Averaged Strain Energy Density Criterion Research Articles

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

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.

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.

Energy TCD - robust and simple failure prediction unifying the TCD and ASED criterion

Robust and simple failure prediction is a relevant and active field of research. The present work aims at unifying the Theory of Critical Distances (TCD) and Averaged Strain Energy Density (ASED) criterion. The proposed Energy TCD is formulated along with analytical expressions for the characteristic length scales and validated using experimental data. On this data set, the accuracy of the Energy TCD is similar to that of the classical methods. Most importantly, the presented methods allow to transfer the point-based calibration technique from notched specimens, which is common for the TCD, to the Energy TCD ASED criterion.

Fracture Load Predictions in Additively Manufactured ABS U-Notched Specimens Using Average Strain Energy Density Criteria.

This paper provides a methodology for the prediction of fracture loads in additively manufactured ABS material containing U-notches. The approach is based on the Average Strain Energy Density (ASED) criterion, which assumes that the material being analysed develops fully linear-elastic behaviour. Thus, in those cases where the material has a certain (non-negligible) amount of non-linear behaviour, the ASED criterion needs to be corrected. In this sense, in this paper, the ASED criterion is also combined with the Equivalent Material Concept (EMC) and the Fictitious Material Concept (FMC), both being corrections in which the non-linear real material is substituted by a linear equivalent or fictitious material, respectively. The resulting methodologies have been applied to additively manufactured ABS U-notched single-edge-notched bending (SENB) specimens combining five different notch radii (0, 0.25, 0.5, 1 and 2 mm) and three different raster orientations (0/90, 45/−45 and 30/−60). The results obtained demonstrate that both the ASED-EMC and the ASED-FMC combined criteria provide more accurate predictions than those obtained directly through the ASED criterion, with the ASED-EMC criterion generally providing safe more accurate predictions, with an average deviation from the experimental fracture loads between +1.0% (predicted loads higher than experimental loads) and −7.6% (predicted loads lower than experimental loads).

Experimental Verification of the Averaged Strain Energy Density Criterion for Brittle Fracture in Blunt V-Notches Under Pure Compression

Experimental Verification of the Averaged Strain Energy Density Criterion for Brittle Fracture in Blunt V-Notches Under Pure Compression

Applicability of strain energy density criterion for fracture prediction of notched PLA specimens produced via fused deposition modeling

The Averaged Strain Energy Density (ASED) criterion is validated for the failure prediction of notched Polylactide Acid specimens fabricated by Fused Deposition Modeling by means of experimental data and the results are compared to the Theory of Critical Distances. The common approach of estimating the ASED control volume radius based on the measured fracture toughness was shown to be suboptimal, arguably because of the difficulties of obtaining the fracture toughness with such complex materials. Therefore, a more robust approach is evaluated in analogy of the TCD and it is shown to successfully extend the range of applicability of the ASED criterion.

Critical Load Prediction in Notched E/Glass-Epoxy-Laminated Composites Using the Virtual Isotropic Material Concept Combined with the Average Strain Energy Density Criterion.

This paper attempts to validate the application of the Virtual Isotropic Material Concept (VIMC) in combination with the average strain energy density (ASED) criterion to predict the critical load in notched laminated composites. This methodology was applied to E/glass–epoxy-laminated composites containing U-notches. For this purpose, a series of fracture test data recently published in the literature on specimens with different notch tip radii, lay-up configurations, and a number of plies were employed. It was shown that the VIMC–ASED combined approach provided satisfactory predictions of the last-ply failure (LPF) loads (i.e., critical loads).

Evaluation of the geometrical discontinuity effect on mixed-mode I/II fracture load of FDM 3D-printed parts

The main objective of this manuscript is to evaluate the capability of the fracture criteria and numerical methods to predict fracture properties of the specimens fabricated using the Fused Deposition Modelling (FDM) 3D-Printing method. Different thermoplastic materials are 3D printed in Semi-Circular Bending (SCB) specimens configuration and subjected to three-point bending loading to investigate their failure behaviour, including final load-bearing and crack path trajectory. The Acrylonitrile Butadiene Styrene (ABS) due to its brittle behavior, was selected for the mixed mode fracture study. The SCB samples with various pre-crack angles indicating different modes of loading conditions are manufactured. Cracked SCB specimens are produced with and without geometrical discontinuities as holes to verify the effect of stress concentration on their fracture behavior. The results of the three-point bending tests demonstrated that the Extended Finite Element-Cohesive Zone Model (XFEM-CZM) and Average Strain Energy Density (ASED) criterion are capable of predicting the fracture behavior of the 3D-Printed ABS material under mixed-mode I/II loading. The appropriate XFEM-CZM damage criterion was used to estimate the crack growth path. The final failure load was obtained using the ASED and XFEM criteria. The maximum error rate between the experimental results and the presented theories was 10%, which confirms the employed criteria' accuracy. The results showed that a stress raiser like a hole in the 3D-Printed specimens might reduce the loading capacity of the material by 17%.

