Residual Stress Gradient Research Articles

Determination of residual stress gradient in a Ti-stabilized austenitic stainless steel cladding candidate after carburization in liquid sodium at 500 °C and 600 °C

Non-destructive residual stress profile measurement with a micrometric depth resolution within the depth of carburized Ti-stabilized stainless steel cladding candidate was carried out by high-energy X-ray diffraction. The samples were carburized in carburizing nuclear liquid sodium at 500 °C and 600 °C for 1000 h. The full residual stress tensor profile was determined thanks to the estimation of the strain-free lattice parameter evolution using the carbon concentration profile measured by electron probe microanalysis and thermodynamic simulation. For the sample carburized at 500 °C, the residual stress genesis was governed by the carbon concentration within the steel and the formation of expanded austenite. For the sample carburized at 600 °C, the residual stress profile in the austenitic matrix depended on the precipitation of M23C6 carbide. Stress relaxation was observed in the intragranular carburization zone. For the two temperatures, compressive residual stresses developed in the carburized zone and tensile stresses developed in the rest of the sample.

Study on SLM Forming Process, Residual Stress and Thermal Fatigue of 24CrNiMo Alloy Steel.

The selective laser melting (SLM) forming process of 24CrNiMo alloy steel was optimized by orthogonal experiment. The density and microstructure of the sample were analyzed, and the optimized process parameters were as follows: laser power 300 W, scanning speed 530 mm/s. The 24CrNiMo alloy steel samples were prepared with optimized parameters. The relationship between residual stress and thermal fatigue and the effect of stress-relieving annealing (SR) on residual stress were analyzed. The density of the sample was found to increase at first and then to decrease with the increase of laser power and then to decrease with the increase of scanning speed. Increasing the laser power and scanning speed widened and deepened the weld. Under the optimized process window, the formability of 24CrNiMo alloy steel samples was improved significantly. The residual stress distribution was tensile stress, which had a negative effect on the thermal fatigue properties of the sample. After SR, the residual stress changed to compressive stress, which had a positive effect on the thermal fatigue properties of the samples. Compared with the deposited state, the thermal fatigue cracks were significantly shortened after SR, which was able to further promote the improvement of thermal fatigue performance. The gradient residual stress test showed that the gradient residual stress in the edge region and the central region of the deposited sample had the same trend, and decreased gradually from the surface layer to the base layer.

Effect of lead angle of hole expansion mandrel on surface integrity and fatigue performance of TC17 titanium alloy hole structure

For the TC17 titanium alloy, the influence of the leading end angle of the mandrel on the expansion strengthening effect of the hole structure was studied, the surface integrity of the hole expansion strengthened under different process parameters was characterized, the high temperature and low cycle of the original and strengthened samples were tested. Fatigue life and the morphological characteristics of fatigue fracture are analyzed. The results show that the lead angle of the mandrel has a significant effect on the surface roughness after expansion. The uneven plastic flow of the metal on the surface of the hole wall during the expansion process leads to uneven residual stress distribution on the hole wall after expansion, and the residual stress amplitude at the exit end of the expansion is the largest, and the hole wall has a certain depth of residual compressive stress gradient field after expansion. When the interference of the core rod is constant, the fatigue life increases with the increase of the rear lead end angle of the mandrel. When the rear lead end angle is 8°, the median fatigue life gain after strengthening can reach 1.74 times, and the strengthening effect is the best, its minimum cycle life is 16331 times, which is higher than the longest cycle life of the original sample (13965 cycles). After strengthening, the origin of the cracks is changed from the multi-source type in the middle of the hole wall to the single-source crack initiation at the inlet end of the expansion.

