Complex Stress State Research Articles

Effect of sintering temperature on ratcheting-fatigue behavior of nanosilver sintered lap shear joint

Purpose The paper aims to study the effect of sintering temperature on the microstructure, shear strength and ratcheting fatigue life of nanosilver sintered lap shear joint. In addition, the Gerber model is used to predict the ratcheting fatigue lives of nanosilver sintered lap shear joints at different sintering temperatures. Design/methodology/approach In this paper, the nanosilver sintered lap shear joints were prepared at three sintering temperatures of 250 °C, 280 °C and 310 °C. The bonding quality was characterized by scanning electron microscopy, X-ray diffraction, transmission electron microscope and shear tests, and the long-term reliability was studied by conducting ratcheting fatigue tests. In addition, three modified models based on Basquin equation were used to predict the ratcheting fatigue life of nanosilver sintered lap shear joint and their accuracies were evaluated. Findings When the sintering temperature is 250°C, the nanosilver sintered lap shear joint shows the porosity of 22.9 ± 1.6 %, and the shear strength of 22.3 ± 2.4 MPa. Raising the sintering temperature enhances silver crystallite size, strengthens sintering necks, thus improves shear strength and ratcheting fatigue life in joints. In addition, the ratcheting fatigue lives of the joints sintered at different temperatures are effectively predicted by three equivalent force models, and the Gerber model shows the highest life prediction accuracy. Research limitations/implications The sintered silver bondline is suffering a complex stress state. The study only takes the shear stress into consideration. The tensile stress and the combination of shear stress and tensile stress can to be considered in the future study. Practical implications The paper provides the experimental and theoretical support for robust bonding and long-term reliability of sintered silver structure. Social implications The introduced model can predict the ratcheting fatigue lives of the joints sintered at different temperatures, which shows a potential in engineering applications. Originality/value The study revealed the relationship between the sintering temperature and the microstructure, the shear strength and the ratcheting fatigue life of the joint. In addition, the Gerber model can predict the ratcheting fatigue life accurately at different sintering temperatures.

The Estimation of the Stress State of the Iron Alloy Strip Material by the Barkhausen Noise Method

This paper presents the effect of the complex strain state resulting from the asymmetric rolling of TRB products on the changes and distribution of the stress state in the material. The evaluation of the stress state in the material was based on measurements of the magnetoelastic parameter (MP) using the Barkhausen magnetic noise method. The key characteristics of the material under study that enabled the use of changes in the MP parameter to assess the stress state were ferromagnetism and a lack of texture. The first of these enabled the detection of the magnetic signals produced when a magnetic field is applied to the material, causing magnetic domains to align and sudden changes in magnetization. On the other hand, the absence of texture in the material precluded the occurrence of magnetocrystalline anisotropy, which could disturb the results of measurements of the magnetoelastic parameter in the material. In order to determine these features in the material under study, its chemical composition was determined, and a phase analysis was carried out using the X-ray diffraction method. The results of these tests showed the possibility of determining the stress state of the material by means of changes in the values of the MP parameter. On this basis, it was shown that in the TRB strips studied, there is a complex state of stress, the values of which and the nature of the changes depending on the direction of the measurements carried out, as well as on the amount of rolling reduction in the studied area of the strip.

Restraining geometrically-necessary dislocations to the active slip systems in a crystal plasticity-based finite element framework

Strain gradients have been cast in the form of geometrically-necessary dislocations (GND) to relate the length-scale dependence of strength and to determine potential sites for failure initiation. The literature contains various different incompatibility measures, the main ones being: the total form (∇×Fp), the rate form for large displacements (∇×γ̇anaFp), and the slip gradient form (∇γ̇a). Here, these different approaches are compared rigorously for the first time. Obtaining GND densities when using the total form is a rank-deficit linear problem, solved by singular value decomposition (SVD) known as the Least Squares Minimization (L2 method). Alternative methods for finding GND densities such as Karush–Kuhn–Tucker (KKT) optimization are also investigated. Both L2 and KKT methods predict unrealistic GND densities on inactive slip systems leading to excessive strain hardening; even for a single crystal single slip case. Therefore, the restriction of GNDs to the active slip systems by using a threshold based on the total slip is proposed. This restriction reveals relatively consistent results for various single crystal single slip cases including: simple shear, uniaxial tension, and four-point bending. In addition, the small numerical differences in the slip leads to large discrepancies in the flow stress due to error accumulation, even for strain-gradient-free uniaxial tension, hence a threshold for the GND density increment (2×102 m−2) is used in all models to avoid formation of erroneous GND densities. Finally, the proposed method is applied to the evolution of the GND density for a grain inside a polycrystal aggregate that posses a complex stress state. The lowest incompatibility error is obtained by both of the total forms that use the curl of the plastic deformation gradient with the active slip system restriction suggesting them to be the most reliable GND measures.

