotted in figure 2.20 which shows the strength versus the volume fraction of fibres. Left of the cross-over point, single fracture occurs whereas multiple fractures occurs on to right. 21 2. Polymer Materials Figure 2.20: Strength of a composite versus the fibre volume fraction of a com- posite with fibres having lower fracture strain than the matrix [6]. The modes at which the fracture of a fibre reinforced polymer occurs are commonly observed to be debonding of the fibre/matrix interface, fibre pullout and delamina- tion fracture. Generally, some fibre pullout occurs at fracture, which will produce shear stresses parallel to the fibres, increasing the toughness. However, to obtain maximum tensile strength, it is wanted that the fibre break rather than being pulled out from the matrix. Figure 2.21 shows a visualisation of fibre pull out and debond- ing at a crack. Figure 2.21: Fibre pullout and debonding at a crack [6]. To further describe the strength of a short fibre reinforced composite, there is a model called the shear lag model developed by Cox. It describes the stress transformation in a composite with straight and aligned fibres. The model assumes that the tensile 22 2. Polymer Materials stress at the fibre ends is small, less or equal to the matrix stress, hence no stress is transferred at the ends. If the matrix has a linearly elastic (a) or elastic-plastic (b) behaviour has some impact on the final properties as seen in figure 2.22 [5]. Figure 2.22: Tensile (σF ) and shear stress (τ) distribution along the length (l) and critical length (lc) of a short fibre in an (a) linearly elastic and an (b) elastic-plastic matrix [5]. For the ideal case with elastic components and bonded interface, it is assumed that no stress is transferred at the end of the fibres, but close to the end, there will be small stresses. Since the fibres are stiffer than the matrix there are deviations in the mean displacement and shear stresses along the interface are built up. The load is transferred to the fibre until the stress corresponding to a continuous fibre composite is reached. For an elastic-plastic matrix, the fibre stress is determined by the constant shear stress of the matrix in the plastic state. For both cases, the fibres are not fully loaded which lowers the reinforcement efficiency compared to continuous fibre reinforcement. As mentioned before, the critical fibre length (lc) is important when looking at the fibre length effects [5]. The prediction of the stress in the fibre (σf ) along the fibre length x is described by Cox according to the following equation [1]. σf = Efεf { 1− [ cosh(na2x l ) cosh(na) ]} (2.23) Ef is the Young’s modulus of the fibre, a is the fibre aspect ratio, l is the fibre length, and n is a dimensionless constant determined by the following equation [1]. n = √√√√[ 2Gm Ef ln(2R/d) ] (2.24) Gm is the shear modulus of the matrix, 2R is the distance from the fibre to its nearest neighbour, and d is the fibre diameter. The shear stress at the interface (τi) is obtained by differentiating equation 2.25. τi = n 2Efε1 sinh(na2x l ) cosh(na) (2.25) 23 2. Polymer Materials By inspecting the cox equation it can be concluded that the aspect ratio along with n has a high impact on the stresses of the fibre and the interface. To describe the failure of fibre reinforced composites under multiaxial in-plane load- ing, several strength (or failure) criterion have been proposed. Some of the most used are the maximum stress criterion, the maximum strain criterion, the maximum work (or the Tsai-Hill) criterion, and the quadratic interaction (or the Tsai-Wu) criterion [6][9][10]. The maximum stress criteria simply postulate that failure will occur when the stress in the material exceeds the corresponding ultimate strength. This includes the ultimate tensile and compression strength in the fibre direction and transverse to the fibre direction along with the ultimate shear stress [6][9][10]. Equations for each failure can be obtained. For tensile loading, these look like σxu = σ1u/ cos2 Φ (2.26) σxu = σ1u/ sin2 Φ (2.27) σxu = −τ12u/ cos Φ sin Φ (2.28) σxu is the failure stress, σ1u, σ2u, and τ12u is the ultimate strength in longitudinal, transverse and shear direction, and Φ is the angle of which the stress is applied relative to the fibre direction. For a lamina with 50% glass fibre, the prediction of failure according to these equations can be plotted as in figure 2.23 [9]. Figure 2.23: Prediction of failure of a lamina with 50 % GF according to maximum stress criteria [9]. 24 2. Polymer Materials The maximum strain criterion similarly postulates that failure occurs when the strain exceeds the corresponding ultimate strain. Both maximum stress and strain criterion are not satisfactory since they do not include any interaction of failure modes [9]. The Tsai-Hill criterion origins from Hill’s yield criterion which in turn origins from the von Mises criterion. Hill’s yield criterion is a generalization of von Mises used for orthotropic materials and described by the following equation [11]. f = F (σ22 − σ33)2+G(σ33 − σ11)2 + (σ11 − σ22)2 + L(σ2 23 + σ2 32) +M(σ2 13 + σ2 31) +N(σ2 12 + σ2 21)− 1 (2.29) F , G, H, L, M , and N are constants obtained by material testing in different orientations and derived by the following equations. F = 1 2( 1 R2 22 + 1 R2 33 − 1 R2 11 ) (2.30) G = 1 2( 1 R2 33 + 1 R2 11 − 1 R2 22 ) (2.31) H = 1 2( 1 R2 11 + 1 R2 22 − 1 R2 33 ) (2.32) L = 3 2R2 23 (2.33) M = 3 2R2 13 (2.34) N = 3 2R2 31 (2.35) Rij is the anisotropic ratios described by the following general equation. Rij = σy,ij σy,ref (2.36) σy,ij is the yield strength in the corresponding test direction and σy,ref is the yield stress in the reference direction, 11 [11]. The Tsai-Hill is instead used when behaviour is different in tension and compression and postulates that failure occurs when the distortion strain energy is exceeded. 