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Indentation tests to determine the fracture toughness of nickel phosphorus coatings
Surface and Coatings Technology 155 (2002) 161–168
Indentation tests to determine the fracture toughness of nickel phosphorus coatings A. Roman, D. Chicot*, J. Lesage ´ Laboratoire de Mecanique de Lille, URA CNRS 1441, U.S.T. Lille, IUT A GMP, Le Recueil, Rue de la Recherche, 59653 Villeneuve d’Ascq, France Received 18 July 2001; accepted in revised form 2 March 2002
Abstract In this paper, Vickers indentation was used to study the resistance to cracking of electroless nickel phosphorus coatings. For low indentation loads, cracking initiates only at the tips of the indent (primary cracking). It was shown that these cracks are of the Palmqvist type. For higher loads, new cracks, for which initiation sites are located on the edges of the indent, begin to form (secondary cracking). It was found that this change in the cracking mechanism occurs when the primary cracks reach the interface with the substrate. This result shows that the interface resistance to cracking is higher than the cohesion of the coating. In addition, it was possible to apply the same formulae whatever the cracking process, if the total number of cracks was divided by 4, like for the first cracking process. Values of fracture toughness Kc s1.5 MPa m1y2 for a 300 8C treatment and 2.1 MPa m1y2 for a 600 8C treatment were found, independent of the coating thickness. 䊚 2002 Elsevier Science B.V. All rights reserved. Keywords: Hardness; Fracture toughness; Nickel phosphorus; Coating
1. Introduction As-deposited NiP coatings are generally reported to be amorphous or more or less crystallized depending on the phosphorus content. For low phosphorus contents the structure is amorphous whereas it is increasingly crystallized for higher phosphorus contents w1,2x. Crystallization of the amorphous phase may be achieved by heat treatment w3x. As a consequence, hardness of the deposits will depend on the post deposition thermal treatment w4x and will affect the wear resistance w5x. For a given treatment duration, the hardness versus temperature relation exhibits a maximum, and the corresponding curve has the characteristic ‘bell’ shape w6x. For temperatures lower than the optimum, hardening is due to the crystallization of the amorphous phase. For higher temperatures, hardness decreases with the grain growth of the Nia phase in addition to the spheroidization of the nickel phosphide (Ni3P). As a consequence of these *Corresponding author. Tel.: q33-320-677326; fax: q33-320677321. E-mail address: [email protected] (D. Chicot), [email protected] (A. Roman), [email protected] (J. Lesage).
differences in the constituents, microstructures and crystallization degree, the resulting mechanical properties were found to be very different w7–9x. Determination of mechanical properties of films and coatings is not as easy as for bulk materials because of the presence of the substrate, the properties of which interfere in the measurement. This is the case particularly for hardness w10,11x and adhesion measurements. Nevertheless, indentation methods are still widespread for the determination of mechanical properties of films and coatings since numerous models, allowing the interpretation of the experimental data, are available in the literature w12x. In the present work, we studied the effect of the load applied during a normal indentation upon the crack initiation, propagation and appearance of decohesion for a 10% P electroless NiP coating as described below. 2. Materials and treatments The material used as the substrate was AISI 4135 steel for which composition in wt.% is given in Table 1. Hardness of the substrate is near 3 GPa after sand blasting and the elastic modulus is 200 GPa. As shown
0257-8972/02/$ - see front matter 䊚 2002 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 7 - 8 9 7 2 Ž 0 2 . 0 0 1 0 9 - 3
A. Roman et al. / Surface and Coatings Technology 155 (2002) 161–168
162
Table 1 Composition of the substrate in weight percent Elements
C
Cr
Mn
Mo
V
Si
Wt.%
0.3
1.25
-1
0.3–0.5
0.1–0.15
0.6
Fig. 1a, its structure presents the aspect of globular pearlite dispersed in the ferrite matrix. The NiP coating was prepared using the Kanigen industrial process w1x consisting of a bath of pH 4.7, composed of nickel sulfate, sodium hypophosphide, caustic soda and lactic acid maintained at a temperature near 90 8C during a period depending on the expected thickness (here, the thickness was 80 mm). Fig. 1b shows the nodular aspect of the coating surface just after the deposition process. The mean radius of the nodules is 40 mm and hardness of the coatings was found to be 8 GPa for 600 8C and
10 GPa for 300 8C treatments. Literature data show hardness lying between 7 and 12 GPa w13,14x. Two post deposition treatments were performed in air at 300 and 600 8C for 6 h. Fig. 2a and Fig. 3a show that the microstructure is different after these treatments. At 300 8C, the coating is homogeneous and no visible sign of nickel diffusion toward the substrate is detected. This is confirmed by electron dispersion spectrometry (EDS) analysis (K radiation) of the elements Ni, P, Cr and Fe (Fig. 2b) and by the corresponding line profiles (Fig. 2c). It is seen, in effect, that the limits of composition for the different elements are very sharp, which indicates that no or limited diffusion is suggested between the coating and the substrate. At 600 8C (Fig. 3b), the limits of the elements are not so well defined and present a shift that suggests the existence of new constituents. In Fig. 4, which is a
Fig. 1. (a) Substrate formed of globular perlite dispersed in a ferrite matrix and (b) nodular structure of the coating.
