compression

ELSEVIER

Materials

Dislocation

Science

and Engineering

(1997)

lOOO- 1003

arrangements in single crystalline tension/compression Joanne Degli-Esposti,

Laboratoire

A234-236

de Physique

des MatPriaux

(URA

CNRS

Alain Jacques, Amand no. 155), Ecole

des Mines

de Nancy,

silicon fatigued in George *

Pare de Saurupt,

F-54042

Nancy,

France

Received 24 February 1997; received in revised form 3 April 1997

Abstract Preliminary results of low-cycle fatigue experiments at high temperatures on [ 1231 silicon single crystals are reported. The effects of temperature (from 1073 to 1373 K), plastic strain rate (from 5 x lo-’ to 5 x lo- 3 s- ‘) and plastic strain amplitude (10W3 and 5 x 10-3) on the mechanical behaviour are investigated. At low temperature and high strain rate, fracture took place after about 100 cycles, while saturation of the maximum stress could be reached at higher temperatures and lower strain rates. Transmission electron microscopy (TEM) observations reveal that a cellular arrangement of dislocations is associated with the latter case while loop-patches are characteristics of the former. 0 1997 Elsevier Science S.A. Keywords:

Dislocations;

Fatigue;

Mechanical

properties;

Silicon

1. Introduction

2. Experimental

A great deal of experimental [l-5] and theoretical [6-l l] research has been done during the last 30 years on fatigue testing of single crystalline metals, either f.c.c. or b.c.c. The main features of the mechanical behaviour of these materials, i.e., the cyclic hardening curve and the cyclic stress-strain curve, are linked to the development of specific dislocation arrangements, loop patches, veins, persistent slip bands with ladder structures or cells. Silicon has been widely used as a model material to study the mechanical behaviour either in monotonic uniaxial tension or compression, or in fracture experiments to investigate the brittle-ductile transition. Si combines the slip geometry of f.c.c. materials with a strong lattice friction, analogous to that observed in b.c.c. crystals at low temperature. This gives the unique possibility to modify the plastic behaviour to a large extent, simply by changing the temperature. This note reports on first results in silicon crystals deformed alternately in tension and compression in the plastic range (low-cycle fatigue).

Cylindrical samples(Fig. l(a)) oriented for single slip (stressaxis parallel to [123]) were machined out dislocation-free, single-crystalline, undoped, float-zone silicon. The graphite grips specially designed for tension/compression testing of ‘brittle’ materials at high temperature are shown in Fig. l(b). Tests were done under neutral atmosphere (70% Ar, 30% He). The elongation was measured at the heads of the sample.

* Tel.: + 33 83584156; [email protected] 0921-5093/97/$17.00 PII

fax:

0 1997 Elsevier

SO921-5093(97)00409-7

+ 33

83579794;

e-mail:

w

S.A. All rights

strain

L 03.5 mm

a

b

tranFig.

Science

5

13 mm

reserved.

1. (a) Sample;

(b) grips

for tension/compression

testing.

J. Degli-Esposti

et al. /Materials

Science

The intrinsic brittleness of Si necessitates specific procedures to prevent fracture at the very beginning of fatigue tests. First, samples had to be pre-strained at 1373 K for a few cycles in order to introduce dislocations in sufficient density for further straining at lower temperature. After stabilisation at the testing temperature, the sample was cyclically loaded at constant frequency but to increasing strains, i.e., at increasing strain rates, until the desired test parameters, plastic strain amplitude per cycle and strain rate, were reached. These conditions were then kept constant all over the experiment (strain-controlled experiment). Unless the sample failed, it was cooled down under cyclic loading, as during the fatigue test. After cooling, (121) slices, perpendicular to the slip plane and parallel to the Burgers vector of the primary slip system [lOl](ill), and (ill) slices, parallel to the primary slip plane, were cut, mechanically polished and thinned by ion milling for transmission electron microscopy (TEM) observations in a Philips CM 200 microscope operating at 200 kV.

and Engineering

A234-236

60

1000-1003

1001

stress WW

50 t

fracture at 100 cycles

-T -T=

loi 0

3. Mechanical

(1997)

= 1173 K 1373 K

!

