Study of the kinetics of arterial crack growth in polymers I. Development of through cracks in thin polymer films under static tension

Abstract

1. The laws governing the development of arterial cracks are determined by thermal-fluctuation processes taking place at the tips of the cracks. This is indicated by the form of the equation (Eq. (4)) giving the rate of crack growth. Any description of the rupture process should therefore be based on the concept of rupture as the gradual accumulation of elementary thermal-fluctuational breakages of the interatomic bonds rather than a critical, catastrophic event which occurs on reaching specific limiting conditions. 2. A study of the kinetics of crack growth provides greater information regarding the rupture process and the physical meaning of the coefficients in Eqs. (4) and (5) than a mere study of such integrated characteristics of rupture as the creep life in relation to the test conditions. 3. The accumulation of breakages of the interatomic bonds at the tip of the crack is closely associated with the relaxation (deformation) processes, which change the structure of the material and lead to its hardening (i.e., to a change in the coefficient α in (4) or γ in (5)). Further study of the rupture kinetics at all stages of development, with due allowance for the part played by relaxation phenomena, should provide a complete picture of the rupture process, starting from the formation and union of the submicro-and micro-cracks and ending with the propagation of the arterial cracks; it should also provide valuable information as to the mutual relationship between deformation and rupture. 4. Many research workers are even at the present time attempting to describe the time dependence of strength in terms of the “Griffith” concepts of crack propagation by introducing a formal dependence of the effective surface energy in the Griffith formula on the test temperature and rate of crack growth [15, 22, 34–36]; we now see our way to the matching of these “modified Griffith concepts” with the concepts of the kinetic theory of strength. Matching of this kind may well be achieved by studying the mutual relationship between the energy required to form unit area of new rupture surface and the energy (γσ) in Eq. (5), characterizing the work performed by the external forces in producing rupture. A study of this mutual relationship may constitute the subject for later research.