MECH L 12 Hybrid Materials (2/2) 1/25 Lecture 12, 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

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

MECH 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.

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

MECH 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

MECH 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

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

MECH 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.

MECH 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

MECH L 12 Hybrid Materials (2/2) 10/25 Compressive deformation behaviour of foams

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

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

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

MECH L 12 Hybrid Materials (2/2) 14/25 Micro-truss core designs for panels 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.

MECH L 12 Hybrid Materials (2/2) 15/ 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

MECH 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

MECH 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

MECH L 12 Hybrid Materials (2/2) 18/25

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

MECH 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

MECH 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

MECH 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

MECH 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, For given density, foams with fine cells are some 5 times stronger than foams with coarse cells Compressive strength density

MECH 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.

MECH L 12 Hybrid Materials (2/2) 25/25 The End Lecture 12 (Hybrids, 2/2)

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