Residual Stress Tensor Distributions in Cracked Austenitic Stainless Steel Measured by Two-Dimensional X-ray Diffraction Method

. The residual stress tensor for cracked austenitic stainless steel was measured by a two-dimensional X-ray diffraction method. Higher von Mises equivalent stress concentrations, attributed to hot crack initiation, were obtained at both crack ends. The stress of 400 MPa at the crack end in the columnar grain region was about two-fold larger than that of 180 MPa in the equiaxed grain region. This difference was caused by a depression in the cast slab.


Introduction
Stress and strain are inevitable in cast materials, and they can cause damage by hot crack initiation, owing to the thermal gradient in the material during solidification and cooling.In this study, we focus on hot cracks, which are defined as cracks initiated in the solid-liquid coexistence region, and include solidification, liquation, and ductility-dip cracks.In continuous casting of Fe-and Ni-based alloys, hot cracks should be prevented because they remain after rolling.A mechanism of crack and deformation generation in the solid-liquid coexistence region has been proposed.However, there has been little discussion of experimental stress values because it is difficult to measure stress and strain on a millimeter scale in cast alloys.If these measurements can be obtained, analysis can prevent the formation of hot cracks in cast alloys.
X-ray diffraction methods have been used to measure stress because they are nondestructive and precise.The conventional sin 2 ψ method is widely used and has been improved over time.Tanaka and coworkers evaluated residual stress distributions for Si 3 N 4 in a Si 3 N 4 /Cu/steel joint over a localized irradiation area of less than 0.03 mm 2 [1,2] .If this method can be applied to cast alloys, the localized stress values will elucidate the initiation of cracks.However, measurements in cast alloys have been prevented by coarse and preferentially oriented grains.In this study, we used the two-dimensional X-ray diffraction method developed by He and Kingsley to measure the distribution of residual stress tensors, which entails irradiating the sample with multidirectional X-rays to obtain diffraction patterns using a two-dimensional detector [3,4] .We optimized this method for measuring residual stress tensors in cast austenitic stainless steel to clarify the effect of crack initiation.

Experimental 1. Specimen
A Fe-20wt.%Ni-20wt.%Cr-Si-Mn-0.4wt.%Al-0.4wt.%Ti(UNS-S33400) alloy was cast using a continuous casting machine.The alloy is a heat resistant austenitic stainless steel with a solidus line temperature of 1370 °C.A specimen 120 × 40 × 15 mm (l × w × d) in size was cut from the shorter side of the slab at a speed of 1.5 mm/min using a cold working method (Fig. 1).The horizontal direction of the slab was defined as the x-axis, the vertical direction as the y-axis, and the casting direction as the z-axis.The measured plane was the cross section against the z-axis.The sample was chemical etched to eliminate surface strain.There were hot cracks initiated along the width (x-axis) of this plane during solidification.The length of the hot cracks was 50 mm.The plane consisted of a columnar and an equiaxed grain region.The maximum size of the columnar grains was 5 mm.However, each grains were consisted by a lot of dendrites which tilt at the range of a few degrees each other by observation of optical microscope.Advanced Materials Research Vol. 996

Measurement of residual stress tensor
The conditions for stress tensor measurement by two-dimensional X-ray diffraction are shown in Table 1.The specimen was held on a stage and tilted an angle of ψ along the cradle, and rotated by an angle of φ around the Cr-Kα X-ray irradiation center.In addition, the specimen was oscillated by 1 mm along the x-and y-axes.These conditions were optimized to obtain a continuous Debye-Scherrer ring from a sufficient number of grains in an area of 9 mm 2 .The X-rays penetrated the specimen to a depth of 5 µm in the measurement area.The X-rays were collimated to 1.0 mm in diameter and diffracted at 2θ 0 = 129°, which corresponds to the γ-austenite (220) plane according to previous X-ray diffraction results.
The measurement areas for residual stress tensor measurements are shown in

