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Science Update

##### in Vol. 10 - September Issue - Year 2009

##### Indentation Technique for Characterization of the Metal Surface Modified by Cavitation Peening

Fig. 1: Cavitation peening for introducing compressive residual stress on metal surface

Fig. 2: Spherical indentation for characterization of the metal surface

Fig. 3: Indentation load-depth curves obtained with finite element analyses

Fig. 4: Procedure of inverse analysis

Fig. 5: Determination of work-hardened yield stress at 200

**Introduction**

Cavitation peening (CP) has been developed as a method to improve the fatigue life of metallic materials [1 - 6]. CP introduces the compressive residual stress near the metal surface, utilizing cavitation impacts produced by injecting a high-speed water jet. The great advantage of CP is that surface roughness is considerably smaller than that of shot peened one, since there is no solid collision in CP.

In order to optimize the peening condition for fatigue life, the underlying mechanism for the improvement of fatigue life must be understood in detail. One explanation is that the residual stress suppresses the initiation of microcracks in the material. However, the mechanism is not so simple. According to our previous experiments [2], the fatigue life of the material modified by CP is longer than that by shot peening (SP) while the layer where the compressive residual stress is introduced by CP is thinner than that by SP. For the complete understanding of the underlying mechanism, the characteristics of the peened surface should be quantitatively evaluated. While the residual stress of the peened surface was evaluated using X-ray diffraction method (e.g., Ref. [1]), the work-hardened yield stress of the peened surface has not been quantitatively measured in previous studies.

The present paper presents a combined experimental/numerical method to determine the yield stress near the surface of the steel SUS316L modified by CP. This method utilizes a depth-sensing instrumented indentation technique using a spherical indenter. Especially, a strategy of inverse analysis using finite element analyses has been established to determine the yield stress from the results of indentation tests.

**Cavitation Peening**

We prepared the specimen processed by CP (denoted by CP specimen), and

the specimen, which was not peened (denoted by NP specimen). The specimens were made of stainless steel JIS SUS 316L. The size of the specimens was 30 mm × 30 mm × 10 mm.

The specimen surface was finished with a grinder. For the CP specimen, the specimen surface was treated by cavitating jet in water, as depicted in Fig. 1(a). The nozzle diameter was 2 mm, the injection pressure was 30 MPa and the pressure of the water-filled chamber was 0.42 MPa. The stand-off distance was 80 mm. The processing time per unit length was 10 mm/s.

Figure 1(b) compares the residual stress measured by X-ray diffraction method between CP and NP specimens. In this comparison, stress factor for X-ray measurement was set to -368.9 MPa/deg. The results revealed that CP introduced a significant compressive residual stress even at 1000 ?m depth from the surface.

**Spherical Indentation**

We conducted spherical indentation tests as illustrated in Fig. 2(a). A spherical indenter with diameter 100 ?m was used. The indentation load was applied by 0.2 mgf load increments within 20 ms intervals until 100 mgf (0.98 N). To exclude the influence of surface roughness on the test results [7], the specimen surface of 200 ?m thickness was removed by electrolytic polishing.

From the measured load-depth curves, the maximum indentation depth hmax was obtained. For NP specimen, hmax = 2.70 ± 0.13 ?m; for CP specimen, hmax = 1.75 ± 0.19 ?m. The results reveal that the maximum indentation depth reduces for CP specimen. We will focus on this difference in the maximum indentation depth hmax.

**Finite Element Analysis**

It is well known that the maximum indentation depth depends on the yield stress and residual stress of the specimen [8,9]. We estimated the effect of yield stress and residual stress on our indentation test results using finite element analyses.

We conducted finite element analyses using a commercial finite element code MSC.Marc. Figure 2(b) illustrates the axisymmetric finite element model used in the analyses. The model size for the specimen was 1 mm radius × 1 mm depth. The indenter was modeled as a rigid body while the specimen was modeled as a homogeneous, isotropic elastic-plastic material. The indentation load was applied through a contact analysis between the indenter and the specimen. In addition, fixed boundary conditions were applied to the bottom of the specimen (in y-direction in Fig. 2(b)).

