To evaluate the state of macro- and micro-residual stresses in cold rolled materials of 0.2 to 3 mm thickness the following test methods were used: Measurements of lattice spacing in different directions (φ,Ѱ)with X-rays and neutron-rays on many diffraction peaks. The X-ray method was employed on the surface of the sheet and of the thinned piece after removing several layers from both sides. The neutron-ray method allows measurements in the interior of a specimen and the average of the strain distribution of the total cross section. The etching deflection method determines the macro-residual stresses. The calculation of the macro- anci micro-residual stresses using X-ray elastic constants (XEC) for polycrystalline material and the compliances of single crystals for groups of grains are described. Homogeneous and heterogeneous materials like steels, (α + β)-brass, nickel and copper with 3 % silver were investigated. The state of residual stresses on the surface and with the depth over the cross section was evaluated or is in the final process of investigation.

In the measurement of residual stresses via diffraction (using x-rays or neutrons) it is strains that are actually determined, by employing the interplanar spacing (dhkl) of the ﹛hkl﹜ planes as an internal strain gauge. The change in this spacing is measured from the shift of diffraction peaks (and Bragg's law) at several orientations of the sample to the incident beam, and the resultant strains are converted to stresses with the “diffraction elastic constants”, S1 (hkl) and S2 (hkl)/2. While these take on the values (- v/E) and (1 + v )/E respectively for an isotropic solid, in anisotropic materials their values depend on marry factors: preferred orientation, shape and orientation of second phases, interaction between grains. In fact there are reports of variation these constants with plastic deformation and theory predicts variations with morphology. While it is possible to calculate approximate values for these constants from theory and the single crystal elastic constants , Si and S2/2 are really not elastic constants in the strictest sense because or these other factors, and it is best to measure them. One of us (I. C. Noyan) has recently examined this problem in some detail , and we summarize his results here.

The oscillation from a linear relation in the 20 vs. sin2ψ diagram has been a most important problem in X-ray stress measurement. There are, therefore, a number of papers concerned with the X-ray elastic constant, lattice strains under stresses and evaluation of stresses of textured materials.

The purpose of the present study is to analyze the three-dimensional orientation distribution of steel sheets by means of the Vector method proposed by Ruer and Baro, and to calculate the elastic modulus of textured sheets by means of a finite element method (FEM) using the three-dimensional orientation distribution, and then to calculate the strain/stress ratios vs. the directions defined by the angles between the specimen normal and the normal to the diffracting planes.

Recent developments in position sensitive detectors (PSD's), solid state power and computer technologies make it possible to design accurate instruments for in-situ stress measurement. Such instruments require compromises in the interests of portability, size and speed stiich may limit accuracy and/or versatility. Furthermore, extraction of a stress tensor from X-ray data is not always straightforward and considerable research is required before an instrument for X-ray stress measurement can be treated as a “black box” to be given to an uneducated operator.

The development of a new instrument for in-situ stress measurement is described in this paper. It was conceived as a field instrument with two position-sensitive proportional counters (PSPC's) for use in the single exposure mode (SET), and incorporates precise angular qontrol of the incident X-ray beam and data analysis to eliminate irregular Bragg peaks owing to coarse grain structure, An experimental instrument was built tc test the concept (1).

X-ray residual stress analysis was performed on four space shuttle hydrogen pump impellers made from Ti-5Al-2,5Sn alloy. Five locations on the outer rim, near the vanes, were measured on each impeller, identified as #1, #2,#3, and #4. Impellers #1 and #4 were test-fired impellers, impeller #2 was a new impeller that had been spin tested, and impeller #3 was a new impeller that had not teen spin tested. The measurement locations on these impellers corresponded to areas of critical stress importance. The purpose of the measurements was to compare the stresses at these locations as a function of impeller processing variables. A description of the Impellers, the test parameters and procedures, stress analysis results, and a technical discussion of these results are presented in this report.

A description of the Impellers, the test parameters and procedures, stress analysis results, and a technical discussion of these results are presented in this report.