Influence of Gradient Residual Stress and Tip Shape on Stress Fields Inside Indented TiN Hard Coating

Nanoindentation of treated surfaces, thin films, and coatings is often used as a simple method to measure their hardness and stiffness. These quantities are technologically highly relevant and allow to qualitatively compare different material and surface treatments but fail to capture the entire extent of the highly complex mechanical interaction between indenter tip and the tested surface. Many studies have addressed this question by analytical or numerical modeling, but they must rely on verification by recalculating indentation curves or ex situ microscopy of surface deformation postexperiment. Herein, results from in situ measurements of the multiaxial stress distributions forming beneath an indenter tip while the tested sample is still under load are presented. A 9 μm‐thick TiN hard coating is tested in 1) as‐deposited state and 2) shot‐peened by Al2O3 particles, using two diamond wedges as indenter tips, with 60° and 143° opening angle, respectively. The results reveal a strong influence of the tip shape on the deformation behavior and the main stress component developing inside the sample while under load. In addition, a crack‐closing effect can be attributed to the exponentially declining near‐surface compressive residual stress gradient that is present in the shot‐peened sample.

Residual stress and mechanical strength of Ce0.8Gd0.2O2-δ-FeCo2O4 dual phase oxygen transport membranes

Ce0.8Gd0.2O2-δ-FeCo2O4 membranes, benefiting from their excellent chemical stability, exhibit a broad application potential in oxygen-consuming industrial processes running in harsh environments. For long-term reliable operation, the membrane needs to possess sufficient mechanical strength. This paper characterizes the typical aspects that challenge the mechanical stability of the sintered membrane, including composition and microstructural defects as well as residual stress and residual stress gradients. It is revealed that mechanical strengths of the sintered membranes increase with decreasing iron cobalt spinel content, that the high iron cobalt spinel content induces microcracks, and that high residual tensile stress gradually decreases from the as-sintered surface to the bulk. Although the residual tensile stress can be reduced by applying an extensive elevated temperature dwell time during cooling, it is suggested to limit the iron cobalt spinel content to a nominal value of 15 wt% to eliminate the residual tensile stress while maintaining a high mechanical strength.

Residual Stress Heterogeneity Induced By Powder Metallurgy Gear Manufacturing Chains

Powder metallurgy represents an alternative to increase sustainability in the manufacturing of automotive gears, but its potential is hindered by a certain lack of knowledge on surface integrity properties that can impair the gear performance. This study explores the effects of the microstructural differences induced by this chain on the residual stress heterogeneity state of gears. X-ray diffraction methods of macro residual stress mapping and line profile analysis were applied for measurements of gear teeth after subsequent steps of the powder metallurgy and the conventional wrought steel chains. The powder metallurgy chain induced more pronounced heterogeneities than the conventional manufacturing, characterized by non-uniform residual stress distributions along the lead and the involute profiles of gear flanks. These non-uniformities observed after carburizing were traced back to the previous steps, surface densification, sintering and compaction. The residual stress distribution patterns of these steps were compatible with the plasticity dynamics of each manufacturing process. Such surface integrity heterogeneities result in a residual stress gradient along the gears functional surface, exposing particular regions to be more susceptible to fatigue effects.

Thin films residual stress profile evaluation using test microstructures: Illustrated on an example of AlN film

In this study, we investigate the residual stress gradient of aluminum nitride thin film deposited by reactive pulse DC magnetron sputtering technique on a 200 mm diameter silicon wafer with a 1 μm layer of plasma enhanced chemical vapor deposition tetraethylorthosilicate. Stress measurements are obtained using in situ fabricated rotational beam microstructures. The rotating beam moves in response to relief of the residual stress on the connecting arms that experience lengthening or shortening due to compressive or tensile residual stresses, respectively. Various arm-beam connecting joints, separation gaps between the arms, and arm lengths are considered to determine the optimum microstructure for localized residual stress evaluation of the sputtered aluminum nitride. The displacement of the rotating beams with four different arm-beam connecting-joint designs is analytically modeled using COMSOL multiphysics finite element method simulation. The results of the analytical model were found to be in agreement with the results observed through experiments. The stress gradient measurements obtained using the microstructures are compared to the Stoney stress evaluated using a wafer bow technique. Although the predicted Stoney stress shows a 220 MPa tensile residual stress, the observed trend in localized stress values shows that the maximum stress is 280 MPa at the center of the wafer and reduces to about 100 MPa at the edge of the wafer.

