Copyright(c)JCPDS-International Centre for Diffraction Data 2,Advances in X-ray Analysis,Vol.43 31 MEASUREMET AD AALYSIS OF RESIDUAL STRESS I ε- PHASE IRO ITRIDE LAYERS AS A FUCTIO OF DEPTH Thomas R. Watkins, * Roger D. England, Cheryl Klepser and. Jayaraman * Oak Ridge ational Laboratory, Oak Ridge, T 37831-664 Cummins Engine Company, Columbus, I 4721 University of Cincinnati, Cincinnati, OH 45221-12 ABSTRACT The observed curvatures in the sin 2 Ψ plots suggest the possibility of the presence of both residual stress and composition gradients as a function of depth, given the nature of the steel nitriding process. In this work, the amount of nitrogen as a function of depth was determined using an electron microprobe, and a Laplace transform function was used to convert the microprobe data to an exponentially weighted volume average as sampled with x-ray diffraction. This corrected data was used to determine the value of the unstressed lattice spacing and thereby separate the effect of nitrogen concentration gradient from the experimentally measured shift in the x-ray diffraction peak location as a function of depth. However, the nitrogen concentration was effectively constant within the 2 µm x-ray depth of penetration and consequently had a negligible effect on the data. The residual stresses were found to be tensile and varied within the 2 µm examined of the 1 µm thick ε-phase layer, using conventional ψ tilt and grazing incidence x-ray diffraction methods. ITRODUCTIO Gas and ion nitriding have become common practice in diesel engine components where wear resistance is critical. The high hardness and the wear resistance of nitrided steels provide an attractive engineering alternative to high cost tool steels. The nitriding operation consists of a twostage heat treatment. In the first stage, a nitrogen rich white layer of largely ε-phase is grown on the surface of the part by the dissociation of anhydrous H 3 at 5 C. In the second stage, the nitrogen from the white layer diffuses into interstitial locations in the martensitic substrate and also forms nitride precipitates, achieving a very hard layer just below the white layer (see Figure 1). Most applications remove the white layer from the part in a post heat treatment machining operation. There are, however, some applications where the white layer remains on the part in an area that is subjected to a high applied stress. Since changes in the residual stress state directly effect the fatigue life of a component, and the composition of the white layer has been linked to fatigue life, characterization of the white layer s residual stress state is needed for modeling and life predictions. The nature of the nitriding operation is such that significant stresses can be imparted into the white layer. These stresses could vary greatly as a function of depth. The nitrogen concentration gradient results in a crystallographic gradient of phases whose unit cell volumes differ from that of the base martensite. Further, the mismatch of the thermal expansion coefficient of the Fe 3 with the martensite could also be a significant source of residual stress. Much of the literature published on nitriding reports a white layer composed of Fe 4. The fatigue properties measured at Cummins on Fe 3 versus Fe 4 white layers showed an increased fatigue life on the parts where the white layer was predominantly Fe 3. In the phase diagram, 1 the region between the Fe 2 (33 at.% ) and Fe 4 (2 at.% ) boundaries is labeled ε-phase. The composition most closely associated with the ε-phase is Fe 3, which is considered an ordered interstitial alloy. 2,3,4 The structure consists of iron atoms in a HCP array with atoms occupying the octahedral interstitial sites, while maintaining equal distance from each other (hexagonal space group, P63/mmc (194) 5 ). The literature available on ε-phase iron nitride is
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Copyright(c)JCPDS-International Centre for Diffraction Data 2,Advances in X-ray Analysis,Vol.43 32 limited to the phase equilibria and crystal chemistry studies which are best summarized in references 1 and 2, respectively. o published data was found describing other properties such as elastic constants or thermal expansion coefficients. This paper discusses the experimental determination of both the nitrogen gradient and the residual stress gradient of a white layer with ε-phase stoichiometry. The paper also discusses the calculation of the change in the unstressed lattice spacing as a function of the nitrogen content. The residual stresses were measured using both the sin 2 ψ method and as a function of depth using grazing incidence x-ray diffraction (GIXD). The nitrogen concentration data was used to determine the unstressed lattice spacing as a function of depth, in order to isolate the change in the measured interplaner spacing associated with the residual stress from that due to the changing interstitial nitrogen occupancy. EXPERIMETAL PROCEDURE Table I lists the details of the experimental conditions for the x-ray measurements. Briefly, a 4- axis (Φ, χ, Ω, 2Θ) goniometer 6 was employed for the stress measurements using the "ψ- and Ω- goniometer geometries" 7(A) for the sin 2 ψ and GIXD techniques, respectively. The (114) reflection from the ε -phase (Fe 3 ) was utilized for the strain measurements. The x-ray elastic constants were determined elsewhere, 8 and found to be 3 GPa and.3 for E and υ, respectively. The Kα 1 -α 2 doublet was fit using a pseudo-voigt function, and the positions for the Kα 1 peaks were used for all calculations. For the sin 2 ψ measurements, the stresses were calculated using the Dölle-Hauk method 7(B) initially assuming a triaxial stress state. Except where noted, the procedures and analyses given in reference 9 were followed for the GIXD work. Briefly, the depth of penetration or angle of incidence was held constant for each strain measurement and Φ was varied. The stresses were calculated using the generalized least-squares approach. 1 Specimen alignment was accomplished using a dial gauge probe, which was accurate to ±5 µm. The relative distance to the goniometer s center of rotation is known, and the diffracting surface is positioned accordingly. Examining LaB 6 powder on a zero background plate ensured goniometer alignment. The maximum observed peak shift for the (51) reflection of LaB 6 (141.7 2Θ) was less than.1 2Θ for Ω tilting (.5 to 116 ). Finally, -325 mesh W powder was dispersed in acetone and painted onto the sample surface. Both the (321) reflection from the strain-free W (131 2Θ) and the (114) reflection from the Fe 3 were scanned as a function of angle of incidence. Figure 2 shows negligible change of the (321) W interplanar spacing as a function of incidence angle for the two samples examined. Thus, the changes observed in the (114) Fe 3 interplanar spacing originate from the sample and not from instrumental effects or sample displacement error. RESULTS AD DISCUSSIO itrided steels are currently used to improve wear resistance and fatigue life, although the mechanism for improvement in fatigue life is not well understood. The residual stress versus depth profile is necessary for understanding the influence of the nitrided layers on fatigue. Here, x-ray diffraction was the primary analysis tool for this work. In Figure 3, Fe 3 and Cr 2 were identified using a Θ 2Θ scan. A minor phase, Cr 2, was present due to the chrome alloying in the 51 steel substrate. Figure 4 shows non-linear sin 2 ψ plots indicating the presence of a gradient. Given that the diffusion plays a part in the nitriding process, both nitrogen and residual stress gradients were assumed to be present. In order to separate the effect of these gradients, a polished cross section (see Figure 1) was prepared for elemental analysis via electron microprobe. In Figure 1, the thin white layer can be seen on the surface. The dark etched region below the white layer is the diffusion zone where nitrogen has migrated into the martensite. The nitrogen concentration was mapped as a function of
Copyright(c)JCPDS-International Centre for Diffraction Data 2,Advances in X-ray Analysis,Vol.43 33 depth with a probe size of 1 µm (see Figure 5). Equivalent multiple data sets from different locations were combined to show the considerable scatter in the measured nitrogen concentration gradient through the sample. The relative positions and trends in Figure 5 were regarded as accurate, showing a pseudo nitrogen plateau region (i.e., white layer) followed by a decaying nitrogen concentration in the diffusion zone. As no standard was available, the absolute values of the data possessed an accuracy of approximately ±1%. Figure 5 provides an independent measure of the nitrogen concentration gradient, which can be used to correct the observed residual stress gradient data. Figure 5 represents a Z-profile, the actual concentration gradient with depth. This Z-profile needs to be converted into a tau profile, 11 the absorption weighted profile as seen from the outer surface and progressing into the white layer (the effective signal). To this end, the formalism given by oyan and Cohen 7C was used and the following definite integral solved for <a>: a = z z / τ ( A + Bn( z)) e dz z z / τ e dz (equation. 1) A similar integral was solved for <c>, where <a> & <c> are the hexagonal lattice parameters; A & B are the regression constants for the lattice parameters as a function of nitrogen concentration (see Figure 6); n(z) = m + m 1 z is the nitrogen concentration as a function of depth; z is the layer depth; and z & τ are the depth and 1/e penetration depth. Since Figure 1 provides a more representative view to determine the average white layer depth than Figure 5, z was taken as 1 µm rather than the 6.5 µm, respectively. Solving, equations 2 and 3 are obtained. a = A + Bm + Bm1 Z eff, (equation. 2) z e Zeff = + / τ τ ( 1 τ) z / τ ( 1 e ) (equation. 