showing yielding, necking, strain hardening and eventually ductile failure; (3) hard
and strong, such as hard PVC and the blend of PS, eventually ductile failure; (4) soft
and tough, such as soft PVC and rubbers; (5) soft and weak, such as aqueous gels.
Shear yielding is the beginning of flow in the solid for permanent deformation,
which locates at the maximum point, i.e. at ds/de¼0. Normally we use the
engineering stresss(F/A 0 ), with the reference to the initial sectional areaA 0.
Upon stretching deformation, the sectional area will be changed; therefore, the
more exact characterization is the true stressF/A¼s(1þe). On the true stress
versus strain curve, the point of tangency extrapolated frome¼1 of the horizon-
tal axis corresponds to the yielding point, and the true stress at this point is the
yielding stress. The plot for the true stress versus the strain is calledConsidere construction(Considere 1885 ).
For semi-crystalline polymers, the necking develops from a local area after shear
yielding, as illustrated in Fig.6.19. This process eventually makes theductile
failureafter absorbing a great amount of energy. Men and coworkers pointed out
that, before shear yielding, the hard elastic network formed by polymer lamellar
crystals affords the dominant elastic strain, and the entanglement network of
amorphous polymers is released only after the lamellar crystals break into small
crystalline blocks (Men et al.2003b). The yielding starts when this breaking
happens, and meanwhile polymer chains are drawn out of their folded states.
Since the folding length in the initial lamellar crystals is nearly constant, the
drawing process does not need larger stress after the yielding, and the sample
displays the necking behavior under almost constant stresses. After reaching
Fig. 6.19Illustration of microstructure evolution upon cold-drawing of semi-crystalline polymers
120 6 Polymer Deformation