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# Micromechanics of Composite Materials

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Understand the basic assumptions and procedures used for for the analysis of composite materials

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### Micromechanics of Composite Materials

2. 2. MDPN452 Dr. Mohammad Tawfik Micromechanics • The basic question of micromechanics is: what is the relationship of the composite material properties to the properties of the constituents?
3. 3. MDPN452 Dr. Mohammad Tawfik The Design Question! • How can the percentages of the constituent materials be varied so as to arrive at the desired composite stiffness and strength?
4. 4. MDPN452 Dr. Mohammad Tawfik Definitions • Macromechanics: The study of composite material behavior wherein the material is assumed homogeneous and the effects of the constituent materials are detected only as averaged apparent properties of the composite material.
5. 5. MDPN452 Dr. Mohammad Tawfik Definitions • Micromechanics: The study of composite material behavior wherein the interaction of the constituent materials is examined in detail as part of the definition of the behavior of the heterogeneous composite material.
6. 6. MDPN452 Dr. Mohammad Tawfik Approaches to Micromechanics • Mechanics of Materials • Elasticity
7. 7. MDPN452 Dr. Mohammad Tawfik Micromechanics Objective • To answer the questions set by micromechanics, the objective becomes: – Determine the elastic moduli or stiffness or compliances of a composite material in terms of the elastic moduli of the constituent materials ( )mimfifii VPVPPP ,,,=
8. 8. MDPN452 Dr. Mohammad Tawfik Micromechanics Objective ( )mimfifii VPVPPP ,,,= MaterialCompositeofVolume FibresofVolume Vf = fm VV −= 1
9. 9. MDPN452 Dr. Mohammad Tawfik Basic Assumptions • The lamina: – Initially stress-free, macroscopically homogeneous, linearly elastic, macroscopically orthotropic • The fibers: – Homogeneous, regularly spaced, linearly elastic, perfectly aligned, Isotropic, perfectly bonded • The matrix: – Homogeneous, Isotropic, linearly elastic, void-free
10. 10. MDPN452 Dr. Mohammad Tawfik Representative Volume • The smallest region or piece of material over which the stresses and strains can be regarded as macroscopically uniform and yet the volume still has the correct proportions of fiber and matrix
11. 11. MDPN452 Dr. Mohammad Tawfik Mechanics of Materials Approach
12. 12. MDPN452 Dr. Mohammad Tawfik Most Prominent Assumptions • In fibre direction, strain in fibres and matrix are equal • Normal to fibre direction, stresses in matric and fibre are equal
13. 13. MDPN452 Dr. Mohammad Tawfik Determination of E1 Rule of Mixture
14. 14. MDPN452 Dr. Mohammad Tawfik Rule of Mixture
15. 15. MDPN452 Dr. Mohammad Tawfik Experimental Results
16. 16. MDPN452 Dr. Mohammad Tawfik Determination of E2
17. 17. MDPN452 Dr. Mohammad Tawfik Determination of E2 • Nondimensionalizing:
18. 18. MDPN452 Dr. Mohammad Tawfik Experimental Results
19. 19. MDPN452 Dr. Mohammad Tawfik Determination of Poisson’s Ratio • We have two values for the Poisson’s Ratio ν12 & ν21.
20. 20. MDPN452 Dr. Mohammad Tawfik Determination of G12
21. 21. MDPN452 Dr. Mohammad Tawfik Determination of G12
22. 22. MDPN452 Dr. Mohammad Tawfik Strength
23. 23. MDPN452 Dr. Mohammad Tawfik Strength • “A chain is as strong as its weakest link” • When the composite material gets loaded, all its components get loaded with different stresses • Nevertheless, strength prediction of the composite materials have not yet reached the accuracy level of the stiffness prediction. i.e. Open research area!
24. 24. MDPN452 Dr. Mohammad Tawfik Longitudinal Tensile Strength • Main assumptions: – All fibres have the same strength – Fibres and matrix behave linearly – Fibres are brittle when compared to matrix – Fibres are stiffer than matrix
25. 25. MDPN452 Dr. Mohammad Tawfik Longitudinal Tensile Strength • The stress that will cause the fibres to fail: • Where is the stress in the matrix as the fibres reach their ultimate stress. • From that: mmffut VV * 1 σσσ += f m fum E E σσ =*         += m f m ffut V E E Vσσ 1
26. 26. MDPN452 Dr. Mohammad Tawfik Longitudinal Tensile Strength
27. 27. MDPN452 Dr. Mohammad Tawfik Longitudinal Tensile Strength
28. 28. MDPN452 Dr. Mohammad Tawfik Minimum and Critical Vf • From the graphs, and using the previous equations, we may calculate: * * mfu mmu criticalfV σσ σσ − − =− * * max mmufu mmu fV σσσ σσ −+ − =
29. 29. MDPN452 Dr. Mohammad Tawfik Longitudinal Compressive Strength • In compression, the failure is dominated by buckling of the fibres! • Long fibres that are supported by softer matrix material tend to buckle causing what is called Microbuckling • Microbuckling causes great reduction in the compression stiffness of the composite material
30. 30. MDPN452 Dr. Mohammad Tawfik
31. 31. MDPN452 Dr. Mohammad Tawfik
32. 32. MDPN452 Dr. Mohammad Tawfik Compressive Strength • The compressive strength is greatly affected by: – Buckling modes – Initial misalignment – Curing procedure
33. 33. MDPN452 Dr. Mohammad Tawfik
34. 34. MDPN452 Dr. Mohammad Tawfik Homework #3 • Read the papers provided to you • Read section 4.4 in textbook • Collect more papers evolving the same topics (at least 3 per topic) • Write down a report on each topic • Due dates: – Tensile Failure; axial and transverse – Compressive failure ; axial and transverse (19/10/2013 23:59)
35. 35. MDPN452 Dr. Mohammad Tawfik Report should include 1. Introduction to the topic (need, problems, history, etc...) 2. Models available in literature (Including the detailed derivation of at least one of the models) 3. Results obtained from different models compared to experimental results (direct from available literature) 4. Conclusions about the models and their accuracy 5. References and bibliography