Strain Energy Density-Predicted Brittle Fracture of U-Notched Components Under Combined Tension/Tear Loading

The study is aimed at experimental verification of the validity of the averaged strain energy density criterion in predicting the brittle fracture of U-notched components under combined tension/tear loading. The fracture experiments are carried out on U-notched rectangular polymethyl methacrylate samples using an improved loading fixture, capable of testing the cracked and notched samples under various combinations of tension and out-of-plane shear. The samples with three different notch tip radii are tested to evaluate the radius effect on their load-carrying capacity. Theoretical and experimental results show that the above criterion can provide satisfactory estimation of the fracture loads applied to notched specimens and is efficient enough in predicting the brittle fracture of U-notched PMMA members under combined tension/tear loading.

Adhesively bonded joint brittle fracture assessment via average strain energy density criterion

AbstractThe average strain energy density (ASED) criterion applied to design of notched mechanical components has been achieved a considerable success over the years thanks to its numerous advantages including the need for a relatively coarse mesh, the use of a scalar rather than vector quantity and the ability to compare the strength of parts with different notch angles. It is known that adhesively bonded joints mechanical strength is governed by the stress singularity arising near the intersection between the adhesive‐substrate interface and the free surface of the bonded joint, even without notches. This is due to the different elastic material properties of the adhesive compared to those of the substrate that induces a constitutive stress singularity. This phenomenon makes the strain energy density criterion particularly suitable for the design of bonded joints, as well. This contribution is aimed at applying the ASED criterion to the static strength assessment of bonded joints. Experimental results taken from literature were found in good agreement with those predicted by the ASED approach.

Using the Equivalent Material Concept and the Average Strain Energy Density to Analyse the Fracture Behaviour of Structural Materials

This paper provides a complete overview of the applicability of the Equivalent Material Concept in conjunction with the Average Strain Energy Density criterion, to provide predictions of fracture loads in structural materials containing U-notches. The Average Strain Density Criterion (ASED) has a linear-elastic nature, so in principle, it does not provide satisfactory predictions of fracture loads in those materials with nonlinear behaviour. However, the Equivalent Material Concept (EMC) is able to transform a physically nonlinear material into an equivalent linear-elastic one and, therefore, the combination of the ASED criterion with the EMC (EMC–ASED criterion) should provide good predictions of fracture loads in physically nonlinear materials. The EMC–ASED criterion is here applied to different types of materials (polymers, composites and metals) with different grades of nonlinearity, showing the accuracy of the corresponding fracture load predictions and revealing qualitatively the limitations of the methodology. It is shown how the EMC–ASED criterion provides good predictions of fracture loads in nonlinear materials as long as the nonlinear behaviour is mainly limited to the tensile behaviour, and how the accuracy decreases when the nonlinear behaviour is extended to the material behaviour in the presence of defects.

On the use of the combined FMC-ASED criterion for fracture prediction of notched specimens with nonlinear behavior

The Averaged Strain Energy Density (ASED) criterion has been widely used for the prediction of fracture conditions in a number of materials containing notch type defects, similarly to other well-known methodologies such as the Theory of Critical Distances (TCD). This criterion is linear-elastic, so the results obtained in linear-elastic materials have been accurate. However, as soon as the material behavior becomes nonlinear, the resulting accuracy decreases. With the aim of using linear-elastic simple methods (such as the ASED criterion) in nonlinear materials, several attempts have been made to convert a physically nonlinear behavior into an equivalent linear behavior. Thus, when the tensile behavior in plain specimens reveals nonlinearity, but the fracture behavior in the presence of defects is linear, the Equivalent Material Concept (EMC) has been successfully validated (EMC-ASED criterion). However, there are situations in which the nonlinear behavior takes place in both tensile and fracture behaviors, and the EMC-ASED criterion loses accuracy and requires further evolution. At this point, the Fictitious Material Concept allows the analysis of nonlinear materials (at both tensile and fracture conditions) to be performed with significant accuracy.In this context, this article provides the prediction of fracture loads in single edge notched bending (SENB) specimens made of short glass fiber reinforced polyamide 6 (SGFR-PA6, 10 wt.%) containing U-notches and different levels of moisture content. The predictions are obtained through the combination of the FMC and the ASED criterion (FMC-ASED combined criterion). The results are significantly more accurate than those obtained through the ASED and the EMC-ASED criteria, but less accurate than those used when combining the FMC with the TCD.

Validation of the Averaged Strain Energy Density Criterion for Additively Manufactured Notched Polylactide Acid Specimens

The applicability of the Averaged Strain Energy Density (ASED) criterion [1] to predict the failure of notched Polylactide Acid (PLA) specimens fabricated by Fused Deposition Modeling (FDM) is validated by means of experimental data reported by Ahmed and Susmel [2], Difficulties when estimating the ASED control volume radius based on the measured fracture toughness are revealed and discussed, whereas the accuracy of the ASED criterion is found to be satisfying when a novel alternative approach is used to define the control volume size.

