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The use of the indentation loading curve to detect fracture of coatings
Surface and Coatings Technology 137 Ž2001. 72᎐76
The use of the indentation loading curve to detect fracture of coatings J. Malzbender U , G. de With Laboratory of Solid State and Materials Chemistry, Eindho¨ en Uni¨ ersity of Technology, P.O. Box 513, 5600 MB Eindho¨ en, The Netherlands Received 15 May 2000; accepted in revised form 29 September 2000
Abstract The indentation load P-displacement h-curve and the derivative ⭸Pr ⭸h 2 are used to assess the onset of radial cracking, delamination and substrate yield. Particle filled hybrid organic-inorganic coatings on glass substrates were used as model materials. 䊚 2001 Elsevier Science B.V. All rights reserved. Keywords: Indentation; Fracture; Sol-gel coatings
1. Introduction Sol-gel coatings are widely used to modify the functional behavior of glass components or to protect the underlying substrate from environmental influences such as particle impact and moisture w1x. It is obvious that, in developing such coatings, their mechanical properties are crucial w2x. Indentation testing is widely used to assess the mechanical properties of coatings, such as the elastic modulus and the hardness w3x. A complication in determining the coating properties is that, as opposed to bulk materials, the effectively measured properties are dependent on the indentation depth due to the combined response of coating and substrate w2,4x. In addition the elastic modulus and hardness can be influ-
U
Corresponding author. Tel.: q31-40-247-3059; fax: q31-40-2445619. E-mail address: [email protected] ŽJ. Malzbender..
enced by fracture of the coating and substrate w2,4x. Thus, it is important to determine the onset of plastic deformation and fracture. It has been shown that fracture leads to a change in the load-displacement curve w5᎐8x. To ease the interpretation at least three other representations can be used. Loubet et al. w5x and Hainsworth et al. w6x suggested a linear relationship between load P and square of the displacement h: P; h 2 . The ratio Prh2 has been used by Hainsworth et al. w6x and the derivative ⭸Pr⭸h2 by McGurk and Page w7x to analyze indentation data. However, Malzbender and de With w8x have shown recently that P; h2 is strictly only true for an ideal indenter, where this relationship for a Berkovich indenter reads w8x:1 Eh2
Ps
(
0257-8972r01r$ - see front matter 䊚 2001 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 7 - 8 9 7 2 Ž 0 0 . 0 1 0 9 1 - 4
E q H Ž 24.5.
4
' (
H E
2
Ž1.
J. Malzbender, G. de With r Surface and Coatings Technology 137 (2001) 72᎐76
As usual E denotes the Young’s modulus, H the hardness and is a geometric constant, which takes a value of 0.72 for a conical indenter. For the non-ideal indenter used in our experiments this relationship is w8x:1 Eh2
Ps
(
E q H Ž 24.5q 8.95rh .
4
' (
H E
2
Ž2.
Thus, for a non-ideal indenter the ratio Prh2 as well as the derivative ⭸Pr⭸h2 are a function of the indentation depth. The non-ideal indenter geometry introduces a monotonous change in the slope of these functions and since we only consider peaks in the derivative this dependency can be neglected in the following considerations. In this paper we present an investigation on the effect of plastic deformation and fracture on the loaddisplacement curve and its derivative as obtained using a Berkovich indenter. This current work elaborates on the previous work of the authors w8x to analyze these relationships and to relate these to fracture of the coating-substrate system.
1
These equations have been reproduced incorrectly in our previous publication w8x.
73
2. Experiments The experiments were carried out using float glass that was coated with an organic-inorganic hybrid coating. The coating fluid contained methyltrimethoxysilane ŽMTMS. and LUDOX Žaverage particle size 20 nm. in a ratio of 1.75. In order to increase the stiffness of the coating one weight per cent tetraethylorthosilicate ŽTEOS. was added. Details on the preparation of these coatings are given elsewhere w2,4x. Indentation experiments were carried out at room temperature and ambient atmosphere using a homebuilt instrument. The load range was 2᎐1000 mN. A Berkovich-type diamond indenter was used. The calibration procedure suggested by Oliver and Pharr w3x was used to correct for the load frame compliance of the apparatus and the imperfect shape of the indenter tip w3,5,6x.
