Calculation Of Stress Field Research Articles

A systematic study of disclination-induced internal stress associated with multiple types of twin-twin reactions in Mg alloys: analytical solutions and numerical calculations

Deformation twinning plays an important role in enhancing the mechanical properties of metals and alloys by mechanisms such as twinning-induced plasticity and strain hardening. However, internal stress concentration associated with the interactions and reactions of twins may also lead to the degradation of ductility and fracture toughness. While the elastic behavior of individual twin types has been extensively studied, the crystallographic reactions among multiple types of twins have not been well recognized, which could produce high-index or irrational twins as well as byproduct disclinations. A theoretical framework to predict twin-twin reaction products and quantify associated internal stress is still unavailable. Here we suggest a general approach to investigate twin-twin reactions through symmetry-dictated characteristic defect analyses and stress field calculations based on disclination theory. By using Mg as an example, a systematic study of multiple types of twin-twin reactions has been conducted. The product defects arising from the reactions and associated internal stress fields have been determined analytically, which are validated by numerical simulations and experimental measurements. This work not only establishes a theoretical foundation for quantifying defect-induced internal stress concentration from complicated twin-twin interactions/reactions, but also offers new insights into the impact of deformation twins on mechanical properties.

NEW APPROACHES TO JUSTIFICATION OF MATERIALS FOR GARMENTS USING THE EXAMPLE OF A MEN’S T-SHIRT

The possibility of using modern methods of virtual fitting of clothes on an avatar of the human body in the process of forming the quality of garments is shown. A general scheme for calculating the me-chanical processes developed in garments when fitting the human body in statics and dynamics is presented, as well as the main directions for automating the calculation process. Based on the chosen numerical method, the problem of selecting textile materials to ensure the required quality of the product was solved using the example of a men’s T-shirt. The mechanical properties of several samples of knitted fabrics for such products were determined. Based on the obtained values, the calculation of stress fields in the parts of a men’s T-shirt in various body avatar poses was carried out. An experimental verification of the modelling results was carried out. Regularities have been established between the mechanical properties of knitted fabric and the nature of stress in the structure of the product. The possibility of their use when choosing textile materials is shown from the point of view of ensuring the required quality of products at the design stage.

Tensile strength of particle reinforced composite with interfacial debonding

Strength prediction of a particle reinforced polymer composite (PRPC) is still challenging. Although a PRPC is overall isotropic, it is more difficult to predict its tensile strength accurately than a continuous fiber reinforced composite (CFRC). One reason for this difficulty is that the calculation of stress fields of the constituents in a PRPC are complicated. The other reason is that the strength of a PRPC is significantly affected by interfacial strength, which is hard to be measured directly. In our research, the discount of the composite strength after debonding is attributed to the intensifying stress concentration. Two stress concentration factors (SCFs) are derived respectively to characterize the stress fluctuations in the matrix caused by the embedded particle before and after debonding. Based on the micromechanics Bridging Model and the matrix true stress theory, these two SCFs can be applied to evaluate the interface strength and the ultimate tensile strength of the composite from the properties of its component materials. Illustrations are presented to verify the efficiency of our theory and analyze the main influencing factors on the strength of the PRPC, including mechanical properties of component materials, particle size and volume fraction.

NGHIÊN CỨU TRƯỜNG ỨNG SUẤT BÁNH CÔNG TÁC TẦNG ĐẦU TIÊN MÁY NÉN ĐỘNG CƠ TUA BIN KHÍ TV3-117 BẰNG MÔ PHỎNG SỐ

This article presents the results of stress field calculations for the first stage compressor impeller using the one-way fluid-structure interaction (FSI) method, which helps determine stress concentration zones and safety factors. Numerical analysis conducted with Ansys software reveals that stress concentration occurs near the blade root on the suction side and within the blade lock-disc zone. In these stress concentration zones, such as the blade lock-disc zone and blade suction side, the minimum safety factor is found to be above 2.27. These findings serve as a foundation for future research on impeller stress fields using two-way FSI methods and for providing recommendations to optimize the stress concentration field in the compressor disc.

