PSI - Issue 13

Zhengkun Liu et al. / Procedia Structural Integrity 13 (2018) 781–786 Z. Liu et al. / Structural Integrity Procedia 00 (2018) 000–000

783

3

dev e and ψ − e = ψ

vol e . If J ≥ 1, ψ +

dev e

vol e and ψ − e = 0. The deformation gradient F is considered

If J < 1, ψ +

e = ψ

e = ψ

+ ψ

through its determinant J = det ( F ). The governing equations of phase-field model for the finite strain brittle fracture in viscoelastic solids can be stated as Div ( FS ) = 0 , ˙ s M = − 2 s � ψ + e − ψ c � + + 2 ψ c ( 1 − s + 4 κ 2 ∇ ( X ) ∙ ∇ ( X ) s ) . (10) with M the mobility factor and � a � ± = ( a ± | a | ) / 2. 3. Numerical example In this section, a 2D single-edge notched tension test has been investigated to analyse the performances of the proposed phase-field model for brittle fracture in viscoelastic solids from di ff erent aspects of view. The material properties in the numerical simulation are shown in Table 1. The phase-field model has been implemented as a user defined element in FEAP (Taylor and Govindjee (2017)).

Table 1. Material parameters used in the numerical simulations. Name Symbol

Value

Unit

N / mm 2

Young’s modulus Poisson’s ratio Relaxation factor 1 Relaxation factor 2 Relaxation time Sti ff ness resistance Fracture toughness Mobility factor Di ff use length

E

11.92

0 . 45

- - -

ν

0 . 3 0 . 7 10

μ 0 μ 1 λ 1

s

10 − 8

-

η κ

mm

3

G c M

N / mm

20

mm 2 / N ∙ s

1000

3.1. 2D single-edge notched tension test

The numerical simulations of brittle fracture for a rectangular plate of length 100 mm, containing a horizontal notch of length 20 mm are performed. The rectangular plate is subjected to uniaxial tension by prescribing a vertical

Fig. 1. Geometry and boundary conditions.