Steep Stress Gradients Research Articles

Extreme load analysis of flexible wave energy converters utilising nonlocal continuum damage mechanics

In recent years, there has been a notable increase in interest towards Flexible Wave Energy Converters (FlexWECs). These flexible energy harvesters solve structural design challenges faced by rigid-body WECs by responding to external loading by changing shapes. Typically, the structures are made from rubber-like materials which pose few challenges from a material modelling point of view. Firstly, the material is in the finite strain regime requiring a hyperelastic modelling approach, but more critically the material response is expected to change during the operational lifetime. There is softening from both time-dependent viscoelasticity and micro-void growth caused by fatigue loading. The goal of this paper is to understand the latter mechanism and how it manifests within a membrane. To account for this damage accumulation, the gradient-enhanced nonlocal damage model is coupled to a hyperelastic Neo-Hookean constitutive law. The framework has been implemented in the commercial finite element software ABAQUS by exploiting its fully coupled thermo-mechanical formulation. A parametric study is performed on two FlexWEC archetypes: a submerged pressure differential and a floating bulge wave attenuator. The performance evaluation of these devices is carried out by analysing the evolution of the pressure–volume relation and pressure-stretch relation, respectively. The results show that the nonlocal aspects of damage in the pressure differential FlexWECs are small due to membrane action, but the saturation of damage does affect the pressure–volume function of each membrane. However, in the case of attenuator, the damage regularisation plays a crucial role in its behaviour due to the steep stress gradient from the crest of the wave. The outcomes from these analyses suggest FlexWEC design is advantageous from a fatigue loading perspective as it always reaches an equilibrium state which minimises the stress-differential, reducing the likelihood of localised crack growth.

Non-Linear Structural Analysis of Shear Flexible FGM Beams

Non-linear structural response of Functionally Graded Material (FGM) beams is studied using the finite element method. The deformations obtained using Euler-Bernoulli beam and Timoshenko beam theories are compared for different length to height ratios, volume fraction exponents and boundary conditions. The percentage errors in lateral deformations for neglecting the effects of shear flexibility are discussed in detail. Through thickness variation of the axial stress shows a shift in the neutral axis from the mid-thickness of beam for homogenous as well as FGM beams and for the boundary conditions considered. The range of volume fraction exponents for the practical design of FGM beams is suggested to avoid steep stress gradients.

Measurement of Residual Stress Distribution in the Depth Direction of Annealed Materials of Lapped Bearing Steel Using Weighted Averaging Analysis Method

This paper reports the results of an experimental examination using X-rays to test annealing materials for lapped bearing steel (STB2), to confirm the validity of the weighted averaging analysis method. The distribution behavior for the αψ-sin2ψ diagram and the presence or absence of differences in the peak method, half-value breadth method, and centroid method were investigated. When lapping the annealed bearing steel (STB2) material, a residual stress state with a non-directional steep gradient appeared in the surface layer, and it was found that the weighted averaging analysis method was effective. If there is a steep stress gradient, the sin2ψ diagram is curved and the diffraction intensity distribution curve becomes asymmetric, resulting in a difference between the peak method, half-value breadth method, and centroid method. This phenomenon was evident when the stress gradient was more than 2~3 kg/mm2/µm. In this case, if the position of the diffraction line is determined using the centroid method and the weighted averaging analysis method is applied, the stress value on the surface and the stress gradient under the surface can be obtained more accurately. When the stress gradient becomes a problem, since the curvature of the sin2ψ diagram appears clearly in the region of sin2ψ > 0.5, it is necessary to increase the inclination angle ψ as much as possible. In the case of a lapping layer, a more accurate value can be obtained by considering σ3 in the weighted averaging analysis method. In an isotropic biaxial residual stress state, the presence or absence of σ3 can be determined as the presence or absence of strain for sin2ψ≈0.4.

