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.