Dependence of Critical Stress Intensity Factor on Crack Depth From the Loading Boundary of Crystalline Silicon

Abstract In the present work, an atomistic scale investigation is done on crystalline silicon to understand the effect of crack depth from the loading (pulling) boundary on the critical near-tip state of stress. For various depths of embedded cracks, the near-tip stress field has been calculated at the critical state just before the crack propagation initiation. This atomistically calculated stress field is found to be quite close to those found using continuum linear elasticity. Thereafter, the critical stress intensity factor (SIF) is calculated for all cases by fitting the atomistically calculated normal stress over inverse square-rooted distance from the crack tip. It has been found that the closer the crack is located to the loading boundary (i.e., lesser depth), the lower is the (locally calculated) critical SIF. This implies that it is easier to initiate crack propagation when the crack is located closer to the loading boundary. The claim is also strengthened by a similar observation of (globally calculated) boundary stresses at the critical state just before crack propagation initiation.

Analytical Solution of Ice–Rock-Model Stress Field and Stress Intensity Factors in Inhomogeneous Media

The stress distribution and fracture parameter calibration of ice–rock models are important aspects of studying rock properties at high altitudes and latitudes. However, progress in ice–rock modeling has been slow and singular, and it is limited due to the discrete nature of rocks and the applicability of fracture mechanics. In this study, a circular inhomogeneous ice–rock model is proposed for the first time, and a method is provided for calculating the stress field of the model under biaxial loading. A method for calculating the single-crack stress intensity factor of the model subjected to biaxial compressive loading is also provided. The novelty of this work is that the inhomogeneous ice–rock model is treated as a superposition of two models, namely, a circular pore plate and circular ice, according to the superposition principle. The key is that the stress field distribution law of the ice–rock model is obtained based on the basis of the displacement continuity of the ice–rock interface. The analytical and approximate solutions of the stress intensity factor of a single crack were also obtained by considering the normal phase effect of the crack surface and combining the stress distribution law of the ice–rock model. Comparison with the CAE method was made to verify the correctness of the stress field and stress intensity factor calculation methods. The evolution laws of lateral pressure coefficients, the elastic modulus ratio of ice and rock on the stress field, and the stress intensity factor were analyzed. The effects of lateral pressure coefficients, elastic modulus ratios, and crack distributions on the failure modes were investigated using the extended finite element method (XFEM). This study can provide a theoretical basis for the evaluation of mechanical properties and prediction of the failure modes of frozen rock bodies.

Stress field and stability calculation method for unloading slope considering the influence of terrain

Stress field and stability calculation method for unloading slope considering the influence of terrain

A new exhaustive semi-analytical method to calculate stress distribution on the surface of a curved beam with circular cross section, with an application to helical compression springs

In mechanical and in civil engineering, stressed curved beams are found in many applications involving failure and fatigue analysis. However, stress formulas of straight beams cannot be applied to curved beams with any reasonable degree of accuracy. Hence, curved beam theory is yet to be properly defined and is only established for particular sets of loads, particular applications, and particular cross-section geometries. This work proposes the first exhaustive solution of stress field calculation on the surface of a curved beam with a circular cross section, computed with an open-access databank preliminary built with FE simulations and considering every kind of static mechanical load applied and any curvatures. Such data are an important prerequisite for probabilistic fatigue life analysis. A numerical campaign was executed with different relative curvatures and was gathered in an open-access stress coefficient databank to facilitate data use. For any given curvature and wire diameter, the method can obtain the distribution of each stress on the surface of the circular curved beam, calculated with any combination of forces and momenta applied on its centroidal line. This calculation method was successfully verified with an application to a cylindrical compression spring. As a result, the present semi-analytical model has a 99.9% accuracy on the maximal Tresca stress calculation, being more than 43,000 times faster than the most realistic FE model. This is a significant breakthrough for researchers and engineers looking to save industrial time, optimization process or fatigue estimations.