Extended wavelet Galerkin method for mixed-mode cracked FGM plate under static and dynamic loads

The extended wavelet Galerkin method (XWGM) is presented for fracture mechanics analysis of functionally graded material (FGM) cracked plates under static and dynamic loads. The nonhomogeneous stress distribution and stress wave transition can be approximated by the piecewise truncated polynomial (B-spline) functions. The steep stress gradients around the crack tip can be captured by superposing the higher resolution wavelet functions with the nature of multiresolution analysis (MRA) in the wavelet theory. Additionally, a trigonometric function and Heaviside function are employed to enrich the wavelet bases for the fracture modeling. The interaction integral method is utilized to evaluate the static and dynamic mixed-mode stress intensity factors taking the inertia and material nonhomogeneity into account. Applicability of XWGM to the FGM crack problems is discussed through the numerical examples.

Ultrathin materials for wide bandwidth laser ultrasound generation: titanium dioxide nanoparticle films with adsorbed dye.

Materials that convert the energy of a laser pulse into heat can generate a photoacoustic wave through thermoelastic expansion with characteristics suitable for improved sensing, imaging, or biological membrane permeation. The present work involves the production and characterization of materials composed of an ultrathin layer of titanium dioxide (<5 μm), where a strong absorber molecule capable of very efficiently converting light into heat (5,10,15,20-tetrakis(4-sulfonylphenyl)porphyrin manganese(iii) acetate) is adsorbed. The influence of the thickness of the TiO2 layer and the duration of the laser pulse on the generation of photoacoustic waves was studied. Strong absorption in a thin layer enables bandwidths of ∼130 MHz at -6 dB with nanosecond pulse laser excitation. Bandwidths of ∼150 MHz at -6 dB were measured with picosecond pulse laser excitation. Absolute pressures reaching 0.9 MPa under very low energy fluences of 10 mJ cm-2 enabled steep stress gradients of 0.19 MPa ns-1. A wide bandwidth is achieved and upper high-frequency limits of ∼170 MHz (at -6 dB) are reached by combining short laser pulses and ultrathin absorbing layers.

Conserving elastic turbulence numerically using artificial diffusivity.

To simulate elastic turbulence, where viscoelasticity dominates, numerical solvers introduce an artificial stress diffusivity term to handle the steep polymer stress gradients that ensue. This has recently been shown [A. Gupta and D. Vincenzi, J. Fluid Mech. 870, 405 (2019)0022-112010.1017/jfm.2019.224; V. Dzanic et al., J. Fluid Mech. 937, A31 (2022)0022-112010.1017/jfm.2022.103] to introduce unphysical artifacts with a detrimental impact on simulations. In this Letter, we propose that artificial diffusion is limited to regions where stress gradients are steep instead of seeking the zero-diffusivity limit. Through the cellular forcing and four-roll mill problem, we demonstrate that this modified artificial diffusivity is devoid of unphysical artifacts, allowing all features of elastic turbulence to be retained. Results are found to conform with direct simulations, reducing the impact of artificial diffusivity from a qualitative scale to a quantitative scale while only requiring a fraction of the numerical resolution.

Subsurface and Bulk Residual Stress Analysis of S235JRC + C Steel TIG Weld by Diffraction and Magnetic Stray Field Measurements

BackgroundDue to physical coupling between mechanical stress and magnetization in ferromagnetic materials, it is assumed in the literature that the distribution of the magnetic stray field corresponds to the internal (residual) stress of the specimen. The correlation is, however, not trivial, since the magnetic stray field is also influenced by the microstructure and the geometry of component. The understanding of the correlation between residual stress and magnetic stray field could help to evaluate the integrity of welded components.ObjectiveThis study aims at understanding the possible correlation of subsurface and bulk residual stress with magnetic stray field in a low carbon steel weld.MethodsThe residual stress was determined by synchrotron X-ray diffraction (SXRD, subsurface region) and by neutron diffraction (ND, bulk region). SXRD possesses a higher spatial resolution than ND. Magnetic stray fields were mapped by utilizing high-spatial-resolution giant magneto resistance (GMR) sensors.ResultsThe subsurface residual stress overall correlates better with the magnetic stray field distribution than the bulk stress. This correlation is especially visible in the regions outside the heat affected zone, where the influence of the microstructural features is less pronounced but steep residual stress gradients are present.ConclusionsIt was demonstrated that the localized stray field sources without any obvious microstructural variations are associated with steep stress gradients. The good correlation between subsurface residual stress and magnetic signal indicates that the source of the magnetic stray fields is to be found in the range of the penetration depth of the SXRD measurements.

