Average Strain Energy Research Articles

Experimental study on multiscale strain localisation based on soil cell element model

The granular and natural characteristics of soil introduce size effects to its deformation and strength properties. Therefore, investigating the phenomenon of strain localisation in soil requires a multi-scale characterisation. This study examined the intrinsic scale patterns in samples with different sizes of reinforcing particles through triaxial compression tests. Additionally, the formation mechanism of microscopic shear bands was investigated using numerical simulation methods. Drawing from the soil cell model theory, the average strain energy release coefficient was introduced to validate the transformation of the overall strain energy of the specimen after reaching the peak stress. This reflects the progressive initiation and competitive process of multiple bands. The results indicate that samples with different sizes and types of reinforcing particles exhibit various failure patterns, including single-type, ‘x’-shaped, ‘v’-shaped, parallel and others. The soil exhibits size effects, with the ratio of intrinsic scale to particle size decreasing as the size of reinforcing particles increases. Prior to the stress peak, non-elastic dissipation energy begins to increase, indicating the initiation of plastic deformation in the soil. Localised strain zones are activated, and after the peak, there is a sharp increase in stress within the shear bands, accompanied by rebound outside the band.

Comparison of Early Postoperative Stress Distribution around Short and Tapered Wedge Stems in Femurs with Different Femoral Marrow Cavity Geometries Using Finite Element Analysis.

In total hip arthroplasty (THA), the ideal stem length remains uncertain; different stem lengths are used in different cases or institutions. We aimed to compare the stress distributions of cementless tapered wedges and short stems in femurs with different femoral marrow geometries and determine the appropriate fit. Finite element models were created and analyzed using HyperMesh and LS-DYNA R11.1, respectively. The 3-dimensional shape data of the femurs were extracted from computed tomography images using the RETOMO software. Femurs were divided into 3 groups based on the Dorr classification. The computer-aided design data of cementless tapered wedge-type and short stems were used to select the appropriate size. In the finite element analysis, the loading condition of the femur was assumed to be walking. Volumes of interest (VOIs) were placed within the femur model at the internal and external contact points of the stem based on Gruen zones. The average stresses and strain energy density (SED) of the elements included in each VOI were obtained from the preoperative and postoperative models. The von Mises stress and SED distributions of the cementless tapered wedge and short stems were similar in their respective Dorr classifications. In both stems, the von Mises stress and SED after THA were lower than before THA. The von Mises stress and SED of the cementless tapered wedge stem were higher than those of short stems. Cementless tapered wedge-type stems tended to have lower rates of change than short stems; however, Dorr C exhibited the opposite trend. In the Dorr classification comparison, the von Mises stress and SED were greater for both stems in the order of Dorr C > Dorr B > Dorr A, from Zone 2 to Zone 6. In Dorr A and B, the short stem exhibited a natural stress distribution closer to the preoperative femur than the tapered wedge stem; however, in Dorr C, the short stem may have a greater effect on stress distribution, suggesting that it may cause greater effects, such as fracture in the early postoperative period, than other Dorr types.

Predicting fatigue life of additively manufactured lattice structures using the image-based Finite Cell Method and average strain energy density

A well-known Achilles' heel of laser powder bed fusion (L-PBF) additive manufactured lattice structures is the difficulty in predicting fatigue properties. The presence of manufacturing-induced defects significantly affects the fatigue resistance of the porous component and must be accurately captured by predictive models. To tackle this challenge, the as-built geometry of the lattice needs to be modeled, which introduces another challenge on the computational front. For the first time, a model based on the computer tomography (μ-CT) reconstruction of the as-built lattice geometry is simulated with the efficient finite cell method and combined with the average strain energy density (ASED) to obtain accurate fatigue predictions. This work presents a workflow for determining the fatigue resistance of lattice metamaterial, followed by a case study for method validation. The validation shows a good agreement between the predicted fatigue life and the experimental results.