Formation Mechanism and Control Method of Residual Stress Profile by Laser Shock Peening in Thin Titanium Alloy Component.

In the laser shock peening process of titanium alloy thin blades, a shock wave will be repeatedly reflected and coupled in the blades, resulting in the failure of the formation of a gradient residual compressive stress layer, which is the key to improve fatigue performance and resist foreign object impact. This paper takes TC17 titanium alloy sheet as the research object to reveal the influence mechanism on residual stress-strain profile of shock wave reflection-coupling by shock wave propagation and key position dynamic response. Based on the result of influence mechanism, two wave transmission methods are proposed to regulate shock wave in order to reduce the intensity of shock wave reflection. The analysis shows that the high strength stress be formed when the shock wave is reflected and coupled in the sheet, which causes the re-plastic deformation and the decrease of transverse plastic strain. This eventually leads to residual tensile stress up to 410 MPa being formed within a 0.5 mm radial direction and 0.3 mm deep of the spot range. The use of “soft” and “hard” wave-transmitting layers greatly reduces the shock wave reflection intensity, and under the condition of the “hard” wave-transmitting layer, a better impedance matching is achieved, resulting in a residual compressive stress of about 400 MPa.

Microstructure, Residual Stresses, and Strain-Rate-Dependent Deformation and Fracture Behavior of AISI 304L Joints Brazed with NiCrSiB Filler Metals

The knowledge of alloy–process–structure–property relationships is of particular interest for several safety-critical brazed components and requires a detailed characterization. Thus, three different nickel-based brazing filler metals were produced with varying chromium and molybdenum content and were used to braze butt joints of the austenitic stainless steel AISI 304L under vacuum. Two holding times were used to evaluate diffusion-related differences, resulting in six specimen variations. Significant microstructural changes due to the formation and location of borides and silicides were demonstrated. Using X-ray diffraction, alloy-dependent residual stress gradients from the brazing seam to the base material were determined and the thermal-induced residual stresses were shown through simulations. For mechanical characterization, impact tests were carried out to determine the impact toughness, as well as tensile tests at low and high strain rates to evaluate the strain-rate-dependent tensile strength of the brazed joints. Further thermal, electrical, and magnetic measurements enabled an understanding of the deformation mechanisms. The negative influence of brittle phases in the seam center could be quantified and showed the most significant effects under impact loading. Fractographic investigations subsequently enabled an enhanced understanding of the fracture mechanisms.

Development of an Electrostatic Comb-Driven MEMS Scanning Mirror for Two-Dimensional Raster Scanning.

Microelectromechanical System (MEMS)-based scanning mirrors are important optical devices that have been employed in many fields as a low-cost and miniaturized solution. In recent years, the rapid development of Light Detection and Ranging (LiDAR) has led to opportunities and challenges for MEMS scanners. In this work, we propose a 2D electrostatically actuated micro raster scanner with relatively large aperture. The 2D scanner combines a resonant scanning axis driven by an in-plane comb and a quasistatic scanning axis driven by a vertical comb, which is achieved by raising the moving comb finger above the fixed comb finger through the residual stress gradient. The analytic formula for the resonant axis frequency, based on the mechanical coupling of two oscillation modes, is derived and compared with finite element simulation. A prototype is designed, fabricated, and tested, and an overall optical Field-of-View (FoV) of about 60° × 4° is achieved. Finally, some possibilities for further improvement or optimization are discussed.

