Stress-free Lattice Spacing Research Articles

Neutron transmission strain tomography for non-constant stress-free lattice spacing

Recently, several algorithms for strain tomography from energy-resolved neutron transmission measurements have been proposed. These methods assume that the stress-free lattice spacing d0 is a known constant limiting their application to the study of stresses generated by manufacturing and loading methods that do not alter this parameter. In this paper, we consider the more general problem of jointly reconstructing the strain and d0 fields. A method for solving this inherently non-linear problem is presented that ensures the estimated strain field satisfies equilibrium and can include knowledge of boundary conditions. This method is tested on a simulated data set with realistic noise levels, demonstrating that it is possible to jointly reconstruct d0 and the strain field.

The Determination of Residual Stress in Quenched and Cold-Compressed 7050 Aluminum Alloy T-Section Forgings by the Contour Method and Neutron Diffraction

Residual stresses were determined through the thickness of quenched and quenched followed by cold compression 7050 aluminum alloy T-section forgings using the contour method and neutron diffraction. 7050 T-section forgings are used for the manufacture of the connecting joints of wing and fuselage. Inevitably high residual stresses are introduced during the quenching process of 7050 T-section forgings, which could be reduced by cold compression to overcome the effect of residual stress on machining deformation. The longitudinal residual stresses obtained by the two techniques achieved good agreement in both trend and magnitude in both the quenched and quenched followed by cold compression 7050 T-section forgings. The stress-free lattice spacing of Al(311), the Bragg reflection used for the neutron measurements, was obtained from a 5-mm slice using the plane-stress condition, and its variation through the thickness is insignificant in both the quenched specimen and quenched followed by cold compression specimen. A comparison of the residual stresses in the quenched specimen and quenched followed by cold compression specimen showed significant changes in range of residual stresses from (− 304, 262 MPa) induced by quenching process to (− 125, 142 MPa) due to 3% cold compression. The percentage reduction in residual stress in the quenched specimen due to 3% cold compression was (46, 59%).

Investigation of residual stress distribution and texture evolution in AA7050 stationary shoulder friction stir welded joints

A study of the residual stress distribution and texture evolution in stationary shoulder friction stir welded (SSFSW) AA7050 plate through non-destructive energy-resolved neutron imaging (NI), monochromatic neutron diffraction (ND) and destructive contour method (CM) is described in this paper. The presence of Bragg edges in the neutron transmission spectra are shown to be effective in determining the longitudinal residual stress and compare well with results obtained by ND and CM. The texture in the weld zone and base metal has been mapped by contrast in the narrow-energy transmission image combined with an analysis of the Bragg edges in the transmission spectra at each pixel showing agreement with the results obtained by electron backscatter diffraction (EBSD) mapping. The ND results were complicated by plastic anisotropy effects in the rolled plate which meant that different reference stress-free lattice spacings were required at each point in the 3 principal directions for this material. NI and CM were unaffected by texture effects in determining residual stress. Compared to conventional techniques, NI is shown to be an effective way of quantifying both texture and residual stress in one shot.

Residual stress analysis in linear friction welded in-service Inconel 718 superalloy via neutron diffraction and contour method approaches

In this study, an analysis of elastic residual stress in Inconel® 718 (IN 718) linear friction welds (LFWs) was carried out. In particular, the suitability of LFW for manufacturing and repair of aero engine components was emulated by joining virgin and in-service (extracted from a turbine disk) materials. The evolution in the residual strains and stresses in the heat-affected zone (HAZ), thermomechanically affected zone (TMAZ) and dynamically recrystallized zone (DRX) of the weld was characterized using the neutron diffraction and contour methods.The results provided insight into diverse challenges in quantitative analysis of residual stresses in welded IN 718 using diffraction techniques. Specifically, judicious selection of the beam width, height and stress-free lattice spacing were seen to be crucial to minimize measurement error and increase accuracy. Further, the contour method – a destructive technique relying on capturing the stress relaxation after electrical discharge machining – was used to characterize the residual stress distribution on two-dimensional plane sections of the welds. Both techniques suggested an increasing magnitude of residual stress originating from the base metal that reached a peak at the weld interface. Both methods indicated that the peak magnitude of residual stresses were below the yield stress of IN 718.

