Influence of the grain size of the alumina coating on crack initiation in indentation

Wear 225–229 Ž1999. 83–89

Influence of the grain size of the alumina coating on crack initiation in indentation Fang Yuan ) , Kazuo Hayashi K. Hayashi Laboratory, Institute of Fluid Science, Tohoku UniÕersity, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan

Abstract A study has been made for indentation to the alumina coating on a cemented carbide substrate. Radial cracks initiate outside the contact circle on the surface of the coating and the critical load of crack initiation increases with the decrease of the thickness of the coating. It is demonstrated that the coating thickness can have a profound influence on the critical load of the radial crack initiation. An elastic–plastic analysis of indentation with a spherical indenter is also made by using the finite element method. The state of stress during indentation Žincluding unloading. is investigated in detail. The tensile stresses, which might lead to crack initiation, are discussed intensively and examined by comparing with experimental results. The results indicate the grain size of the alumina coating is one of the important factors for crack initiation, reflecting the fact that the fracture strength of the coating depends on the grain size of the coating and decreases with increasing grain size. q 1999 Published by Elsevier Science S.A. All rights reserved. Keywords: Indentation; Grain size; Coating; Crack

1. Introduction Ceramic coatings on metal alloy substrates have many applications, for thermal barrier protection, wear and corrosion resistance, enhanced biocompatibility in prosthetic devices, and so on. The failure of ceramic coatings on metal substrates is an important practical problem w1x. The analysis of stress field and initiation of cracks in such coatings becomes very important. The resistance of a coating to contact fracture is usually measured by using indentation tests. The tests involve pressing a spherical indenter over the coating surface, while the indenter is subjected to a progressively increasing load. The load required to initiate fracture in the coating gives a measure of the strength of the coating. Tests of this type are useful to rank the relative strengths of various coated materials. Various studies of fracture damage problems for bulk ceramics have been investigated for more than two decades w2x. It was demonstrated that the grain size of ceramics could have a profound influence on the fracture damage w2x. The basic principles of indentation fracture mechanics were also studied w3x. According to this study, a favorably ) Corresponding author. R & D Center Tochigi. KEIHIN. 2021-8 Hoshakuji, Takanezawa Town, Shioya Country, Tochigi Pref., 329-1233 Japan. Tel.: q81-028-680-1531; Fax: q81-028-680-1515

located flaw runs around the contact region to form a surface crack. Recently, the effect of grain size on Hertzian contact damage was studied w4x, through detailed examination of the deformation and microfracture in aluminas over a range of grain sizes. It was found that grain size had a strong effect on the microcracking damage and the microcrack density increased with grain size. For ceramic coatings, the repeated elastic–plastic indentation of a rigid spherical indenter into ceramic coatings on a half-space possessing various elastic properties and strain hardening characteristics was studied w5x. It was demonstrated that the surface and subsurface stresses were dependent strongly on strain hardening and were relatively less dependent on elastic properties. For an elastic–perfectly plastic half-space with a hard coating indented by an elastic sphere, the highest tensile stresses are the radial stress at the edge of the contact region, being responsible for failures due to the ring crack w6x. Using the finite element method, stresses and deformations were investigated in the case of repeated indentation of an elastic–plastic layered medium by a rigid sphere w7x. The effects of the layer thickness and material properties of the layer and substrate on the stresses were interpreted, and the consequences for subsurface crack initiation were discussed. It was shown that a significant tensile radial stress occurred at the surface near the contact edge that lead to the

0043-1648r99r$ - see front matter q 1999 Published by Elsevier Science S.A. All rights reserved. PII: S 0 0 4 3 - 1 6 4 8 Ž 9 8 . 0 0 3 5 0 - 0