25 2. Polymer Materials This is described as the following equation for a transversely isotropic orthotropic material [6][9][10]. (σ1/σ1u)2 + (σ2/σ2u)2 − σ1σ2/σ 2 1u + (τ12/τ12u)2 = 1 (2.37) Compared to the previous two criteria, the Tsai-Hill criterion considers the inter- action between failure modes. However, there is no distinction between tensile and compressive stress which is of importance as already discussed. To take the ten- sile and compressive stress into account, modifications have been done to form the Tsai-Wu criterion [6][9][10]. F1σ1 + F2σ2 + F11σ 2 1 + F22σ 2 2 + F66σ 2 6 + 2F12σ1σ2 = 1 (2.38) All F ar strength parameters, where F1 and F11 are determined by longitudinal tensile and compressive tests, F2 and F22 determined by transverse tensile and com- pressive tests, F66 is determined by longitudinal shear tests, and F12 is a determined by biaxial testing. Figure 2.24 shows a comparison of the four described criteria [10]. Figure 2.24: Comparison of the four described failure criteria [10]. 2.4 Polyamide 6 GF30 Polyamide (PA) is family of polymers including an amide group built from the com- bination of Oxygen (O) and Nitrogen (N) together with carbon and hydrogen atoms. Due to its excellent properties, Polyamide is one of the most widely used polymers in engineering where it is more commonly known as Nylon [1]. There are various kinds of Polyamides which are depending on the shape and length of the repeating unit, the monomer. Aliphatic Polyamides have a linear configuration, hence they are semi-crystalline. Polyamide 66 (PA66) was the first one to be developed and used in 1938 as a fibre. Polyamide 6 (PA 6) were introduced in 1946 and is produced through ring-opening of Caprolactam [12]. This reaction is presented in figure 2.25. 26 2. Polymer Materials Figure 2.25: Ring opening of Caprolactam to form PA 6. Other commonly used polyamides are PA11, PA12, PA46, PA69, PA610, and PA612 [1][12]. Some of the wanted properties of Polyamides are their fast crystalliza- tion, chemical resistance, toughness, lubricity, fatigue resistance, and mechanical strength [12]. However, due to the molecular formation including CO and NH groups, Polyamides are very prone to absorb water (H2O). The water molecule bond to the polymer through these groups which causes the material properties to change. Test have shown that the PA6 absorbed 2.7 and 9.5 % water in weight when exposed to 50 and 100 % relative humidity (RH) respectively [1]. Figure 2.26 visualize how the water molecules interact with the PA 66 polymer. Figure 2.26: Interaction between water molecules and a PA 66. To increase the mechanical properties of PA 6 it is common to reinforce it with glass fibre. This increases the strength and stiffness which makes it a suitable substitution for metals in structural component to lower the weight. Several authors have investigated the effect of water absorption on the mechani- cal properties of Polyamide materials with and without adding of fibre reinforce- ments. Chaichanawong et. al. [13] investigated how water influenced ultimate ten- sile strength, modulus of elasticity, elongation, yield strength, and flexural strength of PA 66 with different content of short glass fibre reinforcement (0 wt%, 10 wt%, 20 wt%, and 30 wt%). Specimens were immersed in distilled water for 0 to 60 days with a subsequent tensile test and measurement of moisture content. The results are presented in figure 2.27 which indicates that the biggest changes in mechanical properties occur during the first 7 days in water. 27 2. Polymer Materials Figure 2.27: Experimental results of (A) moisture content, (B) ultimate tensile strength, (C) modulus of elasticity, (D) elongation, (E) yield strength, and (F) flexural strength versus immersed time in distilled water [13]. Pivdiablyk et. al. [14] had similar foundings in an experiment with PA 6. Specimens with various fibre directions (0°, 45°, and 90 °) where tensile tested in different temperatures after being exposed to 0 %, 50 %, and 85 % RH. The results show degradation in stress with increasing temperature and increasing RH, but increasing elongation. 