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Macroscopic and Microscopic Residual Stresses in Ceramics Due to Contact Loading

Wulf Pfeiffer and Michael Rombach

Fraunhofer-Institut Werkstoffmechanik, D-79108 Freiburg, Germany

Abstract

The paper deals with microplastic deformation and macroscopic residual stresses in silicon nitride ceramics due to contact loading and their effect on the near-surface strength. Depth-resolving X-ray residual stress measurements on shot peened samples detect high microplastic deformation and macroscopic compressive residual stresses up to 1.3 GPa at the surface decreasing to zero within 10 pm. These high compressive stresses enhance the load bearing capacity in the ball-on plate test up to 50 % compared to polished samples.

1 Introduction

Residual stresses due to mechanical loading has been thought to have not a significant effect on brittle materials like ceramics. Nevertheless, high microplastic deformation and residual stresses have been determined by X-ray diffraction methods for ceramics due to hard machining procedures like lapping and grinding [l], [2]. Both machining induced residual stresses and damage effect the strength.

Figure 1 shows that due to high compressive residual stresses conventionally ground silicon nitride reveals a slightly higher transverse bending strength than creep feed ground silicon nitride although a higher amount of damage is introduced.

residual stress

0 5 10 '

depth I pm

crack depth m

conv. creep

grinding

400

300

200

100

a

strength

conv. creep

grinding

Fig. 1: Residual stresses overcom- pensate the effect of damage on the strength of differently ground silicon nitride.

Recent rolling wear tests of silicon nitride have shown [3] that under rolling wear conditions extremely high compressive residual stresses up to 1 GPa may develop. Since also severe cracks were visible after only a few hundred cycles, the residual stresses may be proposed to give a significant contribution to the surprisingly high overall lifetime of more than lo5 cycles (see Fig. 2).

Copyright (C) JCPDS-International Centre for Diffraction Data 1999ISSN 1097-0002, Advances in X-ray Analysis, Volume 41

This document was presented at the Denver X-ray Conference (DXC) on Applications of X-ray Analysis. Sponsored by the International Centre for Diffraction Data (ICDD). This document is provided by ICDD in cooperation with the authors and presenters of the DXC for the express purpose of educating the scientific community. All copyrights for the document are retained by ICDD. Usage is restricted for the purposes of education and scientific research. DXC Website – www.dxcicdd.com

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cracks after 300 cycles residual stress in MPa 0

-600

-800

cycles in IO3

Fig. 2: Rolling wear tests of silicon nitride: Residual stresses and cracks due to contact loading (3 GPa, 3% slip, dry).

These two examples show that generally the creation of compressive residual stresses in contact loading situations is accompanied by damage. The aim of the investigations was therefore to evaluate basic information about

l the possibility of a controlled development of compressive residual stresses by shot peening

. the depth distribution of residual stresses

0 the effect of residual stresses induced by shot peening on the near-surface.

2 Experimental Details

2.1 Material investigated

The material investigated was a commercially available (Ceramics For Industry, CFI) silicon nitride (GPSN, SN-N3208). The most important material data are given in Tab. 1. The diffraction pattern in Fig. 3 shows, that the material consists mainly of p-silicon nitride. Sintered cylindrical samples with 20 mm diameter and 10 mm height were prepared for shot peening and ball-on-plate tests by a successive grinding and polishing of the flat surfaces.

characteristic strength o. 900 MPa

Weibull modulus 18

Young’ s modulus 310 GPa

Poisson’s Ratio 0.28

fracture toughness Kr, 7.5 MPadm

(from Vickers indentation)

fracture toughness Kn 4.7 MPadm

(from pre-cracked bend test)

I

A * 70.00a> I 0.000 S-theta 50a.a ‘\,PI1SN-l OS.RPW St+I-F03 34-l. RUSSEN S13N4 p-sr:,om N,tr,dC HPSN (hot presses S‘liccn n!tr>le> 5N

Tab. 1: Material data SN-N3208. Fig. 3: CrKa-diffraction pattern of SN-N3208 and lines of corresponding reference pattern 33-l 160.

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2.2 Shot peening

Shot peening was performed with an injection system. Using two different nominal sizes of zirconia beads (fine: 75 urn - 125 pm, coarse: 250 pm - 425 pm, hardness HRC 50-65), two different peening times and two different pressures, 8 different shot peening treatments were applied to the polished silicon nitride samples (see Tab. 2).

sample # 1 #2 #3 #4 #5 #6 #7 #8

bead size fine fine fine fine coarse coarse coarse coarse

pressure 7bar 7 bar 3.5 bar 3.5 bar 7 bar 7 bar 3.5 bar 3.5 bar

time , 2min , 6min , 2min , 6min , 2min , 6min 2min 6min , , ,

Tab. 2: Shot peening parameters.

