Multiaxial Stress Research Articles

Local Yield Stress and Its Unusual Independence on Multi-axial Stress States during Lüders Deformation of Medium-Mn, High-strength Steel

Local Yield Stress and Its Unusual Independence on Multi-axial Stress States during Lüders Deformation of Medium-Mn, High-strength Steel

Stress redistribution and stress triaxiality effect on the fatigue life of notched Ni-based single crystal superalloy at 760℃

The multiaxial stress state caused by geometric discontinuities will result in significant differences in the fatigue performance compared to the uniaxial stress state. It is crucial importance to research the notch fatigue behaviors of nickel-based single crystal (Ni-SX) superalloys at high temperature. This study investigated the impact of stress redistribution and stress triaxiality on the fatigue life of notched Ni-based single crystal superalloy at 760℃. The high temperature fatigue tests were carried out on the specimens under different stress ratios and the stress amplitudes under the same life conditions were obtained. A novel anisotropic damage model, incorporating the influence of stress triaxiality is proposed coupled with crystal plasticity theory. Based on experimental findings, an evaluation of the test parameters was conducted.The results showed that Mises stress, maximum principal stress, normal stress of principal stress along the loading direction, maximum principal strain, and strain along the loading direction were inadequate in reflecting the significant variations of samples observed among different stress ratios. However, the stress triaxiality at the unloading valley exhibited a high sensitivity to changes in fatigue life. To evaluate the fatigue life of notched specimens under different stress ratios, an improved Basquin’s type life prediction model was proposed, utilizing the stress triaxiality at the unloading valley. The proposed model demonstrates a favorable normalization trend for the fatigue life of notched specimens subjected to various stress concentration factor (SCF) conditions.

Plastic behavior of a film type of epoxy adhesive under a wide range of stress multiaxiality conditions

The yield stress of rubber-modified epoxy adhesives is affected by hydrostatic stress in the adhesive layer. It is necessary to clarify whether hydrostatic stress modeling is essential for highly toughened epoxy adhesives and how hydrostatic stress should be considered under high multiaxial stress conditions. The elastic–plastic stress–strain behavior of a film-type epoxy adhesive AF163-2U was examined using a bulk adhesive tension test and a thick adherend shear test (TAST). The exponent Drucker–Prager model with an appropriate hydrostatic-stress sensitivity parameter (λ-parameter = 1.639) fully described the stress–strain curves both for the bulk adhesive tension test and TAST. The Hill’48 model of hydrostatic-stress-independent plasticity also simulated the bulk adhesive tension test and TAST as a response by determining the appropriate anisotropic parameters. To examine the effect of extremely high hydrostatic stress, a butt-joint tensile test and a finite element (FE) simulation were conducted using the exponent Drucker–Prager and Hill’48 models. The Hill’48 model completely failed in the butt-joint tensile test simulation. The exponent Drucker–Prager model, where a higher λ-parameter (=2.1) was required; consequently, it was concluded that the hydrostatic-stress effect should be considered for the adhesive model and the λ-parameter is not a fixed value but increases with increasing hydrostatic stress.

Testing the properties of cemented tailings backfill under multiaxial compressive loading

The engineering design of cemented paste backfill (CPB) typically relies on technical data obtained from tests conducted on CPB samples cured under conventional laboratory conditions. However, these methods often fall short in capturing the complex multiaxial stress curing conditions that CPB masses experience in many underground mines, particularly in deep underground mines. In these mining environments, CPB is subjected to multi-axial stress conditions during the curing process that are challenging to replicate in a controlled laboratory setting. No lab-scale apparatus can currently accurately reproduce these actual field multiaxial stress conditions, especially the intricate interplay of horizontal rockwall closure stresses, vertical self-weight stress, and overburden stresses from upper layers. Moreover, the impact of these conditions on the key engineering properties of CPB is unknown. To address this significant challenge and technology gap, this study has developed a new apparatus for curing and monitoring CPB under realistic multiaxial compressive loading conditions, simulating the complex stress environment encountered in underground mines. The developed apparatus was then utilized to assess the impact of multiaxial stress curing conditions, including vertical stress and horizontal stresses induced by rockwall closures, on key engineering properties (strength, deformation behaviour, self-desiccation) of CPB at early ages. The research results clearly indicate that the application of multiaxial stresses leads to a significant enhancement in the mechanical and physical properties of CPB. This enhancement is supported by observable densification of the pore structure in CPB subjected to multiaxial compressive stresses. In addition, a comprehensive analysis of deformation and strain patterns establishes a direct correlation between multiaxial stresses and the progressive increase in stiffness and hardness of CPB over time. Furthermore, the evolution of matric suction and degree of saturation provides compelling evidence of the significant impact of multiaxial stresses on pore water consumption or self-desiccation. The development of this new apparatus fills a substantial void in CPB research capabilities. Furthermore, the results obtained provide a better understanding of the complex behavior of CPB in multi-stress loading environments, paving the way for the design and optimization of backfill solutions that effectively address the unique challenges posed by deep underground mining operations.