Fig. 2. Metallographic aspect etched of the surface (a), EDS analysis (b) and associated profile lines (c) of the 300 8C heat treated sample.
A. Roman et al. / Surface and Coatings Technology 155 (2002) 161–168
163
Fig. 3. Metallographic aspect etched of the surface (a), EDS analysis (b) and associated profile lines (c) of the 600 8C heat treated sample.
higher magnification of Fig. 3a, four different zones are clearly visible. Starting from the upper surface, zone 1 shows a bi-phased structure composed of the Ni a phase (which contains 0.17% P as a maximum w15x) and of the Ni3P intermetallic compound containing 15% P as predicted by the equilibrium diagram (Fig. 5). Zone 2 does not present any noticeable precipitates and zone 3 corresponds to an interdiffusion zone of the austenite structure in accordance with the Fe–Ni diagram. Finally, a zone of Fe depletion is observed in the outer layer of the substrate. These two latter zones correspond to a strong metallurgical bonding and this will have consequences on the indentation behavior, as we will show in the next part.
crack length lm was obtained by dividing the total length of the surface cracks at each tip of the indent for a given load by 4. For higher loads a change occurs in the mode of cracking (called secondary cracking in the following) characterized by the appearance of new cracks at different locations in the indent. The corre-
3. Indentation tests Indentation tests were performed using a Leco micro indentation hardness tester using a Vickers diamond indenter for loads ranging between 0.1 and 10 N and a Wolpert Vickers macro hardness tester for loads above 10 N. Four types of samples were prepared accordingly to two treatment temperatures and two coating thicknesses. The objective of the indentation was to generate cracks in the surrounding of the indent to study the cracking process and to calculate the toughness of the material. For low applied loads, a similar behavior to that of massive brittle materials was observed for which cracking appears generally at the tips of the indent and progresses in the direction of the diagonals. A mean
Fig. 4. Metallographic aspect of the substrate and the out layer.
A. Roman et al. / Surface and Coatings Technology 155 (2002) 161–168
164
Fig. 5. Nickel phosphorus partial binary diagram.
sponding lm value is, this time, expressed by the following relation where n is the total number of cracks: isn
8li lms
is1
n
applied load with a slope near 0.75 in logarithmic coordinates. In the second zone, the value of the slope is zero or very near zero. That means that in spite of the increase in the number of cracks, the mean crack
(1)
Fig. 6 presents the different features that this secondary cracking may take depending on the treatment and thickness. For example secondary cracks appeared for a load of 100 N for the sample treated at 300 8C and 40 mm thick (Fig. 6b) and for a load of 300 N for the sample treated at 600 8C and of thickness 20 mm (Fig. 6d). The former presents cracks starting from the sides and the latter presents cracks arranged in a somehow ‘spider web’ centered on the indent. Table 2 collects the values of lm obtained for each load. Fig. 7a–d present the mean crack length as a function of the applied load in bilogarithmic coordinates. The results presented in these figures show the same general behavior for the four situations of treatment and thickness. The experimental points arranged in two distinct zones where they can be represented by straight lines of different slopes. The first zone, related to the lowest loads, corresponds to the classic cracking mode where cracks appear only at the tip of the indent. In this zone, the mean crack length increases linearly with the
Fig. 6. Examples of crack initiation and propagation depending on coating thickness and treatment temperature.
