PSI - Issue 2_A

Jean-Benoıt Kopp et al. / Procedia Structural Integrity 2 (2016) 468 – 476 Author name / Structural Integrity Procedia 00 (2016) 000–000

470

3

Macro-branching herein denotes secondary crack extension d typically larger than 1 cm and micro-branching for d ≤ 1 cm. The branching (micro- and macro-) of the principle crack appears because of inertial e ff ects at an approximate crack velocity of 0.6 c r (Yo ff e (1951)). Indeed, inertial e ff ects change the stress field at the crack tip and maximum tension appear in two symmetrical planes in the process zone.

z

u

a

T

H

x

1

L

y

Fig. 1. Sketch of the strip band specimen geometry (SBS) ( L = 200 ± 1 mm, H = 60 ± 5 mm, T = 2 ± 0 . 1 mm) uniformly loaded with imposed displacements u in mode I (top). Post-mortem notched and fractured RT-PMMA sample (bottom): 1-Zoom on the initiation zone where cavitation of rubber particles is visible (whitening of the material around the notch at the initiation of the fracture); 2-Fracture propagation direction; 3-Micro branching: development of a limited branch ( d < 1 cm); 4-Macro-branching: development of a significant branch ( d ≥ 1 cm); 5-Fracture kink. For this sample, no conducting layer has been applied.

2.2. Calculation of the mean dynamic energy release rate < G Id >

2.2.1. Quasi-static G I 0 To estimate the quasi-static energy release rate which is used for reference, it is considered that an increase in crack length ∆ a corresponds to an elastic unloading of a zone of equivalent length ∆ a far ahead of the crack tip. This point of view - which allows to consider a plane stress state - leads to an easier calculation than considering the energy released inside the process zone. In a plane stress state ( σ yy = 0), the quasi-static energy release rate G I 0 is defined as:

H σ 2

2 )

zz (1 − ν

(1)

G I 0 =

2 E

where E is the Young modulus of the material corresponding to the unloading rate at the fracture, ν is its Poison ratio, H 2 is the half-width of the sample and σ zz is the released stress at the fracture. The corresponding strain follows: ǫ zz = 1 − ν 2 E σ zz (Nilsson (1972)). 2.2.2. Dynamic energy release rate G Id If the crack tip position during propagation a ( t ) and the stress or strain state at initiation are known, the dynamic energy release rate G Id can be calculated between two crack tip positions a and a +∆ a by means of a transient dynamic