neutron diffraction stress analysis of near surface stress

NEUTRON DIFFRACTION STRESS ANALYSIS OF NEAR SURFACE STRESS GRADIENTS OF SURFACE TREATED STEEL SAMPLES

Jens Gibmeier1*, Joana Kornmeier2 and Michael Hofmann3

1 Institut für Werkstoffkunde I, Universität Karlsruhe (TH), 76128 Karlsruhe, Germany 2 Helmholtz Zentrum Berlin, Glienicker Strasse 100, D-14109 Berlin, Germany

3 FRM-II, TU München, Lichtenbergstr. 1, D-85747 Garching, Germany

ABSTRACT For a quenched and tempered and subsequently shot peened steel plate of SAE 4140 the residual stress depth distribution was determined non-destructively by means of neutron diffraction at the STRESS-SPEC instrument at the research reactor FRM II, Garching (Germany). In contrast to conventional methods using strain scanning here an alternative approach was chosen. Strain scanning experiments suffer from the fact that for through surface scanning experiments labo-rious corrections have to be applied in order to compensate the geometrical effects of the partly immersed gauge volume. Furthermore the lattice free strain parameters have to be known precisely for stress evaluation. In this project the experiments were carried out according to the well known sin²ψ-method of X-ray stress analysis [1]. The diffraction data were evaluated using the universal plot method [2,3]. For the in-plane residual stress distribution of a shot peened steel the results clearly indicate that the chosen approach is practicable to determine the stress distribution non-destructively up to large depth by simply tilting the sample up to grazing incidence geometry. Within the project it became evident that an appropriate characterization of the neutron beam path is essential for the goodness of the evaluated residual stress data. By using a stress free annealed steel plate an optimal combination of the collimators in the primary and the diffracted beam path and the bending radius of the Si(004)-monochromator were established.

INTRODUCTION In order to use the optimisation potential for technical parts most efficiently the residual stress distribution in the near surface region is of major interest for engineering work. The knowledge of the stress distribution is a necessary prerequisite for exactly tailored near surface layers of highly loaded technical components. The most important and most frequently applied tools for residual stress analysis are the diffraction methods, which generally provide phase selective information (e.g. [4,5]. Notably complex residual stress states exist in the near surface region between the very surface and the bulk material. Here the transition from a biaxial surface residual stress distribution to a triaxial volume stress state proceeds [6,7]. Surface layers affected by mechanical surface treatments like e.g. shot peening typically ranges up to depths of some tenth of a millimetre. For non-destructive stress analysis of the residual stress depth distributions of surface treated steel samples the application of laboratory X-rays or high energy synchrotron radiation in reflection mode covers the region from some micrometers [8] up to a depth of about 150-200 μm [9]. To access the depth region > 200 μm an incremental layer removal technique in combination with a reapplication of X-ray stress analysis (XSA) for the new surfaces can be applied [10,11]. However, this procedure is destructive, laborious and furthermore it has to be checked, whether corrections have to be applied. Using neutron radiation generally penetration

* formerly at Hahn-Meitner-Institute Berlin, Structural Research Division, D-12489 Berlin, Germany

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depths up to several millimetres can be achieved [12,13]. Here most likely a set-up for stress analysis is applied with a scattering angle around 90°. Stresses at the surface can be analysed using a strain scanning technique and a gauge volume, which might only be partially immersed in the sample. Here corrections have to be applied using stress free reference samples [14]. Here an alternative approach was pursued to overcome these shortcomings. The stress depth distribution of shot peened steel samples (SAE 4140) was determined by means of neutron diffraction according to the well known sin²ψ- method, being a standard technique in XSA. The experiments were carried out at the STRESS-SPEC instrument at the research reactor FRM II, Munich. For data evaluation the universal-plot method was applied, which directly assigns stress quantities for each sample orientation to the mean penetration depth τ. By that the stress depth gradient can be determined up to large distances from the sample surface non-destructively. SAMPLE MATERIAL

Shot peened steel plate As sample material state a shot peened 50 × 50 × 10 mm³ plate of steel SAE 4140 was used. The sample state was carefully characterized within a round robin test on the determination of residual stress depth distributions by X-ray diffraction within the scope of the BRITE-EURAM-project ENSPED (European Network of Surface and Prestress Engineering and Design) [15].

