PSI - Issue 21

2

Author name / Structural Integrity Procedia 00 (2019) 000 – 000

Amir H. Benvidi et al. / Procedia Structural Integrity 21 (2019) 12–20 Peer-review under responsibility of the 1st International Workshop on Plasticity, Damage and Fracture of Engineering Materials organizers 13

Keywords: Rubber components, Rounded V-shaped notch, Averaged strain energy density criterion

1. Introduction Rubbers are a group of hyper-elastic materials that have a different structure than some other materials like metals and composites. The existence of long polymeric networks having a high flexibility and completely elastic deformation are among the most important features of this type of materials (Erman et al., 2013a, b; Treloar, 2005). However, existence of any flaw like a crack or notch can reduce the load bearing capacity of rubbers. To assess the fracture of rubber-like materials, some criteria have been provided by researchers so far. The generalized Griffith’s criterion is one of the energy -based criteria which is extended to be used in rubber by Rivlin and Thomas. According to this criterion, the amount of critical energy per unit area is taken as an indicator of crack growth (Rivlin and Thomas, 1953). The J-integral, which was presented firstly by Rice (Rice, 1968), is another criterion based on the energy method. This criterion is applicable to both linear and nonlinear elastic materials. Hocine et al. evaluated the critical value of the J-integral criterion for single-edged and double-edged cracked rubber samples under mode-I loading (Hocine et al., 2003). In another study performed by Hamdi et al. (2007), elastomeric samples with central crack under mixed-mode loading condition were analyzed. Their results showed that the critical value of the J-integral is independent of the crack angle, and therefore this value can be used as a criterion for the start of crack growth in elastomeric materials. However, this criterion does not accurately predict the angle of crack growth (Hamdi et al. 2007). Regarding the fracture of elastomeric parts subjected to multiaxial loading, some studies have been performed. For instance, Hamdi and Mahjoubi (2015) proposed a new criterion based on the equivalent strain, using polar coordinates in the trisectrix plane under biaxial loading. Moreover, a strain-based criterion based on the generalized Podgórski – Bigoni – Piccolroaz formulation was developed very recently by Rosendahl et al (2019) in order to analyze the failure of incompressible hyperelastic elastomers subjected to multiaxial loading. The strain energy density (SED) criterion, which had been previously presented by Sih and Macdonald (1974) for brittle materials was adopted by Hocine et al. (2002) for rubber materials. Their finding on specimens with double edge notch and pure-shear samples revealed that the distribution of the SED around the crack tip is independent of the crack length and the geometry of the rubber samples under mode-I loading. Accordingly, the rupture of rubber specimens with central cracks under mixed-mode loading conditions was investigated by Hamdi et al. (2007). Their results showed that the minimum value of SED is independent of the initial angle of the crack. However, the critical value of SED has a rising trend with increasing the crack angles, and has not been constant. Therefore, the SED criterion in this case was not applicable. The effective stretch (ES) criterion that is based on the physics of rubber materials has recently been presented by Ayatollahi et al. (2016). This criterion is based on two assumptions: the existence of a damage zone around the crack tip and the uniaxial state of stress fields near the crack apex. According to this criterion, when the rubber chains reach their maximum elongation (namely locking stretch), there is no possibility of further elongation for the chains and they are broken. Heydari-Meybodi et al. adopted the ES criterion for mixed-mode loading of cracked rubbers (Heydari Meybodi et al., 2017b). The averaged strain energy density (ASED) criterion is another energy-based criterion, firstly adopted by Berto to evaluate the rupture of rubber specimens weakened by sharp V-shaped notches (Berto, 2015). Due to the nonlinear behavior of the rubber material, he studied the ASED criterion using the nonlinear finite element method. Through the intersection of the SED diagram in terms of different radii of control volume for two different geometries, he estimated the main parameters of this criterion (i.e. critical radius and critical SED) for the corresponding rubber samples. The results have shown that the density of strain energy in the control volume around the stress concentration region is a function of the critical radius. Subsequently, Heydari-Meybodi et al. (2018) characterized a new method for determining the main parameters of the ASED criterion in the case of hyperelastic materials. This method is mainly based on the uniaxial nature of the stress field near the crack tip. In addition, they studied the fracture of rubber-like specimens containing a mixed-mode crack by using the ASED criterion (Heydari-Meybodi et al., 2017a).