ArticlePDF Available

Determination of Forming Limit and Fracture Limit Curves Using Digital Image Correlation

Authors:
  • ArcelorMittal USA

Abstract and Figures

Forming limit curve (FLC) and fracture forming limit curve (FFLC) are valuable tools for failure prediction in forming simulation and die try-out in press shops. In this paper, methods are presented to determine FLC and FFLC for sheets of advanced high strength steels (AHSS) using digital image correlation (DIC). Dome tests were conducted on AHSS specimens using DIC system for strain measurement. For generating FLCs, two approaches are introduced to determine the onset of localized necking by analyzing the strain history at critical locations, one of which has been implemented into the commercial DIC software Vic-3D (Correlated Solution inc.). For determination of FFLC, a method for measuring fracture strains based on the strain path evolution is presented. The measured FLCs for several AHSS were compared to the FLCs using ISO 12004-2, and conventional North American experimental measurements and empirical equations. The results of comparison revealed that FLCs using DIC are in good correlation with other existing data, thus validating the presented methodologies.
Content may be subject to copyright.
INTRODUCTION
Forming Limit Curve (FLC) is a map of principal strains that
delineates safe region from failed region for sheet metals and
is a very useful tool to determine formability limits in stampings.
Since the FLC of steel is able to predict the necking during
sheet forming process, it provides a failure criterion for Finite
Element Analysis (FEA) to judge if the part is feasible with the
specied grade in the part design.
Fracture forming limit curve describes the strain limit of
material that can be formed without fracture. Although FLC is
more often used for failure prediction in sheet forming process,
FFLC with limit of fracture strains is also of important input
when fracture prediction is required, such as in crash
simulations.
Several deformation methods exist to acquire FLC, among
which the most often used ones are Nakajima [1] and
Marciniak tests [2]. The Nakajima test uses a spherical shaped
dome, while Marciniak test uses a at topped dome. For both
testing methods, specimens with a series of widths are used to
generate different strain paths. The conventional method of
determining FLC is to measure the strains just before incipient
necking by reading circle grids which were electrochemically
etched on the surface of the sheet. In North America, Nakajima
test is normally used, and the experimental method to catch
the incipient necking is by trial and error. A series of specimens
are formed rst to different heights with different necking
conditions. Thus the test can be controlled such that it is
terminated at the moment when localized necking is initiated.
This process is done by visual observation or hand feel, thus
the test is time consuming (almost one month per steel) and
often carries large error. In Europe, conventionally a position
dependent approach was used to determine incipient necking
strains for sheet metals formed with Nakajima or Marciniak
testing method, where limit strains from different strain paths
were calculated by the extrapolation of strain distribution in the
failure zone before or after fracture occurred [3]. This FLC
determination approach evolved into ISO 12004-2 [4].
In the last several decades, Digital Image Correlation has been
increasingly applied in mechanical characterization of sheet
metal due to the fact that DIC as a non-destructive technique is
able to provide measurement of full-eld strain history in a fast
and accurate fashion compared to most conventional strain
measurement methods. The mechanism of DIC is based on
the assumption that the pattern feature of a certain area of
surface (e.g. paint particles, grids) does not change before and
after deformation, and the displacement and strain eld can be
determined by comparing pixel by pixel between the deformed
Determination of Forming Limit and Fracture Limit Curves Using Digital
Image Correlation
Gang Huang and Sriram Sadagopan
ArcelorMittal USA
Hubert Schreier
Correlated Solutions Inc.
ABSTRACT
Forming limit curve (FLC) and fracture forming limit curve (FFLC) are valuable tools for failure prediction in forming
simulation and die try-out in press shops. In this paper, methods are presented to determine FLC and FFLC for sheets of
advanced high strength steels (AHSS) using digital image correlation (DIC). Dome tests were conducted on AHSS
specimens using DIC system for strain measurement. For generating FLCs, two approaches are introduced to determine
the onset of localized necking by analyzing the strain history at critical locations, one of which has been implemented into
the commercial DIC software Vic-3D (Correlated Solution inc.). For determination of FFLC, a method for measuring
fracture strains based on the strain path evolution is presented. The measured FLCs for several AHSS were compared to
the FLCs using ISO 12004-2, and conventional North American experimental measurements and empirical equations. The
results of comparison revealed that FLCs using DIC are in good correlation with other existing data, thus validating the
presented methodologies.
CITATION: Huang, G., Sadagopan, S., and Schreier, H., "Determination of Forming Limit and Fracture Limit Curves Using
Digital Image Correlation," SAE Int. J. Mater. Manf. 7(3):2014, doi:10.4271/2014-01-0982.