2.5 Injection Molding of SFRP Injection moulding is one of the most used production method considering thermo- plastic polymers. It has large flexibility in design and it is a perfect solution for mass production due to the rapid processing and low cost at large production volumes [1]. Injection-moulded products can be found in various fields of use, even substituting metal parts. To reach a sufficient strength and stiffness for a structural application, short glass fibres are often added to the polymer blend [15]. A typical injection moulding machine with its main parts are shown in figure 2.28. The injection moulding process can be described in four steps. In the first step, the polymer pellets in the hopper are transferred through the heated barrel by the screw which causes the polymer to melt. In the second step, the screw is pushed forward which increases the pressure so that the melt is injected into the mould cavity through the nozzle and the sprue. In the third step, the pressure is kept to permit packing and continue the melt flow as the melt solidifies and shrinks. After 28 2. Polymer Materials Figure 2.28: Illustration of the injection molding process [16]. sufficient cooling, the mould opens and the part is ejected using the ejector pin in the fourth and last step [17]. Using appropriate parameters in the process is crucial to avoid defects and obtain the wanted fibre orientation. Some of the factors that need to be considered are mould geometry, injection gate positions, injection speed, injection pressure, barrel temperature, mould temperature, mould thickness, holding pressure, notches, sharp corners, melt temperature and fibre content [15][18]. If these factors are considered together with the appropriate part design it is possible to avoid failures in the finished component. For a SFRP, there are mainly two ways of manufacturing the pellet. The conven- tional way is to have the polymer matrix pellets and the short fibres in separate hoppers and mixed in a barrel before extrusion making the fibres randomly aligned into a short fibre pellet (SFP). The other method used is pultrusion where the ma- trix material is melted and infused into continuously unidirectional fibres in a long fibre pellet (LFP). Figure 2.29 illustrates the pellets from the two methods where the length of the pellets are typically 2-4 mm for the conventional method (a) and 10-12mm for the newer method (b) [16]. Figure 2.29: Illustration of (a) a SFP and (b) a LFP [16]. When the pellets are used in the injection moulding process, a severe fibre breakage may occur due to shear stresses caused by the injection screw. The fibre length reduction is around 10 % and 70 % for SFP and LFP respectively, causing a distinct reduction in fibre length distribution [17]. 29 2. Polymer Materials 2.6 Defects in Injection Molding Defects in the injection moulding process are quite common. Depending on the shape of the mould and other parameters such as mould temperature, injection speed, pressure, etc, these defects can largely be prevented. However, it is important to understand what the possible defects are, what causes them to occur, and what impacts they have on the properties of the part. Ten common defects in injection moulding are described. 2.6.1 Flow Lines When the melt is injected into the mould it flows through the cavity until it is filled. The material is cooled continuously and eventually after the cavity is filled, it solidifies. Flow lines occur when the melt flows at varying speed causing the material to change direction, or leaves other visual structures. Others reasons to flow lines can be varying wall thickness or different solidifying speeds due to too low injection speed. 2.6.2 Weld Lines Weld lines are formed when two flow fronts join, causing an inadequate bonding between the fronts. This defect often occurs when the mould is complex and contains multiple gates, inserts and thickness variations [19][20]. Weld lines are visible, hence they have a negative impact on the aesthetics of the part. But the most critical impacts is the lowering of mechanical properties due to three major factors: poor bonding adhesion, frozen-in parallel molecular orientation, and the existence of V- notches [21][22]. Often, weld lines can not be avoided, but having the intended design of the mould can place the weld line at a non-critical area concerning both structural and aesthetic demands [23]. Several investigations of what impact weld lines have on the mechanical properties have been performed. Zhou and Mallick [24] conducted a series of tensile tests with a polyamide (PA) polymer reinforced with 33 wt% short glass-fibre (PA33). The objective was to investigate the effect of fibre orientation and weld line formation on tensile properties. Another study where performed by Ozelik et. al. [25] who investigated the obstacle geometries and injection moulding parameters on weld line strength in tensile and impact test. The material used was plain polypropylene (PP). Demirer and Deniz [26], and Solymossy and Kovacs [27] both performed similar tests using PP30. A comparison of some mechanical properties from the previously mentioned tests is presented in table 2.2. 2.6.3 Vacuum voids Vacuum void or sometimes called air entrapment are small pockets filled with air in the solidified material. There are two main reasons for these occurrences. The first one is due to that bubbles are formed from air, agents, degradation or contamination, and are brought into the mould. Usually, the moulding pressure is pushing the air 30 2. Polymer Materials Table 2.2: Comparison of weld line impact on tensile strength from tests performed by Zhou and Mallick [24], Ozelik et. al. [25], Demirer and Deniz [26], and [27] Article, material E σFmax εult and test [min] [MPa] [MPa] Zhou and Mallick PA33 parallel to MFD 7360 133.8 0.0393 PA33 normal to MFD 4430 86.51 0.0505 PA33 with WL 3800 67.53 0.03 Ozcelik et. al. PP without WL 22.1 0.47 PP with WL 19.7 0.05 Demerier and Deniz PP30 without WL 88.94 PP30 with WL 41.97 Solymossy and Kovacs PP30 without WL 38.3 PP30 with WL 21.3 out, but sometimes the air is trapped and causes the voids [28][20]. The other reason is too big differences in wall thickness. This can either cause some sections to solidify before the whole mould is filled, leaving unfilled voids, or raise the residual stresses, causing the part to cavitate, also leading to the formation of voids[1]. 