YIELDING PROCESS - Fractal Mechanics of Polymers - page 60

where m and n are exponents in the Mie equation [27] setting the intercon-
nection between the interaction energy and distance between particles. The
value of parameter 1/mn can be expressed via the Poisson's ratio, n [27]:

1 12

6(1

- n

n

. (4.18)

=

mn + )

From the Eqs. (2.20) and (4.18) it follows [18]:

1
mn

s
g== .

Y

(4.19)

E

FIGURE 4.8 The stress - strain (s - e) diagrams at loading up to failure (1)
and at cyclic load exertion (2-4) for EP-2: 2 - the first loading cycle; 3 - the
second loading cycle; 4 - the third loading cycle [39].

The Eq. (4.19) gives the strain value with no regard to viscoelastic effect,
that is, diagram s - e deviation from linearity behind the proportionality
limit. Taking into account that tensile strain is twice greater, approximately,
than the corresponding shear strain [42], theoretical yield strain

T

e , cor-
responding to the stability loss by a solid, can be calculated. In Fig. 4.9 t he
comparison of experimental e Y and

e yield strain magnitudes is fulfilled.

T