MEASUREMENTS OF RESIDUAL STRESSES IN A SHAPE WELDED STEEL TUBE BY NEUTRON AND X-RAY DIFFRACTION

Shape welding of a ferritic steel layer on an austenitic steel tube is used to build compressive stresses on its outer surface, and as a result, suppress stress corrosion. Investigations of residual stresses in such bi-layer tubes are important for developing optimal welding techniques. The neutron and X-ray diffraction methods were used to analyze the stress behavior around the welded region on the tube. To this end, strain components in the radial, axial and tangential directions were measured across the weld. The results are compared to the data obtained by the destructive turning out technique and theoretical predictions by the finite element method.


INTRODUCTION
Shape welding is an interesting alternative method, but the existence of uncontrollable residual stress distributions in welded materials prevents its many applications.On the other hand, shape welded ferritic layers on austenitic tubes can help to suppress stress corrosion because these layers produce the compressive stress states on the austenitic tube.The analysis 232 H. KOCKELMANN et al.
of residual stresses through the ferritic weld into the austenitic material can be helpful for the optimization of the corresponding welding tech- nique.In this article, the stress state in shape welded tubes is analyzed by the nondestructive neutron and X-ray diffraction methods and is com- pared to the data obtained by the destructive turning out technique and theoretical predictions of calculations by the finite element method.

THE SAMPLE
Seven layers of ferritic steel 3NiMo 1UP with 135 welding traces and a total length of 1100 mm were welded on a 15 mm thick tube from the austenitic steel X6CrNiTi 1810with an outer radius of 148 mm.The outer radius ofthe manufactured bi-layer tube was 168 mm.For measurements a test specimen was prepared.First, a segment (200 mm long, 70 of arc circumference) was cut from the manufactured tube.With the extensi- ometers in the middle of the segment oriented in the axial and circum- ferential (tangential) directions, the effect of stress release was measured at the inner and outer edges ofthe segment (see Table I).This sample was further simplified bycutting a smaller segment measuring 10 and 12.5 mm along the inner and outer tube walls, respectively, by 30 mm along the tube axis.The radial dimension of the sample was 35 mm.
Parameters of materials, including elastic constants, tensile strength, and hardness were obtained by cutting test specimens.Austenitic steel was found to have E 176 GPa, u 0.3, Rm 536 MPa and the hard- ness 155 HV10.For a ferritic welded material, the average values E= 205 GPa, u=0.3, Rm--695 MPa and the hardness 200 HV10 far from the transition region, where its value reaches 380 HV 10 were found.
By destructive testing methods, such as the hole drilling and turning out techniques residual stresses were determined in different points of the tube.Later, these results will be compared to the results of neutron and X-ray diffraction investigations.

NEUTRON MEASUREMENTS
The neutron strain measurements of the described sample were per- formed on the High Resolution Fourier Diffractometer (HRFD) at the IBR-2 pulsed reactor in Dubna (Aksenov et al., 1993).The HRFD is equipped with a Fourier chopper.This chopper modulates the IBR-2 thermal neutron pulse with the initial width 320 ls.The modulation is performed with the frequency from 0 to 150kHz.The resulting minimum width is 7 ts.The neutron energy is determined by the reverse time-of-flight method on the 20 rn flight path.At present, HRFD has four detectors: DOR-1 and DOR-2 backscattering detectors at the scattering angle +/-152 and DPR-1 and DPR-2P detectors at the angles 4-90.Although DORs are mainly used for precision structural investigations with the resolution about 0.1%, a number ofexperiments to measure residual stresses in different materials were conducted with this detector as well (e.g.Aksenov et al., 1994).Two other detectors are mainly used for residual stress measurements.The resolution Ad/d of these detectors (dis the lattice interplane spacing and Adis the halfwidth of the Bragg reflex) was 0.4-0.5% at d-2, at the maximum modulation frequency 50 kHz.Strain scanning to the depth 2 mm from the sample surface with the area 35 x 30 mm the was conducted with the help of a 4-axes translator.Both radial (x-axis) and tangential (y-axis) strain components along the radial direction were measured simultaneously using two detectors at the scattering angles 4-90.To form the direct beam, a boron nitride (BN) diaphragm with a slit 2 mm wide by 20 mm high (z-axis) was installed at the exit of a mirror neutron-guide.To set the scattered beams at 4-90 BN-diaphragms with the 2 mm slit width were installed at the distance 42 mm from the center ofthe diffractometer.The gauge volumes formed by these diaphragms were 2.1 x 4.5 x 19.4 and 2.1 x 2.6 x 19.4 mm 3 for DPR-1 and the DPR-2P detectors, respectively.
In Figs. and 2, DPR-1 diffraction spectra from the inner and outer sides of the tube are shown.The characteristic minimums at the peak bases are determined of the particularity of the spectra's registration on Fourier diffractometer.In both cases, four reflexes were observed in the 7-as well as in the a-phases.Processing of these spectra by the Rietveld method revealed noticeable texturation ofthe sample in the --phase.The (200) Bragg reflex over the interval of channels from 1710 to 2000 in