Biological invasions alter consumer-stress relationships along an estuarine gradient.

Estuaries represent steep stress gradients for aquatic organisms, with abiotic stress due to temperature and salinity typically increasing with distance into estuary. Invertebrate communities and their predators are strongly influenced by these stress gradients. The environmental stress model predicts that the importance of predation in structuring communities decreases with increasing environmental stress. Estuaries contain a stress gradient for marine organisms this includes salinity, temperature, and other abiotic properties. Additionally, estuaries are hotspots for biological invasions; increased stress tolerance among non-native species could change the predictions of the environmental stress model. In this study, we investigate how introduced species alter the predictions of the environmental stress model by examining the effects of predators on sessile invertebrates across an estuarine gradient. To do this, we deployed recruitment plates across the estuarine gradient of Tomales Bay, California, USA using various caging treatments over the summer of 2019. We found that the effect of predation changed across sites, with the mid-estuary site experiencing the greatest reductions in prey abundance and prey species richness when exposed to predators. This was likely to be due to higher proportions of non-native prey and predator taxa mid-estuary, including solitary ascidians, which are highly susceptible to predation. Overall, predation did not follow the predictions of the environmental stress model, but rather followed the abundance of functional groups with non-native species, whose distribution could be mediated by environmental stress gradients. We suggest that this may be a general result and that communities subject to large numbers of stress-tolerant invaders may have high rates of consumption in high stress areas, contrasting predictions by previous models.

Study on residual stress distribution of Al/Cu dissimilar metal joint manufactured by electromagnetic pulse welding

Electromagnetic pulse welding (EMPW) is a cold-welding technology to connect materials by driving the flyer plate with electromagnetic force to impact the target plate at high speed and it has been adopted to join dissimilar metals. In the present study, a dissimilar metal (2024 aluminum alloy and pure copper) joint was prepared with the EMPW. The contour method was used to get the full map of longitudinal stress distribution in the joint. The stress variation across the thickness was analyzed. The results show that the tensile stress appears at the side of aluminum alloy, and compressive stress occurs at the side of pure copper. The peak tensile stress (260 MPa) appears in the aluminum alloy plate at the location with 0.2 mm from the welding interface. The peak compressive stress in the copper plate is −254 MPa, occurring at the location with 0.1 mm from the welding interface. Within 0.3 mm, the peak tensile stress changes to the peak compressive stress, indicating a steep stress gradient across the EMPW joint. Instantaneous temperature variation, the difference between the coefficient of thermal expansion of aluminum and copper, and the metal-plastic flow induced by impact within the thin welding zone cause the steep stress gradient.

Evaluation of extremely steep residual stress gradients based on a combined approach using laboratory-scale equipment.

Surface treatments characterized by rapid heating and cooling (e.g. laser hardening) can induce very steep residual stress gradients in the direct vicinity of the area being treated. These gradients cannot be characterized with sufficient accuracy by means of the classical sin2Ψ approach applying angle-dispersive X-ray diffraction. This can be mainly attributed to limitations of the material removal method. In order to resolve residual stress gradients in these regions without affecting the residual stress equilibrium, another angle-dispersive approach, i.e. the universal plot method, can be used. A novel combination of the two approaches (sin2Ψ and universal plot) is introduced in the present work. Prevailing limits with respect to profiles as a function of depth can be overcome and, thus, high-resolution surface layer characterization is enabled. The data obtained are discussed comprehensively in comparison with results elaborated by energy-dispersive X-ray diffraction measurements.

