References
209
moduli determined by using Eq. (7.8) from the measured load-depth curves of the
passive Fe (100) surfaces with and without the chromate treatment were E r = 145
GPa and180 GPa, respectively [24]. Consequently, the values of 5
H
E r
≈ 0.13 and
0.08 are calculated, respectively, for the passive Fe (100) surface with and without
the chromate treatment, which are in good agreement with
W e
W t
≈ 0.12 and 0.07,
respectively, obtained experimentally from Fig. 7.23 [52]. The validity of Eq. (7.36)
is proved for both the passive Fe (100) surfaces with and without the chromate
treatment. In Fig. 7.23, the contact depth range where the significant effect of the
chromate treatment emerges is h c ≈ 40 ∼ 60 nm, which is much larger than the
thickness d f ≈ 3 nm of the passive film on iron at 0.25 V (SHE) in pH 8.4 borate
solution. The chromate treatment does not alter or rather reduce the thickness of the
passive film on iron [60].
When the indentation depth exceeds a critical level by several times as much as
the film thickness, the passive film would be locally ruptured at the very edge of the
contact surface where the tensile stress becomes maximum [5]. The local rupture
(breakdown) of the passive film at the very edge of the contact surface may promote
the depth-displacement of the indenter. Assuming that the passive film (Cr-enriched)
with the chromate treatment has a fracture toughness higher than the passive film
without the chromate treatment, a critical load level of the local rupture for the
passive film with the chromate treatment should be higher than that for the passive
film without the chromate treatment. The increase in fracture toughness of the passive
film due to the chromate treatment would bring the increase in hardness since the
passive film resists the depth-displacement of the indenter as far as the load does not
exceed a critical level of the local film rupture.
Furthermore, in the case where the load exceeds a critical level of the local film
rupture, the rupture sites may be repaired by the formation of a new oxide at the sites.
It has been reported that the Cr component enriched in the passive film promotes the
repair (re-passivation) of the rupture sites [66, 67], suggesting that the repair at the
rupture sites for the passive surface with the chromate treatment is faster than that for
the passive surface without the chromate treatment. The fast formation of the new
oxide at the rupture sites due to the chromate treatment leads to the rapid repair, which
would resist the depth-displacement of the indenter to bring the increase in hardness.
The fast formation of the new oxide at the rupture sites due to the chromate treatment
may influence a shape of the unloading curve as seen from Fig. 7.21. Particularly,
the tailing at the latter stage of the unloading curve in addition to the decrease in
stiffness S (corresponding to the initial slope of the unloading curve) seems to be
brought by the raid repair (re-passivation) at the rupture sites due to the chromate
treatment. Therefore, it is deduced that the increase in hardness and the decrease in
reduced elastic modulus (i.e., the increase in work ratio
W e
W t
) of the passive Fe (100)
surfaces due to the chromate treatment result from the high fracture toughness and
rapid repair of the passive films. Further experimental evidence, however, is needed
to confirm the above speculation.
209
moduli determined by using Eq. (7.8) from the measured load-depth curves of the
passive Fe (100) surfaces with and without the chromate treatment were E r = 145
GPa and180 GPa, respectively [24]. Consequently, the values of 5
H
E r
≈ 0.13 and
0.08 are calculated, respectively, for the passive Fe (100) surface with and without
the chromate treatment, which are in good agreement with
W e
W t
≈ 0.12 and 0.07,
respectively, obtained experimentally from Fig. 7.23 [52]. The validity of Eq. (7.36)
is proved for both the passive Fe (100) surfaces with and without the chromate
treatment. In Fig. 7.23, the contact depth range where the significant effect of the
chromate treatment emerges is h c ≈ 40 ∼ 60 nm, which is much larger than the
thickness d f ≈ 3 nm of the passive film on iron at 0.25 V (SHE) in pH 8.4 borate
solution. The chromate treatment does not alter or rather reduce the thickness of the
passive film on iron [60].
When the indentation depth exceeds a critical level by several times as much as
the film thickness, the passive film would be locally ruptured at the very edge of the
contact surface where the tensile stress becomes maximum [5]. The local rupture
(breakdown) of the passive film at the very edge of the contact surface may promote
the depth-displacement of the indenter. Assuming that the passive film (Cr-enriched)
with the chromate treatment has a fracture toughness higher than the passive film
without the chromate treatment, a critical load level of the local rupture for the
passive film with the chromate treatment should be higher than that for the passive
film without the chromate treatment. The increase in fracture toughness of the passive
film due to the chromate treatment would bring the increase in hardness since the
passive film resists the depth-displacement of the indenter as far as the load does not
exceed a critical level of the local film rupture.
Furthermore, in the case where the load exceeds a critical level of the local film
rupture, the rupture sites may be repaired by the formation of a new oxide at the sites.
It has been reported that the Cr component enriched in the passive film promotes the
repair (re-passivation) of the rupture sites [66, 67], suggesting that the repair at the
rupture sites for the passive surface with the chromate treatment is faster than that for
the passive surface without the chromate treatment. The fast formation of the new
oxide at the rupture sites due to the chromate treatment leads to the rapid repair, which
would resist the depth-displacement of the indenter to bring the increase in hardness.
The fast formation of the new oxide at the rupture sites due to the chromate treatment
may influence a shape of the unloading curve as seen from Fig. 7.21. Particularly,
the tailing at the latter stage of the unloading curve in addition to the decrease in
stiffness S (corresponding to the initial slope of the unloading curve) seems to be
brought by the raid repair (re-passivation) at the rupture sites due to the chromate
treatment. Therefore, it is deduced that the increase in hardness and the decrease in
reduced elastic modulus (i.e., the increase in work ratio
W e
W t
) of the passive Fe (100)
surfaces due to the chromate treatment result from the high fracture toughness and
rapid repair of the passive films. Further experimental evidence, however, is needed
to confirm the above speculation.