Calculation Of Stresses Research Articles

Calculation and Analysis of Motor Mechanical Stress for In-Wheel Electric Vehicle Applications

Calculation and Analysis of Motor Mechanical Stress for In-Wheel Electric Vehicle Applications

Determination of mining-induced stress based on mining face hydraulic support stress and micro-seismicity

Understanding dynamic visualization of mining-induced stress is of great significance to disaster prevention and control in coal mining activities. In this study, three theoretical models, including linear, polynomial, and exponential models, are proposed to inverse the mining-induced stress through the acquisition and analysis of hydraulic support stress and micro-seismicity in the coal mining face. The distribution of mining-induced stress in the coal seam are graphed by fitting two key stress parameters including hydraulic support stress and peak stress, and two key zones including goaf zone and in situ stress zone. These key stress parameters and zones are defined based on the critical nodes of the model curve. According to the geological background of Mataihao coal mine in Erdos, Inner Mongolia Autonomous Region, China, the contours of mining-induced stress are graphed through the stress calculation of these three inversion theoretical models. The multi-monitoring data of micro-seismicity, drilling chips, advanced borehole stress and bolts axial force are used to verify the key stress parameters and zones of the theoretical models. It shows that the monitoring data are in good agreement with the distribution of inversed results. It should be emphasized that, if the fault structure exists around the mining face, the mining-induced stress decreases obviously when the mining face is passing through the faults, and the location of the peak stress will be closer to the mining face. The results in this study could provide methods for early prevention of extreme mining-induced stress and disaster control in the mining activities.

Consideration of Heat Transfer Characteristics in Thermal Stress Calculations of Asphalt Mixtures in the TSRST

Consideration of Heat Transfer Characteristics in Thermal Stress Calculations of Asphalt Mixtures in the TSRST

Hierarchical rank-one sequence convexification for the relaxation of variational problems with microstructures

This paper presents an efficient algorithm for the approximation of the rank-one convex hull in the context of nonlinear solid mechanics. It is based on hierarchical rank-one sequences and simultaneously provides first and second derivative information essential for the calculation of mechanical stresses and the computational minimisation of discretised energies. For materials, whose microstructure can be well approximated in terms of laminates and where each laminate stage achieves energetic optimality with respect to the current stage, the approximate envelope coincides with the rank-one convex envelope. Although the proposed method provides only an upper bound for the rank-one convex hull, a careful examination of the resulting constraints shows a decent applicability in mechanical problems. Various aspects of the algorithm are discussed, including the restoration of rotational invariance, microstructure reconstruction, comparisons with other semi-convexification algorithms, and mesh independency. Overall, this paper demonstrates the efficiency of the algorithm for both, well-established mathematical benchmark problems as well as nonconvex isotropic finite-strain continuum damage models in two and three dimensions. Thereby, for the first time, a feasible concurrent numerical relaxation is established for an incremental, dissipative large-strain model with relevant applications in engineering problems.

Stress sensitivity and its influence on high-temperature creep behavior of a novel 2nd-generation low-cost nickel based single crystal superalloy

To meet the application requirements under complex service conditions for aero engine blades, the influence of stress-state on creep behavior of a self-designed Re-low Ni-based single crystal superalloy at 1038 °C over a wide stress range of 137–207 MPa was investigated. With applied stress decreasing from 172 to 137 MPa, the creep life rapidly extends by a factor of 2.41, showing strong stress dependence. Further, the creep mechanisms under different stresses are discussed based on microstructural characterization and threshold stress calculation results. With the increasing applied stress, interfacial dislocation networks exhibit sparse and irregular shapes. Particularly, in necking zone of the fractured specimen at 1038 °C/137 MPa, due to the long-duration accumulation of deformation storage energy, dislocation arrays within γ′ rafts gradually evolve into dislocation walls through recombination and annihilation of dislocations, then develop into subgrain boundaries. Finally, some recrystallization grains with large misorientations (>10°) form by subgrain-rotation. Moreover, based on the calculated threshold stress, dislocations climbing can play a major role in creep deformation throughout the steady-state stage under a stress range of 137–207 MPa. Nevertheless, with the arrival of tertiary stage, the increasing actual stress resulted from necking deformation can also promote dislocations to cut or bypass γ′ rafts under lower stresses (137 and 172 MPa), which is consistent with the final evolution of dislocation substructures. Overall, the findings from this work are helpful to understand the high-temperature creep mechanism of low-cost single crystal superalloys, so as to improve the creep resistance of materials.

