Three-dimensional Stress Distribution Research Articles

3D stress concentration around circular hole under remote biaxial loading

In this study, a theoretical model is proposed to analyze the stress concentration in a plate of finite thickness containing a circular hole under remote biaxial loading. The stresses in a plate with a circular hole under remote biaxial loading is a superposition of the stresses in the unperforated plate and the released stresses induced by opening the hole. For the latter, the stresses at the edge of the hole can be further decomposed into a spherical component and a deviatoric component. The solution due to a spherical component can be readily obtained but the solution due to a deviatoric component is hard to find. According to the literature, the solution of three-dimensional stress distributions in a plate of finite thickness containing a circular hole can be found by four potential functions. The available fundamental solutions of the potential functions satisfying the boundary conditions on the surfaces of the plate contain numerous complicated integrals, which limits their application to the current problem. Nevertheless, these fundamental solutions can be found explicitly by constructing the orthogonal function, which is composed of the Bessel functions. A system of linear equations is established to satisfy the boundary conditions at the edge of the hole. Therefore, the stresses due to a deviatoric component are obtained by solving the linear simultaneous equations. The stress concentration factor calculated by the proposed model is validated with the available numerical and theoretical solutions. It is concluded that the stress ratio, the thickness of the plate, and Poisson's ratio have an important influence on the distribution of the stress concentration factor along the thickness of the plate, especially on the distribution near the surface. Moreover, the proposed model can be extended to analyze the stress concentration at the edge of a circular hole in a plate of finite thickness under remote bending. The model is efficient and reliable, and it can provide a powerful analytical method to analyze three-dimensional stress concentrations around holes under various remote loading in engineering.

Analysis of plate reinforced by straight and curved stiffeners by using novel plate elements with refined through-the-thickness expansion

In this paper, two-dimensional (2D) structural models are used to analyze thin-walled stiffened structures. A novel approach is presented to model both skins and stiffeners using 2D finite elements (FEs) with enhanced capabilities. The deformation of the stiffeners is accurately described using higher order Lagrange polynomials, and the mechanical continuity between the reinforcements and the skin is automatically ensured in correspondence of the Lagrange points. The 2D FEs are built using the Carrera Unified Formulation (CUF), which allows arbitrary refinement of the stiffener kinematics. In this way, any type of deformation can be described and, if a higher-order model is used, the three-dimensional (3D) stress distribution can be evaluated. The proposed model is tested on a stiffened plate and compared with results obtained using traditional FEA, including 3D and 2D models and a combination of 2D and one-dimensional (1D) models for the stiffeners. The results show and demonstrate the reliability of the proposed method, both in terms of displacements and stresses, when compared to the 3D solution. In addition, the computational cost, evaluated here as the number of degrees of freedom (DOFs), is much lower. Finally, the ability of this model to deal with curved stiffeners is demonstrated with practical examples.

Neutronographic Residual Stress Analysis for Materials With Depth Gradients of the Strain Free Lattice Parameter $${{\varvec{d}}}_{0}$$ for the Example of a Case-Hardened Steel 20MnCr5

AbstractIn the present work, ring-shaped samples made from steel 20MnCr5 were low-pressure carburized (LPC) and subsequently hardened by gas quenching (case-hardened). This results in a near-surface gradient in chemical composition, microstructure- and hardness distribution, as well as a three-dimensional residual stress (RS) distribution, which was investigated by neutron diffraction. Near-surface RSs in the ferrite-/martensite- and austenite phase are additionally determined by X-ray diffraction. It is shown that the chemical gradient has an influence on the chosen $${d}_{0}$$ d 0 strategy and how such a reference sample should be extracted. If near-surface RS values are to be determined by neutron diffraction, the pseudo-strain effect must be taken into account. For this purpose, a suitable approach using the “open source” software SIMRES and STRESSFIT is also presented. By combining neutron and X-ray diffraction data, a complete RS distribution over the whole sample can be obtained.