0 100 200 300 400 500 600-800-700-600-500-400-300-200-100

0100

resi

dual

stre

ss [M

Pa]

SAE 4140 - shot peened

depth [µm]

ENSPED Round Robin test on

stress gradientanalysis by XSA

Figure 1: Residual stress depth distributions for shot peened steel SAE 4140 determined in a round robin test (within the scope of the BRITE-EURAM-project ENSPED) using uniform evaluation parameters for all diffraction data (after [15])

12 ENSPED partners participated in the round robin test. The steel was quenched and tempered according to the following process parameters. First the steel plate was annealed for 20 minutes in a salt bath at 850°C before it was quenched in oil (synquench) to room temperature (RT). Subsequently an annealing step at 450°C for 2 hours followed, before the plate was slowly cooled to RT. The hardness after heat treatment was 455 HV 10. Finally the sample was shot peened with an Almen intensity of 0,4 mmA and a coverage of 200% using MI-230 H (55-62 HRC) as shot media. XSA was carried out within the round robin test by means of laboratory X-ray sources. The residual stress depth distribution was determined by using a combination of XSA and incremental layer removal via electrolytic etching of the surface. All participants carried out stress analysis on the {211}-lattice planes of the ferrite using CrKα-radiation. Fig. 1 shows the residual stress depth distributions determined after stress evaluation using uniform evaluation parameters i.e. diffraction elastic constant ½s2 = 6,095×10-6 MPa-1 and the sliding gravity method for peak evaluation using the commercial software package DIFFRACPlus, Bruker AXS.


Reference plate Additional measurements were carried out on a stress free annealed sample of the fine grain con-struction steel S690QL with similar plate dimensions. To exclude an effect from surface rough-ness on the results of neutron stress analysis the sample surface was carefully polished down to 1 µm diamond paste. To ensure that the stress free annealed sample only possess negligible amounts of residual stresses after polishing complementary measurements were carried out using synchrotron radiation in the soft X-ray region (λ = 1,77 Å) at the PDIFF-instrument at ANKA, Karlsruhe (Germany) as well as using high energy synchrotron radiation at the EDDI-experiment [16] at Bessy, Berlin (Germany). At Bessy energy dispersive diffraction was applied by which the residual stress gradients of the steel sample was determined up to depth of about 100 µm. The results (not shown here) indicate that the sample can be assumed as stress free. Only in the very near surface region for depths < 10 µm a gradient of compressive residual stress with about -150 MPa in average was determined, which obviously resulted from the careful fine polishing. After the laborious characterization of the reference plate identical neutron stress analysis was carried out for the reference plate as for the shot peened sample. These additional measurements on the reference sample were carried out in order to extract effects, which might result in anomalous strains i.e. the wavelength distribution within the beam cross section or effects of a partially immersed gauge volume. Finally the results derived for the stress ´free´ reference plate can be used for calibration of the diffraction data determined on the shot peened sample. EXPERIMENTAL Neutron diffraction measurements