Stress-related discrete variable topology optimization with handling non-physical stress concentrations

The accuracy of stress calculation with a fixed mesh significantly affects the stress-based topology optimization, due to potential non-physical stress concentrations in voxel-based topology descriptions. This paper proposes a novel problem-independent machine learning enhanced high-precision stress calculation method (PIML-HPSCM) to address this challenge. As an immersed analysis method, PIML-HPSCM combines the high efficiency of fixed mesh with the accuracy of body-fitted mesh, without complex integration schemes of other immersed methods. PIML-HPSCM utilizes the extended multiscale finite element method to depict the material heterogeneity within high-resolution boundary elements. The accurate stress field can then be calculated conveniently by establishing stress evaluation matrices of high-resolution boundary elements. Moreover, the PIML is independent of problem settings and is applicable for various problems with the same governing equation type. Invoking the offline-trained neural network online can enhance stress calculation efficiency by 10–20 times. The stress-based discrete variable topology optimization, which naturally avoids singular stress phenomenon, is efficiently addressed by the sequential approximate integer programming method with PIML-HPSCM. Results from 2D and 3D examples demonstrate that the stresses calculated by PIML-HPSCM are consistent with those by body-fitted mesh, and optimized designs effectively eliminate stress concentrations of initial designs and have uniform stress distributions.

Use of mobile metallography to assess the extent of damage to high temperature components in power plants

Abstract Microstructural replicas are used in recurrent testing of hot, pressuriszed components to detect creep damage. The test location must be representative of the damage development and subsequent component failure. Poor preparation leads to the formation of artefacts which are considered in the damage assessment. The assessment is subject to method and operator variability. When assessing the life of components based on microstructure replicas, these must be taken into account and, if necessary, extended stress calculations for the component must be used.

Development of coupled fluid-flow/geomechanics model considering storage and transport mechanism in shale gas reservoirs with complex fracture morphology

Field observations frequently demonstrate stress fluctuations resulting from the reservoir depletion. The development of reservoirs, particularly the completion of infill wells and refracturing, can be significantly impacted by stress changes in and around drainage areas. Previous studies mainly focus on plane fractures and few studies consider the influence of complex transport and storage mechanism and irregular fracture geometry on stress evolution in shale gas reservoirs. Based on the embedded discrete fracture model (EDFM) and finite-volume method (FVM), a coupled geomechanics/fluid model has been successfully developed considering the adsorption, desorption, diffusion and slippage of shale gas. This model achieves coupling simulation of natural fractures, hydraulic fractures with complex geometry, storage and transport mechanism, reservoir stress, and pore-elastic effect. The open-source software OpenFOAM is used as the main solver for this model. The stress calculation and productivity simulation of the model are verified by the classical poroelasticity problem and the simulation results of published research and commercial simulator with EDFM respectively. The simulation results indicate that σxx, σyy, σxy and Δσ changes with time and space due to the time effect and anisotropy of formation pressure depletion; Due to the influence of different mechanisms on shale gas storage and transport, the reservoir pressure and stress distribution under different mechanisms are different; Among them, the stress with full mechanisms differs the most compared to the stress without any mechanism. The reservoir with stronger stress sensitivity (smaller Biot coefficient) is less sensitive to formation pressure depletion, and the stress variation range is smaller. For reservoirs with weak stress sensitivity, formation pressure depletion is more likely to lead to stress reversal. Under the influence of fracture geometry, the pressure depletion regions caused by the three types of fracture geometry are approximately rectangular, parallelogram and square, respectively. The corresponding σxx, σyy and Δσ also have great differences in spatial distribution and values. Therefore, the time effect, shale gas storage and transport mechanism and the influence of complex fracture geometry should be considered when predicting pressure depletion induced stress under the condition of simultaneous production. This study is of great significance for understanding the evolution law of stress induced by pressure consumption, as well as the design of infill wells and repeated fracturing.