Residual stress mapping in Inconel 625 fabricated through additive manufacturing: Method for neutron diffraction measurements to validate thermomechanical model predictions

The rapid solidification and subsequent thermal cycles that material is subjected to during additive manufacturing (AM) of a component result in a buildup of residual stresses, which lead to part distortion, and negatively impact the component's mechanical properties. We present a method for using neutron diffraction to validate thermomechanical models developed to predict the residual stresses in Inconel 625 walls fabricated by laser-based directed energy deposition. Residual stress calculations from neutron diffraction measurements depend strongly on the determination of stress-free lattice spacings. After measurement of stressed lattice spacings in Inconel 625 walls, reference samples were obtained by extracting thin slices from the walls and cutting comb-type slits into these slices. Reference lattice spacings were measured in these slices, as well as equivalent slices that were also subjected to stress-relieving heat treatment. These heat treatments changed the reference lattice spacings, and therefore affected residual strain measurements. Further, this study shows the importance of using location-dependent reference lattice spacing, as during AM, the thermal history, and therefore elemental composition and stress-free lattice spacing, vary with position. Residual stresses measured by neutron diffraction along the build direction using comb-type reference samples without heat treatment were in good agreement with thermomechanical modeling predictions.

Phase-specific deformation behavior of a NiAl–Cr(Mo) lamellar composite under thermal and mechanical loads

Phase-specific thermal expansion and mechanical deformation behaviors of a directionally solidified NiAl–Cr(Mo) lamellar in situ composite were investigated by using real-time in situ neutron diffraction during compression at elevated temperatures up to 800 °C. Tensile and compressive thermal residual stresses were found to exist in the NiAl phase and Crss (solid solution) phase, respectively. Based on the evolution of lattice spacings and phase stresses, the phase-specific deformation behavior was analyzed qualitatively and quantitatively. Estimates of phase stresses were derived by Hooke's law on the basis of a simple method for the determination of stress-free lattice spacing in in situ composites. During compressive loading, the NiAl phase yields earlier than the Crss phase. The Crss phase carries much higher stress than the NiAl phase, and displays consistent strain hardening at all temperatures. The NiAl phase exhibits strain hardening at relatively low temperatures and softening at high temperatures. During unloading, the NiAl phase yields in tension whereas the Crss phase unloads elastically. In addition, post-test microstructural observations show phase-through cracks at room temperature, micro cracks along phase interfaces at 600 °C and intact lamellae kinks at 800 °C, which is due to the increasing deformability of both phases as temperature rises.

Investigation of Triaxial Stress State in Retained Austenite during Quenching of a Low Alloy Steel by <i>In Situ</i> X-Ray Diffraction

In situ XRD measurements were performed at ESRF, Grenoble, France (ID11) during quenching of a ball bearing steel AISI 52100 (100Cr6) with varying carbon content in solution. The evolution of austenite lattice parameter during cooling is nearly linear until Ms is reached and then, a divergent behavior can be observed. Assuming that the extrapolation of the linear range to room temperature gives the stress-free lattice spacing, an increasing compressive hydrostatic stress state is resulting. A strong effect of the carbon content was found. These results were confirmed by theoretical calculations based on data from the literature.