2.3 X-ray diffraction analysis

The microplastic deformation was determined using the effect of lattice defects (e.g. dislocations) on the width of the diffraction line. The macroscopic residual stresses were determined on basis of the shift of the diffraction line. The measurement parameters are given in Tab. 3.

lattice radiation diffraction inclination tilt angle \I, 1% s2 penetration depth plain angle 20 angle a (u, = a-28/2) %f

(323) CuKa 141.4” 1% a 570.9” -69.7”s w IO” 4.1.10e6/MPa lumc z,ff c35pm

Tab. 3: Measurement parameters for residual stress and microstrain evaluation.

2.3.1 Microstrain

At high diffraction angles the influence of microstrains on the line width dominates compared to size effects. Using a strain-free reference material with sufficiently large crystallites the line broadening caused by the instrument can be separated. The microstrains are then calculated quantitatively from the integral widths of diffraction lines using the following equations [4], [5]:

/I = 4E, tan(8) (1)

Where: &M = microstrain

P = corrected integral width of the material investigated b = measured integral width of the material investigated B = measured integral width of a strain-free reference material

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2.3.2 Macroscopic residual stresses

In case of the shot peened samples a plane stress state being rotationally symmetric with respect to the

normal on the surface is obtained. The dependency of lattice strain components G+,,,, on the tilt angle I/J

and the macroscopic stress O, can be described by eq. (3):

& - 1s 0 sin21y+s, [WV I w-2 2 v (3)

2.3.3 Depth probing

For depth probing of macroscopic residual stresses and microplastic deformation the inverse Laplace

transformation method was used, see e.g. [6]. The information F(r) gathered by X-rays with a

penetration depth ‘I: from a material with a depth distribution f(z) is a weighted average defined by

j f(z) exp(- @)dz

F(z)= O m

'

(4)

J exp(- z/z)& 0

In case of depth gradients of residual stresses or microstrains F(z) means the peak position or the peak

width, respectively. The first step of the evaluation procedure is to measure a series of F(r) for different values of z by variation of the angle of inclination a (tilt angle v). The next step is to assume

a functional relationship for f(z) with some free parameters. By fitting F(r) to the measured values of

F(z), the free parameters are determined and the depth distribution is evaluated from the inverse Laplace transform, f(z).

As an example for depth probing of the residual stresses using such a procedure, Fig. 4 illustrates the evaluation of the stress-depth distribution of a polished and a shot peened silicon nitride sample assuming the following function for the depth distribution of residual stresses:

~(Z)=a,+a,.(Z-a,).exp(a,.z) (5)

Other types of functions were also tested but resulted in depth distributions similar to eq. (5) within the measurement accuracy.

2f3it-1"

141,6

7

, Laplace transformed stress-profile fitted to the 141,2 ' 0 Or2 Or4 0.6 0‘8.2 I

sin y data (CuKa-radiation).

Fig. 4: Examples of sin2v-distributions obtained on polished and shot peened silicon nitride,

respectively, with the sin2u/-distribution of the

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2.4 Ball-on-plate test

In the ball-on-plate test, the polished and shot peened ceramic plates are loaded by a silicon nitride ball with a diameter of 11.11 mm. Fig. 5 shows the loading situation. The load is increased stepwise until a typical cone-crack appears, see Fig. 6, which follows exactly the maximum tensile stresses. Because of the statistical behavior of ceramics, the load which causes fracture varies from test to test within a certain scatter-band. In this paper, the fracture load F, means the load which causes fracture with a probability of 50%.

Fig. 5: Loading situation in the ceramic ball-on-plate test.

Fig. 6: Cone crack (0 400 pm) at the surface of a plate after loading in the ball-on-plate test.

The stress field of this static ball-on-plate contact is typical for stress fields occurring in contact situation e.g. in roller-bearings: The contact induced stress fields show strong gradients and the tensile stresses, which lead to cracks in brittle materials, are restricted to a very thin surface layer. The advantage of the sphere-on-plate contact problem is that the stress field can be calculated analytically in closed form [7].

3 Results

3.1 Plastic deformation in Ceramics

The possibility of a controlled development of plastic deformation and compressive residual stresses without additional significant damage is supported by the result of contact loading tests (ball-on plate tests), see Fig. 7. The load F was increased until plastic deformation or fracture was observed. If the diameter of the indenter sphere is below a certain critical value, plastic deformation is obtained before fracture occurs.

load F in kN

8

7 plastic deformation

2

1 Fig. 7: Ball on plate test on silicon nitride: 0

2 3 4 5 Development of plastic deformation and fracture as a

sphere radius R in mm function of the ball radius [3].

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3.2 Microplastic deformation and residual stress fields

All shot peening procedures resulted in substantial microplastic deformation and high compressive residual stresses up to 1300 MPa at the surface decreasing to zero within the first 10 pm, see Fig. 8 and Fig. 9. The microplastic deformation and residual stresses differ significantly from the deformation and stress fields of the polished sample showing negligible amounts of deformation and stress.