I I

1

1 I

0

1

2

3

hehaviour

The aim of these preliminary experiments was to obtain preliminary information on the effect of temperature (from 1073 to 1373 K, AE~ = 10p3, i= 5 x 1O-4 s- ‘), average plastic strain rate (from 5 x lo- 5 to 5 x 10-3 s-1, 1173 K, Asr, = 5 x 10 p3), and plastic strain amplitude As,, (at 5 x lop3 and 10p3, i:= 5 x 10 ~ 4 s ~ ‘, 1073 and 1173 K) on the behaviour of silicon in fatigue. The average plastic strain rate is equal to Asr, divided by the time necessary for a half-cycle. 3.1. Temperature

dependence

Fig. 2 shows the evolution of the maximum stress with the cumulative strain under the conditions given above. The stress level decreases with increasing temperature, as expected in silicon where dislocation glide is strongly thermally activated [12]. Hardening is observed in the first cycles, with a continuously decreasing rate. At 1373 K, the peak stress quickly saturates at 10 MPa. At 1173 K, 3 x lo3 cycles were not sufficient for saturation to be obtained. At 1073 K, failure by brittle cleavage along (111) occurred after only about 100 cycles for the three tested samples. (Fracture was always initiated at a surface flaw, so that it is believed that a better surface state would prevent it.) 3.2. Plastic strain-rate

dependence

Fig. 3 shows three curves corresponding to different values of the average plastic strain rate. Increasing the strain rate has a similar effect as lowering the tempera-

Fig. 2. Evolution of the peak stress with the cumulative strain (2n A&J. Effect of temperature (As = 10 3, i: = 5 x 10 4 s - I).

ture: the peak stress per cycle increases, as well as the hardening rate for a given number of cycles. The sample tested at the highest rate failed after 125 cycles. 3.3. Influence of the plastic strain amplitude per cycle It can be appreciated on Fig. 4. At 1173 K, the stress level is the same during the first cycles, but the hardening rate decreases faster at the lower strain amplitude.

4. TEM

observations

Figs. 5 and 6 show typical micrographs obtained in two samples that were fatigued: 800 cycles at 1173 K, da,, = 10p3, i:=5 x 10-s s- i for one of the samples; 100 cycles at 1073 K, AE~ = 5 x lo-‘, 8= 5 x lop4 s-’ for the other. At 1173 K, dislocations are arranged in cells, with a size varying from 4 to 10 urn. The thickness of cell walls is about 0.5 urn. Most dislocations have the primary Burgers vector but tangled configurations suggest a significant amount of cross-slip. Cells are equiaxed in average and walls have no preferred orientations. Within the cells, the dislocation density is about 3 x 10’ cm ~ *, 90% of the dislocation lines belonging to the primary slip system. Dipoles, elongated loops and debris can be seen. Their density is at a minimum in the

J. Degli-Esposti

et al. /Materials

Science

and Engineering

A234-236

(1997)

1000-1003

stress WW

0

2

4

6

Fig. 3. Evolution of the peak stress with the cumulative of the plastic strain rate (T= 1173 K, A$ = 5 x 10e3).

6 strain.

Effect

middle of the cells and increases near the cell walls. Approximately the same dislocation arrangement was observed after only 60 cycles in a sample strained in the

60

stress (MW

same conditions. On (ill) slices, bowing dislocations are also visible in and out of the cell walls. At lower temperature and higher strain rate (Fig. 6), no cells can be seen, but loop patches are present, forming sinuous ‘fragmented walls’. The distance between them, measured parallel to the trace of the slip plane, varies between 2 and 4 urn. The thickness of patches is maximum ( = 0.3 urn) when they are perpendicular to the slip planes. The overall density of defects, either within or between the walls, is larger than in the former case, although of the same order of magnitude. Very few dislocations of non-primary slip systems were observed. Since fracture occurred before stress saturation, it is believed that such a microstructure would have evolved with further cycling, possibly into a veinlike structure.

50 I 40

30

20

10

I

-A+ 1 -BE,,

= 0.001 30.005

)

strain

0 1I

1

0

1

Fig. 4. Evolution of the peak of the plastic strain amplitude

6I 2

II 3

Fig. 5. Dislocation cells in a sample fatigued at 1173 K, Aar = 5 x IO-?, b= 5 x lop5 SC’, number of cycles = 800. TEM micrograph: foil normal [l?]], S: 202. The primary slip direction is horizontal. Marker: 1 urn.

