Equivalent Stress Research Articles

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.

Transient dynamic stress behavior analysis of the axial flow pump as turbine at part loads

To explore the structural dynamic characteristics of the impeller and shaft system of the axial flow pump as turbine, the variation law of impeller transient equivalent stress, deformation, and the impeller and shaft system mode are analyzed by the transient fluid-structure interaction method. Findings indicate that the equivalent stress is centralized at the blade root around the hub and tends to decrease as it moves towards the shroud. The maximum equivalent stress at 1.0Qbep and 1.1Qbep is 1.26 times and 2.0 times higher than that at 0.8Qbep. Blade deformation is significantly influenced by flow rate. The maximum deformation of the blade at 1.0Qbep and 1.1Qbep is 1.6 times and 3.6 times higher than that at 0.8Qbep. The impeller and shaft system with prestress in dry mode has an average natural frequency of the first 10 orders that is 16.7 Hz higher than without prestress. However, with the fluid adding mass and flow damping, the average natural frequency of the first 10 orders of the impeller and shaft system in wet mode is reduced by 278.08 Hz compared with dry mode. In fact, the impeller and shaft system of the axial flow pump as turbine is not prone to vibration.

Micromechanical effects of substrate hardness on graphene nano-cutting quality

In the nanocutting process of graphene, the mechanism on the atomic scale of the effect of substrate hardness on the edge quality of graphene nanoribbons has not been thoroughly investigated. In this paper, we construct a diamond probe (radius of 5 Å) to cut graphene (190 Å × 113 Å) models with different substrates (silicon/sapphire/silicon carbide), molecular dynamics simulations were used to study the effect of substrate hardness and cutting depth on the atomic structure of graphene nanoribbon edges by observing the atomic morphology, the number of C-C bonds, the radial distribution function and friction. The results show that during the nanoindentation stage, when graphene is in the critical damage state, the substrate with high hardness has high deformation strength, the substrate deformation is small, and graphene undergoes deformation is also small, but the force Fz on the probe, the critical graphene stress σz and the equivalent stress are all large, and the number of C atoms with CN=3 is large; At the nano-cutting stage, the breakage of C-C bonds and the generation of edge defects are caused by local stress concentration, and the graphene stress σxx along the x-direction has a clear directionality. With the same cutting depth (critical damage depth of silicon substrate), silicon substrate hardness is small, the graphene nanoribbon obtained has less number of circular defects generated at the edge, less total number of defective atoms, more number of CN=3 atoms, large peak of radial distribution function of graphene after cutting, and graphene integrity is better. The hardness of the silicon carbide substrate is large, and the number of C-C bond breaks in graphene during the cutting process is high. Each substrate is cut at its own critical damage depth, and the substrate hardness has no significant effect on the number of C-C bond breaks, the number of circular defects, the total number of defective atoms, and the number of CN=3 atoms in graphene. When the silicon substrate was used, the stable force of the probe is small, the edge structure of graphene has little impact, the edge effect obtained is good. The cutting depth and substrate hardness have little effect on the graphene temperature during the nano-cutting process. In this paper, the atomic structure of graphene edges after cutting is analysed and investigated on the atomic scale, and the above results are combined to provide theoretical guidance for obtaining efficient and high-quality and low-damage graphene nanoribbon cutting.

Effect of surface rolling process on rolling contact fatigue behavior and failure mechanism of powder metallurgy steel