3) where Z eff is the effective penetration depth of the x-rays. Utilizing the appropriate equations, 12 a stress free lattice parameter was calculated for the (114) reflection as a function of depth. The effect of the correction was negligible, probably because the deepest penetration depth was < 2 µm for copper radiation in iron. Consequently, the curvature observed in Figure 4 was entirely attributed to residual stresses, since a horizontal line can be fitted to the data in this region in Figure 5. The average strain free interplaner spacing, d, was determined from the x-ray data employing the analysis of Hauk et al. 7(D) and was taken as.8559 Å for the (114) reflection of Fe 3. Figure 7 shows the results of the GIXD analysis. The measured residual stress (open circles) for each x-ray penetration depth is designated as the tau profile. The Z profile (solid line) represents an estimate of the actual stress calculated as a function of depth and was deconvoluted from the tau profile using the analysis by Zhu et al. 13 It should be emphasized that the Z-profiles are estimates and are not unique for the data. The reconstructed tau profile (dotted line) was calculated from the solid line and is an estimate of the quality of the solid line. The fit of the reconstructed tau profile to the original tau profile is reasonable, hence, indicating a reliable Z-profile estimate. The tau profiles show the tensile residual stresses decaying rapidly with depth. As the depth of penetration increased, the x-ray penetration volume contained more of the material subjected to either compression or no stress. Thus, the average signal from such volume resulted in stresses
Copyright(c)JCPDS-International Centre for Diffraction Data 2,Advances in X-ray Analysis,Vol.43 34 that approached zero, which would conform with force balance constraints. The Z-profile in Figure 7 shows very high tensile residual stresses, which is contrary to the normal expectation of compressive stresses increasing fatigue strength. In the absence of physical property data, such as thermal expansion coefficient, density, fracture toughness, etc., it is presently difficult to evaluate the residual stresses, even qualitatively. More work needs to be done to characterize the properties of ε - phase Fe 3. The lack of compressive residual stress data to explain the increase in fatigue life associated with the Fe 3 composition white layer suggests that there is another mechanism that increases fatigue life on these parts. Likely, the enhanced fatigue strength is simply a function of the nitrogen interaction within the martensitic substrate. The influence of the stoichiometry of the white layer on fatigue life may be related to the increased volume of nitrogen present in the Fe 3 over the Fe 4 white layer. This increase in nitrogen available could affect the concentration and location of nitrogen in the martensitic substrate, and this could cause the change in fatigue strength. Research is planned using other radiation sources and measurement techniques in order to begin to map the residual stress profile completely through the white layer, and the stresses present in the martensitic substrate just below the interface. SUMMARY The residual stresses present in the white layer were found to be tensile and vary with depth within the first 2 µm of the 1 µm thick white layer. The diffraction measurements of the interplaner spacing were significantly more precise than the electron microprobe measurements for quantifying the interstitial nitrogen present. A simple model for the correction of the strain free interplanar spacing due to variations in nitrogen content as a function of depth was presented. Future work on this project will include the use of other experimental techniques for the measurement of the absolute nitrogen concentration gradient, and the characterization of the stress state in the area near the martensitic interface, and in the martensitic substrate near the white layer. ACKOWLEDGEMETS The authors gratefully acknowledge Dr. A. D. Stoica and Mr. R. Martinez for their help formulating the concentration gradient correction; Mr. L. Walker for the electron microprobe measurements, and Dr. T. Yonushonis for helpful discussions. Research sponsored by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Transportation Technologies, as part of the High Temperature Materials Laboratory User and Fellowship Programs, Oak Ridge ational Laboratory, managed by Lockheed Martin Energy Research Corp. for the U.S. Department of Energy under contract number DE-AC5-96OR22464. REFERECES 1. Phase Diagrams of Binary Iron Alloys, Edited by H. Okamoto, ASM, Metals Park, OH, 1993, pp. 222-42. 2. D. H. Jack and K. H. Jack, Invited Review: Carbides and itrides in Steel Materials and Science Engineering, 11, (1973) pp. 1-27. 3. K. H. Jack, The Iron-itrogen System: The Crystal Structures of ε - Phase Iron itrides, Acta Cryst. 5 44-11 (1952). 4. R. C. Evans, An Introduction to Crystal Chemistry, Cambridge University Press, Cambridge, 1979, pp. 345-8. 5. J. Hanawalt, H. Rinn, and L. Frevel, Analytical Chemistry, 1 457 (1938). 6. H. Krause and A. Haase, X-Ray Diffraction System PTS for Powder, Texture and Stress Analysis, pp. 45-8 in Experimental Techniques of Texture Analysis, DGM Informationsgesellschaft Verlag, 1986, H. J. Bunge, Editor.