Topology Optimization with Explicit Components Considering Stress Constraints

Topology optimization focuses on the conceptual design of structures, characterized by a large optimization space and a significant impact on structural performance, and has been widely applied in industrial fields such as aviation and aerospace. However, most topology optimization methods prioritize structural stiffness and often overlook stress levels, which are critical factors in engineering design. In recent years, explicit topology optimization methods have been extensively developed due to their ability to produce clear boundaries and their compatibility with CAD/CAE systems. Nevertheless, research on incorporating stress constraints within the explicit topology optimization framework remains scarce. This paper is dedicated to investigating stress constraints within the explicit topology optimization framework. Due to the clear boundaries and absence of intermediate density elements in the explicit topology optimization framework, this approach avoids the challenge of stress calculation for intermediate density elements encountered in the traditional density method. This provides a natural advantage in solving topology optimization problems considering stress constraints, resulting in more accurate stress calculations. Compared with existing approaches, this paper proposes a novel component topology description function that enhances the deformability of components, improving the representation of geometric boundaries. The lower-bound Kreisselmeier–Steinhauser aggregation function is employed to manage the stress constraint, reducing the solution scale and computational burden. The effectiveness of the proposed method is demonstrated through two classic examples of topology optimization.

An Aero Engine Disk Sizing and Weight Estimation Approach with Improved Temperature Profiles

Abstract During the predesign phase of an aero engine, interdisciplinary parametric studies are crucial for identifying an optimum engine. As innovative engine concepts emerge, it is essential to study trends aiming to minimize climate impact and one of its key contributors, fuel burn. The comparatively heavy disks, subjected to high thermal and mechanical loads, are central to this analysis due to their high impact on the overall module mass. This paper proposes an approach to achieve a first lightweight mechanical design of disks in the predesign phase. Based on a performance and aerodynamic baseline, the design space and physical boundary conditions are set. Firstly, an initial mass optimized disk is derived using simplified temperature profiles and stress calculations under the Mechanical Design Point conditions. Subsequently, all the module disks are considered and an estimation for each bore temperature is achieved through a novel loop over the entire module and all available operating points. By evaluating the temperature and stress profiles across various operating conditions, the lowcyclefatigue life of each disk can be studied. As part of a highly modular engine predesign framework, this method allows for zooming capabilities of single disk calculations by prescribing individual boundary conditions. The proposed approach already yields an initial assessment of the rotors within a short runtime, facilitating simple iterations with the succeeding design phases due to method and tool commonalities. While the primary focus of the current work is on compressor design, the principles presented are adaptable and expandable to turbine disk applications as well.

Equation for the simplified calculation of the horizontal shear stress in composite beams of rectangular cross-section with considerable width

The theory of elasticity allows describing the law of variation of shear stresses Τzy and Tzx for a beam of rectangular cross-section, however, the expressions are extensive and complex. For beams with a width/depth ratio equal to 0.25, it is allowed to calculate approximately the maximum shear stress Tzy, with the Collignon-Zhuravski equation. Depending on the width/depth ratio of the beam, it will depend on the percentage of error made. Unfortunately, for the shear stress Tzx there is no approximate formula available to determine the value of the shear stress. Using a simplified procedure, a differential beam element was analyzed in the elastic field for different width/depth ratios and a very simple expression was obtained. The results of the approximate formula were compared with the values obtained from the application of the exact formula and the results of a linear numerical analysis using the finite element method. For cross-sections of homogeneous beams and composite beams of considerable width, it is essential to determine the horizontal shear stresses Tzx in particular in the case of vertical planks, arranged side by side, connected solidly by horizontally arranged mechanical connectors, since the shear stresses Tzx developed across the width of the cross-section may considerably exceed the vertical shear stresses Tzy and furthermore govern the pattern, spacing and cross-section of the mechanical connectors. The validity of the approximate expression for calculating the maximum value of the shear stress Tzx was limited to beams with a width/depth ratio between 0.25 and 10.0.

