Homogeneity uniaxial strength

Fig. 8.15. Correlation of the homogeneity of segment lengths (narrow relative length distribution) with uniaxial strength [49, 50, 541.

The strength properties of solids are most simply illustrated by the stress-strain diagram, which describes the behaviour of homogeneous brittle and ductile specimens of uniform cross section subjected to uniaxial tension (see Fig. 13.60). Within the linear region the strain is proportional to the stress and the deformation is reversible. If the material fails and ruptures at a certain tension and a certain small elongation it is called brittle. If permanent or plastic deformation sets in after elastic deformation at some critical stress, the material is called ductile. 

In the following, the relationship between fracture statistics and defect size distribution is discussed for the simple case of tensile tests (uniaxial and homogeneous stress state) on a homogeneous brittle material. The tests are performed on specimens of equal size. It is assumed that the volume of the specimens is V = V. The number of tested specimens (the sample size) isX. In each test the load is increased up to the moment of failure. The strength is the stress at the moment of failure. In each sample the strength values of the individual specimens are different, i.e. the strength is distributed. 

In actual practice, the fibers must overlap each other, even if all are oriented in the same direction, in order to provide homogeneity within the part. At any given failure plane, all the fibers will then be able to share the mechanical stress equally. In practice, maximum utilization of short fibers occurs when the fibers have an aspect ratio that is ten times the critical aspect ratio [35]. Under these conditions, uniaxially oriented short fibers can have tensile strengths equal to 95% of that of the continuous fiber uniaxially oriented composites. In randomly oriented fiber filled composites, the tensile strength is less than one third that of composites in which fibers are uniaxially oriented. 

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