2.6.4 Surface Delamination Surface delamination is a defect where the top layer of the part material is not sufficiently bonded to the underlying material which makes the surface flaky. This defect is caused by contamination or adding of incompatible materials causing failure in the bonds. Another reason for the defect could be excess of mold coating or moisture due to improper drying [20]. Also, the molecular orientation in the surface has a bi-axial orientation whereas the inner layer has more uniaxially aligned fibres [29]. 2.6.5 Sink Marks Sink marks are indentation on the surface of the part, usually where the part has a major change in thickness. These sink marks occur due to the contraction or shrinkage of the polymer melt during cooling. When the melt solidifies slowly the outer surface material is pulled inwards to create the sink mark. Some of the main reasons for the sink mars to occur are too slow solidification, too short and low holding pressure and time, and inappropriate thickness design [20][28]. 2.6.6 Warping Warping is when a part or sections of a part is bent or twisted after mould release and cooling. This is caused by residual stresses in the material induced by either 31 2. Polymer Materials too quick cooling or to great differences in wall thicknesses [20]. 2.6.7 Jetting Jetting occurs when the injection rate is too high, causing an initial jet of melt into the mould cavity. When this jet touches the mould wall it starts to solidify before the whole cavity has been filled. This leaves a pattern of the jet on the part surface along with the decrease of mechanical properties due to insufficient bonding [20]. 2.6.8 Flash Flash is a protrusion of excess material at the edge of the moulded part. The most common places for this to occur is close to the gate or injector pin or at the line between two mould plates. The reason for it can be due to too high pressure, or that the mould is incorrectly designed or worn [20]. 2.6.9 Short Shots A short shot is what happens when the mould cavity is not completely filled by the melt. The main reason for this to occur is a design fault, where a section of the mould solidifies too fast. Either the material is too viscous, the section too narrow or the mould is too cold, which causes the material to solidify before the whole mould cavity is filled. Another reason can be the excess of air trapped in the mould cavity, preventing it to be filled. 2.7 Anisotropy in Short Glass Fibre Reinforced Thermoplastics The term isotropy can be described as uniformity in all directions, often regarding mechanical properties. A homogeneous material like most metals and some polymers can be considered to be isotropic. However, when filler materials such as glass fibres are added, the material characteristics changes and generally accentuates anisotropy. The fibres in the polymer change properties of the material depending on the fibre direction causing the properties to differ in different directions [15]. Generally, the fibres would be aligned along the melt flow direction (MFD). But at further in- vestigation, it can be seen that the material is reaching a skin-shell-core-shell-skin structure [15]. Through a computed tomography performed by Holstrom et. al. [15] the probability density function of the projected fibre angles was obtained for a Polyamide 6 (PA6) material with adding of 15 wt% (PA6 GF15) and 30 wt% (PA6 GF30) glass-fibre. Results indicate that the degree of fibre alignment in the MFD is high in the surface layers of the material, but decreases rapidly in the core layers [15]. For PA6 GF30, simulation of the skin-core-skin layers (a) and the fibre angle relative to the MFD (b) can be seen in figure 2.30. 32 2. Polymer Materials Figure 2.30: (a) Visual simulation of the skin-core-skin structure together with (b) probability density of the fibre angle (α) from MFD (x) [15]. Holmstrom et. al. [15] also performed a series of tensile tests to investigate the impact of fibre direction on strength, stiffness, fracture strain, and Poisson’s ratio. The experiment included the two previously mentioned materials, PA6 GF15 and PA6 GF30, along with plain PA6. The general fibre direction was determined by the specimen orientation angle to the MFD. For PA6 GF15 and PA6 GF30, tests were performed with the orientation angle at 0°, 15°, 30°, 45°, 60°, 75°, and 90°. For PA6, a test was performed with the orientation angle at 0°, 45°, and 90°. Three tests were performed at each angle for all materials. A summary of the tensile tests is presented in table 2.3. According to the result of Holmstrom et. al. [15], the unreinforced PA6 has an anisotropic material behaviour. This is explained by the fracture of the 0°-specimen before the material was cold drawn, which was not the case for the 45°- and 90°- specimens. A gradual decrease of both Young’s modulus and ultimate tensile strength can be seen in all material with increasing the specimen angle to the MFD. However, the maximum strain differs between the two fibre filled material. For PA6 GF15, the maximum strain increases during the first angle shifts and tend to stagnate after 60°. For PA6 GF30, a peak can be seen