1. Indentation-Induced Failure of Hard Coatings
Adnan Abdul-Baqi & Erik van der Giessen
Koiter Institute Delft
F
Introduction
)
max
O R r
(τ
Indentation-induced failure of hard coatings is modelled by means of h a Film (elastic) t
max
normal
σ
cohesive surfaces. Interfacial delamination (normal & shear) and Interface
coating cracking are the failure events being under consideration. z shear
Symmetry axis
For the cohesive surface, the constitutive behaviour is given in terms Substrate (elastic-plastic) ∆ (∆ )
n t
of a traction versus separation law, where we have adopted the uni-
versal binding law used by Xu and Needleman [1]. It is characterized
mainly by the peak traction and the separation energy (Fig. 2).
Results Figure 1. Geometry. Figure 2. Cohesive zone tractions. The
energy for normal or shear separation is
the area under the corresponding curve.
Interfacial delamination:
0 σe/σy 0 1
σzz/σmax
1.40 1.00
1.20 shear delamination
0.75 0.8 normal delamination
1.00 0.50
50 0.80 20
0.25
0.60 0.6
F/Fmax
0.00
z (µm)
z (µm)
0.40 -0.25
0.20 -0.50 0.4
100 40
0.2
(b) 0
150 (a) 60 0 0.5 1 1.5 2
0 50 100 150 0 20 40 60 h/t
r (µm) r (µm)
Figure 3. (a) Shear delamination . t = 5 µm, τ max = 1.2 GPa . Arrows show the shear direction, line Figure 4. Load versus displacement (F-h) curves for
shows the location of the delaminated area. (b) Normal delamination. t = 2.5 µm, σ max = 1.5 GPa . Fig. 3.
Coating cracking:
0 0
σrr/σmax σrr/σmax 1
e
2.00 2.00
1.56 1.56 d
5
0.8
1.11 5 1.11
0.67 0.67
0.22 0.22 0.6
F/Fmax
z (µm)
z (µm)
10 -0.22 10 -0.22 b c
-0.67 -0.67 0.4
-1.11 -1.11
a
15 -1.56 15 -1.56
-2.00 -2.00 0.2
20 (a) 20 (b) 0
0 5 10 15 20 0 5 10 15 20 0 0.5 1 1.5
r (µm) r (µm) h/t
Figure 5. Coating cracking. t = 2 µm, σ max = 11 GPa . (a) First crack at r 1 = 7.0 µm . (b) Second Figure 6. Load versus displacement curve for Fig. 5.
crack at r 2 = 9.4 µm . Labelled points correspond to specific failure types. a
and b on the curve correspond to mode I cracks at loca-
tions r 1 and r 2 , respectively. At c the first crack grows
Conclusions until the interface and at d it shears of f. Point e corre-
sponds to some limited interfacial delamination in the
1. Shear delamination may occur in the loading stage. It is imprinted on the load vs displacement curve by a kink. vicinity of the coating cracks.
2. Normal delamination may occur during the unloading stage, where a circular part of the coating is lifted off
from 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. [1] X.-P. Xu, A. Needleman, Model. Simul. Mater. Sci. Eng. 1 (1993) 111.