A. Roman et al. / Surface and Coatings Technology 155 (2002) 161–168 Table 2 Experimental data Load P (N)
Diagonal d (mm)
Mean crack length lm (mm)
Corrected crack length ls (mm)
(a) Treatment temperatures300 8C, thicknesss40 mm, roughnesss1.08 mm 3 21 31 31 5 29 54 54 10 41 97 97 20 70 140 140 30 88 183 183 50 126 283 283 100 198 297 590 156.25 261 339 745 200 303 252 625 300 373 328 984 400 445 339 1582 500 483 229 1717 625 566 262 1965 1250 812 363 3630 (b) Treatment temperatures300 8C, thicknesss75 mm, roughnesss1.11 mm 3 22 109 109 5 30 201 201 10 42 261 261 20 59 407 407 30 77 459 459 50 109 304 528 100 164 508 564 156.25 242 449 848 200 275 402 1210 300 310 435 2005 (c) Treatment temperatures600 8C, thicknesss20 mm, roughnesss1.08 mm 5 33 20 20 10 67 30 30 20 99 54 54 30 120 86 86 50 142 111 111 100 226 108 265 156.25 278 104 280 200 326 101 358 (d) Treatment temperatures600 8C, thicknesss75 mm, roughnesss1.17 mm 3 22 11 11 5 29 15 15 10 45 26 26 20 65 72 72 30 82 135 135 50 115 187 187 100 182 330 330 156.25 227 330 362 200 274 415 528 300 345 446 563 400 418 484 848 625 535 570 1210 1250 821 698 2006
length remains constant. This observation is not so easy to interpret at first. Nevertheless, some interesting features can be discussed already. For example it is possible
165
to determine the critical crack length (lc, Table 3) corresponding to the transition between the two zones. In order to explain why there is a change and why it appears for different loads depending on thickness and treatment, it is necessary first to know what is the shape of the cracks. By careful sequential polishing with diamond grit it was possible to examine the change in shape of the cracks initiated originally at the tips of an indent. The observations show that the origin of the cracks does not remain in contact with the tips of the indent while they reduce in length. This procedure demonstrates that the cracks initiated at the tips of the indent are of Palmqvist type w16x with a ratio near 6 between the length and the width. Such a ratio between the dimensions of the cracks was also obtained by Bigot w17,18x in a recent work on soda lime coatings. Since the secondary cracking appears for lc equaling approximately six times the coating thickness (i.e. when the crack width equals the coating thickness), it is reasonable to think that when the primary cracks reach the substrate they cannot develop further and secondary cracks initiate at other favorable sites. We defined lm as the ratio between the total crack length and the number of cracks, and found it to be constant. We now define an equivalent crack length ls by dividing by 4 the total crack length (Table 2): isn
8li lss
is1
(2)
4
ls corresponds then to cracks associated to only one tip of the indent. It is remarkable that the calculated values according to this relation follow exactly the same straight line that the values of lm in zone I (Fig. 7a–d). This result, joined to the observation that lm is constant in zone II seems to indicate that the cracking energy per unit surface of crack must be constant, independent of the shape and the position of the crack. To our knowledge, no similar observation was reported in the literature but it could be very interesting to verify this behavior on other types of materials. Since only one line of constant slope is now available for the entire range of loads, which means that the toughness can be calculated using all the experimental points. Some models expressing the fracture toughness of brittle material for Palmqvist cracking under Vickers indentation can be found in the literature, w19–22x: B
E E2y5 P F for al1y2 DHG w19x (0.25F1yaF(2.5
Kcs0.0089C
E E2y5 P F al1y2 DHG
(3)
B
Kcs0.0122C
w20x
(4)
A. Roman et al. / Surface and Coatings Technology 155 (2002) 161–168
166
Fig. 7. Bilogarithmic representation of the relation between mean crack lengths and Vickers indentation loads.