Changes in surface integrity of cemented tungsten carbide with shot peening treatment

This study investigates the changes in the surface integrity of WC-Co cemented carbide, after traditional and dual shot peening treatments, using physical characterization methods in conjunction with finite element simulations. Cast steel balls were used in traditional shot peening, while dual shot peening involved the additional use of ceramic shots. Tensile residual stress was found to coexist with compressive residual stresses within both the WC and Co phases, resulting in the fluctuation of stress amplitude in the surface layer. Steep stress gradients were mainly located in regions near the phase interface, especially around the WC/Co interface. In comparison with traditional shot peening, dual shot peening not only improved the uniformity of residual stress at both the macroscopic and microscopic levels but also refined the microstructure and returned the hardness dispersion to the original value by facilitating the simultaneous and coordinated evolution of the WC and Co phases during further deformation. However, the surface roughness increased significantly after traditional and dual shot peening treatments due to accumulated elastic-plastic deformation. This is likely to deteriorate the surface integrity and thus should be avoided if possible, without compromising the other beneficial effects caused by shot peening.

Effect of stress diffusion on the Oldroyd-B fluid flow past a confined cylinder

• The stress diffusion is thermodynamically consistent. • Mesh convergence is obtained by adding the diffusion term to the Oldroyd-B model. • The diffusion term does not significantly change the velocity profile. For the Oldroyd-B fluid flow past a cylinder, it has been well known that converged solutions for the stress in the wake downstream of the cylinder cannot be obtained when the Weissenberg number exceeds 0.7. This has been an unresolved problem [M.A. Alves, P.J. Oliveira and F.T. Pinho, Annu. Rev. Fluid Mech., 53:509-41, 2021]. This problem has various origins, such as the validity of numerical methods and the constitutive equation. This study examines the relationship between the convergence with respect to mesh refinement and the thermodynamically modified Oldroyd-B fluid, which has a diffusion term. We show that stress diffusion is thermodynamically natural and contributes to the convergence of the numerical solution for the Oldroyd-B fluid flow past a cylinder. Stress diffusion has typically been neglected because of its small value, although it is inherent to real polymers. The diffusion term does not change the flow behavior significantly but facilitates the determination of a mesh converged stress solution for the Weissenberg number up to 0.8. This result cannot be obtained from the original Oldroyd-B model. It is thus revealed that the diffusion term can effectively stabilize the stress in the region of steep stress gradients.

Characterisation of short-length scale residual stress variations within an electron beam welded P91 Ferritic–Martensitic steel plate

In this research, an electron beam (EB) butt-welded P91 steel plate (~9 mm thick) is selected to measure longitudinal residual stresses (acting in the welding direction) using a promising residual stress measurement technique - the contour method. The EB weld causes short length scale residual stresses within the narrow width of the fusion zone with steep stress gradients lateral to the weld line, which presents a new challenge for the residual stress measurements. The special measures were taken for all main steps of the technique to improve its the spatial resolution, thereby the short length scale residual stresses were captured. The success of the measurement is assessed by comparing the contour method result to the neutron diffraction result, and a good agreement were found in the results of both the techniques. These results also shows that the contour measurement results successfully captured the steep stress gradient on both sides of the weld centre-line (0 mm) with tensile stress peaks situated just 2.8 mm apart. It is one of the best resolutions in residual stress length-scale in this component achieved in contour measurements.

Three-dimensional numerical simulation of the interseismic and coseismic phases associated with the 6 April 2009, Mw 6.3 L'Aquila earthquake (Central Italy)

