Averaged Strain Energy Density Research Articles

Tensile fracture of blunt V-notches in rectangular plates additively manufactured from Acrylonitrile Butadiene Styrene with different raster angles

In this research, the tensile fracture behavior of rectangular specimens made of Acrylonitrile Butadiene Styrene (ABS) containing double-edge blunt V-notches is evaluated. The specimens are printed using the fused deposition modeling (FDM) technique with five different raster angles and three different notch tip radii. To simplify the complex calculations related to the anisotropic behavior of these specimens, the Virtual Isotropic Material Concept (VIMC) is used in conjunction with three well-known linear elastic notch fracture mechanics (LENFM) criteria, i.e., the mean stress (MS), point stress (PS), and averaged strain energy density (ASED) criteria as well as the extended finite element method (XFEM). It is shown that all these fracture models can predict the load-bearing capacity of the 3D-printed notched specimens by acceptable accuracies, where the best predictions belong to the MS criterion with the critical distance obtained directly from the finite element method, and the least accurate predictions belong to the XFEM method.

Mixed mode I/II and I/III fracture toughness investigation for preplaced aggregate concrete mixtures: Experimental study and theoretical prediction

AbstractIn this paper, mixed mode I/II and I/III fracture toughness of preplaced aggregate concrete was studied using an edge‐notched disc bend specimen. The results showed the dependency of the fracture toughness value on the mode mixity. The values of modes I, II, and III fracture toughness were obtained to be equal to , , and , respectively. Several theoretical fracture criteria were examined for predicting the trends of experimental data in the tested preplaced aggregate concrete material. The 3D averaged strain energy density criteria provided the best predictions for the KIIIc/KIc ratio. Mixed mode I/III fracture toughness data were between the predicted envelopes of the maximum tensile stress and 3D maximum tangential strain theories. The generalized maximum tangential stress criterion provided accurate predictions for pure mode II and mixed mode I/II fracture data among the investigated mixed mode fracture criteria. By comparing the preplaced aggregate concrete fracture results with those of other types of concrete, it is observed that preplaced aggregate concrete has acceptable and in‐the‐range fracture resistance.

Fracture assessment of polyamide 12 (PA12) specimens fabricated via Multi Jet FusionTM in the presence of geometrical discontinuities

This study aims to study the fracture resistance of additively manufactured polyamide 12 (PA12), specifically when subjected to notches and cracks, and how it varies with the printing direction using Multi Jet Fusion (MJF). The methodology involved conducting tensile tests on V-notched samples, with a focus on different combinations of opening angle (0°-120°) and tip radius (0.2–2 mm). The findings revealed that the sensitivity to the notch opening angle decreased with an increase in the notch tip radius. Furthermore, the fracture resistance for different mode mixities was examined using semi-circular bend (SCB) specimens, with the crack angle varied between 0° and 53°. The results demonstrated two distinct fracture behaviours, namely brittle and ductile, depending on the crack angle. Theoretical analyses revealed that with appropriate tuning, average strain energy density (ASED) can predict the load capacity of notched and cracked PA12 parts manufactured with MJF, within an error range of ± 20 %.

Effect of the notch opening angle on the quasi-static behavior of PLA and carbon fibers reinforced PLA realized through Fused Deposition Modelling

Additive manufacturing provides significant advantages over conventional manufacturing. Among the others, the almost unconstrained freedom in the geometrical design for this technology can be pointed out. However, the geometrical complexness of such components requires for adequate tools to assess both their fracture behavior and fatigue life. A suitable solution for such a design challenge is to rely on the so-called local approaches whose main advantage is to consider a local parameter to evaluate the behavior of the entire component; besides, such methods have the advantage that their critical value can be assumed to be independent on both the overall geometry of the component and the loading conditions. With this purpose, the present work investigates the fracture behavior of notched specimens made of PLA and carbon fiber reinforced PLA realized through additive manufactured technique. The specimen's geometry considered is smooth and double notched while the notch opening angles varies between 30 and 120 degrees. The results of the experimental campaign have been summarized through the averaged strain energy density (SED) method, an energy-based local approach, widely proved to be a valid tool to investigate both fracture in static condition and fatigue failure. The critical value of SED has been obtained through the stress-strain curve of smooth specimens for the two studied materials. After the determination of the control volume characteristic length, R0, the data have been summarized in terms of averaged SED values. The critical loads for the different geometries and the different materials considered are predicted by the method with an average error of ±7%.