Kcs0.0319
P al1y2
(5)
w21x
B
E E2y3B a E1y2 P F C F 3y2 with csaq1 c DHG D l G
Kcs0.0143C
w22x (6)
where E is the Young modulus, H the hardness, P the applied load, a the half diagonal of the indent and l the crack length. Apart from Eq. (6), these relations show that the ratio between the applied load and the factor al1y2 should be constant. Fig. 8 confirms this assumption since a linear relation is found to fit accurately with the experimental
points. Among these relations, only Eq. (5) does not require the knowledge of the elastic modulus. Using this relation we calculate the fracture toughness of the electroless Ni–P coating for the four conditions of thickness and treatment. The calculated values are mentioned in Fig. 8. It can be seen that fracture toughness does not depend on coating thickness and that it is lower for coatings treated at 300 8C than for coatings treated at 600 8C. Kcs1.5 MPa m1y2 for 300(C, Kcs2.1 MPa m1y2 for 600(C. Using these two values, it is then possible to calculate
Table 3 Critical crack length
lc (mm) lcyt
TTs300yts40
TTs300yts75
TTs600yts20
TTs600yts75
300 7.5
450 6
110 5.5
450 6
A. Roman et al. / Surface and Coatings Technology 155 (2002) 161–168
167
Fig. 8. Load vs. al1y2 factor and Kc calculation.
the elastic modulus (E) from a relation that we deduced from Eqs. (3) and (4): B
EsC0.01 D
Kc E5y2 F H Pyal1y2 G
(7)
Pyal1y2 comes from Fig. 8. The calculated elastic modulus for the two treatments are presented in Table 4. These results are in agreement with a value of 160 GPa given by Tsui w13x for an amorphous coating and values between 80 and 180 GPa from Riedel w3x. 4. Conclusions Determination of fracture toughness using Vickers indentation is well known for brittle monolithic materi-
als. In the special case of coatings, depending on the value of the applied load, the substrate may interfere and modify the cracking phenomenon. We have shown here for electroless NiP coatings that when the crack reaches the interface between the coating and the substrate, a change in the cracking process is observed. At this moment, the primary process of the Palmqvist type, transforms into a secondary cracking for which initiation sites are located on the edges of the indent. For the two processes of cracking, the mean cracks lm or ls, obtained by dividing by 4 the total crack length, follow exactly the same linear variation with the applied load. Thus, the same mathematical model can be applied for the calculation of the fracture toughness Kc whatever the
Table 4 Calculated elastic modulus
TTs300 8C TTs600 8C
H (GPa)
Kc (MPa m1y2)
Pyal1y2 (MPa m1y2)
E (GPa)
10 8
1.5 2.1
46.7 65.5
185 147
168
A. Roman et al. / Surface and Coatings Technology 155 (2002) 161–168
cracking process. This surprising result has to be verified on other types of brittle coatings in order to understand the physical meaning of such a behavior. We found that the values of Kcs1.5 MPa m1y2 for the 300 8C heat treatment and 2.1 MPa m1y2 for the 600 8C heat treatment, are independent of the coating thickness. References w1x S.P. Kumar, K.P. Nair, J. Mater. Sci. Lett. 13 (9) (1994) 671. w2x H. Kreye, F. Muller, K. Lang, D. Isheim, T. Hentschel, Z. Metallkunde 86 (3) (1995) 186. w3x W. Riedel, ASM International, Finishing Publications LTD Stevenage, Hertfortshire, England, 1991. w4x R.N. Duncan, Electroless Nickel ’93 Conference Proceedings, Gardner Publications, Inc, Cincinnati, OH, 10-12, 1993. w5x R. Taheri, I.N.A. Oguocha, S. Yannacopoulos, Wear 249 (5-6) (2001) 389. w6x O. Osoviecki, W. Form, J. Forchelet, Rev. Metall. ´ 420 (1985) 581. w7x M.H. Staia, E.S. Puchi, G. Castro, O. Ramirez, D.B. Lewis, Thin Solid Films 355-356 (1-2) (1999) 472. w8x T.Y. Tsui, Y.C. Joo, Mater. Res. Soc. Symp. Proc. 594 (2000) 389.
