Finite Element Modeling and Critical Plane Analysis of a Cut-and-Chip Experiment for Rubber
Rubber surfaces exposed to concentrated, sliding impacts carry large normal and shearing stresses that can cause damage and the eventual removal of material from the surface. Understanding this cut-and-chip (CC) effect in rubber is key to developing improved tread compounds for tires used in off-road or poor road conditions. To better understand the mechanics involved in the CC process, an analysis was performed of an experiment conducted on a recently introduced device, the Instrumented Chip and Cut Analyzer (ICCA), which repetitively impacts a rigid indenter against a rotating solid rubber wheel. The impact process is carefully controlled and measured on this lab instrument, so that the contact time, normal force, and shear force are all known. The numerical evaluation includes Abaqus finite element analysis (FEA) to determine the stress and strain fields during impact. The FEA results are combined with rubber fracture mechanics characteristics of the material as inputs to the Endurica CL elastomer fatigue solver, which employs critical plane analysis to determine the fatigue response of the specimen surface. The modeling inputs are experimentally determined hyperelastic stress-strain parameters, crack growth rate laws, and crack precursor sizes for carbon black–filled compounds wherein the type of elastomer is varied in order to compare natural rubber (NR), butadiene rubber (BR), and styrene-butadiene rubber (SBR). At the lower impact force, the simulation results were consistent with the relative CC resistances of NR, BR, and SBR measured using the ICCA, which followed the order BR > NR > SBR. Impact-induced temperature increases need to be considered in the fatigue analysis of the higher impact force to provide lifetime predictions that match the experimental CC resistance ranking of NR > SBR > BR.ABSTRACT
Experimental CC resistance data from ICCA testing of NR, SBR, and BR compounds for the two impact normal forces of 50 N and 80 N. The results at FN = 80 N were previously published [3], and the 50 N data are shown here for the first time. Plot (a) shows the cycle dependence of 1/P, with P defined in the prior publication [3]. To compare with the simulations, plot (b) shows the earliest data points for CC resistance at n = 500 cycles, for which photographs were taken of the surface cracks.
Deformed cross sections showing maximum principal engineering strains from finite element analysis of the CC experiment during full loading for the three materials at the two normal forces considered.
Fatigue crack growth rate (r = dc/dn) versus energy release rate (tearing energy) data at 23 °C for NR, SBR, and NR compounds. The data points are averages of six cracks, with the associated error bars shown for the standard deviation. The solid lines are fits to the Thomas law (Eq. [3]). Also shown by the yellow vertical bars are the values of T in the critical element (shortest lifetime) from simulations for the two normal forces at three crack sizes of 5, 50, and 1000 μm (Table 2).
Simple tension strain-life curves from Endurica CL crack precursor calibrations for NR (a), SBR (b), and BR (c). The data points are fatigue-to-failure results at strains of 1.0 and 1.5, and the lines show the results from Eq. (4) for the indicated values of c0. A comparison of the three materials is shown in plot (d).
Fatigue lifetime profiles (deformed top views) from Endurica CL fatigue analysis of the structural FEA deformation results at 23 °C using measured crack precursor sizes.
Predicted normal load dependence of impact cycles to 1-mm crack size (lifetime for critical element) at 23 °C using measured crack precursor sizes.
Effect of c0 on cycles to 1-mm crack (predicted lifetime for critical element) at 23 °C for FN = 50 N (a) and FN = 80 N (b). The measured values of c0 for NR, SBR, and BR are indicated by the hollow symbols.
Preliminary results showing the temperature profile from a high-speed infrared camera during impact number 30 for a CB-filled NR compound (upper left). Note that this is not the exact NR compound in this present study, and the testing conditions are slightly different. The strain profile from finite element analysis of the NR compound at FN = 50 N from the present work is also shown to qualitatively compare the high-strain spots with the experimental high-temperature spots from the thermal imaging.
Fatigue crack growth rate (r = dc/dn) versus energy release rate (tearing energy) for the three materials at 23 °C and 60 °C. The solid lines are the Thomas law fits from Fig. 3 for the data of the present study at 23 °C. The dashed lines are results at 60 °C, which were estimated by shifting the 23 °C results using the temperature dependence of TCand cut growth from the literature (see the text and Table 3 for more details).
Effect of temperature on cycles to 1-mm crack (predicted lifetime) using measured values of c0 for FN = 50 N (a) and FN = 80 N (b). The yellow highlighted regions have predicted lifetime rankings for NR, SBR, and BR that match the experimental CC resistance rankings in Figure 1b.
Photographs of ICCA specimens after the indicated number of impact cycles for FN = 80 N. The locations of the elements with the minimum life from the FEA fatigue analysis are indicated for NR and SBR, along with the locations of the elements on both sides of those elements. Damage spheres for these elements are shown, and the large double arrows on each show the predicted crack orientation from critical plane analysis (same for all temperatures and c0 values considered). The yellow arrows point out the smallest cracks with lengths in the 1- to 2-mm range.
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