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Experimental and Numerical Study of Orthotropic Materials

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Experimental and Numerical Study of Orthotropic Materials Master's Degree Thesis ISRN: BTH-AMT-EX--2017/D18--SE Experimental and Numerical Study of Orthotropic Materials Ram Kiran Kesana Yashpal Surendhar Goud Pulicherla Department of Mechanical Engineering Blekinge Institute of Technology Karlskrona, Sweden 2017 Supervisors: Sharon Kao-Walter, Shafiqul Islam, Madeleine Hermann, BTH Experimental and Numerical Study of Orthotropic Materials Ram Kiran Kesana Yashpal Surendhar Goud Pulicherla Department of Mechanical Engineering. Blekinge Institute of Technology. Karlskrona, Sweden. 2017. Thesis submitted for completion of Master of Science in Mechanical Engineering with emphasis on Structural Mechanics at the Department of Mechanical Engineering, Blekinge Institute of Technology, Karlskrona, Sweden. Abstract: In current enterprises, simulations are being utilized to reduce the cost of product development. Along this line, there is an increased enthusiasm for enhancing reliability and accuracy of the simulations. For an accurate and reliable simulation, it is essential to use an accurate material model and provide it with accurate material information. In current scenario, orthotropic materials are being simulated utilizing isotropic material model, as orthotropic material model requires more material data which is not promptly accessible. This research intends to test and identify orthotropic materials and simulate them using orthotropic material model in ABAQUS. Materials utilized as a part of this research were Aluminium, LDPE, PET. Required material data was derived by performing Uni- directional tensile tests, DIC, and an algorithm developed. To get highly accurate material data from DIC, a few kinds of patterns were examined, and a superior pattern was resolved for camera configuration being utilized. Keywords: Digital image correlation(DIC), Inverses method, Low-density polyethylene (LDPE), Polyethylene Terephthalate (PET), Optimization. Acknowledgements This master thesis has been completed at the Department of Mechanical Engineering at Blekinge Institute of Technology (BTH), Karlskrona, Sweden in participation with Tetra Pak AB, Lund, Sweden. We would like to thank our supervisor at BTH, Sharon Kao-Walter for her direction, help and support amid our work. We might likewise express gratitude towards Tetra Pak for providing material utilized as a part of experimental work. We wish to express our genuine gratefulness to Shafiqul Islam and Madeleine Hermann for assisting us with their thoughts, recommendations and perceptions. We are thankful to Wureguli Reheman for suggestions in composing the report for our thesis. We are obliged to the Mechanical Department of BTH for providing the access to the lab equipment, machinery and accessories required for our experiments and CAD lab for simulations to complete our task. Karlskrona, October 2017. 2 Contents List of Tables 5 List of Figures 6 Notations 8 Introduction 10 Materials 10 Background 10 Objective and Method of work 12 Research Questions 14 Theoretical Groundwork 15 Fundamentals of Solid Mechanics 15 Hooke’s Law 16 Yield Surface 17 Lankford Coefficient 17 Hill Yield Criterion 18 Elastic-Plastic 20 Material Model 21 Isotropic Behaviour 21 Orthotropic Behaviour 21 Orthotropic Elasticity 21 Orthotropic Plasticity 23 Inverse Method 24 Digital Image Correlation (DIC) 24 Literature Review 26 Experimental Work 29 Experimental Setup 29 Equipment Configuration 31 Specimen Preparation 32 Experimental Procedure 35 MATLAB 36 Numerical Simulation 41 Components of simulation 42 Elastic Model 42 Plastic Model 42 Element types 43 3 Optimization Procedure 44 Overview 44 Implementation 45 Code Structure 47 DIC working procedure using GOM Correlate 50 Pattern Review 51 Extraction of data 55 Results 56 GOM Correlate 56 Yield Stress Ratios 58 Orthotropic Models 59 Discussions and Conclusions 66 Discussion on Tensile tests 67 Contribution to research 67 Future Work 68 References 70 APPENDIX 71 Plots of data from Experiments 71 True stress-strain plots 77 Load cell calculations 80 Data from recorded videos of LDPE specimen 80 Procedure 81 Modelling in ABAQUS 81 GOM Correlate 84 Modified INP file 86 Considering only one guess variable 88 Programming Scripts 88 MATLAB 88 Python 90 Related images 91 4 List of Tables Table 5.1. Youngs Modulus of materials from MATLAB using Experimental data. 40 Table 9.1. Width change ratio of materials from GOM Correlate. 56 Table 9.2. Width change at 20% elongation during the test from GOM Correlate. 57 Table 9.3. Young's Modulus of materials from GOM Correlate. 58 Table 9.4. Yield stress ratios from Inverse method. 58 Table 12.1. Yield stress data considering only one guess. 88 5 List of Figures Figure 2.1. Force vs Displacement curve parts. .................................................... 