w9x Y. Ichikawa, S. Maekawa, K. Takashima, M. Shimojo, Y. Higo, M.V. Swain, Mater. Res. Soc. Symp. Proc. 605 (2000) 273. w10x J.C. Hay, G.M. Pharr, Thin-Films—Stresses and Mechanical Properties VII, Mater. Res. Soc. Symp. Proc., 605 (2000) 273. w11x S. Milis, J.P. Celis, Thin Solid Films 288 (1-2) (1996) 202. w12x C.B. Ponton, D.R. Rawlings, Mater. Sci. Technol. 5 (1989) 865. w13x T.Y. Tsui, Y.C. Joo, Thin Solid Films 401 (1-2) (2001) 203. w14x Y.Y. Tsai, F.B. Wu, Y.I. Chen, P.J. Peng, J.G. Duh, S.Y. Tsai, Surf. Coat. Technol. 146-147 (2001) 502. w15x S. Skiles, http:yycyberbuzz.gatech.eduyasm tmsyphase diagramsypdyNi-P.JPG w16x S. Palmqvist, Jernkontorets Annaler 141 (5) (1957) 300. w17x R. Bigot, Caracterisation ´ des surfaces et interfaces a` l’aide de ` de doctorat de l’Universite´ l’essai de durete´ Vickers, These des Sciences et Technologies de Lille 1, 1995. w18x A. Iost, R. Bigot, F. Barbieux, P. Vast, J. Mater. Sci. 34 (16) (1999) 3991. w19x K. Niihara, R. Morena, D.P.H. Hasselman, J. Mater. Sci. Lett. 1 (1982) 13. w20x K. Niihara, J. Mater. Sci. Lett. 2 (1983) 221. w21x D.K. Shetty, I.G. Wright, P.N. Mincer, A.H. Clauer, J. Mater. Sci. 20 (1985) 1873. w22x M.T. Laugier, J. Mater. Sci. Lett. 6 (1987) 355.
Indentation tests to determine the fracture toughness of nickel phosphorus coatings A. Roman, D. Chicot*, J. Lesage ´ Laboratoire de Mecanique de Lille, URA CNRS 1441, U.S.T. Lille, IUT A GMP, Le Recueil, Rue de la Recherche, 59653 Villeneuve d’Ascq, France Received 18 July 2001; accepted in revised form 2 March 2002
Abstract In this paper, Vickers indentation was used to study the resistance to cracking of electroless nickel phosphorus coatings. For low indentation loads, cracking initiates only at the tips of the indent (primary cracking). It was shown that these cracks are of the Palmqvist type. For higher loads, new cracks, for which initiation sites are located on the edges of the indent, begin to form (secondary cracking). It was found that this change in the cracking mechanism occurs when the primary cracks reach the interface with the substrate. This result shows that the interface resistance to cracking is higher than the cohesion of the coating. In addition, it was possible to apply the same formulae whatever the cracking process, if the total number of cracks was divided by 4, like for the first cracking process. Values of fracture toughness Kc s1.5 MPa m1y2 for a 300 8C treatment and 2.1 MPa m1y2 for a 600 8C treatment were found, independent of the coating thickness. 䊚 2002 Elsevier Science B.V. All rights reserved. Keywords: Hardness; Fracture toughness; Nickel phosphorus; Coating
1. Introduction As-deposited NiP coatings are generally reported to be amorphous or more or less crystallized depending on the phosphorus content. For low phosphorus contents the structure is amorphous whereas it is increasingly crystallized for higher phosphorus contents w1,2x. Crystallization of the amorphous phase may be achieved by heat treatment w3x. As a consequence, hardness of the deposits will depend on the post deposition thermal treatment w4x and will affect the wear resistance w5x. For a given treatment duration, the hardness versus temperature relation exhibits a maximum, and the corresponding curve has the characteristic ‘bell’ shape w6x. For temperatures lower than the optimum, hardening is due to the crystallization of the amorphous phase. For higher temperatures, hardness decreases with the grain growth of the Nia phase in addition to the spheroidization of the nickel phosphide (Ni3P). As a consequence of these *Corresponding author. Tel.: q33-320-677326; fax: q33-320677321. E-mail address: [email protected] (D. Chicot), [email protected] (A. Roman), [email protected] (J. Lesage).
