Biaxial steady elongation

Small-amplitude oscillatory shear Uniaxial steady elongation Biaxial steady elongation Planar steady elongation Elongational stress growth... 

Best overall fit of the Larson model (left), and the Phan Thien-Tanner model (right) to data for a high density polyethylene (circles) in step shear (a), in steady elongation (b), and in step biaxial extension (c). Adapted from Khan and Larson (1987). 

In Chapter 7 of Volume 2, we present the rheological response of polymeric liquids in steady-state biaxial elongational flow. 

For Steady-State equal biaxial elongational flow, the relative deformation gradient tensor F,(r, t) can be written, with the aid of Eqs. (2.16) and (2.57), as... 

For steady-state equal biaxial elongational flow we have (see Appendix 3F)... 

The two functions and 2 depend on the parameter b as well as on the elongation rate e in steady shear-free flows. When b = 0, the function 2 is zero, and is replaced by the symbol tj, which is called the elongational viscosity . The elongational viscosity describes the resistance to elongational flow if 8 is positive and the resistance to biaxial stretching if e is negative (the terms extensional viscosity and Trouton viscosity have also been used for ). 

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