Mechanism in scratching of calcium fluoride with magneto-plasticity

Magnetic field-tuned dislocation plasticity (i.e., magneto-plasticity) has attracted growing attention for assistance to limit the damage evolution of brittle ceramics in the material removal process. However, the mechanism controlling material removal of brittle ceramics with magneto-plasticity remains far from clear. Therefore, combined stress field modeling and molecular dynamics (MD) simulations were performed for scratching of a ceramic material, calcium fluoride (CaF2), to investigate the magneto-plasticity mechanism during the material removal process of brittle ceramics. The stress field calculation with magneto-plasticity was first conducted, which suggests a general reduction in scratching stress on the subsurface under the magnetic field effect. It is also found that the degree of reduction in scratching stress is significantly influenced by the magnetic field intensity and direction as well as strain rate. The reduced scratching stress is responsible for the suppressed formation and evolution of cracks and defects in scratching. Subsequently, MD simulations in scratching of CaF2 show that the application of a magnetic field can facilitate dislocation nucleation, enlarge the range of dislocation propagation, and regularize the dislocation distribution, indicating the advancement in elastic-plastic transition and dislocation mobility. From the views of energy criterion and crystal plasticity, a magnetic field can decrease the required work and resolved shear stress for dislocation slip, which results in a lower scratching stress level. The combined theoretical method of this study broadens the comprehension of magneto-plasticity on deformation mechanism in the material removal process of ceramics and offers theoretical direction for the application of magnetic field assistance in ceramic processing.

A Three-Dimensional Analytical Solution of Stress Field in Casing-Cement-Stratum System Considering Initial Stress State

Accurate stress field calculation of the casing-cement-stratum system is crucial for evaluating wellbore integrity. Previous models treated in-situ stress as boundary pressure loads, leading to unrealistic infinite displacements at infinity. This study presents a three-dimensional (3D) analytical solution for the stress field within the casing-cement-stratum system in inclined wells, considering in-situ stress and hydrostatic stress in cement as the initial stress state and taking into account stress components related to the axial direction. Assuming a plane strain condition and superimposing the in-plane plane strain problem, elastic uni-axial stress problem and anti-plane shear problem, a 3D analytical solution is obtained. Comparisons with previous models indicate that the existing model overestimates the absolute values of stress components and failure potential of casing and cement in both 2D and 3D scenarios. The presence of initial stress in cement greatly increases the absolute value of the compressive stress state but decreases the failure potential in cement, which has not been well studied. Additionally, a low Young’s modulus and high initial stress state of the cement benefits the cement’s integrity since the maximum Mises stress significantly decreases. The new 3D analytical solution can provide a benchmark for 3D numerical simulation and quick assessment for wellbore integrity.

Topology optimization of turbine disk considering maximum stress prediction and constraints

For the stress-constrained topology optimization of a turbine disk under centrifugal loads, the jagged boundaries of the mesh and the gray densities on the solid/void interfaces could make the calculated stress field inconsistent with the actual value. It may result in overestimating the maximum stress and thus affect the effectiveness of stress constraints. This paper proposes a new method for predicting the maximum stress to overcome the difficulty. In the process, a predicted density is newly defined to obtain stable boundaries with thin layers of gray elements, a transition factor is innovatively proposed to evaluate the effects of intermediate-density elements, two different stiffness penalty schemes are flexibly used to calculate the elastic modulus of elements, and a linear stress penalty is further adopted to relax the stress field of the structure. The proposed approach for predicting the maximum stress value is verified by the analysis of a structure with smooth boundaries and the topology optimization of a turbine disk. An updating scheme of the stress constraint in the topology optimization is also developed using the predicted maximum stress. Some key ingredients affecting the optimization results are discussed in detail. The results prove the effectiveness and efficacy of the proposed maximum stress prediction and developed stress constraint methods.

New Method and Application of Stress Field Calculation for Large Forgings

New Method and Application of Stress Field Calculation for Large Forgings

The impact of the parameters of the constitutive model on the distribution of strain in the femoral head

The rapid spread of the finite element method has caused that it has become, among other methods, the standard tool for pre-clinical estimates of bone properties. This paper presents an application of this method for the calculation and prediction of strain and stress fields in the femoral head. The aim of the work is to study the influence of the considered anisotropy and heterogeneity of the modeled bone on the mechanical fields during a typical gait cycle. Three material models were tested with different properties of porous bone carried out in literature: a homogeneous isotropic model, a heterogeneous isotropic model, and a heterogeneous anisotropic model. In three cases studied, the elastic properties of the bone were determined basing on the Zysset-Curnier approach. The tensor of elastic constants defining the local properties of porous bone is correlated with a local porosity and a second order fabric tensor describing the bone microstructure. In the calculations, a model of the femoral head generated from high-resolution tomographic scans was used. Experimental data were drawn from publicly available database “Osteoporotic Virtual Physiological Human Project.” To realistically reflect the load on the femoral head, main muscles were considered, and their contraction forces were determined based on inverse kinematics. For this purpose, the results from OpenSim packet were used. The simulations demonstrated that differences between the results predicted by these material models are significant. Only the anisotropic model allowed for the plausible distribution of stresses along the main trabecular groups. The outcomes also showed that the precise evaluation of the mechanical fields is critical in the context of bone tissue remodeling under mechanical stimulations.