Stress analyses were carried out at the STRESS-SPEC instrument at FRM II in Garching (Germany). For details about the experimental set-up it is referred to [17]. A primary aperture with dimension 2 × 2 mm² and a radial collimator (FWHM=2,3 mm) on the secondary side in front of the 2D position sensitive He³-detector of dimension 20 × 20 cm² were chosen. The {110}- and {211}- diffraction lines of α-ferrite were analysed using a wavelength of 1.515 Å at nominal diffraction angles 2θ = 43,898° and 80,694°, respectively. Measurements were carried out according to the sin²ψ-technique of XSA [1] using 41 sample tilts between ψ = 0 and 89,5°. The stepsizes Δψ were chosen as follows: 0° ≤ ψ ≤ 72° ⇒ Δψ = 4°, 74° ≤ ψ ≤ 80° ⇒ Δψ = 2° and 81° ≤ ψ ≤ 89,5° ⇒ Δψ = 0,5°. In contrast to the usually applied strain scanning experiments the centre of the nominal gauge volume stays at the very surface during tilting the sample. In order to account for potential misalignment errors the measurements were carried out for the azimuth angles ϕ = 0° and ϕ = 180°. Due to the high flux at the STRESS-SPEC instrument the measurement time only amounts between 8 – 40 minutes with respect to the tilt angle ψ, resulting in a complete measurement time for 41 sample tilts of about 3 hours and 12 minutes. To gain more information from the near surface region additional measurements were carried out in asymmetric mode using additional pre-tilts of the sample of ω = 5° and 10°, thus obtaining larger natural absorption length within the sample and so smaller penetration depth of the neutron beam.

Instrument setting optimization

Prior to the stress analysis on the shot peened steel plates large effort was made in order to minimize anomalous strains generated by from divergence effects. Results of this ambiguous study will be published soon elsewhere. Optimal settings for the optical elements were defined. As an optimum a curvature radius rSi(400) = 8 mm for the Si(400)-monochromator was chosen. For


the primary beam path a 15’ soller collimator (collimator in pile) and on the diffracted beam path a radial collimator show the lowest tendency for the arising of pseudo strains. In fig. 2 the pseudo microstrains vs. sin²ψ determined for the reference steel plate using the above mentioned settings (optimized parameters) are compared to microstrain that result for the similar experiment when using settings that are conventionally applied at STRESS-SPEC. These settings are applied for bulk sample analyses in order to provide a high flux (standard parameters) i.e. no application of primary and secondary soller collimators and using a bending radius rSi(400) = 5,15 mm. The graphs clearly indicate that the pseudo strains are reduced to a minimum when using the optimized settings. Up to large sample tilts the microstrains are much smaller that ± 50 µε. Only for very high sample tilts for ψ > 88° a continuous increase can be noted up to about 200 µε.

0,0 0,2 0,4 0,6 0,8 1,0-800-600-400-200

0200400600

pseu

do-m

icro

stra

in [µ

ε]

sin²ψ

optimizedparameters

standardparameters

sin²ψ - measurementson stress free annealed

reference sample

{211}α-Fe

Figure 2: Pseudo microstrains for measurements according to the sin²ψ-method using optimized parameters (optimized in order to minimize pseudo strains) and standard parameters (conventionally used at FRM II – optimized in order to achieve high flux at the sample)

EVALUATION PROCEDURE For data evaluation the universal plot method proposed by Ruppersberg et al. [2,3] was applied. The general assumption of this method is that a biaxial surface parallel stress distribution exists within the information depth. The restriction for σ33 = 0 is fulfilled by approximation for the shot peened steel plate investigated here. One record for this assumption is presented in [18] for neutron strain scanning experiments on a comparable material state. In the near surface region (< 400 µm) only small values of σ33 < ±50 MPa were determined. Toward the core slightly higher tensile residual stresses normal to the surface occurred. Furthermore XSA gave no indication for the occurrence of shear stresses σ13 or σ23 after shot peening. Hence the effect of σi3 (i = 1..3) on stress analysis was neglected in this work. The basic idea of the universal plot method is to separate the experimental data from the stress depth distributions to be determined. The universal character of the method is to plot the experi-mental data in a single (universal) curve irrespective of the measured {hkl}-diffraction lines and the applied radiation wavelength. The starting point of the analysis is the fundamental equation for XSA for a biaxial stress state with the normal stresses parallel to the surface σ11 and σ22

( ) ( ) ( ) ( )( )[ ]( ) ( )[ ]τστσ

ψϕτσϕτσϕτστεϕψ

2211}{

1

222212

211

}{2

1 sinsin2sincos,2

++

++=hkl

hkl

s

shkl . (1)

}{1

hkls and }{22

1 hkls are the diffraction elastic constants, ϕ is the azimuth angle i.e. the angle between the 1-direction with the projection of the scattering vector onto the sample surface and ψ is the distance angle. τ is the penetration depth which can be calculated according to


