International Journal of Automotive Technology, Vol. 12, No. 2, pp. 225-232 (2011) DO1 10.1007/s12239-011~27-7
Copyright 0 2011 KSAE 1229-91381201 11057-09
OFF-SET CRACK PROPAGATION ANALYSIS
UNDER MIXED MODE LOADINGS
A. E.
ISM AIL^)',
A.
K.
ARBFN),
S. ABDULLAH~)
and
M.
J.
GHAZALF)
"Department of Engineering Mechanics, Universiti Tun Hussein 01111 Malaysia, Batu Pahat 86400, Malaysia
''Department of Mechanical & Materials Engineering, Universiti Kebangsaan Malaysia, Bangi 43600, Malaysia
(Received 9 December 2009; Revised I July 2010)
ABSTRACT-An assessment was carried out herein to study the eccentricity of cracks subjected to mixed-mode loadings. Several loading locations relative to a central line were selected to induce mixed-mode loadings, which were comvuted us in^ a fmte element method. An adaptive meshing technique was adopted during the simulation of'crackpropagation to ensure the singularity of stress at the tip of the crack. The stress intensity failure criterion was nsed and progammed, and the node splitting technique was nsed when the stress intensity factor reached the fracture toughness of the material to simulate crack propagations. It was found that large variations m the stress intensity factor were observed when off-set cracks were used, and that
K,,
decreased when loading distance inmeased, hut increased when the off-set crack distance was increased. Both crack eccentricity and loading distance played important roles in producing mixed-mode loading, compared to the influence of central cracks. Correction factors were introduced to m o w the calculation of stress intensity factors under mixed-mode loadings. Sunulations of nack propagation were also conducted to study the effects of crack eccentricities and loading distances. It was found that the crack length, the loading distance relative to the central crack and the m c k eccentricity dominated calculations of the integrity of cracked structures.KEY WORDS : Mixed-mode loading, Crack eccentxicity, Stress intensity factor, Crack propagation
The complexity of modem engineaing designs demands reliable structural integrity, even in the presence of man-made defects such as holes or cross-sectional changes (Jun et al., 2008; Baek et al, 2008). These defects
are
capable of inducing for a concentration of stress that may lead to crack initiations and potentially fail catastrophically. According to the present design practice guidelines available in (Mumlami, 1987), the calculation of s e s s intensity factors for any cracked strucbx~ is based on the symmetrical loading of a crack, which is. . . .
asu--nfct iceL
however, cracks are normally situated off-axis from tbe central line.
Tne problem of crack eccentricity may not be directly treated by the standard crack configuration, as there are more than two combinations of loadings. For example, a beam subjected to four point bendng moments is subjected to mixed-mode
K,
and K, stress intensity factors. There are several well establishedmethods used to produce mixed-mode loadings, and these methodsare
summarized in (Mendelsohn et al., 2001). These include the Iosipescu arrangement (losipescu, 19671, the Brazilian compressive disk test (Shetty et al., 1986), a rotated and rnodh5ed compact tension method*Corresponding author e-mail: [email protected]
OFF-SET CRACK PROPAGATION ANALYSIS UNDER MIXED MODE LOADWGS 23 1
0.40
5.
CONCLUSIONS
@
In
this work, numerical simulations were conducted to'
0.30 - m . o examine the behavior of cracked structures, in particular,g
csiW=o.~ loaded beams with mixed-mode loadings. Three important5
aspects were considered: crack lengths, crack eccenhicitiese
0209
.-
and loading distances from the midline. Several conclusions 2z
can be drawn:.-
% 0.10 (1) The developed mathematical model was successfully
used to determine stress intensity factors (K, and K,,)
and simulate static crack propagation
in
high-strength0.00 steel beams under mixed-mode loadings.
0.~0 0.10 0.50 0~60 0.m 0.80 (2) Computational analysis was carried out for variable off-set c-ack gmwtb r r k , deItn(n>,V'
[image:7.605.32.255.88.244.2] [image:7.605.32.258.283.436.2]crach and loading distances. Crack eccentricity played an Figure 17. Effect of Da/W on the Kfi,, ratio for different d/W
0.30 0.40 0.50 O.W 070 0.80 sack #oWm ratio. ddiuid/IP
impoaant role in reducing the K, value, and therefore,
correction factors were introduced to compensate for variations in the stress intensity factor.
(3) The loading distance relative to the central crack was
found to reduce K,. However, no relationship in the decrease as a function of a/W was noted.
(4) The results of the simulations confirmed the existence of the
K,[
stress intensity factor when the cracks were offset from the midline and the loading distance was increased. The crack propagation simulation revealed that a dominant K,, factor around the crack tip producesan inclined crack at an angle with respect to the vertical line.
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