Experimental and numerical study on the effect of friction between crack faces on fracture parameters of hot mix asphalt concrete

This article investigates the effect of friction between crack faces in ASCB (asymmetric semi-circular bend) specimen on fracture parameters of hot mix asphalt concrete. To achieve this, fracture tests were conducted on ASCB specimens containing cracks with different angles (0, 10, 20, 30, and 40°). In addition to the fracture tests, friction tests were also performed by designing a simple fixture. Subsequently, finite element analyses were carried out, and friction coefficients between crack faces were calculated based on the results of fracture and friction tests. Furthermore, two fracture criteria, ASED (average minimum strain energy density) and MTS (maximum tangential stress), were examined under two different scenarios: assuming zero-friction and non-zero friction between crack faces to predict fracture load and fracture strength. The fracture tests showed that with an increase in the crack angle, the fracture load initially decreased up to the crack angle of 20°, and then increased. Furthermore, the friction tests revealed that an increase in the normal load led to an increase in the friction coefficient. As per finite element results, the crack face contact occurred at a crack angle of 13.1°. Hence, crack faces in the ASCB specimens with the crack angles of 20, 30, and 40° had friction, which significantly affected the fracture parameters. The results also indicated that the average error values for the MTS and ASED criteria compared to the experimental results were 22.8 % and 18.8 %, respectively, when the friction` between crack faces is ignored, and 12.4 % and 4.0 % for the scenario that the friction effect is taken into account. The ASED criterion demonstrated higher accuracy than MTS criterion. Additionally, the average error value of fracture strength predicted by the ASED criterion with assuming non-zero friction was 4 %, indicating good predictive accuracy for fracture strength.

Analysis of high temperature and strain amplitude effects on low cycle fatigue behavior of pitting corroded killed E350 BR structural steel

High-tension structural steels are prone to accelerated fatigue damage from pitting corrosion and high-temperature. Despite adverse effects, research on their low cycle fatigue (LCF) behavior is limited. Specifically, studies analyzing temperature-dependent pit sensitivity effects, considering pit-related material’s susceptibility to surface topographic features variation and stress concentration are lacking. This study conducts LCF tests on pitting corroded killed E350 BR structural steel at multiple strain amplitudes and high temperatures. It develops temperature-dependent parameters, such as the cyclic softening pit sensitivity factor, suitable for integration into existing approaches like total cyclic plastic strain energy density (CPSED), power-law, average strain energy density (SED), Coffin-Manson, and pit stress intensity factor (pit-SIF). Further, it proposes multiple linear regression-based prediction models relating total CPSED and average SED with strain amplitude and temperature. Corroded specimens show higher plastic deformation and reduced peak stress, fatigue life, and total CPSED compared to uncorroded ones. The developed parameters, integrated with average SED approach, predicts LCF life within an error band of ±1.5, while power-law relationship reduces it to ±1.2. Moreover, pit-SIF approach estimates fatigue life within an error band of ±1.5. The findings provide critical knowledge for enhanced component design, leading to structural safety, performance, and fire resilience.

Nonlinear viscoelastic effect on the fatigue performance of wood tar-based rejuvenated asphalt

The nonlinear viscoelasticity (NLVE) effects of rejuvenated asphalt are often neglected during fatigue degradation, potentially leading to misjudgment of its true fatigue performance. To more accurately quantify the fatigue life of rejuvenated asphalt under NLVE effects, frequency sweep (FS), incremental stress sweep (ISS), and linear amplitude sweep (LAS) tests were used to study two types of rejuvenated asphalt. FS and ISS tests respectively obtained the dynamic modulus |G*|LVE and |G*|NLVE representing the linear viscoelasticity (LVE) and NLVE of rejuvenated asphalt, and incorporated them into the simplified viscoelastic continuum damage (S-VECD) model to establish the fatigue failure criterion and predict the fatigue life of rejuvenated asphalt under high strain levels in LAS tests. The findings indicate that the NLVE-based-S-VECD model quantifies fatigue damage in rejuvenated asphalt lower than the LVE model, and the fatigue life of rejuvenated asphalt increases significantly after considering the NLVE effect. Besides, the failure difference (∆GR) and failure area difference (∆A) defined during the modeling process explain the impact of NLVE on the fatigue failure criterion average pseudo strain energy release rate (GR) of rejuvenated asphalt, validating the necessity of incorporating NLVE into the fatigue performance analysis of rejuvenated asphalt. Therefore, it's necessary to account for the impact of NLVE effect on the fatigue performance of rejuvenated asphalt in engineering practice, which will contribute to the development and application of rejuvenator.

