Normal Stress Components Research Articles

Assessment of multiaxially loaded safety components with uniaxial stress state in fatigue critical sites caused by design

AbstractThe focus of this study, using results obtained with hollow specimens of the alloy Al 2024 T3 (AlCuMg2 T3) with a one‐sided bore, was to determine if, under multiaxial loading, the fatigue strength in a notch with a uniaxial stress state can simply be assessed without the application of any multiaxial strength hypothesis. In the fatigue critical location, the bore edge, only a superimposition of normal stress components, resulting from axial loading or/and torsion, occurs. In the case of out‐of‐phase loading, the resulting local uniaxial stress is even lower than the stress under in‐phase loading and leads to an increase of fatigue life to crack initiation under the non‐proportional loading, which is not observed in the case of multiaxial stressing/straining of the material itself. As the local stress state in the crack initiation site is uniaxial, the application of a multiaxial strength hypothesis, for the failure criterion of crack initiation (l=0.2 mm), is not necessary. Furthermore, the benefit of non‐homogenous stress distributions, which allow locally higher stresses than the levels given by the Woehler‐line for unnotched specimens, was underlined by considering highly‐stressed, material‐volume‐related support factors.

Probing trade-off between critical size and velocity in cold-pray: An atomistic simulation

The detailed mechanism of bonding in the cold spray process has remained elusive for both experimental and theoretical parties. Adiabatic shear instability and hydrodynamic plasticity models have been so far the most popular explanations. Here, using molecular dynamics simulation, we investigate their validity at the nanoscale. The present study has potential applications in the fabrication of ultrathin layers in the electronics industry. For this aim, we considered Ti nanoparticles of different diameters and Si substrates of different orientations. It is shown that very high spray velocities are required for a jet to be observed at the nanoscale. We propose a method for thermostating the substrate that enables utilizing high spray velocities. For the first time, we demonstrate an oscillatory behavior in both the normal and radial stress components within the substrate that can propagate into the particle. We have shown that neither the adiabatic shear instability model nor the hydrodynamic plasticity model can be ignored at the nanoscale. In addition, the formation of a low-resistance titanium silicide proper for electronic application is illustrated.

Permanent deformation and particle crushability of calcareous sands under cyclic traffic-induced loadings through simple shear apparatus

This study focuses on investigating permanent deformations, encompassing normal and shear strains, of calcareous sandy soils subjected to drained cyclic traffic-induced loadings. The investigation utilizes a Simple Shear (SS) apparatus allowing for variations in both normal and shear stress components over each cycle and incorporates Principal Stress Rotation (PSR), a feature not replicable in conventional cyclic uniaxial triaxial tests which is the key aspect of this research. The study also accounts for the harmonically changing the effective horizontal stress resulting from cyclic variations of effective vertical stress, conducted under a horizontally constrained boundary condition with zero lateral strain. A series of drained cyclic simple shear experiments is carried out, implementing a heart-shaped stress path, encompassing up to 1000 cycles. The objective of the study is to analyze permanent normal and shear deformations, along with associated total particle crushing, using both sieving analyses and 2D image processing of particles. The study also evaluates the impact of an initial static shear stress originating from the longitudinal slope of roads. The findings highlight the influences of induced cyclic amplitudes of stress components, principal stress and strain rate rotation, and initial static shear stress on the development of permanent strains. Furthermore, the research characterizes particle crushability in terms of total crushability over such loading, examining its dependency on relative density and variations in both shear and normal stress components.

