1. Delamination of a Strong Thin Film From a Ductile Substrate
During Indentation Loading and Unloading
Adnan Abdul-Baqi & Erik van der Giessen
Koiter Institute Delft
Introduction The cohesive surface model
Indentation loading and unloading of a strong elastic In the description of the interface as a cohesive surface, a small dis-
film on a ductile substrate is modeled. The film is con- placement jump ∆ between the film and substrate is allowed, with nor-
sidered to be elastic, the substrate is elastic perfectly- mal and tangential components ∆ n and ∆ t respectively. The
plastic and the indenter is spherical and rigid (Fig. 1). corresponding tractions we adopt in this study are those used by Xu and
The interface is modeled by means of a cohesive surface. Needleman [1]. Figure 2 shows these tractions in their uncoupled form.
˙
h 1.5 3
∆t = 0
1 2 ∆n = 0
R 0.5
1
a 0
t max
max
increasing ∆ t 0
T /τ
−0.5
T /σ
h
n
coating t −1 −1
increasing ∆ n
−1.5
interface (a) −2
(b)
−2
substrate −2.5
−1 0 1 2 3 4 5 6
−3
−3 −2 −1 0 1 2 3
∆n/δn ∆t/δt
Figure 1. Geometry. Figure 2. (a) Normal traction versus normal separation. (b) Tangential traction versus tangential separation.
Results
0.00 σe/σy 0.00 σyy/σmax 2
0.5
φ (J/m2)
1.40
1.0 n
1.26
0.4 a
1.11 0.8 1.75 a 150
0.02 0.97 0.01 0.5 0.3 b b 200
0.82
0.3 c 400
0.68 1.5 0.2
0.53 0.1 c d 600
0.39 -0.1 0.1 e >> 600
0.04 0.24 0.02 1.25 d e
-0.4 0
z (mm)
0.10 1 1.15 1.3 1.45 1.6 1.75
z (mm)
-0.6
F/(πR σy)
2
1
0.06 0.03
0.75
0.5
0.08 0.04
(a) (b) 0.25
0.10 0.05
0.00 0.02 0.04 0.06 0.08 0.10 0.00 0.01 0.02 0.03 0.04 0.05 0
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2
r (mm) r (mm) h/t
Figure 3. (a) Contour plot of the Von Mises effective stress at the maximum indentation depth
Figure 4. Load versus displacement curves for dif-
( h max = 2t ), φ n = 150 ( J ⁄ m 2 ). Arrows show the shear direction, line shows the location of the tan-
ferent values of interfacial energies. Curve (e) repre-
gentially delaminated area. (b) Contour plot of the vertical stress component at the end of the unloading
sents the case of a perfect interface.
stage ( F = 0 ), φ n = 500 ( J ⁄ m 2 ).
1
Conclusions
0.8
1. For relatively weak interfaces, delamination occurs in the loading stage. It is
0.6 E imprinted on the load vs displacement curve by a ‘kink’.
E/Emax
el
E
pl
E
int
0.4
∫ F dh 2. Normal delamination occurs during the unloading stage, where a circular part
E + E +E
el pl int
0.2
of the coating is lifted off from the substrate. It is imprinted on the load vs dis-
placement curve by a ‘hump’.
0
0 0.5 1 1.5 2
h/t
Figure 5. Evolution of elastic, plastic, interfacial and
applied work during the loading and unloading process. [1] X.-P. Xu, A. Needleman, Model. Simul. Mater. Sci. Eng. 1 (1993) 111.