Although several observations have been reported in the literature before a strong earthquake, their relation with the forthcoming event is often controversial. Since many physical processes and parameters govern the dynamics of preparation, initiation, and occurrence of earthquakes, their understanding is essential for explaining anomalous seismological, geophysical, hydrological and geodetic signals before a strong earthquake that may be considered for seismic monitoring and hazard assessment.In this work, the interseismic and coseismic stress and strain fields associated with the 6 April 2009, Mw 6.3 L'Aquila earthquake are calculated via a 3D numerical model designed to simulate the crustal interseismic loading and the coseismic brittle episodic dislocation along the fault. The model adopts a framework of gravitational and tectonic forces that are compatible with the geodynamics of the Central Apennines region of the Italian territory. The model assumes a brittle upper crust, where the fault has stick-slip behaviour, and a plastic deeper crust, where the fault is in stationary creep.The results indicate that the concurrent action of gravitational and tectonic forces determines steep interseismic stress gradients at the transition between the creeping and locked fault planes that promote the coseismic subsidence of the hanging wall. The interseismic strain above the transition between that locked upper fault and its unlocked lower shear zone develops a dilated volume in the hanging wall and a contracted volume in the footwall. These stress and strain variations are compatible with seismological, geophysical and geodetic anomalies observed before the earthquake, i.e., Vp/Vs anomalies and location of foreshocks. Interseismic stress and strain patterns invert during the coseismic stage. The dilated volume, formed during the interseismic phase, will be contracted at the coseismic stage and, conversely, the footwall volume previously contracted will be expanded.

The Formation of $$ \left\{ {10\bar{1}2} \right\} $$ Deformation Twin in Hybrid TiB-TiC Reinforced Titanium Matrix Composites

Deformation twins play a significant role in the plastic deformation of titanium matrix composites and improve their ductility. In this work, $$ \left\{ {10\bar{1}2} \right\} $$ deformation twins nucleated in the parent grains with a hard orientation of prismatic slip and changed the local orientation become a soft orientation, resulting in a good balance between high strength (yield strength of 1068 ± 9 MPa and ultimate tensile strength of 1167 ± 1MPa) and high ductility (elongation of 8.7 ± 0.2 pct) at room temperature for hybrid TiB-TiC reinforced Ti-6Al-4V matrix composites. TiB, TiC and grain boundaries worked as a barrier to dislocation mobility, and resulted in different dislocation substructures distributing around the short TiB fibers and TiC particles. The strain incompatibility resulted in a high local stress concentration which promoted twin nucleation and influenced twin propagation. The nonuniform strain caused a stress gradient inside the grains, and the steep stress gradient hindered the twin propagation. Low stress was not enough to drive the dislocation slip of the twins and dislocation decomposition at the twin tips; thus, the growth of the deformation twins stopped in the parent grains.

Investigations of internal stresses in high-voltage devices with deep trenches

Deep trenches, as essential elements of silicon chips used in electronic high-power and high-frequency devices, are known as starting points for dislocation generation under the influence of internal mechanical stresses resulting mainly from the difference in the thermal expansion coefficients between silicon and silicon dioxide. Since the electrical insulation of the devices requires a sequence of mechanical, chemical, and high-temperature processes during the preparation of the deep trenches, including the formation of an amorphous SiO2 edge layer, the emergence of the internal stresses is hardly avoidable. The method of cross correlation backscattered electron diffraction in the scanning electron microscope is used here to quantitatively determine the magnitude and local distribution of internal stresses in silicon around the deep trenches after four different process steps. For this purpose, Kikuchi diffraction images are recorded of the wafer cross section areas along lines perpendicular and parallel to the deep trenches. After Fourier transformation, these images are cross correlated with the Fourier transform of the diffraction image from a stressfree reference sample site. The well-established numerical evaluation of cross correlation functions provides the complete distortion tensor for each measuring point of the line scan, from which the stress tensor can be calculated using Hooke's law. It is found that the in-plane normal stress component σ11 perpendicular to the long edges of the deep trench is larger than the other stress components. That means it essentially determines the magnitude of the von-Mises stress, which was determined as a general stress indicator for all measuring points, too. A characteristic feature is the local distribution of the stress component σ11 with maximum tensile stresses of some hundred megapascals at transition between Si and amorphous SiO2 on the long edges of the deep trench, and with even higher maximum compressive stresses immediately below the bottom of the deep trench. At a distance of about 2 μm from the edges of a single deep trench, all stress components decrease to negligibly small values so that steep stress gradients occur. The range and distribution of tensile and compressive stresses are in accordance with finite element simulations; however, the measured stresses are higher than expected for all investigated states so that dislocation formation seems to be possible. The influence of the electron acceleration voltage on the determination of the internal stresses is discussed as well.