X-ray diffraction (XRD) utilizing copper K-alpha radiation and the single exposure technique (SET) was used for residual stress measurement on two different thermal treatments of Al-300 alumina rods. The measurements were performed in the axial and tangential directions on forty halves of twenty broken rods. The twenty rods were intially annealed for 8 hours at 1000°C; then ten were slow cooled and ten were equilibrated at 1450°C then force-air quenched. A fine mesh sapphire (alumina) powder was used as a zero stress standard for the determination of calibration validity of the position sensitive scintillation detector based (PSSD) stress measuring instrument used for this study. This instrument was developed at the Materials Research Laboratory of The Pennsylvania State University.

X-ray stress analyses were performed on seven (7) nickel-plated camshafts from helicopter transmissions. The purpose of this investigation was to determine if this residual stress technique was useful in determining the state of stress in load-bearing plated surfaces of critical reworked aircraft components. Specifically, it was desired to characterize six different stages of nickel plating processing. These were: as-plated, plated and baked, machined, machined and baked, ground, and ground and baked. Three different radiation wavelengths with different penetrations were used In this investigation. CrKα , CoKα , and CuKα, radiations were each used on all of the camshafts. These wavelengths were selected to determine if there were stress gradients in the plated layers. This paper presents and discusses the results of these studies.

XRD has been found to be a useful technique for investigating both surface and interior stresses in. adhesive bonded joints. For the interior stresses, to gain access to the joint interface, adherends were chosen such that one adherend was relatively transparent to the X-radiation used and the other was not. Incident X-rays then penetrated the first adherend and the adhesive, and were diffracted from just below the surface of the second adherend.

In prior work it was shown that the measured stresses due to an applied load agreed quite well with stresses calculated for the same joint using the TEXGAP-2D finite element program, except at one extremity of the bond. One explanation proposed for the discrepancy was that a small debond was present at this extremity. In the present study, therefore, an investigation was made of a joint contfli'nitig an intentional debond at this extremity.

The X-ray fractographic technique was applied to fatigue fracture surfaces of tempered AISI 4340 steel. Residual stresses and half-value breadths were measured by the X-ray diffraction.

In the present paper, the residual stresses and plastic strains on fatigue fracture surfaces and some parameters in the fracture mechanics were investigated. A simple model of mechanics was proposed to explain these experimental results.

Silicon carbide and 6061 aluminum alloy possess very different thermalexpansion coefficients; 3-3 and 22.5.10-6K-1, respectively. Thus, one expects large internal strains and stresses in these composites because the two constituents form interfacial bonds at high temperatures and are cooled to ambient temperatures. From a simple elastic model, one expects a hydrostatic tensile stress in the aluminum matrix and a-hydrostatic compressive stress in the silicon-carbide particles. Using conventional diffraction geometry, using Cu Kα radiation, we studied three surfaces of a plate specimen. For both phases, we determined the unit-cell dimensions for two situations: unmixed and mixed in the final composite. The silicon-carbide particles showed a compressive stress and the aluminum matrix a tensile stress, seventy-five percent of the yield strength. Measurements show that both stress tensors are approximately hydrostatic.

Knowledge of the errors in a diffraction measurement of residual strains and stresses is useful information, not only in its own right, but also because it permits automation of a measurement to an operator-specified precision. There are three sources of these errors.

Of major importance in the determination of residual stress via diffraction is the accuracy of the measurement of the scattering angle (2 θp) of a Bragg peak. This determines the accuracy of the interplanar (d) spacing and hence the strain and stress. In the U.S., the most commonly accepted method of determining peak position is a parabolic fit near the top of a peak. (While a diffraction peak is not parabolic, this is a satisfactory function near the maximum.) The error in this procedure has been derived and tested, and it has been shown that a multipoint fit with a least 7 points is rapid and as precise or more precise than the centroid, the bisector of the half width, or cross correlation, except for sharp peaks in which case the centroid or cross correlation are slightly better. Thus a parabolic fit is generally useful and, since a least-squares fit to this function is readily carried out on modem micro-processors, automatical of a stress measurement is possible, including evaluation of errors.