Integrated Fibrous Iontronic Pressure Sensors with High Sensitivity and Reliability for Human Plantar Pressure and Gait Analysis.

Flexible sensing systems (FSSs) designed to measure plantar pressure can deliver instantaneous feedback on human movement and posture. This feedback is crucial not only for preventing and controlling diseases associated with abnormal plantar pressures but also for optimizing athletes' postures to minimize injuries. The development of an optimal plantar pressure sensor hinges on key metrics such as a wide sensing range, high sensitivity, and long-term stability. However, the effectiveness of current flexible sensors is impeded by numerous challenges, including limitations in structural deformability, mechanical incompatibility between multifunctional layers, and instability under complex stress conditions. Addressing these limitations, we have engineered an integrated pressure sensing system with high sensitivity and reliability for human plantar pressure and gait analysis. It features a high-modulus, porous laminated ionic fiber structure with robust self-bonded interfaces, utilizing a unified polyimide material system. This system showcases a high sensitivity (156.6 kPa-1), an extensive sensing range (up to 4000 kPa), and augmented interfacial toughness and durability (over 150,000 cycles). Additionally, our FSS is capable of real-time monitoring of plantar pressure distribution across various sports activities. Leveraging deep learning, the flexible sensing system achieves a high-precision, intelligent recognition of different plantar types with a 99.8% accuracy rate. This approach provides a strategic advancement in the field of flexible pressure sensors, ensuring prolonged stability and accuracy even amidst complex pressure dynamics and providing a feasible solution for long-term gait monitoring and analysis.

Elementary processes in dilatational plasticity of glasses

Materials typically fail under complex stress states, essentially involving dilatational (volumetric) components that eventually lead to material decohesion/separation. It is therefore important to understand dilatational irreversible deformation—i.e., dilatational plasticity—en route to failure. In the context of glasses, much focus has been given to shear (volume-preserving) plasticity, both in terms of the stress states considered and the corresponding material response. Here, using a recently developed methodology and extensive computer simulations, we shed basic light on the elementary processes mediating dilatational plasticity in glasses. We show that plastic instabilities, corresponding to singularities of the glass Hessian, generically feature both dilatational and shear irreversible strain components. The relative magnitude and statistics of the strain components depend both on the symmetry of the driving stress (e.g., shear versus hydrostatic tension) and on the cohesive (attractive) part of the interatomic interaction. We further show that the tensorial shear component of the plastic strain is generally nonplanar and also extract the characteristic volume of plastic instabilities. Elucidating the fundamental properties of the elementary micromechanical building blocks of plasticity in glasses sets the stage for addressing larger-scale, collective phenomena in dilatational plasticity such as topological changes in the form of cavitation and ductile-to-brittle transitions. As a first step in this direction, we show that the elastic moduli markedly soften during dilatational plastic deformation approaching cavitation. Published by the American Physical Society 2024

An Analytical Model for the Initial Stiffness of Bearing Connections with Slotted Holes

In steel structures, cover plate joints are mainly used with normal round holes, but slotted holes, where the slot is oriented perpendicular to the direction of the bearing force, make it possible to release displacements in selected directions and thus better control the complex state of stresses in the connected plates. This study investigates the initial stiffness of a cover plate with a single slotted hole. The aim of this paper is to propose an analytical model that predicts the initial stiffness of slotted holes with respect to experimental results obtained on a panel of different geometries. This approach makes it possible to evaluate the effects of the end distances on the bending of the plate compared to the bearing under the bolt. A large panel of geometries is tested to quantify the experimental value of initial stiffness using Digital Image Correlation (DIC) technique compared to Linear Variable Differential Transformer (LVDT) sensors. To evaluate the initial stiffness, a method of processing experimental data is developed that allows a reproducible determination of stiffnesses. An analytical model is then proposed based on the improvement of existing models available in the literature. It is validated for different specimen geometries considering the contribution to the initial stiffness due to bending, shearing and support of the steel plate under the bolt. The comparisons show that the proposed analytical model can predict the initial stiffness of different geometries of tested specimens with slotted holes.