An elastic-plastic analysis using updated Lagrange configuration was conducted based on J2 flow theory with isotropic hardening. We substituted the strain hardening relation measured by uniaxial tension tests on NP specimens. The Young’s modulus and 0.2 % offset yield stress for NP specimen were E = 172 GPa and ?y = 219 MPa. Poisson’s ratio was set to ? = 0.3.

In general, the yield stress increases due to work hardening by material processing. Figure 3(a) presents the results when the yield stress ?y is varied. When the yield stress is large (?y = 300 MPa), the indentation depth decreases. A large yield stress allows a high stress near the indented surface, which leads to a small deformation of the specimen.

Moreover, CP introduces a compressive residual stress near a metal surface. Figure 3(b) compares the result considering an equibiaxial compressive residual stress ?r = -313 MPa with that obtained by neglecting the residual stress. A large compressive stress serves as a resisting force against dent formation, which leads to an apparent increase in the indentation load.

Therefore, in our case, both an increase in yield stress and a compressive residual stress reduce the maximum indentation depth for a fixed indentation load. To determine the work-hardened yield stress from the results of a depth-sensing indentation, we must distinguish the effect of increased yield stress from the residual stress effect.

**Strategy of Inverse Analysis**

As described above, it is difficult to interpret the indentation test results when the yield stress and residual stress are changed simultaneously. The issue has been seldom addressed in the previous literature [10,11]. Our strategy transforms these complicated situations into a simple, one-parameter inverse problem by predetermining the residual stress and Young’s modulus using other experiments. Figure 4 schematically illustrates this procedure.

The residual stress ?r on the peened surface was measured based on sin2? method using X-ray diffraction system. We used ?-diffractometer method for measuring X-ray diffraction. The inclination angle of crystal lattice ? was set to 0, 10, 20.8, 28.1, 34.3, 40 deg. The X-ray tube used was a Cr tube operated at 35 kV and 8 mA. The diffractive plane was the (311) of ?-Fe, and the reference diffractive angle 2?0 was 148.5 deg. The diffractive angle 2? ranged from 142.6 deg to 154.3 deg with 0.15 deg increments within 8 seconds intervals. By these procedures, the residual stress ?r was obtained as

“formula can not be displayed online” (1)

where E is Young’s modulus on the peened surface.

Here we should note that Young’s modulus on the peened surface reduces by CP process, as reported by experiments [12]. Therefore, the effect of the degradation of Young’s modulus should be incorporated for the appropriate evaluation. (We depicted Fig. 1(b), following a general X-ray measurement procedure, and thus the values in the figure have some differences due to the local degradation of Young’s modulus.)

For correction, we determined Young’s modulus of the peened surface using bending tests on cantilevered specimen. The specimen size was 90 mm length × 12 mm width × 3 mm thickness. Both surfaces of the specimen were processed by CP. From the measured load-deflection relation, Young’s modulus was derived based on the beam theory. Here we assumed that Young’s modulus varies as a linear function of the depth from the surface within the peened depth ?=700 ± 24 ?m. We determined the peened depth with repeated surface removal, monitoring the indentation depth and detecting the transition position between peened and unpeened sites. By these procedures, Young’s modulus on the peened surface (200?m depth from the surface) was determined as E = 117 GPa. Young’s modulus on the peened surface is remarkably smaller than that of NP specimen (172 GPa).

Substituting Young’s modulus into Eq. (1), the residual stress ?r on the peened surface (200?m depth from the surface) was determined as ?r = -313 ± 26 MPa. By obtaining these experimental values, only one parameter to be determined from indentation test results is the yield stress.

**Determination of Work-HardenedYield Stress**

Using the finite-element analyses with changing ?y and fixed E = 117 GPa and ?r = -313 MPa, we can obtain one-to-one correspondence between work-hardened yield stress and maximum indentation depth hmax, as shown in Fig. 5. Therefore we can determine the work-hardened yield stress inversely from the experimental data of maximum indentation depth. From Fig. 5, the work-hardened yield stress on the peened surface (200??m depth from the surface) is determined as 435 MPa; the estimation error is approximately ± 100 MPa due to the data scatter in indentation tests. The determined value of yield stress is remarkably larger than that of NP specimen (219 MPa).

