Search Results (47)

The paper proposes and tests an approach to determine the stress intensity factors (SIF) of cracks subjected to mode III using full-field displacements as opposed to the crack opening displacement (COD) method, which uses only two data points. The proposed scheme fits displacement data into Williams’ series for cracks, solving the equations using the over-deterministic Least Squares Method (LSM). The method is tested in tubes with through-cracks under axial and cyclic torque loading, and both proportional and non-proportional loading. The Digital Image Correlation (DIC) technique measured the displacement fields, and an approach is presented to address the curvature error in the tube samples. The experimentally determined SIF and SIF ranges with the proposed method are compared with respective values found using COD equations showing a pronounced nonlinear variation. It is concluded that for most, both methods agree, and for the LSM, the number of expansion terms in Williams’ series seems to make no difference, exhibiting less noisy results than the COD method and effectively addresses nonlinear variations in SIF calculations across different loading conditions, ultimately enhancing the understanding of crack behavior under mode III loading. Full article

Rib–deck (RD) welded joints in orthotropic steel bridge decks are prone to different fatigue crack mechanisms. Standard fatigue design methods are inadequate for some of these mechanisms under multiaxial non-proportional loading conditions. This study presents a framework to assess fatigue damage at RD welded joints, considering the different crack mechanisms based on the equivalent structural stress method and its extension to multiaxial non-proportional fatigue, which is the path-dependent maximum stress range (PDMR) cycle counting algorithm. The method is validated for uniaxial loading by using experimental data from the literature. Additionally, non-proportional fatigue damage at RD welded joints of a suspension bridge girder is investigated under simulated random traffic loading. The analyses reveal the limitations of the nominal stress approach to account for complex stress field variations. The PDMR method, more suited to capture the stress path dependency of non-proportional fatigue damage than the hot spot and critical plane-based methods, predicts higher fatigue damage. A comprehensive fatigue test campaign of full-scale RD welded joints is necessary to better understand their fatigue behaviour under multiaxial loading. Until more experimental data are available, the PDMR method is recommended for fatigue verifications of welded RD joints as it yields safer predictions. Full article

A non-proportional reduction in strength parameters is widely used in slope stability assessment, but the current asynchronous reduction in strength parameters only considers the cohesion c and internal friction angle φ, which is suitable for slope stability assessment under static loads. Under seismic loads, however, tension at the rear edge of the slope often accompanies the appearance of ground cracks. In order to consider the relationship between tensile strength, cohesion, and the internal friction angle reduction coefficient, starting with the linear softening attenuation law of soil material strength parameters, a functional relationship between cohesion and internal friction angle is obtained. Then, considering that the failure of microelements in the tensile and shear zones conforms to the tension and shear of joint failure, the relationship between tensile strength, cohesion, and the internal friction angle reduction coefficient is derived. By establishing a homogeneous slope model and comparing and analyzing the progressive instability failure modes of slopes under static and seismic conditions, the stability and potential slip surface differences of slopes under two different working conditions are explored. The research results indicate that slope instability is a gradual, cumulative failure process under both static and dynamic conditions. The instability mode of the slope under static conditions is shear failure. In contrast, under dynamic loads, the instability failure of the slope is manifested as shear failure upward at the foot of the slope and tensile failure downward at the top of the slope. The stability coefficient of slopes under earthquake conditions is reduced by 17.3% compared to that under static conditions. Under earthquake conditions, the potential sliding surface under an asynchronous reduction in strength parameters is shallower than that under static conditions and deeper than that without an asynchronous reduction in strength parameters. Overall, the research results provide a reference for slope stability analysis and support design optimization under earthquake loads. Full article