Developing rapid expressions for calculating average strain energy density and J-integral in VO-notched components under tension

Developing rapid expressions for calculating average strain energy density and J-integral in VO-notched components under tension

Application of modified fracture criteria incorporating T-stress for various cracked specimens under mixed mode I-II loading

Accurate assessment of fracture behavior and life prediction of cracked materials based on the mixed mode fracture criteria is of utmost importance in fracture mechanics. In this study, the modified fracture criteria incorporating T-stress for mixed mode I-II cracks were comprehensively reviewed. Additionally, a comparative analysis was conducted between the experimental results obtained from five different cracked configurations and the theoretical predictions according to these modified criteria. Moreover, a brief discussion was held regarding the effect of T-stress on both crack initiation angle and fracture toughness, accompanied by providing some suggestions. The results revealed that the predictive accuracy of modified criteria exhibited noticeable variations across different cracked configurations due to the significant disparities in both the sign and magnitude of T-stress around the crack tip. However, it was observed that the predicted curves based on the modified fracture criteria for the semi-circular bend and edge-crack triangular specimens had remarkable similarities owing to their similar biaxial stress ratio B. When the mode II loading dominated, the generalized maximum tangential stress, generalized minimum strain energy density and generalized averaged strain energy density criteria were suitable for the semi-circular bend, edge-crack triangular, central crack rectangular and short bend beam specimens with positive T-stresses, whereas the maximum tangential strain, generalized maximum tangential stress and generalized maximum tangential strain energy density criteria could provide better theoretical predictions for central cracked Brazilian disk specimens having a negative T-stress.

A novel elastic strain energy density approach for fatigue evaluation of welded components

The averaged elastic strain energy density (SED) within a characteristic volume radius R has been investigated and applied for characterizing the fatigue strength of welded joints for decades. However, engineering applications are still relatively rare. The main reason is that the calculation process is cumbersome due to fine mesh size and circular pattern requirements. This study proposes a novel approach of SED without requiring special finite element size and special layout requirements. First, a novel approach of the notch stress solution is presented. As a result, the present solution differs from the conventional approach which has been focused on notch tip singular stress field. Then, an averaged strain energy density can be obtained analytically by taking advantage of the new notch stress solutions presented in this study. Both the closed-form notch stress solutions and resulting expression for average strain energy density have been validated by FEA results. Subsequently, a large number of fatigue tests published in the literature are selected to examine the effectiveness of the evaluation approach of SED on interpreting fatigue behaviors of welded joints. Finally, a procedure for practical engineering application is established and verified by a group of fatigue tests of 3D gusset welded components.

Fracture Load Estimations for U-Notched and V-Notched 3D Printed PLA and Graphene-Reinforced PLA plates using the ASED Criterion

This paper addresses the estimation of critical loads in FFF (Fused Filament Fabrication) printed polymers and composites containing notches. Particularly, the analysis is focused on the fracture load estimations of 39 PLA (polylactic acid) and 39 graphene reinforced PLA (PLA-Gr) printed plates containing two different types of notches (U- and V-notches) and combining different plate thicknesses and defect length to plate width (a/W) ratios. The addition of graphene (1 wt.%) increases both the yield stress and the ultimate tensile strength, also reducing the strain at rupture and, thus, generating a material whose behavior is closer to linear elasticity. Among the different assessment tools that may be used to estimate critical loads, this work applies the well-known Averaged Strain Energy Density (ASED) criterion, which compares the averaged strain energy over a certain control volume at the notch tip with the corresponding critical value, the latter being a material property. This approach has a linear-elastic nature, so its application to non-fully linear materials may require the use of specific corrections or calibrations. For the two materials analyzed here, PLA and PLA-Gr, it has been observed that the ordinary linear-elastic ASED criterion provides good estimations for the PLA-Gr material, whereas the pristine PLA, with more evident non-linear behavior, the obtainment of accurate results requires a previous specific calibration of the ASED material parameters

Numerical and experimental analysis of the notch effect on fatigue behavior of polymethylmethacrylate metal based on strain energy density method and the extended finite element method