3. Results and discussion A plot of a typical load displacement curve for various coating thicknesses is given in Fig. 1a, Fig. 2a and Fig. 3a. These curves are difficult to analyze, e.g. in Fig. 1a only a change in slope at a load of approximately 24 mN can be seen. A similar inflection point or a small peak can be seen in Fig. 2a and Fig. 3a at different loads. Optical microscopy confirmed that these inflec-
Fig. 1. Load᎐displacement Ž P᎐h. curve for a 1.5-mm-thick coating in Ža., Pr h 2 vs. h 2 in Žb. and ⭸Pr⭸h2 vs. h2 in Žc.. The minima in the ⭸Pr⭸h 2 curve are indicated by arrows. The second order minima and peaks at very low and very high h 2 are due to the averaging procedure.
74
J. Malzbender, G. de With r Surface and Coatings Technology 137 (2001) 77᎐76
Fig. 2. Load᎐displacement Ž P᎐h. curve for a 3.5-mm-thick coating in Ža. P r h2 vs. h 2 in Žb. and ⭸Pr⭸h2 vs. h 2 in Žc. Žfor further details see also Fig. 1..
tion points corresponded to the onset of radial cracking in the surface of the coating. Plots of Prh2 vs. h 2 are shown in Fig. 1b, Fig. 2b and Fig. 3b, where the kinks as observed in Fig. 1a, Fig. 2a. and Fig. 3a can be seen more clearly. A plot vs. h2
is used to simplify the analysis procedure. It has been shown previously that smoothing of the data before differentiation using a moving average can change the curve significantly w8x. Taking intervals of 40 data points, building the mean and calculating the derivative
Fig. 3. Load᎐displacement Ž P᎐h. curve for a 6.8-mm-thick coating in Ža. P r h2 vs. h 2 in Žb. and ⭸Pr⭸h2 vs. h 2 in Žc. Žfor further details see also Fig. 1..
J. Malzbender, G. de With r Surface and Coatings Technology 137 (2001) 72᎐76
⭸Pr⭸h2 Žsee Fig. 1c, Fig. 2c and Fig. 3c., reveals a clearer image of the changes in the load displacement curve and yields additional information to the simple ratio of Prh2 in Fig. 1b, Fig. 2b and Fig. 3b. For example, in Fig. 1c minima in ⭸Pr⭸h2 can be seen at values of h 2 of approximately 0.33 m2 Ž Ps 10 mN., 0.63 m2 Ž Ps 24 mN. and 0.85 m2 Ž Ps 29 mN.. In order to associate the features in the loading curve and its derivative with the fracture events, indentations were made at various loads between 0 and 1000 mN and the indentation marks were analyzed directly after the measurements using an optical microscope. Images of radial cracks and delaminations obtained thereby have been shown previously by the authors w2,4,8x. It appeared that the first two minima correspond to the onset of radial cracking and delamination. The third minimum is probably due to substrate yield. It can be considered that the substrate will deform plastically if the stress exceeds the yield strength of the material, which can be approximated as Hr3 w9x. This leads for the substrate to a value of approximately 2 GPa. In fact, it was observed in our measurements that the indentation pressure was approximately 1 GPa at the contact depth that corresponds to the supposed substrate yield, but the measurement was influenced by the fracture of the coating, which leads to a displacement of the indenter at constant load and thereby an underestimation of the indentation pressure w10x. Moreover, the indentation depth at the onset of the supposed substrate yield was on average 60% of the
75
coating thickness indicating a significant substrate influence, which is not reflected in the indentation pressure w2,4,8x. The minima in Fig. 2c and Fig. 3c can be related in a similar way to the fracture features and substrate yield. Chipping of the coating led to a significant change of the load-displacement curve, i.e. considerable displacement at constant load, and has been investigated separately w2,4,8x. The consistency of the observed features is illustrated in Fig. 4, which shows the load of radial cracking, delamination and substrate yield as a function of the layer thickness as determined using ⭸Pr⭸h2 and where it can be seen that the critical loads increase with the coating thickness. As can be seen from Fig. 1c, Fig. 2c and Fig. 3c the change of the elasto-plastic response of the coating-substrate system for different coating thicknesses also leads to a decrease of the average ⭸Pr⭸h2 value for thicker coatings. Both effects can be considered to be due to a reduced influence of the harder and stiffer substrate with increasing layer thickness. The decrease in ⭸Pr⭸h2 with increasing layer thickness is simply due to the same change in properties over the layer thickness, as reflected in ⭸P, with increasing thickness, as reflected in ⭸h 2 . The increase in critical load is mainly due to the decreasing component hardness, as elaborated below. Lawn and Evans w11x analyzed the initiation of radialrmedian cracks under a Vickers indenter in an elasticrplastic indentation field for monolithic materi-
Fig. 4. Load of the initiation of radial cracks Ža. delamination Žb. and substrate yield Žc. vs. coating thickness. The lines are parabolic fits.