Distortion and residual stress measurements of induction hardened AISI 4340 discs

10 Induction hardened discs with two initial hardness levels were used for exploring the influences of the variation of initial hardness as well as induction hardening (IH) recipes on the heat treatment distortions and hardening depth. The results show that for the same initial hardness, the larger the energy input, the higher the distortion size as well as the hardening depth. For a given induction hardening recipe, the increase in initial hardness leads to a deeper hardening depth but a smaller distortion. One disc was selected for the residual stress investigation in three orthogonal directions by neutron diffraction (ND). The corresponding stress-free lattice spacing d0 was measured from the same material using both ND and X-ray diffraction (XRD) methods. The ND results show that the variation of d0 in the hardened layer is significant and should be taken into account for stress calculation. However, regarding the core region, the d0 value measured by XRD is more reliable. Accordingly, a combination of the ND-measured d0 profiles in the hardened layer and the XRD-measured d0 value in the core was adopted for the determination of residual stress distributions.

Evaluations of stress-free lattice spacings and residual stresses in a quenched carbon steel cylinder using neutron diffraction

Microstructure-dependent stress-free lattice spacings (d0) were measured using neutron diffraction in a comb-like specimen fabricated from a quenched carbon steel cylinder. The d0 values increased with cylinder radius due to the increase in the martensite (α′) fraction with the radius and were comparable to d0 values calculated using the lattice parameter of each phase, taking the auto-tempering effect into consideration. Using the measured d0 values, we suggested a relationship between the d0 and α′ fraction and evaluated macroscopic residual stresses in the quenched steel cylinder.

Effect of spatial variation of stress-free lattice spacings on measured residual stresses

When neutron diffraction is used to measure residual stresses, estimates of the unstressed lattice spacing ( d0) are often required. These are generally measured on a sample that is considered representative of the component. In the case of welded samples, the possibility of variation in weld shape between the d0 sample and the area where stresses are determined must be taken into account. To assess this, d0 values are measured on an area considered representative of the sample, and then are re-measured on a sample cut from the actual strain measurement plane. The residual stresses are re-calculated with these new d0 values and the results compared to those based on the initial d0 measurement. Methods of estimating these errors are discussed. The errors in residual stress that arise from the spatial variation of d0 values are greater than the commonly reported peak fitting errors. These errors can be estimated and should be included in the reported residual stress measurements. Cutting a d0 sample from the measurement plane makes this a destructive technique.

Improved procedure for computing residual stresses from neutron diffraction data and its application to multipass dissimilar welds

Neutron diffraction is an important tool for residual stress measurement in welded structures. The calculation of stresses from measured lattice spacings generally requires the stress free lattice spacing a priori. For dissimilar metal welds common to nuclear reactor pipeline systems, the stress free lattice spacing is a complex function of position due to the chemistry and microstructure inhomogeneity in the weld region, and its experimental determination can be both time consuming and unreliable. An improved approach is developed to calculate the residual stress field without the use of stress free lattice spacing. Its applicability is examined and justified in two multipass dissimilar metal welds made of 304L stainless steel plate and nickel alloy 82 filler metal using different heat inputs. The spatial variation in stress free lattice spacing is qualitatively discussed using the weld metal dilution mechanism. The improved approach is shown to be simple and practical for residual stress determination in dissimilar metal welds.

Lattice Plane Spacing Change in Hardened Layer of Chrome Molybdenum Steel after Carburizing and Quenching

Block specimens of chrome molybdenum steel with 0.20 mass% C, SCM420, were carburized in carrier gas and quenched in oil bath. The hardness and carbon content gradients in the hardened layer were measured experimentally. The carburized surface of one block specimen was gradually removed by electrolytic polishing. Ten thin plates were cut from the total case depth of the other block specimen. An experimental method to determine the stress-free lattice plane spacing of the hardened layer was examined using x-ray and neutron radiations. As a result, the stress-free lattice plane spacing change in the hardened layer could be determined successfully by measuring neutron diffraction peaks from Fe-211 of the thin plates during rotating ±90° around the specimen axis. Using x-ray, the stress-free lattice plane spacing at the carburized surface could be also determined by measuring the 2θ-sin2ψ diagrams of either removed surface of block specimen or thin plate. However, under the carburized surface, the Kα2 diffraction from the heat-treated eutectoid phase was superimposed on x-ray diffraction peak because the subsurface microstructure was composed of martensitic and heat-treated eutectoid phases. The stress-free lattice plane spacing under the carburized surface could not be determined using x-ray. Furthermore, the stress-free lattice plane spacing of Fe-211 was found to decrease with increasing the distance from the carburized surface and be expressed by the cubic function of the carbon content in the hardened layer.