Analysis of nonlinear Timoshenko–Ehrenfest beam problems with von Kármán nonlinearity using the Theory of Functional Connections

In this paper, the Theory of Functional Connections (TFC) is used to analyze static beams, accounting for the von Kármán nonlinearity and using the Timoshenko–Ehrenfest beam theory. The authors extend their earlier framework on linear beam bending problems to nonlinear bending problems using TFC. The TFC results and performance parameters are then compared to those of the Finite Element Method (FEM) to both validate the TFC solutions and compare computational efficiencies. In addition, this paper also focuses on the benefits of using TFC over FEM for stress analysis of beam bending problems. Also, a TFC methodology to solve buckling and free vibration problems for the linearized Timoshenko–Ehrenfest beam equations is introduced and validated. The results within this paper suggest that for most static beam bending problems, TFC provides more accurate solutions in terms of the residuals of the differential equations and a faster solution time when compared to the FEM using linear or quadratic approximations. Also, TFC has the added benefit of calculating stress fields that are continuous and smooth everywhere within the domain of the beam while FEM is limited to a piece-wise continuous stress field.

Application of the Generalized Method of Moving Coordinates to Calculating Stress Fields near an Elliptical Hole.

The distribution of stresses near holes is of great importance in fracture mechanics and material modeling. The present paper provides a general stress solution near a traction-free surface for an arbitrary piecewise linear yield criterion, assuming plane-strain conditions. The generalized method of moving coordinates is proven efficient in this case. In particular, the solution reduces to evaluating one ordinary integral. The boundary value problem solved is a Cauchy problem for a hyperbolic system of equations. Therefore, the stress solution in the plastic region is independent of other boundary conditions, though the occurrence of plastic yielding at a specific point is path-dependent. The general solution applies to calculating the stress field near an elliptic hole. It is shown that the parameter that controls the pressure-dependency of the yield criterion affects the stress field significantly. The aspect ratio is less significant as compared to that parameter. However, for a given material, the aspect ratio should also be considered to predict the stress field accurately, especially in the near vicinity of the hole. The solution reduces to an available solution for the pressure-independent yield criterion, which is a particular yield criterion of the considered class of yield criteria.

Asymptotic stress field around the blunt and sharp notches in bimaterial media under mixed mode I/II loading

This paper provides a simple approximate solution for the stress and displacement fields around the blunt notches in bimaterial media under in-plane loading. The Kolosov-Muskhelishvili's method is used to determine the stress and displacement components according to the complex potential functions. Then, by imposing the boundary conditions of bimaterial blunt V-notches, the asymptotic solutions of the stress and displacement fields are obtained. Due to the convenient selection of the boundary conditions, the solution is shown to be the same as the one proposed by Williams’ for sharp V-notches, in case the notch tip radius becomes zero. Finally, finite element method is employed to benchmark the precision of the suggested asymptotic solution. Some sample examples are selected, and the results obtained by the proposed analytical solution are compared with the numerical results of the finite element method. It is demonstrated that the proposed stress field is not only applicable to obtain the stress distribution around the blunt V-notches but also is suitable for stress field calculation around some other types of bimaterial notches.