The effect of surface rolling process on the surface microstructure and rolling contact fatigue of the Fe-2Cu-0.6 C powder metallurgy steel was investigated in the present investigation. Results indicated that a densified and hardened layer with a densification depth of 330 μm and a surface hardness of 330 HV0.1 was generated in the surface layer after rolling process. Ferrite grain and pearlite lamellae became typical fibrous structures on the top surface. The microstructure of pearlite was presented by two typical features. One was that the discrete cementite plates were severely curled and wavy. The other one was that the cementite plates remained parallel to each other, but were a reticular structure at a macroscopic level. The rolling contact fatigue (RCF) test showed that the RCF life of the rolled sample was superior. The L10, L50, L63.2 life increased by 182%, 105%, 92%, respectively. Surface initiated spalling was the main fatigue failure mode. Subsurface equivalent contact stress and local equivalent stress were calculated. The results showed that surface cracks were due to the repetitive tensile stress, which caused pits. Subsurface cracks nucleated and propagated in the region where the local equivalent stress was higher than the matrix yield strength, which caused spalling as connecting with surface cracks. The surface densified layer plays an important role in improving the rolling fatigue resistance of the material.

Reliability assessment of bridge hangers based on fault tree with response surface

Bridge hangers play a crucial role in transmitting forces and supporting bridge structures. The condition of these hangers directly impacts the overall safety of the bridge. However, they are susceptible to fatigue failure due to cyclic loads like wind and vehicle traffic. Therefore, evaluating the fatigue performance of bridge hangers is vital. Typically made up of multiple parallel steel wires, the failure of even one wire can affect the fatigue performance of the entire hanger. This underscores the importance of considering the individual components’ impact on the system as a whole. This study presents a time-dependent reliability assessment model for bridge hangers based on the S-N curve of steel wire. Additionally, a system-level reliability assessment model is developed using fault tree analysis, taking into account the influence of broken wires and stress redistribution on the hanger system. The model is solved using response surface methodology, and through five numerical simulations, the study examines the effect of key parameters, including the number of broken wires, equivalent structural stress, and total cycles on the system’s reliability.

Multi-condition simulation analysis of a sliding hydraulic support system based on elastoplastic mechanics

In response to the challenges of supporting fractured and weak surrounding rock in deep coal mines in the Huainan region of China, a self-moving hydraulic support system for roof support was designed and developed. This innovative solution addresses the difficulties encountered in providing continuous support to roof structures. Based on the theory of elastoplastic mechanics, a numerical analysis model was established to calculate the mechanical parameters such as the displacement, stress, and strain of hydraulic supports during the stepping process under multiple operating conditions. The results of the numerical simulation were compared and verified with those from an actual working site. The results show that the maximum equivalent stress is 245.33 MPa for operating condition 1, 246.82 MPa for operating condition 2, and 245.27 MPa for operating condition 3. The maximum stress values under the three working conditions do not exceed the yield strength of the material, satisfying the requirements for normal bracket support operations. These research findings can establish a theoretical framework for the comprehensive assessment of the reliability and stability of hydraulic supports and the optimization of construction processes.

Mapping the defect acceptance for dynamically loaded components by exploiting DIC-based full-field receptances

Potential defect acceptance can be seen dependable upon the mapping of effective strains on the whole surface, due to dynamic loading of the components as they are mounted. With proper constitutive models and loading spectra, the experiment-based mapping of the equivalent stresses can be achieved from optical full-field receptances in an extremely dense grid, also for lightweight parts, without inertia distortions thanks to contactless measurements. Fatigue spectral methods turn this mapping into components’ life distributions, for a clear assessment of the material’s utilisation: a risk grading mapping for potential defects can be formulated in the area of inquiry in order to discriminate between safe and dangerous locations. By following this experiment-based approach, potential defects in exercise and production might be tolerated in safer locations, under the chosen dynamic task, with great savings in costs and maintenance. Among the image-based full-field measurement techniques, Hi-Speed DIC has proved to work in many environments, to be able to estimate full-field receptances of real components in their effective assembling and loading conditions, in different cases of industrial interest. The quality achieved by DIC in the receptance maps helps in numerically deriving the strain FRFs on the sensed surface. Extended scenarios – with newly modelled coloured noises for an advanced excitation definition from two shakers – and a vibrating rectangular plate, as real mounted component, are highlighted in details to prove the effectiveness of DIC-based risk index mapping under defect acceptance criteria.

