Extension strain

Thus, the force resultant produces twisting of the iaminate as evidenced by the K y term in addition to the usuai normal strains (extension) and (contraction) as readily seen in Figure 4-9a. 

Strain=(Extension during test/Initial extension) x 100... 

In Figure 21.8, a softening temperature for the polystyrene endblock is shown as a function of endblock molecular weight (ranging from about 6000 to 30000). The softening temperature is characterized as the onset of test specimen creep (in a small-strain dynamic mechanical test in tensile mode), the creep point occurring when strain extension becomes considerable in order to maintain the appropriate stress level to continue the test. This softening temperature lies below the measured Tg, and it is an indication of the... 

Because rubbery materials are virtually incompressible in bulk, the value of Poisson s ratio is close to 0.5. Young s modulus E is therefore given by 3G to good approximation however, the predicted relation between stress and tensile strain (extension), e (=X - 1), is linear only for quite small extensions (Figure 1.8), so that Young s modulus is applicable only for extensions or compressions of a few percent. 

One objective of the dynamic testing of materials and components, in addition to determining the number of cycles to break, is to establish the causes and pattern of failure. Normally, in such tests the stress and strain (extension) are measured and an elastic modulus derived from these values. However, this can be only the initial step in the direction of developing a coniplete description of the failure pattern. This analysis is based on the work by F. Orth and G. W. Ehrenstein Kassel [300]. 

Example Thin film undergoing plane strain extension... 

For the case of thin films being deformed plastically under the action of equi-biaxial states of stress, the stress history follows a straight line path in stress space. In some of the experimental methods for study of thin film plasticity that have been described in this section, the in-plane stress components are not equal, in general, and the trajectory in stress space during deformation is not a straight line. Consider a film material being deformed under plane strain extension in the a —direction the plane strain constraint is enforced in the. j—direction. The elastic modulus is E and the Poisson ratio is Pf = 0.3. The initial yield locus for the material in terms of tensile yield stress stress (Tyf is the Mises condition. The material... 

Fig. 7.34. The trajectory in stress space resulting from plane strain extension of an elastic-plastic film. The film material is assumed to undergo isotropic linear hardening, as described in the text.

Integration of the differential equations from first yield for an elapsed time of t = 1 yields the result shown in Figure 7.34. The dash curve is the initial yield locus. Note that the stress trajectory deviates sharply from linearity once yielding begins, even though the state of deformation is always uniaxial plane strain extension. 

Furthermore, the total strain (extension) of the element is additive (i.e., the sum of the strains in the spring and dashpot) ... 

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