New analytical model for multi-layered composite plates with imperfect interfaces under thermomechanical loading

AbstractA new analytical model for thermoelastic responses of a multi-layered composite plate with imperfect interfaces is developed. The composite plate contains an arbitrary number of layers of dissimilar materials and is subjected to general mechanical loads (both distributed internally and applied on edges for each layer) and temperature changes, which can vary from layer to layer and along two in-plane directions. Each layer is regarded as a Kirchhoff plate, and each imperfect interface is described using a spring-layer interface model, which can capture discontinuities in the displacement and stress fields across the interface. Unlike existing models, the governing equations and boundary conditions are simultaneously derived for each layer by using a variational procedure based on the first and second laws of thermodynamics, which are then combined to obtain the global equilibrium equations and boundary conditions for the multi-layered composite plate. A general analytical solution is developed for a symmetrically loaded composite square plate with an arbitrary number of layers and imperfect interfaces by using a new approach that first determines the interfacial normal and shear stress components on one interface. Closed-form solutions for two- and three-layer composite square plates are obtained as examples by directly applying the general analytical solution. Numerical results for two-, three- and five-layer composite plates under different loading and boundary conditions predicted by the current model are provided, which compare well with those obtained from finite element simulations using COMSOL, thereby validating the newly developed analytical model.

Effect of Tip Gap Size on the Tip Flow Structure and Turbulence Generation in a Low Reynolds Number Compressor Cascade

Abstract Efficient and compact axial compressors are currently undergoing rapid development for use in microcooling systems and small-scale vehicles. Limited experimental work concentrates on the inner flow field of the compressors working at such low Reynolds numbers (Re∼104). This study examines the vortical structures and the resulting turbulence production in the transitional flow over a C4 compressor blade at a Reynolds number Re of 24,000, with a specific focus on the impact of tip clearance. The particle image velocimetry measurements reveal the tip flow structures in detail, including the tip leakage vortex (TLV) and its induced complex vortical structures. The tip secondary flow at the low Reynolds number can be divided as the tip leakage flow (TLF)/vortex and transitional boundary layer both at the end walls and the blade surfaces. The TLV propagates at the highest spanwise positions and farthest pitchwise positions at the middle tip gap size (τ/C = 3%) for the three tip gap sizes investigated. The tip flow fluctuations decrease from τ/C = 5% to τ/C = 3% and then increase from τ/C = 3% to τ/C = 1%. The spatial distribution, streamwise evolution, and individual Reynolds normal stress components contributing to the turbulent kinetic energy (TKE) are discussed. The primary contributors to the turbulence generation are examined to elucidate the flow mechanism leading to the distinct anisotropic turbulence structure in the tip region with various tip gap sizes.

Intergranular stress and plastic strain formation during laser scanning of additively manufactured stainless steel: An experimentally-driven thermomechanical simulation study

A novel experiment-driven modelling and simulation approach is proposed to study the formation of intergranular stresses and plastic strains during laser scanning of additively manufactured 316L stainless steel. Recently, laser scanning experiments were performed using a unique coupling between a continuous-wave laser and a scanning electron microscope. These experiments form the basis for the development of a thermo-elasto-viscoplastic polycrystal model endowed with the minimum necessary physics of the problem in order to facilitate simulating sufficiently large domains to obtain reasonable stress magnitudes. The case of a single laser line scan performed in vacuum is analyzed in detail. Polar dislocation density magnitudes and distribution predicted from the simulation are compared with those measured experimentally. Results reveal that for 93% of the grains in the lasered zone, a statistical measure of the predicted polar dislocation density (Nye’s) tensor lies within a factor of 2 (higher or lower) of the experimental one; this result sets a benchmark for future experiment-simulation comparisons. Subsequent investigation studies the origin of the local residual stresses and plastic strains. On the lasered surface, the grain surface-averaged normal residual stress component and plastic strain component along the scan direction reaches a value ∼1.7GPa and 0.04, respectively. The contribution of elastic anisotropy, plastic heterogeneity and strengthening due to microstructure refinement after laser scanning on the formation of stresses and plastic strains is studied in detail.