Current limitations and future research needs for predicting soil precompression stress: A synthesis of available data

Precompression stress, compression index, and swelling index are used for characterizing the compressive behavior of soils, and are essential soil properties for establishing decision support tools to reduce the risk of soil compaction. Because measurements are time-consuming, soil compressive properties are often derived through pedotransfer functions. This study aimed to develop a comprehensive database of soil compressive properties with additional information on basic soil properties, site characteristics, and methodological aspects sourced from peer-reviewed literature, and to develop random forest models for predicting precompression stress using various subsets of the database. Our analysis illustrates that soil compressive properties data primarily originate from a limited number of countries. There is a predominance of precompression stress data, while little data on compression index or recompression index are available. Most precompression stress data were derived from the topsoils of conventionally tilled arable fields, which is not compatible with knowledge that subsoil compaction is a serious problem. The data compilation unveiled considerable variations in soil compression test procedures and methods for calculating precompression stress across different studies, and a concentration of data at soil moisture conditions at or above field capacity. The random forest models exhibited unsatisfactory predictive performance although they performed better than previously developed models. Models showed slight improvement in predictive power when the underlying data were restricted to a specific precompression stress calculation method. Although our database offers broader coverage of precompression stress data than previous studies, the lack of standardization in methodological procedures complicates the development of predictive models based on combined datasets. Methodological standardization and/or functions to translate results between methodologies are needed to ensure consistency and enable data comparison, to develop robust models for precompression stress predictions. Moreover, data across a wider range of soil moisture conditions are needed to characterize soil mechanical properties as a function of soil moisture, similar to soil hydraulic functions, and to develop models to predict the parameters of such soil mechanical functions.

Mechanical response and stress equation of pressure pipe liner passing across circular corrosion

Corrosion is one of the most common forms of damage to pressure pipes. CIPP liner can improve the mechanical properties of the pipe with corrosion. It is very important to study the mechanical response of corrosion pipes rehabilitated by CIPP liner. In this study, a three-dimensional finite element model of a pressure pipe rehabilitated with CIPP liner under the condition of circular corrosion is established, and the model is evaluated by using the experimental and analytical results. Afterward, the influence of each parameter on the stress and displacement of the liner is analyzed. Finally, the liner stress calculation equation is obtained based on 870 sets of data. The results show that the finite element results are in good agreement with the experimental and analytical results. The maximum stress of the liner first occurs at the center of the corroded circle, and as the corrosion diameter increases, the maximum stress gradually shifts to the edge. The maximum stress of the liner increases first and then tends to be stable with the increase of the corrosion diameter, and the friction coefficient has little effect on the liner stress.

Regulating the microstructure and mechanical properties of Al-Cu-Li alloys via optimizing Cu/Li ratio and homogenization

The effect of homogenization process on the microstructure evolution and mechanical properties of Al-Cu-Li alloys with various Cu/Li ratios (ranging from 2.4 to 3.7) are studied using scanning electron microscopy (SEM), transmission electron microscopy (TEM) and synchrotron radiation X-ray computed tomography (SR-CT) analysis. The results show that with the increase in the Cu/Li ratio, the volume fraction of the secondary phase (fv) in the as-cast alloys gradually increases, and the morphology of the secondary phases transforms from spherical-like to chain-like. For the single-step homogenization (SSH), the fv decreases with increasing homogenization temperature and time. The 510 ℃ /24 h is identified as the optimal SSH regime due to the alloys exhibiting a lower fv and a shorter SSH time than other SSH regimes. Interestingly, the alloys processed by double-step homogenization (DSH) exhibit a lower fv compared with the SSH process. The residual secondary phases consist of a small number of regular block-Al2Cu, dispersed Al20Cu2Mn3 phase and spherical-like Zr-rich phase after SSH and DSH. Furthermore, according to the results of diffusion kinetics analysis, the secondary phases can be dissolved completely into the matrix after homogenization treatment at 510 °C for 22.9 h. Therefore, the 450 ℃ / 12 h+510 ℃ / 24 h (DSH-24) is determined as the optimal homogenization regime. After DSH, a large number of spherical-like GP-Li and Al3Li nanoparticles are precipitated during natural aging. The critical resolved shear stress calculation model suggests that the Al-4.1Cu-1.3Li alloy with a Cu/Li ratio as 3.2 possess high yield strength. The Al-4.1Cu-1.3Li alloy processed by DSH-24 exhibits excellent mechanical properties, with yield strength of 299 MPa, ultimate tensile strength of 449 MPa, and elongation of 18.8 %. This study provides a foundation for the development of high-performance Al-Li alloys.