Progressive fatigue damage modeling of laminated composites using a novel combined fatigue life model

The progressive fatigue damage (PFD) model is a comprehensive method to simulate the fatigue damage behavior of laminated composites under multiaxial cyclic stress. The generalized material property degradation (GMD) technique is a component of the PFD model. Also, the fatigue life modeling of a UD ply under a uniaxial state of stress is a subcomponent of the GMD technique. The present article compares and evaluates the results achieved by using different fatigue life models within the GMD technique. For this purpose, three commonly used fatigue life models (the normalized fatigue life model, the Luders fatigue life model, and the unified fatigue life model) were considered. Based on the capabilities of these models in predicting the fatigue life of unidirectional plies, a combined fatigue life model is developed and integrated into the progressive fatigue damage model. The results demonstrate that using the combined fatigue life model improves the prediction accuracy of the PFD model.

Multiscale-based multiaxial fatigue model of short fiber reinforced polymer composites under high-cycle proportional loading

Due to the inhomogeneity and anisotropy of short fiber-reinforced polymers (SFRP), even uniaxial loading can induce multiaxial stress states inside them, which significantly increases the difficulty of grasping their fatigue behavior. To efficiently predict the fatigue life of SFRP under proportional multiaxial stress, a multiaxial high-cycle fatigue model is proposed, relying upon the multiscale modeling strategy capable of integrating the influence of fiber microstructure. Taking the fiber-matrix interface stress at the critical region as the internal driving factor of fatigue fracture is the core assumption verified by microscopic observations. Off-axial fatigue tests with different orientations and stress ratios are performed to validate the fatigue model. Results show that the prediction accuracy has reached an acceptable level, and the quadratic polynomial surface can well represent the relationship between fatigue life and multiaxial stresses. This work provides an efficient tool for multiaxial fatigue life prediction and expounds the failure behavior of SFRP from multiscale perspectives.

Biaxial compressive capacity of textile-reinforced concrete

The structural behaviour of textile-reinforced concrete (TRC) components under uniaxial compressive loading has already been studied. However, for practical applications, multi-axial loading conditions are often of great importance. It is well known from steel-reinforced concrete that multiaxial compressive stresses lead to increased compressive strength. The extent to which this assumption can be transferred to TRC components should be investigated. This paper investigates the influence of textile carbon grid reinforcement on the compressive capacity of disc-shaped concrete specimens. The specimens were subjected to a biaxial compressive load in the plane of the reinforcement. Emphasis was placed on the influence parameters of production type of the disc specimens (laminated or poured), impregnation material of the carbon textile (polystyrene or epoxy resin) and number of reinforcement layers. It was found that the general presence of a textile reinforcement as a two-dimensional interference plane had the greatest influence on the compressive capacity of the specimens, while the other parameters investigated played a minor role. Depending on the load ratio in the two compression axes, there were increases or decreases in capacity compared to the uniaxial tests. This has to be taken into account in the design of the corresponding components. Finally, an outlook is given on future investigations planned to support and extend the results presented in this paper.

