Hertzian fracture of textured Si3N4

Pergamon

1359-6454(95)00443-2

HERTZIAN

FRACTURE

Acta mater. Vol. 44, No. 8, pp. 3025-3034, 1996 Copyright Q 1996 Acta Metallurgica Inc. Published by Elsevler Science Ltd Printed in Great Britain. All rights reserved 1359-6454/96 $15.00 + 0.00

OF TEXTURED

S&N4

P. D. MILLER and K. J. BOWMAN School of Materials

Engineering,

(Received

Purdue University, 1289 Materials and Electrical West Lafayette, IN 47907, U.S.A.

3 November

1995; in revised form

28 November

Engineering

Building,

1995)

Abstract-The Hertzian fracture behavior of a fine grained silicon nitride with an aligned microstructure was investigated. Fracture toughness anisotropy has previously been related to quantitative texture analysis in silicon nitride and ceramic composites using Vickers indentation. Indentation with hard spheres on hot pressed and plane-strain forged silicon nitrides on varying surface orientations results in profound demonstrations of crack initiation and propagation. Crack initiation was observed to occur at orientations of lowest toughness followed by completion of surface cracking at higher loads. In plane-strain forged materials, the observed elliptical cracks resulted from fracture toughness anisotropy. Sliding ball tests demonstrate that the wear behavior of this material depends on sliding plane, direction and sign of direction, implying the ability to produce more wear resistant materials through preferred microstructural Copyright Q 1996 Acta Metallurgica Inc. orientation.

1. INTRODUCTlON Lawn and others [l-S] have demonstrated Hertzian fracture in evaluating microstructural processes both in static and cyclic contact. The spherical contact geometry induces a hydrostatic compressive stress state below the indenter, thereby suppressing tensile cracking in this localized region. For low toughness materials, contact is generally considered linearelastic until the initiation of conical cracks around the indenter at a critical load level [3, S-81. For coarse-grained polycrystalline materials, permanent non-linear deformation is attributed to shear related mechanisms causing local microcracking events [l&4]. This damage is reported to initiate below the surface and spread. Isolated damage events such as cone cracking are suppressed until greater loads. The Hertzian indentation technique is not amenable to direct fracture toughness measurement since permanent deformation may occur at high loads and crack growth occurs below the specimen surface. Pointed indenter geometries such as Vickers and Knoop, however, provide plastic saturation below the contact at the onset of loading, providing a more severe loading condition. Average crack lengths propagating from the corners of Vickers indents have been widely utilized as a method of estimating fracture toughness for isotropic materials. The Vickers based indentation fracture method has also been used for measuring the relative toughness anisotropy of materials having crystallographic and morphologic textures by using the various crack lengths emanating from the indent [9-141. Early work on silicon nitride by Lange [ 151 and Weston [ 161 demonstrated that b-grain alignment during hot pressing led to strength and fracture 3025

toughness anisotropy. Recent work by Bowman et al. models various mechanisms leading to preferred crystallographic orientation in ceramics [13, 14, 17191. Fracture toughness anisotropy using Vickers indentation was related to quantitative texture analysis for different specimen orientations in hot pressed, open-die forged and channel die (plane strain) forged silicon nitride [13, 141. These results indicate a strong orientation dependence of toughness on textured silicon nitride. This investigation focuses on the fracture behavior of similarly oriented silicon nitrides using Hertzian contact. Of particular interest are the initiation size and geometry of the cracks associated with spherical indentation in textured silicon nitrides. 2. EXPERIMENTAL

