X-ray Diffraction Stress Measurements Research Articles

A Simple Calibration Method to Consider Plastic Deformation Influence on X-ray Elastic Constant Based on Peak Width Variation

The sin²⁡ψ method is the general method for analyzing X-ray diffraction stress measurements. This method relies on the estimation of a parameter known as 12S2hkl, which is generally considered as a material constant. However, various studies have shown that this parameter can be affected by plastic deformation leading to proportional uncertainties in the estimation of stresses. In this paper, in situ X-ray diffraction measurements are performed during a tensile test with unloads on a low-carbon high-strength steel. The calibrated 12S2hkl parameter varies from 3.5×10−6 MPa−1 to 5.5 ×10−6 Mpa−1, depending on the surface condition and on the plastic strain state, leading to a maximum error on the stress level of 40% compared to reference handbook values. The results also show that plastic strain is responsible for 6 to 14% of the variation, depending on the initial surface sample condition. A method is then proposed to correct this variation based on the fit of the 12S2hkl evolution with respect to the peak diffraction width, the latter being an indication of the plasticity state. It is shown that the proposed methodology improves the applied stress increment prediction, although the absolute stress value still depends on pseudo-macrostresses that also vary with plastic strain.

Ambient formation of high pressure Ag2Si2O5 and non-stoichiometric Ag0.3Al0.7 alloy under confinement

We report results of Field Emission Scanning Electron Microscopy (FESEM), Energy Dispersive Analysis of X-rays (EDAX), X-ray Photoelectron Spectroscopy (XPS), X-ray Reflectivity (XRR), and X-ray Diffraction (XRD) and residual stress measurement studies of Ag-silica composite films on Al(001) co-deposited from precursors and spin-coated at different frequencies under ambient conditions. FESEM and EDAX show Ag nanoparticle formation, and XRD, XPS, and XRR show Ag0.3Al0.7 alloy and Ag-rich silicate Ag2Si2O5 formation in all samples. The alloy is non-stoichiometric and non-equilibrium, while the silicate forms at high oxygen pressure. XRR shows the presence of three layers, nanoparticles on top, silicate in the middle, and alloy at the bottom, on an Ag-doped Al substrate. Film thickness decreases exponentially with frequency. Individual layers increase in crystal domain size with a frequency of 3000 rpm when the silicate layer thins below unit cell thickness and the growth has a two-dimensional preference. Our results suggest total confinement by film thinning and local confinement from the Ag nanolayer. Residual stress measurements on the films deposited at 500 and 5000 rpms show a gradual increase in the tensile stress. The increase in spinning frequency reveals the formation of high pressure ambience.

In Situ Study of the Interface-Mediated Solid-State Reactions during Growth and Postgrowth Annealing of Pd/a-Ge Bilayers.

Ohmic or Schottky contacts in micro- and nanoelectronic devices are formed by metal-semiconductor bilayer systems, based on elemental metals or thermally more stable metallic compounds (germanides, silicides). The control of their electronic properties remains challenging as their structure formation is not yet fully understood. We have studied the phase and microstructure evolution during sputter deposition and postgrowth annealing of Pd/a-Ge bilayer systems with different Pd/Ge ratios (Pd:Ge, 2Pd:Ge, and 4Pd:Ge). The room-temperature deposition of up to 30 nm Pd was monitored by simultaneous, in situ synchrotron X-ray diffraction, X-ray reflectivity, and optical stress measurements. With this portfolio of complementary real-time methods, we could identify the microstructural origins of the resistivity evolution during contact formation: Real-time X-ray diffraction measurements indicate a coherent, epitaxial growth of Pd(111) on the individual crystallites of the initially forming, polycrystalline Pd2Ge[111] layer. The crystallization of the Pd2Ge interfacial layer causes a characteristic change in the real-time wafer curvature (tensile peak), and a significant drop of the resistivity after 1.5 nm Pd deposition. In addition, we could confirm the isostructural interface formation of Pd/a-Ge and Pd/a-Si. Subtle differences between both interfaces originate from the lattice mismatch at the interface between compound and metal. The solid-state reaction during subsequent annealing was studied by real-time X-ray diffraction and complementary UHV surface analysis. We could establish the link between phase and microstructure formation during deposition and annealing-induced solid-state reaction: The thermally induced reaction between Pd and a-Ge proceeds via diffusion-controlled growth of the Pd2Ge seed crystallites. The second-phase (PdGe) formation is nucleation-controlled and takes place only when a sufficient Ge reservoir exists. The real-time access to structure and electronic properties on the nanoscale opens new paths for the knowledge-based formation of ultrathin metal/semiconductor contacts.