ψθμηψθψθτ

cossin2sinsincossinsin 22222 +−

= (2)

where η characterizes a rotation around the scattering vector. Here η = 0° corresponds to the Ω-mode and η = 90° to the Ψ-mode, respectively [7]. ( )hkl,τεϕψ and ( )hklij ,τσ with i,j = 1,2 are the Laplace distributions of the lattice strain and the stresses, respectively. The link between the Laplace distributions with the according distribution in real space is given by

( ) ( ) ( ) ( ) dzedzezdzedzehklzhklD

zD

zij

Dz

Dz ∫∫∫∫ −−−− ==

00ij

00

and,, ττττϕψϕψ στσετε . (3)

In case that the thickness of the sample D is large with respect to the penetration depth τ the upper limit of the integral terms is often replaced by infinity. Here D = 10 mm was used.was considered by the thickness of the plate (10 mm). For measurements in the azimuths ϕ = 0° and ϕ = 90° it follows from eq (1) for a general plane stress state

( ) ( ) ( ) ( )[ ]( ) ( ) ( ) ( )[ ]τστστσψτε

τστστσψτε

ψ

ψ

2211}{

1222}{

21

/90

2211}{

1112}{

21

/0

sin,

sin,

2

2

++=

++=

°

°

hklhkl

hklhkl

sshkl

sshkl (4)

The lattice strains ( hkl, )τεϕψ are calculated from the lattice distances ( )hkld ,τϕψ which are directly determined from the measured Bragg angle by using the strain free lattice parameter

. The latter one can be determined self consistently as a good approximation from the measured d vs. sin²ψ - distributions by interpolation in the strain free direction ψ

( hkld ,* τϕψ )*. If the

diffraction elastic constants are well known ψ* is given for a plane stress state by [4]

}{22

1}{1

* 2arcsin hklhkl ss−=ψ . (5)

Using ( hkl,τεψ ) , which is the average sum of the lattice strains according to

( ) ( ) ([ hklhklhkl ,,, /90/021 τετετε ψψψ °° += )] (6)

Ruppersberg et al. [2] defined

( ) ( ) ( ) ( )[ τστστψ

τεψ22112

1}{

12}{

221 2sin

,+==

+u

sshkl

hklhkl ] (7)

Eq (7) is called a ´universal-curve´, since it covers all experimental quantities on the left hand side which can be plotted vs. the penetration depth τ and gives always the sum of the normal stresses parallel to the surface in Laplace-space regardless of the experimental conditions (i.e. {hkl}-planes studied, the wavelength chosen or the type of τ-variation applied). In order to calculate the stresses in real space a simple Ansatz of the form

( ) ( )11

1 !11 −+

= −∑= nijn

N

n nij zazσ with n = 1..4 (8)

was chosen here. This function can be easily transformed into the Laplace-space. In the current case of a shot peened sample the further assumption can be made that a rotational stress state exists. Thus the surface parallel stress component σ ||(τ) can be expressed by


( ) ( ) ( )[ ]τστστσ 221121

|| += (9)

Considering the Laplace transform of eq (8) and plotting the experimental data from eq. (7) versus the penetration depths τ a least square fit using the polynomial provides the unknown an, which can be used to plot the stress distribution in real space. Special attention has to be paid concerning the calculation of the information depth τ. In contrast to applications using soft X-rays the information depth τ is not only reliant on the natural absorption of the radiation within the material under study as defined by eq. 2, but is also limited in depth by the nominal gauge volume defined by the primary and secondary slit systems. An effective information depth τ must be defined with respect to the constrictive character of the gauge volume. This particularly means that by a nominal gauge volume of approximate dimension 2 × 2 × 2 mm³ defined by the apertures in the primary and secondary beampath the information depth simply defined by the centroid of a volume of the material volume irradiated by the beam can not exceed 500 µm. Consequently, the information depth τ must be defined by calculating the material volume irradiated by the neutron beam for each sample tilt ψ and weighting the information depth given by the geometry of the gauge volume by the natural absorption. This procedure becomes rather complicate and laborious for any sample tilt ψ. APPLICATION FOR SHOT PEENED STEEL PLATE Figure 3 shows the lattice microstrains directly calculated from the diffraction data for the {211}- and for the {110}-lattice planes of the ferrite phase of the shot peened steel samples for measurements carried out in symmetric diffraction geometry.