Failure analysis of the suspender fracture in a railway self-anchored suspension bridge: Damage identification, fatigue mechanism and remaining life prediction

A suspender fracture accident was reported in a railway self-anchored suspension bridge, arousing intensive concern to fatigue issue in the suspender end connector area which is exposed to complex stress states and cyclic traffic loads. Some critical issues involving the fatigue mechanism, the damage identification, and the remaining life prediction were investigated on the basis of on-site and lab tests, numerical simulations, and theoretical analyses. It was found that the root of an ear-plate screw with threads becomes the fatigue-prone detail since action of stress concentration and the unexpected cyclic bending. Also, an effective crack identification scheme by the ultrasonic phased array inspection as well as a verified prediction method for remaining life were proposed. Short suspenders in the main span are significantly affected by the cyclic bending, resulting in the extremely lower fatigue life than that of a long or side-span suspender. Suggestions for a classified disposal plan are provided based on fatigue risk for individual suspender.

Generalizing multiaxial vibration fatigue criteria in the frequency domain: A data-driven approach

Random vibration fatigue of structures is intrinsically multiaxial, driven by complex stress states. Non-proportional multiaxial stresses exacerbate fatigue damage compared to proportional stresses. Frequency domain fatigue analysis is generally more efficient for structures operating near natural frequencies. However, handling non-proportional multiaxial stress effects in the frequency domain remains challenging. This paper introduces a data-driven framework that reformulates time domain multiaxial fatigue failure criteria into their frequency domain counterparts, explicitly addressing non-proportional effects. The method introduces a non-proportional correction factor into the power spectral density of equivalent stress, determined through a data-driven approach, converting various time domain multiaxial fatigue criteria into their frequency domain equivalents. Combined with modal decomposition analysis, this approach efficiently evaluates multiaxial vibration fatigue for engineering structures, effectively accounting for non-proportional stress effects.

Mechanical properties of recycled aggregate concrete reinforced with steel fibers under triaxial loading

The use of steel fiber reinforced recycled concrete (SFRAC) can help achieve resourceful reuse of construction waste and environmental sustainability. However, SFRAC structural members may experience complex stress states. Therefore, triaxial compression tests were conducted on 168 cylindrical SFRAC specimens to investigate their mechanical properties. The failure modes, stress-strain behavior, strength, and deformation of SFRAC under triaxial compression were observed. The effects of lateral confining pressure, steel fiber (SF) content, and recycled coarse aggregate (RA) replacement rate on these properties were analyzed. The internal micro-morphology of SFRAC was analyzed using SEM to better understand its failure mechanism under compression. The result shows that an increase in lateral confining pressure alters the failure mode of SFRAC specimens, resulting in a significant increase in peak strength and ductility. The enhancement of the elastic modulus by steel fibers decreases as the lateral confining pressure increases, suggesting a coupling effect between the two parameters. The inclusion of steel fibers in SFRAC did not have a significant impact on its failure mode or compressive strength. And yet, it did increase the ductility and toughness of the material, with an optimal steel fiber content of 1 % (by volume). On the other hand, the addition of recycled coarse aggregate resulted in a significant reduction in the concrete's compressive strength, by almost 17 %. Finally, several common material failure criteria for concrete were used to evaluate the impact of RA substitution rate and SF content on the strength of SFRAC. The Willam-Warnke failure criterion showed a higher strength. These findings provide a theoretical basis for future engineering applications of SFRAC.

