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##### The Difficulty Of Measuring The Residual Stress At Shot Peened Surfaces

Fig. 1: Bragg-reflection at the different atomic layers

Fig. 2: Different orientation angles ? and measurement direction

Fig. 3: The different angles ? cause different orientated atomic layers

Fig. 4: Measured residual stress at the different ?-angles

Abstract: The residual stresses at shot peened surfaces are often interesting to value the quality of the peening process. A non-destructive method is the measurement by x-ray diffraction. But you have to give an exact specification to get the same results, which will be shown in this paper.

1. Introduction

The shot peening process is used in many cases to improve the fatigue of work pieces or automotive components. The higher the compressive residual stress is the better the durability of the shot peened component. An attractive way is to measure the residual stress at the surface by x-ray diffraction because it is non-destructive.
If you measure load stress by x-rays at shot peened surfaces the result is strongly dependent of the roughness of the surface [Mü 93]. On the other hand the different incident angle of the x-rays to measure the residual stresses might have also an influence on the results.

2. Basics of residual stress by measurements by x-rays

The residual stress measurement by x-rays bases on the so called Bragg-reflection. An incident x-ray beam is reflected at several atomic layers. If the path difference of two different reflected waves is exactly one or a multiple of one wavelength λ, you get a constructive interference (see fig. 1). (If the path difference is λ/2 the waves will have destructive interference and the amplitudes will add to zero.) The constructive interference gives a well detectible signal at a special angle θ. If you combine the wavelength λ of the x-rays and the angle θ in the right way you get Bragg’s law: λ = 2 d sin θ with d the distance between the atomic layers
In this special case the incident angle and reflected angle are the same in respect to the surface, because the atomic layers are parallel to the surface. This means the orientation angle Y is Y = 0°. If you vary the orientation angle Y of the atomic layers by beaming in another direction on the surface of the component, the beam will be reflected at other orientated layers. (see fig. 2 and fig. 3)
By using different angles Y the elastic-plastic theory says that sin²Y is proportional to θ. The use of a special anode material (normally chromium for steel) and a filtering system you know exact the wavelength of the x-rays. Hook’s law tells us that the relative change ?d/d is proportional by using the Young module E.
Now you have a connection between Y, the obtained reflections angle θ and the residual stress, because the distance d0 of an atomic lattice without stress and the according angle θ0 are well known.
The x-rays are reflected within a thin layer in the component of around 10 ?m. The area of the measurements lies between 1 mm² and 50 mm².

3. Some thoughts before

The surface of shot peened components has a typical roughness Rz of Rz = 10 ?m to 40 ?m. The measured layers by x-rays have a thickness of around 10 ?m as mentioned above. It depends on the different wavelength of the x-rays (or with other words the material of the anode). The intensity of the x-ray beam drops exponential with the depth. That means the residual stresses in layers at or near the surface determine the result, because the detector averages over all reflection in respect of the intensity.
The structure of the shot peened surface is as big as or bigger than the thickness of (all) used atomic layers for determining the residual stress. As a consequence the surface structure and the orientation angle Y of the incident beam must have an influence on the result.

4.1 Experimental procedure and results

A flat sample of spring steel with the dimensions of 300 mm * 100 mm * 10 mm with a tensile strength of around Rm = 1550 N/mm² was shot peened with nearly 100 % coverage. The roughness of the surface was Rz = 25 ?m. The residual stress at the surface was measured in an area of 8 mm diameter. Only three Y-angles with a total difference of 10° were used to determine the stress. The measurement was repeated at least 5 times to get significant results. The average Y-angle was varied between 5° and 53°. Figure 4 shows the result. The diamonds show the mean value of the residual stresses and the lines the according standard deviations.
Now the following assumption was made: The results for the three lower angles and for the four highest angles each are nearly on the same level. These two levels were joined by two horizontal lines. The connection between these two levels was joined by a straight line with the help of the value of the Y-angle of 15°.

The two fitted levels give the residual stress values:

 mean Y-angle residual stress 5° - 15° -624 MPa 20° - 53° -499 MPa

By using the lower Y-angle you can measure about 25 % more compressive residual stress than with high orientation angles.

4.2 Interpretation and conclusions

At lower Y-angles the value of the compressive residual stress is higher and at higher Y-angles lower. If the angles are lower the x-rays can reach the ground structure of the shot peened surface. At the ground of an impact hole the material cannot make much relaxation. At the peaks of the surface the material is relaxed, because it has no support from the side and can lower the compressive residual stress by expanding.
If you measure residual stresses at shot peened surfaces by x-rays, which has the advantage of a non-destructive measurement, the exact conditions have to be laid down for a long term. In this case the results are comparable.
The best way is to determine a residual stress profile. Not only is the surface value important. Taking the concept of local durability [Ba 09, Wo 88] the shaping of the residual stress zone into the depth is also important. E.g., if you stress peen a component the crack initiation is beyond the residual stress layer under the surface. [Ba 09, Mü97].
Quite a lot of specifications have to be renewed to speak the same language.

5. References

Mü 93: Müller, Eckehard: Messung von Lastspannungen bei verschiedenen Oberflächenrauhigkeiten mit Hilfe eines Röntgendiffraktometers; HTM 48 (1993) 1/93, pp. 50 – 52
Mü 97: Müller, Eckehard: Eigenspannungsabbau an spannungsgestrahlten
Torsionsproben unter dynamischer Belastung, Materialwissenschaften und Werkstofftechnik 28 (1997), pp. 549 - 556
Wo 88: H. Wohlfahrt: Einfluß von Mittelspannungen und Eigenspannungen auf die lokale Dauerfestigkeit, VDI-Berichte Nr. 661, VDI-Verlag, Düsseldorf 1988, pp. 99 - 127
Ba 09: Steven Baiker (Hrsg): Shot Peening, MFN , 2.Auflage, Wetzikon, 2009 (www.mfn.li), pp. 136 – 139

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