PROCEDURE

Specimens were fabricated using nearly equiaxed a-S&N4 powder (H. C. Starck LC-12SX), with 15 wt% sintering additives of yttrium-aluminum-garnet with the ratio 3YzOj:5A1203. The powders were ball milled in ethanol for 2 h, and oven dried at 110°C for 24 h. Billets 38 mm in diameter by 26 mm high were hot pressed to greater than 98% theoretical density at 1650°C for 2 h in 0.5 atm. nitrogen. The hot pressed billets were cut to fit into a graphite channel die 13 mm in width and compressed to 50% nominal height reduction with reference axes ED, ND and TD defined in Fig. 1. This corresponds to a true strain of - 0.69 in the plane strain condition. The samples were then deformed at a strain rate between lo-’ and 10m4s-’ at an applied stress of 15 MPa at 1750°C. Immediately after the forging run was completed, furnace power was cut off and the samples were cooled slowly in the hot press. The

3026 resulting

MILLER and BOWMAN: microstructures

consisted

of the

HERTZIAN

preferred

in the unconstrained direction (ED). In SEM observation of etched surfaces, the materials exhibited a relatively uniform grain size with an apparent aspect ratio of seven, and an average grain diameter approximately 0.4 pm. Stiffness constants were also measured using ultrasonic techniques, where compression and shear mode waves were propagated along specimen axes (ED, ND and TD). To further quantify the microstructure, X-ray pole figures were measured and used to calculate the orientation distribution function (ODF). The material demonstrates a basal texture in the extrusion direction (ED) with a preferred orientation of approximately 5.2 multiples of a random distribution (MRD). Further details on the observed textures for these materials are found in Refs [13, 14, 201. Samples were cut on a surface grinder to dimensions of 3 x 4 x 10 mm and 6 x 6 x 20 mm. Although the surfaces were hand polished through a series of decreasing grit sizes to 5 pm diamond finish, some grain pullout on surfaces was observed. Approximately 50 pm of material was removed by polishing to avoid effects of machining damage. The polished surfaces were coated with a layer of gold approximately 5 nm thick to aid in determination of the contact area. Tests were conducted in ambient air at various loads and specimen orientations for approximately 15 s. After initial microscopic observation, samples were further polished and examined at approximately 35 pm depth increments to study the subsurface shape of cracking. Vickers indents were performed using a hardness testing apparatus, whereas spherical indentation and sectioning were performed following the approach of Guiberteau et al. [3] with a 4 mm Si3N4 ball (Toshiba Tungaloy Co. Ltd.) at a constant crosshead speed of alignment

of

the

elongated

t

grains

FRACTURE

OF S&N4

0.05 mm/min. Sliding ball experiments were conducted using a screw-driven stage at a translation speed of approximately 10 mm/min. A 3.2 mm tungsten carbide ball bearing was used for this set of experiments at an applied load of 500 N.

3. CONTACT

DAMAGE IN ANISOTROPIC MATERIALS

3.1. Static indentation The degree of fracture toughness anisotropy observed in silicon nitride deformed in plane strain compression is demonstrated by the 196 N Vickers indent on the transverse direction (TD) surface in Fig. 2. Also shown is a Vickers indent rotated 45” on the same surface. The work by Lee et al. for equivalently processed material yielded similar results, with the ratio of apparent fracture toughness anisotropy between two and three, using the same indenter orientation [ 13, 141. This differs from typical hot pressed materials which exhibit apparent toughness anisotropy less than 1.5 [13-16, 211. Hertzian indentation in the pressing, or normal direction (ND) of hot pressed Si,N4 results in circular crack traces as demonstrated in Fig. 3. Cracks initiate outside the contact diameter at surface flaws, and subsequently spread around to close the circle [3, 5, 7, 8, 22, 231. These shallow (less than 0.1 contact diameter) ring-shaped cracks initiate nearly perpendicular to the surface, and subsequently develop into cone-shaped cracks which propagate at an angle from the surface of approximately 22” [22]. Indentation of the oriented, plane strain forged material on the TD surface is initially elastic to loads of at least 1000 N for the 4 mm S&N, ball. At greater loads, crack initiation occurs in the plane and direction demonstrating the lowest toughness as shown in Fig. 4(a). At higher loads the initiating

ND

Fig. 1. Hot pressed material (upper) undergoes in the thickness direction (transverse direction, (ED). Flow lines at surface caused

50% nominal height reduction in channel die. Constraint TD) causes flow in the unconstrained, extrusion direction from deformation of graphite lubricant sheet.