Sediment transport in urban streams is a critical environmental issue, with significant implications for water quality, ecosystem health, and infrastructure management. Accurately estimating suspended sediment concentration (SSC) is essential for effective long-term environmental management. This study investigates the relationships between streamflow, turbidity, and SSC in Dry Creek, South Australia, to understand sediment transport dynamics in urbanised catchments. We collected grab samples from the field and analysed them in the laboratory. We employed statistical modelling to develop a sediment rating curve (SRC) that provides insights into the sediment transport dynamics in the urban stream. The grab sample measurements showed variations in SSC between 3.2 and 431.8 mg/L, with a median value of 77.3 mg/L. The analysis revealed a strong linear relationship between streamflow and SSC, while turbidity exhibited a two-regime linear relationship, in which the low-turbidity regime demonstrated a stronger linear relationship compared to the high-turbidity regime. This is attributed to the urbanised nature of the catchment, which contributes to a first-flush effect in turbidity. This contributes to sediment hysteresis, resulting in non-proportional turbidity and SSC responses to streamflow changes. The findings demonstrate the effectiveness of a streamflow-based SRC for accurately predicting sediment discharge, explaining 97% of the variability in sediment discharge. The sediment discharge predicted using the SRC indicated a sediment load of 341.8 tonnes per year along the creek. The developed sediment rating curve provides a valuable tool for long-term sediment management in Dry Creek, enabling the assessment of downstream environmental risks. By addressing data limitations, this study contributes to a deeper understanding of sediment transport dynamics in urbanized environments, offering insights for informed decision-making and effective sediment management strategies. Full article

The largest normal stress excursion during contiguous turn time instants of the maximum torsional stress is presented as an innovative path-independent fatigue damage quantity upon the critical plane, which is further employed for characterizing fatigue damage under multiaxial loading. Via using the von Mises equivalent stress formula, an axial stress amplitude with equivalent value is proposed, incorporating the largest torsional stress range and largest normal stress excursion upon the critical plane. The influence of non-proportional cyclic hardening is considered within the presented axial equivalent stress range. Moreover, according to proposed axial equivalent stress amplitude, an energy-based damage model is presented to estimate multiaxial fatigue lifetime upon the critical plane. In order to verify the availability of the proposed approach, the empirical results of a 7050-T7451 aluminum alloy and En15R steel are used, and the predictions indicated that estimated fatigue lives correlate with the experimentally observed fatigue results well for variable amplitude multiaxial loadings. Full article

During the manufacturing and service of thin metal sheets, different stress states occur, often caused by non-proportional loading conditions. They can lead to localization of inelastic deformations as well as to damage and failure processes. In the present paper, a series of experiments with newly designed biaxially loaded specimens is presented to analyze the damage and failure behavior of thin ductile metal sheets under non-proportional load paths. Bands of holes with different orientation have been milled in critical regions of the specimens to localize stresses and strains. In compression tests, a special downholder is used to avoid buckling. During the loading processes, strain fields in critical regions of the specimens are monitored by digital image correlation technique. After the experiments, fracture surfaces are investigated by scanning electron microscopy showing different damage and fracture modes depending on the loading history. The experiments clearly demonstrate the efficiency of the thin specimens and the experimental program. Full article

In order to clarify the fracture behavior of a unidirectional CFRP under proportional loading along the fiber (0°) and fiber vertical (90°) directions, a biaxial tensile test was carried out using a cruciform specimen with two symmetric flat indentations in the thickness direction. Three fracture modes were observed in the specimens after the test. The first mode was a transverse crack (TC), and the second was fiber breakage (FB). The third mode was a mixture mode of TC and FB (TC&FB). According to the measured fracture strains, regardless of the magnitude of the normal strain in the 0° direction, TC and TC&FB modes occurred when the normal strain in the 90° direction, ${\epsilon }_y$, ranged from 0.08% to 1.26% (positive values), and the FB mode occurred when ${\epsilon }_y$ ranged from −0.19% to −0.79% (negative values). The TC&FB mode is a unique mode that does not appear as a failure mode under uniaxial tension; it only occurs under biaxial tensile loading. Biaxial tensile tests were also conducted under non-proportional loading. The result showed three fracture modes similarly to the proportional loading case, each of which was also determined by the positive or negative value of ${\epsilon }_y$. Thus, this study reveals that the occurrence of each fracture mode in a unidirectional CFRP is characterized by only one parameter, namely ${\epsilon }_y$. Full article