differences in the constituents, microstructures and crystallization degree, the resulting mechanical properties were found to be very different w7–9x. Determination of mechanical properties of films and coatings is not as easy as for bulk materials because of the presence of the substrate, the properties of which interfere in the measurement. This is the case particularly for hardness w10,11x and adhesion measurements. Nevertheless, indentation methods are still widespread for the determination of mechanical properties of films and coatings since numerous models, allowing the interpretation of the experimental data, are available in the literature w12x. In the present work, we studied the effect of the load applied during a normal indentation upon the crack initiation, propagation and appearance of decohesion for a 10% P electroless NiP coating as described below. 2. Materials and treatments The material used as the substrate was AISI 4135 steel for which composition in wt.% is given in Table 1. Hardness of the substrate is near 3 GPa after sand blasting and the elastic modulus is 200 GPa. As shown
0257-8972/02/$ - see front matter 䊚 2002 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 7 - 8 9 7 2 Ž 0 2 . 0 0 1 0 9 - 3
A. Roman et al. / Surface and Coatings Technology 155 (2002) 161–168
162
Table 1 Composition of the substrate in weight percent Elements
C
Cr
Mn
Mo
V
Si
Wt.%
0.3
1.25
-1
0.3–0.5
0.1–0.15
0.6
Fig. 1a, its structure presents the aspect of globular pearlite dispersed in the ferrite matrix. The NiP coating was prepared using the Kanigen industrial process w1x consisting of a bath of pH 4.7, composed of nickel sulfate, sodium hypophosphide, caustic soda and lactic acid maintained at a temperature near 90 8C during a period depending on the expected thickness (here, the thickness was 80 mm). Fig. 1b shows the nodular aspect of the coating surface just after the deposition process. The mean radius of the nodules is 40 mm and hardness of the coatings was found to be 8 GPa for 600 8C and
10 GPa for 300 8C treatments. Literature data show hardness lying between 7 and 12 GPa w13,14x. Two post deposition treatments were performed in air at 300 and 600 8C for 6 h. Fig. 2a and Fig. 3a show that the microstructure is different after these treatments. At 300 8C, the coating is homogeneous and no visible sign of nickel diffusion toward the substrate is detected. This is confirmed by electron dispersion spectrometry (EDS) analysis (K radiation) of the elements Ni, P, Cr and Fe (Fig. 2b) and by the corresponding line profiles (Fig. 2c). It is seen, in effect, that the limits of composition for the different elements are very sharp, which indicates that no or limited diffusion is suggested between the coating and the substrate. At 600 8C (Fig. 3b), the limits of the elements are not so well defined and present a shift that suggests the existence of new constituents. In Fig. 4, which is a
Fig. 1. (a) Substrate formed of globular perlite dispersed in a ferrite matrix and (b) nodular structure of the coating.
Fig. 2. Metallographic aspect etched of the surface (a), EDS analysis (b) and associated profile lines (c) of the 300 8C heat treated sample.
A. Roman et al. / Surface and Coatings Technology 155 (2002) 161–168
163
Fig. 3. Metallographic aspect etched of the surface (a), EDS analysis (b) and associated profile lines (c) of the 600 8C heat treated sample.
higher magnification of Fig. 3a, four different zones are clearly visible. Starting from the upper surface, zone 1 shows a bi-phased structure composed of the Ni a phase (which contains 0.17% P as a maximum w15x) and of the Ni3P intermetallic compound containing 15% P as predicted by the equilibrium diagram (Fig. 5). Zone 2 does not present any noticeable precipitates and zone 3 corresponds to an interdiffusion zone of the austenite structure in accordance with the Fe–Ni diagram. Finally, a zone of Fe depletion is observed in the outer layer of the substrate. These two latter zones correspond to a strong metallurgical bonding and this will have consequences on the indentation behavior, as we will show in the next part.
crack length lm was obtained by dividing the total length of the surface cracks at each tip of the indent for a given load by 4. For higher loads a change occurs in the mode of cracking (called secondary cracking in the following) characterized by the appearance of new cracks at different locations in the indent. The corre-
3. Indentation tests Indentation tests were performed using a Leco micro indentation hardness tester using a Vickers diamond indenter for loads ranging between 0.1 and 10 N and a Wolpert Vickers macro hardness tester for loads above 10 N. Four types of samples were prepared accordingly to two treatment temperatures and two coating thicknesses. The objective of the indentation was to generate cracks in the surrounding of the indent to study the cracking process and to calculate the toughness of the material. For low applied loads, a similar behavior to that of massive brittle materials was observed for which cracking appears generally at the tips of the indent and progresses in the direction of the diagonals. A mean
Fig. 4. Metallographic aspect of the substrate and the out layer.