The fitting of a parabola by least squares regression to the upper portion of diffraction peaks is commonly used for determining lattice spacing in residual stress measurement. When Kα techniques are employed, the presence of the Kα doublet is shown to lead to significant potential error and non- linearities in lattice spacing as a function of Sin2ψ caused by variation in the degree of blending of the doublet. An algorithm is described for fitting Pearson VII distribution functions to determine the position of the Kα component, eliminating errors caused by defocusing of diffraction peaks of intermediate breadth. The method is applied to determine the subsurface residual stress distribution in ground TI-6 AI- 4 V, comparing directly the use of parabolic and Pearson VII peak profiles, and is shown to provide precision better than ± 1%% in elastic constant determination.

It is well known that all of the six independent components of the strain tensor can be calculated if the linear strains in six appropriate directions are known (e.g.). That calculation is to solve a system of linear equations, whose coefficients are defined by the orientations of the measured planes. The strains are determined by lattice plane distance measurements using X-rays.

The linear equation system can only be solved if the matrix of coefficients has rank. Whether this condition is met or not can be decided without calculating a determinant just from geometric relationships among the planes to be measured. A demand beyond that necessary condition is to make the matrix of coefficients so that the accuracy of the calculated strain tensor is best. From error calculation we know that there exist distinct ratios between the inevitable measurement errors and the errors of the calculated strain components. These ratios depend strongly on the geometric relationship among the lattice planes. It is the purpose of this paper to show how lattice planes should be chosen in order to get these ratios as small as possible i.e. to get a maximum of accuracy at a given number of measurements, or a minimum of experimental effort if a distinct limit of error is to be reached.

The General Purpose Powder Diffractometer (GPPD), a high resolution (∆d/d=0.002) time-of-flight instrument, exhibits a resolution function that is almost independent of d-spacing. Some of the special properties of time-of-flight scattering data obtained at a pulsed neutron source will be discussed. A method is described that transforms wavelength dependent data, obtained at a pulsed neutron source, so that standard structural least-squares analyses can be applied. Several criteria are given to show when these techniques are useful in time-of-flight data analysis.

Irregular backgrounds in time-of-flight neutron powder diffraction data and nonlinear backgrounds in angle dependent neutron powder diffraction data. were corrected by fitting fifth degree polynomials to those portions of the data most affected. The anomalous background intensities were in both cases due to non Bragg scattering. The polynomial fitting was carried out over a sufficiently widerange of the profile to avoid interfering with the Bragg peaks. The corrected data gave internally consistent results for the crystallographically nonequivalent (Si,Al) -0 (1) and(Si, Al) -0 (2) bond lengths in zeolite rho and compare favorably with previous refinements of this Zeolite in space group Im3m. Internal and external in consistencies of bond lengths are just as diagnostic of refinement difficulties as negative isotropic temperature factors or non positive definite an isotropic temperature factors are.

Rietveld profile refinements using high-resolution pulsed neutron povder diffraction data, collected at IPNS, often reveal broad intensity contributions from sources other than the crystalline materials being studied. Such non-crystalline intensity hampers standard Rietveld refinement, and its removal and/or identification is imperative for successful refinement of the crystalline structure. A Fourier-filtering technique allows removal of the non-crystalline scattering contributions to the overall scattering pattern and yields information about the noncrystalline material. In particular, Fourier transformation of residual intensities not accounted for by the Rietveld procedure results in a real-space correlation function similar to a radial distribution function (RDF). From the inverse Fourier transform of the correlation function a Fourier-filtered fit to the diffuse scattering is obtained. This mathematical technique was applied to data for crystalline quartz, amorphous silica, and to a simulated diffraction pattern for a mixture of the two phases.

A neutron powder diffractometer at the University of Missouri Research Reactor (MURR) uses a linear position sensitive detector (PSD) which has increased both resolution and data acquisition rates. Rietveld analysis works as well with this system as with more conventional single and multi- Soller slit detector systems. This analysis has been successfully applied to problems involving more than 75 parameters and 1200 reflections and a future instrument upgrade should allow analyses which involve 100-150 parameters. A special advantage of the PSD instrument is that it needs only small (1-2 gm) samples to achieve high statistical accuracy.