Investigation of residual stress within linear friction welded steel sheets by alternating pressure via X-ray diffraction and contour method approaches

This paper presents a thorough investigation of the influence of the applied pressure on the behavior and distribution of residual stress (RS) within linear friction welded medium carbon steel sheets. The RS in the longitudinal and transverse directions was determined using the X-ray diffraction (XRD) technique. The contour method (CM) was also used to provide 2D maps of RS normal to the cut surface. The RS results determined by the CM were verified with those obtained by the XRD. Both measurement techniques were able to discern the influence of the applied pressure on the behavior of the induced RS. It was noticed that a large change in the applied pressures led to a pronounced variation in RS behavior. With the increase of the applied pressure, the tensile RS gradient near the weld line was decreased. Further, the compressive RS induced in the vicinity of the weld line was decreased, and its behavior was flattened with the increase of the applied pressure. The influence of the applied pressure on the trend of the full-width at half-maximum (FWHM) of the XRD peak and the microhardness distribution was also examined. A remarkable increase was noticed in the FWHM and microhardness at the weld line with the increase of the applied pressure. The behavior of the microhardness at the weld line demonstrated the role of the FWHM as an index of the material hardening.

Limitations on MEMS design resulting from random stress gradient variations in sputtered thin films

Residual stress gradients often negatively affect the performance of MEMS devices, causing film curvature and changing the designed gaps of released structures. In this work, we built folded beams designed to compensate for the film curvature and keep the actuator gaps of sensitive resonant switches constant. While the average stress gradient is cancelled by our designs, we find that random variations in the stress gradient (rather than random variations in device dimensions) cause the majority of the observed variation in actuator gap. To our knowledge, this has not previously been reported, and represents an important limitation on MEMS designs using sputtered films. The standard deviation of the 400 nm contact gap for a folded beam of total length 152 µm and width 108 µm was measured to be about 134 nm. Using parameters measured from test cantilevers, our simulations predict that about 98% of the variation in contact gap is due to stress gradient variation, rather than variations in device geometry.

Correlative cross-sectional characterization of nitrided, carburized and shot-peened steels: synchrotron micro-X-ray diffraction analysis of stress, microstructure and phase gradients

Mechanical properties of case modified steels depend decisively on the near-surface gradients of residual stresses, microstructures, phases and chemical composition, which are generated by the empirically well-established case-hardening techniques. Currently, however, to obtain the correlation between near-surface structure–property gradients, applied hardening process parameters and steels’ overall performance is a very challenging task. In this work, high-energy synchrotron cross-sectional X-ray diffraction (CSmicroXRD) using a pencil beam cross-section of 20 × 500 μm2 and complementary analytical techniques are used to characterize the surface-to-bulk gradient of (i) a plasma nitrided steel W300, (ii) a carburized case hardening steel (grade 18CrNiMo7-6) and (iii) a shot-peened high strength steel, type 300M. CSmicroXRD analysis reveals complex gradients of martensite and austenite phases, residual stresses in both phases, crystallographic texture and the evolution of diffraction peak broadening with a spatial resolution of ~20 μm. These parameters are correlated with the gradients of hardness, morphology-microstructure and with the changes in N and C concentrations and/or retained austenite formation/depletion in all three model samples. Finally, the correlative micro-analytics approach indicates the complexity of near surface structure-property relationships as well as the importance of innovative cross-sectional characterization, which allows for assessing gradual near-surface physical and/or chemical changes accompanying thermo-chemical and mechanical surface treatments.

Strain depth profiles in thin films extracted from in-plane X-ray diffraction

Thin films generally contain depth-dependent residual stress gradients, which influence their functional properties and stability in harsh environments. An understanding of these stress gradients and their influence is crucial for many applications. Standard methods for thin-film stress determination only provide average strain values, thus disregarding possible variation in strain/stress across the film thickness. This work introduces a new method to derive depth-dependent strain profiles in thin films with thicknesses in the submicrometre range by laboratory-based in-plane grazing X-ray diffraction, as applied to magnetron-sputtering-grown polycrystalline Cu thin films with different thicknesses. By performing in-plane grazing diffraction analysis at different incidence angles, the in-plane lattice constant depth profile of the thin film can be resolved through a dedicated robust data processing procedure. Owing to the underlying intrinsic difficulties related to the inverse Laplace transform of discrete experimental data sets, four complementary procedures are presented to reliably extract the strain depth profile of the films from the diffraction data. Surprisingly, the strain depth profile is not monotonic and possesses a complex shape: highly compressive close to the substrate interface, more tensile within the film and relaxed close to the film surface. The same strain profile is obtained by the four different data evaluation methods, confirming the validity of the derived depth-dependent strain profiles as a function of the film thickness. Comparison of the obtained results with the average in-plane stresses independently derived by the standard stress analysis method in the out-of-plane diffraction geometry validates the solidity of the proposed method.

