Experimental Characterization of Ductile Damage using Nanoindentation
C.C. Tasan1,2, J.M.P. Hoefnagels2, R.H.J. Peerlings2, M.G.D.Geers2
1)
The Netherlands Institute for Metals Research (NIMR), PO Box 5008, 2600GA,
Delft, The Netherlands
2)
Eindhoven University of Technology, Department of Mechanical Engineering, PO Box 513,
5600MB, Eindhoven, The Netherlands
e-mail: c.tasan@tue.nl, tel:+31 40 247 5169, Fax:+31 40 2447355
ABSTRACT
With the increased use of advanced high strength steels in the automotive industry, ductile fracture has become an
important limiting factor in sheet metal forming operations. Ductile fracture occurs through the evolution of ductile
damage, i.e. void nucleation, growth and coalesence. In order to modify the currently existing forming simulations to
take into account the ductile fracture phenomena in a physically relevant way, it is necessary to find experimental
means of obtaining growth relations and parameters describing the damage evolution. In this work, a mechanical
method has been attained to investigate this problem. Dog-bone specimens of IF steel are tested in a tensile stage,
and the damage evolution during the tensile test is measured by a series of indentation experiments. A parameter
describing the local damage state is obtained by comparing the hardness values with damage and without damage.
Preliminary results show that this is a promising method to measure the material’s intrinsic damage behaviour.
INTRODUCTION
In most types of sheet metal forming processes, such as drawing, stretching and bending operations, necking is
the primary limiting factor in defining safe forming regions. However, it is also observed that material failure can occur
without any significant neck formation, especially for non-traditional forming materials with relatively low formability,
such as some aluminum alloys and high strength steels [1]. The mechanisms of such failures are not very clearly
identified but it is believed that internal damage is the determining parameter involved in ductile fracture (Fig. 1).
FIGURE 1. Safe forming regions as defined by Marciniak [2]
The micromechanisms that are responsible for damage formation and evolution are relatively well understood.
Based on this understanding, continuum damage models have been proposed in the literature and implemented
forming simulations [3]. In these models, evolution of damage affects the forming characteristics by degrading the
yield stress. However, these models require damage growth relations and parameters for which experimental
identification of damage distribution (void size and spatially-resolved density) is required.
Several methods have been examined during the past decades for this purpose; both direct measurement of the
void area and also indirect measurement through other material properties such as variation of density, propagation
of ultrasonic waves, change in electrical resistance, stiffness, hardness, acoustic emission etc. [4]
Among these methods, microindentation analysis appears to be the most promising mainly because it yields
spatially-resolved damage information [5]. It has been established experimentally and theoretically that hardness is
related linearly to yield stress. So following Lemaitre's [4] approach one can quantify damage comparing the
microhardness of the damaged material, H, with the microhardness of the undamaged material, H', by using the
following formula:
D = 1- H / H’
(1)
The main objective of this work is to assess the potential and limitations of this method in characterization of
sheet metal alloys.
EXPERIMENTAL METHODOLOGY
Tensile tests are conducted with interstitial free steel specimens using a micro-tensile stage from KammrathWeiss. The local strains at the surface are measured using an image correlation software (ARAMIS) and following
metallographic surface preparation, microhardness tests were carried out along the specimen surface (Figure 2).
Specimen surface preparation prior to the nanoindentation experiments is done with great care: surface
roughness is measured with confocal microscopy, the amount of material removal is monitored via SEM analysis and
the amount of hardening due to specimen preparation itself is taken into account. Nanoindentation experiments are
carried out also in the Continuous Stiffness Measurement (CSM) mode, therefore the variation of hardness with the
depth of indentation is measured aiming to find a plateau value for the hardness below the deformed surface.
a
b
FIGURE 2. (a) A stage of the image correlation analysis, showing the diffuse neck and the deformation of the facets
(b) Indent locations on the tensile specimen
RESULTS AND DISCUSSION
The results of the tensile tests are shown below in Figure 3. It can be seen that the tensile behaviour of the dog-bone
shaped IF steel specimens is reproducible.
Tensile Behaviour of IF Steel
300
Eng. Stress (MPa)
250
200
150
100
50
0
0
10
20
30
40
50
60
Eng. Strain (%)
FIGURE 3. Results of the tensile tests on the IF specimens
The result of the image correlation analysis, which is carried out in real time with the tensile test, is given out in
Figure 4. The difficulty with the image correlation in the case of high deformations is the thickness reduction in the
necking zone, which causes the cameras to be out of focus. In this case, this problem is overcome by using two
cameras in a stereo setup. A full local strain map of the tensile specimen could be obtained as a result of this
analysis. The locations of indentations are also shown in Figure 4.
FIGURE 4. Results of the image correlation analysis, showing the von mises strains of the specimen at the point of
fracture. Indent locations are also shown.
Following the tensile test, the specimen surface has to be prepared for the nanoindentation experiments (Figures
5-6). There are three goals in specimen preparation: removing material down to the center plane of the specimen,
obtaining a low surface roughness and keeping the surface deformation due to mechanical preparation steps as low
as possible. The latter two goals have been found to be crucial for obtaining reliable microhardness results. As seen
in the top micrographs showing the thickness cross section in Figure 5, material removal to the central plane is
achieved with success. This is important in order to be able to do indents in the neck zone, where damage is most
relevant.
a
b
c
d
.