MILLER

and BOWMAN:

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OF Si,Nd

ND t

1OOpm

ND t

Fig. 2. (a) Vicke rs inden It on (b) Same as in (a) but roti

t1.ansverse

direction

(TD) surface of plane strain forged silicon nitride, 196 N. grain orientation and specimen geometry.

1t1 zd 45”. Insets on left show the preferred

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cracks grow completing an ellipse at the sample surface as demonstrated by Fig. 4(b). Recall that experimentally the ratio of high to low fracture toughness orientations is nearly three (Fig. 2). This implies that flaws in high toughness orientations can be up to nine times longer than in low toughness orientations before crack initiation occurs. Also, due to the morphological anisotropy of the microstructure, an orientation dependent size and distribution of inherent flaws can be envisaged. Since the observed anisometry is directly related to the crystallographic texture, the contributions from fracture energy anisotropy and flaw distribution cannot be separated. From polish-through experiments, the shape of the subsurface propagation for hot pressed and textured silicon nitride was estimated, as shown schematically in Fig. 5 for the latter. The behavior of the hot pressed material was fully symmetric. However, as expected from the initiation behavior of the oriented material [Fig. 4(a)], the crack front is lobed, running deeper at low toughness orientations. 3.2. Crack shape considerations With the observed toughness and crack initiation behavior of this oriented material presented, the focus will now turn to suggesting reasons for the observed elliptical shape of crack traces. Elastic anisotropy due to the preferred crystallographic alignment of the silicon nitride grains would lead to an anisotropic stress state below the indenter. Strong elastic anisotropy certainly would produce means for anisotropic cracking. However, longitudinal and shear stiffnesses measured using ultrasound at three

ND

FRACTURE

OF Si,N4

mutually orthogonal directions relative to the pressing axis are within 10 percent of each other, indicating near elastic isotropy [21]. In contrast, for single crystal silicon, stiffnesses can differ by more than loo%, depending on orientation. However, observed cracking for spherical indents on the {loo}, { 11 l} and { 110) surfaces of silicon in work by Lawn [23] demonstrates less radial deviation in crack traces than is observed in the present silicon nitride. Lawn also asserts that the non-circular cracking is due to the anisotropy in surface energy rather than elasticity. Since the aligned microstructure mitigates differential thermal expansion anisotropy arising from local crystal misorientations, and the specimens used in this investigation possessed minor texture gradients, bulk residual stresses are not expected to be responsible for the elliptical cracks observed on the specimen surface. In addition, the cooling rate of the hot press was considered sufficiently slow to avoid residual stresses through the specimen thickness. However, to further investigate the possibility of residual stress gradients causing toughness anisotropy, bulk material was annealed in air at 1200°C for 350 h, and furnace cooled. Comparison of the toughness of annealed specimens cut from the bulk material with as-processed specimens showed no decrease in fracture toughness anisotropy. As previously shown, Vickers indentation results clearly demonstrate fracture toughness anisotropy, therefore yielding an orientation dependent fracture toughness, K,,. In isotropic fracture mechanics, where K,, is not dependent upon orientation, cracks grow at the orientation of highest applied stress intensity.

TD

Fig. 3. 2000 N indentation

using 4 mm silicon nitride ball on normal of as-hot-pressed material.

or pressing

direction

(ND) surface

MILLER

and BOWMAN:

HERTZIAN

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OF Si3N4

IND

TD

ED

ED

Fig. 4. (a) 1625 N indent on the TD surface. Specimen was coated with thin layer of gold to aid in contact area measurement. (b) 3000 N indent on TD surface. Surface was lightly polished to enhance cracks.