Fatigue life enhancement mechanism and lifetime prediction of AA6061-T6 open-holed sheet treated by electromagnetic driving dynamic cold expansion

In this study, mechanisms of fatigue life enhancements of electromagnetic driving dynamic cold expansion (DCE) open holed sheets were investigated by testing fatigue life and obtaining residual stress fields experimentally and numerically. Furthermore, a fatigue life prediction method based on three-dimensional stress distributions was proposed. Results showed that DCE method extended higher fatigue life and produced more uniform residual stress along hole axial direction than static cold expansion (SCE) method. The differences in stress distribution led to different fatigue crack initiation and propagation modes of DCE and SCE specimens. Moreover, the predicted fatigue life results were in accordance with experimental data. • Dynamic cold expansion extended larger fatigue life for holed-sheets. • More uniform residual stress was induced by dynamic cold expansion. • Fatigue cracks propagated horizontally in dynamic cold expanded specimens. • Proposed method to predict fatigue life had good agreement with experiments.

Residual stress distribution and fatigue performance investigations of electromagnetic force-based dynamic cold expansion open-holed sheet

In this study, residual stress distributions and fatigue performances of electromagnetic driving dynamic cold expansion (DCE) open-holed sheets were investigated. Fatigue behaviors were tested, and residual stress fields were obtained experimentally and numerically. Furthermore, a fatigue life prediction method based on three-dimensional stress distribution was proposed. Results showed that DCE method extended higher fatigue life and produced more uniform residual stress along hole axial direction than static cold expansion (SCE) method. The stress distribution differences led to different fatigue crack initiation and propagation modes of DCE and SCE specimens. Uniform stress distributions along axial direction in DCE specimens contributed to random initiations and horizontal propagations of fatigue cracks, while the fatigue cracks in SCE specimens usually initiated at the mandrel entrance layer and propagated to the mandrel exit layer. Moreover, the predicted fatigue life results agreed well with experimental data.

Torqued and conventional cantilever for uprighting mesially impacted molars: A 3-dimensional finite element analysis

The objective of this study was to evaluate the effects of the torqued cantilever (TC) and conventional tip-back cantilever (CC) made of stainless steel (SS) and titanium-molybdenum alloy (TMA) on the uprighting of mesially impacted mandibular molars using three-dimensional finite element analysis. The 3-dimensional mandibular model included part of the mandible with mesially tipped and impacted mandibular second molar, periodontal ligament (PDL), molar tube, mini-implant, and cantilevers. Four finite element method models (TC-SS, TC-TMA, CC-SS, and CC-TMA) were created to simulate different skeletally anchored uprighting mechanics. CC mechanics involved a known 0.019 × 0.025-in helical cantilever acting on a buccal molar tube. TC mechanics included a 0.019 × 0.025-in cantilever capable of producing mesial root torque by acting on a tube positioned on the molar disto-occlusal surface with the slot in a buccolingual direction. Three-dimensional molar displacement and stress distribution on the molar PDL were recorded. The SS cantilever produced almost twice as much molar displacement as the TMA. TC mechanics showed more evident mesial displacement of the molar root apexes. CC mechanics had greater molar rotation. TC uprighting moment produced greater molar mesial extrusion and greater intrusion of the distal root apex. The dual deflection system of the TC mechanics induced the lowest stress on the PDL, regardless of the metallic alloy. TC delivered a more efficient uprighting moment to the molar with less unwanted tooth movement and stress on the PDL and a more accessible site for bonding the molar tube.

Mapping of three-dimensional residual stresses by neutron diffraction in nickel-based superalloy discs prepared under different quenching conditions

Large interior residual stresses, generated during various thermomechanical treatments, could greatly affect not only the machining dimension precision during subsequent machining processes but also the structural stability under service in superalloy components. In this paper, neutron diffraction measurements have been carried out to characterize the three-dimensional residual stress distributions in IN718 superalloy discs quenched with different media, including water, oil, air and insulation. Three-dimensional residual stress maps have been derived in these specimens. It was found that, in the water-quenched, oil-quenched and air-cooled specimens, the residual stresses are compressive near the surface balanced by tension within the interior, with the peak magnitude stresses of 560 MPa, 480 MPa and 120 MPa, respectively. It was evidenced that there is no obvious residual stress in the insulation-cooled specimen. The corresponding Vickers hardness maps show a larger hardness at the core and smaller hardness near the surface in the water-quenched, oil-quenched and air-cooled specimens, whereas there is a larger hardness near the cylindrical surface and smaller hardness at the central axis in the insulation-cooled specimen, achieved by the differential cooling rate control. Our investigations show that the coordinated regulation of residual stress and microstructure and properties can be realized by reasonably selecting cooling media.

