CE 5310 Lecture Notes - Lecture 11: Ann Arbor, Michigan, Arc Welding, Finite Element Method
Ductile Web Fracture Initiation in Steel Shear Links
Shih-Ho Chao, S.M.ASCE1; Kapil Khandelwal, S.M.ASCE2; and Sherif El-Tawil, M.ASCE3
Abstract: Tests conducted in the 1980s showed that well-detailed short shear links can exhibit stable and ductile cyclic behavior. Recent
tests of prevailing A992 rolled shapes revealed that shear links designed according to current seismic specifications can fail by ductile
fracture in the link web, a mode of failure that was not observed in earlier tests. This paper investigates the observed ductile fractures
through computational structural simulation. An existing criterion for judging the propensity for ductile fracture initiation in steel is
modified based on published tests results for notched bars to better pinpoint the location of ductile fracture initiation. Validated finite-
element analyses of previously tested shear links are conducted and the results postprocessed to evaluate the potential for ductile fracture
of specimens with several different types of details. Reasons for the occurrence of web fractures in new A992 steel beams as opposed to
older links are discussed. An alternative stiffener configuration that mitigates ductile fracture and is at the same time practical to construct
is proposed.
DOI: 10.1061/共ASCE兲0733-9445共2006兲132:8共1192兲
CE Database subject headings: Bracing; Frames; Finite element method; Buckling; Fractures; Ductility; Steel.
Introduction
Shear links have been successfully used in eccentrically braced
frames 共EBFs兲for over 20 years 共Gálvez 2004兲. Shear-link-like
members have also been used as coupling beams in hybrid
coupled walls comprised of reinforced concrete walls connected
via steel coupling beams 共El-Tawil et al. 2002兲. Their primary
function in both types of systems is to dissipate earthquake energy
through large inelastic deformations. Shear links are classified
into three categories: short, intermediate, and long, depending on
the structural and geometric properties of the links 共AISC 2002兲.
When architectural constraints permit, short links which dissipate
energy primarily through inelastic shear distortion are preferred to
longer links that dissipate energy through plastic hinge rotation.
Mechanisms that involve inelastic shear deformation are gener-
ally perceived to be more ductile than those involving flexure-
related plastic hinge deformations.
Research conducted in the 1980s has shown that well-detailed
short shear links exhibit stable and ductile cyclic behavior without
brittle failure before reaching a plastic rotation of 0.1 rad 共e.g.,
Hjelmstad and Popov 1983; Malley and Popov 1983兲. The current
detailing requirements and expected rotation angle for shear links
in the AISC Seismic Provisions 共AISC 2002兲are mainly based on
test results of links made from ASTM A36 共Fy=250 MPa兲wide-
flange shapes as used in the 1980s. In view of the prevailing A992
rolled shapes, testing on shear links made from ASTM A992 steel
共Fy=345 MPa兲was conducted at the University of Texas, Austin
共Arce 2002; Gálvez 2004兲to investigate the adequacy of current
requirements for EBF links with higher nominal strength.
As shown in Fig. 1, the tests revealed a new failure mode for
shear links, which was not reported in the A36 shear links tested
in the past, i.e., ductile web fracture of the link initiating at the top
and bottom ends of the stiffener welds. The fracture first occurred
at the termination of the fillet welds and then propagated horizon-
tally along the link web. Due to this web fracture, most of the test
links could not achieve the target plastic rotation angles required
by the 2002 AISC seismic provisions. The unexpected fractures
appeared to stem from stress and strain concentrations that occur
when stiffener-to-web welds are terminated too close to the k-area
共McDaniel et al. 2003兲. Other factors that are thought to play a
role in these failures include: close stiffener spacing 共Richards
2004兲, overstringent loading protocols for EBF links 共Richards
and Uang 2003兲, and low fracture toughness in the k-area 共Arce et
al. 2003; Okazaki et al. 2004兲.
Several investigators have studied web fracture in shear links
using nonlinear finite-element analyses 共McDaniel et al. 2003;
Dusicka et al. 2004; Richards 2004兲. The common conclusion
from the studies published to date is that the high plastic strain
concentration at the termination of welds is responsible for crack
initiation. However, plastic strain in itself is not the primary rea-
son that ductile fracture initiates 共El-Tawil et al. 1999兲.
Ductile fracture mechanisms in steel have been studied by
various researchers since the late 1960’s. Research shows that
ductile fracture initiation occurs in three distinct stages, namely
nucleation, growth, and coalescence of microvoids in a plastically
deforming metal matrix. Microvoids nucleate at inclusions or sec-
ond phase particles 共carbides and sulfides兲, either by decohesion/
debonding at the particle–matrix interfaces or by fracture of the
particles themselves. Void nucleation is followed by a void
growth stage where voids grow and interact until localized plastic
1Post Doctoral Research Fellow, Dept. of Civil and Environmental
Engineering, Univ. of Michigan, Ann Arbor, MI 48109-2125. E-mail:
2Ph.D. Candidate, Dept. of Civil and Environmental Engineering,
Univ. of Michigan, Ann Arbor, MI 48109-2125. E-mail: kapilk@
engin.umich.edu
3Associate Professor, Dept. of Civil and Environmental Engineering,
Univ. of Michigan, Ann Arbor, MI 48109-2125 共corresponding author兲.