Elliptic Rigid Inclusion in Soft Materials of Harmonic Type

Abstract We investigate finite plane deformations of an elliptic rigid inclusion embedded in a soft matrix that is made of a particular class of harmonic-type hyperelastic materials. The inclusion is assumed to be perfectly bonded to the matrix, which is subjected to a constant remote in-plane loading. Utilizing the Cauchy integral techniques associated with conformal mappings, we derive closed-form solutions for the full-field deformation, Piola stress, and Cauchy stress in the entire matrix. Numerical examples are presented to illustrate the current solutions in comparison with those established from linear elasticity theory. We find that in terms of the Cauchy stress around the inclusion, the maximum normal stress component always appears at the endpoints of the major axis of the inclusion, irrespective of the magnitude of the remote loading, while the maximum hoop stress component occurs not exactly at the above-mentioned endpoints when the remote loading exceeds a certain value. In particular, we identify an exact explicit formula for determining the relative rotation of the inclusion during deformation induced by a remote uniaxial loading of arbitrarily given magnitude and direction.

The strain ratio-dependent multiaxial low cycle fatigue behaviour and life prediction of 316L stainless steel based on critical plane at elevated temperature

The study mainly investigates the effect of strain ratio on the multiaxial low cycle fatigue behaviour of 316L at 550 °C. The evolution of both axial and torsional stress amplitude is observed to go through three stages: cyclic hardening, softening and fracture. What's different is that the torsional loading experiences fewer cyclic hardening cycles compared to the axial loading. Regarding the interaction between axial and torsional stresses, it is observed that as the torsional strain increases, the axial deformation response presents a lower peak stress and a higher softening rate, while the torsional peak stress and softening rate hardly changes with the increase of axial strain amplitude. The fracture pattern is obtained through three-dimensional (3D) depth-of-field observation. It is discovered that as the strain ratio increases, the fracture pattern transits from tensile failure mode to shear failure mode. Furthermore, the orientation angle of the fracture surface increases and lies between the critical plane angle of maximum shear strain and maximum normal strain, indicating a mixed failure mode. Additionally, a comparison of nine representative critical plane models reveals that the energy-based models can better predict the multiaxial fatigue life influenced by the strain ratio. Finally, based on the analysis of deformation and failure mechanisms, a normal damage parameter weakening factor (NDWF) is introduced into the KBM-R model, and an improved normal stress component (INSC) is introduced into the Wu-R model. The two modified models well capture the impact of strain ratio and accurately predict the multiaxial fatigue life of both 316L and P92 steel.

New Approach of Normal and Shear Stress Components for Multiple Curvilinear Holes Which Weakened a Flexible Plate

In this article, a thin infinite flexible plate weakened by multiple curvilinear holes is considered. The strength shapes are mapped outside a unit circle with the assistance of particular conformal mapping under certain conditions. The mathematical model that governs the rounded forces of the current physical problem is the boundary value problem of elastic media. This study is applicable to many phenomena throughout nature, like tunnels, caves, and excavations in soil or rock. The Cauchy method for complex variables is used to get the closed forms of Gaursat functions and change the problem to a second-type integrodifferential equation with a Cauchy kernel, which is used for a large area of the contact problems. Then, the normal and shear stress components that act on the model are derived. Afterward, some of the physical applications are studied, and different stress components at specific values in each application are calculated and plotted using Maple 2023.

On the Micro-Stress Fields in Fibre-Hybrid Polymer Composite Laminae with Periodic Microstructure Under Transverse Tension and Transverse Shear Loading

AbstractThis paper investigates the effect of intra-laminar fibre hybridisation, i.e., primary and secondary fibres within a matrix, on the homogenised properties and micro-stress fields in uni-directional polymer composite laminae. The study is focused on S-glass/epoxy laminae which are hybridised with secondary fibres (e.g., polypropylene). Two-dimensional repeating unit cells (2D RUCs) with periodic microstructures are developed to conduct the micro-mechanical analyses under transverse tensile and transverse shear loading conditions. Uni-directional fibre-hybrid S-glass/epoxy laminae with different secondary fibres are studied by varying (a) the periodic microstructure and (b) the material properties of the constituent fibres to assess the effect of such geometric and material variations on the homogenised elastic lamina properties and intra-lamina micro-stress fields. The results show that intra-laminar fibre hybridisation significantly affects the elastic lamina properties and micro-stress fields. Notably, the presence of the secondary fibres significantly increases or reduces the stress fields in the matrix and at the fibre-matrix interfaces (i.e. normal and shears stress components)–depending on the microstructure and the stiffness of the secondary fibres–which could be explored to manipulate the damage modes and thus energy dissipation mechanisms.