J. Malzbender, G. de With r Surface and Coatings Technology 137 (2001) 77᎐76
76
als. They determined that the critical load for the crack initiation P U is: P U s 21.7= 10 3
4 K IC H3
Ž3.
where K IC is the fracture toughness. Especially for the thinner coatings it has to be considered that the stress field is modified even at the critical load by the underlying substrate, i.e. a part of the load is carried by the substrate. Thus, introducing the composite hardness into Eq. Ž3., which appears reasonable as a first approximation since the original derivation of the equation is based on the hardness as defined by the ratio of load to area, the critical load will be reduced for the thinner coatings in agreement with our observations. In conclusion, the use of the derivative ⭸Pr⭸h2 of the indentation load-displacement data allows the determination of different fracture and deformation features and is therefore, a helpful tool to analyze the behavior of coated material, which gives additional
information to the commonly determined elastic modulus and hardness. References w1x H. Bach, D. Krause, Thin Films on Glass, Springer-Verlag, Berlin, 1997. w2x J. Malzbender, G. de. With, J. Non-Cryst. Solids 265 Ž2000. 51. w3x W.C. Oliver, G.M. Pharr, J. Mater. Res. 7 Ž1992. 1564. w4x J. Malzbender, J.M.J. den Toonder, G. de With, Thin Solid Films 366 Ž2000. 139. w5x J.L. Loubet, J.M. Georges, J. Meille, in: P.J. Blau, B.R. Lawn ŽEds.., Microindentation Techniques in Materials Science and Engineering, Philadelphia, 1986, p. 72. w6x S.V. Hainsworth, T.F. Page, Mat. Res. Soc. Symp. Proc. 436 Ž1997. 171. w7x R. McGurk, T.F. Page, J. Mater. Res. 14 Ž1999. 2283. w8x J. Malzbender, G. de With, Surf. Coat. Technol. 127 Ž2000. 265. w9x D. Tabor, The Hardness of Metals, Oxford, 1951, p. 102. w10x J. Malzbender, J.M.J. den Toonder, G. de With, Thin Solid Films 372 Ž2000. 134. w11x B.R. Lawn, A.G. Evans, J. Mater. Sci. 12 Ž1977. 2195.
The use of the indentation loading curve to detect fracture of coatings J. Malzbender U , G. de With Laboratory of Solid State and Materials Chemistry, Eindho¨ en Uni¨ ersity of Technology, P.O. Box 513, 5600 MB Eindho¨ en, The Netherlands Received 15 May 2000; accepted in revised form 29 September 2000
Abstract The indentation load P-displacement h-curve and the derivative ⭸Pr ⭸h 2 are used to assess the onset of radial cracking, delamination and substrate yield. Particle filled hybrid organic-inorganic coatings on glass substrates were used as model materials. 䊚 2001 Elsevier Science B.V. All rights reserved. Keywords: Indentation; Fracture; Sol-gel coatings
1. Introduction Sol-gel coatings are widely used to modify the functional behavior of glass components or to protect the underlying substrate from environmental influences such as particle impact and moisture w1x. It is obvious that, in developing such coatings, their mechanical properties are crucial w2x. Indentation testing is widely used to assess the mechanical properties of coatings, such as the elastic modulus and the hardness w3x. A complication in determining the coating properties is that, as opposed to bulk materials, the effectively measured properties are dependent on the indentation depth due to the combined response of coating and substrate w2,4x. In addition the elastic modulus and hardness can be influ-
U
Corresponding author. Tel.: q31-40-247-3059; fax: q31-40-2445619. E-mail address: [email protected] ŽJ. Malzbender..
enced by fracture of the coating and substrate w2,4x. Thus, it is important to determine the onset of plastic deformation and fracture. It has been shown that fracture leads to a change in the load-displacement curve w5᎐8x. To ease the interpretation at least three other representations can be used. Loubet et al. w5x and Hainsworth et al. w6x suggested a linear relationship between load P and square of the displacement h: P; h 2 . The ratio Prh2 has been used by Hainsworth et al. w6x and the derivative ⭸Pr⭸h2 by McGurk and Page w7x to analyze indentation data. However, Malzbender and de With w8x have shown recently that P; h2 is strictly only true for an ideal indenter, where this relationship for a Berkovich indenter reads w8x:1 Eh2
Ps
(
0257-8972r01r$ - see front matter 䊚 2001 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 7 - 8 9 7 2 Ž 0 0 . 0 1 0 9 1 - 4
E q H Ž 24.5.