Evaluating residual stresses in compositionally graded TiN films via ab initio and Rietveld simulation

The grazing incidence X-ray diffraction (GIXRD) stress measurement method, based on the classic sin2ψ method, is a well-established procedure for the evaluation of compressive residual stresses (CRS) in thin deposited films. Problems arise when using this approach in single-phase compositionally graded films, since both mechanical and diffraction properties vary with film depth. A method of obtaining CRS gradient was developed which consists in simulating a stressed GIXRD pattern via Rietveld simulation and ab initio obtained X-ray elastic constants (XECs) in order to evaluate the stress profile across the film. This work successfully describes the CRS profile of compositionally graded TiN films obtained by Grid Assisted Magnetron Sputtering (GAMS), insofar as the biaxial stress assumptions are valid and within the limits imposed by the sin2ψ method.

Residual stress measurements on a deep rolled aluminum specimen through X-Ray Diffraction and Hole-Drilling, validated on a calibration bench

Residual stress measurements are notably affected by a high sensitivity to errors in input data. Measurements should then be presented together with an estimation of their accuracy. A common strategy is to carry out more measurements and/or to compare the results of different techniques. However, error contributions due to biases could be dangerously left unseen. In a previous work, the authors presented a calibration bench which can impose a known bending stress distribution on a specimen while simultaneously performing X-Ray Diffraction (XRD) or Hole-Drilling Method (HDM) residual stress measurements. Since the external load can freely be applied and removed, the superposition principle can be exploited to simultaneously identify either the reference bending stress distribution or the actual residual stress distribution, with the same experimental setup. A deep rolling treatment was measured and analyzed on the calibration bench with both XRD and HDM. First, residual stresses on the surface were evaluated with XRD measurements, then electrochemical material removal was performed to investigate stresses at higher depths. After that, HDM measurements were carried out and compared with the results of XRD. Both methods were also used to identify the known bending stresses, providing an additional validation of the residual stress results.

Control of residual stress in metal additive manufacturing by low-temperature solid-state phase transformation: An experimental and numerical study

Directed energy deposition (DED) technology commonly known as additive manufacturing (AM), is a rapid prototyping method for fabricating metallic functional components with minimum finishing operations. However, excessive tensile residual stress (RS) is often a potential source of structural failure due to the fact that it can cause surface/subsurface cracking of DED parts. In this work, the RS properties in DED specimens made of the low-temperature transformation (LTT) pre-alloyed powders was investigated. A DED model coupling the finite element (FE) and thermo-mechanical-metallurgical (TMM) analysis was constructed, and was experimentally validated by thermographic system and X-ray diffraction (XRD) stress measurements. An additional set of RS prediction for the DED specimen, using increased inter-track idle time was developed to reveal the effects of thermal history on TMM evolution behavior and RS distribution. The combination of experiment and predictive simulation provided an insight into the non-linear thermo-metallurgical evolution and the formation mechanism of compressive RS during DED of LTT alloy, and showed the great potentiality of LTT powder in minimizing the RS in DED parts by the austenite-to-martensite transformation on cooling.

