A Critical Examination of a Numerical Fracture Dynamic Code

Abstract

After upgrading the energy dissipation algori thm , numerical experiments were conducted to assess the rel iability of the explicit dynamic finite element code, HCRACK. Two dynami c fracture specimens , i.e., the wedge-loaded rectangular DCB (RDCB) specimen and the wedge-loaded tapered DCB (TDCB) spec imen , which were studied experimentally by Kalthoff et al , were then analyzed wi th this updated fracture dynami c code. Using the experi mentally determined dynamic fracture toughness , K ID , versus crack velocity , ~~, relation , the RDCB specimen was analyzed first by the "propagation method " where good agreements between calculated and measured K ID versus a relations were observed. The calculated a versus time , t, relation was then used as input data in the "generation method" where the resul tant K 10 were virtually identical to those obtained in the propagation method. Error analyses of the generation method were also made first by using the experimentally determined a versus t relation and secondly by artificially perturbing this relation .A TDCB specimen was then analyzed with both the propagation and generation methods by using the K ID versus ~ relation established for this specimen and the measured a versus t relation , respectively. The KEYWORDSDynamic fracture, dynamic finite element analysis , dynamic fracture toughness, crack arrest stress Intensity factor.----~~~1

The dependence of the dynamic material toughness on the velocity and on some loading parameters

“…We find that the peak encountered in Fig. The rise time is thus increased by a factor of 1.128 (see (8)). In Fig.…”

“…with Gdi yn being obtained from the numerical analysis (see for example [6,8]) and A(V) being the function derived by Freund [12] based on the work of Atkinson and Eshelby [11]. Although (4) and A(V) were originally developed for plane strain conditions, they can be adjusted to handle plane stress cases (see [13] for example).…”

“…Figures 7a, 7b and 7c describe the variation of the normalized dynamic stress intensity factor during the propagation of cracks which are accelerated to a terminal velocity of 0.5 Cr, starting with initial lengths of 0.2 W and 0.3 W. Each of the figures correspond to a different S~-n combination and thus to a different rise time (see (8)). Qualitatively all the K~ yn curves behave in the same manner, irrespective of the specific rise time considered; the K~ yn level first decreases to a level which is below the stress intensity factor at initiation (K~c) and then, when the crack speed approaches the terminal velocity, the Kid y" stabilizes at a level which is belaw K~ c for Common to all these SEN cases is the decrease in the K f y" level immediately after initiation of fracture.…”

“…Various kinds of nodal force (stress) reduction forms have been used [7,8,9]. The associated abrupt release of the nodal forces, in finite element schemes, or of the stresses, in finite difference schemes, at the crack tip, introduces spurious noise which affects the correct solution.…”

Numerical studies in dynamic fracture mechanics

“…In the use of eight-noded isoparametric elements, it was demonstrated in [25] that both the corner and midside nodes on the crack element should be released simultaneously. Studies using different nodal release mechanisms, as in (16a-c), were discussed in [26,27]. From the authors' experience, the use of "linear relaxation" (as in (16c), while employing eight-noded elements, yields smoother results than the other "nonlinear" relaxation techniques.…”