2014-01-0982
Published 04/01/2014
Copyright © 2014 SAE International
doi:10.4271/2014-01-0982
saematman.saejournals.org
574
Downloaded from SAE International by Gang Huang, Wednesday, July 23, 2014
and undeformed images of specimens. Figure 1 shows the
schematic of DIC mechanism. During DIC analysis, in the
undeformed image a subset is rst designated around the point
where strain will be measured, then the point of interest on the
deformed images is tracked by matching the subset between
deformed images and reference image based on the
assumption that the feature (e.g. gray scale) does not change
after deformation of specimen. Once the point of interest is
tracked, the displacement and thus the strain can be
determined.
Figure 1. Schematic of tracking process in DIC analysis
With the high popularity of its application in deformation
measurement, DIC has been recently also used in
determination of FLC. There are two categories of incipient
necking criteria to generate FLC. One is the position
dependent approach, which is aligned with the ISO 12004-2 to
determine the limit major/minor strains using an inverse
parabola tting of designated length along cross-section lines
perpendicular to fracture line on both sides of necking zone [4].
The other category is of time-dependent approaches, which
analyzed the evolution of strain(s) at critical location(s) from
DIC to determine the moment of incipient necking. Huang et al.
developed a criterion based on the peak of the second
derivative of strain with respective to time for determination of
the moment of incipient necking [5]. Volk proposed a method of
strain rate frequency diagram from which the onset of necking
is assumed at sudden increased number of measurement
points for higher strain rate inside the necking zone [6].
Feldman et al. presented a criterion for incipient necking based
on the assumption that necking started when the rate of
difference between maximum and average strains in the
necking zone diverged from initial linearity [7].
The main advantage of the position dependent approach is
that only a few images are needed to generate limit strain point
at specic strain path. However, the limit strains are
determined only by postulation using curve tting without direct
access to the real moment of incipient necking. For time-
dependent approaches, the advantage over the time-
dependent approach is that strains are temporally analyzed to
detect the incipient necking moment; however, the varied
methods depend heavily on the mathematical assumption and
process to nd the onset of necking.
It has been reported [7,8] that all the position-dependent and
time-dependent approaches tend to generate FLCs close to
those using the conventional method or ISO 12004-2 practiced
in Europe. Prior to this paper, no approach was reported that
can match the FLC data with North America (NA) experimental
method or the Keeler -Brazier equation. To provide an accurate
and efcient way to generate FLC data which match NA
experimental method/K-B equation, an incipient necking
criterion with mixed time and position dependent approach has
been developed at ArcelorMittal Global R&D, and is presented
in this paper.
The approaches presented in this paper for determination of
FLC are based on strain measurement from DIC. Two criteria
to determine incipient necking are presented, and the resulting
FLCs of several materials are compared with conventional
data. Meanwhile, a method to determine FFLC using DIC is
also presented.
EXPERIMENTAL PROCEDURE
Materials
Seven materials were used in this study. Table 1 shows the list
of materials with tensile properties. The properties were
determined using the ASTM E-8 standard for tensile testing.
Table 1. Steel grades and tensile properties
Huang et al / SAE Int. J. Mater. Manf. / Volume 7, Issue 3 (June 2014)
575
Downloaded from SAE International by Gang Huang, Wednesday, July 23, 2014
In Table 1, CR stands for uncoated steel and GA stands for a
galvannealed coating. DP refers to the dual phase
microstructure and TRIP for transformation induced plasticity
microstructure. TRIP steels have a small percentage of
retained austenite in the microstructure that transforms to
martensite upon deformation. M900 is a fully martensitic
material. The DP980SF steel grade has a higher YS/UTS ratio
and has been developed specically for stretch anging
applications.
Experiment
A dome tester with DIC system was used to form a dome
shape (Figure 2). An MTS servo hydraulic testing system was
employed to conduct LDH tests where Nakajima testing
method was applied. The steel blanks were 177.8 mm long
with the width varying from 25.4 to 177.8 mm to represent
different strain paths. A hemispherical punch with diameter of 4
inches was used. Tests were performed on 3-5 blanks for each
width of each steel grade. The blanks were prepared with
spray paint speckles on the surface. During the forming
process, two cameras oriented with a xed angle were
positioned above the forming equipment, as shown in Figure 2.
Images of the specimen and the speckle pattern were recorded
simultaneously by the two cameras at speed of 15-20 frames/
second during forming until fracture occurred. Then the
dedicated DIC software, Vic 3D (from Correlated Solutions
Inc.), was used to analyze the acquired images to calculate the
major and minor strains of every point of the deformed
specimens at each imaging moment.
