Use of an eight-node element for fast fracture problems

Abstract

In recent years, several finite element analyses of a fast running crack (of opening mode in linearly elastic isotropic bodies) have been conducted by various investigators [1][2][3][4]. These investigations have basically the same approach of modeling the crack propagation by the sequential release of nodes along the crack path. As the crack tip is modeled to move from one node to the next, the condition of the released node is smoothly relaxed from that of zero displacement to that of zero external nodal force normal to the crack plane. The negative work done by diminishing the force at the released node is assumed to represent the energy release mechanism of a running crack. These finite element models [1-4] utilized the conventional four node elements.In another investigation [5] parabolic elements have been employed where nodes were released instantly one after the other to model the running crack. This sudden release of the nodes has been attributed as a deficiency in the finite element model of crack propagation since there is no release of mechanical energy at the crack tip [i-4]. On the other hand, practical experience has in general shown that for a given number of total degrees of freedom greater accuracy is achieved by use of fewer higher order elements in place of larger number of simple element. This report thus presents the investigation of a running crack with the help of parabolic elements with an energy release mechanism.The performance of an eight node element with relaxation technique was studied by analyzing a uniformly expanding crack in a square region subjected to uniform tension, ~ acting on the edges parallel to the crack trajectory.During the initial phase of crack propagation, i.e., before a wave emitted at the start of crack propagation hits the crack after having reflected from the outer boundaries, the situation corresponds to Broberg's problem [6]. The finite element breakdown, shown in Fig. i, represents one quarter of the region due to symmetry and consists of 50 quadratic elements and 351 degrees of freedom. Very stiff massless truss elements, shown in Fig. I, were employed to constrain the vertical nodal displacement along the crack path. When the running crack tip reached a node, the corresponding truss was decoupled, and the force in the truss was relaxed linearly over time duration of crack tip translation from one node to the next with the given velocity.Plane stress was assumed. The value of Poisson's ratio was taken equal to 0.3 which gives Cp/C 2 = 1.69, where Cp is plate wave velocity and C 2 is shear wave velocity.The finite element program NONSAP [7] was employed with Newmark's time integration scheme and consistent mass formulation.Two cases of crack velocity, V = 0:159 Cp and V = 0.318 Cp, were investigated.The energy release rate for each increment of crack extension was computed from the global energy balance involving the I n t Journ o f F r a c t u r e 16 (1980) R34 strain energy, kinetic energy, and potential of remote loads computed at the end of each incremen...

Experimental and numerical studies on dynamic crack growth in layered slate rock under wedge impact loads: part I—plane strain problem

“…Since both ABAQUS standard and ABAQUS explicit do not support dynamic crack propagation analysis, a method that applied the Mall and Luz 21 and Sun and Han 16 procedure to model delamination crack propagation was used to simulate the dynamic crack propagation process. In this procedure crack propagation was simulated by sequentially releasing the constrained degree of freedom on the boundary nodes along the crack propagation path, step‐by‐step, according to the calculated time.…”

Numerical studies in dynamic fracture mechanics

“…It is important to recognize that the above procedure of moving the crack-tip from B to D involves several time-steps At. 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].…”