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F. Yuan, K. Hayashir Wear 225–229 (1999) 83–89

formation of ring cracks, and large tensile radial and hoop stresses occurred just beneath the interface that might promote the initiation of subsurface circumferential and radial cracks just beneath the layer interface. Regarding an elastic–plastic half-space with a ceramic coating indented by an elastic sphere, the problem of cracking and spalling of the coating, especially the formation of radial cracks was discussed in detail w8x, emphasizing the influence of the thickness of coating. The indentation experiment of ceramic on the cemented carbide substrate subjected to indentation by a sphere showed that radial and lateral cracks were formed on the surface and spalling of the coating were caused, for a sharp diamond indenter w9x. In the case of a blunt SiC indenter, ring cracks were formed, but radial cracks never occurred and spalling was not so severe. The load for initiation of cracks depends on the thickness of the coating and radius of the indenter. For ceramic coatings on metal substrates subjected to indentation of spherical indenters, the plastic deformation was apparent as a confined drop-like zone immediately beneath the contact and the ring cracks outside the contact penetrate formed w10x. In this paper, we examine systematically the role of grain size on contact damage due to indentation into ceramic coatings. The main aim of the study is to correlate experimental observations of crack initiation on the coating surface with corresponding FEM simulations. We evaluate the tensile stress distributions in the ceramic coating, and thereby establish a basis for prospective fracture mechanics analysis of observed crack patterns.

3. Experimental results Scanning electron micrographs of the surface damage obtained for coating thickness t s 5 mm and at a load W s 600 N are shown in Fig. 1. Plastic deformation is apparent as a residual impression at the contact center. Radial cracks are generated and extensive spalling of the coating takes place outside the contact area as shown in Fig. 1Ža.. It is in good agreement with those obtained

2. Experimental procedure Alumina ŽAl 2 O 3 . coatings of three different thickness Ž1, 5, 10 mm., deposited on cemented carbide ŽWC–Co. substrates by chemical vapour deposition ŽCVD., are investigated in the study. The indentation experiments are carried out using the Rockwell hardness tester. A conical diamond indenter with spherical tip of radius of curvature 200 mm is used. The mechanical and physical properties of the coatings and the substrate are shown in Table 1 w9x. Range of the normal load is 10 N–1500 N in the experiment and the tests are conducted at slow loading rates, typically over a period of 30 s. After unload, the specimens are ultrasonically cleaned with acetone before being observed, then the contact surfaces are observed by the optical microscope and higher magnification views are obtained by scanning electron microscope ŽSEM.. Cracks on the surface of the coating are observed when the load larger than a certain load, and in order to obtain an accurate measurement of the load at fracture, the tests are conducted again near that load. The critical load of the crack initiation thus is observed. For each thickness of the coating, about ten such tests are carried out near the critical load.

Fig. 1. Surface view ŽSEM. of indentations in 5 mm thickness coating ŽW s600 N..

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Fig. 2. Schematical presentation of the radial crack propagation and spalling of the coating.

experimentally by Diao et al. w9x. Fig. 1Žb. and Žc. are the magnified view of Fig. 1Ža., showing higher magnification view of the surface topography of the specimen. A radial crack radiates near the contact edge and propagates into the substrate in the contact area, as shown in Fig. 1Žb. and Žc.. For the cases of coating thickness of 1 and 10 mm, radial cracks and spalling are also observed. The ring cracks are generated occasionally at the smaller load near the contact edge for coating thickness t s 1 mm. The sequence of the radial crack propagation and spalling of the coating is shown schematically in Fig. 2. On loading, the cracks to from first are radial cracks that spread outward from the contact edge. As the load increases the number and the length of the radial cracks increase. A part of the coating outside the contact area is spalled at a large load. Then extensive spalling takes place at larger load resulting in a large area of exposed substrate as shown in Fig. 2.

Fig. 4. SEM photographs of coating surface with radial crack Ž t s 5 mm..

The relationship between the critical load of the radial crack initiation and the coating thickness is shown in Fig. 3. The data points are the critical load values of the radial crack initiation obtained from the indentation test and the solid curve is an empirical fit through these data points. It can be seen that the critical load for the generation of the radial cracks is strongly affected by the coating thickness. The critical load decreases with the coating thickness. This result seems to be different from the fracture pattern diagram, which can be seen that the critical normal load for the generation of radial cracks is very little affected by the coating thickness w9x. Fig. 4 shows SEM photographs of the coating surface with radial cracks. These show that cracks propagated not along the grain boundaries but through the grain. For bulk Al 2 O 3 material, cracks propagate along the grain boundaries w11,12x. Contrary to this, in the case of the coating, the transgranular fracture is formed on the surface of the ceramic coating as show in Fig. 4.

4. Finite element analysis and results

Fig. 3. Relationship between the critical load of the radial crack initiation and the coating thickness.