This paper presents a model to calculate the opening angle of crack initiation in notched fractures subjected to multiaxial loading. To validate the proposed model, a study was performed on polished AZ31B-F magnesium alloy specimens under multiaxial high-cycle fatigue loading. The specimens exhibited a notch in the smaller cross-sectional area, which was created with a special drilling jig to promote the formation of fatigue cracks in this localized area of the specimen. The load paths used in the experiments and numerical analyses were proportional and non-proportional, resulting in different stress states in the crack front opening, which were determined by finite element analysis to validate the proposed model. To obtain more accurate numerical results for these estimates, these finite element analyses were performed using the nonlinear Chaboche plasticity model of ABAQUS^® 2021 software. A sensitivity analysis was also performed to determine which load component—axial or torsional—has a greater influence on the fatigue strength and contributes significantly to the crack opening process. The results show that the type of load path and the stress level of each load component—axial and torsional—has a strong influence on the opening angle of the notch crack and the fatigue lifetime of the specimen. This result is confirmed not only by the experimentally determined fatigue strength, but also by a fractographic analysis performed on the surface of the specimens for both load paths. Moreover, the results show an acceptable correlation between the experimental results and the estimates obtained with the proposed model and the stresses obtained with the finite element analysis. Full article

The effectiveness of a ductile fracture model in accurately predicting fracture initiation has been demonstrated. In this study, we concentrate on applying the ductile fracture model to pre-cracked structures constructed from SUS304L stainless steel with experimental and numerical analyses. The Swift hardening law was employed to extend the plastic behavior beyond the onset of necking. Additionally, the Hosford–Coulomb model, integrated with a damaged framework, was utilized to predict ductile fracture behavior, particularly under non-proportional loading conditions. Tension tests were conducted on various specimens designed to illustrate various fracture modes resulting from geometric effects. Numerical analyses were conducted to explore the loading histories, utilizing an optimization process to calibrate fracture model parameters. The proposed fracture model is validated against pre-cracked structures detailed in a reference paper. The results convincingly demonstrate that the fracture model effectively predicts both fracture initiation and propagation in pre-cracked structures. Full article

This paper proposes a robust design-optimization approach for eBike drive units that incorporates the highly variable driver-dependent load collectives and system conditions into a fatigue calculation. In an initial step, the relevant influences and loads on the investigated system are examined and reviewed in relation to the current normative requirements. From a methodical viewpoint, this paper presents a surrogate-based simulation-based approach to assess reliability across the entire geometry according to a probabilistic fatigue calculation. The probabilistic evaluation considers the several measured load collectives of different drivers and driving scenarios to enable a robust and type-oriented bike design. In addition to methods of fatigue calculation, this approach also includes common methods of order reduction and reliability-based design optimization. To avoid additional uncertainties in the calculation, this approach considers a complex critical-plane-based multiaxial-fatigue calculation to correctly evaluate the multiaxial and non-proportional stress state across the whole geometry. A data-based surrogate model that supports the fatigue calculation by predicting the load across the given uncertainties is the key to the efficient assessment of the service life of the eBike. Lastly, the identified uncertainties in the design of eBike drive units are investigated and evaluated by this method. Full article

This paper deals with the study of the mechanical responses of ductile metals under biaxial non-proportional cyclic loading tests. The biaxially loaded HC specimens manufactured from 4 mm thick aluminum alloy sheets (EN AW 6082-T6) are subjected to various loading paths, including monotonic and cyclic loading conditions. The aim is to investigate the plastic, damage, and fracture behavior of the material under these different loading scenarios. In terms of numerical aspects, a modified anisotropic two-surface cyclic plastic–damage continuum model is used to predict the material behavior in the load-displacement field and different strain fields. Numerically predicted stress states are analyzed in detail to gain a better understanding of the damage mechanisms. Moreover, the scanning electronic microscopy (SEM) pictures taken from the fracture surfaces confirm the dependency of the damage mechanisms on the loading histories. The present work indicates the importance of considering different loading conditions for the accurate prediction of material responses. Full article

