78 A. F. Fahem et al. the traditional methods, the spiral crack specimens were used to measure Mode-I fracture toughness of the static and dynamic conditions as well [12–15]. Two types of specimens were tested. Dumbbell-shaped specimens are tested in uniaxial tension while spiral v-notch spiral crack specimens are used to determine the Mixed-Mode (I/III) fracture toughness. The uniaxial tension test provides the PC material e\response used in finite element modeling to calculate fracture toughness parameters for PC. 13.2 Determination of Material Behavior of PC 13.2.1 Specimen Preparation and Experimental Setup Polycarbonate is known to be an elastic-viscoplastic material. Dumbbell-shaped specimens of Type IV, as shown in Fig. 13.1, are used in uniaxial tension experiments, as per American Society for Testing and Materials (ASTM) D638–14 [16]. The specimen is prepared by machining to the size shown in Fig. 13.1. The experiments are performed with a loading rate of 1 mm/min. The load is acquired from the load cell mounted on the load frame, while the strain is measured using 2D-DIC (Digital Image Correlation). The in-plane strain components are acquired using Vic-2D software, a 2D-DIC software from Correlated Solutions Inc. [17, 18]. 13.2.2 Uniaxial Tension Response The engineering stress versus strain curve is shown in Fig. 13.2. The load versus deformation was recorded up to failure. In general, PC shows quasi-ductile behavior with elastic and viscoplastic conditions. The elastic modulus and Poisson’s ratio of the material were calculated using the linear elastic part of the stress-strain curve and are mentioned in Table 13.1. The material yielded at 63.7 MPa. The true stress versus strain curve can be obtained from the engineering stress-strain curve and is shown in Fig. 13.3. The behavior of the PC can be divided into four stages, as shown in Fig. 13.3. Stage one starts from point O and ends at point A. This stage has a linear elastic behavior with initial hardening developing near point, the initial yield stress of the material. Segment AB represents Stage two. In this region, the stress drops and it is also referred to as the softening stage. Stage three, from point B to point C, is the section with maximum extension. In this stage the material exhibits viscoplastic behavior (orientation hardening). Point C corresponds to the ultimate tensile stress. Stage four is the last stage where the stress drops by small amount below the ultimate tensile stress. This stage ends at the failure denoted by point D. Thus, it is seen that PC exhibits quasi-ductile behavior with elastic and viscoplastic behavior. The plastic strain was obtained by decomposing the strain into elastic and plastic strain components. The true stress-plastic strain data along with the material properties shown in Table 13.1 were input into the finite element model. Abaqus, Finite Element Analysis (FEA) was used for all the numerical simulations in this study. A numerical simulation was performed on a uniaxial test specimen (model without crack is shown in Fig. 13.4a) to verify that the finite element output gave the same Fig. 13.1 Dumbbell-shaped specimen (ASTM D638–14, Type IV)
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