Stiffness of reinforced concrete structures under bending considering shear and axial forces (part 2)

The paper presents a physical and computational model for determining the parameters of limit states of reinforced concrete structures under complex stressed state - bending with axial and shear forces. Based on the adopted scheme of cross-section discretization and A.R. Rzhanitsyn's theorem of duality between force and deformation parameters, the forward and backward transfer for determining the coefficients of the stiffness matrix of reinforced concrete rod structures with inclined and normal cracks have been constructed. Stiffness of structures in the zone of inclined cracks is determined using the model of composite strips which separate the zone with inclined cracks. The hypothesis about the character of deformation distribution in a complex-stressed reinforced concrete element with inclined cracks is accepted.For this model the conditional shear modulus is obtained, which allows to determine the average relative linear and angular strains of concrete and reinforcement at the point adjacent to the shear joint between inclined cracks. Based on this model and using the experimentally obtained value of the relative shear in the inclined crack, the dowel forces in the reinforcing bar intersected by the inclined crack were determined. The application of the obtained analytical relationships in the practice of designing reinforced concrete structures allows not only to clarify significantly the definition of displacements and width of opening of inclined and normal cracks, but also to maximize the convergence of the design and physical model based on experimental data.

A discrete approach for modelling the permeability evolution of granite under triaxial and true-triaxial stress conditions

In deep underground engineering, modelling the seepage characteristics of rock masses under complex stress conditions is crucial for the safe construction and stable operation of a project. The permeability of the rock mass is not only controlled by its internal pore structure but is also closely related to the deformation and fracturing of the rock. Although discrete methods offer advantages in describing the formation and development of fractures, these methods still face challenges due to the difficulties in establishing microscopic seepage models. This paper introduces a new hydro-mechanical coupled numerical model. In this model, a simple method is proposed to couple the Rigid-Body-Spring Method (RBSM) for rock deformation and fracturing simulation and the Equivalent Matrix-Fracture Network (EMFN) for seepage simulation. Subsequently, the model is employed to simulate the permeability of granite under three-dimensional stress conditions. The simulation results show that under hydrostatic stress conditions, the model accurately captures the decrease in permeability due to pore compression and collapse. Additionally, under deviatoric stress conditions, it reveals the stage-wise increase in permeability caused by granite fracturing. Finally, the model is applied to study the permeability evolution behaviour of rocks under true triaxial stress conditions. The results unveiled the significant impact of the intermediate principal stress on permeability evolution and revealing the microscopic mechanisms underpinning these effects. This paper paves a way for enhancing the application of discrete methods in forecasting the permeability evolution behaviour of intricate rock masses.

The “Third Body” Approach to Joining of Metals by Simple Shear under Pressure

A continuum mechanics approach to cold welding (CW) of metals under shear is considered. The main idea is to treat a weld joint as an extra material—a “third body” in its own right. Its properties stem from plastic co‐deformation of the two contacting alloys. The mechanical characteristics of the weld joint, i.e., its strength and plasticity in the complex stress state, are determined by the deformation history of the “third body.” The proposed approach enables a unified description of the CW process itself, as well as the subsequent variation of shape of the composite material with the weld joint.

Dynamic mechanical response and crack evolution law of raw coal loaded by dynamic-static coupling under three-dimensional constraints

This paper presents the investigation of the dynamic mechanical properties of coal rock under complex stress conditions at depth, based on the improved Separate Hopkinson Pressure Bar Test System. A total of 15 groups of coal samples were used to perform dynamic impact tests under different conditions. The changing rules of dynamic strength, crushing, fractal dimension and damage modes of coal under different stress conditions were analyzed. A total of nine groups of coal samples were selected for numerical simulation using ANSYS/LS-DYNA. The results show that: (1) The stress–strain curves of coal specimens under different strain rates, different confining pressures and axial pressures have basically the same trend and the curves show a certain jump forward. (2) The peak dynamic stress of the coal specimens increased linearly with the increase of strain rate and confining pressure, and the ambient pressure limited the expansion of internal cracks of the coal specimens under impact loading. Based on the experimental and simulated data, the maximum relative errors between the experimental and simulated data were determined to be 2.9578% for Group A, 6.177% for Group B, and 6.382% for Group C, respectively. (3) The damage modes of the coal samples under the three-dimensional dynamic-static combined loading were mainly “X” type and “conical” shear damage. The fractal dimension increases with the increase of strain rate, decreases with the increase of confining pressure, and first decreases and then increases with the increase of axial pressure. This research achievement can provide theoretical support for the prevention of dynamic disasters in deep coal mine engineering.

Study on Plastic Constitutive Relation and Ductile Fracture Criterion of AM60B Magnesium Alloy.

