Chapter 13 Determination of Mixed-Mode (I/III) Fracture of Polycarbonate Ali F. Fahem, Vijendra Gupta, Addis Kidane, and Michael A. Sutton Abstract In many engineering applications, Mode-III type loading in the crack tip region is more common. Since loading in structures oftentimes is quite complex, the crack tip region generally experiences Mixed-Mode conditions. In this work, torsional loading experiments are performed by employing a modified spirally cracked cylindrical specimen. The cylindrical specimen used in all experiments is machined to incorporate a full revolution, spiral v-notch crack. The v-notch crack is inclined at an angle of 67.5◦ with respect to the specimen centerline to obtain Mixed-Mode (I/III) crack tip conditions under torsional loading. By combining the experimental measurements with detailed numerical simulations, the Mixed-Mode (I/III) fracture parameters for polycarbonate (PC) are quantified using an interaction integral method. The elastic-viscoplastic material response of the PC material, required for numerical simulations, is determined by performing standard tensile loading experiments. The Mixed-Mode (I/III) fracture toughness, as well as the stress intensity factors for Mode-I and Mode-III crack tip conditions are presented and discussed. Keywords Spiral crack · Mixed-Mode (I/III) fracture · Torsion load · Numerical method · Polycarbonate 13.1 Introduction Engineering applications of amorphous polycarbonate (PC) material have expanded in the last 20 years. The general mechanical behavior of this type of material is elastic-viscoplastic, which is inelastic and rate dependent [1]. Thus, understanding its behavior in both static and dynamic conditions is important for structural integrity and safe design. In fracture mechanics, the notch sensitivity, crazing phenomena, yield strength, ductile-brittle fracture transition, and fracture toughness were studied by many investigators in both static [2–6] and dynamic [1, 7] cases. However, most of these studies used the loading conditions of a single fracture mode, i.e. Mode-I, Mode-II, or Mode-III, and few of them tested Mixed-Mode (I/II) fracture [8]. Internal crazes and plastic deformation ahead of a crack tip were the most commonly observed behavior in PC materials. The craze condition, which appears to be a type of plastic deformation, is referred to as brittle fracture in the polymer [9]. Liu et al. studied the Mixed-Mode (I/III) of fracture mechanics of Polymethyl Methacrylate plastic (PMMA) and Al. 7050. They used a circumferentially notched cylindrical bar subjected to two far-field loading conditions, torsion and uniaxial tension [10]. They investigated the brittle and ductile crack behavior transition related to the fracture mode. They found that “the elastic theory predicts the crack propagation direction and the tensile-shear transition accurately for both brittle and ductile engineering materials.” Boyce, in 1986 [11], studied the rate-dependent constitutive model of glassy polymers. In this work, torsional far-field loading was applied on a cylindrical spirally cracked specimen to generate stress fields related to a Mixed-Mode condition around the crack front, including Mode-I, Mode-III, and Mixed-Mode (I/III). The fracture toughness for Mixed-Mode (I/III) conditions was calculated numerically by using the experimental data as input. The experimental data used in the simulations included the material’s behavior (elastic-viscoplastic) and the fracture load. Unlike A. F. Fahem ( ) Department of Mechanical Engineering, University of Al-Qadisiyah, Al-Qadisiyah, Iraq Department of Mechanical Engineering, University of South Carolina, Columbia, SC, USA e-mail: Ali.Fahem@qu.edu.iq; afahem@email.sc.edu V. Gupta · A. Kidane · M. A. Sutton Department of Mechanical Engineering, University of South Carolina, Columbia, SC, USA e-mail: vijendra@email.sc.edu; kidanea@cec.sc.edu; sutton@sc.edu © The Society for Experimental Mechanics, Inc. 2021 S. Xia et al. (eds.), Fracture, Fatigue, Failure and Damage Evolution, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-60959-7_13 77
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