In this paper, the theories of the proportional limit and yielding based on the small deformation mechanism in glassy state, discussed in the earlier issue, are formulated and compared with the experimental results obtained in part I.
A theory of proportional limit is formulated in connection with the following two cases.
First, it is assumed that the proportional limit is observed on a load-elongation curve when the average rotational angle or average strain of the segments reaches a critical value.
Second, it is assumed that the secondary bond supporting the segment, in which the strain or rotational angle has reached a critical value, begins to break, the proportional limit is observed when the proportion of the broken segments reaches a certain value.
Next, it is found that the following equations are applicable to the explanation of the yield point in the small strain region. where
ezp is the strain of proportional limit;
eszy the yield strain in the small strain region; σ
ys the yield stress in this region;
k a constant,
s the average inter-molecular slip at the yield point, and
E Y'oungs modulus.
To the yield stress in the small strain region, another theoretical equation is introduced. This treatment is based on the following assumptions:
1) All the segments in which strain has become larger than a critical value,
eay have an equal tension,
pay.
2) The yield point is observed, when the proportion of these segments reaches a certain value. Finally, the yield stress in the large strain region (the primary yield stress of high orientation samples) is approximately expressed by the equation given below. where
c0 is a constant, θ the angle between the fiber axis and segmental axis, and
py the average yield strength of molecular chains and is experimentally given by a exponential function of orientation factor.
In addition, the experimental relationship between the logarithmic primary yield stress and the Young's modulus is linear, and the elastic limit and the yield point in glassy state fairly depend upon the orientation of amorphous molecular chains.
View full abstract