Functionally Graded Materials

1. Functionally Graded Materials

2. Definition Functionally graded materials (FGM) are composite materials which are designed to present a particular spatial variation of their properties. This is usually achieved by forming a compound of two components whose volume fraction is changed across a certain direction.

3. Origin/Motivation • The “first” FGM was developed in Japan in 1984-85 as the result of a spaceplane project. • Although the concept of FGM is recent, many materials that fit the description have existed for decades. • Some FGM also occur naturally: • Bones and teeth • Seashells

4. Origin/Motivation Better adherence of a protective layer (against corrosion, for instance) Minimization of interfacial stresses between different materials (e.g. due to temperature variation) Increase in local fracture thoughness Relocation of maximum stresses on a load bearing component

5. Origin/Motivation FGMs allow better customization and tailoring of materials for specific tasks Stiffer at clamped end Softer at clamped end Material gradation in Y direction More variety in material selection for engineering design

6. Classification of FGMs FGMs may be compositionally or micro-structurally graded The gradient is established through a transition function (usually volume fraction as a function of one or more spatial coordinates) FGMs come in several types, depending on their constituents (e.g. ceramic-metal, metal-metal…)

7. Gradation Continuous Stepped

8. Ceramic-Metal TiC-Ni, Mullite-Mo, Al-AlB2 Metal-Metal/Intermetallic W-Cu, W-Mo, Al-Al3Fe Metal-Polymer Al-Polycarbonate Others Single material (variation in porosity) Glass - Ceramic Ceramic - Ceramic

9. Modeling of FGMs Some researchers decided upon a basic unit to describe FGMs The maxel represents the smallest entity in which the composition of a continuously graded FGM can be defined Pure Component A % Component A % Component B Pure Component B It is the equivalent of the build resolution in rapid prototyping processes (quantitized by voxels – hence maxel = material voxel)

10. Modeling of FGMs 1) Assume a preset variation

11. Modeling of FGMs 2) Linear rule of mixtures (function of local volume fraction) In general, applicable only to metal-metal FGMs, may be used as a first approximation for different compositions 3) Halpin-Tsai More complex, takes into account the aspect ratio of the inclusions (s)

12. Modeling of FGMs 4) More: Mori-Tanaka Empirical rule of mixtures … Other properties such as the Poisson ratio and thermal expansion coefficient follow similar trends. Hardness and fracture thoughness of the resulting material are more difficult to predict and some examples will be given further ahead.

13. TUNGSTEN-COPPER Tungsten surface: Hard, refractory material Copper surface: Good electric and thermal conductivity

14. TITANIUM CARBIDE-NICKEL Maximum fracture thoughness is achieved for 30 wt.% Ni. The metal phase surrounds the TiC particles and hence acts as a toughening phase. Peak in hardness and flexure strength due to metal phase changing its behavior from dispersive to connective

15. MULLITE (AL6SI2O13) -MOLYBDENUM Smoother variation favors resistance to thermal shock (VfMo = 1 – (x /L) p)

16. ALUMINUM-POLYCARBONATE This type of materials is being researched for its special properties of full wave transmission on one side (Al) and full dissipation on the other, making it suitable for NDT (Non-Destructive Testing) probes.

17. Optimal Design As mentioned earlier, FGMs lend themselves well to being optimized for various performance measures. An example:

18. Optimal Design Multiobjective optimization – generation of a Pareto front using genetic algorithms

19. Experience aquired from research into FGMs has produced its results. Knowledge has been gained on which transition functions are best suited for specific tasks and material types.

20. Aerospace Applications Ceramic-metal FGMs are particularly suited for thermal barriers in space vehicles. They have the added advantage that the metal side can be bolted onto the airframe rather than bonded as are the ceramic tiles used in the Orbiter. Other possible uses include combustion chamber insulation in ramjet or scramjet engines

21. Fuel Cell Technology Creating a porosity gradient in the electrodes, the efficiency of the reaction can be maximized

22. Nuclear Fusion Reactors Modification to heat exchangers in tokamak fusion reactors Reduction of interfacial stresses → prevention of delamination effects → increase in lifetime

23. JET SOLIDIFICATION - Solid freeform process - Ultimately requires sintering of the resulting green body PRESSURE FILTRATION - Versatile process that can be adapted to produce both axial and radial gradients - Also requires sintering

24. DIRECTIONAL SOLIDIFICATION - Melt processing (no sintering step required) - Only axial gradients - Material processed at low speed on which the shape of the transition function is heavily dependant upon

25. SINTERING - Using a conventional oven, microwave or laser beam - External pressure may or may not be applied

26. Processing Methods

27. Conclusions Functionally graded materials are still a very recent area of research (and thus very active) Current research is mostly focused on uncovering the complex nature of fracture mechanics due to material nonhomogeneity as well as in developing/improving forming processes so that the target gradient is achieved with precision