Abstract This work investigates the effect of the notch on fatigue behavior by combining two methods: the extended finite element method (XFEM) and the averaged strain energy density (ASED) method, which considers the combined action of bending and shear loading. The ASED method has already been proven accurate for assessing the failure of components in the presence of sharp and blunt notches, and several results are available in the literature for different materials. These results were compared with those obtained from the experimental tests reported here. The main purpose of this study was twofold: The first part is an experimental study of fatigue in rotary bending of specimens weakened by U and V notches made of polymethyl-methacrylate (PMMA) material. Two values for the radius were used for the U-notches (0.2 and 2 mm) and two angles for the V-notches (20° and 140°). The second part of the study consisted of performing several simulation tests using the Cast3m software for different angles and radii. The local approach based on the mean value of the ASED acted over a finite-sized volume surrounding the highly stressed regions. The maximum principal stress located at the notch edge defined the center of the control volume. If the notch is blunt, the control volume assumes a crescent shape with its width measured along the notch bisector line. When the notch is considered pointed (V-notched) or is a crack, the control volume becomes a circle with its center at the notch tip. The presence of geometric discontinuities in structures affects their lifetime by reducing it, producing a high concentration of local energy around the notch tip. Good convergence was obtained between the numerical simulation and experimental results for the ASED in a finished zone surrounding the notch tip.

Effects of copper additives on load carrying capacity and micro mechanisms of fracture in 3D-printed PLA specimens

This study deals with the effects of employing copper additives on the fracture resistance and fracture micro-mechanisms of 3D-printed Polylactic Acid (PLA) specimens under mixed mode I/II loading. Several comparative fracture tests are conducted on pre-cracked Semi-Circular Bend (SCB) specimens made of pure PLA and particulate copper-reinforced PLA (PLA/Cu) printed using the Fused Deposition Modeling (FDM) technique. The SCB specimens are fabricated in three different layer orientations. The comparison of the experimental results reveals that employing copper additives increases the load carrying capacities (LCCs) of the pre-cracked SCB specimens with the flat, on-edge, and upright layer orientations by 2.9%, 15.5%, and 27.7%, respectively. In addition, to determine the tensile properties of two desired materials, dogbone specimens made of PLA and PLA/Cu in three different layer orientations are fabricated and tested. The experimental results obtained from the characterization tests similarly indicate that the presence of copper additives in 3D printed PLA specimens increases ultimate tensile strength by 15.9%, 14%, and, 10.4% in the three flat, on-edge, and upright layer orientations, respectively. Aside from performing experimental tests, the LCCs of pre-cracked specimens are predicted theoretically by utilizing Equivalent Material Concept (EMC) combined with the well-known Average Strain Energy Density (ASED) criterion. It is shown that the EMC-ASED criterion can estimate accurately the experimental LCCs of both FDM-PLA and FDM-PLA/Cu specimens. Finally, the Scanning Electron Microscope (SEM) technique is employed to provide a better understanding of the effects of copper additives on the micro-mechanisms of fracture.

Fracture Load Prediction of Non-Linear Structural Steels through Calibration of the ASED Criterion

In this work, the application of the Average Strain Energy Density (ASED) criterion for the estimation of failure loads in materials with nonlinear behavior containing U-shaped notches is presented. The ASED criterion was originally defined to predict failure in the presence of notches in materials with linear-elastic behavior. However, most structural materials (e.g., ferritic-pearlitic steels) can develop non-linear behavior (e.g., elastoplastic). In this sense, this work proposes to extend the use of the ASED criterion to materials that exhibit plasticity by a thorough calibration of their characteristic parameters, and the subsequent extrapolation of the liner-elastic formulation of the ASED criterion to non-linear situations. To validate this methodology, a wide range of structural steels (S275JR, S355J2, S460M, and S690Q) were used operating in the ductile-to-brittle transition range, with six different notch radii (0 mm, 0.15 mm, 0.25 mm, 0.50 mm, 1.0 mm, and 2.0 mm). The results obtained demonstrate that the proposed calibration of the ASED criterion allows for accurate predictions of failure loads. Therefore, it is shown that, for the notch radii analyzed in this work and for testing temperatures within the material ductile-to-brittle transition range, it is possible to extrapolate the ASED criterion to obtain estimates of failure loads in materials with U-shaped notches that exhibit ductile behavior.

Equivalent loads from the life-cycle of acetabular cages in relation to bone-graft transformation

Background and ObjectivesBone grafts placed behind acetabular cages change their structure in response to mechanical stimuli. The full consideration of lifestyle loads is extremely resource-intensive, so a method using substitutive loads was proposed to reduce the calculation cost. The aim of the study is to present and prove this method. MethodsBy means of mechanical equations and using the force vectors from the literature which have the same initial point and their relative frequency, while applying a linear model, the average strain energy density distribution for all load cases can be calculated, compiling a matrix from the external loads. From the elements of this matrix, three substitutive load vectors can be calculated, which can be proven to produce the same strain energy density distribution by averaging their effects. The feasibility of using this to model the transformation of bone grafts placed behind acetabular cages is demonstrated with a finite element model, along with a reference calculation. ResultsThe substitutive load vectors could be calculated in closed form and the simulations showed that they produced a similar density distribution to the reference model with a numerical calculation error range. Accordingly, the density distribution calculated from bone graft transformation is almost the same. ConclusionsIn addition to the aforementioned linearity and the same initial point limitations, the applied method is able to produce the substitutive load vectors with which the calculation of the strain energy density distribution and the bone graft's new density distributions can be carried out faster.

