1. MECH4301 2008 L# 11 Hybrid Materials 1/28 Mech 430-1 2008 Lecture 11 Design of Hybrid Materials or Filling Holes in Material Property Space (1/2) Textbook Chapter 13 Reading Materials: Technical Papers Folder Penalty Functions ( P. Sirisalee, M. F. Ashby, G. T. Parks and P. J. Clarkson, "Multi-Criteria Material Selection of Monolithic and Multi-Materials in Engineering Design", Adv. Engng. Mater., 2006, 8, 48-56.) (simple, quite readable) Hybrids ( M. F. Ashby and Y. J. M. Brechet, "Designing hybrid materials", Acta Materialia, 2003, 51, 5801-5821.) (advanced reading)

2. MECH4301 2008 L# 11 Hybrid Materials 2/28 Holes in Material Property Space big empty area E Is it possible to create a material to fill this empty space? (A compliant- high thermal conductivity material ??)

3. MECH4301 2008 L# 11 Hybrid Materials 3/28 Making Hybrid Materials Hybrid materials combine the properties of two or more monolithic materials, (CFRP, GFRP) or of one material and space (foams), or of a single material in two different forms, (dual phase steels, eutectic alloys, PSZ, ABS) Shape and scale add two more dimensions.

4. MECH4301 2008 L# 11 Hybrid Materials 4/28 What might we hope to achieve? Best of both Rule of mixtures Weakest link Least of both Zn-coated steel Unidirectional (fibre) composites (stiffer, stronger) CFRP; GFRP Particulate (filler) composites (harder, cheaper) Wax-metal sprinklers

5. MECH4301 2008 L# 11 Hybrid Materials 5/28 Hybrid Materials defined A hybrid material is a combination of two or more materials in a predetermined configuration, relative proportion and scale (size and shape), optimised for a specific engineering purpose. A + B + Configuration + Scale

6. MECH4301 2008 L# 11 Hybrid Materials 6/28 L need strong electrically conductive material for power line Example of a Hybrid material filing a hole in the Material Property Space Trade-off surface Best point empty Resistivity 1/TS A + B + conf + scale Cu => min elect. resist. Fe => max TS interleaving fine strands

7. MECH4301 2008 L# 11 Hybrid Materials 7/28 Hybrid Materials: four families of Configurations 4 hybrid configurations: Composite Sandwich Lattice Segment See list of properties in Fig. 13.4, p. 344 Keyword to understand hybrids Lecture 11 Lecture 12

8. MECH4301 2008 L# 11 Hybrid Materials 8/28 Hybrid Materials of Type 1: Fibre and Particulate Composites

9. MECH4301 2008 L# 11 Hybrid Materials 9/28 Properties of Hybrids It is difficult to calculate/predict the actual behaviour of the composite. Easier to find general bounds and limits that bracket the expectations/possibilities. Criteria of Excellence: Material Indices. Used to decide whether (or not) the hybrid outperforms existing materials.

10. MECH4301 2008 L# 11 Hybrid Materials 10/28 Fibre and particulate composites: the maths 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. pp. 351-353 Exercise 9.2

11. MECH4301 2008 L# 11 Hybrid Materials 11/28 Composites for a stiff beam of minimum mass Bounds for the elastic moduli of hybrids Beryllium fibres Aluminium alloys Alumina fibres E  E 1/2 /  (beams) Beryllium fibres have a stronger effect due to their low density; Alumina gives almost no gain. Criterion of excellence better

12. MECH4301 2008 L# 11 Hybrid Materials 12/28 (Exercise 9.1) creating ligth/stiff composites Compare composites made of Ti matrix, reinforced with ZrC, Alumina, SiC fibres

13. MECH4301 2008 L# 11 Hybrid Materials 13/28 Solution to Exercise 9.1 Ti matrixE  UD composites, Eq. 13-2 for upper bound and Eq. 13-3 for lower bound, Eq. 13-1 for  Selection lines for tie rods, beams and panels Use parametric plotting find upper/lower bounds

14. MECH4301 2008 L# 11 Hybrid Materials 14/28 Exercise 9.1: Parametric plotting of E and  (f : free parameter) fE // (GPa)E + (GPa)  (Mgr/m 3 ) 0111.00 4.60 0.05114.51119.804.54 0.1118.25128.604.48 0.2126.52146.204.36 0.3136.02163.804.24 0.4147.08181.404.12 0.5160.09199.004.00 0.6175.62216.603.88 0.7194.49234.203.76 0.8217.90251.803.64 0.9247.72269.403.52 1287.00 3.40 E Ti = 111 GPa  Ti = 4.6 Mgr/m 3 E Alumina = 287 GPa  Alumina = 3.4 Mgr/m 3 Repeat procedure for ZrC and SiC fibres

15. MECH4301 2008 L# 11 Hybrid Materials 15/28 Solution to Exercise 9.1 Ti matrixE  Selection lines for tie rods, beams and panels Alumina fibers shift the properties in the best direction

16. MECH4301 2008 L# 11 Hybrid Materials 16/28 Hybrid Materials: four families of configurations Composite Sandwich Lattice Segment

17. MECH4301 2008 L# 11 Hybrid Materials 17/28 Beams and Panels: Shaping increases efficiency (more GPa/kg) E 1/2 /  E 1/3 /  Low density materials are paramount for efficient panels => foamed cores