A. Roman et al. / Surface and Coatings Technology 155 (2002) 161–168
164
Fig. 5. Nickel phosphorus partial binary diagram.
sponding lm value is, this time, expressed by the following relation where n is the total number of cracks: isn
8li lms
is1
n
applied load with a slope near 0.75 in logarithmic coordinates. In the second zone, the value of the slope is zero or very near zero. That means that in spite of the increase in the number of cracks, the mean crack
(1)
Fig. 6 presents the different features that this secondary cracking may take depending on the treatment and thickness. For example secondary cracks appeared for a load of 100 N for the sample treated at 300 8C and 40 mm thick (Fig. 6b) and for a load of 300 N for the sample treated at 600 8C and of thickness 20 mm (Fig. 6d). The former presents cracks starting from the sides and the latter presents cracks arranged in a somehow ‘spider web’ centered on the indent. Table 2 collects the values of lm obtained for each load. Fig. 7a–d present the mean crack length as a function of the applied load in bilogarithmic coordinates. The results presented in these figures show the same general behavior for the four situations of treatment and thickness. The experimental points arranged in two distinct zones where they can be represented by straight lines of different slopes. The first zone, related to the lowest loads, corresponds to the classic cracking mode where cracks appear only at the tip of the indent. In this zone, the mean crack length increases linearly with the
Fig. 6. Examples of crack initiation and propagation depending on coating thickness and treatment temperature.
A. Roman et al. / Surface and Coatings Technology 155 (2002) 161–168 Table 2 Experimental data Load P (N)
Diagonal d (mm)
Mean crack length lm (mm)
Corrected crack length ls (mm)
(a) Treatment temperatures300 8C, thicknesss40 mm, roughnesss1.08 mm 3 21 31 31 5 29 54 54 10 41 97 97 20 70 140 140 30 88 183 183 50 126 283 283 100 198 297 590 156.25 261 339 745 200 303 252 625 300 373 328 984 400 445 339 1582 500 483 229 1717 625 566 262 1965 1250 812 363 3630 (b) Treatment temperatures300 8C, thicknesss75 mm, roughnesss1.11 mm 3 22 109 109 5 30 201 201 10 42 261 261 20 59 407 407 30 77 459 459 50 109 304 528 100 164 508 564 156.25 242 449 848 200 275 402 1210 300 310 435 2005 (c) Treatment temperatures600 8C, thicknesss20 mm, roughnesss1.08 mm 5 33 20 20 10 67 30 30 20 99 54 54 30 120 86 86 50 142 111 111 100 226 108 265 156.25 278 104 280 200 326 101 358 (d) Treatment temperatures600 8C, thicknesss75 mm, roughnesss1.17 mm 3 22 11 11 5 29 15 15 10 45 26 26 20 65 72 72 30 82 135 135 50 115 187 187 100 182 330 330 156.25 227 330 362 200 274 415 528 300 345 446 563 400 418 484 848 625 535 570 1210 1250 821 698 2006
length remains constant. This observation is not so easy to interpret at first. Nevertheless, some interesting features can be discussed already. For example it is possible
165
to determine the critical crack length (lc, Table 3) corresponding to the transition between the two zones. In order to explain why there is a change and why it appears for different loads depending on thickness and treatment, it is necessary first to know what is the shape of the cracks. By careful sequential polishing with diamond grit it was possible to examine the change in shape of the cracks initiated originally at the tips of an indent. The observations show that the origin of the cracks does not remain in contact with the tips of the indent while they reduce in length. This procedure demonstrates that the cracks initiated at the tips of the indent are of Palmqvist type w16x with a ratio near 6 between the length and the width. Such a ratio between the dimensions of the cracks was also obtained by Bigot w17,18x in a recent work on soda lime coatings. Since the secondary cracking appears for lc equaling approximately six times the coating thickness (i.e. when the crack width equals the coating thickness), it is reasonable to think that when the primary cracks reach the substrate they cannot develop further and secondary cracks initiate at other favorable sites. We defined lm as the ratio between the total crack length and the number of cracks, and found it to be constant. We now define an equivalent crack length ls by dividing by 4 the total crack length (Table 2): isn