Figure 2. Setup of LDH test using DIC system and LDH specimen
For comparison, conventional measurements of FLC based on
NA experimental method and ISO 12004-2 were also
conducted. The experimental procedures of ISO 12004-2 are
detailed in reference [4]. Using the NA experimental method,
the samples (width of 25.4 to 177.8mm and length of
177.8mm) were rst electrochemically gridded with circles of
diameter 2.54mm, as shown in Figure 3. Then the samples
were formed with trial and error to acquire the testing outcome
with incipient necking based on nger touch. Thereafter, the
samples with incipient necking were inspected with a camera
system to measure the strains, and then FLC was drawn as
lower bound to the necking points. The major drawback for this
technique is that it needs considerable amount of time to
generate one experimental FLC, and it is dependent on the
skill and experience of the operator.
Figure 3. Samples formed using the traditional NA technique for
determination of FLC
For determination of FFLC using DIC, the same experimental
procedures for FLC were applied, where the samples with
different widths were formed up to fracture, and pictures
acquired by cameras were analyzed to determine the facture
strain for different strain paths.
INCIPIENT NECKING CRITERIA
Two incipient necking criteria have been developed to
determine FLCs of AHSS at ArcelorMittal Global R&D-East
Chicago. The rst criterion was based on the time-dependent
behavior of major strain history at the critical position where
fracture occurred. The second criterion was based on the strain
history relationship between the critical position (with ultimate
fracture) and other position; therefore it is of a method of mixed
time-dependence and position dependence.
Criterion 1
It is assumed that when the necking occurs inside the sheet
metal through thickness direction, the major strain or minor
strain is subject to some instant change caused by instability.
This should be reected by the change of strain or derivative of
some order.
Figure 4 shows an example dome sample after fracture and its
contour of major strain distribution determined from DIC on the
picture frame right before fracture. The position with maximum
major strain on the contour was selected as the critical point
where the necking and fracture occurred, as shown in Figure 4.
Huang et al / SAE Int. J. Mater. Manf. / Volume 7, Issue 3 (June 2014)
576
Downloaded from SAE International by Gang Huang, Wednesday, July 23, 2014
Figure 4. Point of interest to extract the major strain history. (a)
Specimen after fracture. (b) Major strain distribution with highlighted
position right before fracture occurred
The main task for FLC determination using DIC is to identify
the imaging moment of incipient necking. Within the contour of
strain distribution, the critical point with the eventual maximum
major strain was investigated for incipient necking
identication. It should be noted that, depending on the
specimen geometry and the friction coefcient between punch
and specimen, the position of maximum major strain might not
be xed during the course of forming. Therefore, as shown in
Figure 4, the point with maximum major strain on the image
right before fracture was used to analyze the strain data to
detect the incipient necking moment. The method of analysis is
described in Figure 5.
Figure 5. Histories of strain, strain rate and second derivative
First, the major strain history from beginning up to fracture was
plotted for the critical point. Second, the rst derivative with
respect to time (or strain rate) was calculated numerically; as
shown in Figure 5, the rst derivative was monotonically
increasing up to fracture, and no noticeable instant change or
peak was present. Next, the second derivative of strain with
respect to time was calculated and plotted. As shown in Figure
5, a peak of second derivative was evident before fracture. It
was presumed that the rate of change of strain rate reaches
maximum when local instability occurred due to the strain path
switched to plane strain [9]. Therefore, it was assumed that
incipient necking was at the moment of peak of the second
derivative. Finally, with incipient necking moment identied, the
major and minor strains at the same moment for the specimen
of specic strain path can be determined, which constitutes
one incipient necking data point of FLC. Similarly, by applying
the same procedure the data points for other strain paths can
also be determined, and a complete FLC can be developed.
Criterion 2
It has been reported that Criterion 1 of incipient necking
identication gave rise to consistently conservative FLCs of
AHSS compared to those using NA experimental method or the
K-B equation. To efciently generate FLCs of AHSS consistent
with the NA practice of using K-B equation, so that the data can
be utilized by press shop for die try-out, a new criterion is
needed.
Figure 6. An example of major strain contour with critical point and
offset locations (the circles) right before fracture
In order to abide by the mechanism of localized necking, a
mixed time and position dependent method has been
developed to detect the incipient necking moment. When a
sheet metal is subjected to localized necking during forming
process, physically the major strain within the necking zone
keeps increasing, while for the area away from the necking
zone the major strain reaches a plateau or peak value. Figure
6 shows the contour of major strain with the maximum in the
center for image frame right before fracture; the circles
surrounding the maximum strain represent the offset locations.
Figure 7 delineates the major strain histories of the critical point
and one offset point.
