Ultinite Mechanical Properties of Polymer Fibers a Theoretical Approach
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ULTINITE MECHANICAL PROPERTIES OF POLYmER FIBERS A THEORETICAL APPROACH
Yves
Termonia and Paul
Smith
Research and Development Department Experimental Station Inc. I. du Pont de Nemours and Co., Wilmington, Delaware 19898
Central E.
Abstract A stochastic Monte-Carlo approach, based on the kinetic theory of fracture, has been used to study the axial maximum tensile strength of polymer fibers. The approach is entirely microscopic and the inhomogenous distribution of the external stress among atomic bonds near the chain ends is explicitly taken into account. Both primary and secondary bonds are assumed to break during fracture of the polymer fiber. The approach has been applied to perfectly oriented and ordered polyethylene and poly(p-phenylene-terephthalamide) fibers. The influence of the molecular weight, temperature ard strain rate on the axial tensile properties are presented. I.
INTRODUCTION
In this paper, we describe a new theoretical approach to explore the limits of the tensile strength of fibers comprised of perfectly oriented and packed polmner molecules of finite molecular weight. The model, which was introduced elsewhere [1,2], is based on the kinetic theory of fracture [3,4]. It is entirely microscopic and takes into account the inhomogeneous distribution of stress among atomic bonds near chain ends. The model is similar to that forwarded by Dobrodumov and El'yashevitch [5], but it is more complete since both primary and secondary bond breakages are taken into account. Our approach has been applied to perfectly oriented and ordered polyethylene (PE) and poly(p-phenylenetercphthalamide) (PPTA) fibers. As such, the present study deals with the maximum tensile strength of defect-free polymers. The influence of the molecular weight, temperature and strain rate on the tensile properties are presented. A few conments are devoted to long term properties.
II.
MODEL
The model is based on the kinetic theory of fracture [3,4]. According to that theory, a bond in the absence of external mechanical forces breaks whenever it becomes excited beyond a certain level, U, the activation energy of the bond. For chains in the process of being strained, the activation energy barrier is linearly decreased by the local stress [3,61. Mat. Res. Soc. Syup. Proc. Vol. 79. 1987 Materials Research Society
398
Thus, in bond i is
the presence given by
of
stress,
the
vi = T exp[ (-Ui + Biai)/kT where T is the thermal vibration (absolute) temperature, Bi is an linear dimension is of the order of the local stress
rate of breakage
of a
I
(1)
frequency, T is the activation volume whose the bond length and ai is
(2)
ri = Ki ei Here, Ki and ej are respectively.
the elastic constant and the local
strain,
The above kinetic model has been simulated on a 3-dimensional (x,y,z) array of 6x6x1000 nodes. A 2-dimensional representation of the array of nodes is given in Fig.
I.
y
Figure for the
1. Two-dimensional representation of the array of nodes and of bonds. K 1 and K2 are the elastic constants primary and for the se
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