This paper presents a finite element analysis of the bi-directional orthogonal model, which incorporates individual crack strain separation and tracking. The objective of this research is to expand the current shear friction model to manage bi-directional cracking at any angle, allowing for a more universal model that can be applied to intricate structures and non-proportional loading cases. The proposed model was initially developed as a total strain-based model, with the assumption that crack strains are equivalent to total strains, but it was subsequently recalculated to improve accuracy by separating crack strains from total strains. Furthermore, a separate crack strain formulation was created to account for strains in the concrete’s uncracked portions and locked-in crack strains. The article then discusses the testing of various convergence methods and loading programs to achieve high convergence. Comparative analyses of the generalized shear friction model with other models for crack orientation, and loading cases similar to those of a reinforced concrete membrane, are also presented. The MATLAB program successfully applied the bi-directional cracking model for one finite element under a uniform cyclical strain state, using a secant stiffness formulation. Full article

Under strain control tests and cyclic loading, extruded magnesium alloys exhibit a special mechanism of plastic deformation (“twinning” and “de-twining”). As a result, magnesium alloys exhibit an asymmetric material behavior that cannot be fully characterized with the typical numerical tools used for steels or aluminum alloys. In this sense, a new phenomenological model, called hypo-strain, has been developed to correctly predict the cyclic stress–strain evolution of magnesium alloys. On this basis, this work aims to accurately describe the local cyclic elastic–plastic behavior of AZ31B-F magnesium alloy under multiaxial cyclic loading with Abaqus incremental plasticity. The phenomenological hypo-strain model was implemented in the UMAT subroutine of Abaqus/Standard to be used as a design tool for mechanical design. To evaluate this phenomenological approach, the results were correlated with the uniaxial and multiaxial proportional and non-proportional experimental tests. In addition, the estimates were also correlated with the Armstrong–Frederick nonlinear kinematic hardening model. The results show a good correlation between the experiments and the phenomenological hypo strain approach. The model and its implementation were validated in the strain range studied. Full article

In this work, the magnesium alloy AZ31BF subjected to proportional and non-proportional loads has been studied. For this purpose, a series of experimental multiaxial fatigue tests were carried out according to the ASTM E466 protocol. The main objective was to determine the relationship between the multiaxial fatigue strength of this alloy under these two different types of loading. The results showed that the AZ31BF magnesium alloy has different fatigue strengths depending on the loading type. Based on these results, it was found that the ratio between proportional and non-proportional damage in AZ31BF magnesium alloy varies depending on the number of loading cycles. To represent this variation, parameter Y was used to modulate the non-proportional damage of AZ31BF. In this way, two Y functions were considered, one for the normal stress component and the other for the shear stress component. The results obtained for the non-proportional parameter Y are of particular interest since the multiaxial fatigue models do not distinguish between these two types of loading when evaluating fatigue life. In this sense, the results of this study can be used in these models to overcome this limitation. Full article

As is well-known, non-proportional fatigue loading, such as asynchronous one, can have significant detrimental effects on the fatigue behavior of metallic materials by reducing the fatigue strength/fatigue limit and by leading to a fatigue damage accumulation increased with respect to that under proportional loading. In the present paper, the novel refined equivalent deformation (RED) criterion is applied for the first time to estimate the fatigue lifetime of materials, sensitive to non-proportionality, subjected to asynchronous loading under low-cycle fatigue regime. The present criterion is complete since it considers: (i) the strain path orientation, (ii) the degree of non-proportionality, and (iii) the changing of material cyclic properties under non-proportional loading. To evaluate its accuracy, this criterion is applied to examine two different metals (a 304 stainless steel and a 355 structural steel) whose experimental data under multiaxial asynchronous loading are available in the literature. More precisely, the parameters of the criterion are firstly determined by using experimental strain paths, and then the computed refined equivalent deformation amplitude is used to represent the experimental data with a satisfactory accuracy. Finally, a comparison with the results obtained through two other criteria available in the literature is performed, highlighting the good prediction of the present RED criterion. Full article