Combined Neutron and X-Ray Diffraction Analysis for the Characterization of a Case Hardened Disc

The present work has been executed within the framework of the collaborative research center on Distortion Engineering (SFB 570) in order to evaluate the residual stress state of a disc after carburizing and quenching as well as to validate a simulation procedure. The combined use of X-ray and neutron diffraction analysis provided information about the residual stress states in the whole cross section. However, the stress free lattice spacing d0 for the neutron diffraction experiments is problematic and induces systematic uncertainties in the results and the application of a force balance condition to recalculate d0 might be a solution for improving the reliability of the results. Comparison of experimental results with simulation showed that an overall satisfying agreement is reached but discrepancies are still present.

Residual stress measurements on a stress relieved Zircaloy-4 weld by neutron diffraction

The macroscopic stress distribution across an annealed Zircaloy-4 gas tungsten arc weld was measured by neutron time-of-flight diffraction at the SMARTS diffractometer at Los Alamos National Laboratory. The stresses after annealing are about 40% lower than those in the same weld prior to heat treatment. The intergranular strains in the reference coupons, which give the macroscopic stress free lattice spacings, are consistent with the difference in cooling the strongly textured plate and the weakly textured weld.

Study of the Residual Strain in Lap Joints

Both experiments and finite element analysis were carried out to study the residual strain (stress) in the riveted lap joint for a better understanding of the fatigue life of fuselage lap joints. A force-controlled riveting process was used to apply a constant load ramp to install the rivets. Strain variations on the joint surface were measured using microstrain gauges during the riveting process. Because neutrons are known to penetrate through many centimeters of aluminum alloys, neutron diffraction was used to provide a nondestructive technique to determine strains at certain depths in the joint. Parallel to the experimental testing, a two-dimensional axisymmetric finite element model was developed to simulate the riveting process. Both material and geometric nonlinearities, as well as nonlinear contact boundary conditions, were used in this numerical model. Comparisons between the numerical simulations and experimental results focused on the rivet driven head deformations and strain variations, and the results showed that the current two-dimensional axisymmetric finite element model using the proper boundary conditions can reliably be used to determine the residual strains (stresses) present in joints that were induced during the riveting process. Nomenclature C = material parameter D = rivet shank diameter Dmax = maximum rivet shank diameter after riveting d = spacing between lattice plane d0 = stress-free lattice spacing E = Young’s modulus m = material parameter r = distance to fastener hole centre e = normal strain etrue = true strain θ = diffracted neutrons’ angle λ = wavelength of the incident neutron beam ν = Poisson’s ratio σ = normal stress σtrue = true stress beyond the initial yield stress σy = initial yield stress

Principle and Method of X-Ray Computer Tomography on Residual Stress Measurement

X-ray computer tomography for non-destructively measuring residual stress with depth resolution was suggested to aim at improving of traditional X-ray stress analysis in this paper. Based on higher penetrating capacity of X-ray in low atomic order materials it could non-destructively measure three-dimensional residual stresses and calculate the stress free lattice spacing, d0, by current X-ray stress analyzer with taper slits. The evaluation of reliable results were controlled by three criteria, linear correlation coefficient, R, Poisson’ ratio, ν, and the stress free lattice spacing, d0. Finally, the residual stresses in the axial direction around the weld of arc Beryllium weldment could be calculated by this method.

