stress is . The remaining fraction bears an average stress . For , average stress is with . The composite stress is modified as following: The above equations assumed the fibers were aligned with the direction of loading. A modified rule of mixtures can be used to predict composite strength, including an orientation efficiency factor, , which accounts for the decrease in strength from misaligned fibers. where is the fiber efficiency factor equal to for , and for . If the fibers are perfectly aligned with the direction of loading is 1. However, common values of for randomly oriented are roughly 0.375 for an in-plane two-dimensional array and 0.2 for a three-dimensional array. Appreciable reinforcement can be provided by discontinuous fibers provided their lengths are much greater than the (usually) small critical lengths. Such as MMCs. If there is fiber-matrix delamination. is replaced by friction stress where is the friction coefficient between the matrix and the fiber, and is an internal pressure. This happens in most resin-based composites. Composites with fibers length less than contribute little to strength. However, during composite fracture, the short fibers do not fracture. Instead they are pulled out of the matrix. The work associated with fiber pull-out provides an added component to the fracture work and has a great contribution to toughness. Application There are also applications in the market, which utilize only waste materials. Its most widespread use is in outdoor deck floors, but it is also used for railings, fences, landscaping timbers, cladding and siding, park benches, molding and trim, window and door frames, and indoor furniture. See for example the work of Waste for Life, which collaborates with garbage scavenging cooperatives to create fiber-reinforced building materials and domestic problems from the waste their members collect: Homepage of Waste for Life See also Fiber volume ratio Fracture mechanics Plastic composite (disambiguation) Plastic lumber Wood plastic composite Fibre-reinforced plastic References 3. Thomas H. Courtney. "Mechanical Behavior of Materials". 2nd Ed. Waveland Press, Inc. 2005. Woodworking materials Composite materials Recycled building materials Plastics Fibre-reinforced composites