A probabilistic average strain energy density approach to assess the fatigue strength of additively manufactured cellular lattice materials

In cellular lattice materials, fatigue failure assessment using an intricate finite element (FE) model of the entire specimen is neither feasible nor economical. To address this complex task, we propose a multi-step FE analysis methodology that can be employed for these metamaterials. FE models are created using the three-dimensional reconstructions from the μCT scans of the specimen. Subsequently, a combination of the average strain energy density approach and extreme value statistics is used to assess the fatigue behavior of the entire specimen. The methodology was employed on two types of cubic cellular lattice materials and validated using experimental fatigue results.

Structural and Electrical Properties of CuS Nanoparticles and PPy/CuS Hybrid Nanocomposite Chemically Synthesized by Facile Approach

Objective: In the present study, cupric sulfide (CuS) nanoparticles (NPs) were synthesized in deionized (DIW) water using an eco-benign, simple, and cost-effective chemical route that requires no surfactant or template. Methods: Polypyrrole/cupric sulfide (PPy/CuS) hybrid nanocomposite (HNC) was synthesized using an in-situ chemical oxidative polymerization method in the presence of obtained CuS NPs. The X-ray diffraction (XRD) analysis confirmed the hexagonal structure of CuS, whose crystalline nature was preserved in the HNC. For CuS NPs and PPy/CuS HNC, elastic properties, such as intrinsic microstrain, internal stress, dislocation density, strain energy density, stacking faults, and intercrystalline separation, were used to analyze the crystal imperfections and distortions. Results: Field emission scanning electron spectroscopy (FESEM) micrographs revealed that CuS NPs and PPy/CuS HNC have particulate and globular morphology, respectively. The values of the average intrinsic strain, dislocation density, internal stresses, and strain energy density of PPy/CuS HNC were estimated to be ~2 × 10-3, ~8.8166 × 1015 m-2, 164.263 MPa, and 127.278 KJ m−3, respectively, which were observed to be higher than those of CuS NPs. Conclusion: The DC electrical conductivity of as-synthesized samples was measured at room temperature in pelletized form, using the standard four-probe method, and conductivity values were estimated to be ~480 Scm-1 and ~4 Scm-1 for CuS NPs and PPy/CuS HNC, respectively.

Accuracy of osseointegrated screw-bone construct stiffness and peri-implant loading predicted by homogenized FE models relative to micro-FE models

Computational predictions of stiffness and peri-implant loading of screw-bone constructs are highly relevant to investigate and improve bone fracture fixations. Homogenized finite element (hFE) models have been used for this purpose in the past, but their accuracy has been questioned given the numerous simplifications, such as neglecting screw threads and modelling the trabecular bone structure as a continuum. This study aimed to investigate the accuracy of hFE models of an osseointegrated screw-bone construct when compared to micro-FE models considering the simplified screw geometry and different trabecular bone material models.Micro-FE and hFE models were created from 15 cylindrical bone samples with a virtually inserted, osseointegrated screw (fully bonded interface). Micro-FE models were created including the screw with threads (=reference models) and without threads to quantify the error due to screw geometry simplification. In the hFE models, the screws were modelled without threads and four different trabecular bone material models were used, including orthotropic and isotropic material derived from homogenization with kinematic uniform boundary conditions (KUBC), as well as from periodicity-compatible mixed uniform boundary conditions (PMUBC). Three load cases were simulated (pullout, shear in two directions) and errors in the construct stiffness and the volume average strain energy density (SED) in the peri-implant region were evaluated relative to the micro-FE model with a threaded screw.The pooled error caused by only omitting screw threads was low (max: 8.0%) compared to the pooled error additionally including homogenized trabecular bone material (max: 92.2%). Stiffness was predicted most accurately using PMUBC-derived orthotropic material (error: -0.7 ± 8.0%) and least accurately using KUBC-derived isotropic material (error: +23.1 ± 24.4%). Peri-implant SED averages were generally well correlated (R2 ≥ 0.76), but slightly over- or underestimated by the hFE models and SED distributions were qualitatively different between hFE and micro-FE models.This study suggests that osseointegrated screw-bone construct stiffness can be predicted accurately using hFE models when compared to micro-FE models and that volume average peri-implant SEDs are well correlated. However, the hFE models are highly sensitive to the choice of trabecular bone material properties. PMUBC-derived isotropic material properties represented the best trade-off between model accuracy and complexity in this study.