4
' (
H E
2
Ž1.
J. Malzbender, G. de With r Surface and Coatings Technology 137 (2001) 72᎐76
As usual E denotes the Young’s modulus, H the hardness and is a geometric constant, which takes a value of 0.72 for a conical indenter. For the non-ideal indenter used in our experiments this relationship is w8x:1 Eh2
Ps
(
E q H Ž 24.5q 8.95rh .
4
' (
H E
2
Ž2.
Thus, for a non-ideal indenter the ratio Prh2 as well as the derivative ⭸Pr⭸h2 are a function of the indentation depth. The non-ideal indenter geometry introduces a monotonous change in the slope of these functions and since we only consider peaks in the derivative this dependency can be neglected in the following considerations. In this paper we present an investigation on the effect of plastic deformation and fracture on the loaddisplacement curve and its derivative as obtained using a Berkovich indenter. This current work elaborates on the previous work of the authors w8x to analyze these relationships and to relate these to fracture of the coating-substrate system.
1
These equations have been reproduced incorrectly in our previous publication w8x.
73
2. Experiments The experiments were carried out using float glass that was coated with an organic-inorganic hybrid coating. The coating fluid contained methyltrimethoxysilane ŽMTMS. and LUDOX Žaverage particle size 20 nm. in a ratio of 1.75. In order to increase the stiffness of the coating one weight per cent tetraethylorthosilicate ŽTEOS. was added. Details on the preparation of these coatings are given elsewhere w2,4x. Indentation experiments were carried out at room temperature and ambient atmosphere using a homebuilt instrument. The load range was 2᎐1000 mN. A Berkovich-type diamond indenter was used. The calibration procedure suggested by Oliver and Pharr w3x was used to correct for the load frame compliance of the apparatus and the imperfect shape of the indenter tip w3,5,6x.
3. Results and discussion A plot of a typical load displacement curve for various coating thicknesses is given in Fig. 1a, Fig. 2a and Fig. 3a. These curves are difficult to analyze, e.g. in Fig. 1a only a change in slope at a load of approximately 24 mN can be seen. A similar inflection point or a small peak can be seen in Fig. 2a and Fig. 3a at different loads. Optical microscopy confirmed that these inflec-
Fig. 1. Load᎐displacement Ž P᎐h. curve for a 1.5-mm-thick coating in Ža., Pr h 2 vs. h 2 in Žb. and ⭸Pr⭸h2 vs. h2 in Žc.. The minima in the ⭸Pr⭸h 2 curve are indicated by arrows. The second order minima and peaks at very low and very high h 2 are due to the averaging procedure.
74
J. Malzbender, G. de With r Surface and Coatings Technology 137 (2001) 77᎐76
Fig. 2. Load᎐displacement Ž P᎐h. curve for a 3.5-mm-thick coating in Ža. P r h2 vs. h 2 in Žb. and ⭸Pr⭸h2 vs. h 2 in Žc. Žfor further details see also Fig. 1..
tion points corresponded to the onset of radial cracking in the surface of the coating. Plots of Prh2 vs. h 2 are shown in Fig. 1b, Fig. 2b and Fig. 3b, where the kinks as observed in Fig. 1a, Fig. 2a. and Fig. 3a can be seen more clearly. A plot vs. h2
is used to simplify the analysis procedure. It has been shown previously that smoothing of the data before differentiation using a moving average can change the curve significantly w8x. Taking intervals of 40 data points, building the mean and calculating the derivative
Fig. 3. Load᎐displacement Ž P᎐h. curve for a 6.8-mm-thick coating in Ža. P r h2 vs. h 2 in Žb. and ⭸Pr⭸h2 vs. h 2 in Žc. Žfor further details see also Fig. 1..