Stress Engineering as a Strategy to Achieve High Ferroelectricity in Thick Hafnia Using Interlayer

Binary oxides of Hf0.5Zr0.5O2 (HZO) have attracted considerable attention of the ferroelectric research community, owing to their excellent ferroelectric properties and CMOS compatibility. In particular, HZO films of a relatively high thickness (>10 nm) are studied widely for sensor and display applications. However, one of the major constraints of HZO materials is the formation of monoclinic phases (m-phase) with increasing film thickness resulting in the degradation of its remanent polarization ( ${P}_{r}$ ). Herein, we present a stress engineering method to achieve high ferroelectricity in thick hafnia using an interlayer. In our work, we attempted to address the aforesaid limitation of HZO by inserting a dielectric interlayer and elucidated the influence of interlayer on the relatively thick HZO films. high resolution TEM (HRTEM) analysis revealed that the presence of interlayer allows the growth of the top and bottom HZO layer in an independent direction thereby preventing the loss of ferroelectricity in HZO films with higher thickness by controlling its grain size. Similarly, grain angle incidence X-ray diffraction (GIXRD) and residual stress measurements suggest that the interlayer affects the o-phase formation from the t-phase owing to the tensile stress applied to the HZO films because of the coefficient of thermal expansion (CTE) mismatch between the HZO and interlayer. In our study, an improved $2{P}_{r}$ value of 30.2 $\mu \text{C}$ /cm2 was achieved by inserting a TiO2 dielectric interlayer in a relatively thicker HZO film. We believe that this approach can be adopted in various applications such as sensors, displays, and memory devices.

A systematic study on the effects of shot peening on a mild carbon steel: Microstructure, mechanical properties, and axial fatigue strength of smooth and notched specimens

Used with the right combination of parameters, shot peening process can be regarded as a severe plastic deformation method that can greatly enhance the strength of mechanical components by inducing surface grain refinement, increasing the hardness, and generating compressive residual stresses in the top surface layer. The present experimental study explores the effects of gradual rise of shot peening kinetic energy on microstructure, mechanical properties, and fatigue behavior of AISI 1045 carbon steel by changing the process parameters over a wide range of Almen intensity (20-32A) and surface coverages (100-3000%). Microstructural observations, X-ray diffraction, microhardness and residual stress measurements were carried out to analyze the effects of grain refinement as the kinetic energy of the peening process increased. In addition to compression-tension axial fatigue tests, fatigue crack growth measurements were also performed on specimens in both smooth and notched configurations. The results demonstrated that increasing the kinetic energy of the process is an effective technique to achieve nanostructured surface layer combined with superior mechanical properties. Severe shot peening treatment significantly improved the fatigue strength of the treated specimens, while the continuous growth of surface coverage proved to have detrimental effects on fatigue behaviour.

Influence of cobalt doping on residual stress in ZnO nanorods

Cobalt-doped (0%, 5%, 10%, 15%, and 20%) zinc oxide (ZnO) nanorods were deposited on silicon wafers by a chemical bath deposition technique. Variations in energy band gap and stress due to cobalt doping were analyzed by X-ray diffraction techniques, optical measurements and modeled by density functional theory calculations. Also, the direct residual stress in ZnO nanorods was investigated by measuring the difference in curvature across the doped ZnO thin films deposited on a silicon substrate using the Bow Optic wafer stress measurement system. The stress in doped ZnO films was found to be of compressive in nature. The residual stress in doped ZnO thin films was found in the range of 0.0427–1.0174 GPa. The residual stress was also found to scale with the cobalt doping concentration in ZnO thin film. Also, the crystalline structure of various cobalt doped ZnO nanorods films was confirmed by X-ray diffraction analysis to be of the wurtzite structure. The bandgap of cobalt-doped ZnO was red-shifted from 3.30 eV to 3.21 eV as the cobalt concentration in ZnO nanostructures varied from 0% to 20%. A linear relationship between stress and bandgap shifting in cobalt-doped ZnO nanorods was obtained based on x-ray diffraction and direct stress measurements.