Fatigue strength of welded joints of marine aluminum alloy extrusion stiffened plate considering welding effects

Due to the low stiffness of thin-plate welded structure, the influence of welding effect on fatigue evaluation of thin-plate welded structure cannot be ignored. Extruded stiffened plates are tried to be used in hull structures because of their excellent forming technology, which can greatly reduce welding deformation and defects. By carrying out fatigue tests of extruded reinforced welded joints and traditional T-shaped welded joints, the S-N curves of typical T-welded joints are obtained and compared. Furthermore, the residual stress and welding deformation of stiffened model and traditional T-model are predicted by numerical simulation. The welding effects are introduced into the calculation of hot spot stress as the initial value, and the hot spot stress class curves of extruded reinforced welded joints and traditional T-welded joints are renewed. Compared with traditional welded joints, extruded welded joints are less affected by residual stress and welding deformation. The study revealed that residual stress and welding deformation exhibited a higher sensitivity to the fatigue strength of traditional thin-plate welded structures.

Nanoindentation of B4C-HfB2 particulate ceramic composite doped with Cr–B compounds

Mechanical behavior of B4C - HfB2 particulate ceramic composite doped with CrB + Cr3B4 chromium boride compounds were studied by nanoindentation. Hardness, Young's modulus, and indentation stress - indentation strain behavior of B4C and HfB2 phases was computed. It was found that hardness and Young's modulus of B4C matrix phase in B4C - HfB2 doped with Cr - B was increased as compared to those hardness and Young's modulus of pure B4C. It was also found that indentation stress was relieved by “pop-in” events in some of the B4C grains, however, the “pop-in” discontinuous events were always observed upon indentation of HfB2 grains, that lead to a decrease in hardness of HfB2 from 40 to 50 GPa before “pop-ins” to 28–32 GPa after “pop-ins”. The obtained results can be further used in calculations of thermal residual stresses in B4C and HfB2 phases of B4C - HfB2 particulate ceramic composite.

Research on the correlation between roughness parameters and contact stress on tooth surfaces and its dominant characteristics

The contact performance of the tooth surface is a crucial factor affecting the operational lifespan of gears. There is a significant correlation between tooth surface topography and contact stress, as well as fatigue performance. To investigate the influence of different topography parameters on tooth surface contact stress, this paper performs analytical calculations on asperity contacts of rough tooth surfaces based on reconstruction modeling. Through efficient calculations, sufficient correlation analysis data is obtained. The neural network analysis method is used to measure the degree of influence of roughness parameters on tooth surface contact performance. Research on the correlation between micro-topography parameters and maximum contact stress on tooth surfaces, as well as regression analysis, is conducted. The results show that: (1) Considering rough surfaces, the tooth surface contact stress field exhibits two stress peaks in the near-surface layer and sub-surface layer, with a maximum Mises stress increase of up to 30 % compared to a smoother surface. (2) In the case of low roughness (Sa < 0.2 μm), the amplitude of the maximum Mises stress peak in the near-surface layer is close to that in the sub-surface layer. However, as the roughness amplitude increases, the amplitude of the near-surface stress peak increases sharply. (3) Ranking the roughness parameters based on their influence on contact stress, the main parameters characterizing contact performance are identified as Spk, Vmp, and Sq. The peak characteristics of the surface are the decisive factors affecting fatigue extremes, which are stronger than the traditional surface roughness parameter Sq. This paper establishes a direct correlation model between tooth surface topography parameters and contact stress, providing a foundation for simplifying stress calculations considering complex topographies and offering new insights for fatigue-resistant design of tooth surfaces.

