We used finite element analyses (FEA) on Abaqus to study flexural properties of additive manufactured beams using polylactic acid (PLA) polymer. Experimental stress–strain data from flexural testing are used to define elastic–plastic properties of the material in the computation software. The flexural experiments are used to validate the FEA approach suggested. The method provides good results of deflection and stress with errors well below 10% in most of the cases. Therefore, by using the proposed approach, costs related to repeated experimental works can be avoided. In addition, the flexural rigidities of the additive manufactured beams are studied. Five different beam stiffener designs (diamond, honeycomb, square, triangular and wiggle) are studied based on beam bending theory. The force–deflection data from the flexural tests are used to determine the area moments of inertia of the beams. The honeycomb stiffener showed the highest force–deflection behaviour that led to the highest calculated area moment of inertia. However, with the lowest force–deflection behaviour, the square stiffener had the lowest calculated area moment of inertia.
The linear viscoelastic behaviour of an injection moulding grade polypropylene is studied using theoretical and computational methods. Polypropylene has a variety of engineering applications as a component. However, it commonly exhibits viscoelastic deformations. This paper analyses the creep and recovery responses of the BJ368MO polypropylene copolymer using the Burgers and generalised Maxwell models. Within the linear viscoelastic regime, an experimental creep strain at $20\ \text{MPa}$ 20 MPa is used to determine the rheological constants of the models. These constants (springs and dashpots) are determined using a nonlinear least-squares curve fitting of the experimental creep. Then they are used to predict the creep and recovery responses of the polymer at three different stresses, $10\ \text{MPa}$ 10 MPa , $12.5\ \text{MPa}$ 12.5 MPa and $15\ \text{MPa}$ 15 MPa . The experiments are made using tensile specimens designed according to the ASTM D638-14standard. The theoretical evaluations are made using the creep and recovery equations derived from their constitutive. Whereas COMSOL Multiphysics software is used during the finite element (FE) analyses. The results of the theoretical and FE calculations are verified using creep and recovery experiments. Based on the validation analyses, both viscoelastic models showed lower deviations from the experimental results when a computational approach is used. In addition, the viscoelastic models are compared by evaluating the residuals of the creep and recovery strain predictions. The theoretical analyses showed better predictions at $12.5\ \text{MPa}$ 12.5 MPa and $15\ \text{MPa}$ 15 MPa stresses when the generalised Maxwell model is used. However, the improvements are attributed to the recovery predictions. When FE is used, the Burgers model showed lower mean absolute percentage errors (MAPEs) in all creep and recovery predictions. The model has a minimum of 6.37% error at the $10\ \text{MPa}$ 10 MPa stress and a maximum of 8.23% error at the $15\ \text{MPa}$ 15 MPa . By comparison, the generalised Maxwell model showed a minimum of 9.24% error at $12.5\ \text{MPa}$ 12.5 MPa and a maximum of 12.8% error at $15\ \text{MPa}$ 15 MPa stresses. The novelty of this paper is on predicting the creep and recovery behaviour of the polymer using the FE and theoretical approaches in the linear viscoelastic regime. The findings suggest that the FE analyses using the Burgers viscoelastic material model provide better predictions, with all calculated errors falling below 10%.
We propose a conservative method for the calculation of the maximum stress concentration factor (SCF) for an interacting notch-hole pair and for a double semi-circular notch (i.e., a notch that has an additional small semi-circular notch ahead of its tip). The method is based on a linearly elastic Airy stress function solution for a circular hole. The notch-hole and double notch configurations are aligned vertically with respect to uniform uniaxial (horizontal) stress. This means, a uniform horizontal tension is applied to a notch-hole pair that lie on a vertical axis. For the notch-hole pair, the maximum interacting SCFs are calculated for edge to edge gaps equal to hole sizes of 2.5a, 5a, 10a and 15a, where a is the hole radius. The analytical results are validated by 2-D finite element calculations. The presented simple approach provides good results with errors well below 10% in most cases compared to the detailed finite element analyses. Fatigue notch factors that can be thought of as the effective SCFs in fatigue analyses are determined. By using the simple approach, computationally costly finite element analysis can be avoided.
The creep and recovery behaviors of a tough polylactic acid polymer are investigated experimentally and theoretically. We studied the influence of manufacturing methods and parameters on the viscoelastic responses. Experimental comparisons were carried out on 13 different samples manufactured using fused deposition modeling (FDM) and injection molding methods. The sample variations in the FDM were based on four infill densities (70-100%) and 3 infill directions $$(0^\circ ,45^\circ ,90^\circ )$$ ( 0 ∘ , 45 ∘ , 90 ∘ ) . Theoretically, the Burgers and Weibull’s models are used to predict the creep and recovery responses of the samples. Our experimental findings suggest that the injection-molded samples perform better in creep for most of the cases. However, at higher stress loadings, the 90 and 100% infill density samples showed excellent creep resistance behaviors at the $$90^\circ$$ 90 ∘ infill direction. On the other hand, the theoretical creep and recovery predictions were based on the nonlinear least-squares regression method. The Burgers model predicted the creep responses with reasonable accuracies. A maximum of $$5.83\%$$ 5.83 % mean absolute percentage error (MAPE) was found for the 0° infill direction and 80% infill density sample. On the contrary, the model lacks accuracy in recovery strain predictions, showing an average of 173.15% MAPE for all studied samples. Introducing Weibull’s distribution improved the accuracies showing a 3.44% average MAPE for all samples.
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