Local Yield Stress and its Unusual Independence on Multi-axial Stress States during Lüders Deformation of Medium-Mn, High-strength Steel

Local Yield Stress and its Unusual Independence on Multi-axial Stress States during Lüders Deformation of Medium-Mn, High-strength Steel

Determination of multiaxial creep stress rupture criteria for 316H stainless steel at 600 °C

In this work, the applicability of three different methods, denoted as the direct method, the indirect method, and the simple empirical method based on uniaxial creep damage tolerance parameter, λ, for the determination of multiaxial stress rupture criterion (MSRC) is assessed. The assessment involves four commonly-used MSRCs, the Sdobyrev and Hayhurst-Leckie (denoted as SHL), the Cane, the Nix and the Huddleston MSRCs. To this end, creep tests on both uniaxial and circumferentially-notched tension (CNT) specimens of 316H stainless steel are carried out at three net-section stress levels, that is, 300 MPa, 320 MPa and 340 MPa, and at 600 °C. The results show that all the three methods are suitable for the determination of MSRC for the steel examined. Of these, the direct method data-based simple empirical equation is attractive as it takes good advantage of uniaxial creep data in terms of reflecting the operative creep failure mechanism, and therefore may serve as an alternative for the determination of the SHL MSRC, particularly when multiaxial test data is not available. Moreover, the determined SHL, Cane and Huddleston MSRCs are found to be equally effective in the creep life prediction of both uniaxial and CNT specimens, while the effectiveness of the Nix MSRC in life prediction depends on position for stress output and material. In addition, factors influencing the determination of MSRC for stainless steels are discussed in terms of experimental data available in the literature.

Effective mechanisms responsible for increased strength and fracture strain of carbon fiber-reinforced plastic/steel hybrid laminates

The tensile properties of carbon fiber-reinforced plastic (CFRP)/steel laminates have been observed to exceed the expected values predicted by the rule of mixture. While the CFRP/steel laminate is expected to fail at the failure strain of the CFRP lamina, it was observed that hybridization with a steel lamina improves the failure strain. This study investigates numerically and analytically the roles of each influential mechanism responsible for this enhancement, including the thermal residual strain, bridging effect, effect of compressive transverse stress on CFRP layers, and effect of tensile transverse stress on steel layers. To assess these mechanisms, multiple finite-element and analytical models were developed. A mesoscale finite-element model was proposed, which uses novel random fiber distribution algorithm capable of reproducing random fibers with high fiber volume fractions exceeding 65%. Rather than the meso-scale model, macro finite-element models and analytical relationships were developed to assess each hybrid mechanism. Analysis showed 6% increase of the failure strain due to thermal effect and up to 11% increase of strength due to multiaxial stress in steel layer. The results of this study contribute to a deeper understanding of the role of each phenomenon that contributes to improved tensile properties in hybrid CFRP/metal laminates.

Energy harvesting using magnetostrictive materials: Effects of material anisotropy and stress multiaxiality

Low-frequency vibrations are common as background noise in urban and industrial environments. They originate from natural or artificial sources: road vehicles, industrial machinery, wind, etc., and constitute a ubiquitous energy source. In the framework of energy harvesting, magnetostrictive materials are an attractive alternative solution to the brittleness and geometrical limitations of piezoelectric materials. While numerous previous works dealt with uniaxial stress on selected materials, the exploration of the effects of multiaxial loadings and material anisotropy has not yet been investigated as a way to improve the performance of low-frequency vibration energy harvesting systems. In this work, we investigated the capability of grain-oriented electrical steel in an energy-harvesting context. This material has been selected as a model material, notably as it is abundant and cost-effective. It shows limited magnetostriction but significant elastic, magnetic, and magnetostrictive anisotropy. We combined experimental and predictive simulation results to discuss the possibility of increasing the levels of harvested energy by playing with the orientation of magnetic and mechanical stimuli. Various orientations of magnetic field and mechanical stress were considered with regard to the rolling direction of the material. Unexpectedly high energy density amounts, up to 10 mJ·cm−3, were obtained, competing with giant magnetostrictive materials like Terfenol-D or Galfenol.

Reducing stress concentrations in static and fatigue tensile tests on unidirectional composite materials: A review

The longitudinal tensile strength is an important basic property of unidirectional (UD) composites or plies that often governs failure in multidirectional laminates. The standard tensile testing methods almost always result in sample failure near the grip. Finite element analyses revealed the presence of multiaxial stress concentrations, including longitudinal, transverse, and shear stresses in the tabbed section of the standards’ recommended design. There are still unknowns and uncertainties about the causes of these stress concentrations and ways to eliminate them. A major challenge is obtaining acceptable failure within the gauge section and yielding the highest tensile strength of UD composites. This paper reviews the different methods for performing quasi-static and fatigue tensile tests on UD composites. The primary sources of stress concentrations and the parameters that affect them are reviewed using the available experimental and modeling investigations. We survey the effects of the different specimen and end tab designs as well as test setups on quasi-static and fatigue loading. Specific proposals are made for each of the discussed parameters for more reliable results.