Copyright(c)JCPDS-International Centre for Diffraction Data 2,Advances in X-ray Analysis,Vol.43 35 7. I. C. oyan and J. B. Cohen, Residual Stress, Measurement by Diffraction and Interpretation, Springer-Verlag, ew York, 1987: A, pp. 11-12; B, pp. 125-6; C, pp. 157-159 and D, pp. 126-13. 8. T. R. Watkins, L. Riester, R. D. England and C. Klepser, Determination of X-ray Elastic Constants for Iron itride, To Be Published. 9. E. S. Zanoria, T. R. Watkins, K. Breder, L. Riester, M. Bashkansky, J. Reintjes, J. G. Sun, W. A. Ellingson and P. J. Blau, Assessment of Techniques for Characterizing the Surface Quality of Ground Silicon itride, J. Mater. Eng. and Perf. 7 [4] 533-47 (1998). 1. R. A. Winholtz and J. B. Cohen, Generalized Least-squares Determination of Triaxial Stress States by X-ray Diffraction and the Associated Errors, Aust. J. Appl. Physics 41 189-99 (1988). 11. P. Predecki, Determination of Depth Profiles from X-ray Diffraction Data, Powder Diffraction 8 (2) 122-126 (1993). 12. B. D. Cullity, Elements of X-ray Diffraction Addison-Wesley, Reading, Mass., 1978, p. 51. 13. X. Zhu, B. Ballard, and P. Predecki, "Determination of z-profiles of diffraction data from τ- profiles using a numerical linear inversion method, pp. in Advance X-Ray Analysis, Vol 38, Plenum Press, ew York, Y, USA, 1995. 14. Y. Inokuti,. ishida, and. Ohashi, Formation of Fe 3, Fe 4, and Fe 16 2 on the Surface of Iron, Met. Trans., 6A 773-84 (1975). White Layer ~.1 mm Diffusion Zone ~.28 mm Substrate Figure 1- Optical micrograph of the sample cross-section after etching with 5% nital. Table I - Experimental conditions of the x-ray measurements. Parameter Condition Equipment Scintag PTS goniometer MAC Science 18 kw rotating anode generator Scintag thermoelectrically-cooled Si(Li) detector Power 16 kw; 4 kv, 4 ma Radiation Cu kα, λ = 1.5459 Å Incidence slit divergence.35 Receiving slit acceptance.25 ; radial divergence limiting (RDL) Soller slit Source to specimen distance 36 mm Specimen to back slit distance 28 mm Tilt axis and angles ψ;, ±28.2, ±42, ±55 (equal steps of sin 2 Ψ) GIXD axis and angles Ω;.8, 1, 1.5, 6.7, 1, 13.3, 3 Scans.2 2Θ/step; 1 s/step
Copyright(c)JCPDS-International Centre for Diffraction Data 2,Advances in X-ray Analysis,Vol.43 36.858 Interplanar Spacing (Å).856.854.852.85.848.846 (114) Fe 3 (321) Tungsten Powder.844 2 4 6 8 1 Incidence Angle ( ) Figure 2 GIXD scans for Fe 3 and W powder at φ = show that the observed interplanar spacing changes for Fe 3 are free from instrumental aberrations. Intensity (cpm) 8 7 6 5 4 3 2 1 ---(11) Cr 2 ---(1) Fe 3 --------(2) Fe3 ----(11) Fe 3 ---(21) Cr 2 ---(12) Fe 3 ---(211) Cr 2 ---(11) Fe 3 --------(13) Fe 3 ---(32) Cr --------------------------------(2) 2 Fe 3 ----(112) Fe 3 ------------------------(4) Fe 3 -----(22) Fe 3 4 6 8 1 12 14 2 theta ( ) Figure 3 A Θ-2 Θ Scan of the surface of a nitrided sample. ---(114) Cr 2 -----(23) Fe 3 ------------------(21) Fe 3 ------(114) Fe 3 ----------------------------(212) Fe 3 ---------(15) Fe 3
Copyright(c)JCPDS-International Centre for Diffraction Data 2,Advances in X-ray Analysis,Vol.43 37 128.45 128.4 2theta ( ) 128.35 128.3 128.25 128.2 phi= phi=45 phi=9 128.15.1.2.3.4.5.6.7 Sin 2 ψ Figure 4 on-linear sin 2 Ψ plot for the (114) Fe 3 indicates the presence of at least one gradient. Error bar represents typical standard deviation. 4 35 3 (at%) 25 2 15 1 5 White Layer 5 1 15 2 25 3 Z Diffusion Zone Depth (µm) Figure 5 The nitrogen concentration as a function of depth.
Copyright(c)JCPDS-International Centre for Diffraction Data 2,Advances in X-ray Analysis,Vol.43 38 16.7 23.1 28.6 33.3 Atomic % itrogen Figure 6 Lattice parameters of ε - iron nitride as a function of nitrogen content. (After Inokuti, et al., 1975) 14 Residual Stress (MPa) 12 1 8 6 4 2 (114) Fe 3 Z-profile Tau-profile Reconstructed from Z-profile.5 1 1.5 2 Depth (µm) Figure 7 The residual stresses as a function of depth.