Impact of weld restraint on the development of distortion and stress during the electron beam welding of a low-alloy steel subject to solid state phase transformation

Electron beam (EB) welding has a low tolerance to inter-part gapping distortion and can generate complicated stresses, which pose challenges to weld quality and integrity. This study investigates welding distortion and stresses in an EB welded plate made from SA508 Grade 4N low-alloy steel. A thermal-metallurgical-mechanical model was developed to predict the temperature, micro-constituents, hardness, distortion and stresses in the EB weldment; the predictions are in good agreement with experimental results. Different restraint conditions on the weld plane were modelled to examine their effects on distortion and stresses. If welding is performed with no restraint, inter-part gapping develops ahead of the beam position that could exceed the tolerance for a sound weld. In contrast, tack welds at the plate ends significantly reduce this gapping, but induce additional tensile stress at the stop-end tack weld. This stress is particularly high as the beam approaches the tack weld. Increasing the extent of the tack weld reduces the tensile stress, while increasing number of distantly distributed narrow tack welds does not help. A full through-length restraint eliminates the opening gap and minimises the development of tensile stresses ahead of the beam that could potentially break the restraint. The applied restraint on the weld plane has little effect on the final residual stress field, since this field mostly develops during cooling after the EB weld is complete. The weld-induced martensitic transformation suppressed tension or promoted compression in the EB weld and heat affected zone (HAZ). A steep gradient of residual stress exists, with high tensile stress concentrated in a narrow region immediately outside the HAZ.

Influence of load spectrum on contact fatigue damage of a case carburized wind turbine gear

Contact fatigue failures are becoming increasingly prominent in heavy-duty gears due to the remarkable effects on service lives and reliabilities of associated machines such as wind turbines. The contact fatigue estimation of such gears is complicated due to the coupling effect of mechanical properties, lubrication and stochastic wind loadings. A numerical model was established to evaluate the contact fatigue damage evolution of a megawatt level wind turbine carburized gear pair based on the measured wind load spectrum. The elastohydrodynamic lubrication (EHL) theory was employed to compute the gear contact pressure and subsequently, the stress responses were obtained efficiently through the discrete convolute, fast Fourier transformation (DC-FFT) algorithm. The hardness and the residual stress gradients were captured via the Vickers hardness test and X-ray diffraction method, respectively. The Dang Van multiaxial fatigue criterion and the Basquin equation were adopted to estimate the fatigue lives under stochastic loadings, based on which the contact pressure-life curve was further profiled. Finally, the gear damage accumulation under this load spectrum was evaluated via the linear Palmgren-Miner rule. Results indicate that both the subsurface and transition area failures should be considered in gear design. The fatigue life prediction should consider the load spectrum rather than solely rely on a constant amplitude loading condition.

Gradient of Residual Stress and Lattice Parameter in Mechanically Polished Tungsten Measured Using Classical X-rays and Synchrotron Radiation

In this work, the stress gradient in mechanically polished tungsten sample was studied using X-ray diffraction methods. To determine in-depth stress evolution in the very shallow subsurface region (up to 10 μm), special methods based on reflection geometry were applied. The subsurface stresses (depth up to 1 μm) were measured using the multiple-reflection grazing incidence X-ray diffraction method with classical characteristic X-rays, while the deeper volumes (depth up to 10 μm) were investigated using energy-dispersive diffraction with white high energy synchrotron beam. Both complementary methods allowed for determining in-depth stress profile and the evolution of stress-free lattice parameter. It was confirmed that the crystals of tungsten are elastically isotropic, which simplifies the stress analysis and makes tungsten a suitable material for testing stress measurement methods. Furthermore, it was found that an important compressive stress of about − 1000 MPa was generated on the surface of the mechanically polished sample, and this stress decreases to zero value at the depth of about 9 μm. On the other hand, the strain-free lattice parameter does not change significantly in the examined subsurface region.

