Why does usually length of fiber increase the tensile of strength of a composites but this strength decrease with increase the diameter of fiber ? Any idea .
Why tensile strength of carbon fiber increase with reducing its diameter?
Strength of a composite having discontinuous fibers will be less than that of a composite having continuous fibers. However, if the length of the fiber is greater than a critical length, Lc, the difference in strengths of these two composites will be insignificant.
The critical length of fiber is given by the relation:
Lc = σfd/2τ0
where σf = fiber stress, τ0 = interfacial shear stress.
When the length of the fiber is shorter than the critical length, the plastic zone in the matrix will reach the mid-length of the fiber before the fiber is strained to its failure strain. Note that, in a fiber composite, all the load is supported by the fiber and the matrix just transmits the load to the fiber. Plastic zone of the matrix impairs its ability to transmit the load to fiber and decreases strength of the composite.
Strength of carbon fiber is influenced by the internal and surface defects (flaws). As the diameter increases, the concentration of defects increase which in turn decrease the strength. Heating the fiber to above 1000 - 1200 C could reduce the internal defects. Etching the fibers could control the surface flaws.
I agree with Krishnan Raja Sir. When we do single fiber testing, the Distribution or Deviation of tensile strength is larger for fibers with higher length. This is because of Distribution of microcracks and defects within the fibers along the length of fiber (coming from manufacturing and handling process). Since the number of weak spots are higher the probability of the failure at lower load is higher leading to Overall reduction of the fiber strength.
I suspect it has to do with the amount of surface per unit weight of fiber. All other things being equal, long fibers will have fewer breaks per unit weight and hence have somewhat more "useful" area per unit weight for the resin to bond with the fiber (which greatly influences strength). When you increase fiber diameter, you are decreasing the surface are per unit weight of fiber and hence reducing the area that the resin can bond with the fiber. Although individual large diameter fibers have greater tensile strength than an individual small diameter fiber of the same material; in a composite most of the strength comes from the resin to fiber surface adhesion. Similiarily in a yarn, most of the strength comes from the surface friction among fibers and not from the strength of individual fibers.
The role of interphase layer (intermediate between fiber and matrix) is a very important. We must take into account not only diameter and length of fiber, but thickness and gradient of mechanical properties of the interphase layer too.
Others have good explanation on effect of increase in fiber length. With length increase, fiber becomes main load carrying member rather than only to help load distribution. It is shown by critical fiber length equation shown in replies above.
By reduction fiber diamter, there is lower density of defects in cross-section which inceeases strength. It happens in metal wires too. In simpler language, as we approach towards thickness of single crystal, there will be huge strength.
Do an Einstein thought experiment. Imagine a carbon fiber a mile in diameter. From processing we know more anomalies occur with thicker composite processing. So more voids, cracks, ect... lower strength. As we process thinner and thinner, we get better at minimizing these issues....higher strength.
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