Experimental and numerical studies of fatigue behavior of Ti6Al4V alloy treated by laser shock peening

Laser shock peening (LSP) is applied as the laser surface treatment technology to improve the fatigue resistance of aircraft parts with complex geometric features. In this paper, the effects of laser energy inputs on residual stresses and fatigue properties for hole-structured specimens of Ti6Al4V alloy treated by LSP are studied. Changes of residual stress distributions, fatigue behaviors and fracture morphologies are analyzed with different laser-induced shock pressures. The results show the fatigue life is prolonged by 137% compared with the untreated specimens due to the introduction of compressive residual stresses. The sectional observations of fatigue fracture morphology show the inwards movement of fatigue crack initiation positions and the complexity of fracture cracks after LSP treatment. The simulation results confirm that the fatigue life with different laser energy inputs depends strongly on the three-dimensional stress distribution around the hole. Among them, high surface compressive stresses and deep stress affected layers play a decisive role in improving fatigue life. The results in this study broaden the knowledge of fatigue behavior and explore engineering potentials of improved fatigue life for complex industrial specimens.

Predictions of three-dimensional contact stresses of a radial truck tire under different driving modes

In pavement design, vehicle load is typically simplified as vertical circular uniform loading. Due to the vehicle dynamic effect and deformation of a tire, non-uniform three-dimensional contact stresses are produced at the contact interface between the tire and pavement under different driving modes. For this paper, an 11R22.5 truck radial tire was selected. Considering the geometric nonlinearity and large deformation of the tire and nonlinear characteristics of tire-pavement contact, the Neo-Hookean and Rebar models are used to simulate the hyperelastic rubber material and rubber-cord composite material, respectively. The three-dimensional contact stress distribution under static, free rolling, acceleration, braking, and cornering modes was simulated and analyzed. The results show that inflation pressure, axle load, and friction coefficient of the tire significantly affect the three-dimensional contact stress distribution. Further, three-dimensional stresses are non-uniformly distributed, rather than in the traditional simplified circular uniform load. The three-dimensional stress distribution of tire-pavement in different driving modes is also significantly different. The vertical and lateral stresses in the state of cornering are the largest, the longitudinal stress in the state of braking is the largest as well. The research results provide reference for future pavement design and pavement damage analysis.

Study on Temporal and Spatial Characteristics of Overlying Strata in the Deep Coal Mining Process

This study adopts the stress relief method to test the in situ stress in the field to obtain the in situ stress distribution characteristics of no. 2 + 3# coal seam. A three-dimensional model was established with the no. S3012 working face as the engineering background, and the measured in situ stress values were applied to the three-dimensional model, and the spatial-temporal evolution characteristics of coal and rock mass around the stope during coal seam mining were studied. The specific conclusions are as follows: the three-dimensional stress distribution map in front of, behind, and on both sides of the working face in the process of coal mining are obtained. As the working face goes on, the maximum value of the supporting stress formed in front of, behind, and on both sides of the working face shifts to the corner, presenting a “hump-like” distribution. The stress concentration coefficient of front, back, and both sides of stope increases linearly with the increase of the mining size. Under the same mining size, the stress concentration coefficient in front of stope is the smallest, and the stress concentration coefficient on both sides is the largest. The three-dimensional displacement field distribution nephogram of overlying strata in the process of coal mining is obtained. With the continuous advance of the working face, the roof strata of coal seam undergo the continuous dynamic subsidence process, and the roof subsidence increases continuously, showing the shape of “bowl” with sharp bottom. In the process of working face mining, the roof displacement of coal seam showed an “O” shape evolution characteristic. The three-dimensional distribution cloud map of the plastic zone of coal and rock mass in the process of the working face mining was obtained, and the failure volume of the plastic zone gradually increases with the continuous progress of the working face.