FIGURE
The spectrum of the investigated sample in the 7-phase measured wit.hDPR-1 for 4 h.As a result of Rietveld fitting, the cubic lattice constant a= 3.5909(1)A was obtained.700 o z lOO t881-13s.h,DPR-1 of HRFD 4 hours, x:18.ram, y,,1.83mm alpha-phase, sample N 2el Fig. had the intensity nearly 8 times higher than the calculated value for randomly oriented grains.This peak was omitted in the fitting procedure.Practically no texturation was found in the a-phase.
Finding of all available peak positions in the measured spectra allows strain to be evaluated, if the stress-free reference values of the lattice spacing d kt are known.However, there were some difficulties in deter- mining the values of these quantities.We tried to determine do kt using powder samples from the austenitic steel part of the tube as well as welded material.It looked as if these powders did not provide stress-free reference states of the tube constituents.Filling and annealing of these materials might cause structural changes and falsify the do kt values, e.g. the martensitic phase could be built during the cold forming process of austenitic steel.In the welded ferritic material the carbon content can be changed and, hence, do kt can be altered.In such an unclear situation, the so-called boundary (edge) values measured far away from the transitional layer were used as free-stress spacings (see Table II).
We have estimated the strain in the ferritic part of the investigated shape welded tube (a-phase) and for the austenitic region of the speci- men (-),-phase) for different orientations of the scattering vector Q available from the neutron diffraction experiment on HRFD.To clarify the role of grain interaction stresses (residual stress of II kind see Pintschovius, 1992), the character of the dependence of the strain on the orientation factors I' is investigated.In the case of the cubic lattice, the orientation factor is F (h2k 2 d-h212 if-k212)/(h 2 -t-k 2 d-12)2.As is seen from Fig. 3, the strain values vary nonlinearly as the factor F varies.This points to the presence of strong grain interaction stresses.Unfortunately, this circumstance causes some difficulties in the analysis of the macroscopic stress state, i.e. the residual stress of I kind is diffi- cult to be extracted in this case.FIGURE 3 The dependence of the strain values in the radial and tangential direc- tions on the orientation factor P for the inner wall of the austenitic steel tube (x 10.5 mm).The d are calculated from the lattice constant obtained by Rietveld fitting (see Fig. 1).In the position x =-5.5 mm, the difference between two strain components is shown.
Because of the difficulties in measuring microstresses, the choice of reflexes for the evaluation ofmacrostresses in each phase is a subject for discussion.In the following, pairs ofreflexes for the c-and-),-phases with equal orientation factors F will be picked up (see Table II).Thus, the appearance ofuncontrollable fluctuations due to plastic anisotropy will be prevented.Good results for all scanned positions were obtained only for (200)-reflexes (F 0).Therefore, these reflexes will be used in the further discussion.In Fig. 4, the results for (200) reflexes are summarized.
In the general case, the obtained data are insufficient for the cal- culation of residual stresses.However, if we assume that the x-, y-, and z-axis are the principal axes for the stress tensor of the investigated sample, the components of the tensor can be calculated by the formula (in the elastic model approximation): where r, t, a indicate the radial, tangential and axial directions of the scattering vector Q.Since the axial component was not measured in the experiments, we can calculate only the difference between the tangential -15 -10 -5 0 5 10 15 20 X, mm FIGURE 4 The dependence of the radial and tangential components of the strain e on the location of the gauge volume x for (200) reflexes with the orientation factor I'--0 as measured with the DPRol and DPR-2P detectors for the investigated sample in the a-and the 7-phases.The position x =0 corresponds to the transition layer between the austenitic and ferritic parts of the sample.
and radial components of the stress tensor: E ttY O't tYr d- (et e). (2) Using this formula we are calculated the stress difference in the tan- gential and radial directions obtained from the neutron data in dependence on the gauge volume location.Comparing this result with that by the destructive turning out technique applied to an uncut tube, the stress release during cutting has to be accounted for (see Table I).Assuming that the released stress varied linearly over the interval from the outer to the inner edge and that the radial component did not change essentially during cutting, the residual stress in the uncut tube can be predicted from the neutron diffraction data.The corrected neutron results are shown on Fig. 5. Also, on Fig. 5 the theoretical estimate of the stress state by the finite element method is presented.
For the ferritic part of the tube, good agreement of the neutron result with the theoretical and turning out results can be found.For the aus- tenitic side, disagreement is certainly related to the uncontrollable influ- ence of microstress of II kind on the results of neutron measurements.
-1 -10 -5 0 5 10 15 20 x, mm X-RAY MEASUREMENTS X-ray diffraction measurements were made with the Seifert dif- fractometer XRD 3000 PTS-MR using Cr-Kal radiation and a positive sensitive detector.The sample surface near which neutron measure- ments were done was smoothed and electropolished.
The sin 2 k-method was applied to determine the distribution of the radial (rr) and axial (a) stress components along the radial scan line.If in the sample coordinate system (x, y, z) the scattering vector Q has the angle b with axis y and his projection on the analyzing plane (x, z) has the angle o with the axis x then the strain along Q is equal (see, e.g., where 0. 0.11 cos2 t/9 -O'12 sin 2qo + 0"22 sin 2 qo 0"33, 0"/j are the compo- nents of the stress tensor in the coordinate system (x, y, z).For the Q direction perpendicular to the surface 0: 70"33 (0"11 + 0"22)- ( 4) -= do : The difference e-e_L will not practically change if we assume that do .d +/- e,, e+/-d'ec' d-L ' d'pc d+/- do d+/-cot 0+/-(20 20a_). ( 5)   We have then: l+v l+v e e+/----0" sin 2 b + E (0"13 COS --0"23 sin qo) sin 2b. ( 6) If the shear stresses 0"13, 0"23 are negligible in the volume sampled by the X-ray beam, this equation predicts a linear dependence of d, (or 20) vs. sin E b.The stress 0" may be found from the slope m of the least- squares curve fit to the experimental data 20: 1 E me cot 0+/-. (7) 0"--21+v In the opposite case the so-called b-splitting of the dependence d vs.
sinEb measured for the positive and negative values ofb will be observed.
For the ferritic part, quite satisfactory linear plots 20(211) VS. sinEp for the (211) reflex were obtained.In Fig. 6, the experimental values 20(211 (qo=0) measured in the points x 1.5 and 13.5 mm for the @-tilt 0, +22 , +33 , 4-42 , 4-50 , and 4-60 are exemplified.To recover all components of the strain tensor, the measurements were conducted for the qo-tilt 0, 45 , 90.In Fig. 7, the difference of the radial and axial components 0"11 0"22 0"r 0"a is shown as a function of the location of the X-ray spot on the sample surface.Good agreement between X-ray data and the results of the turning out method was observed.A more complicate situation is observed for the austenitic part.In Fig. 8, the example ofthe observed plot 20(220) VS. sinEb for the (220) reflex is shown.x, mm FIGURE 7 The dependence of O" --O" on the coordinate x, where x =0 corresponds to the transition layer.The determination of stress is not feasible because of strong non- linearities and the presence of b-splitting on this plot.Some special method of data processing is needed to evaluate stresses in this case.

