RESIDUAL STRESS ESTIMATION OF TI CASTING ALLOY BY X-RAY SINGLE CRYSTAL MEASUREMENT METHOD

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1 4 RESIDUAL STRESS ESTIMATION OF TI ASTING ALLOY BY X-RAY SINGLE RYSTAL MEASUREMENT METHOD Ayumi Shiro 1, Masayuki Nishida, Takao Hanabusa and Jing Tian 4 1 Graduate Student, The University of Tokushima, Tokushima, Japan Kobe ity ollege of Technology, Kobe, Hyogo, Japan The University of Tokushima, Tokushima, Japan 4 Harbin Institute of Technology, Harbin, hina ABSTRAT Recently, titanium casting technology has attracted attention in the industrial fields. Since the casting metals involve various kinds of residual stresses due to heat shrinkage, inclusion particles and so on, the accurate estimation of residual stresses is desired in the engineering field. The aim of the present study is to evaluate the nondestructive stress of titanium casting material by X-ray stress measurement. The sin ψ method for the usual X-ray stress measurement was used to evaluate the residual stresses. However, it was unsuitable for the measurement of titanium casting materials because of their coarse grains. Therefore, the single crystal X-ray diffraction method was employed for the present system. From the present investigation, the method for single crystal systems could be applied to the residual stress measurement. INTRODUTION Titanium has several advantageous properties, such as high strength, thermal and corrosion resistance, and light weight. Due to these properties, the demand for titanium is expected to rise in the future. asting technology is an effective method to produce engineering parts from titanium. However, casting generates residual stresses within a body due to non-uniform cooling rate. Since the residual stresses influence the mechanical properties of casting materials, residual stress measurement becomes important. This study aimed to provide the nondestructive stress evaluation of titanium casting materials using a X-ray stress measurement technique. There is currently little in the literature about X-ray stress measurement of titanium. It has been observed that a large X-ray absorption and a hexagonal closed packed (H) crystal system of titanium results in weak diffraction intensities. A large grain size in the casting body is another difficulty for X-ray stress measurement. Experimental approaches for X-ray stress measurements of a single crystal specimen or an individual grain of a polycrystalline specimen had already been developed by several researchers 1-). In the present study, we measured the stresses of individual grains appeared on the surface of a titanium cast sample. The X-ray stress measurement method for single crystal system was used instead of the sin ψ method. A three-axis sample table was prepared for the flexible measurement of X-ray diffraction. After determining the crystal orientation, lattice strains at independent poles of hkl diffraction were measured and then residual stresses were calculated from the theory of elasticity.

2 This document was presented at the Denver X-ray onference (DX) on Applications of X-ray Analysis. Sponsored by the International entre for Diffraction Data (IDD). This document is provided by IDD in cooperation with the authors and presenters of the DX for the express purpose of educating the scientific community. All copyrights for the document are retained by IDD. Usage is restricted for the purposes of education and scientific research. DX Website IDD Website -

3 414 SAMLE REARATION The measuring sample is Ti-6Al-4V alloy manufactured by vacuum casting. After buff polishing and chemical etching, coarse crystal grains were observed on the surface of sample as shown in Fig. 1. Table 1 shows the composition of the etching solution. Table 1 omposition of etching solution. omposition Amount Distilled water Hydrogen peroxide ( %) otassium hydrate (4 %) ml 5 ml 1 ml 8mm Fig. 1 Surface of titanium casting sample. RINILE OF SINGLE RYSTAL STRESS MEASUREMENT BY X-RAY DIFFRATION 4) Fig. defines three types of the artesian coordinate system, sample coordinate i, laboratory coordinate L i, and crystal coordinate i.. is coincident with the surface normal to the sample and L defines the normal to the diffraction plane. ε L is the normal strain measured along the L direction by X-ray diffraction. Fig. shows the relationships between the three types of the coordinates system. where π, γ and ω are the directional cosines between coordinate axes. L Sample system i ij, ij Laboratory system L i ij L, ij L (hkl)plane L O 1 1 rystal system i ij, ij L 1 Fig. Relation among three coordinate systems. Fig. Relation of the transformation matrices. The normal strain ε L in L direction is written as ε ij in crystal coordinate i by the following equation:

