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Constitutive equations of crack layer growth
Author(s) -
Kadota K.,
Chudnovsky A.
Publication year - 1992
Publication title -
polymer engineering and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.503
H-Index - 111
eISSN - 1548-2634
pISSN - 0032-3888
DOI - 10.1002/pen.760321607
Subject(s) - polyethylene , materials science , constitutive equation , polymer , differential equation , thermodynamics , process (computing) , mechanics , composite material , mathematical analysis , mathematics , computer science , physics , finite element method , operating system
Many engineering polymers such as polyethylene undergo cold drawing. Consequently, a slowly growing crack in polyethylene is preceeded by a process zone consisting of drawn material. The crack and the process zone are considered to be a single entity called the Crack Layer (CL). The equilibrium size and shape of the process zone can be determined by minimizing the Gibbs potential of the material. The result is a system of integro‐differential equations which does not have analytic solutions. To simplify the problem, the analysis is limited to the “thin” process zones which have been observed frequently in many polymers. Using thermodynamics, the driving forces for the crack and process zone growths are expressed in terms of the partial derivatives of the Gibbs potential with respect to corresponding variables (the crack length and the process zone size). Kinetic equations for the CL growth are proposed. These equations take the form of Onsager‐type linear relations between the rates of crack and process zone growth and the driving forces. The equations are good descriptions of the experimentally observed nonmonotonic CL growth in polyethylene. CL stability analysis is used to obtain estimates of lifetimes.