A gray iron, JIS FC 300, was fabricated by casting in a stress frame mold with a size of 200 mm, 100 mm, and 20 mm (length, width, and thickness, respectively), as shown in Figure 1. The stress frame has two thin rods outside and one thick rod inside to produce compressive stress and tensile stress after casting, respectively, due to different shrinkage suggested by Gustafsson et al., (2009); Pal, (2017). The material after casting was treated with annealing and vibratory stress relief treatment referring to Dawson and moffat, (1980); Wang et al., (2013); Wang et al., (2014); Wang et al., (2015). The samples in each condition (as cast, annealed, and annealed and vibratory stress relief) were subsequently subjected to cyclic heating. The vibratory stress relief treatment was conducted with a modified motor and adapter to vibrate the material at a frequency of 80–120 Hz. The load current of the stress relief motor was controlled to reach an amplitude about ±15 m/s² gravity acceleration measured by an amplitude sensor. The cyclic heat treatment was applied by heating and cooling from 28 to 90°C for 20 cycles. In this study, the investigated as-cast gray iron comprised presumably large grain sizes with relatively uniform distribution; thus, the effect of the microdefects originating from the heterogenous grain sizes (Wang et al., 2018) can be neglected.

Synchrotron X-ray measurements were conducted at the BL07 beamline in the National Synchrotron Radiation Research Center (NSRRC), Taiwan. Before measurement, the beamline was optimized by adjusting the vertical focus mirror, horizontal focus mirror, K-B mirror, and Si (111) double crystal monochromator (DCM) to obtain maximum intensity and the smallest divergence of the X-ray beam. The energy resolution of synchrotron X-ray was 10^–4 eV at an energy of 18 KeV. The penetration depth was estimated to be 70 µm.

X-ray diffraction patterns were recorded at the BL07 beamline by utilizing a 6-circle diffractometer manufactured by Bruker. The incident and diffracted angles were fixed to collect the α-ferrite (BCC) diffraction peak of (211). Peak position, peak intensity, and peak width were obtained by a single-peak fitting procedure using a pseudo-Voigt function. The lattice strain (elastic strain) was calculated as follows: ε h k l = d h k l − d 0 , h k l d 0 , h k l (1) where d_0,hkl is the stress-free d-spacing.

Because of the low penetration of X-ray in gray iron, it was assumed that the residual stress was in a plane stress condition. The azimuthal-dependent lattice strains can be expressed as follows: f x x ε x x + f x y ε x y + f y y ε + y y f x z ε x z + f y z ε y z = ε h k l Φ (2) where ε i j is the strain tensor component and f i j is a function of diffraction geometry.

Details of the theory can be found in the references reported by He, (2000); He, (2009). Based on the experimental geometry in this study, a plane stress condition was assumed as the external load to the thin plate sample, where σ z z = σ x z = σ y z = 0 , ε x z = ε y z = 0 . The equation can be further reduced to f x x ε h k l , x x + f x y ε h k l , x y + f y y ε = h k l , y y ε h k l Φ (3) where, f x x = sin 2 ⁡ φ ⁡ cos 2 ⁡ θ (4) f x y = − sin ⁡ 2 ⁡ φ ⁡ cos 2 ⁡ θ (5) f y y = cos 2 ⁡ φ ⁡ cos 2 ⁡ θ (6) f y z = − cos ⁡ φ ⁡ sin ⁡ 2 ⁡ θ (7) f z z = sin 2 ⁡ θ (8) where θ is the peak position at the azimuthal angle φ . In the plane stress condition, the contribution of terms f _yz and f _zz can be neglected due to the small diffraction angle 2θ. Consequently, the equation was dominated by the first three terms, ɛ _hkl,xx , ɛ _hkl,xy , and ɛ _hkl,yy . By performing the linear least-squares regression of all the measured azimuthal-dependent lattice strains, the normal and shear strain components (ɛ _hkl,xx , ɛ _hkl,yy , and ɛ _hkl,xy ) of the material at the measured positions can be obtained as done by Wu et al., (2016). The azimuthal angle was controlled by rotating the sample with a high precise motor. Figure 2 shows an example of the fitting.

The residual stress analyses of the gray iron samples using neutron diffraction were carried out at the TG3 beamline using the KOWARI residual strain instrument at the Australian Nuclear Science and Technology Organization (ANSTO), Australia. Due to the long penetration depth of neutrons, the KOWARI instrument can measure the residual stresses within the bulk of the material. By using an appropriate slit size, 3 × 3 mm slits on the primary beam and 3-mm radial collimators on the detector, spatially resolved measurements can be made within the samples. The results can subsequently be averaged to obtain a more generalized picture. The stresses are determined with the equation: σ x = E x ( 1 + υ ) ( 1 − 2 υ ) ( ( 1 − υ ) ε x + υ ( ε y + ε z ) ) (9) where the strains are calculated via Eq. 1, E and v are Young’s modulus and Poisson’s ratio, respectively.

