PSI - Issue 3

G.M. Domínguez Almaraz et al. / Procedia Structural Integrity 3 (2017) 562–570 Author name / Structural Integrity Procedia 00 (2017) 000–000

567

6

The potential regression equation is: S = 415.41N -0.343 , where S is the high stress at the neck section of specimen and N the number of cycles of ultrasonic fatigue life. The nature of PMMA is viscoelastic exhibiting time dependent strain, which leads to dependence on frequency and temperature under fatigue testing (Huang et al., 2014, Cheng et et al., 1990, Osswald, 2010). Under conventional fatigue frequency ranging from 1 to 100 Hz, the fatigue crack growth (FCG) rates decrease as the fatigue frequency increases in the PMMA (Jia et al., 2006). At the ultrasonic fatigue frequency of 20 KHz carried out in this study, moderate effect of frequency is expected on the FCG rate, since the applied strain and stress are very low: 9 MPa of maximum applied stress and less than 0.1 % of strain: the strain rates present moderate effect on PMMA at very low strain and stress values (Osswald, 2010). Three principal phenomena are related to fatigue testing on polymer materials: hysteretic heating, creep and rate sensitivity (ASM International 2003, Liu et al., 2009, Jin et al., 2015). The internal damping of polymers induces hysteretic heating under cyclic loading, which is represented by the out of phase of stress and strain during the loading time: even if the area of hysteretic loops does not vary significantly with the frequency (Liu et al., 2008), the increase of frequency induces a decrease on the strain and, consequently, a decrease of the total dissipation energy of the loop. Under very high frequency of 20 KHz, low loading of 9 MPa and very low strain (less than 0.1%), the hysteretic heating was controlled by immersion of specimen in water, leading to the higher temperature of only 59% (65° C), the glass transition temperature of this material at the neck section of specimen, which allows to assume a predominant mechanical domain over the thermal domain. Concerning the creep effect, it is commonly observed on fatigue tests of polymeric materials, particularly for nonzero mean stress load ratio (R  -1) (Lin et al., 2011). The dimensions of tested specimens in this work were measured before and after the ultrasonic loading under load ratio R = -1, leading to very low variation of dimensions and, therefore, no creep effect was considered under these conditions. Furthermore, the strain rate sensitivity of PMMA has been studied by nano-indentation measurements (Jin et al., 2015), and the principal findings of this work were: a) the loading force increases as strain rate increases to attain the same displacement, as a consequence of viscous relaxation (viscous deformation decrease during the loading), which is higher with lower strain rates, b) the elastic modulus and hardness increase to an asymptotic value with the increase on strain rate. The strain rate under ultrasonic fatigue testing of PMMA was close to 6.4 s -1 , and no variation of strain rate was applied; thus, no strain rate sensitivity was studied under the last condition. 3.2 Fracture surfaces and discussion In Figure 7a, 7b and 7c are depicted the fracture surfaces for the testing specimens loaded at 5.96 MPa; whereas on Figure 7d, 7e and 7f the corresponding for 8.94 MPa. The crack initiation of PMMA under ultrasonic loading is clearly a dynamic fracture phenomenon where crack tip speed has been higher than 10 -1 m/s, which leads to assume no important effect of surrounding water on the crack initiation and propagation (Michalske and Frechette, 1980, Josserand et al., 1995). Even if micro-plastic deformation is observed on the fracture surfaces, Figure 7b and 7e, it is attributed to high frequency loading, not to plasticization at the crack tip induced by water. Different mechanisms have been cited between surrounding liquids and polymers subjected to low speed crack propagation, such as: physico-chemical interactions (Dominguez et al., 2015), surface tension, hydrogen bonding breakage, or the absorption of elastic energy by the liquid; none of these mechanisms are considered in this work, due to the crack tip speed under ultrasonic loading. A principal difference between quasi-static fracture and dynamic fracture is the stress waves on the fracture surfaces on the latter, as shown in Figures 7b and 7e (Gonzales et al., 2016); furthermore, under dynamic loading rates the stress intensity factor of crack tip increases proportionally, leading to higher resistance of material to crack propagation (Weerasooriya et al., 2006). In order to evaluate the stress intensity factor range threshold of this polymeric material immersed in water and under ultrasonic fatigue testing, a compact tension (CT) specimen was fabricated following the same procedure as the previous for the dog bone specimen, but this time with dimensions according the ASTM E647-00 Standard: W = 42 mm, B = 6 mm, h = 42 mm and a = W/3 = 14 mm. Ultrasonic loading was applied in Mode I and the crack growth was monitored with a high speed camera.