FIGURE 5. Top (c, d) and side (a, b) view SEM images of a typical fractured tensile test specimen showing the
amount of material removal in the thickness direction and removal of the surface roughness.
10mu
-10mu
10mu
-10mu
10mu
-10mu
10mu
-10mu
FIGURE 6. Results of the confocal microscope analysis. Two locations are shown on the topmost image. Results on
the middle row show the roughness prior to preparation. Results on the bottom row show the roughness after
preparation (height scales are equal for all measurements).
The SEM pictures at the bottom of Figure 5 show that surface roughness due to the tensile test is also removed
effectively. However, a more detailed analysis is found to be necessary to be sure to keep roughness effects in the
hardness tests to a minimum. Therefore, roughness analysis is also carried out using a confocal microscope, the
results of which are shown in Figure 6. The analysis is done in two regions of the fractured tensile test specimen, one
near the clamps and the other near the fracture zone. To see the effect of specimen preparation, the roughness
measurement is carried out twice, before and after the grinding and polishing steps. It is seen that surface roughness
is decreased below 1 micron in both regions.
However there are still a few issues regarding the specimen preparation protocol which are to be further
investigated. Although CSM nanoindentation results show that a plateau is reached for the hardness values, a more
detailed investigation of the effect of specimen preparation to the obtained hardness results is required. Currently, the
effect of each grinding and polishing step is measured and compared using hardness tests, to establish a preparation
procedure which involves the minimum amount of surface hardening possible within a reasonable time frame.
The results of the hardness tests and the post-processing of the results to achieve the damage variable are
given in Figure 7. Here, on the top left the hardness profile of the IF specimen is shown. As seen, hardness increases
due to strain hardening moving away from the clamps, however near the neck it decreases as a result of damage.
On the bottom left, the result of the image correlation analysis showing local equivalent strains at the point of fracture
is given. These two data are used together to form the diagram on the top right; hardness data on y-axis and strain
data on x-axis. The continuous curve is the measured hardness profile of the ‘damaged’ material; whereas the dotted
line, which is obtained by extrapolation, represents the hardness profile of the ‘undamaged’ material. Finally, using
equation (1), the damage variable D is calculated and tabulated as a function of mises strain in right bottom.
A similar analysis is also carried out with a standard low carbon steel, the results of which are shown in Figure 8.
Here, most probably due to the relatively less formable character of this alloy, a more localized necking region is
formed prior to fracture. This results in a more localized damage accumulation, as seen in Figure 8(a). However, the
general shape of the damage vs strain curves are similar to those of the IF steel (Figures 7(d) and 8(d)).
One point to be investigated further is the method of obtaining the ‘undamaged’ material hardness. Currently, an
extrapolation procedure is carried out for this purpose. However other alternatives are being investigated to come up
with this curve.
Although from Figures 8(d)-9(d) it is hard to conclude if this measurement of the material’s intrinsic dependence
of damage on strain is correct, the graphs do show a plausible damage evolution, with a gradual increase in damage
starting form the point of necking. Nevertheless, it is planned in the next part of the project to compare the results
obtained with this procedure to the results of another, independent method.
a
Hardness vs Mises Strain
c
Hardness (GPa)
3.5
3
2.5
2
1.5
1
0.5
0
0
20
40
60
80
100
120
140
Mises Strain (%)
Damage vs Mises Strain
d
Damage
0.5
b
0.25
0
0
20
40
60
80
100
120
Mises Strain (%)
FIGURE 7. The results of the IF steel (a) The hardness profile with the indent locations shown on the specimen
surface (b) The results of the image correlation analysis (c) Hardness vs strain graphs (d) damage vs strain graph.
Hardness (GPa)
a
Hardness vs Mises Strain
c
2.5
2
1.5
1
0.5
0
0
20
40
60
80
100
120
140
160
180
140
160
180
Mises Strain (%)
b
d
Hardness (GPa)
b
Damage vs Mises Strain
0.5
0.4
0.3
0.2
0.1
0
0
20
40
60
80
100
120
Mises Strain (%)
FIGURE 8. The results of the low carbon steel (a) The hardness profile with the indent locations shown on the
specimen surface (b) The results of the image correlation analysis (c) Hardness vs strain graphs (d) damage vs strain
graph.
CONCLUSION
A quantitative method to measure damage accumulation during tensile tests of sheet metals is investigated. It is
seen that qualitatively this method provides promising results, however the sensitivity of the quantitative gains, i.e.
damage parameters, are currently being investigated.
ACKNOWLEDGMENTS
This work is funded by The Netherlands Institute of Metals Research (NIMR) (project no: MC2.05205a), which is
gratefully acknowledged.
REFERENCES
1. Hooputra, H., Gese, H., Dell, H., Werner, H., Int. Jour. of Crash, Vol.9, p.449-463, 2004
2. Marciniak, Z., The mechanics of Sheet Metal Forming, Arnold, London, 1992
3. Mediavilla, J., Peerlings, R.H.J and Geers, M.G.D, Engng. Fracture Mech., 73(7), 895 – 916, 2006
4. Lemaitre, J., A Course on Damage Mechanics, Springer-Verlag, Berlin, 1996
5. Mkaddem, A., Gassaea F., Hambli, R., Journal of Materials Processing Technology, Vol.178, p.111-118, 2006