E-mail: [email protected]
Note. Associate Editor: Scott A. Civjan. Discussion open until
January 1, 2007. Separate discussions must be submitted for individual
papers. To extend the closing date by one month, a written request must
be filed with the ASCE Managing Editor. The manuscript for this paper
was submitted for review and possible publication on April 29, 2005;
approved on October 17, 2005. This paper is part of the Journal of
Structural Engineering, Vol. 132, No. 8, August 1, 2006. ©ASCE, ISSN
0733-9445/2006/8-1192–1200/$25.00.
1192 / JOURNAL OF STRUCTURAL ENGINEERING © ASCE / AUGUST 2006
flow and necking of the intervoid matrix occurs. The final phase
of ductile fracture occurs when adjacent microvoids coalesce to-
gether into a crack. Ductile fracture properties are therefore con-
trolled by the growth and coalescence of voids and
ductility depends on the growth phase of microvoids, which is
strongly influenced by stress triaxiality, i.e., the presence of high
triaxial stresses.
This paper investigates ductile fracture of shear links through
computational simulation. First, an existing criterion for judging
the propensity for ductile fracture initiation in steel is modified
based on published tests results for notched bars. Detailed finite-
element analyses of previous tests of shear links are conducted
and the results postprocessed to evaluate the potential for ductile
fracture of specimens with several different types of details. Rea-
sons for the occurrence of web fractures in A992 steel beams are
discussed and an alternative stiffener configuration that mitigates
ductile fracture and is at the same time practical to construct is
proposed.
Ductile Fracture Initiation Criteria
The most popular ductile fracture initiation models in the litera-
ture are based on continuum micromechanics and generally in-
volve study of void growth, interaction, and coalescence under
given stress/strain conditions. In these models, it is generally as-
sumed that ductile fracture initiates when microvoids growing
within a plastically deforming steel matrix reach some critical
percentage of the material volume, i.e., when a specific porosity is
reached. Other models have been proposed to characterize steel
microstructure, including models based on continuum thermody-
namics 共e.g., Lemaitre 1985兲and variational bounds 共e.g., Ponte
Castaneda and Zaidman 1994兲.
McClintock 共1968兲proposed one of the earliest microme-
chanical void growth models. He theorized that fracture occurs
when two neighboring voids come into contact and proposed a
failure criterion in terms of critical strain and stress values. He
specified that failure occurs when strain and stress quantities over
a region of the order of the void size attain critical values. Rice
and Tracey 共1969兲showed that the void growth rate is propor-
tional to the increment of equivalent plastic strain and an expo-
nential function of the triaxial stress state. Fracture initiation
criteria based on the Rice and Tracey model have been developed
and used by several researchers. In such models, fracture is as-
sumed to occur when the void growth ratio reaches a critical
value over the characteristic length of the material, e.g.,
Rousselier 共1987兲and Rakin et al. 共2004兲used the model for
monotonic loading applications, while Kanvinde 共2004兲proposed
a modified model for very low cycle fatigue. In other related
research, Benzerga et al. 共1999兲studied the effects of void shape
and interparticle spacing on void coalescence using localization-
based and plastic limit-load-based models.
Using the assumption of a critical volume fraction of voids,
Hancock and MacKenzie 共1976兲proposed an expression for the
failure strain in steel as a function of the triaxial stress state and a
material constant. They also recognized the importance of length
scale and asserted that it is not sufficient for the failure criterion
to be reached at a single point but, rather, the failure criterion
must involve a certain minimum amount of material which is a
characteristic of the scale of physical events leading to local fail-
ure. Their model was used by several researchers including
Mackenzie et al. 共1977兲and Bandstra et al. 共1998兲.
Gurson 共1977兲proposed a yield criterion and flow rules for a
porous 共dilatant兲ductile, isotropic material by assuming that the
material behaves as a smeared continuum. Yielding is governed
by a yield surface that exhibits weak hydrostatic stress depen-
dence, while the classical plasticity rules assume that yielding is
independent of the hydrostatic stress. Tvergaard 共1981兲modified
the Gurson model by introducing additional parameters which
account for interaction of cavities to better fit experimental results
for plane strain problems. Tvergaard and Needleman 共1984兲fur-
ther modified the Gurson model by introducing an effective po-
rosity parameter which accounts for increasing cavitation after the
voids start to coalesce to more closely match experimental obser-
vations. The modified Gurson model is implemented in commer-
cial software such as ABAQUS and has been used by Dos Santos
and Ruggieri 共2003兲and Rakin et al. 共2004兲.
Performance Indicators Based on Micromechanics
According to Hancock and Mackenzie 共1976兲, the strain at ductile
fracture initiation is
f=aexp
冉
− 1.5m
¯
冊
=aexp共− 1.5T兲共1兲
where f=failure strain, a=material constant; and mand
¯
=hydrostatic and Mises stresses, respectively. The ratio between
the hydrostatic and Mises stresses is called stress triaxility, T.