Performance Optimization Design Study of Box-Type Substations Subjected to the Combined Effects of Wind, Snow, and Seismic Loads

As a pivotal node in both urban and rural power grids, the box-type substation not only serves the functions of power conversion and distribution but also need to provide structural support and environmental adaptability. However, deficiencies in strength, stiffness, or vibration characteristics may lead to vibration and noise issues, and extreme environmental changes can pose risks of structural damage. This study aims to verify and optimize the seismic resistance and environmental adaptability of box-type substations through finite element simulation methods. Using SOLIDWORKS, a three-dimensional model of the box-type substation was constructed, and static and dynamic analyses were conducted using Ansys Workbench to comprehensively evaluate the dynamic response of the box-type substation under wind, snow loads, and seismic action. Through iterative simulations and a comparison of multiple design solutions, the structural optimization of the substation was achieved. The optimized structure balances strength and stiffness, significantly reducing the weight of the substation body, with the wall thickness reduced by 60%. Additionally, the phenomenon of stress concentration on the side walls was eliminated, ensuring that the equivalent stress is below the material yield strength. This research provides methods and empirical results for enhancing the performance and reliability of box-type substations under seismic conditions, confirming the feasibility of a lightweight design, while ensuring structural safety.

Topology optimization of AISI 4140 steel with surface texture filled by multi-solid lubricants for enhancing tribological properties

Wind power gears will be excessively worn due to lubrication failure during operation. Herein, the tribological properties of rubbing pairs are improved by filling solid lubricants into surface texture. In texture design, three types of topological textures (Circle (C), Hexagon (H) and Circle/Hexagon (CH)) were obtained by cell topology optimization, and then three cases with 20%, 30%, and 40% density were designed for each texture. Next, SnAgCu and TiC were deposited in texture of AISI 4140 steel (AS) to obtain 9 kinds of self-lubricating surfaces. Among them, AS with 30% CH density (AS-CH30) exhibits excellent mechanical and tribological properties. Compared with AS-C and AS-H, the maximum equivalent stress of AS-CH was decreased by 10.86% and 5.37%, respectively. Friction coefficient and wear rate of AS-CH30 were 79.68% and 78% lower than those of AS. The excellent tribological performances of AS-CH30 can be attributed to the synergistic effect of topological surface and solid lubricants. Topological surface can not only reduce fluctuation of equivalent stress, but also promote the stored lubricants to be easily transferred at the contact interface to form a 200 nm lubricating film containing solid lubricants (mainly), oxides and wear debris.

Fatigue life analysis of scraper conveyor chain ring under different chain speeds and loads

This study aims to explore how different chain speeds and loads impact the fatigue life of the scraper conveyor chain ring. To achieve this, the study validates the reliability of a coupled simulation involving multi-body dynamics and the discrete element method. It also acquires time-varying tension load spectra under various operational conditions. The research evaluates the effects of distinct chain speeds and loads on parameters such as chain tension, vibration acceleration in the Y and Z-directions of the chain ring. Furthermore, finite element simulation is employed to examine stress distribution changes and fatigue life trends within the three-chain ring structure. The findings demonstrate that Y and Z-direction vibration accelerations of the chain ring correlate positively with the load. Additionally, the vibration acceleration in the Y-direction correlates positively with the chain speed. Across different chain speeds and loads, the maximum equivalent stress in the chain ring exhibits dynamic variations mirroring the load spectrum. Within the elastic deformation range of the chain ring, the highest stress within the transition region correlates linearly with chain tension. Load has a greater effect on the fatigue life of chain rings than chain speed. The fatigue life within the transition region of the chain ring decreases exponentially with increasing load at a constant chain speed. Conversely, at a constant load, chain ring life correlates positively with chain speed. Specifically, the fatigue life of the chain ring in LS 22 amounts to 32.64 days. When both chain speed and load are adjusted by 25%, the chain ring's lifespan reduces by 51.66% during simultaneous increments and increases by 39.26% with concurrent reductions in speed and load.