0,0 0,2 0,4 0,6 0,8 1,0

sin²ψ

0,0 0,2 0,4 0,6 0,8 1,0

-2500

-2000

-1500

-1000

-500

0

500

latti

ce m

icro

stra

in [µ

ε]

sin²ψ

{211}α-Fe {100}α-Fe

SAE 4140 SAE 4140 –– shotshot peenedpeened

0,0 0,2 0,4 0,6 0,8 1,0

sin²ψ

0,0 0,2 0,4 0,6 0,8 1,0

-2500

-2000

-1500

-1000

-500

0

500

latti

ce m

icro

stra

in [µ

ε]

sin²ψ

{211}α-Fe {100}α-Fe

SAE 4140 SAE 4140 –– shotshot peenedpeened

Figure 3: Lattice microstrains calculated from the diffraction data for the {211} lattice planes

(left) and the {110} lattice planes (right) for shot peened steel SAE 4140.

The presented curves clearly illustrate the strongly curved ε vs. sin²ψ - distributions which disqualifies the data for direct evaluation using the sin²ψ-method. The microstrain distributions depict the residual stress gradients of the in-plane stress component. The error bars included in the graphs actually emphasizes the good quality of the measured diffraction data. The lattice microstrains for both {hkl}-plane families considered here were evaluated according to the above presented algorithm. Special attention was paid to the strain free direction. Here the stress data exhibit a strong scatter due to the low lattice strain values. This effect was already discussed in [2]. Therefore data in the strain free direction has been omitted during evaluation.


0 50 100 150 200 250-800

-600

-400

-200

0

σ(τ) σ(z)

resi

dual

stre

ss [M

Pa]

information depth z,τ [µm]

SAE 4140 – shot peened

Figure 4: Residual stress depth profiles determined from the lattice strains for the {211}- and the {110}-diffraction lines of the ferrite phase. σ(τ) presents the Laplace-distribution and σ(z) the residual stress distribution in real space, respectively.

Fig. 4 presents the residual depths distribution in Laplace space σ(τ) as well as the respective distribution in real space σ(z), which is the stress quantity of high practical importance for engineers. σ(z) was calculated by inverse Laplace transformation of σ(τ) using the above described procedure. This only results in satisfactory stress distributions in real space if a sufficient number of reliable measuring data in the region of interest exist. For evaluation only data up to information depths of approximately 250 µm were taken into account. This limitation was considered due to the apparent inaccurate assignment of stress quantities to the information depth τ for higher distances to the surface. Here, further effort concerning the data evaluation has to be put in near future work in order to explore the complete depth range assessable by the approach. A further influencing factor concerning the information depth results from the used 2D detector. For the present configuration diffraction data are averaged over a ψ-range of ±4° which has a strong effect on the calculation of σ(τ). Here further optimisation is needed in order to reduce the integration effect and thus to obtain more reliable stress quantities. However, the results for σ(z) determined that way are in good agreement with residual stress distributions determined in a round robin test for identical samples (see fig.1). In general the approach is suitable to determine in-plane residual stress depth distributions non-destructively up to a depth of about 450-500 µm when using a nominal gauge volume of dimension 2 × 2 × 2 mm³ as applied in the present case. Higher depths are reachable theoretically when using a larger nominal gauge volume. In general the method can be applied for general residual stress states with σ33 = 0, which was successfully applied using high energy synchrotron radiation (e.g. [19]). In case the strain free lattice parameter d0 does not vary within the information depth of the experiment the herein proposed method has the advantage that d0 can be extracted from the measured data self-consistently. No further effort has to be put in order to provide a suitable stress ´free´ sample for the proper determination of d0. In general the method can be applied to sufficiently flat surface areas without applying any correction if a proper alignment of the instru-ment and the sample surface with respect to the goniometer center and the nominal center of the gauge volume can be assured. CONCLUSIONS An approach is proposed for the non-destructive analysis of residual stress depth distributions with σ33 = 0 by means of neutron diffraction for measurements carried out according to the sin²ψ - method. One major advantage in contrast to the usually applied strain scanning methods is that the strain free lattice parameter can be determined self-consistently from the measured data. For


