Bhushan B. Handbook of Micro/Nano Tribology, Second Edition

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modeled load–displacement curve. OACD is the loading curve. DE is the unloading. Since the ﬁrst ringlike

through-thickness cracking does not always lead to a step in the loading curve in some ﬁlms, the second

ringlike through-thickness crack should be considered. It should be emphasized that the edge of the

buckled ﬁlm is far from the indenter; therefore, it does not matter if the indentation depth exceeds the

ﬁlm thickness or if deformation of the substrate occurs around the indenter when we measure fracture

toughness of the ﬁlm from the released energy during the second ringlike through-thickness cracking

(spalling). Suppose that the second ringlike through-thickness cracking occurs at AC. Now, let us consider

the loading curve OAC. If the second ringlike through-thickness crack does not occur, it can be under-

stood that OA will be extended to OB to reach the same displacement as OC. This means that the crack

formation changes the loading curve OAB into OAC. For point B, the elastic–plastic energy stored in the

ﬁlm/substrate system should be OBF. For point C, the elastic–plastic energy stored in the ﬁlm/substrate

system should be OACF. Therefore, the energy difference before and after the crack generation is the area

of ABC; i.e., this energy stored in ABC will be released as strain energy to create the ringlike through-

thickness crack. According to the theoretical analysis by Li et al. (1997), the fracture toughness of thin

ﬁlms can be written as

(10.33)

where E is the elastic modulus, n is Poisson’s ratio, 2πC

is the crack length in the ﬁlm plane, U the strain

energy difference before and after cracking, and t is the ﬁlm thickness.

By using Equation 10.33, the fracture toughness of the 0.4-µm-thick cathodic arc carbon coating is

calculated. U of 7.1 nNm is assessed from the steps in Figure 10.65a at the peak indentation loads of

200 mN. The loading curve is extrapolated along the tangential direction of the loading curve from the

starting point of the step up to reach the same displacement as the step. The area between the extrapolated

line and the step is the estimated strain energy difference before and after cracking. C

of 7.0 µm is

measured from SEM micrographs in Figure 10.65b. Second ringlike crack is where the spalling occurs.

For E = 300 GPa measured using nanoindenter (Table 10.5) and an assumed value of 0.25 for n, fracture

toughness values is calculated as 10.9 MPa .

10.7.3 Nanofatigue

Delayed fracture resulting from extended service is called fatigue. Fatigue fracturing progresses through

a material via changes within the material at the tip of a crack, where there is a high stress intensity.

There are several situations: cyclic fatigue, stress corrosion, and static fatigue. Cyclic fatigue results from

cyclic loading of machine components; e.g., the stresses cycle from tension and compression occurs in a

loaded rotating shaft. Fatigue also can occur with ﬂuctuating stresses of the same sign, as occurs in a leaf

spring, in a dividing board. In a low ﬂying slider in a head–disk interface, isolated asperity contacts occur

during use and the fatigue failure occurs in the multilayered thin-ﬁlm structure of the magnetic disk

(Bhushan, 1996). Asperity contacts can be simulated using a sharp diamond tip in an oscillating contact

with the thin-ﬁlm disk.

Li and Chu (1979) developed an indentation fatigue test, called impression fatigue. In this test, a

cylindrical indenter with a ﬂat end was pressed onto the surface of the test material with a cyclic load

and the rate of plastic zone propagation was measured.

Wu et al. (1991) developed a nanoindentation fatigue test by modifying their nanoindenter. The cyclic

indentation was implemented by servo controlling the PZT stack to drive the indenter so that the load

cell output followed a 0.1-Hz sinusoidal loading pattern, and the latter was speciﬁed by the cyclic

frequency and the lower and upper limits for the desired load range. The lower limit for all the tests was

set at about 0.2 mN to perform a full load cycle indentation fatigue. A nonzero limit was required in

−

()





































order to activate the load cell servo control mode. Several maximum loads, namely, 4, 16 and 24 mN,

were used. The following results can be obtained: (1) endurance limit, i.e., the maximum load below

which there is no coating failure for a preset number of cycles; (2) number of cycles at which the coating

failure occurs; and (3) changes in contact stiffness measured by using the unloading slope of each cycle

which can be used to monitor the propagation of the interfacial cracks during cyclic fatigue process.

They used a conical diamond indenter with a nominal 1-µm tip. Applied load and penetration depth

were simultaneously monitored during the entire test.

Typical nanoindentation fatigue results for a 0.11-µm DC planar magnetron-sputtered amorphous

carbon ﬁlms on (100) silicon substrate deposited at argon pressure of 30 mtorr is shown in Figure 10.68

(Wu et al., 1991). The test was run at a maximum cyclic load of 4 mN and 0.1 Hz for a total of 105 cycles

with fracture in the 93rd cycle. An SEM micrograph of the damaged zone (Figure 10.68c) shows that the

plastic deformation attributed primarily to the silicon substrate occurred in the central indent area, and

moreover the carbon coating spalled around the indent and resulted in several isolated carbon ﬂakes as

well as cantilevered ﬂakes. Wu et al. reported that in a single indentation test, the critical indentation

FIGURE 10.68 Typical microindentation fatigue results from 0.11-µm-thick DC-sputtered amorphous carbon on

(100)Si, (a) the direct outputs from a strip chart recorder of applied load (LC) and indenter position (IND)

(Maximum load = 4 mN, frequency = 0.1 Hz) (b) a plot of the indentation fatigue loading curve vs. total penetration

depth (the plot includes only the load cycles from 91 to 100; note the abrupt depth increase started from the 93rd

cycle), and (c) SEM micrograph of the fatigue indent. (From Wu, T.W. et al., 1991, Surf. Coat. Technol. 47, 696–709.

With permission.)

load required to crack the carbon coating was about 6 mN. The critical indentation load was extracted

by using the criterion of the applied load at which a load drop appeared along a loading curve. Evidently,

the endurance limit can be signiﬁcantly lower than the critical load of a single indentation. This scenario

is analogous to the fatigue strength vs. tensile strength in macrotests. Wu et al. further reported that the

carbon ﬁlms deposited at an argon pressure of 6 mtorr exhibited an endurance limit of about 24 mN,

about a factor of six higher than the ﬁlm deposited at 30 mtorr. Scratch resistance of the ﬁlm at 30 mtorr

was also poorer as compared to that deposited at 6 mtorr (Wu et al., 1989, 1900b; Wu, 1991).

10.8 Closure

Depth-sensing nanoindentation hardness measurement techniques are commonly used to measure nano-

mechanical properties of surface layers of bulk materials and of ultrathin coatings. The nanoindentation

apparatus continously monitors the load and the position of the indenter relative to the surface of the

specimen (depth of an indent) during the indentation process. The area of indent is then calculated from

a knowledge of the geometry of the tip of the diamond indenter. Mechanical property measurements

can be made at a minimum penetration depth of about 20 nm (or a plastic depth of about 15 nm).

Typically, a three-sided pyramidal (Berkovich) diamond indenter is used for measurements. Mechanical

properties that can be measured are elastic–plastic deformation behavior, hardness, Young’s modulus of

elasticity, scratch resistance, ﬁlm–substrate adhesion, residual stresses, time-dependent creep and relax-

ation properties, fracture toughness, and fatigue.

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