The present work aims to analyze the buckling behavior of nonlinear elastic columns with different open cross-sections and slenderness ratios to verify the limits of the modified Ludwick law to predict the critical buckling load. The results of the analytical formulation based on the modified Ludwick law are compared with a FEM numerical model using the Marlow hyperelastic behavior and experimental results conducted on flax/PLA specimens with three different open cross-sections. The comparative results show that the numerical predictions agree with the experimental results in all the cases. The FEM model can exactly reproduce the buckling behavior of the C-section columns. However, the prediction errors for the C90 and C180 columns are higher than for the C60 columns. Moreover, the theoretical estimations indicate that the C90 cross-section column is the limit of application of the modified Ludwick law to predict the critical buckling load of nonlinear elastic columns with open cross-sections, and the C180 column is out of the prediction limits. Generally, the numerical and theoretical models underestimated the scattering effects of the predictions because more experimental variables were not considered by the models.
The aim of the present work is to provide a methodology to evaluate the influence of stacking sequence on the ballistic performance of ultra-high molecular weight polyethylene (UHMWPE) protections. The proposed methodology is based on the combination of experimental tests, numerical modelling, and Artificial Neural Networks (ANN). High-velocity impact experimental tests were conducted to validate the numerical model. The validated Finite Element Method (FEM) model was used to provide data to train and to validate the ANN. Finally, the ANN was used to find the best stacking sequence combining layers of three UHMWPE materials with different qualities. The results showed that the three UHMWPE materials can be properly combined to provide a solution with a better ballistic performance than using only the material with highest quality. These results imply that costs can be reduced increasing the ballistic limit of the UHMWPE protections. When the weight ratios of the three materials remain constant, the optimal results occur when the highest-performance material is placed in the back face. Furthermore, ANN simulation showed that the optimal results occur when the weight ratio of the highest-performance material is 79.2%.
The objective of this work is to analyze the influence of the cross-section of a bumper beam made of fully biodegradable composites. Flax/PLA bumper beams were manufactured with four types of cross-sections with different degree of roundness. Specimens were subjected to low velocity impacts and the post-impact behavior is evaluated under three-point bending tests. Results indicate that different cross-sections can be selected if the objective is to maximize the impact performance or the post-impact residual properties. The bumper beam with the higher roundness exhibits the best impact performance, while an intermediate section exhibits the best after impact residual mechanical properties.
Significant progress has been made in green composites developing fully biodegradable composites made of microbially degradable polymers reinforced with natural fibers. However, an improvement in the development of numerical models to predict the damage of green composites is necessary to extend their use in industrial applications of structural responsibility. This paper is focused on developing a numerical model that can predict the failure modes of four types of bumper beams made of flax/PLA green composites with different cross sections. The predictions regarding energy absorption, contact force history, and extension of delamination were compared with experimental results to validate the FEM model, and both results revealed a good agreement. Finally, the FEM model was used to analyze the failure modes of the bumper beams as a function of the impact energy and cross-section roundness. The impact energy threshold defined as the maximum absorbed-energy capability of the beam match with the impact energy that produces delaminations extended through all the cross sections. Experimental and numerical results revealed that the threshold energy, where the maximum energy-absorption capability is reached, for Type A is over 60 J; for Type B and C is around 60 J; and for Type D is at 50 J. Since delamination is concentrated at the cross-section corners, the threshold energy decreases with the cross-section roundness because the higher the roundness ratio, the wider the delamination extension.
This paper presents the fatigue limit of flax/PLA composites with different fiber reinforcement architectures. The configurations of the analyzed flax/PLA composites are [0°]8, [0°/90°]s, [+45°/−45°]s, [90°]4, stacking sequences, and basket weave laminates. The methods used to estimate the fatigue limit are the fitting of stress versus number of cycles data using Weibull and Basquin equations, the surface thermographic technique with bilinear and exponential models to analyze the evolution of temperature increment, and volumetric dissipated energy. According to the results found, superficial temperature and the maximum strain reached stabilization over 2000 cycles for σmax/σut < 0.7, which was used to determine cyclic stress–strain curves and the fatigue limit. The cyclic stress–strain shows a nonlinear behavior for all laminates, having a good correlation to the Ramberg–Osgood model. Furthermore, having the stabilized temperature and volumetric dissipated energy, the exponential model was used to evaluate the fatigue limit and compared to the values found by Basquin and bilinear models. The fatigue limit found by Basquin and bilinear models shows conservative values compared to the exponential models. The results also show that temperature measurement using infrared thermography is quite sensitive to the environmental temperature variation, especially at low stress applied, and finally, the comparison of these methods on different reinforcement configurations provides a guide to select a proper technique in each case.
The main contribution of this work is validating the Ludwick law to model the nonlinear mechanical behavior in the prediction of the critical buckling load of nonlinear elastic columns. The critical buckling loads of specimens with different slenderness ratios were obtained by conducting experimental tests on flax/PLA columns with pinned–pinned boundary conditions. The modified Ludwick law parameters were calibrated to fit the stress–strain curve obtained in tensile tests of flax/PLA specimens. The flax/PLA specimens were manufactured using the compression molding method. Moreover, a numerical model considering the Marlow hyperelastic constitutive model was used to predict the critical buckling load. Theoretical predictions using Ludwick law and numerical results were in excellent agreement with experimental data. Results showed that the maximum error of the numerical predictions for critical buckling load is 14.3%, and the maximum error of the theoretical predictions is 8.0%. Additionally, a parametric study was developed to analyze the influence of material's nonlinearity on the numerical prediction accuracy of the Marlow model.