8li lss
is1
(2)
4
ls corresponds then to cracks associated to only one tip of the indent. It is remarkable that the calculated values according to this relation follow exactly the same straight line that the values of lm in zone I (Fig. 7a–d). This result, joined to the observation that lm is constant in zone II seems to indicate that the cracking energy per unit surface of crack must be constant, independent of the shape and the position of the crack. To our knowledge, no similar observation was reported in the literature but it could be very interesting to verify this behavior on other types of materials. Since only one line of constant slope is now available for the entire range of loads, which means that the toughness can be calculated using all the experimental points. Some models expressing the fracture toughness of brittle material for Palmqvist cracking under Vickers indentation can be found in the literature, w19–22x: B
E E2y5 P F for al1y2 DHG w19x (0.25F1yaF(2.5
Kcs0.0089C
E E2y5 P F al1y2 DHG
(3)
B
Kcs0.0122C
w20x
(4)
A. Roman et al. / Surface and Coatings Technology 155 (2002) 161–168
166
Fig. 7. Bilogarithmic representation of the relation between mean crack lengths and Vickers indentation loads.
Kcs0.0319
P al1y2
(5)
w21x
B
E E2y3B a E1y2 P F C F 3y2 with csaq1 c DHG D l G
Kcs0.0143C
w22x (6)
where E is the Young modulus, H the hardness, P the applied load, a the half diagonal of the indent and l the crack length. Apart from Eq. (6), these relations show that the ratio between the applied load and the factor al1y2 should be constant. Fig. 8 confirms this assumption since a linear relation is found to fit accurately with the experimental
points. Among these relations, only Eq. (5) does not require the knowledge of the elastic modulus. Using this relation we calculate the fracture toughness of the electroless Ni–P coating for the four conditions of thickness and treatment. The calculated values are mentioned in Fig. 8. It can be seen that fracture toughness does not depend on coating thickness and that it is lower for coatings treated at 300 8C than for coatings treated at 600 8C. Kcs1.5 MPa m1y2 for 300(C, Kcs2.1 MPa m1y2 for 600(C. Using these two values, it is then possible to calculate
Table 3 Critical crack length
lc (mm) lcyt
TTs300yts40
TTs300yts75
TTs600yts20
TTs600yts75
300 7.5
450 6
110 5.5
450 6
A. Roman et al. / Surface and Coatings Technology 155 (2002) 161–168
167
Fig. 8. Load vs. al1y2 factor and Kc calculation.
the elastic modulus (E) from a relation that we deduced from Eqs. (3) and (4): B
EsC0.01 D
Kc E5y2 F H Pyal1y2 G
(7)
Pyal1y2 comes from Fig. 8. The calculated elastic modulus for the two treatments are presented in Table 4. These results are in agreement with a value of 160 GPa given by Tsui w13x for an amorphous coating and values between 80 and 180 GPa from Riedel w3x. 4. Conclusions Determination of fracture toughness using Vickers indentation is well known for brittle monolithic materi-
als. In the special case of coatings, depending on the value of the applied load, the substrate may interfere and modify the cracking phenomenon. We have shown here for electroless NiP coatings that when the crack reaches the interface between the coating and the substrate, a change in the cracking process is observed. At this moment, the primary process of the Palmqvist type, transforms into a secondary cracking for which initiation sites are located on the edges of the indent. For the two processes of cracking, the mean cracks lm or ls, obtained by dividing by 4 the total crack length, follow exactly the same linear variation with the applied load. Thus, the same mathematical model can be applied for the calculation of the fracture toughness Kc whatever the
Table 4 Calculated elastic modulus
TTs300 8C TTs600 8C
H (GPa)
Kc (MPa m1y2)
Pyal1y2 (MPa m1y2)
E (GPa)
10 8
1.5 2.1
46.7 65.5
185 147
168
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