18. MECH4301 2008 L# 11 Hybrid Materials 18/28 Hybrids of Type II. Sandwich Structure: properties defined Face: E f Thickness t Increases I, takes load Core: E c Thickness c Prevents shear ! Volume fraction of face material :- -- f = 2t/d Core fraction : 1-f = 1-2t/d=(d-2t)/d=(c+2t-2t)/d = c/d Correct typos in txtbk p. 359

19. MECH4301 2008 L# 11 Hybrid Materials 19/28 A Sandwich Panel as a Monolithic Material: the Maths Rule of mixtures for density Fibre composites Sandwich panels Rule of mixtures for stiffness Fibre composites (tension) Sandwich panels (bending) equivalent flexural modulus (Eq. 13-17b) f = 2t/d E face  face

20. MECH4301 2008 L# 11 Hybrid Materials 20/28 Unidirectional composites compared with sandwich structures  E 1/3 /  facecore Sandwich Panel: 3 times more efficient (GPa/kg, in bending) than the Unidirectional Composite (in tension) sandwich U-D Composites in tension, “in plane” value. E

21. MECH4301 2008 L# 11 Hybrid Materials 21/28 Figure 13-16 from textbook revisited Polymer Foam reinforced with Ti wires, Eqs. 13-2 and 13-3 Criterion of excellence for panels (slope 3)  E Sandwich structure: 3 times more efficient (GPa/kg, in bending) than the U-D Composite (in tension) Panel with Ti faces and Foamed core Eq. 13-17a K=1 Parametric plotting ?

22. MECH4301 2008 L# 11 Hybrid Materials 22/28 Parametric plotting of E and , f disposable parameter Polymer Foam reinforced with Ti wires, Eqs. 13-2 and 13-3 fE // (GPa)E + (GPa)  (kg/m 3 ) E panel 00.25 2500 0.055.80.26467.515.8 0.111.30.2868530.1 0.222.40.31112054.2 0.333.50.36155572.9 0.444.60.42199087.0 0.555.60.5242597.1 0.666.70.622860103.9 0.777.80.833295108.0 0.888.91.243730110.1 0.999.92.454165110.9 1111 4600111 E panel => Eq.13.17a, K =1, p. 360 E Ti 111 GPa;  Ti = 4600 kg/m 3 E foam = 0.25 GPa,  foam = 250 kg/m 3 Sandwich structure: 3 times more efficient (GPa/kg, in bending) than the U-D Composite (in tension)

23. MECH4301 2008 L# 11 Hybrid Materials 23/28 Overloading of a sandwich panel leads to failure Failure of panels Face yields Face buckles Core fails (shear) Face/core debonding Piercing of face by localised force These mechanisms compete with each other

24. MECH4301 2008 L# 11 Hybrid Materials 24/28 Can we create a flexible electrically conductive material? => Percolation Percolation: properties that switch on and off E Resistivity Rubber filled with graphite big empty area

25. MECH4301 2008 L# 11 Hybrid Materials 25/28 Percolation A bottle full of marbles is only 66% full (75% full if the marbles are in an FCC of HCP arrangement). Between 25 and 34% of the volume is empty, interconnected space. Percolation may happen along the interconnected interstices. You need at least about 25-30% volume fraction of “liquid” to have interconnection (continuity) from top to bottom, hence percolation of properties. Percolation: important design tool for hybrids

26. MECH4301 2008 L# 11 Hybrid Materials 26/28 Switching percolation on and off V = 0.05 Isolated particles V = 0.10 Small Isolated clusters V = 0.15 Long Isolated clusters V = 0.2 Long interconnected clusters: percolation switches on Minimum volume fraction for percolation: about 20% Particles dispersed in a continuum matrix

27. MECH4301 2008 L# 11 Hybrid Materials 27/28 Percolation relates to the existence of a continuous path trough the structure. Dispersed particles touch at V f >0.2 Mixing metallic powders with polymers result in electrically conducting polymers. The property disappears (switches-off) at V f <0.2. Percolation: properties that switch on and off Elastomer- metal hybrids fill the gap Resistivity E Percolation affects other properties as well: Thermal conductivity Ductility and fracture toughness of composites Percolation is affected by the shape of the particles (fibres tend to touch each other more often than round particles) Examples: fridge magnets, electrically conductive polymers, pressure sensitive pads ( electronic drums)

28. MECH4301 2008 L# 11 Hybrid Materials 28/28 Flexible ferromagnets: not just Fridge Magnets Magnetostriction ( or Joule effect) is a property of ferromagnetic materials that causes them to change their shape when subjected to a magnetic field. The reciprocal effect, the change of the susceptibility of a material when subjected to a mechanical stress, is called the Villari effect. (Wikipedia)ferromagneticmagnetic field

29. MECH4301 2008 L# 11 Hybrid Materials 29/28 Answer to Exercise 9.2. Minimise thermal distortion Solved with Eq. 13-7 through 13.10. (p. 352, full equations, parametric plots) Mg alloys  Better this way /  Criterion of excellence (gradient 1)

30. MECH4301 2008 L# 11 Hybrid Materials 30/28 The End Lecture 11

31. MECH4301 2008 L# 11 Hybrid Materials 31/28 E-  chart: Creating composites High performance fibers Metal matrix composites Poly-matrix composites Polymers Metals Hybrids fill previously empty areas

32. MECH4301 2008 L# 11 Hybrid Materials 32/28 Bounds for the expansion coefficient/conductivity of hybrids E 9.2   Aluminium alloys SiCBN  / Better this way Adding SiC to Al enhances performance. BN reduces performance Criterion of excellence