Let us consider an elastic–plastic coating on an elastic–plastic substrate subjected to indentation by an elastic sphere and introduce a cylindrical coordinate sys-

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Fig. 5. Indentation model.

tem Ž r, u , z . as shown in Fig. 5. We solve this axisymmetric problem by using the finite element method ŽFEM.. The coating and the substrate are assumed to follow the von Mises yield criterion with isotropic strain hardening. On the contact area between the indenter and the coating, the friction is assumed to be zero. Following the uni-axial stress strain relation is assumed to be given in the form w13x:

s scŽ a q´ p .

n

fixed to be 0.11 w14x. The procedure of the finite element analysis is exactly the same as that of the previous paper w8x, so that the details of the analysis are not presented here for the sake of brevity. Computed distributions of the radial and circumferential components of stress Ž sr , su . on the surface and the shear stress Ž sr z . along the interface between the coating and the substrate are shown in Fig. 6 for t s 5 mm and W s 45 N. The arrow points out the contact radius. As shown in Fig. 6Ža. for loading, the radial and circumferential stresses are significantly compressive at the center of the contact area. There is an annulus area around the contact edge in which both of the stress components are tensile. The two stress components have peak values near the contact edge, and

Ž 1. p

where c and a are material constants, ´ is the plastic strain and n is the strain hardening exponent; here n is

Fig. 6. Stresses distribution on the surface and along the interface ŽW s 45.0 N, t s 5 mm. Ža. on loading, Žb. after unload.

Fig. 7. Distribution of stresses sr and su with respect to z near the contact edge ŽW s 45.0 N, t s 5 mm. Ža. on loading, Žb. after unload.

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the circumferential stress su is slightly higher. The radial stress sr becomes compressive out side of the annulus region. The shear stress sr z along the interface has a maximum value in the contact region at about half of the contact radius. After unload, as shown in Fig. 6Žb., the residual radial and circumferential compressive stress at the center of the contact region, decreases to about half of those on loading. The maximum radial tensile stress near the contact edge decreases, but the circumferential stress increases significantly after unload. Fig. 7 shows the variation of stresses along the z-direction near the contact edge, showing that the radial sr and circumferential su stress are largest on the surface. According to Fig. 7, the radial and circumferential stresses are tensile on the surface and become compressive at the interface. Also, a discontinuity of the normal stresses sr and su occurs at the interface. Hence, the crack formation would be promoted at the coating surface near the contact edge where the maximum tensile stress is attained. Fig. 8 shows maximum stresses on the coating surface and at the interface as a function of the load W for t s 5 mm. The maximum stresses increase with increasing load. At the beginning of loading, maximum stresses increase

Fig. 9. Variation of maximum stress with the coating thickness ŽW s 45.0 N. Ža. on loading, Žb. after unload.

Fig. 8. Maximum stresses on the surface and along the interface as a function of load W ŽW s 45.0 N, t s 5 mm. Ža. on loading, Žb. after unload.

rapidly, and the maximum radial stress is larger than the circumferential stress. The maximum circumferential stress increases and exceeds the maximum radial stress with increasing load. After unload ŽFig. 8Žb.., the maximum radial tensile stress is smaller than that for loading, but the circumferential stress becomes larger than that for loading. Let us employ the simple criterion of failure that cracking takes place at a point where the maximum principal stress reaches the tensile strength. As shown in Fig. 6, there are maximum tensile stresses near the contact edge on the surface, indicating that cracking occurs at the contact edge on the surface. When the tensile strength of the coating is smaller than the stress at the intersection ŽA in Fig. 8Ža.. between the maximum radial stress sr and the maximum circumferential stress su on loading, the maximum radial stress sr reaches the tensile strength of the coating first and, thus, a circumferential crack is formed on the surface. Otherwise, if the tensile strength of the coating is higher than the stress at the intersection, the maximum circumferential stress su on loading reaches the tensile strength first, leading to radial cracks on the surface near the contact edge. Even if cracking does not occur during loading, there is a possibility that radial cracks are induced during unloading because of increasing of the residual stress su as shown in Fig. 8Žb..

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compressive value on the surface and decreases monotonously with depth. It is shown in Fig. 10Žb. that the residual stress sz has a maximum tensile value near the interface. The shear stress sr z at the interface, as shown in Fig. 6, has a maximum value in the contact region. Fig. 10Žb. shows that there is a tensile residual stress at the interface. In general, these two kinds of stress would lead to spalling of the coating. If it is caused by shear stress sr z at the interface, it occurs on loading. However, the spalling of coating occurs during unloading if it is caused by residual stress sz on the interface.

