1. MECH4301 2008 L 12 Hybrid Materials (2/2) 1/25 Lecture 12, 2008. Design of Composites / Hybrid Materials, or Filling Holes in Material Property Space (2/2) Textbook Chapter 13, Tutorial 6 Papers (light reading): Microtruss core 1 Microtruss core 2

2. MECH4301 2008 L 12 Hybrid Materials (2/2) 2/25 Hybrid Materials: four families of configurations Composite Sandwich Lattice Segment

3. MECH4301 2008 L 12 Hybrid Materials (2/2) 3/25 Review: Fibre and particulate composites: the math Rule of mixtures for density (exact value) Rule of mixtures for stiffness Along the fibres (upper bound, Voigt) Across the fibres (lower bound, Reuss) Same sort of equations for strength, heat capacity, thermal and electrical conductivity, etc.

4. MECH4301 2008 L 12 Hybrid Materials (2/2) 4/25 Hybrid Materials: four families of configurations Composite Sandwich Lattice Segment

5. MECH4301 2008 L 12 Hybrid Materials (2/2) 5/25 Hybrid Materials of Type 2: Sandwich Panels Strong/stiff faces carry most of the load (flexural stiffness) Core is lightweight, Resists shear

6. MECH4301 2008 L 12 Hybrid Materials (2/2) 6/25 A Sandwich Panel as a Single Material: the math Rule of mixtures for density Fibre composites Sandwich panels Rule of mixtures for stiffness Fibre composites (tension) Sandwich panels (bending) equivalent flexural modulus E face

7. MECH4301 2008 L 12 Hybrid Materials (2/2) 7/25 Hybrid Materials: four families of configurations Composite Sandwich Lattice Segment

8. MECH4301 2008 L 12 Hybrid Materials (2/2) 8/25 Lattices: Bending dominated vs. Stretch dominated structures Bending dominated structures Cable Leaf spring We use Shaping to give the sections a LOWER flexural stiffness per kg than the solid sections from which they are made.

9. MECH4301 2008 L 12 Hybrid Materials (2/2) 9/25 Bending dominated structures: Foams F F F F Very flexible structure = low effective E* Prove this Prove: Proportionality constant of order 1

10. MECH4301 2008 L 12 Hybrid Materials (2/2) 10/25 Compressive deformation behaviour of foams

11. MECH4301 2008 L 12 Hybrid Materials (2/2) 11/25 Collapse of foams metallic foam (plastic hinges) elastomeric foam (elastic buckling) ceramic foam (hinges crack)

12. MECH4301 2008 L 12 Hybrid Materials (2/2) 12/25 Stretch dominated structures flexible over-constrained rigid bending-dominated (mechanism) stretch-dominated structures

13. MECH4301 2008 L 12 Hybrid Materials (2/2) 13/25 Stretch dominated structures: A micro-truss structure

14. MECH4301 2008 L 12 Hybrid Materials (2/2) 14/25 Micro-truss core designs for panels http://www.cellularmaterials.com/coredesigns.asp Periodic cellular material cores are based on a regularly repeating geometric unit, or cell, like a cube (square honeycomb) or pyramid. This technology allows for consistently spaced open-cells, which facilitate the addition of materials like magnets, cables, or ceramics, for example and therefore increase functionality. The open cells also permit fluid flow that can achieve more efficient thermal management.

15. MECH4301 2008 L 12 Hybrid Materials (2/2) 15/25 http://etd.gatech.edu/theses/available/etd-11222005-162952/unrestricted/wang_hongqing_v_200512_phd.pdf http://www.srl.gatech.edu/publications/2005/DETC2005-85366.pdf Bone: Foam (bending dominated) or micro- truss (stretch dominated)? A foam in a panel’s core behaves like a micro-truss structure, only with slightly less efficiency

16. MECH4301 2008 L 12 Hybrid Materials (2/2) 16/25 micro-truss hybrids: ultraligth, high flexural stiffness Foams: ultraligth solids Micro-truss: linear relationships Flexural loading Foams: power law relationships (involve the second moment I) Loaded in compression Bending dominated vs. Stretch dominated structures Panels with foamed cores: linear relationship as well E (flex) =(  /  s )E face =3f E f (the foam as panel core behaves like a micro-truss structure) 1/3 of the bars are loaded in tension

17. MECH4301 2008 L 12 Hybrid Materials (2/2) 17/25 Stiffness vs density for foams and micro-truss structures Foams E f =(  /  s ) 2 E s Slope 2 Micro-truss Slope 1 Micro-truss structures fill up another hole in property space E  panels also belong in here (slope 1) E flexural =3f E face

18. MECH4301 2008 L 12 Hybrid Materials (2/2) 18/25 http://www.cellularmaterials.com/advantages.asp

19. MECH4301 2008 L 12 Hybrid Materials (2/2) 19/25 Hybrid Materials: four families of configurations Composite Sandwich Lattice Segment

20. MECH4301 2008 L 12 Hybrid Materials (2/2) 20/25 bricks take compression but not tension or shear carry out-of- plane forces and bending carry in-plane loads require a continuous clamping edge Examples of topological interlocking Unbonded structures that carry load

21. MECH4301 2008 L 12 Hybrid Materials (2/2) 21/25 Damage tolerance of segmented structures: Weibull statistics Metals m = 25Ceramics m = 5 Max slope = Weibull modulus m V t = volume of whole body V s = volume of one element n = V t /V s number of elements P* = critical failure probability D, D* = fraction /critical fraction/ of elements that failed  t *  s * = design stress, damage and of solid body and segmented body V o,  o, m = Weibull parameters K c stress concentration factor P  Design  for single large element segmented body fails at  *, D* Effect of segmentation on available stress

22. MECH4301 2008 L 12 Hybrid Materials (2/2) 22/25 Ashby & Brechet, 2003 Scale effects on the strength of micro- truss structures metalsceramics Gain in strength Loss of strength  * s /  * t = 1 Finer this way Weibull modulus m The strength of low Weibull modulus (ceramics) micro- truss structures increases with segmentation The strength of high Weibull modulus (metals) micro-truss structures does not increase with segmentation

23. MECH4301 2008 L 12 Hybrid Materials (2/2) 23/25 The strength of ceramic foams of different cell sizes coarse cells fine cells 5x Colombo and Bernardo, Composites Sci. Tech., 2003, 63, 2353-2359. For given density, foams with fine cells are some 5 times stronger than foams with coarse cells Compressive strength density

24. MECH4301 2008 L 12 Hybrid Materials (2/2) 24/25 Hybrids: The main points Combining properties may help filling holes and empty areas in material property-space maps. Appropriate Hybrid materials can be created by combining material properties and shape, the latter at either micro or macro scale. Properties of hybrid materials can be easily bracketed by simple mathematical relationships which allow straight forward description of behavior. These functional relationships allow exploring new possibilities.

25. MECH4301 2008 L 12 Hybrid Materials (2/2) 25/25 The End Lecture 12 (Hybrids, 2/2)

26. MECH4301 2008 L 12 Hybrid Materials (2/2) 26/25 Schematic illustrations of microtruss lattice structures with tetrahedral, pyramidal, Kagome and woven textile truss topologies doi:10.1016/j.actamat.2004.09.024doi:10.1016/j.actamat.2004.09.024 Acta Materialia Cellular metal lattices with hollow trusses Douglas T. Queheillalt and Haydn N.G. Wadley