A platform for high-fidelity patient-specific structural modelling of atherosclerotic arteries: from intravascular imaging to three-dimensional stress distributions.

The pathophysiology of atherosclerotic lesions, including plaque rupture triggered by mechanical failure of the vessel wall, depends directly on the plaque morphology-modulated mechanical response. The complex interplay between lesion morphology and structural behaviour can be studied with high-fidelity computational modelling. However, construction of three-dimensional (3D) and heterogeneous models is challenging, with most previous work focusing on two-dimensional geometries or on single-material lesion compositions. Addressing these limitations, we here present a semi-automatic computational platform, leveraging clinical optical coherence tomography images to effectively reconstruct a 3D patient-specific multi-material model of atherosclerotic plaques, for which the mechanical response is obtained by structural finite-element simulations. To demonstrate the importance of including multi-material plaque components when recovering the mechanical response, a computational case study was conducted in which systematic variation of the intraplaque lipid and calcium was performed. The study demonstrated that the inclusion of various tissue components greatly affected the lesion mechanical response, illustrating the importance of multi-material formulations. This platform accordingly provides a viable foundation for studying how plaque micro-morphology affects plaque mechanical response, allowing for patient-specific assessments and extension into clinically relevant patient cohorts.

Evaluation of bending and post-buckling behavior of thin-walled FG beams in geometrical nonlinear regime with CUF

In this paper, the nonlinear behavior of beams with one-dimensional (1D) Functionally Graded Materials (FGM) is investigated by Carrera Unified Formulation (CUF). In the study, kinematic variants of CUF are extended with Lagrange Extension (LE), thus adopting Layer-Wise (LW) approach. In the CUF formulation combined with geometric nonlinear equations, the Lagrangian approximation and Newton–Raphson linearization scheme are used with the method based on arc length constraint. It is assumed that the variation of material properties in the thickness direction follows an exponential grading. The displacement and stress distributions of the Functionally Graded (FG) cantilever beam under transverse/axial loading are investigated for different compositional gradient exponents. The three-dimensional (3D) stress distributions of FG beams are investigated with the 1D CUF model and the results are confirmed by the literature. The effect of the compositional gradient exponent on the mechanical behavior is expressed and it is emphasized that the combined formulation is time-efficient and highly sensitive in determining the nonlinear behavior.

Method for Calculating Plastic Deformation of High Resolution and Large Contact Area

AbstractIn a rolling contact, the tribological properties in terms of friction, wear, and fatigue are significantly influenced by the surface roughness. Due to solid contact of the surfaces in the contact area, the roughness and thus also the tribological properties change during the service life of the contact. The initial load leads to major changes of the tribological properties figured out by Brecher et al. (2019, “Influence of the Metalworking Fluid on the Micropitting Wear of Gears,” Wear, 61(434–435), p. 202996). Prediction of the initial changes in topography in the contact area is necessary for specific optimization of rolling contacts. Especially for dry rolling–sliding contact, the roughness of the surfaces is crucial for the lifetime, which is part of the investigations within the DFG priority program 2074 (357505886). In this work, an elastic-plastic contact algorithm for calculating plastic deformation for dry contact of rough surfaces with large contact area and high resolution is presented. Due to the nonlinearity behavior associated with plastic deformation, the plastic contact algorithm is based on an iterative approach. An optimized meshing strategy is implemented to calculate the elastic pressure distribution on the surface. Corresponding to the two-dimensional pressure distribution, the three-dimensional stress distribution allows the consideration of residual stresses and interactions of the microscopic peaks of the rough surface. Furthermore, the three-dimensional plastic strain distribution allows the application of an analytical approach to represent the plastic deformation of the surface. Finally, the solution of a plastic contact calculation with an exemplary topography measured on a real rough surface is presented.