flat surfaces no corrections have to be applied for a partially immersed gauge volume. However attention has to be paid for stress calculation in the stress free direction. The application of the proposed approach for a shot peened steel sample illustrate that in general the method is suitable to monitor residual stress depth gradients up to large penetration depth non-destructively. Here data were evaluated up to information depth of approximately 250 µm. The high flux of the reactor FRM II is beneficial for the complex approach in order to provide reasonable measuring times for the determination of the individual stress components. However, care has to be taken in order to minimize pseudo-strains. This has been assured by optimizing the beam path of the neutron beam i.e. by choosing the right bending radius of the monochromator as well as the most convenient optics elements. Comparing to applications using soft X-rays the constrictive character of the gauge volume has to be taken into account for data evaluation in order to avoid erroneous stress data. ACKNOWLEDGEMENTS

We thank FRM II for granting us beamtime at STRESS-SPEC, Bessy for granting us beamtime at EDDI and Dr. Steven Doyle for contributing measurements at PDIFF@ANKA. Special thank is acknowledged to Prof. Ch. Genzel, Helmholtz-Zentrum Berlin (Germany) who finally initialized the idea for this project as well as to Thorsten Manns of Institute for Materials Engineering, University of Kassel (Germany) for providing the stress ´free´ steel sample. REFERENCES

[1] E. Macherauch, P. Müller, Z. angew. Physik, 1961, 13, 305 - 312. [2] H. Ruppersberg, I. Detemple, J. Krier, phys. stat. sol. (a), 1989, 116, 681 - 687. [3] H. Ruppersberg, I. Detemple, J. Krier, Z. Kristallographie, 1991, 195, 189 - 203 [4] V. Hauk (ed.), Structural and Residual Stress Analysis by Nondestructive Methods, Elsevier

Science B.V., 1997 [5] I.C. Noyan, J.B. Cohen. Residual Stress, Measurement by Diffraction and Interpretation,

Springer (New York), 1987 [6] T. Hanabusa, K. Nishioka, H. Fujiwara, Z. Metallkunde, 1983, 74, 307-313 [7] H. Ruppersberg, Mat. Sci. Eng. A, 1997, 224, 61-68 [8] V. Hauk, E. Macherauch, Adv. X-ray Analysis, 1984, 27, 81-99 [9] W. Reimers, M. Broda, G. Brusch, D. Dantz, K.-D. Liss, A. Pyzalla, T. Schmackers, T.

Tschentscher, J. Nondestructive Evaluation, 1998, 17, 129-140 [10] V. Hauk, R.W.M. Oudelhoven, G.H.J. Vaessen, Metal. Trans. A, 1982, 13, 1239-1244 [11] M.A.J. Somers, E.J. Mittemeijer, Metal. Trans. A, 1990, 21, 189-204 [12] A.J. Allen, M.T. Hutchings, C.G. Windsor, C. Andreani, Adv. Physics, 34 1985, 445-473 [13] A. Pyzalla, J. Neutron Research, 2000, 8, 187-213 [14] L. Pintschovius, B. Scholtes, R. Schröder in: Microstructural Characterization of Materials

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[15] J. Gibmeier, J. Lu, B. Scholtes, Mat. Sci. Forum, 2002, Vols. 404-407, 659-664 [16] Ch. Genzel, I.A. Denks, J. Gibmeier, M. Klaus, G. Wagener, Nucl. Instr. Meth. A, 2007,

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neutron diffraction stress analysis of near surface stress

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