As shown in Figure 7, the peak of major strain was reached
before fracture at the end of the major strain history for the
critical point, which was monotonically increasing. Therefore,
the incipient necking was considered to occur at the moment of
peak strain for the offset point, denoted as tmax. However, due
to the strain gradient tmax might be dependent on the selection
of offset point. On the other hand, tmax might be also affected
Huang et al / SAE Int. J. Mater. Manf. / Volume 7, Issue 3 (June 2014)
577
Downloaded from SAE International by Gang Huang, Wednesday, July 23, 2014
by the fact whether the localized necking or fracture was
initiated in the center or off the center, which was mainly
determined by the tooling condition (Nakajima or Marciniak),
frictional conditions and specimen geometry. To address this
issue, an algorithm was developed to determine the offset point
to extract tmax for two individual situations of critical points. With
tmax acquired, the major and minor strains can then be
extracted at tmax for the sample of the specic strain path.
Similarly pairs of major and minor strains can be determined
for other strain paths as well to form the complete FLC.
Figure 7. Major strain histories at Critical and Offset Points
As an effort to develop an automated system to determine the
FLC using DIC, the incipient necking Criterion 2 has been
implemented into the commercial software Vic-3D (Correlated
Solutions Inc.).
FFLC MEASUREMENT
The fracture forming limit curve provides the limit of strain for
sheet metals before fracture initiation. In a sense similar to
FLC, FFLC composed of limit of major and minor strains under
strain paths varied from being uniaxial to equibiaxial. However,
FFLC might well extend strain limit beyond localized necking till
fracture, especially for ductile materials. With application of
DIC, compared to conventional measurement methods the
local strains at facture zone are relatively easy to measure.
However, for cases of high localization of strain at fracture
zone with indication of steep in-plane strain gradient, the
fracture strain measurement can be highly dependent on the
gauge length (similar to grid size) used in DIC, and
consequently there could be considerable uncertainty in
fracture strain results which constitute FFLC. To circumvent the
associated difculty to reduce the measurement uncertainty, a
hybrid method was developed to measure the fracture strains
for FFLC.
It was documented [8] that, after localized necking starts within
the necking zone the major strain increases rapidly while the
minor strain keeps close to a constant, such that the stress
state switches from original state (drawing or stretch) to plane
strain, as shown in Figure 8 for schematic describing the strain
paths for typical FLC and FFLC of steels. With the minor strain
being close to constant and also based on the fact that prior to
necking there is no localization, the minor strain can be readily
measured using DIC without much uncertainty caused by the
issue of gauge length. While the major strain is drastically
increasing after necking and highly dependent on the selection
of gauge length, the thickness strain can be measured rst
using a point micrometer, and thereafter the major strain can
be calculated using the measured thickness strain and minor
strain with assumption of volume conservation. With the
determined pair of major and minor fracture strains for different
strain paths, a complete FFLC can be generated. It should be
noted that, with the void nucleation and growth inside the
necking zone due to damage accumulation after necking, the
material volume is not strictly a constant; however, with small
volume fraction of voids before fracture for majority of AHSS,
the volume conservation can still be applied for determination
of fracture strain within reasonable error to some extent of
condence.
Figure 8. A schematic of strain paths of FLC and FFLC
RESULTS AND DISCUSSIONS
In this section, the results of FLCs of several steels using two
different incipient necking criteria are presented, followed by
the results of FFLC determined using the measurement
method as previously described.
FLCs Using Criterion 1
The results of FLC using DIC based on incipient necking
Criterion 1 for materials of 1.4mm DP590 CR, 1.2mm DP780
CR and 0.96mm TRIP780 GA are shown in Figures 9, 10 and
11, respectively.
Huang et al / SAE Int. J. Mater. Manf. / Volume 7, Issue 3 (June 2014)
578
Downloaded from SAE International by Gang Huang, Wednesday, July 23, 2014
Figure 9. FLCs of 1.4mm DP590 determined using Criterion 1 and
other methods.
Figure 10. FLCs of 1.2mm DP780 determined using Criterion 1 and
other methods.
Figure 11. FLCs of 0.96mm TRIP780 determined using Criterion 1 and
other methods.
For comparison, also plotted in Figures 9, 10 and 11 are the
FLC data determined using NA experimental method, K-B
equation and ISO 12004-2 for the three materials. Nakajima
tests were also tested on other AHSS to determine FLCs;
however, for the same coils of materials, only DP590 CR and
DP780 and TRIP780 were tested according to ISO 12004-2.