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However, as observed in Fig. 2(b), materials exhibiting orientation dependent fracture toughness can demonstrate situations where the crack orientation differs from the orientation of maximum applied stress intensity (see also Ref. [23]). In explanation of this observed behavior, it is attractive to treat the fracture toughness as an orientation dependent tensor. This was first suggested for crack deflection modeling in this system by Lee et al. [14]. For simplicity, we consider only Mode I behavior in a material with a fiber texture and the corresponding value of the ratio of high to low toughness of three. Plotting the fracture toughness calculated from the toughness tensor in polar coordinates results in an ellipse. The applied stress intensity surrounding the Mode I loading is related to the trigonometric angular function cos3(Q/2) [24]. For the isotropic case, the plot of this superimposed by a normalized constant fracture toughness indicates that at 0 = 45” (in specimen coordinates), the applied stress intensity matches the fracture toughness. This simply verifies that for isotropic materials, cracks initiate and grow at maximum stress intensity. Figure 6 plots this, along with the superposition of the normalized orientation dependent fracture toughness. For the anisotropic material, fracture initiates at shallower angles than Q = 45”, where the applied stress intensity is greater than the orientation dependent fracture toughness. This region is indicated by the shaded portion of the figure. With this idealized Mode I loading, the first orientation at which the fracture driving force exceeds resistance to fracture is at Q = 22.5”. For demonstration purposes, we assume the stress state at a Vickers indenter diagonal is Mode I. The experimental result in Fig. 2(b) exhibits an average

OF S&N4 ND

Mode

I crack

-

-

-.

K, applied

-

K,, isotmpic K,c anisotropic

\

(from tensor)

ED

Fig. 6. Schematic representation of applied stress intensity superimposed with fracture toughness of isotropic and anisotropic materials. Note that although crack growth is favorable for both cases at 45”, the anisotropic material favors crack growth at shallower angles and lower stress intensity as demonstrated by the shaded region.

crack trajectory of 19= 34”. This result is midway between the calculated anisotropic case and the isotropic case, indicating uncertainties such as the complex stress state surrounding the indenter, and oversimplification of the fracture toughness. This simple calculation of preferred crack path, and the experimental verification from Vickers indentation aids in explaining the shape of the cracks observed in Hertzian indentation. In the spherical case, although cracks initiate at the lowest toughness orientation, their path deviates from the applied circular stress state by the same mechanism as demonstrated above. In addition, however, one must account for a decrease in stress as a function of radial position, cf. [5, 7, 221. The orientation of crack growth therefore equilibrates the toughness anisotropy experimentally observed with the applied mixed-mode stress intensity which is a function of both crack misorientation and radial position from the center of the indenter. Also, from this equilibrium, one can note that the shape or aspect ratio of the crack trace is a function of the initiating radius. 3.3. Further effects of toughness anisotropy

Fig. 5. Schematic representation of crack traces obtained from polish-through experiments. TD type indent on highly textured at low

material. Note greater depth of crack penetration toughness orientations. Overall crack front is indicated by shaded line.

To further demonstrate the effect of toughness anisotropy on fracture behavior, Hertzian contact experiments were conducted on a surface at a grain tilt angle of 45”, Fig. 7. At indenter loads of 1000 N, initiation is observed from surface traces to occur along the side of the indent exhibiting most alignment with grain orientation. Crack growth around the indent is arrested by the change of crack orientation from the initial low toughness orientation, to that of

MILLER

and BOWMAN:

HERTZIAN

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OF Si3Nd

TD

top side

Fig. 7. 1000 N indent

on 45“ section.

Note lack of crack closure. enhance cracks.