It is currently a challenge to accurately predict the deformation and fracture behavior of metal parts in automobile crashes. Many studies have shown that the deformation and fracture behavior of materials are significantly affected by the stress state during automobile crashes with complex stress state characteristics. In order to further promote the application of die-cast magnesium alloys in automobiles, it is particularly important to study the material deformation and fracture behavior of die-cast magnesium alloys. In this paper, the mechanical properties of the AM60B die-cast magnesium alloy sheet under four stress states (shear, tension, R10 notch tension, and cupping) were designed and tested. Based on the von Mises isotropic constitutive model and Swift weighted Hockett-Sherby hardening model, the plastic constitutive model of die-cast magnesium alloy was established. Based on the plastic model and the fracture model (JC, MMC, and DIEM) considering the influence of three stress states, the deformation and fracture behavior of the AM60B die-cast magnesium alloy front-end members in three-point bending were predicted by experiments and finite element simulation. The experimental results show that the deformation mode and loading-displacement curve trend of the AM60B die-cast magnesium alloy front members are the same, the crack initiation point and crack initiation time are the same, and the crack shape is similar. The results show that the complex stress state constitutive model parameters and the DIEM fracture model obtained in this paper can accurately predict the deformation and fracture failure behavior of the AM60B die-cast magnesium alloy sheet.

Experimental study on mechanical properties of conical head for bolted spherical joints

As a typical grid structure joint, bolted spherical joints are widely used in various engineering. However, as the key component of the bolted spherical joint, the conical head has not formed a unified specification and standard in China. At the same time, the mechanical properties and failure mode of the conical head are not clear. Therefore, this paper has carried out axial tension tests on 18 specimens with 6 kinds of conical heads. Combined with finite element analysis, the mechanical properties, failure mode, bearing capacity, and the factors affecting the bearing capacity of the conical head under axial tension were studied. The calculation formula of the bearing capacity of the conical head was proposed. The results show that the conical head is in a complex stress state of bending, shear and compression at the same time, and the failure mode of the conical head is the shear failure of the bottom plate. The thickness of the bottom plate of the conical head and the bolt specification will affect the bearing capacity of the conical head. The conical head's bearing capacity decreases with decreasing bottom plate thickness and bolt specification. However, the thickness of the bottom plate and the bolt specification will not affect the failure mode of the conical head.

Study on the evolution of permeability properties of limestone under different stress paths

Abstract Stress path change has a great relationship with the effect of deformation and strength of rock. However, the underground rock body is in the engineering environment where the stress field, seepage field, and other fields are coupled to change, the law of fluid flow in the rock body is complex and variable. The change in the stress field has an important effect on the seepage characteristics of rock body; therefore, it is necessary to study the pattern of rock permeability evolution pattern by different stress paths. This study is based on the study of limestone, conducting triaxial unloading seepage mechanics experiments, the evolution of permeability properties of limestone specimens was analyzed based on the test results. The results show that in the conventional triaxial loading seepage test, the permeability of the limestone decreases before the rock stress reaches the peak intensity and increases after that. Increasing axial pressure unloading surrounding pressure compression section, permeability loss rate and effective stress are in line with the changing law of Gaussian distribution function. Under the action of constant axial pressure unloading surrounding pressure, with the increase in unloading amount, the permeability rate of change appears to increase slowly, and in the late stage of unloading section, the permeability rate of change appears to surge. Unloading section permeability change rate and cumulative unloading amount are in line with the law of change of the exponential function. Creep unloading pressure seepage test found that unloading pressure stage strain-time and permeability-time evolution characteristics are in line with the exponential rule of change. The experimental results of this study can provide an important experimental and theoretical basis for the permeability analysis of low-permeability rock body under complex stress conditions in underground engineering.

Математическое моделирование и визуализация сложнонапряженного состояния при переломе диафиза бедренной кости

The purpose of this work is to establish the possibility of using the finite element analysis method to study complex stress states in case of a femur fracture with subsequent data visualization. Experimental data were obtained on a solid-state mathematical parametric model of the femur, created on the basis of computer tomogram data, and repeating studies on native biological objects. As a result of mathematical modeling, oblique transverse and helical fractures of the diaphysis of the femur with elements of helical deformation were studied. The application of finite element analysis made it possible to visualize and predict the stresses arising in bone tissue under the impact of a blunt solid object in a complex stress state and the morphological features of femoral shaft fractures under different torsional loading forces of the proximal part of the femur. The data on the mechanism and morphology of the femoral shaft fracture obtained during modeling are confirmed by the results of original full-scale experiments.