As shown in Figures 9, 10 and 11, the FLCs determined using
incipient necking Criterion 1 are consistently lower than those
from NA experimental method and K-B equation; e.g., the FLC0
using Criterion 1 is lower than FLC0 using NA experimental by
0.055, 0.045 and 0.038 in true strain for DP590, DP780 and
TRIP780 respectively. However, FLCs using Criterion 1 are in
very good agreement with those determined by ISO 12004-2,
the difference of FLC0 between two methods is 0.01, 0.011 and
0.015 for DP590, DP780 and TRIP780, respectively. This
implies that using Criterion 1 will most probably result in FLCs
matched with ISO 12004-2.
FLCs Using Criterion 2
The same images acquired from LDH tests on 1.4mm DP590,
1.2mm DP780 and 0.96mm TRIP780 for FLCs using DIC
based on incipient Criterion 1 were reanalyzed using incipient
necking Criterion 2. In addition, Criterion 2 was applied to
analyze the images with DIC from LDH tests on 0.8mm DQSK,
1.54mm TRIP590, 1.6mm DP980SF and 1.2mm M900 to
determine FLCs.
Figures 12, 13, 14, 15, 16, 17 show the results of FLC using
Criterion 2 for the 7 materials. The FLCs determined using NA
experimental method and K-B equation are also included for
comparison. Although NA experimental method was not
applied to 0.8mm DQSK and the curve was not available for
comparison, it is generally assumed that for conventional
steels of FLC using K-B equation should be very close to that
from NA experimental measurement. It should be noted that
gauge length of 2 mm was used for all FLCs using Criterion 1
and Criterion 2, which is close to the grid size used in
generating traditional NA FLCs.
Figure 12. FLCs of DQSK determined using Criterion 2 and K-B
equation.
Huang et al / SAE Int. J. Mater. Manf. / Volume 7, Issue 3 (June 2014)
579
Downloaded from SAE International by Gang Huang, Wednesday, July 23, 2014
Figure 13. FLCs of DP590 determined using Criterion 2 and other
methods.
Figure 14. FLCs of TRIP590 determined using Criterion 2 and other
methods.
Figure 15. FLCs of TRIP780 determined using Criterion 2 and other
methods.
Figure 16. FLCs of DP780 determined using Criterion 2 and other
methods.
Figure 17. FLCs of DP980SF determined using Criterion 2 and other
methods.
Figure 18. Incipient necking data of M900 determined using Criterion 2
and FLCs using other methods.
Huang et al / SAE Int. J. Mater. Manf. / Volume 7, Issue 3 (June 2014)
580
Downloaded from SAE International by Gang Huang, Wednesday, July 23, 2014
As shown in Figures 12, 13, 14, 15, 16, 17, for all six materials
the FLCs determined using incipient necking Criterion 2 are in
very good agreement with the data generated from NA
experimental method and the traditional NA FLC (K-B
equation) along nearly all strain paths, except for DP980SF of
which the FLC using Criterion 2 is quite different under the
biaxial stretch conditions while it agrees well with data from NA
experimental method. On the other hand, the results imply that
K-B equation well predicted the FLCs for nearly all the 6
materials under nearly all strain paths. However, it was of very
different case for M900. As shown in Figure 18 for FLC data
from DIC using Criterion 2, from NA experimental method and
K-B equation, the K-B equation substantially underestimated
the experimental FLC, with the FLC0 difference of nearly 0.05.
Nonetheless, the incipient necking data points are in very good
agreement with NA experimental data, in spite of the limited
data points that are available.
For a comprehensive comparison between incipient necking
criteria 1 and 2, FLCs generated using the two criteria plotted
in Figures 19 and 20 for DP590 and DP780, as two examples.
As shown in Figures 19 and 20, the FLCs determined using
Criterion 2 is noticeably higher than using Criterion 1 for both
materials. This implies that Criterion 1 detected the necking
earlier, while there might be some small amount of necking
might have occurred prior to the necking moment identied by
Criterion 2. Accordingly, depending on the need and practice of
OEMs or press shops from different regions, the selection
between the two incipient necking criteria can be made. For
example, for the users in North America who follow NA
experimental method or K-B equation, Criterion 2 is
recommended, while for users following ISO 12004-2, Criterion
1 is recommended; or for some users, the FLCs generated
from Criterion 1 and Criterion 2 can be applied as up and low
bounds.
Figure 19. Comparison of DP590 FLCs generated using incipient
necking Criterion 1 and Criterion 2.
Figure 20. Comparison of DP780 FLCs determined using incipient
necking Criterion 1 and Criterion 2.