Dealing with multiaxial non-proportional fatigue with varying mean stress: Invariant and critical plane approaches for component-like structural adhesive joints

A comparative investigation between an invariant-based approach using the signed Beltrami-stress and critical-plane approach using the Findley-stress is carried out for the fatigue lifetime prediction of an epoxy structural adhesive under multiaxial non-proportional loading with varying mean stress. Fatigue experiments with uniaxial and multiaxial loading (proportional and non-proportional) are done at stress ratios of −1 and 0.1. Two adhesive joints are evaluated: a hollow-cylinder butt-joint (HCBJ, sample with homogeneous stresses distribution), and a flange-rod-joint (FRJ, component-like specimen with complex stress state). For both geometries, multiaxial loading and an increasing mean stress lead to fatigue strength reduction, whereas the phase-shift effect is less pronounced. A systematic procedure for parameter determination is implemented for both approaches. For predictions of the HCBJ-sample, stresses are analytically obtained. For validation with the FRJ-sample, FEA-based stress calculation is used. For both joints, the critical plane approach results in more accurate predictions than the invariant-based approach. In comparative terms, the invariant-based approach is experimentally more complex, by requiring a mean stress correction, but its numerically simpler with lower calculation time. The critical-plane approach requires fewer experiments for parameter determination and provides more accurate results for non-proportional loading. However, it is more numerically demanding with larger computing time.

Two-Stage Analysis Method for the Mechanical Response of Adjacent Existing Tunnels Caused by Foundation Pit Excavation

With the advancement of urban underground space networks, there has been a rise in foundation pit projects near existing tunnels. The construction of these foundation pits adjacent to existing tunnels can result in soil disturbance and stress redistribution, leading to additional deformation and internal force within the tunnels. This paper delves into the two-stage analysis method, outlining the calculation of additional stress in the initial stage considering various engineering factors and the methods for determining tunnel displacement and internal force in the subsequent stage. Through an engineering example and numerical simulations, the theoretical calculations were validated. The maximum displacement generated by the tunnel is −4.85 mm and −5.10 mm, respectively. The maximum error is only 5.9%, which confirms the validity of the theoretical approach. The analysis demonstrates that incorporating the unloading model of the bottom and surrounding side walls of the foundation pit is essential when calculating additional stress in the first stage. Moreover, the presence of engineering dewatering and double-hole tunnels can counterbalance the additional stress, with deviations of only 4.4% and 2.5%, respectively. In the second stage, factoring in the shear action and lateral soil action in the foundation and tunnel model enhances the accuracy of stress mode representation (accuracy increased by 18.8% and 29.3%, respectively). Additionally, accounting for the buried depth effect of the tunnel, soil non-uniformity, and foundation nonlinearity helps prevent excessive foundation reactions.

Approximation‐based implicit integration algorithm for the Simo‐Miehe model of finite‐strain inelasticity

AbstractWe propose a simple, efficient, and reliable procedure for implicit time stepping, regarding a special case of the viscoplasticity model proposed by Simo and Miehe (1992). The kinematics of this popular model is based on the multiplicative decomposition of the deformation gradient tensor, allowing for a combination of Newtonian viscosity and arbitrary isotropic hyperelasticity. The algorithm is based on approximation of precomputed solutions. Both Lagrangian and Eulerian versions of the algorithm with equivalent properties are available. The proposed numerical scheme is non‐iterative, unconditionally stable, and first order accurate. Moreover, the integration algorithm strictly preserves the inelastic incompressibility constraint, symmetry, positive definiteness, and w‐invariance. The accuracy of stress calculations is verified in a series of numerical tests, including non‐proportional loading and large strain increments. In terms of stress calculation accuracy, the proposed algorithm is equivalent to the implicit Euler method with strict inelastic incompressibility. The algorithm is implemented into MSC.MARC and a demonstration initial‐boundary value problem is solved.