A theory crack healing in polymers

TLDR

The paper presents a theory of crack healing in polymers, outlining stages of surface rearrangement, approach, wetting, diffusion, and randomization, and introduces new concepts for strength predictions. The authors model the recovery ratio as a convolution of an intrinsic healing function Rh(t) and a wetting distribution φ(t), with Rh(t) derived from a reptation model of chain diffusion in a tube. The theory yields scaling laws for fracture stress, strain, and energy during healing, with σ,ε∼t¹⁄⁴, E∼t¹⁄², and dependence on molecular weight, temperature, and pressure, and predicts complete healing time t∞∼M³ exp(P) exp(1/T). The paper also discusses chain fracture, creep, and stress relaxation.

Abstract

A theory of crack healing in polymers is presented in terms of the stages of crack healing, namely, (a) surface rearrangement, (b) surface approach, (c) wetting, (d) diffusion, and (e) randomization. The recovery ratio R of mechanical properties with time was determined as a convolution product, R = Rh (t)*φ(t), where Rh (t) is an intrinsic healing function, and φ(t) is a wetting distribution function for the crack interface or plane in the material. The reptation model of a chain in a tube was used to describe self-diffusion of interpenetrating random coil chains which formed a basis for Rh (t). Applications of the theory are described, including crack healing in amorphous polymers and melt processing of polymer resins by injection or compression molding. Relations are developed for fracture stress σ, strain ε, and energy E as a function of time t, temperature T, pressure P, and molecular weight M. Results include (i) during healing or processing at t<t∞, σ,ε∼t1/4, E∼t1/2; (ii) at constant t<t∞, σ,ε∼M−1/4, E∼M−1/2; (iii) in the fully interpenetrated healed state at t = t∞, σ,ε∼M1/2, E∼M; (iv) the time to achieve complete healing, t∞ ∼M3, ∼exp P, ∼exp 1/T. Chain fracture, creep, and stress relaxation are also discussed. New concepts for strength predictions are introduced.