Parametric optimization of selected auxetic structures

Auxetic materials exhibit an interesting, counterintuitive behavior—when subjected to uniaxial tension, they stretch laterally, and when uniaxially compressed, they shrink laterally. In contrast to conventional materials, in auxetics, the value of Poisson’s ratio is negative. Behavior of auxetic materials is an effect of their internal structures. The auxetic effect depends mostly on the geometry of their internal unit cells and not on the properties of the bulk material. This paper presents the results of parametric optimization of selected two-dimensional auxetic unit cells with the aim to identify the geometrical parameters which exhibit the strongest influence on the value of Poisson’s ratio in each unit cell, and to identify geometries which exhibit the strongest auxetic effect. The optimization was conducted through numerical simulation with the use of the finite element method in commercial software. Response surface optimization and multi-objective genetic algorithm (MOGA) were applied. Obtained candidate geometries were verified via additional FEM analyses and confirmed to have improved auxetic effect and reduced equivalent stress. 5 × 5 structures composed of reference and optimized geometries of analyzed unit cells were subjected to similar analyses and it was confirmed that the optimization of singular unit cells caused an improvement of auxetic effect and reduction in equivalent stress in regular structures composed of multiple unit cells.

МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ РАСПРЕДЕЛЕНИЯ НАПРЯЖЕНИЙ В СТЕНКАХ КОНУСНЫХ ИМПЛАНТАТОВ ИЗ СПЛАВА ВТ6

Today, an interdisciplinary approach to solving the problems of implantology is the key to the effective use of intraosseous dental implants. The possibilities of preclinical modeling of the state of bone tissue and the future implantation and prosthetic beds allow us to assess the possible risks of implant rejection, calculate the necessary tightening force of screws in implantation systems and predict the points of application and stress distribution of dental implantation materials, taking into account the latter, the desire to improve modeling will allow us to obtain a predictable treatment result. In this study, a mathematical model of the stress distribution on the walls of a conical implant was investigated, taking into account the physical properties of the VT 6 material, an assessment was carried out using the example of computer models with embedded alloy characteristics, and the Mises distribution indicators were calculated. It is worth noting that the VT6 alloy has a very high quality, thanks to alloying additives. This titanium alloy includes aluminum, which has a beneficial effect on the strength of implants, as well as vanadium, which can increase the strength of the metal and make it more ductile. Titanium alloy VT6 has characteristics that are comparable to those of stainless steel, due to which it is considered as an inert metal for use in the oral cavity. The novelty of the proposed model lies in the fact that it operates with the minimum possible set of input data and provides adequate estimates of the most significant output parameters that are necessary for practical application. The obtained analytical results are illustrated by examples of calculating equivalent stresses in implants and peri-implant tissue for real structures of the future orthopedic prosthesis.

An integrated experimental and analytical approach on mechanical characterization of advanced powder metallurgy aluminium metal matrix composites reinforced with different particulates