Development of New Stress Measurement Method Using Neutron Diffraction

In this study, we proposed the high-versatility stress measurement method using neutron diffraction which can determine the residual stress states by measuring the lattice strains in two or three orthogonal directions even if the measured diffraction families were different in all three directions. In addition, we also proposed the stress measurement method without using the stress-free lattice spacing d0 which was measured using the powder sample or annealed sample. To verify this method, the residual stress distributions in a shrink-fit ring and plug specimen of aluminum alloy A7075 with texture were measured. The profile of the measured stress distributions almost agreed with the simulated stress distributions in the assumption of the plane stress condition. Our method which can determine the tri-axial stress states using observed lattice strains in two orthogonal directions was secondly applied to evaluate the stress states of A7075, high tensile strength steel HT1000, and Ni-base alloy NCF600 loaded in-situ. Measured stresses almost agreed with theoretical value with 10 MPa to 60 MPa error. On the other hand, the residual stress states of NCF600 were measured under the uni-axial loading condition by the stress measurement method without using the measured d0. Estimated lattice constant a was almost agreed with the lattice constant of its annealed sample, and changes in stress states evaluated using the proposed method coincided with the theoretical value.

Residual Stresses in Linear Friction Welded IMI550

Residual stresses in linear friction welded (LFW) IMI550 have been determined by means of high energy synchrotron X-ray diffraction. Specimens were studied in the as-welded, and three different post weld heat treated conditions. Mid-thickness-mid-width line scans were recorded across the weld line in the three principal directions of the welds. For calculating the nominal residual strain the stress-free lattice spacing was taken from far field measurements. The separation of a chemical induced and strain induced shift of the reflection was carried out by determining the variation of the d-spacing across the weld line. This was done on thin slices cut from the centre region of a LFW sample using the biaxial sin2 ψ-technique on a collimated laboratory X-ray source. Results show large tensile stresses close to the weld line for the as-welded sample and the sample post weld heat treated at the aging temperature typical of IMI550. Moderate residual stresses were observed after increasing the post weld heat t...

OS04W0182 Neutron diffraction study of residual stress in the induction hardened S45C round bar

The thermal residual stress at the internal positions of central circular sectional plane of an induction hardened S45C round bar was measured nondestructively by neutron diffraction. The neutron diffraction equipments, RESA installed at JRR-3M reactor and Sirius at KENS were used. We observed the SEM image of the sliced specimen cut from the round bar to investigate the existence of martensitic phase. The sliced specimen was also used for the determination of the stress free lattice spacing in the case of coexistence of martensitic phase and ferritic phase. The Young's modulus and the Poisson ratio were obtained by the neutron diffraction of the specimen for tension test. As a result, the residual stress for radial direction at the surface of the bar is nearly equal to zero, and those for hoop and axial directions are near -900 MPa, which is largely compressive. These three stresses gradually increase to tensile one as we approach the center of the sectional plane. These results show a good coincidence with the result of FEM analysis.

Neutron-diffraction measurements of stress

Experiments on bent steam-generator tubing have shown that different diffraction peaks, (1 1 1) or (0 0 2), give different results for the sign and magnitude of the stress and strain. From an engineering standpoint, the macroscopic stress field cannot be both positive and negative in the same volume, so this difference must be due to intergranular effects superposed on the macroscopic stress field. Uniaxial tensile test experiments with applied stresses beyond the 0.2% offset yield stress, help to understand this anomaly, by demonstrating the different strain response to applied stress along different crystallographic axes. When Zr-alloys are cooled from elevated temperatures, thermal stresses always develop, so that it is difficult to obtain a stress-free lattice spacing from which residual strains may be derived. From measurements of the temperature dependence of lattice spacing, the temperature at which the thermal stresses vanish may be found. From the lattice spacing at this temperature the stress-free lattice spacings at room temperature can be obtained readily. To interpret the measured strains in terms of macroscopic stress fields it is necessary to know the diffraction elastic constants. Neutron diffraction measurements of the diffraction elastic constants in a ferritic steel for the [1 1 0], [0 0 2] and [2 2 2] crystallographic axes, in directions parallel and perpendicular to the applied stress are compared with theoretical diffraction elastic constants.