Investigation of the Application of a C-ring Geometry to validate the Stress Relief Heat Treatment Simulation of Additive Manufactured Austenitic Stainless Steel Parts via Displacement

AbstractDirected energy deposition is a metal additive manufacturing process that builds parts by joining material in a layer-by-layer fashion on a substrate. Those parts are exposed to rapid thermo-cycles which cause steep stress gradients and the layer-upon-layer manufacturing fosters an anisotropic microstructure, therefore stress relief heat treatment is necessary. The numerical simulation can be used to find suitable parameters for the heat treatment and to reduce the necessary efforts to perform an effective stress relieving. Suitable validation experiments are necessary to verify the results of the numerical simulation.In this paper, a 3D coupled thermo-mechanical model is used to simulate the heat treatment of an additive manufactured component to investigate the application of a C-ring geometry for the distortion-based validation of the numerical simulation. Therefore, the C-ring samples were 3D scanned using a structured light 3D scanner to quantify the distortion after each process step.

Residual Stress Distribution in Water Jet Peened Type 304 Stainless Steel

In materials with a surface treatment such as shot peening, the residual stress gradient in the surface layer is severe. When measuring the residual stress distribution near the surface with a severe stress gradient by the neutron diffraction method, the gauge volume must be removed from the measurement sample. However, when the gauge volume deviates from the sample, a pseudo peak shift occurs and accurate stress distribution cannot be evaluated. Therefore, it is necessary to evaluate the pseudo peak shift in advance under the same conditions, as in the case of actual residual stress measurement, using a sample in an unstressed state. In this study, the stress distributions in the surface layer of a type 304 stainless steel plate and bar with simulated stress-corrosion cracks which were subjected to water jet peening—giving a surface layer residual stress equivalent better than that of normal shot peening—were evaluated considering the pseudo peak shift. As a result, the residual stress distributions in the surface layer were measured in good agreement with the measurement result obtained by the sequential polishing X-ray diffraction method. It was clarified that the residual stress distribution in the near surface with steep stress gradient can be evaluated by the neutron diffraction method.

Distortion-based validation of the heat treatment simulation of Directed Energy Deposition additive manufactured parts

Directed energy deposition additive manufactured parts have steep stress gradients and an anisotropic microstructure caused by the rapid thermo-cycles and the layer-upon-layer manufacturing, hence heat treatment can be used to reduce the residual stresses and to restore the microstructure. The numerical simulation is a suitable tool to determine the parameters of the heat treatment process and to reduce the necessary application efforts. The heat treatment simulation calculates the distortion and residual stresses during the process. Validation experiments are necessary to verify the simulation results. This paper presents a 3D coupled thermo-mechanical model of the heat treatment of additive components. A distortion-based validation is conducted to verify the simulation results, using a C-ring shaped specimen geometry. Therefore, the C-ring samples were 3D scanned using a structured light 3D scanner to compare the distortion of the samples with different post-processing histories.

Element proportion effect on internal stress from interfaces and other microstructural components in Cu–Pb alloys

ABSTRACTPolycrystalline materials like Cu–Pb alloy consist of four types of microstructural components, including grain cells, grain boundaries, triple junctions and vertex points, the mechanical properties of which governed by the atomic proportion of the alloy elements to a certain degree. The internal stresses from such microstructural components are quite different. Due to experimental limitations, the internal stresses from the alloy materials are difficult to measure directly, especially in the microstructural components. Here, we report a bottom-up approach using an atomistic calculation to obtain atomic properties in Cu-based alloy, as well as that in the microstructural components. The results reveal that a steep stress gradient exists at the interfaces of the alloy, which decreases significantly with the increase of the Pb. The defects evolution process in the alloy samples are investigated during tensile loading, revealing that the defect nucleation is delayed due to the decreasing von Mises stress gradient in the interfaces region as Pb increased. And the increased hydrostatic pressure in the interfaces regions, as a secondary factor can promote the defect nucleation. Among alloy samples with a grain size of 18.58 nm, that with 6.6 at.% Pb has minimal defects and the best mechanical properties.