A simplified approach for predicting last ply failure load of VO-notched laminated composite components

In this study, the last ply failure (LPF) load of composite laminates with VO-notches under pure mode I and mixed mode I/II was investigated experimentally, analytically, and numerically. The efficiency of the virtual isotropic material concept (VIMC) in combination with a new combined failure criterion was also evaluated. The J-integral and average strain energy density failure criteria were combined with VIMC. Using analytical expressions for the J-integral and the average strain energy density (ASED), the prediction of the fracture load of notched components was simplified and expedited. The experimental fracture loads of notched specimens were determined for quasi-isotropic and cross-ply laminates under mode I and mixed mode I/II. The fracture loads were predicted using analytical expressions for the J-integral and ASED, combined with VIMC. The VIMC-ASED and VIMC-J-integral failure criteria demonstrated good accuracy in predicting the LPF, with the highest accuracy for mode I, slightly reduced accuracy for mixed mode I/II. VIMC, in combination with energy-based failure criteria, effectively predicts the fracture load. The use of analytical expressions further simplified and expedited the prediction process without losing accuracy, making it a practical approach for engineering applications. Additionally, this approach significantly reduces the time and cost associated with extensive experimental testing.

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.

Experimental study on failure mechanism of soft rock-coal bodies in abandoned mines under cyclic dynamic loading

During the construction and operation of a pumped storage power station in an abandoned mine, the soft rock-coal body structure, comprising the roof and the residual coal pillars, encounters a complex stress environment characterized by cyclic loads. The study of its failure mechanism under cyclic dynamic loading holds significant theoretical and practical importance to stay the safety and stability of the abandoned mine pumped storage power station. In this paper, we take “roof-residual coal pillar” soft rock-coal combinations with different percentages of rock as the research object, and study their mechanical properties, failure mechanism, energy evolution characteristics and acoustic emission distribution characteristics through cyclic dynamic loading experiments. The results of the experiment indicate that: (1) Both weak cyclic dynamic loading and high rock percentage enhance the deformation resistance of soft rock-coal combinations. Under low-disturbance horizontal cyclic loading, its peak strength and modulus of elasticity increase with increasing rock percentage. (2) Under low-disturbance horizontal cyclic loading, an increasing trend is observed in the average total strain energy density, dissipation energy density, and elastic energy density of the combinations as the percentage of rock increases. (3) Under low-disturbance horizontal cyclic loading, as the percentage of rock increases in the soft rock-coal combinations, the degree of failure in the rock body part progressively intensifies, while the destruction of the coal portion progressively decreases. (4) The large number of acoustic emission signals are generated at the instant of destabilization and destruction of the coal-rock combinations, mainly dominated by the signals generated by the destruction of the coal body. Acoustic emission counts and absolute energy at key point N2 decrease as the percentage of rock increases. The b value is primarily distributed in the cyclic dynamic loading stage and the failure stage, both displaying zones of sudden increase and sudden decrease in b value.

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 %.

Impact of uniaxial strain on physical properties of zigzag graphene nanoribbons with topological defects

The synergistic regulation mechanism of uniaxial strain, topological defects, edge passivation atom and nanoribbon width on the geometric and electronic structures of zigzag graphene nanoribbons have been studied systematically by first-principles. It is found that the average formation energy and strain energy of X-N 1 N 2-LD-ZGNR (X = H, F and O, as well as, N 1 = N 2 = 3, 4 and 5) increase with the increase of uniaxial strain, and this relationship is also dependent of edge passivation atom species and nanoribbon width. And the edge of 55-LD-ZGNR passivating with O and F atoms is more beneficial than H atom for system stability. The stress–strain curve shows that the limiting strain of zigzag graphene nanoribbon depends on edge passivation atom species and nanoribbon width. The Young’s modulus in the case of ε > 3% and Poisson’s ratio except O-33-LD-ZGNR at ε = 1% of X-N 1 N 2-LD-ZGNR decrease with the increase of the tensile strain, and is dependent of nanoribbon width and edge atom species. And O-55-LD-ZGNR is easier than F-55-LD-ZGNR and H-55-LD-ZGNR to be stretched or compressed. The magnetism is induced in both H-55-LD-ZGNR and F-55-LD-ZGNR, and remains with the increases of uniaxial tension strain. What is more, magnetic property of O-55-LD-ZGNR can be regulated by applying uniaxial strain, and the band gap of the O-N 1 N 2-LD-ZGNR (N 1 = N 2 = 3, 4 and 5) system can be regulated by adjusting the uniaxial tensile strain and nanoribbon width. Our research provides a new method to open the graphene band gap, which can provide some new theoretical guidance for the application of graphene in electronic devices and other fields. The band gap of the O-LD-ZGNDR system is opened as the uniaxial tensile strain increases.

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.