As expected, the deformation and stress fields depend on the shot peening conditions. The highest surface stresses are created using long peening times whereas high peening pressures lead to deep- reaching compressive stress fields. In general, the size of the beads does not seem to have a dominant influence on the deformation and stress fields.

residual stress in MPa

0

-200

-400

-600

-800

-1000

0' ’ -1400 ’ I 0 1 2 3 4 0 1 2 3 4

depth in pm depth in pm

microstrain in IOE-3 3-

polished

01 0 1 2 3 4

depth in pm

residual stress in MPa

Fig. 8: Depth distributions of microplastic deformation and residual stresses of polished and shot peened silicon nitride samples (fine beads).

0 1 2 3 4

depth in pm

-600 \

Fig. 9: Depth distributions of microplastic deformation and residual stresses of polished and shot peened silicon nitride samples (coarse beads).

The type of functions evaluated for the depth distributions of deformation and stresses are in general qualitatively comparable. Thus, it can be concluded that the macroscopic residual stresses are mainly determined by the amount of microplastic deformation. Nevertheless, in case of the samples shot peened using high pressures and long times the depth distributions of microplastic deformation and residual stresses show significant differences concerning the relationship between macroscopic residual stresses and microplastic deformation. The severe shot peening conditions are obviously able to develop the highest microplastic deformation near the surface, while the corresponding stress

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distributions show a drop of the stress level near the surface. This may be due to the additional effect of macroplastic deformation due to severe shot peening conditions.

3.3 Experimentally determined load capacities

The load capacities F, determined experimentally in the ball-on-plate test point out the significant gain of strength (up to 50 %) of the shot peened samples with respect to the polished reference samples (see Fig. 10). The increase of the load capacity depends mainly on the peening time for the fine beads and on the peening pressure for the coarse beads. The highest load capacity is found for the long time shot peening at high pressure using coarse grained beads. As these samples show the deepest reaching residual stress fields, it can be concluded that mainly the depth of the shot peening induced residual stress field is responsible for the gain in load capacity.

12 peening time

2 min 11 .m-6min..

5 10 .5 -t 9 9 aI

z 2 8

fine beads

coarse beads

7

6 3,5 7

peening pressure in bar

, Fig. 10: Experimentally determined polishea load capacities of polished and shot

peened silicon nitride samples.

4 Conclusions

Shot peening is a common procedure to improve the strength of metal components. Up to now, it has not been successfully applied to ceramics, as these brittle materials have been assumed to show no significant plastic deformation due to mechanical loading and hence would not develop any residual stresses improving the strength.

The presented results show, however, that under specific shot peening conditions (applied for patent) in brittle materials like silicon nitride substantial microplastic deformation and high compressive stresses up to more than 1 GPa can be introduced near the surface. The depth distributions can be evaluated quantitatively by advanced X-ray diffraction techniques.

Exposing these strengthened surfaces to contact loading situations, which are characterized by a steep near-surface stress gradient, a significant gain in load capacity and strength can be evaluated. As additional investigations [7] have shown, that shot peening may introduce also damage, further investigations will concentrate on the evaluation of shot peening conditions which result in an optimum combination of residual stresses and damage.

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5 References

[l] W. Pfeiffer, T. Hollstein. Characterization and Assessment of Machined Ceramic Surfaces. In 2nd Intern. Confer. on Machining of Advanced Materials (MAM), VDI-Verlag, Dusseldorf, Germany ,VDI-Berichte Nr. 1276, 587-602, 1996.

[2] W. Pfeiffer, T. Hollstein, E. Sommer: Strength properties of surface-machined components of structural ceramics. Fracture Mechanics, 25th Vol., ASTM STP 1220, 19-30, Amer. Sot. for Testing and Materials, Philadelphia, USA, 1995.

[3] T. Hollstein, M. Rombach, W. Pfeiffer, M. Popp: Vollkeramische Walzlager aus Siliciumnitrid: Anwendung, Auslegung und Optimierung. VDI Berichte Nr. 1151,3-l 1, 1995.

[4] G.K.Williamson, W.H. Hall, X-ray line broadening from filed aluminum and wolfram, Acta Met. 1 (1954), pp. 22-31.

[5] T.R. Anantharaman, J.W. Christian, Acta Cryst. 9 (1956), pp. 479-486.

[6] H. Ruppersberg, I. Detemple, J. Krier: Evaluation of strongly non-linear surface stress fields (3,,(z) and q&z) from diffraction experiments. Phys. Stat. Sol., 681, 1989.

[7] W. Pfeiffer, M. Rombach: Residual stresses and damage in ceramics due to contact loading. To be published in: Proc. of the ICRSS, Linkopping, Sweden, 1997.

[S] M. Rombach: Experimental and theoretical investigations on plastic deformation and brittle cracking in a ball-on-plate contact of ceramic materials. Ceramics charting the future, Edit. P. Vincenzini, Techna Srl, 1055-1064, 1995.

Copyright (C) JCPDS-International Centre for Diffraction Data 1999ISSN 1097-0002, Advances in X-ray Analysis, Volume 41