13 Figure 5.1. Tensile-testing Machine. ..................................................................... 30 Figure 5.2. Grippers for Aluminium. .................................................................... 30 Figure 5.3. Pneumatic Grippers for LDPE and PET. ............................................ 31 Figure 5.4. Machine and Cross direction. ............................................................. 32 Figure 5.5. (a) Specimen cutting directions. (b) Specimen dimensions. .......... 34 Figure 5.6. Force vs Displacement of LDPE from the experiment. ...................... 37 Figure 5.7. Force vs Displacement of PET from the experiment. ......................... 38 Figure 5.8. Load vs Displacement of 4mm Aluminium from the experiment. ..... 38 Figure 5.9. Load vs Displacement of 2mm Aluminium from the experiment. ..... 39 Figure 7.1.Core tasks. ............................................................................................ 45 Figure 7.2. Code working flowchart. .................................................................... 48 Figure 8.1. DIC spray patterns on Aluminium specimens. ................................... 50 Figure 8.2. Pattern review. .................................................................................... 51 Figure 8.3. Three Surface Components. ................................................................ 52 Figure 8.4. (a) Less diverse grey scale. (b) Dark spot. (c) White spot near dark area. ....................................................................................................................... 52 Figure 8.5. Suitable pattern for DIC. ..................................................................... 54 Figure 8.6. Results from suitable pattern. ............................................................. 55 Figure 9.1. Orthotropic Aluminium 2mm MD. ..................................................... 60 Figure 9.2. Orthotropic Aluminium 2mm CD. ...................................................... 60 Figure 9.3. Orthotropic Aluminium 2mm 45degrees. ........................................... 61 Figure 9.4. Orthotropic PET MD. ......................................................................... 62 Figure 9.5. Orthotropic PET CD. .......................................................................... 62 Figure 9.6. Orthotropic PET 45 degrees. ............................................................... 63 Figure 9.7. Orthotropic LDPE MD. ...................................................................... 64 Figure 9.8. Orthotropic LDPE CD. ....................................................................... 64 Figure 9.9. Orthotropic LDPE 45degrees. ............................................................. 65 Figure 10.1. Comparison of old pattern with new MATLAB pattern. .................. 68 Figure 12.1. Load vs Displacements of PET MD for all specimens. .................... 71 Figure 12.2. Load vs Displacements of PET CD for all specimens. ..................... 72 Figure 12.3. Load vs displacements of PET 45 degree of all specimens. ............. 72 Figure 12.4. Load vs displacements of LDPE MD for all specimens. .................. 73 Figure 12.5. Load vs displacements of LDPE CD for all specimens. ................... 73 Figure 12.6. Load vs displacements of LDPE 45 degree for all specimens. ......... 74 Figure 12.7. Load vs displacements of Aluminium 4mm MD for all specimens. 74 Figure 12.8. Load vs displacements of Aluminium 4mm CD for all specimens. 75 6 Figure 12.9. Load vs displacements of Aluminium 4mm 45 degree for all specimens. ............................................................................................................. 75 Figure 12.10. Load vs displacements of Aluminium 2mm MD for all specimens. 76 Figure 12.11. Load vs displacements of Aluminium 2mm CD for all specimens. 76 Figure 12.12. Load vs displacements of Aluminium 2mm 45 degree for all specimens. ............................................................................................................. 77 Figure 12.13. True stress-strain curves of PET. .................................................... 78 Figure 12.14. True stress-strain curves of LDPE. ................................................. 78 Figure 12.15. True stress-strain curves of Aluminium 4mm. ................................ 79 Figure 12.16. True stress-strain curves of Aluminium 2mm. ................................ 79 Figure 12.17. (a) 45degrees. (b) CD. (c) MD. .................. 81 Figure 12.18. Material data. ................................................................................... 82 Figure 12.19. 45-degree model with material orientation. .................................... 83 Figure 12.20. Increments. .....................................................................................
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