4 415 L i i ij ( ). In the H system, the stress-strain relation is described as follows 5) compliances S ij. (1) using the elastic S S S ( S S S S S ) S S S S S. () As the main purpose is the description of the normal strain ε L in terms of the stresses σ ij in the sample coordinate system, we use the following relationship between σ ij and σ ij with the help of transformation matrix π in Fig... () ij ik jl kl Substituting eqs. () and () for eq.(1), ε L is written as follows under the condition of plane stress state. L ( A A 1 ( A A ( 1 1 A A A A 6 4 A ) A ( 4 A A ) 5 1 A {A A A A ( ) )}, A ) (4) where A S A A A S A S S A S S S S S S S { ( S S)}. Having three ε L values in the independent direction, the stress components σ, σ and σ can be calculated from eq. (4).

5 416 As indicated in Fig.4, the H crystal coordinate system (a 1, a, c) is different from the artesian coordinate system (x 1, x, x ). Therefore, the H coordinate system should be changed to the artesian coordinate system. Eq. (5) shows the transformation from Miller indices (hkl) in the H system to the artesian coordinate system (HKL). By the same meaning, eq. (6) is the direction indices, where λ= c/a is the lattice parameter ratio of the crystal system. H K L h h k U V W u w u v l : plane indices (5) : direction indices (6) The direction cosines of the coordinate transformation between L and i are defined by γ k. When diffraction plane is shown by HKL, γ k is described in the following equations: H K L,,. (7) H K L H K L H K L Furthermore, the direction cosines of the coordinate transformation between i and i are defined by π ij. We then define four angles, ψ, α, φ and β, as shown in Fig.5. ψ and α determine the angle between the surface normal and axis and φ is the rotating angle around axis. β is defined as the following equation:. (8) Finally, the directional cosine matrix π ij is described as follows: ij cos sin sin cos cos cos sin 1 cos sin sin cos cos sin sin sin. cos (9) c x a a 1 x 1 x Fig. 4 onversion of the coordinate system. 1 a 1, 1 Fig. 5 Definition of α, ψ and φ (Stereographic projection).

6 417 EXERIMENTAL ROEDURE In the present study, the Schulz reflection method was used to produce a stereographic diagram. 6) This method requires a three-axis sample table which allows a rotation of the sample about surface normal axis and horizontal axis. Three axes are the ψ, χ and θ-θ as shown in Fig. 6. The three axes ψ, χ and θ-θ intersect each other at a point on the sample surface. This point also coincides with the irradiation position of X-ray beams. At first, a stereographic diagram was measured by rotating the sample table. Fig. 7 shows the stereographic diagram measured in the near-edge region on the surface of sample. The described poles are consistent with two crystals existing in the irradiation area. Fig. 8 shows an enlarged view of the stereographic diagram and diffraction profiles of θ-θ scan at each pole. The plane indices are specified at each pole, and peak positions are determined from the profiles. The X-ray stress measurement is based on the Bragg s law (eq. (1)): d sin, (1) where λ is the X-ray wavelength, d the interplanar spacing and θ the diffraction angle. We evaluate the interplanar spacings by measuring diffraction angles. Lattice strain is then calculated from the following equation: d d, () d where d is the stress free lattice spacing, d the lattice spacing measured by X-ray diffraction. Finally, the stress components are calculated by eq. (4). If we have three strains corresponding to independent three poles, the stress components σ, σ and σ are calculated by the simultaneous equation. If more than three poles exist, the multiple linear regression analysis is used for the determination of the three components. onditions of X-ray stress measurement and the elastic compliances of titanium are shown in Table and Table 7), respectively. --axis X-ray -axis Specimen X-ray -axis Fig. 6 Schematic diagram of three axes ψ, χ and θ-θ. Fig. 7 Stereographic diagram at a near-edge region of the sample surface.