Design and preparation of gradient graphite/cermets self-lubricating composites

Based on the functionally graded materials (FGMs) design concept, the laminated-graded graphite/cermets self-lubricating composite was prepared to achieve the integration of mechanical properties and lubrication performance of the cermet. The effects of the layer number and thickness of graded structure on residual stresses in the gradient composites were investigated by finite element method (FEM). From the FEM analyses, the optimal gradient structure design was obtained corresponding to the following parameters: the number of graded layers n=2 and the thickness of graded structure t=1mm. According to the optimum design, a graded graphite/cermets self-lubricating material with two layers was fabricated by a typical powder metallurgy technique. Compared with the homogenous graphite/cermets composite, the surface hardness and indentation fracture toughness of graded composite were increased by approximately 15.9% and 6.3%, respectively. The results of X-ray diffraction (XRD) stress measurement identified the existence of residual compressive stress on the surface of graded composite. Additionally, the friction and wear tests revealed that the wear resistance of the graphite/cermets self-lubricating composite was improved significantly via the graded structural design, whereas the coefficient of friction changed slightly.

475°C Embrittlement of Duplex Stainless Steel—A Comprehensive Microstructure Characterization Study

Abstract The effect of 475°C embrittlement on microstructure development of grade 2205 duplex stainless steel was investigated. Spinodal decomposition products and associated precipitates in ferrite, austenite, and at interphase boundaries were characterized using analytical transmission electron microscopy (TEM) and scanning electron microscopy (SEM) techniques. Micro-analyses confirmed the presence of Cr-enriched α'' and Cr-depleted α' spinodal structures in the ferrite after 5 h of aging at 475°C. Long-term aging for 255 h resulted in heavily-faulted R-phase precipitates with sizes of ∼50–400 nm, χ-phase, and ε-Cu in the ferrite, TiN and Cr2N precipitates in the austenite, and a continuous network of M23C6-carbides at interphase boundaries. A significant hardness increase was observed after 255 h of aging, which was accompanied by a reduction of ferrite fraction. X-ray diffraction (XRD) stress measurements showed a general reduction of residual stresses in both ferrite and austenite with aging. Electron backscatter diffraction (EBSD) showed increased local misorientations, primarily close to precipitate interfaces within the ferrite, indicating the development of strain heterogeneities in the microstructure. The data presented provided a better understanding of 475°C embrittlement in duplex stainless steel, suggesting that not only the ferrite alone is responsible for embrittlement. A comprehensive microstructure characterization study has been provided and the explanation for 475°C embrittlement of duplex stainless steel has been discussed.

The In-Depth Stress Distribution for 1H13 Specimen after Cutting

Abstract Measuring the in-depth stress state is of vital importance for materials scientists. Strain gauges methods are capable of yielding information only about the surface stress state. Diffraction methods using synchrotron or neutron radiation, which allow totally non-destructive stress measurements inside the material, are not widely available. In this context, the best widely available method combines the X-ray diffraction stress measurements and gradual removal of the outer layer by means of electropolishing. Here, this method was applied to the specimen made of 1H13 stainless steel cut with under water on a corundum cut-off wheel. The idea was to investigate how deeply an additional stress state resulting from cutting was introduced and whether the technique of combining of X-ray diffractometry and electropolishing can be used widely for determining the stress state inside the specimen.

High frequency mechanical impact treatment (HFMI) for the fatigue improvement: numerical and experimental investigations to describe the condition in the surface layer

Post-treatment techniques like the high frequency mechanical impact treatment (HFMI) exhibit a significant fatigue life enhancement of welded joints. The effectiveness of this mechanical impact treatment is primarily based on the combination of three effects: the local hardness increase, compressive residual stresses and reduced notch stress concentration at the weld toe. The goal of the present study was to develop a computationally efficient approach for predicting residual stresses induced by the HFMI process on steel specimens. For that purpose, explicit simulations of this post weld treatment technique were performed utilizing the software package ABAQUS. Although, the focus of this study is to find suitable process and material parameters as input for the numerical simulation. For this, the impact velocity, contact force and permanent indentation depth of a pneumatic HFMI-tool were measured. Concerning material modelling, an enhanced combined material model with strain rate dependency was applied. Furthermore, the simulated residual stress field was experimentally validated by X-ray diffraction and neutron diffraction residual stress measurement. The results of the simulations are in good agreement with the experimental results, showing that the material hardening model used for simulation has a high influence on the calculated residual stress values.