at 45°. This is presumed to be due to shear like deformation [15]. Furthermore, Holmstrom et. al. conclude that orthotropic elasticity is a reliable approximation for the investigated fibre-reinforced materials. A similar tensile test was preformed by Mortazavian and Fatemi [30] who inves- tigated anisotropy effect on tensile properties in combination with temperature changes. The material used in this test was a PA6 matrix with adding of 35 wt% glass-fibre and 10 wt% rubber. The orientation angle of the specimens in relation to the MFD in this tests where set to 0°, 45°, and 90°. Results from the tests at room temperature shows that the tensile strength and young’s modulus relative to the 0°specimen experience a drop of about 33 % and 38 % for the 45°specimen and 33 % and 31 % for the 90°specimen respectively. The maximum strain was increased by 175 % for the 45°and 8 % for the 90°specimen. Monte et. al. [31] also performed several tensile tests to investigate the anisotropic behaviour of glass-fibre reinforced PA66. The amount of added reinforcement ma- terial was 35 wt% and the specimen orientation angle to the MFD was set to 0°, 5°, 33 2. Polymer Materials 10°, 20°, 30°, 45°, 60°, and 90°. A summary of the tensile tests is presented in table 2.3. Appelsved [32] has also investigated the anisotropic behaviour of glass-fibre rein- forced PA6/66. This material was conditioned and reinforced with short glass fibre and tensile tested with specimens oriented at 0°, 30°, 60°, and 90°relative to the MFD. A summary of the tensile tests is presented in table 2.3. Table 2.3: Comparison the impact of specimen angle relative to MFD on tensile properties from the tests performed by Holmstrom et. al. [15], Mortazavian and Fatemi [30], Monte et. al. [31], and Appelsved [32]. Material, θ E σFmax εult vin−plane vout−of−plane article and [deg] [MPa] [MPa] [-] [-] [-] specimen thickness PA6 GF30 0 7319 136.2 0.059 0.41 0.39 Holmstrom 15 7006 130.2 0.070 0.41 0.45 3 mm 30 5902 116.7 0.094 0.42 0.41 45 5122 103.1 0.145 0.41 0.42 90 4967 98.3 0.069 0.23 0.53 PA6 GF35 0 7111 130 0.053 Mortazavian 45 4444 87 0.147 3 mm 90 4889 87 0.058 PA66 GF35 0 8555 152 0.023 Monte 10 8417 150 3 mm 20 8056 147 30 7667 142 45 7167 132 0.033 90 7106 118 0.028 PA6/66 GF 0 6000 107 0.051 Appelsved 30 4125 84 0.068 3 mm 60 2963 63 0.075 90 2486 60 0.088 34 3 CAE - Predicting and Preventing in use Failure An important step of the product development process is to verify that the developed component will withstand the loads when it is used which can be done through mechanical testing. However, doing tests on finished products is expensive both since the component often is tested to failure, but also because if the component fails too early, it has to be redesigned. This is not only expensive but also time- consuming. One way to minimize premature failure in mechanical testing of the finished part is to use Computer Aided Engineering (CAE) before the product is manufactured. Using computational software to design and test is a time-efficient and an economical way of developing a new product. The general CAE process includes the design of a 3D CAD model with subsequent Finite Element Analysis (FEA) of the model to determine its structural function. Depending on the material used in the component, different material models are used to decribe the material behaviour. At Thule, there is an interest in considering the fibre direction and some process-induced weaknesses of fibre reinforced polymers in the CAE. To realise this a mould flow analysis has to be done and transferred to the FEA software. FEA, material models, and mould flow analysis are described in the following sections. 3.1 Finite Element Analysis - LS-DYNA FEA is a simulation of a physical component or phenomena using a numerical problem-solving methodology based on the Finite Element Method (FEM). Through the use of a calculating FEA software, it is possible to analyze real-world problems, such as structural analysis, fluid flow, and heat transfer, all in a computer. This is done by breaking down the overall problem into smaller and simpler parts that are easier to solve. These are the finite elements. These small elements are connected through the generation of a mesh that covers the whole body of the problem. For all element in the mesh, a partial differential equation is solved and combined to get an overall result. Hence, a higher density of elements requires more computational power, but the result will usually be more precise. There are two main types of structural FEA, quasi-static and dynamic. Quasi- 35 3. CAE - Predicting and Preventing in use Failure static problems neglect intertial forces whereas problems do. Within these types of FEA, it is possible to have linear or nonlinear problems. When the linear static analysis is used for a structural problem the relationship between the applied force and displacement behaves linearly. The stress remains within the elastic range of the material and the stiffness matrix is constant. This is expressed as the following equation. [K]{u} = {f} (3.1) Where [K] is the stiffness matrix, {u} is the displacement vector and {f} is the load vector. If the problem follows the dynamic rules, the corresponding equation is formulated as. [M ]{u′′(t)}+ [C]{u′(t)}+ [K]{u(t)} = {f(t)} (3.2) The [M ] is the mass matrix, [C] is the damping matrix, {u′′(t)}, {u′(t)}, {u(t)}, and {f(t)} is the time varying acceleration, velocity, displacement, and load vector respectively. If the problem instead is non-linear, there are three attributes of the system that can behave nonlinear, namely geometry, material, and constraints and contacts. This can include changing boundary conditions, large deformations, and material which do not exhibit linearly elastic behaviour. When a nonlinear dynamic FEM is used there are two approaches regarding the time incrementation during solving. In the implicit approach, a global equilibrium has to be established for each time increment, which means each increment has to converge. This makes it possible to have big time increments but this means that the computing time is high. On the contrary, the explicit approach does not have to converge each increment and instead assume global equilibrium exists. For each increment, the local finite elements variables are calculated before continuing with the next one. This calculates each increment very fast, but to maintain the equilibrium and accuracy of the solution, the increments have to be very small. The software that Thule uses for their FEA is called LS-DYNA which has a diverse use within multiple areas in need of FEA. The code that LS-DYNA is built from origins from highly nonlinear, transient dynamic FEA using explicit time integration. The elements in the mesh can take various shapes with different calculating proper- ties depending on what is of interest for a certain simulation. The different elements are described by its element formulation (ELFORM in LS-DYNA). The three most used shapes for solid elements are tetrahedrons, pentahedrons and hexahedrons. Another thing to consider when selecting element is its properties, especially when it comes to integration points and rotational degrees of freedom, and with this, the subsequent CPU time. For this report, there is a specific interest in two element formulations, named ELFORM 4 and ELFORM 13. Both have the shape of a tetra- hedron but the major difference is the number of integration points. ELFORM 36 3. CAE - Predicting and Preventing in use Failure 13 only has one, whereas ELFORM 4 has five. Also, ELFORM 4 has six degrees of freedom per node (three translation and three rotational) whereas ELFORM 13 only has three (translation). This causes ELFORM 13 to be a bit less accurate, but ELFORM 4 to require more CPU time since it is scalable to the amount of integration points [33]. 3.2 Material Models - LS-DYNA For the FEA to work properly, not only the shape and boundary conditions need to be correct, but also the material needs to have the right properties and behave correctly. This is included through a material model that includes all the impor- tant material parameters and properties for the devoted material. To get the right response characteristics of the material, the included parameters must be carefully chosen. Materials such as metals are relatively well documented regarding material prop- erties which makes it relatively easy to. For more complex materials such as com- posites, all properties can not be defined by simple parameters. Therefore, there could be a need of using multiple material models. It could also include the need for physical testing to find the right characteristics and fit them towards a material model. Furthermore, it is also necessary to fit the material model with the right failure criteria and damage model. As mentioned previously, the material models are built from numerous attributes and parameters. There are seven attributes a model can include, which are described as follows [34]. STRATE - Strain-rate effects FAIL - Failure criteria EOS - Equation-of-State required for 3D solids and 2D continuum elements THERMAL - Thermal effects ANISO - Anisotropic/orthotropic DAM - Damage effects TENS - Tension handled differently than compression in some manner Furthermore, the parameters included in each model varies a lot. For each model there is a card including several parameters to capture the material characteristics. The variables include common properties such as Density, Young’s modulus, Yield stress, etc, but also more uncommon or complex properties such as Load Curves, Damping factor, etc. [34]. Failure criteria are described by mathematical expressions. The expression captures the essential behaviour of a material during failure. Some common mathematical failure criteria are Tsai-Wu (brittle fracture), Tsai-Hill (brittle fracture), von Mises (yielding), Tresca (yielding), Chang-Chang, Puck etc. [34]. In this thesis, three material models distributed by LS-DYNA are evaluated and discussed for further implementation. These material models are; Mat_24 (piece- 37 3. CAE - Predicting and Preventing in use Failure wise linear plasticity), Mat_157 (anisotropic elastic-plastic), and Mat_215 (4A mi- cromech). The attributes of these material models are presented in table 3.1. Table 3.1: Material model attributes of the three evaluated materials [34]. Material STRATE FAIL EOS THERMAL ANISO DAM TENS Mat_24 X X Mat_157 X Mat_215 X X X X The material models can be tailored to fit a material better trough the usage of a software called LS-OPT. This software can be linked to LS-DYNA to perform var- ious kinds of optimizations. Material models can be calibrated in Ls-OPT through repeated simulations of tensile tests varying parameters until the simulations agree with the physical tests. 