Geometry effect on fracture behavior of V-notched specimens

Geometric constraint is one of the important issues that affect the fracture behavior of different notched components. Specimens with the same notch geometry can have different fracture strengths due to the geometric constraints around the notch tip. In this paper, the fracture behavior of three different testing specimens made of General Purpose Polystyrene (GPPS) has been studied using an energy-based criterion namely the Average Strain Energy Density (ASED) criterion. According to the formulation of the ASED criterion, all the stress terms around the notch tip were taken into account by considering a volumetric energy-based criterion and the brittle fracture of different GPPS specimens with various geometry constraints were well predicted.

On Suitability of the Averaged Strain Energy Density Criterion in Predicting Mixed Mode I/II Brittle Fracture of Blunt V-Notches with Negative Mode I Contributions

The main goal of the present research is to check the suitability of the well-known brittle fracture criterion, namely the averaged strain energy density (ASED), in predicting mixed mode I/II brittle fracture of round V notches under negative mode I conditions. For this purpose, it is attempted for the first time to theoretically predict the fracture loads of numerous round-tip V-notched Brazilian disk (RV-BD) specimens made of PMMA and subjected to mixed mode I/II loading with negative mode I contributions that have been most recently reported in the open literature. It is revealed that ASED criterion is suitable for brittle fracture prediction not only under conventional mixed mode I/II loading conditions, but also under mixed mode I/II loading with negative mode I contributions.

Rupture assessment of rubber/clay nanocomposites containing a crack by means of an energy-based fracture criterion

Due to the growing use of nanotechnology in the modern era, the application of nanomaterials in elastomers has also been increased. Although some limited experiments are available in the previous studies regarding the fracture behavior of rubber nanocomposites containing a crack, no criteria have been presented so far. To fill this gap, the current research is devoted to develop a criterion for rupture assessment of rubber nanocomposites weakened by a crack. First, some fracture tests are performed on cracked rubber/clay nanocomposites. The prepared nanocomposites are made of ethylene–propylene-diene monomer/styrene-butadiene rubber/CLOISITE 15. Afterwards, the averaged strain energy density (ASED) criterion, as one of the most used energy-based criteria, is extended and utilized in nano-reinforced hyperelastic materials. The nearly uniaxial state of stress field next to the crack tip in rubber nanocomposites, which is the main prerequisite for the criterion extension, is proved by means of non-linear finite element modelling. Finally, the estimations of the criterion is compared with the corresponding experimental data and good agreement is achieved which reveals the high performance of the ASED criterion in the case of cracked rubbers filled with nanoparticles.

Ductile Failure Prediction of U-Notched Bainitic Functionally Graded Steel Specimens Using the Equivalent Material Concept Combined with the Averaged Strain Energy Density Criterion

In this paper, the ductile fracture of bainitic functionally graded steel has been studied. Fracture tests was performed on U-notched specimens made of bainitic functionally graded steel under mode I. The averaged strain energy density criterion combined with equivalent material concept was employed to predict the ductile fracture of bainitic functionally graded steel. For this purpose, first, based on equivalent material concept, the mechanical properties of virtual brittle functionally graded steel were obtained. Then the averaged value of strain energy density over a well-defined control volume was calculated by finite element analysis for U-notched virtual brittle functionally graded steel. After that, the fracture loads was obtained based on the averaged strain energy density criterion. The agreement between experimental fracture loads and theoretical predictions was good.

Fracture analysis of rounded-tip V-notched components made of rubber-like materials using averaged strain energy density criterion

Nowadays, hyperelastic materials such as rubbers and elastomers have become increasingly important in research and industry. However, the existence of any geometric discontinuities like a crack or notch will affect the behavior of rubbers. Thus, the prediction of rupture condition in these materials is of paramount importance. One of the energy-based criteria, which has attracted many attentions due to its convenience in use and high precision, is the averaged strain energy density (ASED) criterion. Based on this criterion, a limited amount of energy in a specified volume around the stress concentration region controls the fracture of components. This criterion, which was already utilized extensively for brittle materials, has been recently extended for being used in cracked components having non-linear behavior like rubbers. On the other hand, by examining the previous studies, it can be concluded that despite the importance of rounded V-shaped notch, no research has been carried out in the presence of this type of stress concentration in hyperelastic materials. As a consequence, this study is devoted to investigate the rupture of rubbers containing a round-tip V-shape notch using the ASED criterion. To this end, first, some experiments are performed for rounded-tip V-notched rubber samples. Afterwards and in order to utilize the ASED criterion for predicting the rupture loads of tested samples, some finite element modeling considering both geometric and material non-linearities are performed. The comparison between the estimations of the ASED criterion and the corresponding experimental data reveals the high efficacy of this criterion in hyperelastic materials weakened by round-tip V-shape notches.