Fatigue failure investigation of thick plate butt‐welded joints with incomplete penetration effect

AbstractThe objective of this paper was to investigate the fatigue performance of the thick plate structural steel butt‐welded joints influenced by its geometrical factors, such as the notch angles, incomplete penetration length, and plate thickness. Utilizing experimental tests, finite element calculations, and analytical models, the fatigue behavior of various weld joint shapes and dimensions was analyzed, and the discrepancy of fatigue strength for different incomplete penetration lengths was evaluated using the nominal stress method. Meanwhile, the local approaches, including notch stress intensity factor (NSIF), averaged strain energy density (SED), effective notch stress (ENS) method, peak stress method (PSM), and implicit gradient effective stress (IGES) method, are employed to assess the fatigue life of thick plate welded joints. According to the results, incomplete penetration ratios in butt‐welded joints led to a decrease in fatigue strength. The analytical solutions of butt‐welded joints in high cycle regime based on SED results were obtained to estimate the fatigue characteristic values for different plate thickness and incomplete penetration ratios. The proposed equations could illustrate the relationship between the nominal stress and local SED dealing with the variations of incomplete penetration length and geometrical dimensions. Moreover, the results obtained by the analysis of ENS, PSM, and IGES could be deduced by the analytical models to determine the fatigue life of welded joints.

An innovative experimental energy-based approach for the life prediction of notched details

Fatigue assessment of mechanical components can be very challenging due to the presence of macroscopic defects and notches. However, local approaches as the Stain Energy Density, have shown how the fatigue resistance is strictly related to the local stress field near the notch tip and not on the overall dimensions of the component. It is necessary to know some peculiar material’s parameters to apply those local approaches. A short way to obtain such parameters can be to apply Thermographic Methods, such as the Risitano’s Thermographic Method and the Static Thermographic Method, monitoring the energy release during stepwise fatigue and static tensile tests. In this work, experimental tests were performed on plain and double edge steel notched specimens. The SED method has been applied through finite element models, with the easy application of the volume-free procedure, to evaluate its trend at several stress levels. The analysis of the energy release and of the local averaged strain energy density during a static tensile test may be adopted as a novel approach to relate the local stress state with a macroscopic stress value that introduce in the material the first micro plasticization leading to the failure of the component.

On the combined use of averaged strain energy density criteria (ASED) and equivalent material concept (ECC) for the fracture load prediction of additively manufactured PLA v-notched specimens

On the combined use of averaged strain energy density criteria (ASED) and equivalent material concept (ECC) for the fracture load prediction of additively manufactured PLA v-notched specimens

Heat treatment effects on fracture resistance of additively manufactured PLA specimens under mode I loading

AbstractThe current paper deals with the influence of heat treatment on the tensile, flexural, and fracture strength of polylactic acid (PLA) specimens made by the fused deposition modeling (FDM) technique. Three different temperatures of 80°C, 100°C, and 120°C were used to anneal the dog bone and enlarged compact tension (ECT) specimens to examine the mechanical and fracture performance of the FDM‐PLA parts, respectively. The fracture behavior was assessed using the equivalent material concept (EMC) combined with the J‐integral, average strain energy density (ASED), and maximum tangential stress (MTS) criteria, and the theoretical estimates were compared with the experimental results. Finally, the effectiveness of these criteria was discussed comprehensively, and the failure mechanisms in the broken tensile and flexural specimens were investigated using scanning electron microscopy (SEM). Overall, applying heat treatment to the FDM specimens could improve their structural integrity by around 57% from the fracture resistance point of view.

Length scale parameters to estimate fatigue lifetime of 3D-printed titanium alloy Ti6Al4V containing notches in the as-manufactured condition

The accuracy of the Theory of Critical Distances, Gradient Elasticity and the Averaged Strain Energy Density criterion in estimating fatigue lifetime of notched additively manufactured Ti6Al4V is assessed against numerous experimental results generated under load ratios equal to −1 and 0.1. The 3D-printed Ti-alloy under investigation was tested by keeping the notches in the as-manufactured condition. The common feature of the considered design approaches is that they all make use of a material length scale. The validation exercise based on the generated experimental results demonstrates that the length scale concept can be extended successfully also to the fatigue assessment of notched 3D-printed metallic components.