PSI - Issue 13

A. Spagnoli et al. / Procedia Structural Integrity 13 (2018) 137–142 A. Spagnoli et al. / Structural Integrity Procedia 00 (2018) 000–000

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Fig. 2. Experimental cutting resistance curves of polystyrene specimens with no initial cut. Two tests with a sharp blade and a manually-blunted blade, respectively, are considered.

stant of the neo-Hookean law (Rivlin and Thomas, 1953) is c = µ/ 2 = E / 6 = 0.23 MPa, being µ the shear modulus of the material. In soft materials, one of the principal issues is how to define the fracture resistance or fracture toughness. As the zone of large deformation might be significant, LEFM approximation generally does not apply, and thus the critical stress intensity factor, commonly used in brittle fracture, cannot be defined. Instead, the energetic approach is more appropriate, which leads to the definition of a critical energy release rate G c . The definition of a critical fracture energy for soft materials originates from the pioneering works of Rivlin and Thomas (1953), who formulated the concept of a material critical energy, which was then termed tearing energy . Several experimental configurations have been proposed in order to measure the tearing energy in soft materials. In the present work, we have used the so-called single-edge crack test, according to which the critical energy is defined as (Greensmith, 1963): where W ( λ c ) is the strain energy density of an uncracked sample of the material, and λ c is the critical stretch at which the material tore apart, which depends on the initial length of the crack a . An alternative method is presented in McCarthy et al. (2007), where the fracture resistance is computed from a cutting experiment: the compensation for the frictional e ff ects is obtained by running the blade twice, the first time in the flawless specimen and the second following the open cut. Four coupon specimens (length = 78-88 mm, width = 24.8-25.9 mm, thickness = 4.2-4.6 mm) with an edge crack ( a = 1.8, 3, 4, and 5 mm) for tearing tests were prepared. Tensile tests were performed under displacement control with rate of 33 µ m / s (see experimental curves in Fig. 3). Fracture energy, calculated using the method of (Greensmith, 1963) G c , turns out to be in the range 0.89-1.16 N / mm with a mean value of 1.02 N / mm. According to Irwin’s relation (bearing in mind the questionable validity of this relation in the presence of large strain), we have a mean value K c = 37.52 MPa √ m under plane stress conditions. Twenty-eight cutting tests on silicone rubber plates (length L = 56 mm, width 2 W = 40 mm, thickness t = 4.4 mm) were performed, considering di ff erent penetration rates (ranging from 8 to 100 µ m / s) and initial cut lengths (including also cases with no initial cut). Some experimental penetration curves of force against displacement are reported in Fig. 4. After an initial stage up to D ≈ 4 mm, the curves highlight a subsequent stage with a F / t vs D slope of about 0.1 N / mm 2 , where external work is consumed by strain energy and friction during blade indentation. This stage terminates when the blade tip hits the initial cut end, i.e. when D ≈ 24 mm. At this point, an additional amount of energy has to be given to the system by the external force to propagate the initial cut. This energy jump corresponds to a force increment of about 0.6 N / mm. G c = 6 √ λ c W ( λ c ) a (1)