Your clutch lining material will be Organic, Ceramic, Kevlar or Feramalloy.
Twin and Single Clutch
Organic is the choice of most OEMs. Organic offers durability, smooth engagement and are gentle on matting surfaces. The downside is they do not like heat and require a fairly high clamping force to maintain grip as the co-efficient of friction is only around 0.32. Organic friction discs will almost always be a full face discs with the organic material made from phenolic resins, metallic powder or metal oxides and moulded or woven in construction.
The heavy duty options will have more metallic material in the mixture and also have a pressure plate of higher clamping value.
Organic clutch material

 Kevlar like organic needs a fairly high clamping force due to it having a similar co-efficient of friction to organic. Its advantage is its ability to withstand heat. Often Kevlar is able to withstand 40-50% more heat than organics. Just like organic Kevlar offers smooth engagement and minimal wear of matting surfaces. This friction material will often last two to three times longer than the organic option. These are a good option for slightly modified vehicles and off road use.

Kevlar Material

 Ceramic offers the highest co-efficient of friction of all the materials coming in at 0.48-0.55. This means that they can be used with a lower clamping force pressure plate and or high output applications.  Ceramic clutches are known to wear mating surfaces heavily. This wear also makes them shudder on engagement. They can take more heat but slipping will cause heavy wear and result in a burnt up pressure plate and flywheel. The material is a mix of sintered bronze, ceramic material, copper, tin, iron, silicon dioxide and carbon. These are the competition clutches. 

Feramalloy is a newer material and will possibly replace ceramic facings. It offers similar levels of wear and temperature resistance to ceramics. The advantage is it has a better static to dynamic ratio. What this means is smoother engagement and less shudder or chatter than ceramics. 
Ceramic face
I just have to add carbon carbon. In this setup both the friction material and the matting surfaces are amorphous carbon.  This material grips more as it gets hotter and is extremely light. Cost of  production is very high and these tend to be only a top level motorsport item. A good compromise is to use a carbon clutch disc, steel flywheel and pressure plate. 
Single and twin plate clutch set ups  is a story for another day.
Carbon Carbon Clutch


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