Results of FFLC
The FFLCs determined using the method with combination of
measurement from DIC and thickness measurement are
shown in Figures 21 and 22 for two materials. Also included in
Figures 21 and 22 are FLCs determined using incipient
necking criteria 1 and 2. Although only limited data of FFLC are
available from this study, demonstrated from Figures 21 and 22
FFLCs of the two materials are linear for varied strain paths,
which is consistent with the traditional theoretical prediction for
steels.
Figure 21. FFLC of 1.4mm DP590
Huang et al / SAE Int. J. Mater. Manf. / Volume 7, Issue 3 (June 2014)
581
Downloaded from SAE International by Gang Huang, Wednesday, July 23, 2014
Figure 22. FFLC of 1.2mm DP780
CONCLUSIONS
Two incipient necking criteria are presented to determine FLC
using DIC. The rst criterion is based on strain evolution at
critical location where localized necking and fracture occurs,
while the second criterion takes into account the strain history
of offset location and its relationship with strain evolution of
critical location. The FLC data determined using the two criteria
are in very good agreement with existing conventional data
using ISO 12004-2 and NA experimental method, indicating
that the two criteria are able to more efciently generate FLCs
that match ISO 12004-2 and NA experimental method,
respectively. Meanwhile, a method to measure FFLC is also
introduced, which is able to provide strain data for fracture
prediction.
REFERENCES
1. Nakajima, K., Kikuma, T., Asaku, K., “Study on the Formability of
Steel Sheet,” Yawata Technical Report 264, 1968.
2. Marciniak, Z. and Kuczynski, K., “Limit strains in the process of
stretch forming sheet metal”, International Journal of Mechanical
Science 9, 1967, 609-620.
3. Bragard, A., Baret, J.-C., Bonnarens, H.: “A simplified Technique
to Determine the FLD at the Onset of Necking”, C.R.M. 33, 1972,
53-63.
4. “Metallic materials -Sheet and strip - Determination of forming limit
curves - Part 2: Determination of forming limit curves in laboratory”,
ISO Standard, ISO-DIS 12004-2, 2006.
5. Huang, G., Sadagopan, S., Yan, B., “Digital Image Correlation
Technique and Its Application in Forming Limit Curve,” IDDRG
2008 International Conference, June 2008, Olofström, Sweden.
6. Volk, V., “New Experimental and Numerical Approach in the
Evaluation of the FLD with the FE Method,” Proceedings of the
FLC Zurich 2006, March 2006, ETH Zurich, Switzerland.
7. Feldmann, P., Schatz, M. and Aswendt, P., “Automatic FLC-Value
Determination from 4D Strain Data,” IDDRG 2009 International
Conference, June 2009, Golden, USA.
8. Sriram, S., Huang, G., Yan, B., and Geoffroy, J., “Comparison of
Forming Limit Curves for Advanced High Strength Steels Using
Different Techniques,” SAE Int. J. Mater. Manuf. 2(1):472-481,
2009, doi:10.4271/2009-01-1173.
9. Lee, Y.-W., “Fracture Prediction in Metal Sheets,” PhD thesis,
Massachusetts Institute of Technology, 2005.
CONTACT INFORMATION
Gang Huang
Applications Technology, Automotive Product Applications
ArcelorMittal Global R&D - East Chicago
3001 E. Columbus Drive, East Chicago, IN 46312
gang.huang@arcelormittal.com
219-399-6561
ACKNOWLEDGMENTS
The authors thank Dr. Benda Yan and Dr. Blake Zuidema for
their support and constructive suggestions.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical,
photocopying, recording, or otherwise, without the prior written permission of SAE International.
Positions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE International. The author is solely responsible for the content of the
paper.
Huang et al / SAE Int. J. Mater. Manf. / Volume 7, Issue 3 (June 2014)
582
Downloaded from SAE International by Gang Huang, Wednesday, July 23, 2014
... After testing, the dedicated Digital Image Correlation (DIC) software, Vic 3D (from Correlated Solutions Inc.), was used to analyze the acquired images to calculate the major and minor strains of every point of the deformed specimens at each imaging moment. The instance of incipient necking was determined using a mixed time and position dependent approach which has been published elsewhere [2]. ...
... Figure 6 shows the FLC0 of the two materials determined using DIC and the traditional NA method using circle grid analysis and the finger touch method to determine incipient necking. A combined time and position dependent method was used [2] with DIC to determine the point of incipient necking. As seen in Figure 6, the results using DIC and the traditional NA method are comparable for both steels. ...