(a) Top; (b) side. Surface

polished

to

MILLER and BOWMAN:

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TD

Fig. 8. Sliding ball contact on 45” section at 500 N using 3.2 tungsten carbide ball. Sliding in ND.

higher toughness. Multiple concentric “thumb-nail” shaped secondary cracks form for loads up to 3000 N, precluding the closure of the surface traces at this specimen orientation. Cross-sections of three cracks at the specimen orientation shown in Fig. 7, demonstrate that the subsurface cracks propagate at an angle from the surface of approximately 33”. To investigate the wear properties of this oriented material, sliding ball tests were conducied by moving the sphere down the vertical axis (ND) on the surface shown in Fig. 7(a). These results, shown’ in Fig. 8 indicate a lack of symmetry about the sliding direction as observed in isotropic materials [25, 261. In addition, tests were conducted at the same load by sliding the ball in a horizontal manner on the same material surface. Results for sliding to the right and to the left as viewed in Fig. 9 indicate a significant difference in the amount and character of damage. Qualitatively, one can immediately note that as observed for static indentations, cracks resist growing through orientations of high toughness. These results also demonstrate several additional factors. First, as expected from the Vickers indentation work presented (Fig. 2, [13, 14]), spherical indentation and sliding behavior are dependent on the surface plane’s orientation relative to the preferred microstructural alignment. In sliding experiments, the dependence of sliding (or shearing) direction within a given plane is also

established. Specifically, aligning grains in the direction of sliding places the highest surface stresses at orientations of highest toughness, thereby resisting crack initiation [25, 261. Upon crack initiation, however, when cracks follow a transition to a more conical geometry, the optimal grain orientation may be different. These initial tests imply that wear properties can be tailored through texture in the microstructure, however, further investigation is required to better understand the behavior. 4. SUMMARY The use of an orientation dependent fracture toughness explains the observed fracture behavior of anisotropic materials in which crack growth directions were shown to deviate from orientations of highest applied stress intensity. For sharp, blunt and sliding blunt indenters, a full description of orientation is required to relate behavior to physical properties. The implications of this fracture behavior on contact damage, contact fatigue and wear processes all deserve further consideration. Acknowledgements-We would like to thank Professor Y. Mutoh of Nagaoka University of Technology for donating silicon nitride balls. We also extend thanks to Brian Lawn of the National Institute of Standards and Technology for helpful discussions. This work was supported by the National 9121948.

Science

Foundation

under

Grant

No.

DMR-

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and BOWMAN:

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OF Si,N.,

1OOpm

Fig. 9. Sliding ball contact

on 45” section at 500 N using 3.2 mm tungsten carbide to the right. (b) Sliding direction to the left.

ball. (a) Sliding direction

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12. X. N. Huang and P. S. Nicholson, J. Am. Ceram. Sot. 76, 1294 (1993). 13. F. Lee and K. J. Bowman, J. Am. Ceram. Sot. 75,174s (1992). J. Am. 14. F. Lee, M. S. Sandlin and K. J. Bowman, Ceram. Sot. 76, 1793 (1993). 15. F. F. Lange, J. Am. Ceram. Sot. 56, 518 (1973). 16. J. E. Weston, J. Mater. Sci. 15, 1568 (1980). 17. Y. Ma and K. J. Bowman, J. Am. Ceram. Sot. 74,294l (1991). 18. M. S. Sandlin, F. Lee and K. J. Bowman, J. Am. Ceram. Sot. 75, 1522 (1992). 19. Y. Ma, F. Lee and K. J. Bowman, Mater. Sci. Engng A175, 167 (1994). 20. P. D. Miller, D. Collins, I. Golinkin and K. J. Bowman, Textures Microstructures 24, 31 (1995). results. 21. P. D. Miller, unpublished 22. F. C. Frank and B. R. Lawn, Proc. R. Sot. A299, 291 (1967). 23. B. R. Lawn, J. appl. Phys. 39, 4828 (1968). 24. B. R. Lawn, Fracture ofBrittle Solids, ed. 2. Cambridge University Press, Cambridge (1993). 25. B. R. Lawn, Proc. R. Sot. A299, 307 (1967). J. Mater. Sci. 22, 989 (1987). 26. R. Mouginot,