Thermo-mechanical model for simulating laser cladding induced residual stresses with single and multiple clad beads

A three dimensional finite element (FE) model was developed to simulate residual stress induced for laser cladding of AISI 4340 steel powder onto a similar substrate material. A laser power attenuation model was proposed for the laser-powder-interaction zone under the coaxial powder feeding nozzle. The thermal analysis integrated the deposition of clad beads with laser heating. This was performed using user-defined subroutines to thermally activate clad element conductivity and surface heat transfer film conditions simultaneously with the translating attenuated laser heat flux. The FE model investigated three case studies: (i) laser heating without powder feeding, (ii) deposition of single clad bead and (iii) deposition of double adjacent clad beads. The numerical results of the thermal field were compared with thermocouple measurements and heat affected zone (HAZ) sizes from experimental specimens cross-sectioning. X-ray diffraction (XRD) stress measurements were performed to validate the modeled residual stress in case (ii). The FE model was subsequently applied to simulate cladding 10 clad beads over an area to study the effects of depositing multiple successive clad beads on residual stress field.

Determination of average X-ray strain (AXS) on TiN hard coatings using cos2αsin2ψ X-ray diffraction method

For stress measurement on thin films and coatings using X-ray diffraction (XRD) methods, the uncertainty is commonly acknowledged to be from elastic constants. However, the uncertainty can be due to the statistical fluctuation of strain measured by XRD. In this study, we proposed a method where the average X-ray strain (AXS) was determined using cos2αsin2ψ XRD technique at several rotational (ϕ) angles to improve the accuracy of the measurement of X-ray stress or X-ray elastic constants (XECs). The major concept was to increase sampling volume by measuring X-ray strain at multiple rotational angles. TiN hard coating on Si (100) substrate was selected as the model system, where the residual stress was determined by laser curvature technique and the accompanying lattice strain was measured by cos2αsin2ψ method. The average effective elastic constant (AEXEC) could be attained by substituting the residual stress into the slope of AXS vs. cos2αsin2ψ plot. The AEXEC was served as an indicator to validate the AXS measurement. By substituting AEXEC in conventional sin2ψ XRD stress measurement, the deviation of the result from the stress obtained by laser curvature method was less than 7%, indicating that AXS effectively reduced the uncertainty in XECs and thus increased the accuracy of stress measurement. The concept of increasing sampling volume was also confirmed using synchrotron X-ray source, where the statistical fluctuation in X-ray strain could be further reduced by performing the measurement at all azimuthal direction. The experimental results showed that the uncertainty on XEC measurement by sin2ψ method was less than 10%, if sufficient sampling volume was provided. Furthermore, using AXS and elastic constant measured by nanoindentation (ENIP) to calculate X-ray stress, the stress deviation from that by laser curvature method could be substantially reduced even down to 3% with sufficient sampling points. Therefore, AXS may serve as a convenient parameter, when combining with ENIP, in X-ray stress measurement, by which residual stress of hard coatings comparable to that by laser curvature method can be obtained without using XECs.

X-ray diffraction and fracture based analysis of residual stresses in stainless steel–epoxy interfaces with electropolishing and acid etching substrate treatments

The aim of this study is to investigate the effect of a stainless steel surface condition on the thermal residual stresses at a bi-material interface. AISI 304 stainless steel–epoxy specimens with either as-received, nitric acid etched or electropolished substrates were prepared. Exact specimen curvatures and an analytical method were used to estimate residual stresses and the behaviour of the epoxy layer. X-ray diffraction stress measurement (XRD) was performed to determine the interfacial stress state. In addition, a method was developed to examine the interface fracture toughness of the specimens. Based on the results, the residual stress estimation at the interface was confirmed and the effect of the surface treatments on the interface fracture toughness was evaluated.

