A comparison between K $K$ and G $G$ approaches for a viscoelastic material: the case of environmental stress cracking
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A comparison between K and G approaches for a viscoelastic material: the case of environmental stress cracking of HDPE Marco Contino1 · Luca Andena1 · Vincenzo La Valle1 · Marta Rink1 · Giuliano Marra2 · Stefano Resta2 Received: 4 February 2019 / Accepted: 5 September 2019 © Springer Nature B.V. 2019
Abstract According to linear elastic fracture mechanics the stress intensity factor and the energy release rate are two fracture parameters linked by the elastic modulus and Poisson’s ratio of the considered material. This concept has been extended to the analysis of linear viscoelastic materials, by introducing time-dependent quantities; it is also used for nonlinear viscoelastic polymers, even if its accuracy in this case is still an open question. In this work the slow crack growth and the environmental stress cracking resistance of two high-density polyethylene grades were investigated, differing for their molecular weight distribution and fracture resistance. The description of the fracture behavior of the two materials provided by the stress intensity factor or the energy release rate turned out to be equivalent, despite the nonlinear mechanical behavior exhibited by the two polymers. Moreover, a time-dependent effective modulus, related to the two fracture parameters, was evaluated: its value was in good agreement with the modulus experimentally determined from tensile tests. A constant relevant effective strain was found despite the different testing conditions (i.e. applied mechanical loading, temperature and presence of an active environment), its value being equal for the two considered polyethylenes. Keywords Fracture mechanics · Pseudo-elastic approach · Nonlinear mechanical behavior · Slow Crack Growth · Environmental Stress Cracking · HDPE
1 Introduction The stress intensity factor K describes the stress field around a crack within an elastic body; the energy release rate G in turn is the elastic energy change caused by an increase of the crack area. These two parameters, which have been at first defined within the linear elastic fracture mechanics (LEFM) theory, can be used to describe the fracture behavior of many
B M. Contino
[email protected]
1
Dipartimento di Chimica, Materiali e Ingegneria Chimica “G. Natta”, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
2
R&D Division, Fater S.p.A., Via Ardeatina 100, 00071 Pomezia, Rome, Italy
Mech Time-Depend Mater
materials, providing a useful fracture criterion. As proved by Irwin (1957), according to the LEFM theory these two fracture parameters can be related following their two equivalent approaches; for plane strain conditions, the well-known relationship holds: G=
K 2 (1 − ν 2 ) E
(1)
in which E and ν are the elastic modulus and Poisson’s ratio of the considered material, respectively. The stress intensity factor and the energy release rate are used as fracture parameters also within several viscoelastic theories, whose best-known examples are those proposed by Schapery (1975a,b,c) and by Williams and Marshall
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