These results reveal that the metal surface is remarkably work-hardened by CP. The work-hardening effect can be observed even at the depth 200 ?m. These results imply that the plastic strain pre-introduced by the work-hardening process may increase the low-cycle fatigue life of the CP specimen. Otherwise, the large pre-strain may serve as a source of the compressive residual stress, which suppresses the initiation of the surface crack. These discussions will be addressed in our future work. In either case, the present indentation technique will be a very powerful tool for monitoring the work-hardened state of the peened surface and for quantitatively investigating the peening effect on the fatigue life.

**Acknowledgement**

M. N. acknowledges the support of MEXT under the Grant-in-aid for Young Scientists (B) 21760649. The authors acknowledge the support of JSPS under the Grant-in-aid for Scientific Research (A) 20246030.

**References**

1. Soyama, H., Saito, K. and Saka, M., 2002, “Improvement of Fatigue Strength of Aluminum Alloy by Cavitation Shotless Peening,” Journal of Engineering Materials and Technology, Trans. ASME, Vol. 124, No. 2, pp. 135-139.

2. Odhiambo, D. and Soyama, H., 2003, “Cavitation Shotless Peening for Improvement of Fatigue Strength of Carbonized Steel,” International Journal of Fatigue, Vol. 25, Nos. 9-11, pp. 1217-1222.

3. Soyama, H., 2004, “Introduction of Compressive Residual Stress Using a Cavitating Jet in Air,” Journal of Engineering Materials and Technology, Trans. ASME, Vol. 126, No. 1, pp. 123-128.

4. Soyama, H. and Macodiyo, D.O., 2005, “Fatigue Strength Improvement of Gears Using Cavitation Shotless Peening,” Tribology Letters, Vol. 18, No. 2, pp. 181-184.

5. Soyama, H., 2006, “Improvement of Fatigue Strength of Metallic Materials by Cavitation Shotless Peening,” Metal Finishing News, Vol. 7, March Issue, pp. 48-50.

6. Soyama, H., 2007, “Improvement of Fatigue Strength by Using Cavitating Jets in Air and Water,” Journal of Materials Science, Vol. 42, No. 16, pp. 6638-6641.

7. Mencik, J. and Swain, M.V., 1995, “Errors Associated with Depth-Sensing Microindentation Tests,” Journal of Materials Research, Vol. 10, No. 6, pp. 1491-1501.

8. Swadener, J.G., Taljat, B. and Pharr, G.M., 2001, “Measurement of Residual Stress by Load and Depth Sensing Indentation with Spherical Indenters,” Journal of Materials Research, Vol. 46, No. 16, pp. 5755-5767.

9. Cao, Y.P. and Lu, J., 2004, “A New Method to Extract the Plastic Properties of Metal Materials from an Instrumented Spherical Indentation Loading Curve,” Acta Materialia, Vol. 52, No. 13, pp. 4023-4032.

10. Cao, Y.P. and Lu, J., 2004, “A New Scheme for Computational Modeling of Conical Indentation in Plastically Graded Materials,” Journal of Materials Research, Vol. 19, No. 6, pp. 1703-1716.

11. Larsson, P.L., 2006, “Modelling of Sharp Indentation Experiments: Some Fundamental Issues,” Philosophical Magazine, Vol. 86, Nos. 33-35, pp. 5155-5177.

12. Sekine, Y., Kai, A. and Soyama, H., 2008, “Reduction of Young's Modulus of Surface Modification Layer of Stainless Steel SUS 316 L by Cavitation Shotless Peening,” Transactions of the Japan Society of Mechanical Engineers. A. Vol. 74, No. 742, pp. 901-908.

Masaaki Nishikawa (Dr. Eng.)

Associate Professor

Department of Nanomechanics,

Tohoku University

6-6-01 Aoba, Aramaki, Aoba-ku, Sendai,

980-8579, Japan

E-mail: nishikawa@mm.mech.tohoku.ac.jp

Hitoshi Soyama (Dr. Eng.)

Professor

Department of Nanomechanics,

Tohoku University

6-6-01 Aoba, Aramaki, Aoba-ku, Sendai,

980-8579, Japan

E-mail: soyama@mm.mech.tohoku.ac.jp