Hysteresis loops, fatigue testing

For non-transparent specimens, as shown by Bucknall and Stevens useful information relative to the deformation mode can be obtained by recording hysteresis loops as a function of cycles. Figure 6 shows hysteresis loops obtained at 0.2 Hz at various N values for PS tested at a stress amplitude of 24.1 MPa and Fig. 7 for HIPS tested at 17.2 MPa. For PS, with Nf = 1,451 cycles, there is no detectable change in loop area at this stress amplitude up to the final cycle. This illustrates the highly localized nature of the fatigue-induced damage zone in PS and indicates that, for this polymer, hysteresis loop observations are not an effective method for detecting craze... 

For a HIPS sample tested at a stress amplitude of 17.2 MPa and a frequency of 0.2 Hz, hysteresis loops taken at various cycles (Fig. 7) indicated that craze initiation was first observed for this sample after about 20 cycles, while 283 cycles were required to fracture. For similar fatigue tests carried out at the lower frequency of 0.02 Hz, the cycles to fracture were decreased (from 283 to 64) and loop asymmetry and craze formation began sooner, at about 1-2 cycles. The changes produced in hysteresis loops with cycling are shown in Fig. 19. With decrease of test frequency reduces, the entire S-N curve shifts to the left as shown by Fig. 18, and, because of the increased time for each cycle, fatigue induced craze initiation occurs earlier in the specimen lifetime. 

Figure 12.5. Hysteresis loops developed during fatigue tests of ABS and HIPS [BucknaU, 1988].

The plastic strain energy density can be physically interpreted as the energy of distortion associated with the change in shape of a volume elanent and is related to failure, particularly under conditions of ductile behavior, as it often occurs in many of the polymeric materials submitted to cyclic mechanical solicitation (Kanchanomai and Mutoh, 2004). According to the mathematical model proposed by Morrow (American Society for Testing and Materials, 1965), the strain energy density can be evaluated numerically as the inner area of the saturated hysteresis loop for the uniaxial fatigue experiments (Fig. 7.6), and is expressed mathematically as ... 

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