Initially, the KOWARI instrument was optimized to maximize the neutron flux of the sample at a wavelength of 1.67 Å and to yield an approximately 90° diffraction angle for the α-ferrite diffraction peak of (211) and hence a cuboid gage volume. For a particular crystallographic direction being probed, Young’s modulus and Poisson’s ratio values were calculated using IsoDec software (Kröner model) proposed by Gnäupel-Herold, (2012). The sample was then translated and rotated on a sample stage to map out the strains in the three orthogonal directions.

The stress-free d-spacing, d_0,hkl, strongly influences the determination of the residual stress. Even a tiny deviation of d_0,hkl will cause a serious variation of the lattice strain. According to Withers et al., (2007), there are several reference standards to determine the stress-free d-spacing, including powders, filings, cubes, and combs. The main aim of all these methods is to utilize the free surface, as much as possible, as this is least likely to be constrained. This study probed the stress-free d-spacing by collecting the diffraction patterns from all the three directions at the corner of the samples as close as possible to the surface. The through-thickness direction (the thinnest) was then assumed to be in plain stress, and a d_0,hkl was calculated via deconvolution. With this method, a reasonable stress-free d-spacing is achieved.

The residual stresses measured with synchrotron X-ray, assuming a plane stress condition, in the stress frame of the gray iron are shown in Figure 3. Figure 3A presents the residual stresses at point 2 (outside, thin), point 5 (middle, thick), and point 8 (outside, thin) of the stress frame before cyclic heating. As noted, the annealing process will enlarge the residual stresses and modify the stress distribution on the surface. One can expect this phenomenon, although annealing can facilitate the relaxation of the structure, and the material will experience additional thermal effects during cooling. Different cooling rates on the surface and inside the bulk will give rise to thermally induced residual stresses. Synchrotron X-ray measurement collected the diffraction patterns on the top surface of the sample. The thermal stress issue should be much more serious; thus, higher stress and confused distribution on the surface of the gray iron after annealing can be observed in Figure 3A. It can be realized that the vibratory stress relief technique can reduce the stress effectively. Not only ε _xx and ε _yy , shear stress ε _xy converged to zero when the material suffered from the vibratory stress relief treatment.

Figure 3B shows the residual stresses in the stress frame of the gray iron after cycling heating treatment, probed with synchrotron X-ray. Both the normal and shear stresses between casting, annealing, and annealing associated with the vibratory stress relief technique became unity after cycling heating, and there were no significant differences between them. It means that the cycling heating treatment can maintain and stabilize the residual stress on the surface of the material, even when the value of the stress was still high. The stabilized stress can help stabilize the size variation of the material. Because gray iron is an important material, being the components of machine tools, the stabilized stress and size variation will be very important for the machine tools to maintain high accuracy.

Figure 4 shows the residual stress in the stress frame of the gray iron probed with a neutron diffraction technique. Figures 4A,B display the stresses of the material before and after cycling heating treatment, respectively. The value was obtained by averaging the stress in each depth. As noted in Figure 4A, only the stress component along L-direction manifested the variation of the residual stress at different points of the stress frame. The results meet one’s expectation by using the stress frame which contains two thin plates outside and one thick plate in the middle. Due to different shrinkage as cooling, the outside plates display compressive stress, while the middle plate exhibits tensile stress. The interaction between compressive stress and tensile stress occurs along L-direction. The stress along L-direction of the stress frame was already evidenced by using a strain gage reported by Pal, (2017). The compressive stress state in the outside plates and tensile stress state in the middle plate of the stress frame were also observed in this study. As noted, points 1–3 and points 7–9 in the stress frame reveal the compressive stress, while points 4–6 present the tensile stress condition. Consistent results indicated that the measurement of the residual stress with a neutron source is reliable.

In Figure 4A, annealing and vibratory stress relief treatments can reduce the tensile stress at points 4–6, while the compressive stresses at points 1–3 and points 7–9 do not change evidently. The material with the tensile stress state is instable and the structure is loose. As a result, annealing and vibratory stress relief treatments can rearrange the atoms in the loose structure.

It is very interesting to compare the residual stresses in the gray iron after further cycling heating treatment. As indicated in Figure 4B, the residual stresses in the gray iron with the as-cast state and annealing state are altered violently after the cycling heating. The residual stress at points 4–6 becomes highly nonuniform after cycling heating. Only the gray iron with the vibratory stress relief treatment maintains almost the same value of the residual stress after cycling heating. It implies that the vibratory stress relief treatment can stabilize the residual state, even the materials experiencing further cyclic change in temperature.

The phenomenon was also revealed in the depth profile analysis of the residual stress in the gray iron after cycling in Figure 5. Gray iron with the vibratory stress relief treatment shows similar residual stress distribution in depth, at point 5, after cycling heating, while the residual stresses in the other two states of materials vary irregularly with depth after cycling heating treatment. The results imply that the vibratory stress relief technique stabilizes the residual stress on the surface or inside the bulk of the gray iron, with the materials experiencing further cyclic heating treatment. It is interesting that the depth profile analysis does not disclose the specifically compressive stress on the surface of the material as usual. It is maybe due to the probing depth at the first point of 3 mm, which is not shallow enough to exhibit surface effect.