CONCLUSION
Putting into operation in 1992 of the HRFD has allowed the beginning of realization of the residual stress investigation program in bulk sam- ples for industrial applications (Aksenov et al., 1995).The first neutron diffraction investigations of residual stresses in shape welded tubes yielded satisfactory results.Qualitative, and even quantitative, agreement with the destructive turning out method, as well as with results of the finite element method calculation can be acknowledged.However, in subsequent investigations a more complete analysis of the resi- dual stress state will be carried out.We are planning to measure all three stress components with a larger tube segment using the new 5-axis Huber goniometer on HRFD.For this purpose, the sin E -method

FIGURE 2
FIGURE 2 The spectrum of the investigated sample in the c-phasoe measured with DPR-1 for 4 h.The obtained cubic lattice constant was a--2.8673(1)A.

FIGURE 5
FIGURE 5 Comparison of theoretical and corrected experimental stress values for the difference between the tangential and radial components.

FIGURE 6
FIGURE 6The dependence of 20(z;1) (q=0) vs. sin2b measured for the positive and negative values of b for the ferritic part.

FIGURE 8
FIGURE 8The dependence of 20(220) (9--0) VS. sinEb measured for the positive and negative values of k for the austenitic part.

TABLE II The
do free-stress spacings and the I" orientation factor for the a-and the