Article
Full-text available
This paper presents the results of intentional Aluminum addition on formability of commercial DP1180 steel grades produced at ArcelorMittal. Formability was evaluated using a suite of tests such as bending under tension test, the plane strain forming limit, crack propagation resistance using compact tension test, hole expansion, bendability, etc. Results of these formability tests demonstrated that the local formability, especially the resistance to edge fracture of the product with higher Al addition was improved in comparison with the nominal product. In addition, more detailed microstructural characterization and mechanical behavior of the products was conducted to further the understanding of the effect of Al on the performance of Dual Phase microstructures.
... DIC is a non-contact optical technique that can measure full-field two-dimensional or three-dimensional surface deformation. It is a highly responsive method and it requires a simple surface treatment on the test samples [38][39][40]. The DIC algorithm searches for a one-to-one association of points (pixel) in the series of the images taken during testing and calculates the ...
... DIC is a non-contact optical technique that can measure full-field two-dimensional or three-dimensional surface deformation. It is a highly responsive method and it requires a simple surface treatment on the test samples [38][39][40]. The DIC algorithm searches for a one-to-one association of points (pixel) in the series of the images taken during testing and calculates the deformation for each stage [41]. ...
Article
Full-text available
The effect of the microstructure heterogeneity on the tensile plastic deformation characteristic of friction-stir-welded (FSW) dual-phase (DP) steel was investigated for the potential applications on the lightweight design of vehicles. Friction-stir-welded specimens with a butt joint configuration were prepared, and quasi-static tensile tests were conducted, to evaluate the tensile properties of DP980 dual-phase steels. The friction-stir welding led to the formation of martensite and a significant hardness rise in the stir zone (SZ), but the presence of a soft zone in the heat-affected zone (HAZ) was caused by tempering of the pre-existing martensite. Owing to the appearance of severe soft zone, DP980 FSW joint showed almost 93% joint efficiency with the view-point of ultimate tensile strength and relatively low ductility than the base metal (BM). The local tensile deformation characteristic of the FSW joints was also examined using the digital image correlation (DIC) methodology by mapping the global and local strain distribution, and was subsequently analyzed by mechanics calculation. It is found that the tensile deformation of the FSW joints is highly heterogeneous, leading to a significant decrease in global ductility. The HAZ of the joints is the weakest region where the strain localizes early, and this localization extends until fracture with a strain near 30%, while the strain in the SZ and BM is only 1% and 4%, respectively. Local constitutive properties in different heterogeneous regions through the friction-stir-welded joint was also briefly evaluated by assuming iso-stress conditions. The local stress-strain curves of individual weld zones provide a clear indication of the heterogeneity of the local mechanical properties.
... Time-dependent FLCs are higher than ISO ones (Δ<0.05 in absolute). It has been reported by Huang [11] and the GDDRG [12], that the position dependent method gives rise to consistently conservative FLCs for AHSS. It detects the "beginning of instable necking" while there might be some small amount of necking might have occurred prior to the necking moment identified by the time dependent method. ...
Article
Full-text available
In body design, Finite Element Analysis becomes an unavoidable step in optimizing forming processes to ensure the feasibility of a specific designed shape. Different failure criteria exist but the Forming Limit Diagram remains the most used criterion. It can be built in a wide variety of forms but the most usual one is composed only of a Forming Limit Curve (FLC) which represents the onset of localized necking limit of sheet metal. FLC is determined experimentally by standardized Nakajima or Marciniak tests. However, both present lots of roadblocks in the accurate determination of product formability limits due to the use of counter-blanks, no linear strain paths and because they are not adapted for high ductility steels. Tensile tests were performed in the past to determine the left hand side of the FLCs. They were not included into the ISO 12004-2 standard because of technical reasons although they present lots of advantages (frictionless, no curvature effect and planar configuration). Now, thanks to the current advanced technologies and tools, these issues are overcome. In this paper, the advantages of tensile tests compared to Nakajima or Marciniak ones are briefly discussed. The design and conceptualization of specific jaws to perform plane strain tensile tests on AHSS are presented. A wide range of AHSS was characterized through plane strain tensile tests and results were compared to formability limits determined by the usual practice using Nakajima tests. Different evaluation strategies were used to determine the maximum formability: the position dependent method, the time dependent one and close to fracture.
Article
Full-text available
The plasticity and formability of a commercially-pure aluminum sheet (AA1100-O) is assessed by experiments and analyses. Plastic anisotropy of this material is characterized by uniaxial and plane-strain tension along with disk compression experiments, and is found to be non-negligible (e.g., the r-values vary between 0.445 and 1.18). On the other hand, the strain-rate sensitivity of the material is negligible at quasistatic rates. These results are used to calibrate constitutive models, i.e., the Yld2000-2d anisotropic yield criterion as the plastic potential and the Voce isotropic hardening law. Marciniak-type experiments on a fully-instrumented hydraulic press are performed to determine the Forming Limit Curve of this material. Stereo-type Digital Image Correlation is used, which confirms the proportional strain paths induced during stretching. From these experiments, limit strains, i.e., the onset of necking, are determined by the method proposed by ISO, as well as two methods based on the second derivative. To identify the exact instant of necking, a criterion based on a statistical analysis of the noise that the strain signals have during uniform deformation versus the systematic deviations that necking induces is proposed. Finite element simulation for the Marciniak-type experiment is conducted and the results show good agreement with the experiment.