Strain-life estimation of the last stage blade in steam turbine during low volume flow conditions

Based on the elastic-plastic analysis, the local strain-life of the last stage of steam turbine under the low volume flow conditions is predicted. Considering the unsteady flow steam force and local high temperature of blade, the three-dimensional transient flow field, strain distribution and stress distribution of the last stage blade are calculated by the two-way fluid structure interaction method. Under low volume flow conditions, the temperature of blade tip increases with the decrease of volume flow. In addition, the self-excited unsteady frequency of rotor -stator clearance vortex is obtained at 90% span. According to the distribution of maximum equivalent stress on the rotor blade surface, three dangerous points are identified, which are located at the blade tip of the pressure surface (DP1), 90% span of the suction surface (DP2) and the trailing edge at the blade root of the pressure surface (DP3). With the decrease of volume flow, the equivalent stress and strain range of dangerous points increase, so the strain- life of dangerous points decreases. Among them, the strain-life of DP2 is the shortest at case3 condition. The strain response frequency of DP2 is consistent with the self-excited unsteady frequency of rotor -stator clearance vortex, which proves that it is necessary to consider the unsteady steam flow force in strain-life calculation. This study provides theoretical guidance for the safe operation time of the steam turbine under low volume flow conditions.

A hygrothermal stress finite element analysis of laminated beam structures through hierarchical one-dimensional modeling

A new multi-field beam model based on Carrera’s Unified Formulation (CUF) is offered in this article to efficiently solve the hygro-thermal-mechanical problem of beam structures with high-fidelity. Several beam models have been hierarchically derived in the framework of CUF with consideration of the hygro-thermal stresses. By adopting the principle of virtual displacement, the element stiffness matrix can be derived into a compact form. The temperature and humidity profile is generated from the Fourier’s heat conduction and Fick’s law, respectively. With simply supported and cantilever configurations being adopted, hygro-mechanical and hygro-thermal-mechanical analyses are carried out for different beam slenderness ratios. Results are provided in terms of three-dimensional displacement and stress distributions. The proposed one-dimensional CUF-based beam model has been validated against traditional three-dimensional FEM-based solutions, and an excellent correlation has been achieved. It is found that an accurate result can be obtained through the proposed CUF-based beam model with reduced computational costs.

Complete nondestructive evaluation of three-dimensional residual stress distribution using X-ray diffraction

It is interesting to consider just how many of us don't think about the importance of mechanical engineering when we go about our daily lives. Whether we are crossing bridges, getting into our cars, riding on trains, flying in planes or entering buildings, we are relying on mechanical engineers and researchers to have performed an enormous amount of calculations to ensure the integrity of these structures. Indeed, the main purpose of many engineering activities is to design structures against failure. By employing physics, mathematical principles, experience, technical knowledge and modelling capabilities, teams can confidently predict the safe operations of complex engineering systems. Dr Masaru Ogawa, who is based at the Department of Mechanical Systems Engineering, Kogakuin University, is working alongside Professor Alexander M Korsunsky and a number of researchers to elucidate the origins and effects of residual stresses. They are using the eigenstrain reconstruction method to estimate 3D residual stress distribution.

Accurate through-the-thickness stress distributions in thin-walled metallic structures subjected to large displacements and large rotations

The present paper presents the evaluation of three-dimensional (3D) stress distributions of shell structures in the large displacement and rotation fields. The proposed geometrical nonlinear model is based on a combination of the Carrera Unified Formulation (CUF) and the Finite Element Method (FEM). Besides, a Newton-Raphson linearization scheme is adopted to compute the geometrical nonlinear equations, which are constrained using the arc-length path-following method. Static analyses are performed using refined models and the full Green-Lagrange strain-displacement relations. The Second Piola-Kirchhoff (PK2) stress distributions are evaluated, and lower- to higher-order expansions are employed. Popular benchmarks problems are analyzed, including cylindrical isotropic shell structure with various boundary and loading conditions. Various numerical assessments for different equilibrium conditions in the moderate and large displacement fields are proposed. Results show the distribution of axial and shear stresses, varying the refinement of the proposed two-dimensional (2D) shell model. It is shown that for axial components, a lower-order expansion is sufficient, whereas a higher-order one is needed to accurately predict shear stresses.

