0 20 40 60

0

20

40

60

σzz/σmax

r (µm)

z (µ

m)

1.00

0.75

0.50

0.25

0.00

-0.25

-0.50

0 50 100 150

0

50

100

150

σe/σy

r (µm)

z (µ

m)

1.40

1.20

1.00

0.80

0.60

0.40

0.20

Adnan Abdul-Baqi & Erik van der Giessen

Koiter Institute Delft

Indentation-Induced Failure of Hard Coatings

Results

Figure 4. Load versus displacement (F-h) curves forFig. 3.

1. Shear delamination may occur in the loading stage. It is imprinted on the load vs displacement curve by a kink.

2. Normal delamination may occur during the unloading stage, where a circular part of the coating is lifted offfrom the substrate. It is imprinted on the load vs displacement curve by a hump.

3. Coating cracking may occur during the loading stage. The first circumferential crack occurs outside the con-tact area. The crack is imprinted on the F-h curve as a kink.

4. On further loading, subsequent cracking occurs with crack spacing of about 1.25 times the coating thickness.

Figure 1. Geometry.

O

F

a Film (elastic)

Interface

Substrate (elastic-plastic)

Sym

met

ry a

xis

r

h

z

tIndentation-induced failure of hard coatings is modelled by means ofcohesive surfaces. Interfacial delamination (normal & shear) andcoating cracking are the failure events being under consideration.For the cohesive surface, the constitutive behaviour is given in termsof a traction versus separation law, where we have adopted the uni-versal binding law used by Xu and Needleman [1]. It is characterizedmainly by the peak traction and the separation energy (Fig. 2).

Interfacial delamination:

Coating cracking:

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

h/t

F/F

ma

x

shear delamination normal delamination

(a)(b)

R

0 5 10 15 20

0

5

10

15

20

r (µm)

σrr/σmax

z (µ

m)

2.00

1.56

1.11

0.67

0.22

-0.22

-0.67

-1.11

-1.56

-2.00

0 5 10 15 20

0

5

10

15

20

r (µm)

σrr/σmax

z (µ

m)

2.00

1.56

1.11

0.67

0.22

-0.22

-0.67

-1.11

-1.56

-2.00

Figure 5. Coating cracking. . (a) First crack at . (b) Secondcrack at .

t 2 µm, σmax 11 GPa= = r1 7.0 µm=r2 9.4 µm=

0 0.5 1 1.50

0.2

0.4

0.6

0.8

1

h/t

F/F

ma

x

b c

d

e

a

Figure 6. Load versus displacement curve for Fig. 5.Labelled points correspond to specific failure types.aandb on the curve correspond to mode I cracks at loca-tions , respectively. At c the first crack growsuntil the interface and atd it shears off. Point e corre-sponds to some limited interfacial delamination in thevicinity of the coating cracks.

r1 and r2

[1] X.-P. Xu, A. Needleman, Model. Simul. Mater. Sci. Eng. 1 (1993) 111.

(a) (b)

Figure 3. (a) Shear delamination. . Arrows show the shear direction, lineshows the location of the delaminated area. (b)Normal delamination. .

t 5 µm τmax, 1.2 GPa= =t 2.5 µm, σmax 1.5 GPa= =

∆n (∆

t)

σ max

(τ m

ax)

normal

shear

Figure 2. Cohesive zone tractions. Theenergy for normal or shear separation isthe area under the corresponding curve.

Conclusions

Introduction