X-Ray Diffraction Measurements for Riveted Joints. The Application of a Novel Methodology

The X-ray diffraction method is the best, widely available, non-destructive measurement method used to determine the residual and load stresses in crystalline materials. This method can be applied without any limitations to flat specimens. Depending on the equipment geometry, the type of material and geometry of the specimen, there are many limitations, restrictions and recommendations which have to be fulfilled to obtain reliable results. This was the reason for working out a methodology for X-ray diffraction stress measurements for riveted specimens.The first case to analyze is the necessity of choosing an X-ray tube suitable for the specimen material which will give the diffraction peaks in the range of 2Θ angles between 120° and 180°. Afterwards it is crucial to make the best selection of Bragg’s angle 2Θ. In the vast majority of cases the best selection is the possibly biggest 2Θ angle because of the best accuracy of the measurement. However, for example for aluminum alloys (for CrKα radiation), this choice is not so obvious. It is much more convenient to perform measurements not for the highest diffraction angle. The best selection in this case is 2Θ=139,3°, and not 156,7°. Other selections which are necessary to be made before

Diffraction Plane Dependence of Micro Residual Stresses in Uniaxially Extended Carbon Steels

In the stress measurement using X-ray or neutron diffraction, an elastic anisotropy as well as a plastic anisotropy of crystal must be carefully considered. In the X-ray and neutron diffraction stress measurement for polycrystalline materials, a particular {hkl} plane is used in measuring lattice strains. The dependence of an X-ray elastic constant on a diffraction plane is a typical example caused by an elastic anisotropy of the crystal. The yield strength and the work hardening rate of a single crystal depend on a crystallographic direction of the crystal. The difference in the yield strength and the work hardening rate relating to the crystallographic direction develops different residual stresses measured on each {hkl} diffraction after plastic deformation of a polycrystalline material. The present paper describes the result of the neutron stress measurement on uniaxially extended low and middle carbon steels. A tri-axial residual stress state developed in the extended specimens was measured on different kind of {hkl} diffraction plane. The measurement on the {110}, {200} and {211} diffraction showed that residual stresses increased with increasing the plastic elongation and the residual stresses on {110} were compressive, {200} were tensile and those on {211} were the middle of the former two planes. Received: 30 September 2010; Revised: 28 October 2010; Accepted: 1 November 2010

Depth and Lateral Variation of Machining-Induced Residual Stress for a Nickel Base Superalloy

This paper investigates the variation of residual stress with depth and radial location in a nickel base superalloy, RR1000, introduced by face finish turning. X-ray diffraction stress measurement has revealed that the hoop stress at the surface becomes less tensile towards the centre of the face, whilst the level of radial sub-surface compression increases. The unstrained lattice spacing d0 and the diffraction peak width (FWHM) were used to make inferences regarding the thermal excursion and the plastic work, respectively. It was found the increase in the compressive stress from the outer towards the inner radius was associated with an increase in thermal excursion.

Effects of Ultrasonic Deep Rolling on Fatigue Performance of Pre-Corroded 7A52 Aluminum Alloy

The effects of ultrasonic deep rolling (UDR) on the fatigue behavior of pre-corroded 7A52 aluminum alloys were investigated. By means of X-Ray diffraction stress measurements and scanning electron microscopy (SEM), residual stress and fractograph of 7A52 aluminum alloys with and without UDR treatment were analyzed. The results indicated that the UDR produced compressive residual stresses with depth approaching 1mm. UDR treatment can extend the fatigue life of the pre-corroded 7A52 specimens to a large extent, depending on the level of corrosion and UDR parameter. For the slightly corrode specimens, the UDR treatment changed the fatigue crack nucleation site from surface to the transition zone between the compressive residual stresses and tensile stresses, resulted in a much longer fatigue life. For the severely corrode specimens, the crack still nucleated by intergranular cracking, however, due to the compressive residual stresses introduced and the closure of the corrosion pits and corrosion micro-crocks, UDR treatment still improved fatigue performance of the pre-corroded 7A52 aluminum alloy substantially.