PSI - Issue 13

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

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

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resulting material properties are: Young’s modulus E = 1.3 GPa, tensile strength σ R = 24 MPa, ultimate strain R = 2.5%, Poisson’s ratio (literature value) ν = 0.40-0.42. Polystyrene is one of the so-called glassy polymers, for which the fracture behaviour often can be described with good approximation using LEFM. However, it should be noted that polystyrene, di ff erently from other glassy polymers (such as PMMA), might display some critical issues during the test. A complication with polystyrene is the di ffi culty of obtaining a really sharp crack. The only working method known to authors is to generate a flaw using fatigue cracking; in the other cases, such as razor cracking, the result might be inaccurate, because of crazing (Cotterell, 2010). It has also been observed that crazing, essentially a process of localised plastic deformation, results in a toughening e ff ect, increasing the measured toughness up to 20% (Marshall et al., 1973). We carried out one test on a single-edge notched specimen (length = 150 mm, width = 37 mm, thickness = 1.2 mm, pre-crack a = 3 mm), and applied increments of axial displacement of 10 µ m / s up to ultimate fracture instability. From the maximum force measured before rupture, we were able to compute the fracture toughness K c through well established LEFM equations. The resulting value is equal to about K c = 2.44 MPa √ m under plane stress conditions. Five specimens (length L = 60 mm, width 2 W = 40 mm, thickness t = 1.2 mm) were submitted to cutting tests with no initial cut, apart from one specimen where an initial cut of length 6 mm was present. The blade geometry is that given in Sec. 2.1, apart from one test where the blade tip was manually blunted with an emery paper. The penetration results in terms of force per unit thickness against displacement are reported in Fig. 2. The curves highlight a first stage up to D ≈ 3 mm, with a F / t vs D slope of about 30 N / mm 2 , where external work is consumed by strain energy and friction energy loss during blade indentation. This stage can be described by the indentation mechanism of a rigid wedge in an elastic solid. For instance, Truman et al. (1995), within the range of large wedge angles, showed a linear dependence of the penetration force with the penetration displacement (according to Truman et al. (1995) the resulting F / t vs D slope is of the order of 100 N / mm 2 ). After a small drop of the penetration force F / t related to the cut formation (see the energy balance G = F t − dU s tda − dU f tda , where, according to Irwin’s relation, G = G c = 4.58 N / mm), the second stage of the curves in Fig. 2, with a slope of about 1.5 N / mm 2 , is characteristic of a steady state crack propagation up to a penetration depth D equal to the blade width b = 18 mm. In the third stage, the slope of the F / t vs D curve becomes negligible. During steady state of cut propagation, considering the compressive stresses due to blade thickness onto the target plate yields a strain energy derivative per unit thickness ( dU s / dD ) / t which tends to be independent on D . On the other hand, a linear dependence occurs for the derivative of energy dissipation due to friction dU f / dD / t . From elementary calculations, considering uniaxial compression in the plate portion (of volume W × D × t ) encompassing the penetrating blade for strain energy calculation, and uniform Coulomb friction along the blade surfaces (of total area D × t ) in contact with the target material for frictional energy dissipation, one can work out a constant value of the order of 1 N / mm for the former, and a value of the order of 10 N / mm when D = 1 mm for the latter. Bearing in mind the energy balance G = F t − dU s tda − dU f tda , these values show that the contribution of strain energy is negligible in comparison to friction in the penetration curves of Fig. 2. Based on a few FE calculation, it turns out that the SIF value of full penetration of the blade in a cut of length a is K D = a = 2.65 MPa √ m and hence K c / K D = a = 0.92. This indicates that the ratio D / a is less than unity when K I , D = K c , as also observed in the experimental tests. All the test specimens were in-house prepared using a commercial silicone rubber (Zhermack Dental Elite Double), a rubber-like incompressible material featuring large deformation. The specimens were allowed at least 24 hours of resting time; temperature variations between di ff erent tests were not significant, although we have noticed some scatter in the measured forces, which might also depend on this aspect. Incidentally, viscoelastic e ff ects are rather evident for this class of materials, and it is known that higher loading rates may result in greater measured cutting forces. Literature values of friction τ f falling in the range of 70-80 kPa, can be adopted for the contact of a rigid blade with a soft matter. Two coupon specimens (length = 74 mm, width = 25 mm, thickness = 3.7 mm) were tensile tested under a dis placement control with rate of 33 µ m / s. The response is typical of a rubber-like material, and it can be well described by neo-Hookean law (Mooney-Rivlin and Odgen work equivalently well for uniaxial stretching). The resulting con- 2.3. Soft polymer