Thermo-mechanical stress analyses of solid oxide fuel cell anode based on three-dimensional microstructure reconstruction

During high-temperature operation of a solid oxide fuel cell, the stresses caused by mismatch of thermal expansion coefficients between different materials and external mechanical loads may cause the rising of damage risk of nickel-yttria-stabilized zirconia anode. It is quite difficult to quantify the mechanical characteristics of a composite anode without investigating on the stress distribution in its real microstructure. However, the high operating temperature and extremely complex microstructure in micro-scale determine the high difficulty in in-situ measurement of thermo-mechanical stress distribution. In this work, the microstructures of six different anode samples, fabricated by using identical nickel oxide-yttria-stabilized zirconia powder mixture, are reconstructed in three-dimension based on the dual-beam focused-ion-beam-scanning-electron-microscopy. The three-dimensional thermo-mechanical stress distributions of different microstructures are conducted at operating temperature based on the finite element method. The effects of both thermal expansion coefficients mismatch between nickel and yttria-stabilized zirconia and external mechanical loads are analyzed. The mechanical failure probabilities of yttria-stabilized zirconia phase in different reconstructions are estimated based on the obtained stress distributions to investigate the influence of microstructure characterizations on nickel-yttria-stabilized zirconia anode strength.

Stress Distribution in Silicon Subjected to Atomic Scale Grinding with a Curved Tool Path.

Molecular dynamics (MD) simulations were applied to study the fundamental mechanism of nanoscale grinding with a modeled tool trajectory of straight lines. Nevertheless, these models ignore curvature changes of actual tool paths, which need optimization to facilitate understanding of the underlying science of the machining processes. In this work, a three-dimensional MD model considering the effect of tool paths was employed to investigate distributions of stresses including hydrostatic stress, von Mises stress, normal and shear stresses during atomic grinding. Simulation results showed that average values of the stresses are greatly influenced by the radius of the tool trajectory and the grinding depth. Besides the averaged stresses, plane stress distribution was also analyzed, which was obtained by intercepting stresses on the internal planes of the workpiece. For the case of a grinding depth of 25 Å and an arc radius 40 Å, snapshots of the stresses on the X–Y, X–Z and Y–Z planes showed internal stress concentration. The results show that phase transformation occurred from α- silicon to β- silicon in the region with hydrostatic stress over 8 GPa. Moreover, lateral snapshots of the three-dimensional stress distribution are comprehensively discussed. It can be deduced from MD simulations of stress distribution in monocrystalline silicon with the designed new model that a curved tool trajectory leads to asymmetric distribution and concentration of stress during atomic-scale grinding. The analysis of stress distribution with varying curve geometries and cutting depths can aid fundamental mechanism development in nanomanufacturing and provide theoretical support for ultraprecision grinding.

Crack initiation characteristics of ring chain of heavy-duty scraper conveyor under time-varying loads

Crack initiation characteristics of ring chain of heavy-duty scraper conveyor under time-varying loads were investigated in this study. The dynamic tension of ring chain of the heavy-duty scraper conveyor was obtained using the time-varying dynamic analysis. Finite element analyses of three-dimensional contacts between adjacent chain rings at straight and bending segments were carried out to explore three-dimensional stress distributions of chain rings. The crack initiation life of chain ring was predicted employing the multiaxial fatigue theory. The results show that the ring chain is subjected to time-varying dynamic tensions during operation. During tension-tension contact fatigue, as compared to the straight segment of ring chain, the bending segment engaging in the sprocket presents an overall lower (or higher) equivalent stress distribution in the case of flat (or vertical) chain ring, respectively. Maximum equivalent stresses at the contact regions of adjacent chain rings both present time-varying dynamic characteristics similar to evolutions of dynamic tension. During tension-torsion contact fatigue, an increase in torsion angle level causes unobvious difference between equivalent stress distributions at contact regions of adjacent rings. Predicted crack initiation lives of chain rings during tension-tension contact fatigue indicates more severe fatigue damages of the vertical chain ring at the straight segment and of the flat chain ring at the right bending segment.