T. P. LI, X. L. TIAN
Open Access JAMP
(2)
In Equation (2),
is initial yielding stress of ma-
terial, N is strain hardening index, E is young’s modulus,
and for material of A533B, parameters defined in Equa-
tion (2) are fixed a s
5
0
400,2 10,0.1MPa EMPa N
σ
= =×=
.
3.2. Finite Element Model
According to ASME fracture toughness test standard
E1820 [6], the geometric character of contact tension
specimen can be plotted as Figure 1: w is 50.8 mm as
width of specimen, B is 127 mm as depth of specimen,
and size of the remanent part can be deduced by the pro-
portion in Figure 1. Geometric size in Figure 1 is used
to build the finite element model.
Software Warp3d is used here for model creation and
element C3D8 is selected. Since plastic deformation is
included in simulation, crack tip singularity is not consi-
dered in this paper. Plot in Figure 2 is the half model of
contact tension specimen, one-layer element with Gurson
model property is assigned to the crack face, and the
elastic-plastic material relationsh ip in Equation (2) is still
suitable for the remanent part. In this paper, some para-
meters such as aspect ratio and Gurson element height
are fixed in simulation as
12 3
1.46, 0.931, 2.131qq q= ==
and
, where
is the height of element
with Gurson model property.
The boundary condition is: all node freedom in depth
direction is fixed; node freedom in vertical direction for
symmetric surface except crack face is fixed; in order to
remove rigid displacement of the whole model, one of
the nodes far from loading position and crack surface is
Figure 1. Schematic plot of contact tension specimen.
Figure 2. Finite element model of contact tension specimen.
fixed in horizontal direction. Displacement loading me-
thod is used.
3.3. Calculation Results
Software Warp3d is used to simulate fracture process of
contact tension specimen. Effects of initial porosity
,
critic porosity
and load control parameter
em-
bedded in Warp3d on fracture process are studied in si-
mulation.
1) Effect of load control parameter
on
value
For the simulation of this part, initial crack length ratio
is
, initial porosity rate is
, critic
porosity ratio is
and only load control para-
meter is changeable. It is shown in Figure 3 that, curve
of
value vs. displacement loading is affected little by
load control parameter, and the specimen is perfect now
with no crack extension. As displacement
increasing,
curves are distinct with different
: smaller
value
is related with stable crack extension, such as there is a
platform in curve corresponding to
; curves
with larger
are related with unstable crack extension
since there is a downtrend in these curves.
2) Effect of critic porosity
For the simulation of this part, initial crack length ratio
is defined as
, load control parameter is de-
fined as
, initial porosity is defined as
, and only critic porosity
is changeable.
It is shown in Figure 4 that almost no effect of
on
result can be observed.
3) Effect of initial porosity
For the simulation of this part，initial crack length ratio
is defined as
, load control parameter is de-
fined as
, critic porosity is defined as
, and only initial porosity
is changeable. It
is shown in Figure 5 that curves of
value vs. dis-
placement loading are coincident with smaller loading.
As loading
increases, yielding is found around crack
tip since smaller
(
) corresponding to
more perfect material, and there is an uptrend for
value because yielding zone is expanding. As
in-
creases, there is a downtrend in curve, since material
with larger porosity rate is fragile, and relaxative stress
can be observed around crack tip with crack surface ex-
tension.
