Finite element and experimental investigation on the effect of repetitive shock in corrugated cardboard packaging 827
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Fig. 11. Effect of mesh refinement on various model energies: (a) Internal energy, (b) Kinetic energy, (c) Plastic energy dissipation and (d) Energy balance .
Fig. 12. Numerical and experimental damaged box.
Low fatigue cycle, also called “Oligocyclique Fatigue”, is characterized by high stress and low fatigue life. For the limited endurance fatigue, lifetime is intermediate and varies rapidly in function of applied stress. For unlimited endurance fatigue, the lifetime is infinite. In this study, for oligocyclique and limited endurance fatigue, the number of shocks necessary for the box to damage is determined directly from the Abaqus simulations since the number of cycles is low. However, the number of cycles to damage the box can be very high and it is practically not feasible to perform a cycle-by-cycle simulation. To reduce computational costs, we propose a simple method consisting in extrapolating the equivalent plastic strain after some training cycles. This method is based on a trend line, established during finite element analysis for training cycles. This trend is used to extrapolate the remaining cycles. For oligocyclique fatigue, damage of the box is observed after the first shock both experimentally and numerically as shown in Fig. (12). For limited endurance fatigue, damage of the box is observed after several shocks given in Table (4). We can see that our numerical model gives the same order of magnitude as the experimental results. For the unlimited endurance fatigue, we stopped experimental testing after a thousand shocks considering that the box reaches the unlimited endurance zone. We compare in Table (5) shock numbers for box to undergoes damage obtained for experimental tests and with the extrapolation method. Despite the various simplifying assumptions, the proposed model gives satisfactory results. Figure (13) represents the experimental and numerical damage boundary curve of the studied box that define its fragility based on its sensitivity to acceleration and the that occurs during shock. To compare the velocity change experimental and simulation results, Figs. 14(a) and 14(b) display experimental and simulation frequency distribution for grouped data. The distributions are asymmetric and positively skewed, the values tend to cluster toward the lower end of the scale. Hence, in these sets of points, the mean is higher than the median because the latter is dragged in the direction of the tail. Figs. 14(c) and (d) show a good comparison of the approximated Probability Density Function (PDF) and Cumulative Distribution Function (CDF) of experimental and numerical velocity change variables.
Journal of Applied and Computational Mechanics, Vol. 7, No. 2, (2021), 820-830
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