Full-field eigenstrain reconstruction for the investigation of residual stresses in finite length weldments

The reconstruction of welding residual stresses has been performed based on the assumption of continuous processing conditions, owing to the limitations of reconstruction methods. This assumption prevents the attainment of a comprehensive understanding of mechanical deformations in the entire weld zone. The voxel-based eigenstrain (inherent strain) reconstruction method emerges as an appropriate approach for the full-field reconstruction of residual stresses in finite length weldments without such assumption. The innovative reconstruction capability of this advanced method is presented in this study, aiming to comprehend all components of residual stresses and eigenstrains in finite length weldments with discontinuous processing properties using only a single component of experimental data belonging to a limited portion of the specimen. Numerical experiments were conducted to develop the tools. These tools were validated using a case study employing experimental data obtained through contact profilometry measurements from the surface of discharge machine cutting (minimally disturbing cutting) in a bead-on-plate weldment of Inconel alloy 740H designed for ultra-supercritical power generation. The reconstructed two components of normal residual stresses that do not align with the available experimental data were validated by independent neutron diffraction strain scanning quantifications. Furthermore, the reconstruction of residual stresses in the intact component prior to cutting was carried out using the eigenstrains associated with the post-cut state of the weldment.

An incompressible liquid slit between dissimilar anisotropic elastic media

We use the Stroh sextic formalism to solve the generalized plane strain problem associated with a finite incompressible liquid slit lying between dissimilar anisotropic elastic half-planes subjected to a system of uniform remote stresses. The liquid slit admits an internal uniform hydrostatic stress field and is perfectly bonded to the surrounding media. By enforcing the interface conditions on the solid-solid and liquid-solid interfaces, a Riemann-Hilbert problem of vector form is obtained and is solved analytically using a decoupling procedure. An application of the residue theorem following the imposition of the incompressibility condition of the liquid slit leads to the determination of the internal uniform hydrostatic tension within the liquid slit. When the elastic bimaterial is orthotropic, the internal uniform hydrostatic tension is equal to the remote normal stress component perpendicular to the surfaces of the liquid slit. The presence of the liquid slit will inhibit crack growth along the anisotropic elastic bimaterial interface.

Explicit analytical solutions for the full plane-stress field in sandwich beams under flexure governed by zigzag warping

We provide analytical solutions for the full stress field of straight sandwich beams with identical skins subject to linear elastic flexure governed by zigzag warping, where all layers obey Timoshenko’s kinematics. As a main novelty, we make use of an equilibrium equation for the Cauchy continuum to recover of the through-the-thickness normal stress component, σy. The new estimates are accurate for a wide range of relative stiffness between skins and core and suitable boundary conditions, as it can be demonstrated through the comparison with detailed finite element simulations where the sandwich is modelled as a two-dimensional continuum. As a main practical result concerned with the study of delamination, we find that at a core–skin interface of a cantilever sandwich subjected to a uniformly distributed load, in a region close to the fully-clamped cross-section, σy is a tensile stress of magnitude larger than that of the shear stress. On this basis, we infer that the availability of good estimates for σy, along with those for the longitudinal and shear stresses, may be important for the accurate design of sandwich panels.