Study on biaxial bending fatigue performance of Engineered Cementitious Composites (ECC)

Structural components such as bridge deck, highway pavement and thin-walled roof dome often are subjected to the biaxial and even multi-axis stress state due to the external load. Also, the fatigue effect cannot be ignored due to the moving vehicle load in the design of these structures. If engineering cementitious composites (ECC) is used in the above traditional concrete structures, their performance, such as easy cracking and short service life can be greatly improved. However, the biaxial bending fatigue performance of ECC should be analyzed in detail. At present, the biaxial bending test methods of cement-based materials include biaxial bending test (BFT) and centrally loaded round panel test (RPT). This study used both RPT and BFT test methods to analyze the biaxial fatigue performance of ECC and used four-point bending test (4PBT) uniaxial fatigue test as a reference. The stress levels S were set as 0.5, 0.6 and 0.7. The uniaxial and biaxial bending fatigue failure procedures of ECC were analyzed by plotting the three-stage deflection development curve, the fatigue damage and strain relationship curve based on the linear cumulative fatigue damage theory, and the S–N curve. The fatigue life of ECC biaxial bending specimens was greater than that of uniaxial bending specimens. At S = 0.5, the fatigue life: BFT > RPT. At S = 0.6, the fatigue life of BFT and RPT specimens was close. At S = 0.7, the fatigue life: BFT < RPT. With increasing stress level, the fatigue life of BFT specimen decreases more than that of RPT specimen. The lognormal distribution model and Weibull distribution model were used to fit the uniaxial and biaxial bending fatigue life of ECC, respsectively. Using the double logarithmic fatigue equation, fatigue life under the failure probability PF of 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 was derived. The survival rate represents the level of safety reservation, which could provide reference and basis for the design of ECC bridge deck and highway pavement with different safety reservation requirements.

A magneto-elastic vector-play model under rotating fields and multiaxial stress states

A magneto-elastic vector-play model under rotating fields and multiaxial stress states

Fatigue strength of adhesively bonded deep drawn sheet specimens under multiaxial loading with variable amplitudes

Adhesive bonding is a frequently used joining technology in the manufacturing of vehicle bodies. In comparison to conventional spot-welded designs, adhesive bonding provides a higher stiffness due to a planar load transfer. Furthermore, there are advantages in damping behavior and chemical separation in multi-material designs.Up to now, there exists still quite some uncertainty in the fatigue assessment of adhesively bonded joints due to a lack of reliable assessment approaches. This is especially true for the case of more complex in-service loading conditions as variable amplitude loading, due to the sparse database of experimental fatigue results, which are needed for the development of new methods. For this reason, the results of such tests are presented in this paper on component-like specimens, so called bowl specimens, where even uniaxial loading results in multiaxial stress state due to the complexity of the geometry. These specimens consist of a deep drawn sheet that is bonded with a thermosetting structural adhesive to a planar sheet and are subjected under cyclic loading. They were loaded uniaxially and multiaxially, with (φ = 90°) and without phase shift (φ = 0°).As a complex shaped and stressed sheet metal specimen, the bowl specimen closely resembles components of e.g. vehicle bodies, which is why the conducted tests are presented for a better understanding of such vehicle structures. It is shown that a phase shift leads to an increase of the fatigue life. Furthermore, the cyclic stiffness degradation is discussed, which often serves as a failure relevant parameter in real structures.

Multiaxial fatigue on cableway installations components: use of the Dang Van criterion based on detail categories of EN 1993-1-9 standard.