5. Discussion

I 4

stress with the cumulative strain. Effect (T = 1173 K, B = 5 x 10 e-4 s - ‘).

From these very first experiments, only some trends can tentatively be derived: (i) The saturation stress was clearly reached only once, making impossible to draw any cyclic hardening

J. Degli-Esposti

et al. /Materials

Science

and Engineering

A234L236

(1997)

1000-1003

1003

detail was obtained so far about the interaction (screening) between the crack and dislocations in fatigue conditions. Using the conventional Orowan relation cc!,,= sp,bv where s is the Schmid factor, pm the mobile dislocation density, b the Burgers vector modulus, and u the average dislocation velocity and the known dislocation velocity in silicon [13]: v = A(z/zJ” exp( - Q//CT)

Fig. 6. Loop patches in a sample fatigued at 1073 K, Aar = 5 x lo-‘, 8=5 x 10-4 s-1, number of cycles = 100. TEM micrograph: foil normal [IT]], g: 202. The primary slip direction is horizontal. Marker: 1 urn.

curve. Further experiments are needed to compare the fatigue behaviour of Si with that of f.c.c. or b.c.c. materials. (ii) Not surprisingly, a strain rate decrease and temperature increase both decrease the peak stress and the time to saturation. (iii) The dislocation microstructures observed till now are rather homogeneous at the sample scale. No persistent slip bands were observed, which is not surprising since a well-defined vein-like structure was not yet formed in the samples that were observed by TEM. (iv) When fracture occurred, the origin of the crack could be traced to an existing surface defect and was not the result of fatigue damage. Some limited crack growth must have taken place, together with plastic deformation, before the crack reaches a critical size. No

where A = 2.9 x lo3 m s- ‘, r0 = 1 MPa, m = 1.2 and Q = 2.2 eV. One can calculate the mobile dislocation density necessary to ensure the imposed plastic strain rate at the observed stresslevel and also the mean free path, L, that a mobile dislocation can travel during a half-cycle, assuming that the applied r is totally effective, which obviously overestimates v and L and underestimates pm. In the sample fatigued at 1073 K, it comes to pm 3 6 x lo7 cme2 and L ~45 urn. In the sample fatigued at 1173 K, pm> 6 x lo6 cm - 2, L z 2.4 mm. In both cases, pm is much lower than the total dislocation density and L is much larger than the distance between loop patches or cell walls. Hence, it is not sure that the average dislocation kinetics is ratecontrolled by the lattice friction, to any extent. Further work is currently being done in order to extend the range of experimental conditions, towards lower temperatures and plastic strain amplitudes and towards larger numbers of cycles.

References [l] J.R. Hancock, J.C. Grosskreutz, Acta Metall. 17 (1968) 77. [2] P. Lukas, M. Klesnil, J. Krejci, Phys. Status Solidi 27 (1968) 545. [3] L.L. Lisiecki, O.B. Pedersen, Acta Metall. Mater. 39 (1990) 1449. [4] Z.S. Basinski, S.J. Basinski, Progr. Mater. Sci. 36 (1992) 89. [5] U. Holzwarth, U. Essmann, Appl. Phys. A 58 (1994) 197. [6] A.T. Winter, Philos. Mag. 30 (1974) 719. [7] D. Kuhlman-Wilsdorf, C. Laird, Mater. Sci. Eng. 27 (1977) 137. [S] H. Mughrabi, Acta Metall. 31 (1983) 1367. [9] D. Walgraef, E.A. Aifdntis, Int. J. Eng. Sci. 24 (1985) 1351. [lo] M.V. Glazov, C. Laird, Acta Metall. Mater. 43 (1995) 2849. [ll] O.B. Pedersen, A.T. Winter, Phys. Status Solidi 149 (1995) 281. [12] M. Omri, C. T@te, J.P. Michel, A. George, Philos. Mag. A 55 (1987) 601. [13] A. George, G. Champier, Phys. Status Solidi 53 (1979) 529.