Self-Diffusiophoresis and Symmetry-Breaking of a Janus Dimer: Analytic Solution

A self-diffusiophoretic problem is considered for a chemically active dimer consisting of two equal touching spherical colloids that are exposed to different fixed-flux and fixed-rate surface reactions. A new analytic solution for the autophoretic mobility of such a catalytic Janus dimer is presented in the limit of a small Péclet number and linearization of the resulting Robin-type boundary value problem for the harmonic solute concentration. Explicit solutions in terms of the physical parameters are first obtained for the uncoupled electrostatic and hydrodynamic problems. The dimer mobility is then found by employing the reciprocal theorem depending on the surface slip velocity and on the normal component of the shear stress acting on the inert dimer. Special attention is given to the limiting case of a Janus dimer composed of an inert sphere and a chemically active sphere where the fixed-rate reaction (Damköhler number) is infinitely large. Examples are given, comparing the numerical and approximate analytic solutions of the newly developed theory. Singular points arising in the model are discussed for a dimer with a fixed-rate reaction, and the flow field around the dimer is also analysed. The new developed theory introduces a fast way to compute the mobility of a freely suspended dimer and the induced flow field around it, and thus can also serve as a sub grid scale model for a multi-scale flow simulation.

Oscillatory singularity for bending of a partially clamped nanoplate with consideration of surface effect

This article studies a partially clamped flexible ultrathin elastic nanoplate with surface effect. An emphasis is to analyze the singular elastic behavior near the tips of partially clamped boundary. A mixed boundary value problem associated with a partially clamped nanoplate having parabolic deflection is presented and solved. Using the Kirchhoff plate theory incorporating the Gurtin–Murdoch surface elasticity, some basic equations for nanoplates with surface elasticity are established. With the aid of the Fourier transform and the superposition principle, two coupled singular integral equations with Cauchy kernel are derived during bending of the nanoplate and then converted to a singular integral equation with two Cauchy kernels. The exact solution to the singular integral equation with two Cauchy kernels is determined and the oscillatory singular elastic fields near the tips of the clamped boundary are given in elementary functions. The bending moments and the normal stress components in the vicinity of the tips simultaneously have the oscillator singular behavior like r−3/2−iɛ, r being the distance from the tip and ɛ relying on the material properties. Besides, the effective shear force possesses an r−5/2−iɛ singular behavior. The influences of the geometrical parameters and material properties of nanoplates on the oscillatory singular behavior are presented graphically. When surface effect is neglected, the solution is applicable to classical thin plates with partially clamped boundary.

Analysis of a viscoelastic fluid flow with Cattaneo–Christov heat flux and Soret–Dufour effects

The present study concentrates on the motion of a third-grade fluid with magneto-hydrodynamics (MHD) over a stretching surface. Additionally, the Cattaneo–Christov model is employed to derive information about the heat flux, which is subsequently utilized to ascertain the heat transmission properties. The inquiry involves an assessment of the impact of thermal relaxation time on the boundary layer. The considered fluid is a type of non-Newtonian fluid that deal with both shear thinning and shear thickening behaviors. The study also involved calculating all normal stress components that are not accounted for by either the power law model or the second grade model. The motion of fluid is attributed by linear stretching, and the momentum flow is observed with the help of Soret–Dufour effects. The Cattaneo and Christov model is particularly beneficial for describing transmission of heat in materials with high thermal conductivity, where the classical Fourier’s law may not be accurate. The examination of the transport properties of velocity, heat, and mass involves the consideration of the temperature effect on variable viscosity and thermal conductivity, which are linearly associated with each other. A set of partial differential equations (PDEs) that are nonlinear in nature has been derived, and some boundary conditions have been identified that yield satisfactory results. Using similarity transformation a system of nonlinear PDE’s are modify into dimensionless system of ordinary differential equations (ODE’s). The homotopy analysis method (HAM) is applied in a convenient manner to obtain solutions for transform equations, while the impact of relevant flow parameters is visually demonstrated. Adequate graphical and tabular results are achieved using a semi-analytical approach. Moreover, the Cattaneo–Christov equation can provide a better understanding of the thermal behavior. It allows for a more comprehensive analysis of the thermal response, ensuring that the heat transfer models used are appropriate for such conditions.