J. Malzbender, G. de With r Surface and Coatings Technology 137 (2001) 72᎐76
⭸Pr⭸h2 Žsee Fig. 1c, Fig. 2c and Fig. 3c., reveals a clearer image of the changes in the load displacement curve and yields additional information to the simple ratio of Prh2 in Fig. 1b, Fig. 2b and Fig. 3b. For example, in Fig. 1c minima in ⭸Pr⭸h2 can be seen at values of h 2 of approximately 0.33 m2 Ž Ps 10 mN., 0.63 m2 Ž Ps 24 mN. and 0.85 m2 Ž Ps 29 mN.. In order to associate the features in the loading curve and its derivative with the fracture events, indentations were made at various loads between 0 and 1000 mN and the indentation marks were analyzed directly after the measurements using an optical microscope. Images of radial cracks and delaminations obtained thereby have been shown previously by the authors w2,4,8x. It appeared that the first two minima correspond to the onset of radial cracking and delamination. The third minimum is probably due to substrate yield. It can be considered that the substrate will deform plastically if the stress exceeds the yield strength of the material, which can be approximated as Hr3 w9x. This leads for the substrate to a value of approximately 2 GPa. In fact, it was observed in our measurements that the indentation pressure was approximately 1 GPa at the contact depth that corresponds to the supposed substrate yield, but the measurement was influenced by the fracture of the coating, which leads to a displacement of the indenter at constant load and thereby an underestimation of the indentation pressure w10x. Moreover, the indentation depth at the onset of the supposed substrate yield was on average 60% of the
75
coating thickness indicating a significant substrate influence, which is not reflected in the indentation pressure w2,4,8x. The minima in Fig. 2c and Fig. 3c can be related in a similar way to the fracture features and substrate yield. Chipping of the coating led to a significant change of the load-displacement curve, i.e. considerable displacement at constant load, and has been investigated separately w2,4,8x. The consistency of the observed features is illustrated in Fig. 4, which shows the load of radial cracking, delamination and substrate yield as a function of the layer thickness as determined using ⭸Pr⭸h2 and where it can be seen that the critical loads increase with the coating thickness. As can be seen from Fig. 1c, Fig. 2c and Fig. 3c the change of the elasto-plastic response of the coating-substrate system for different coating thicknesses also leads to a decrease of the average ⭸Pr⭸h2 value for thicker coatings. Both effects can be considered to be due to a reduced influence of the harder and stiffer substrate with increasing layer thickness. The decrease in ⭸Pr⭸h2 with increasing layer thickness is simply due to the same change in properties over the layer thickness, as reflected in ⭸P, with increasing thickness, as reflected in ⭸h 2 . The increase in critical load is mainly due to the decreasing component hardness, as elaborated below. Lawn and Evans w11x analyzed the initiation of radialrmedian cracks under a Vickers indenter in an elasticrplastic indentation field for monolithic materi-
Fig. 4. Load of the initiation of radial cracks Ža. delamination Žb. and substrate yield Žc. vs. coating thickness. The lines are parabolic fits.
J. Malzbender, G. de With r Surface and Coatings Technology 137 (2001) 77᎐76
76
als. They determined that the critical load for the crack initiation P U is: P U s 21.7= 10 3
4 K IC H3
Ž3.
where K IC is the fracture toughness. Especially for the thinner coatings it has to be considered that the stress field is modified even at the critical load by the underlying substrate, i.e. a part of the load is carried by the substrate. Thus, introducing the composite hardness into Eq. Ž3., which appears reasonable as a first approximation since the original derivation of the equation is based on the hardness as defined by the ratio of load to area, the critical load will be reduced for the thinner coatings in agreement with our observations. In conclusion, the use of the derivative ⭸Pr⭸h2 of the indentation load-displacement data allows the determination of different fracture and deformation features and is therefore, a helpful tool to analyze the behavior of coated material, which gives additional
information to the commonly determined elastic modulus and hardness. References w1x H. Bach, D. Krause, Thin Films on Glass, Springer-Verlag, Berlin, 1997. w2x J. Malzbender, G. de. With, J. Non-Cryst. Solids 265 Ž2000. 51. w3x W.C. Oliver, G.M. Pharr, J. Mater. Res. 7 Ž1992. 1564. w4x J. Malzbender, J.M.J. den Toonder, G. de With, Thin Solid Films 366 Ž2000. 139. w5x J.L. Loubet, J.M. Georges, J. Meille, in: P.J. Blau, B.R. Lawn ŽEds.., Microindentation Techniques in Materials Science and Engineering, Philadelphia, 1986, p. 72. w6x S.V. Hainsworth, T.F. Page, Mat. Res. Soc. Symp. Proc. 436 Ž1997. 171. w7x R. McGurk, T.F. Page, J. Mater. Res. 14 Ž1999. 2283. w8x J. Malzbender, G. de With, Surf. Coat. Technol. 127 Ž2000. 265. w9x D. Tabor, The Hardness of Metals, Oxford, 1951, p. 102. w10x J. Malzbender, J.M.J. den Toonder, G. de With, Thin Solid Films 372 Ž2000. 134. w11x B.R. Lawn, A.G. Evans, J. Mater. Sci. 12 Ž1977. 2195.