Study on Hydrogen Diffusion Behavior during Welding of Heavy Plate.

For the multi-layer and multi-pass welding process of the heavy plate, the hydrogen diffusion behavior was numerically simulated to study the effect of solid-state phase transition (SSPT) on the hydrogen diffusion in the thickness direction, and the influence of the residual stress-induced diffusion after SSPT. The calculation results were compared with the experimental results. The comparison shows that the distribution of hydrogen concentration in the direction of thickness was in good agreement. The position with the most severe cold cracking sensitivity was located at a 20–30 mm depth from the top surface in this article. After welding, the hydrogen concentration in this position was kept at a high level for a long time under the effect of the size-constraint effect of the heavy plate and the existence of welding residual stress gradient. In addition, the SSPT reduced the residual stress level of weld metal (WM) significantly, increased that of the heat affected zone (HAZ), and the hydrogen was redistributed under the influence of stress. In the process of phase transformation, the parameters of hydrogen diffusion property of the material changed dramatically in a short time, the hydrogen diffusion coefficient increased in order of magnitude, and the solubility decreased in order of magnitude. This directly led to the upward diffusion of hydrogen in WM, and produced a self-gathering effect. For a welded joint of heavy plate, the self-gathering effect between passes was effective in the short-range and ineffective in the long-range.

Identify the distribution of 2D residual stresses around notches based on the Willis-form equations

ABSTRACT This paper proposes a new non-destructive method to reconstruct the distribution of residual stresses around notches from the measured displacements under external loads. For this purpose, a linear finite element method based on the Willis-form equations is firstly established to calculate the displacements, so that they explicitly contain the impact of the gradient of residual stresses, which can be efficiently determined through the analytical solution of the stress distribution around notches due to remote virtual loads. Then, the remote virtual loads are identified by minimizing the discrepancy between the calculated and the measured displacements. In this way, the distribution of residual stresses can be naturally obtained by substituting the identified remote virtual loads into the analytical solution. Because the number of remote virtual loads is very limited, the identification is very efficient. However, since this is an ill-posed problem, regularization is discussed by comparing the performance of the optimal sensor placement method, the Tikhonov-Morozov method and the Tikhonov- L-curve method. Both numerical and experimental results of a plate with an elliptical hole under tension are used to check the validity of the proposed method. It is demonstrated that the distribution of residual stresses around the notch could be successfully identified by using all regularization methods. However, the optimal sensor placement method could give more reliable results.

High-power electro-mechanical behavior of a capacitive microwave power sensor with warped cantilever beam

In this paper, high-power up to 4000 mW electro-mechanical behavior of a capacitive micro-electromechanical systems (MEMS) microwave power sensor using cantilever beam is investigated. Due to residual stress gradients, the power sensor is proposed for a warped cantilever beam connected to coplanar waveguide (CPW) structure. The proposed sensor is fabricated using the GaAs monolithic microwave integrated circuit (MMIC) process. It is demonstrated that the output response of this sensor exhibits non-linear characteristics under high power levels (more than 1000 mW). The measurement results can be classified as three regions: linear region (1–1000 mW), saturated region (1000–2500 mW), and over-saturated region (2500–4000 mW). Their corresponding sensitivities are 2.8 fF/W, 1.03 fF/W, and 0.32 fF/W at 10 GHz, respectively. The non-linear output response of the power sensor is mainly caused by impedance mismatch at X-band (8–12 GHz). Furthermore, an electro-mechanical model of power sensor based on warped cantilever beam is proposed. The results are well in agreement with the calculated ones using this model by software that employs the finite element method (FEM), which provides the potential prospect for the design of capacitive power sensor.