Load-Carrying Capacity of Thin-Walled Composite Columns with Rectangular Cross-Section under Axial Compression.

The aim of the current study was to determine the load capacity of composite columns subjected to axial compressive load. The subjects of the study were two types of columns with a rectangular cross-section, with different edge lengths. The tested columns had a closed cross-section. Four different fiber arrangements were analyzed for both cross-sections studied. The research was realized using interdisciplinary methods to determine the mechanism of damage to the composite material, with particular emphasis on damage initiation and propagation. Experimental tests were realized on a testing machine, the analysis was carried out with an acoustic emission system, and image analysis using visual assessment system of deflections of the walls of the structure. In addition, a number of numerical analyses were realized based on advanced modeling techniques for fiber-reinforced composites. A comparative analysis of both quantitative and qualitative results is presented for both analyses. The innovation of the presented research lies in the development of a custom method for modeling structures made of composite material with special emphasis on the failure phase. This will allow to accurately reflect the modeling of thin-walled structures with closed cross-section subjected to loading in a complex stress state.

Analysis of strength characteristics of loess before and after freezing using a hollow cylinder torsional shear apparatus

This paper aims to comprehensively analyze the influence of the principal stress angle rotation and intermediate principal stress on loess's strength and deformation characteristics. A hollow cylinder torsional shear apparatus was utilized to conduct tests on remolded samples under both normal and frozen conditions to investigate the mechanical properties and deformation behavior of loess under complex stress conditions. The results indicate significant differences in the internal changes of soil particles, unfrozen water, and relative positions in soil samples under normal and frozen conditions, leading to noticeable variations in strength and strain development. In frozen state, loess experiences primarily compressive failure with a slow growth of cracks, while at normal temperature, it predominantly exhibits shear failure. With the increase in the principal stress angle, the deformation patterns of the soil samples under different conditions become essentially consistent, gradually transitioning from compression to extension, accompanied by a reduction in axial strength. The gradual increase in the principal stress axis angle (α) reduces the strength of the generalized shear stress and shear strain curves. Under an increasing α, frozen soil exhibits strain-hardening characteristics, with the maximum shear strength occurring at α = 45°. The intermediate principal stress coefficient (b) also significantly impacts the strength of frozen soil, with an increasing b resulting in a gradual decrease in generalized shear stress strength. This study provides a reference for comprehensively exploring the mechanical properties of soil under traffic load and a reliable theoretical basis for the design and maintenance of roadbeds.

True triaxial energy evolution characteristics and failure mechanism of deep rock subjected to mining-induced stress

In deep rock engineering, complex stress conditions are encountered, which leads to difficulties in engineering disaster prevention and control. To investigate the failure behaviors and mechanisms of deep rock mining, a series of tests was designed for mining-induced failure at different simulated depths using a multifunctional true triaxial geophysical (TTG) apparatus. The results showed that both the simulated depth and mining disturbance affected the deformation characteristics of the sandstone specimens. With increasing depth, the strength gradually increased. The peak strength increased fastest in the single-sided unloading failure test (SUFT) and slowest in the stress loading and unloading failure test (SLUFT). The failure mode also changed significantly. In the displacement loading failure test (DLFT), the failure mode gradually changed from tensile failure to shear failure. In the SLUFTs, the failure mode of the specimens changed from layer cracking to shear failure. In the SUFTs, the failure mode of the specimen transitioned from layer cracking to tensile shear failure and then to shear failure. Scholars have previously proposed an elastic strain energy calculation method for true triaxial stress conditions. An elastic strain energy calculation method applicable to different mining disturbance was proposed under true triaxial stress conditions, and the evolution characteristics of the work done, elastic strain energy, and dissipated energy were analyzed. Additionally, a method to quantitatively characterize the relationship between macroscopic cracks and dissipated energy was proposed, and microscopic fracture analysis was performed using scanning electron microscopy (SEM). Different depths and various types of mining-induced failure were fully considered, and the specimen deformation, failure type, energy evolution (including dissipation), and failure mechanisms were analyzed. The results can provide guidance for deep underground engineering projects.