Over the last few decades, ‘Discontinuously Reinforced Particulate Composites (DRPCs)’ are a popular class of composite materials with considerable challenge in processing, characterization and machinability because of their increased strength-weight ratio, stiffness, specific strength and oxidization when compared to various metals and their alloys. This paper discusses experimental and numerical investigation on mechanical characteristics of aluminum metal matrix reinforced with various reinforcement particulates such as silicon carbide, aluminium oxide, and zirconium oxide, compaction pressure (kN) and hold time (s) based on Design of Experiments (DOE) and Finite Element Analysis. Initially this paper discusses the process optimization of Aluminum Matrix reinforced with different particulates experimentally to identify the favourable processing conditions by varying reinforcement materials, compaction pressure (kN) and hold time (s) based on TDOE (Taguchi’s Design of Experiments). Further, this paper concentrates to determine ‘maximum principal stress, equivalent elastic strain and equivalent (von-mises) stress’ based on Finite Element Analysis (ANSYS Workbench-2023R1). The results of the experimentation showed that the highest hardness values were achieved with ZrO2 reinforcement material. Increasing the compaction pressure from 8 to 12 kN resulted in a slight decrease in surface roughness and porosity. Higher compaction pressures have assumed to facilitate better particle distribution and improved interfacial bonding, leading to smoother surfaces and lower void content. The simulation results showed that the maximum principal stress achieved were (2235.8 MPa) SiC, (3444.4 MPa) Al2O3, and (3582.5 MPa) ZrO2. The equivalent elastic strain achieved was (0.2488) SiC, (0.2421) Al2O3 and (0.262) ZrO2. The equivalent (Von Mises) stress achieved was (28751 MPa) for SiC, (24880 MPa) for ZrO2 and (26972 MPa) for Al2O3. This experimentation and simulation demonstrated that the PM process can be used to fabricate DRAMMC with different reinforcement particulates. The understanding gained experimentally and analytically from this research can be applied for future processing of Aluminum Matrix Reinforced with different particulates.

Analysis of the mechanical response of solid rocket engine propellant under acceleration shock

The increased-range solid rocket engine of new ammunition often needs to withstand extremely high acceleration overload, leading to damage to the propellant’s structural integrity. To address this issue, this paper constructs a nonlinear viscoelastic constitutive model for the CMDB propellant by using low- and high-strain rate mechanical property tests. Combined with the secondary development of explicit dynamics and numerical simulation technology, the mechanical response of a certain type of solid rocket propellant under different acceleration impacts is analyzed. The results show that under acceleration impact loads, the propellant will compress, rebound, and recover over time, continuously cycling. Its axial displacement, maximum equivalent stress, and maximum equivalent strain exhibit irregular sinusoidal wave-like periodic cycles. Looking at the time when the peaks appear, the time when the maximum equivalent stress appears always lags behind the time when the maximum axial displacement peak appears. Due to the viscous effect of the viscoelastic material of the propellant, the time when the equivalent strain peak appears will lag behind the equivalent stress. Because of the material’s damping effect, both the peak values of the maximum equivalent stress and equivalent strain decrease over time. Under continuous high acceleration impact loads, this viscous damping phenomenon continuously diminishes, and the peak value of the propellant’s axial displacement gradually increases.

Research on the Influence of Cone Angle on the Sealing Performance of Pipeline Joint

In order to evaluate the sealing performance of the pipe connectors, we developed a simplified 3D model by adjusting the cone angle of the nozzle and analyzing the contact pressure of the sealing structure, the width of the contact surface, and the equivalent stress as the response quantities. Based on a finite element analysis approach, we found that increasing the cone angle of the nozzle improves the sealing performance, but may negatively affect structural reliability and maintenance. As such, the optimal range for the nozzle cone angle is relatively reasonable between 55° and 60°. Furthermore, we use a sealed interface leakage model to calculate the joint leakage rate under theoretical conditions.

In situ measurement of three-dimensional intergranular stress localizations and grain yielding under elastoplastic axial-torsional loading