El-Tawil et al. 共1999兲defined a material independent rupture
index 共RI兲as the ratio between the plastic equivalent strain index
and the ductile fracture strain 关calculated using Eq. 共1兲兴 multiplied
by the material constant a, such that
RI = aPEEQ
f
=PEEQ
exp共− 1.5T兲共2兲
El-Tawil et al. 共1999兲used RI as an indicator of the propensity for
ductile fracture initiation in steel moment resisting connections.
The advantage of the index is that it does not include any material
constants and so it can be directly applied in parametric studies.
Ricles et al. 共2000兲successfully used the RI proposed by El-Tawil
et al. 共1999兲to develop an optimal access hole geometry for mo-
Fig. 1. Web fractures initiating from ends of stiffener-to-web welds
共Specimen 4A, Arce 2002; courtesy of T. Okazaki and M.
Engelhardt, used with permission兲
JOURNAL OF STRUCTURAL ENGINEERING © ASCE / AUGUST 2006 / 1193
ment resisting connections, which was subsequently adopted by
AISC 共2002兲.
The RI in Eq. 共2兲was used by the authors to investigate the
fracture potential of circular notched bars with varying notch radii
tested by Kuwamura and Yamamoto 共1997兲. Kuwamura and
Yamamoto 共1997兲showed that for sharp notches, fracture initiates
a small distance under the surface of the notch where triaxiality is
maximum whereas for blunt notches, fracture initiates at the cen-
ter of specimen, again at the location of highest triaxiality. Toribio
and Ayaso 共2004兲also noted that fracture initiates at locations of
highest triaxiality. Analysis results show that the RI in Eq. 共2兲is
indeed capable of showing that sharper notches increase the po-
tential for cracking, i.e., RI increases substantially as the radius
decreases. However, the index predicts a fracture initiation loca-
tion that is slightly off from the location observed in tests of
sharp-notched specimens. For example, Fig. 2共a兲shows that RI
achieves its maximum value at the surface of the notch, which is
slightly shifted from the correct location just under the surface of
the notch.
A modification of Eq. 共2兲is proposed to remedy the problem
identified above: the RI is computed using the maximum triaxi-
ality achieved during the load history rather than the triaxiality
computed at a given load step. The modified rupture index 共MRI兲
is therefore
MRI = PEEQ
exp共− 1.5 max关T兴兲 共3兲
Experience with MRI shows that in addition to demonstrating that
sharper notches increase the potential for fracture, the location of
the maximum index coincides more closely with the location of
maximum triaxiality, and is close to the experimentally observed
fracture initiation location 关Fig. 2共b兲兴.
In the computation of the MRI, the plastic equivalent strains
and triaxiality values are averaged over a characteristic length of
the material which represents the length over which physical
processes 共void growth and coalescence兲are occurring. This is
conveniently achieved by using an element size equal to the char-
acteristic length. In this research, the characteristic length is taken
as 0.3 mm, which corresponds to the upper limit for A572-Grade
50 steel as reported by Kanvinde 共2004兲.
It is reiterated that MRI is not calibrated to be used as a crite-
rion for fracture initiation; it is only an indicator of the propensity
for fracture at a particular location and is used in this respect to
distinguish between alternative structural details. An important
restriction for using this rupture index is that it is valid for cases
where void nucleation strain is small compared to strains over
which the voids grow because the void nucleation strain is not
included in this model, which is reasonable for structural steel.
Shear Link Specimens Tested by Arce „2002…
and Gálvez „2004…
The test setup for the shear link tests at the University of Texas,
Austin is shown schematically in Fig. 3共a兲共Arce 2002 and Gálvez
2004兲. The setup was devised so that the unequal moments that
Fig. 2. Distribution of: 共a兲RI; 共b兲MRI in bar with 1-mm notch tested by Kuwamura and Yamamoto 共1997兲
Fig. 3. 共a兲Test setup for shear link specimens tested by Arce 共2002兲;
共b兲model of test setup
1194 / JOURNAL OF STRUCTURAL ENGINEERING © ASCE / AUGUST 2006
Document Summary
Ductile web fracture initiation in steel shear links. Shih-ho chao, s. m. asce1; kapil khandelwal, s. m. asce2; and sherif el-tawil, m. asce3. Abstract: tests conducted in the 1980s showed that well-detailed short shear links can exhibit stable and ductile cyclic behavior. Recent tests of prevailing a992 rolled shapes revealed that shear links designed according to current seismic speci cations can fail by ductile fracture in the link web, a mode of failure that was not observed in earlier tests. This paper investigates the observed ductile fractures through computational structural simulation. An existing criterion for judging the propensity for ductile fracture initiation in steel is modi ed based on published tests results for notched bars to better pinpoint the location of ductile fracture initiation. Validated nite- element analyses of previously tested shear links are conducted and the results postprocessed to evaluate the potential for ductile fracture of specimens with several different types of details.