Rotation of the Stress Tensor in a Westerly Granite Sample During the Triaxial Compression Test

We simulated the spatiotemporal modelling of 3D stress and strain distributions during the triaxial compression laboratory test on a westerly granite sample using finite-difference numerical modelling implemented with FLAC3D software. The modelling was performed using a ubiquitous joint constitutive law with strain softening. The applied procedure is capable of reproducing the macroscopic stress and strain evolution in the sample during triaxial deformation until a failure process occurs. In addition, we calculated focal mechanisms of acoustic emission (AE) events and resolved local stress field orientations. This detailed stress information was compared with that from numerical modelling. The comparison was made based on the 3D rotation angle between the cardinal axes of the two stress tensors. To infer the differences in rotation, we applied ANOVA. We identified the two time levels as the plastic deformation phase and the after-failure phase. Additionally, we introduced the bin factor, which describes the location of the rotation scores in the rock sample. The p values of the test statistics F for the bin and phase effects are statistically significant. However, the interaction between them is insignificant. We can, therefore, conclude that there was a significant difference in the time between the rotation means in the particular bins, and we ran post hoc tests to obtain more information where the differences between the groups lie. The largest rotation of the stress field provided by the focal mechanisms of AE events from the numerically calculated stress field is observed in the edge bins, which do not frame the damage zone of the sample.

Damage separation model: A replaceable particle method based on strain energy field.

We present a realistic model for simulating particle fragmentation in granular assemblies, the damage separation model (DSM), that addresses the limitations of previous methods by replacing the particle with smaller ones after fragmentation. The method is based on the calculation of the strain energy field inside the particle, and it solves the two major issues of the existing replaceable particle methods: the oversimplification of particle stress, and the unrealistic geometrical constraints needed in postbreakage replacements. Our model is formulated with three modules: (i) a boundary element calculation of stress and strain fields inside the spheropolygons that represent individual particles; (ii) a strain-energy-based theoretical framework to determine the onset of fragmentation; and (iii) an advanced geometrical algorithm, the subset separation method (SSM), to handle the postbreakage replacements in the discrete element simulations. Especially, the SSM effectively calculates the fragments required by the replacement with no geometrical limitation on the number, location, and orientation of the fracture planes. A uniaxial compression test based on laboratory setups is used to validate the method. A comparison is further conducted to study the performance of four different replaceable irregular particle methods. Results indicate that our method overcomes most of the existing issues, including stability, accuracy, and artificial constraints on the number and shape of fragments. The DSM has great potential for capturing the morphological changes of particle breakage and comminution with an unprecedented numerical resolution.

STRESS FIELD IN A SHEAR ZONE, AND FORMATION OF THE MAIN FAULT

Using the analytical approximation method, we calculated stress field parameters for cases with different relative positions of Riedel shears and loads required for shearing. Considering an internal friction angle of 30°, and the distance between adjacent shears exceeding 0.7 of the characteristic shear length, we estimated the Coulomb stress that can lead to fracturing. In the areas between the shears, it is below the shear strength value. This means that if an increase in the external load is lacking, there are no prerequisites for the formation of new fractures that may connect adjacent shears. If the shears are spaced closer to each other (i.e. at distances less than 0.7 of the shear length), the shear strength is exceeded in the areas between them, and new shears can occur there and connect the Riedel shears to each other. Therefore, in observations of a natural system of Riedel shears, it becomes possible to assess whether this system is sufficiently stable in its current status, or, in case of a critical increase in the Coulomb stress in the areas between adjacent shears, the equilibrium can be easily disturbed, and there is a possibility that the main fault forms in the strike-slip zone under study.

Theoretical modeling and calculation of stress fields in precision optical lens subjected to multi-point adhesive bonding assembly

In optical precision assembly, most optical components are fixed by multi-point adhesive bonding. However, the stress fields generated in lenses by radial stress in the adhesive significantly influence the imaging quality of precision optical lenses. To date, the adhesive bonding process is conducted empirically, meaning that the stress in lenses cannot be actively or quantitatively controlled. Therefore, to improve the current passive process, a theoretical mechanical model of an optical lens was established, and a novel stress potential function was proposed to derive the analytical solution of stress components in lenses under an arbitrary number of multi-point radial stresses. The results revealed a quantitative relationship between the radial stress in the adhesive and the stress field in the optical lens. Furthermore, a new experimental device was developed, and a systematic experimental method was proposed to apply multi-point quantitative radial loads on an optical lens and measure its real-time stress distribution, which further verifies the accuracy and validity of the proposed theoretical model. This study provides a theoretical approach for the quantitative control of lens stress and optimization of adhesive bonding configuration in optical precision assembly process, which is a basis to enhance the imaging accuracy of precision optical instruments.