3.2.1 Mat_24 Mat_24 is one of the most used material models in LS-DYNA due to its long history, reliable characteristics and relatively short computing time. The model is built on elastoplastic properties including arbitrary stress as a function of strain, with the possible inclusion of strain rate dependency [34]. The plasticity follows the von Mises theory. The strain rate can be accounted for in three options. One way is to use the Cowper and Symonds model, which scales the yield stress with a factor where strain rate is included. A second more general way is to use the variable LCSR which input a load curve to scale the yield stress where the scale factor is defined. A third way of including strain rate dependency is to reference the function to a table using the variable LCSS [34]. This material model is commonly used for metals, or as a typical go-to material model when unsure about what else to use. For an application with a composite material, as in this case a short fibre reinforced polymer, a more complex material model is required. The model has to capture some essential properties which differ from a homogeneous isotropic material. Also, the properties of a composite material are highly dependent on the manufacturing method, which will be discussed later. Two models which possess the possibility to capture the right material behaviours are the Mat_157 and the recently developed Mat_215 [35]. These two models follow different principles. The material card for Mat_24 is presented in figure A.1. The parameters for Mat_24 are described in table A.1. 3.2.2 Mat_157 Mat_157, is a combination of two models, the anisotropic elastic model Mat_002 and the anisotropic plastic model Mat_103_P. This model captures the anisotropic characteristics of a material such as a fibre filled polymer with plasticity following Hill’s yield criterion. It is also possible to define Tsai-Wu or Tsai-Hill criterion for a brittle orthotropic failure. The model has a hybrid approach including both a micro and macro mechanical approach [34]. 38 3. CAE - Predicting and Preventing in use Failure The macro-approach works on the composite such as it follows a linear elastic or- thotropic material behaviour presented in section 2.3.5 which includes 9 material properties. These include tensile modulus in 3 axes, shear modulus in three planes, and Poisson’s ratios, all following a local fibre coordinate system. All material model parameters have to be determined through material testing before the model can be used [34][35]. The micro-mechanics approach works on each constituent of the composite and instead follow the Mori-Tanaka model and includes material properties of all con- stituents. This part is important in order to consider the local fibre orientations in the material and to compute the anisotropic material data. The material card for Mat_157 with all the input parameters for a solid material is presented in figure A.2. The parameters for Mat_157 are described in table A.2. 3.2.3 Mat_215 To consider the local anisotropy and fibre orientation in a short fibre reinforced material further, Mat_215 has been developed by 4A. The model is based on the calculation of thermoplastic composite properties using the Mori-Tanaka (Mean Field) Theory, Eshelby’s inclusion model and orientation averaging. The model also includes a elasto-viscoplastic matrix behaviour and fibre and matrix failure can be implemented through maximum stress criterion and damage initiation and evolution model (DIEM) respectively [35]. The material card for Mat_215 is presented in figure A.3. The parameters for Mat_215 are described in table A.3. Further description of the material models for Mat_24, Mat_157, and Mat_215 and their parameters can be found in [34]. 3.3 Mold Flow Analysis - moldex3D To analyse the melt flow and fibre direction of an injection moulded component with fibre reinforcement, Thule uses Moldex3D [36]. Similarly to FEA, the CAD model of the component is imported and a finite element mesh with the proper parameters, size, and geometry is generated. Inlets to the mould are placed and the parameters of the simulation set. From the analysis, it is possible to see the melt flow in the mould and determine where possible defects can occur. Through tailoring of the process parameters, certain defects can be avoided or minimized. Also, by knowing where it is a high risk of defects it is possible to reconsider the design of the component or take the defect into account when the component is brought to FEA. Another important function of Moldex3D is the prediction of fibre orientation since it has a big impact on the performance of the component. In each element of the mesh, a fibre direction is obtained which make it possible to visualize material 39 3. CAE - Predicting and Preventing in use Failure anisotropy and regions where fibre orientation is of interest. The results from the simulation can then be exported to a FEA software through a mapping tool called Envyo [37]. It uses a micromechanical interface to capture the wanted material properties. Hence, defects, fibre orientation and anisotropy can be considered in the structural FEA of a component. Through this type of analysis, it is possible to identify any potential issue and fix them before production. 