Indentation Fracture
and How to Apply to
Thin Films
Huai Huang
Outline
Indentation test
 Indentation fracture mechanics

 Stress
field and Crack system
 Fracture Mechanics Analysis

Fracture toughness measurement on thin
film
What is Indentation test


Easy and cheap to perform:
Properties:
 Elastic properties : Modulus
 Plastic properties: Hardness
 Time dependent properties: Creep
 Fracture properties
Hertzian Stress field

For smooth sperical
indenter
Hertzian cone crack
p0  P /  a 2  (3E / 4 k )(a / r )
Pr
K   3/ 2
c
   ( )
However X can’t be exactly
calculated
Indentation Stress field
For a normal point load P the stress
field can be given by Boussinesq field:
Radial-median crack

Under a point load
p0  P /  0 a 2  H
Fracture Mechanics Analysis
System behave like a center-loaded, half-penny crack, for
which the stress intensity factor is given by:
K
Pr
c 3/ 2
The stress field can be expressed (by Hill’s expending cavity
solution) as:
Pr
E 1/ 2
P ( ) cot 2 / 3
H
Combining the above two equations and assuming the crack arrests when it
grows to a length at which the stress intensity factor is just equal the
fracture toughness
Experiment within 40% accuracy
Other Fracture property
Inert Strength
 R-curves
 Crack-velocity exponent
 Crack initiation
 Crack propagation

Hard film on a soft substrate

Load vs displacement can be simulated as
Indentation fracture for thin film
Mechanical properties were extracted from
displacement profile minima
 Typical loads 1000gram and crack length
100um: Small crack threshold need.
 Solution: Change of indenter geometry
sharper indenter needed to reduce critical load

 Vickers
indenter: threshold 25 grams
 Cube corner indenter: 0.5 grams
 (Same theory can be apply to different indenters)
Indentation on Low K


Equation should not be directly applied, Since the crack
shape is not half-penny shape.
As a first order approximation, Equation can be used to
estimate the low-K films fracture toughness. Low-K
dielectric films fracture toughness was estimated to
range from 0.01 to 0.05 MPa·m1/2
Summary



Indentation test can provide fracture property
such as fracture toughness. Indentation Fracture
mechanics is discussed.
Reduced crack threshold load can apply
indentation test to very thin film.
Theoretical explanations (include analytical or
FEM simulation solution) of thin film indentation
fracture are needed.
References
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1, M. F. Doerner and W. D. Nix, A Method for Interpreting the Data form Depth-Sensing
Indentation Instruments, J. Mater. Res. 1, 601-609 (1986)
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(1993)
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201–210, (2003)