PSI - Issue 21

Amir H. Benvidi et al. / Procedia Structural Integrity 21 (2019) 12–20 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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A review of literature reveals that no study has been devoted so far regarding the rupture of rubber parts with a blunted V-shaped notch. Indeed, among various types of discontinuities, V ‐ notches are frequently found in engineering structures. Unlike cracks which are usually undesirable objects, notches are often deliberately introduced in the components due to the requirements of practical design. Moreover, V-notch configurations are frequently encountered in engineering components due to manufacturing process, design optimization, and so on (Cheng et al., 2016). However, the high stress gradient that exists near the notch tip can considerably reduce the load bearing capacity and strength of structural components. Therefore, as a stress raiser in the structures, the notch apex is a likely zone for crack initiation and eventual failure of the structure. As a result, because of the frequent existence of notches in engineering structures, the investigation of an appropriate criterion for rupture prediction of specimens containing notches is still an active field of research. The importance of criterion presentation is multiplied when the goal is to present a criterion for materials having non-linear behaviors. This complex situation exists for elastomers and rubbers due to their concurrent geometry and material non-linearities. In this research, the ASED criterion is adopted to assess the rupture of blunted V-shaped notches through both experimental and numerical analyses.

Nomenclature a

Notch depths

d Notch tip diameter E Elastic modulus of material Mode-I fracture toughness Critical radius of control volume ̅ Different radii of control volume Critical value of SED ̅ Mean value of strain energy density Ultimate tensile strength Poisson’s ratio Final stretch in a uniaxial tensile test Notch opening angle 2. ASED criterion for hyperelastic material

According to the ASED criterion, the value of strain energy averaged in a finite volume around the stress concentration region could be utilized as a criterion for fracture assessment of parts (Lazzarin and Zambardi, 2001). Lazzarin et al. studied the behavior of elastic materials under static and fatigue loading conditions. The results of their research on linear elastic materials showed that under the static and fatigue loading conditions, the limited amount of energy in a small volume around the tip of the notch is effective on the fracture of parts. Based on the ASED criterion, failure occurs when the mean value of strain energy density, ̅ , over the control volume around the stress concentration region, , is equal to critical value of SED, , (Lazzarin and Zambardi, 2001). The critical value of SED for brittle and quasi-brittle materials with linear elastic behavior can be obtained as follows: 2 2 t c W E   (1) It should be noted that the amount of does not depend on the sample geometry (Lazzarin and Berto, 2005). The value of is another parameter of this criterion which for brittle material is independent of geometry but it depends on the condition of loading. The shape of the critical volume for specimens containing crack, sharp V-notch and blunt V-notch is a circle, a sector of circle and a crescent shape, respectively. The critical radius for cracked brittle samples is obtained according to the following relations (Berto and Lazzarin, 2009):