5. Discussion

Fig. 10. Stress along the axis of symmetry ŽW s 45.0 N, t s 5 mm. Ža. on loading, Žb. after unload.

Fig. 9 shows the variation of maximum stresses with respect to the coating thickness when W s 45 N. On loading, as shown in Fig. 9Ža., the radial stress has a peak value when thickness t is about 5 mm. The circumferential stress has the highest value at t s 1 mm, and decreases with increasing thickness. The circumferential stress is larger than the radial stress for any thickness. The residual circumferential stress has a peak value when the thickness is 1 mm and decreases slightly with increasing thickness, it keeps almost the same level for the thickness larger than 5 mm as shown in Fig. 9Žb.. The radial crack will be caused more easily for thinner coating. These results agree with those obtained experimentally w9x with the same materials as those used here. The stress sz along the axis of symmetry for W s 45 N and t s 5 mm is shown in Fig. 10. Fig. 10Ža. shows that the stress sz has a maximum

In general the grain sizes of CVD ceramic coatings are found to vary with coating thickness, while with increasing thickness an increase in the average grain size is generally observed w15x. Also, a more coarse grained microstructure generally displays a lower cohesive strength as compared with a fine grained microstructure. Analysis of the FEM surface stresses shows that the maximum residual circumferential stress is the maximum stress on the coating surface, and it increases with the decrease of the thickness of the coating as showing in Fig. 11. It is recognized that if the fracture strength of the coating is same for a coating of different thickness, the radial crack on the coating surface will form more easily for a thin coating. However, the experimental result shows that the critical load of the crack initiation increases with decrease at the thickness. This tendency disagrees with the FEM results. It may imply that the fracture strength of the coating increases with the grain size decrease due to the decrease of thickness. The experimental results confirm that the grain size on the coating surface decrease with the thickness. The grain size is about 0.6 mm for the coating of 1 mm thickness and the grain size are 2 mm and 3 mm for the coatings of 5 mm and 10 mm thickness, respectively.

Fig. 11. Relationship between the maximum residual circumferential stress and the coating thickness.

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The two results are well in accord with each other. This leads to the conclusion that the strength of the coating depends on the coating thickness, and the main factor controlling this phenomenon is the change in grain size.

Acknowledgements The authors wish to express their gratitude to Prof. K. Kato and Prof. T. Umehara, Tohoku University, for their encouragement, a device and helpful discussions.

Fig. 12. Relationship of the fracture strength of coating and the coating thickness.

According to Kingery et al. w1x, the relationship between the grain size d and the fracture stress sf may be expressed follows w2x

sf s s 0 q k 1 dy1 r2

Ž 2.

where k1 s

ž

3pgeff E 1yÕ2

1r2

/

Ž 3.

Here, s 0 is the constant, geff is the effective surface energy, E and n are the Elastic modulus and Poisson’s ratio. The equation has the form of the Petch relation and predicts that the strength should increase with decreasing grain size Žas dy1 r2 .. The concepts of brittleness and ductility are also reflected in the fracture surface energies derived from studies of controlled crack propagation. For small grain sizes, the fracture surface energy of polycrystalline ceramics apparently increases with increasing grain size. The effective surface energies of Al 2 O 3 is about 40–45 Jrm2 when the grain size smaller than 3 mm w11x. The grain sizes of the specimens used in our experiment are 0.6 mm–3 mm. Assuming the material properties do not change with the coating thickness, then the effective surface energy is about 40 Jrm2 . From Eqs. Ž2. and Ž3., the fracture strength for different grain size are estimated as shown in Fig. 12. Here, we have determined s 0 to be 4 GPa so that we can get the best fit between the result calculated from Eqs. Ž2. and Ž3. and the experimental data. Dashed lines in Fig. 12 indicate fracture strength estimated by substituting the data just stated above into Eqs. Ž2. and Ž3.. On the other hand, the fracture strength can also be estimated by using the stresses obtained by the finite element analysis and the critical load obtained by the indentation experiment stated in Section 3. The result thus obtained is indicated by the solid line in Fig. 12.

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