Comments on Existing Analytical Solutions to the Wave-Induced Cyclic Response of a Porous Seabed of Infinite Thickness

Abstract This paper deals with the wave-induced cyclic response of a porous seabed (by means of oscillating parameters: pore-fluid pressure, soil displacement components, effective normal stress and shear stress components) due to a surface sinusoidal water-wave propagating over a seabed of infinite thickness. The main existing analytical solutions to the governing problem are critically discussed, pointing out their meaningful errors and doubtful items. A phase-lag phenomena is particularly studied as an immanent part of any complex-valued analytical solutions having a cyclic nature.

Poiseuille and thermal transpiration flows of a dense gas between two parallel plates

The Poiseuille and thermal transpiration flows of a dense gas between two parallel plates are investigated on the basis of the Enskog kinetic equation under the diffuse reflection boundary condition. In contrast to the case of an ideal gas, the density and the gradients of pressure and the normal stress component in the flow direction are not uniform in the direction normal to the plates for a dense gas. The non-uniform normal stress gradient contributes also to the acceleration or deceleration of the thermal transpiration flow for small Knudsen numbers. The profiles of mass and heat flows as well as the net mass flows are obtained for various Knudsen numbers and ratios of the molecular diameter to the distance of plates. In the analysis of the Poiseuille flow, most characteristics of a force-driven flow with a small force are recovered. However, for the case of a dense gas, differences between the force-driven and the present pressure-driven flows are observed even within the linearized regime for small force and pressure gradient, especially at the microscopic level. The behaviour of the velocity distribution functions, in particular, the way in which they approach the ones for the Boltzmann equation as the molecular diameter becomes smaller, is clarified.

Determination of the Relationship between Proportional and Non-Proportional Fatigue Damage in Magnesium Alloy AZ31 BF

In this work, the magnesium alloy AZ31BF subjected to proportional and non-proportional loads has been studied. For this purpose, a series of experimental multiaxial fatigue tests were carried out according to the ASTM E466 protocol. The main objective was to determine the relationship between the multiaxial fatigue strength of this alloy under these two different types of loading. The results showed that the AZ31BF magnesium alloy has different fatigue strengths depending on the loading type. Based on these results, it was found that the ratio between proportional and non-proportional damage in AZ31BF magnesium alloy varies depending on the number of loading cycles. To represent this variation, parameter Y was used to modulate the non-proportional damage of AZ31BF. In this way, two Y functions were considered, one for the normal stress component and the other for the shear stress component. The results obtained for the non-proportional parameter Y are of particular interest since the multiaxial fatigue models do not distinguish between these two types of loading when evaluating fatigue life. In this sense, the results of this study can be used in these models to overcome this limitation.

Liquefaction behavior of inherently anisotropic sand under cyclic simple shear: Insights from three-dimensional DEM simulations

Inherent fabric anisotropy has been widely recognized to have significant effects on the liquefaction behavior of sand. A discrete element method (DEM) study was conducted to investigate the liquefaction behavior of inherently anisotropic sand under cyclic simple shear conditions. In the DEM model, the under-compaction method was modified to generate uniform and inherently anisotropic specimens. A series of DEM simulations of undrained cyclic simple shear tests were performed to investigate the effects of bedding plane angles with a full spectrum ranging from −90° to +90°. The relative magnitudes of the three effective normal stress components were compared and analyzed. The internal structure evolution was quantified through a contact-normal-based fabric tensor that could describe the load-bearing structure of granular specimens. The simulation results show that the effect of bedding plane angle on the liquefaction resistance of anisotropic sand is not monotonic. For example, as the bedding plane angle of specimen increases from 0° to 90°, the liquefaction resistance first decreases and then increases, with the most detrimental scenario occurs at 45°. This could be explained by correlating the magnitudes of shear modulus with the discrepancy between the loading direction and the direction of fabric during each cycle.