The three-dimensional grain-averaged response of solid bar samples under non-proportional (NP) elastoplastic axial-torsional loading was investigated using in situ high energy diffraction microscopy (HEDM) and companion crystal plasticity finite element (CPFE) modeling. Important stress metrics including applied shear (σθZ) and axial (σZZ) stress tensor components, stress and stress deviator tensor invariants (I1, J2, and J3), von Mises equivalent stress (σVMgrain), maximum resolved shear stress (mRSS), stress triaxiality (η), and lode angle parameter (θ‾) values were tracked for ∼ 300 grains under two different loading conditions: (1) Torsion-dominated loading (low NP) and (2) Tension-torsion loading (high NP) in equiatomic NiCoCr, a representative multicomponent face-centered cubic (FCC) superalloy. Overall, significant stress localizations existed within both samples as evidenced by the radial dependence of grain-resolved σθZ, σVMgrain , and J2; by comparison, I1, J3, η, and θ‾ metrics did not show discernible trends within the volume. These stress localizations reveal a complex interplay between axial and shear stress components (e.g., stress coupling) resulting in grain yielding near the sample surface largely driven by shear stress, whereas internal grain yielding was largely accommodated by axial stress. Grain-resolved stress localization trends were described well by the CPFE model, although some discrepancies in magnitude occurred, particularly for volumetric stress metrics (I1 and η) due to initial type II residual stress distributions. The superposition of initial residual stress states onto CPFE grain-resolved data significantly improved model accuracy for η. This suggests that residual stresses more strongly influence the simulation of volumetric rather than deviatoric (yield) stress metrics.

Effect of crack on morphology evolution of the precipitates in Nickel-based superalloys under applied stress

Nickel-based superalloys are widely used in turbine blades and aviation engine due to their outstanding mechanical property at elevated temperatures. The superior mechanical property of nickel-based superalloys is highly relevant to the morphology evolution of γ′ precipitates in the γ matrix phase. At high temperature, the directional coarsening of γ′ precipitates may result in rafting behavior under applied stress. In addition, defects such as the cavities, inclusions and micro-cracks introduced during the manufacturing process in superalloys have significant influence on the evolution of the γ′ precipitates. In this work, a phase field model with crack and precipitate as order parameters has been proposed to investigate the effect of crack on the morphology evolution of the γ′ precipitates. The morphology evolution and volume fraction evolution of the γ′ precipitates in the Nickel-based superalloys with different cracks have been investigated under the tensile and shear stresses. It is found that the local high equivalent stress and high elastic strain energy near the crack lead to the migration of solute atoms from the high stress region to the low stress region. The migration of solute atoms results in the disappearance of the γ' phases in the vicinity of cracks, which is consistent with the experimental observation. The disappearance of the γ' phases around the crack reduces the volume fraction of the γ′ precipitates, which will affect the mechanical property of the superalloys.

THE METHOD OF SELECTING THE MOST APPROPRIATE MODIFICATION OF THE MECHANISM USING COMPUTER TECHNOLOGIES

The article presents a method for identifying the most appropriate modification of the mechanism with the required output shaft rotation frequency by constructing various geometric models and calculation schemes. This technique based on the design and analysis of modification of the vibration stand mechanism for testing measuring equipment and products for vibration resistance and vibration resistance. The strength analysis of contact stresses and bending stresses in the engagement zone of the elements under various external and boundary conditions was performed using analytical and computer methods. A 3D geometric model of the parts is being created with the display of traces of operation on the surface of the parts, anticorrosion coatings, using materials of various heat treatment in the Compass 3D V.21 package. The most appropriate modification of the mechanism is identified by analyzing the distributions of maximum equivalent stresses according to Mises, the main stresses according to geometric models of parts. If these stresses exceed the limit values or the mechanism is underloaded, the geometric dimensions of the transmission parts should be changed, another material for the transmission parts should be selected and the strength calculations should be repeated.

A simple fatigue methodology for filled natural rubbers under positive and negative R ratios

This paper suggests a simple methodology to optimize the uniaxial fatigue predictions for filled natural rubbers. In this study, the stress ratio R effect on rubber fatigue life is investigated numerically. For this purpose, a Finite Element model is developed to determine both amplitude and mean stress values in the critical zone of the considered specimen. The suggested model incorporates the R ratio effect using an equivalent stress amplitude. It is proven that the new model can efficiently describe the fatigue life for a large R -value interval with higher accuracy.

Determination of equivalent stresses of pipes made of 12Kh1МF steel using FEM method, taking into account changes in geometry and scaling during operation

Determination of equivalent stresses of pipes made of 12Kh1МF steel using FEM method, taking into account changes in geometry and scaling during operation