In order to predict fatigue lifetime of cableway installations components, EN 1993-1-9 standard (Eurocode 3) is commonly used. However, EN 1993-1-9 is based on a major hypothesis : stress state has to be uniaxial. But for some components, this uniaxial hypothesis is not verified (for example : fixed grip of chairlift submitted to horizontal tightening stress and vertical load stress, or chairlift structure stressed by gravity and lateral shake when passing a tower). It then appears important to use a fatigue criterion taking into account multiaxial stress state. Our research work proposes to apply for fatigue study the Dang Van criterion, which takes into account multiaxial stress state. Results are then compared to Eurocode SN curves, representing a huge experimental database on unixaxial fatigue, that we propose to use in multiaxial fatigue thanks to an appropriate recalibration. The scientific originality of this work lies in the justification of that Dang Van criterion's recalibration. Therefore, a theorical study ensures that our use of Dang Van's multiaxial criterion is still consistant with the Eurocode SN curve even if these SN curves are experimentally performed under uniaxial stress state. Finally, that hitherto unpublished use of the Dang Van criterion makes it possible to consider the entire database of detail categories defined in NF EN 1993-1-9, by generalising their use for components under multiaxial fatigue.

Interrelationships of stress-induced martensitic phase transformation and pitting corrosion in iron-based shape memory alloys

Orientation dependence of stress-induced martensitic transformation under compression and the influence of a corrosion attack on superelastic properties were investigated for Fe42.7Mn34.7Al13.4Ni7.7Cr1.5 (at.−%) single crystals. The results of incremental strain tests show that the crystallographic orientation has a considerable impact on the superelastic performance, eventually resulting from the formation of twinned or detwinned martensite to accommodate strain as well martensite variant interaction. In order to investigate the effect of a corrosive environment on the mechanical performance and martensitic transformation, compression specimens were immersed in a 5.0 wt.−% NaCl solution for 24 h before tested in incremental strain tests. The immersion of the compression specimens revealed a partial surface corrosion attack including localized pitting corrosion. The localized corrosion attack increased the number of active martensite plates, most probably due to an induced multiaxial stress state. Further investigations on specimens subjected to −6% compressive strain revealed that areas with retransformed martensite serve as nucleation zones for corrosion damage. Stress-induced corrosion cracks developed, which eventually deteriorate functional response.

Investigation of small punch creep damage and rupture behavior in 347H stainless steel by means of experiments and a numerical simulation

The creep behavior of 347H stainless steel was investigated by small punch creep test (SPCT). Finite element simulations coupled with a strain damage model were employed to reveal the creep deformation mechanism of 347H stainless steel. The experimental results showed that the SPC curves of 347H stainless steel had a stagnation stage before the primary creep stage, and the duration of the accelerated stage of SPCT was shorter than that of uniaxial creep tests. The competition between precipitation strengthening and dislocation motion causes the deflection rate in the stagnation stage decreases first and then increases. A similar change of deflection rates was observed in the following creep stages, which can be attributed to the stress redistribution and crack propagation in the SPCT specimen. The present work provides a comprehensive understanding of the creep behavior and fracture mode of 347H stainless steel under multiaxial stress, and could promote the development of a new method for characterizing material properties through SPCT.

Surrogate-Based Calculation Method for Robust Design Optimization Considering the Fatigue Probability for Variable Service Loads of eBike Drive Units

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.

Holistic estimation and sensitivity-based experiment design method of composite laminate first-ply failure models using statistical approaches

In this paper, a probabilistic approach is presented to simultaneously evaluate all strength and additional fitting parameters of a pre-selected composite first-ply failure model using known uniaxial and multiaxial failure stress states. The method processes all available mechanical test results in terms of failure stress states as one batch of data. For parameter fitting it implements the Maximum Likelihood Method and controlled numerical sampling techniques. The present work introduces the theoretical background as well as investigates the effect of the selection of the underlying strength distribution function type. The biggest benefit of this approach is the simultaneous handling of all available test data as well as the generality in terms of assumed strength distribution function and failure model type. In addition, the automatic evaluation of the uncertainty of all strength parameters enables introduction of a safety factor quantification related to uncertainty in material properties as one of the main contributors to scatter sources. A local sensitivity-based stress-state determination process is also introduced to design a set of input failure stresses that guarantee the identifiability of all parameters thus, ensuring robustness of the fitted constants. The entire methodology is demonstrated through the example of the Tsai-Wu model by processing experimental data and by comparing the results against the literature.