Chapter
This chapter investigates the deformation involved with the stress state, the stress distribution, and the strain distribution in the flange area in more detail for the purpose of further comprehension of the deep‐drawing process and the modification of the experimental parameters. In hole‐flanging, a sheet billet with a hole in the center is processed by a punch to produce plastic deformation in the periphery of the hole. In designing draw dies, the whole stamping part should be kept at a tension state with a certain amount of plastic deformation. The viscous pressure medium in viscous pressure forming features semi‐solidity, which offers the technology an advantage of sealing over hydraulic forming. As defects or fractures always bear close relation to specific forming process, material formability is investigated in connection with individual fundamental sheet‐metal‐forming process such as drawing, upsetting, stretching, and bending.
Article
Full-text available
In our study, one-dimensional PbI2/polyvinylpyrrolidone (PVP) composition fibers have been prepared by using PbI2 and PVP as precursors dissolved in N, N-dimethylformamide via a electrospinning process. Dipping the fibers into CH3NH3I solution changed its color, indicating the formation of CH3NH3PbI3, to obtain CH3NH3PbI3/PVP composite fibers. The structure, morphology and composition of the all as-prepared fibers were characterized by using X-ray diffraction and scanning electron microscopy.
Article
Mechanical properties of steel sheets governing the press formability were determined and the lubricating effect in stretch forming was made clear. Forming limit determined in model experiment was shown to be useful as the criterion for evaluating the forming severity in practical forming and also for finding countermeasures in forming conditions in order to improve the forming severity and for selecting appropriate steel sheet.
Article
Forming Limit Curves (FLCs) have been used in press shops for decades during die development and more recently as failure criteria when used in conjunction with FEA for part feasibility analysis. Around the world there are different techniques used to determine the FLC. The differences between the techniques lie in tooling, specimen geometry and in the method used to determine the critical strains. A comprehensive study on FLCs of selected AHSS was carried out at ArcelorMittal Global R&D, where the different commonly used techniques and a new technique employing Digital Image Correlation (DIC) were employed to determine the FLCs. This paper presents results of these comparisons.
Article
One of the most important failure modes of thin-walled structures is fracture. Fracture is predominantly tensile in nature and, in most part, is operated by the physical mechanisms of void nucleation, growth, and linkage. For ductile sheet, fracture is preceded by necking. Prediction of necking which limits sheet metal formability is well established and has been developed over the past several decades. However, an in-depth understanding of the mechanical process inside the neck leading to sheet metal fracture is lacking. This is true for both static and high intensity, short duration loads. Furthermore, there is an ever increasing need to raise the safety envelope of existing protective structures against localized extreme loading. The present thesis addresses four parts of the many outstanding issues in sheet metal fracture. In the first part, the new Bao-Wierzbicki (BW) fracture criterion formulated in terms of the accumulated equivalent plastic strain with the stress triaxiality as a weighting function is considered. Using the equations of plane stress von-Mises plasticity and the strain-to-stress mapping procedure, the BW fracture criterion is transformed to the spaces of the principal tensile strains and stresses in a sheet and compared with experimental results for various materials. An extensive comparative study of the most widely used fracture criteria is then conducted.
Digital Image Correlation Technique and Its Application in Forming Limit Curve
  • G Huang
  • S Sadagopan
  • B Yan
Huang, G., Sadagopan, S., Yan, B., "Digital Image Correlation Technique and Its Application in Forming Limit Curve," IDDRG 2008 International Conference, June 2008, Olofström, Sweden.
New Experimental and Numerical Approach in the Evaluation of the FLD with the FE Method
  • V Volk
Volk, V., "New Experimental and Numerical Approach in the Evaluation of the FLD with the FE Method," Proceedings of the FLC Zurich 2006, March 2006, ETH Zurich, Switzerland.
Automatic FLC-Value Determination from 4D Strain Data
  • P Feldmann
  • M Schatz
  • P Aswendt
Feldmann, P., Schatz, M. and Aswendt, P., "Automatic FLC-Value Determination from 4D Strain Data," IDDRG 2009 International Conference, June 2009, Golden, USA.