7 418 Fig. 8 Enlarged stereographic diagram and θ-θ profiles at each pole. Table onditions of X-ray stress measurement. haracteristic X-rays ukα Incident slit Receiving slit ollimator arallel beam slit Tube voltage 4 kv Tube current ma hkl plane 4 θ = 8.5 Diffraction angle 1 θ = χ -oscillation range ±. deg ψ -oscillation range ±. deg Filter Nickel Irradiated area φ1 mm Table Elastic compliances of titanium. (1/1 Ga) S S S S S EXERIMENTAL RESULTS AND DISUSSIONS Fig. 9 and 1 show the results of residual stresses σ and σ in each crystal which exists on the sample surface, respectively. One data point corresponds to the stress in one crystal. Different stresses shown by one to four data points at the individual distance from the center indicate that the stress is different from one crystal to another even in one irradiated area.

8 419 Residual stress, Ma Distance from center, mm Fig. 9 Distribution of residual stress σ. σ Reisudal stress, Ma Distance from center, mm Fig. 1 Distribution of residual stress σ. σ σ σ (a) σ (b) σ Fig. Model of residual stress distribution in a homogeneous casting metal with fine grains. Fig. shows a model of residual stress distribution in a homogeneous casting metal with fine grains. In the process of solidification, the outer part first begins to solidify and then the inner part solidifies. Due to the different cooling rate between the outer part and the inner part, the hoop residual stress, σ, of the outer part becomes compressive and that of the inner part becomes tensile as shown in Fig. (b). The radial residual stress, σ, at the edge of the specimen must be zero and the stress at the center must be the same as the hoop residual stress. Therefore, tensile stresses distribute from the center to the edge as shown in Fig. (a). Usually, no shear stresses should exist in the surface. However, the present results on a coarse

9 4 grained sample shows that the stress in each grain does not obey the normal distribution like the model. Furthermore, Fig. shows the non-zero shear stress distribution. The shear stresses in each crystal are different from the stresses in other crystals. The results obtained in this study suggest that the individual grains of large size exhibit a different stress state both in the magnitude and the direction of the principle axis as shown in Fig.. The state of different stresses in different grains of a polycrystalline material is expressed as Heyn stress 8) or the intergranular stress. The present experimental results are a typical case of the intergranular stress 9). Similar results were obtained in case of pure iron that had been plastically elongated by %. 1) x Residual stress, Ma Distance from center, mm Fig. Distribution of shear residual stress σ. x 1 ONLUSIONS Residual stresses in a titanium casting material composed of coarse grains were measured by the X-ray technique for single crystal materials. The conclusions are as follows: 1. The X-ray stress measurement method for a single crystal system is formalized to measure residual stresses in an H crystal.. Even in the irradiated area, the residual stresses are different in each crystal. Furthermore, the direction of principal axis is different in each crystal. REFERENES [1] Y. Yoshioka, S. Ohya and Y. Suyama: roc. 5 th Int. onf. Residual Stresses (1997) pp [] K. Akita, T. Miyakawa, K. Kakehi, H. Misawa and S. Kodama: roc. 5 th Int. onf. Residual Stresses (1997) pp [] H. Suzuki, K. Akita, Y. Yoshioka and H. Misawa: roc. 6 th Int. onf. Residual Stresses () pp [4] T. Hanabusa and H. Fujiwara: JSMS, (1984) pp [5] J. F. Nye: hysical roperties of rystals, Oxford at the larendon press (197) p.. [6] B. D. ullity and S. R. Stock: Elements of X-ray Diffraction, rentice Hall (1) p [7] The Japan Inst. Metals: Data book of Metals (1996) p.. [8] G. B. Greenough, rogress in Metal hysics, (195) pp [9] M. Ortiz, R. Lebensohn,. Turner and A. ochettino: roc. 5 th Int. onf. Residual Stresses (1997) pp