4 Fatigue Life Prediction of Natural Rubber in Antivibratory Applications 33 4.4.3 Discussion Even though the lifetime reinforcement is reduced at elevated temperature due to the crystallite melting, it appears that SIC effects still occur. It surely opens discussions on the crystallinity level required to induce such a reinforcement: Is the sole presence of few crystallites able to delay crack initiation? Furthermore, since the crystallinity is generally considered as null at 90◦C under quasi-static loadings at strains below 200%, the mechanisms of crystallite growth and melting under fatigue loadings remain to be explored. Considering fatigue life prediction, since temperature significantly affects the fatigue life under nonrelaxing loadings, it appears crucial to take this effect into account into modeling the fatigue life. As discussed in the introduction, this will provide a finer predictive approach and help antivibratory part developers to answer car manufacturers specification and better designing the parts. Based on these considerations, a lifetime prediction model denoted “Rbloc” has been developed; it accounts for the effect of temperature and loading ratio. It is here kept confidential due to industrial secrecy; however, a fatigue life correlation on Diabolo samples is presented in the next section in the case of variable amplitude loadings. 4.5 Fatigue Life Correlation 4.5.1 Fatigue Life Correlation Conditions The fatigue life correlation is performed by comparing the experimental fatigue life (Ni,exp) with the predicted one (Ni,calc). The prediction is carried out by calculating a damage quantity Dwith the linear Miner’s rule as D= 1/Ni,j, with Ni,j the number of cycles at crack initiation for the loading condition j obtained by the experiment. Then, the calculated fatigue life Ni,calc corresponds to the number of cycles for which D=1. The experimental fatigue life is given by the number of cycles corresponding to the drop in stiffness, according to the end-of-life criterion. For each loading condition, the experiment was carried out on 8 Diabolo samples and the mean fatigue life was considered in the analysis. Two variants of Rblocare here used to demonstrate the need of accounting for the lifetime reinforcement (i.e., the effect of the loading ratio). Variant #1 is the reference. It does not consider the lifetime reinforcement since the fatigue lives Ni,j used to access Dare calculated based on data obtained at R=0, regardless of the real loading ratio experimentally experienced. In other words, Variant #1 predicts the fatigue life by only using εmax as the damage predictor. On the contrary, Variant #2 indexes the fatigue lives based on the experimental Rdeduced from the input signal. In this case, the prediction combines the relative contributions of Rand εmax. Three signals defined by blocs of sinus and denoted Signals #1, #2, and #3 were used. Each signal is defined in terms of force by a repetition of 1730 blocs, which corresponds to 121,944 cycles per signal. They are issued from a Rainflow treatment of a road track signal acquired on a torque rod. The force level has been modified to be applicable to Diabolo samples. Typically, the amplitudes of the compression cycles were reduced in absolute value and the force was adjusted to induce a fatigue life in the order of magnitude of 105 cycles, to be representative of antivibratory applications. Since Rbloc aims at accounting for the lifetime reinforcement under nonrelaxing loadings, the signals are voluntarily highly nonrelaxing. • Signal #1 is the reference signal (see Fig. 4.2); it covers loading ratios from−0.15 to 0.35, the mean loading ratio being Rε,mean =0.0865. • Signal #2 presents the same maximum loading as Signal #2, but the minimum is increased so that the mean loading ratio increases as well: Rε,mean =0.1975. It will be used to address the effect of Rblocto account for the lifetime reinforcement, since the latter is promoted at increasing loading ratio. • Signal #3 is used to investigate high loading ratios; it covers Rfrom−0.15 to 0.7 withRε,mean =0.2131.
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