Strain defined

This is normally very high and very little can be done by the manufacturer to vary it. An important related property is the critical strain, defined as the... 

The mechanical concepts of stress are outlined in Fig. 1, with the axes reversed from that employed by mechanical engineers. The three salient features of a stress-strain response curve are shown in Fig. la. Initial increases in stress cause small strains but beyond a threshold, the yield stress, increasing stress causes ever increasing strains until the ultimate stress, at which point fracture occurs. The concept of the yield stress is more clearly realised when material is subjected to a stress and then relaxed to zero stress (Fig. Ih). In this case a strain is developed but is reversed perfectly - elastically - to zero strain at zero stress. In contrast, when the applied stress exceeds the yield stress (Fig. Ic) and the stress relaxes to zero, the strain does not return to zero. The material has irreversibly -plastically - extended. The extent of this plastic strain defines the residual strain. 

When using the generalised Hooke s law strain energy function there are a number of possible strain definitions that can be used depending on the situation. When material deformation is very small the infinitesimal strain approach is a valid approximation with the strain defined as... 

The reaction of a material to a tensile stress is to stretch or elongate. This is measured as tensile strain, defined as the elongation or increased length per initial length. Strain is a dimensionless unit that is usually expressed as a percent (percent elongation). 

Here, e. and Epj are homogeneous inelastic strains defined in the respective phase domains L and are dimensionless constants satisfying + /ps Lj =1(1 the identity tensor of rank 4) M, and Mj are constants having the same dimension as the elastic modulus and satisfying +/pszM2 = 0 N, and Nj are also dimensionless constants relating to... 

This value has been used as abscissa for the stress/strain curve in fig.5. Fig.6 shows a corresponding curve obtained without change of strain path. It shows the well-known stages HI, IV and V. Fig.5 has been similarly divided into stages B, C and D. Careful investigations of microstructure [3,11] have shown that stages B, C and D correspond to II, IV and V. Comparison of the onset strains shows that the strain defined by eq.(4) is much less efficient to produce the corresponding structures. It should therefore be corrected by an efficiency factor r so that... 

The ratio of shear stress to rate of strain defines the viscosity as... 

It is now possible to compare the changes in interfacial area produced in unidirectional shear, equation (11.7), uniaxial elongation, equation (11.19) and planar extension, equation (11.20). However, as pointed out be Cheng, this comparision needs to be done on a rational basis. For example, it is possible to examine the area ratios at equal strain defined by y, = Te = 7pe and it is clear from this viewpoint that effectiveness in generating new surface area increases in the order simple shear, uniaxial extoision to planar extension. It is clear that at large strains the advantage is heavily in favour of the extensional flows. If a value of strain equal to 10 is considered (Mohr states that most shear mixers exceed this value) then the area ratios SISn are given in Table 11.1. However,... 

The extension is converted to strain, defined as the extension, Al, divided by the original length, lo. 

The authors calculated the strain hardening intensity values as a measure of melt strength using the ratio of riE.noniinear/ HE,linear ( )- The slope of log versus Hencky strain defines the strain hardening intensity. As seen in Fig. 7.42 (a), effective improvements in melt strength required over 50 wt% PBSA which decreases the tensile modulus. 

A common example is to identify r with the cumulated plastic deviatoric strain defined... 

---