40 4 Tensile Test of PA6 GF30 To obtain material properties and characterize the anisotropic mechanical behaviour of the PA30 material to be used in the Mat_157 material model, a tensile test where performed on specimen extracted from an injection moulded plate at angles of 0 °, 15°, 30°, 45°, 65°, and 90°relative to the MFD. Three tests were performed at each angle. Mould fill simulations of the injection moulded plate performed in Moldex3D and a tensile test of the specimens were simulated in LS-DYNA. These simulations was performed at angles of 0°, 45°and 90°relative to the MFD with the three material models Mat_24, Mat_157, and Mat_215. 4.1 Mechanical Tensile Test The tensile tests of PA6 GF30 were conducted at Thule in Hillerstorp. 4.1.1 Setup - Mechanical Tensile Test The experimental setup for the tensile test included a test rig (Instron 2530 test machine with a 50 kN static load cell), specimen grips (Instron 2716), extensometer (Instron 2639), software (Bluehill 3 [38]), and test specimens. An experimental setup is shown in figure 4.1. Figure 4.1: Experimental setup for tensile tests. 41 4. Tensile Test of PA6 GF30 Specimens were extracted from an injection moulded PA6 GF30 plates with the ge- ometry 120x105x2 mm using water jet cutting. Two specimens were extracted from each plate as close to the centre of the plate as possible. The specimen dimensions were obtained from ISO 527-2 1AB standard and scaled to fit the plates. A model of the specimen with its dimensions can be seen in figure 4.2. Three specimens were tested for each angle and two specimens at the same angle were extracted from each plate. For the 90°specimens, the grip of the specimen was slightly shortened to fit the plate. Specimens were pulled at a rate of 50 mm/min. Figure 4.2: Dimension of tensile test specimens scaled from ISO 527 1AB. The stress (σ) and strain (ε) was calculated according to the following equations. σ = F A = F w0t0 (4.1) ε = l l0 (4.2) Where w0, t0, and l0 is the original width, thickness, and length respectively, F is the applied force, A is the cross-section area, and l is the final length. 4.1.2 Results - Mechanical Tensile Test The stress-strain curves of tensile tests are plotted in figure 4.3. 42 4. Tensile Test of PA6 GF30 Figure 4.3: Stress strain curves from one tensile test per angle. The mean value of Young’s modulus and ultimate tensile strength and strain at fracture from all tests are presented in table 4.1. Table 4.1: Test results from tensile tests of PA6 GF30 specimen at different angles. θ E σFmax εult [°] [MPa] [MPa] [-] 0 8700 166 0.032 15 7800 142 0.034 30 6200 122 0.048 45 5400 111 0.042 65 4900 99 0.031 90 4600 93 0.030 The fracture of all specimens are presented in figure 4.4. Figure 4.4: Fracture of all specimens at different angles. 43 4. Tensile Test of PA6 GF30 4.2 Simulation of Tensile Test The simulation of the tensile test of PA6 GF30 were carried out at Thule in Hiller- storp. 4.2.1 Setup - Simulation in Moldex3D A CAD model of the injection moulded specimen plate was modelled and imported to Moldex3D. Inlet was placed along one short side of the plate. A mesh was generated with 1.5 mm element length and with the shape of a prism. The plate with the mesh and inlet can be seen in figure 4.5. Figure 4.5: Plate in Moldex3D with finite element mesh and inlet marked in red. Material Grilon BG30 was selected and process parameters were selected according to manufacturing recommendations. 4.2.2 Result - Simulation in Moldex3D Degree of fibre orientation in the skin layer of the injection moulded plate can be seen in figure 4.6. Figure 4.6: Degree of fibre orientation in the skin layer of the injection moulded plate. The colour scale denotes the degree of orientation; red denotes highly oriented fibres, whereas blue denotes randomly oriented fibres. 44 4. Tensile Test of PA6 GF30 Degree of fibre orientations in cross-sections transverse and parallel to the MFD in the injection moulded plate can be seen in figure 4.7. Figure 4.7: Degree of fibre orientation in the two cross-sections of the injection moulded plate. The colour scale denotes the degree of orientation; red denotes highly oriented fibres, whereas blue denotes randomly oriented fibres. 4.2.3 Setup - Simulation of Tensile Test A tensile test specimen of the same dimension as the specimens in the mechanical testing was modelled and imported to LS-DYNA. A mesh with ELFORM 16 shells with five integration point through the thickness was generated. The local fibre direction and distribution obtained from the simulation in Moldex3D were mapped to the specimen model in LS-DYNA at 0°, 45°, and 90°using Envyo [37]. The grip on one side of the specimen (red cross) was assigned a fixed boundary condition and the other grip (red arrow) was displaced according to figure 4.8. Figure 4.8: Setup of the tensile test simulation. The red cross indicates the fixed boundary condition and the red arrow indicates the displacement. All simulations was performed in LS-DYNA using an explicit solver. 4.2.4 Results - Simulation of Tensile Test The stress-strain curves from simulation of tensile test with 0°and 90°specimens with material model Mat_24, Mat_157, and Mat_215 are plotted in figure 4.9. 45 4. Tensile Test of PA6 GF30 Figure 4.9: Stress-strain curves from simulation of tensile test of 0°and 90°specimens with material model Mat_24, Mat_157, Mat_215 and result from mechanical tensile test. 4.3 Discussion - Tensile Test of PA6 GF30 In accordance with the literature [5][15][6