Residual stress tensor distribution along hot cracks
The measurement conditions where a continuous Debye-Scherrer ring was obtained are shown in Fig. 2. The curved line was set at 2θ 0 = 129° and the detected diffraction angle range was from 114° to 144°.The Debye-Scheller ring obtained after 90 s irradiation shown in (b) was weaker compared with the Diffracted X-ray plot than the ring obtained after 1200 s shown in (a).The error range was reduced by increasing irradiation time.In contrast, if preferentially oriented grains occupied a large proportion of the measurement area and if the specimen was not oscillated during measurements, the ring would not have the shape shown in (c).The error in the residual tensor values would also be much higher for preferentially oriented grains and static measurements.Advanced Materials Research Vol. 996 Figure 3 shows the residual stress tensor distribution along the direction of the hot cracks.The horizontal axis indicates the distance from the left crack end, and the vertical axis indicates the residual stress tensor values.Normal (σ xx , σ yy , σ zz ), shear (σ xy , σ yz , σ xz ), principal (σ 1 , σ 2 , σ 3 ), and equivalent (σ VM ) stress values are shown.The following results were obtained from the distribution.Normal stresses along the horizontal direction of the slab, σ xx , were higher than σ yy along the longitudinal direction of the slab at all measurement points and the error for the values was within 30 MPa.There were stress concentrations for σ xx and σ yy in a 5 mm 2 area at both crack ends.This indicates that stress may remain and initiate hot cracks.The normal stresses at the left crack end, where σ xx was 350 MPa and σ yy was 300 MPa, were higher than those at the right crack end, where σ xx was 200 MPa and σ yy was 100 MPa.σ zz along the casting direction of the slab was -50 to 15 MPa and the error for the values was within 15 MPa.Although these values had error range, it could be because the strain along the cast direction was lower and the specimen was under plane stress condition.Shear stresses σ xy , σ yz , and σ zx were within 100 MPa and the error for the values was within 20 MPa in all measured areas.Principal stresses σ 1 and σ 3 showed the same behavior as σ xx and σ zz .This was because the shear stresses were so low that σ 1 had a value similar to σ xx , although they were higher than the normal stresses along other axes, thus the maximum principal stress also followed a similar trend.σ zz also followed this pattern.Although σ 2 showed a trend similar to σ yy , the compressive stress values near the left crack end were -150 MPa, and fluctuated slightly from the right crack end to inner area of the slab.The von Mises equivalent stress, σ VM, was similar to σ 1 , because σ 2 and σ 3 were lower than σ 1 .The elastic strain of the specimen was affected mainly by the tensile stress along the x-axis.Local maximum values of 400 and 180 MPa were measured at the left and right crack ends, respectively.

Fig. 1 .
Fig.1.Schematic of the specimen prepared from a continuously cast austenitic stainless steel slab.The cross section was taken against the casting direction.The enlargement shows the area around the cracks.The dotted square shows the measured area and the broken vertical line in the specimen shows the boundary between the columnar and equiaxed grains.The shape of the cracks is shown in (c), where the cracks were initiated intermittently.

Fig. 1 .
The residual stress tensor values were the average values for a 9 mm 2 area.The measurement points were around hot cracks.Many measurements were taken near the crack ends, because very precise values were required to assess the effect of hot cracks on the residual stress tensor distributions.Twenty-five combinations of specimen tilt angles along the ω, ψ, and φ axes were used, and the measurement time for each combination was 90-1200 s, depending on how long it took obtain a continuous Debye-Scherrer ring.Residual stress tensor values were obtained by analyzing the shift, broadening and twist of the X-ray diffraction peak and shape of a Debye-Scherrer ring compared with that of the stress-free crystal lattice.Measured values might be different from the values predicted by peak shift of Debye-Scherrer ring simply.The results were analyzed with values of Young's modulus, the longitudinal elastic modulus, and Poisson's ratio as 197 and 74 GPa, and 0.33, respectively.These values were obtained by preparatory experiments.The normal, shear, principal, and von Mises equivalent stresses were calculated.

Fig. 2 .
Fig. 2. Debye-Scherrer rings obtained from the two-dimensional detector.The diffraction angle was 132°, and the detected area was 117 to 147°.(a) shows the results for irradiation time of 1200 s, (b) shows results for an irradiation time of 90 s and (c) shows the results for an irradiation time of 90 s without oscillation of the specimen.
(a) Obtained Debye-Scherrer ring irradiated for 1200 s, oscillated for 1 mm (b) Irradiation time: 90 s Oscillation range Distance from left crack-end[mm]

Fig. 3 .
Fig. 3. Residual stress tensor distributions along hot cracks.(a) Normal and shear stress (b) Principal and von Mizes equivalent stress.