#### Description

An energy release rate based simulation method for dynamic fracture mechanics is developed to model crack initiation and propagation in elastic–plastic solid. Potential crack surface is modeled by a series of paired nodes bonded together by nodal constraint forces before crack propagation. The nodal constraint force of the paired nodes at the current crack tip is linearly decreased to zero in a specified time interval to mimic the crack propagation with a corresponding crack speed. During this process, the nodal force vectors and the nodal displacement vectors of the paired nodes are obtained. Based on the force-displacement curve, energy release rate can be calculated. It is found that energy release rate is monotonically decreasing with crack speed, a physical phenomenon predicted by Freund [1]. In this study, we hypothesize that the energy release rate is equal to a constant critical value during the entire crack propagation process. Hence, we may find the variable crack speed as a function of time. It is noticed that crack initiation is a special case of crack propagation with the crack speed approaching zero. The direction of crack propagation is determined by an iterative routine that adjusts the mesh such that the crack path is perpendicular to the nodal force of the paired nodes. The constitutive theory of the material is formulated based on large strain plasticity with return mapping algorithm. Notice that small strain elasticity is a special case of large strain plasticity. Hence we can verify our numerical results with those in linear elastic fracture mechanics. It is found that (1) the magnitude of crack tip stress decreases when large strain, instead of small strain, is considered; (2) node releasing method is adequate to determine the critical stress intensity factor with very high accuracy; (3) node releasing method enables one to simulate the fracture phenomenon with no initial crack—therefore ideally a simple tension test is sufficient to determine the critical energy release rate of a material; (4) crack speed asymptotically approaches to Rayleigh wave speed in case of elasticity, mode I, plain stress, and fixed grip; (5) crack speed asymptotically approaches to approximately half of Rayleigh wave speed if plasticity is considered; (6) plasticity affects the direction of crack propagation. REFERENCE [1] Freund, L.B. Dynamic Fracture Mechanics. Cambridge University Press: New York, 1990.

#### Recommended Citation

Wang, L.,
&
Lee, J.
(2014).
Energy release rate based dynamic crack propagation.
In A. Bajaj, P. Zavattieri, M. Koslowski, & T. Siegmund (Eds.).
*
Proceedings of the Society of Engineering Science 51st Annual Technical Meeting, October 1-3, 2014
*,
West Lafayette: Purdue University Libraries Scholarly Publishing Services, 2014.
http://docs.lib.purdue.edu/ses2014/mss/cfm/1

Energy release rate based dynamic crack propagation

An energy release rate based simulation method for dynamic fracture mechanics is developed to model crack initiation and propagation in elastic–plastic solid. Potential crack surface is modeled by a series of paired nodes bonded together by nodal constraint forces before crack propagation. The nodal constraint force of the paired nodes at the current crack tip is linearly decreased to zero in a specified time interval to mimic the crack propagation with a corresponding crack speed. During this process, the nodal force vectors and the nodal displacement vectors of the paired nodes are obtained. Based on the force-displacement curve, energy release rate can be calculated. It is found that energy release rate is monotonically decreasing with crack speed, a physical phenomenon predicted by Freund [1]. In this study, we hypothesize that the energy release rate is equal to a constant critical value during the entire crack propagation process. Hence, we may find the variable crack speed as a function of time. It is noticed that crack initiation is a special case of crack propagation with the crack speed approaching zero. The direction of crack propagation is determined by an iterative routine that adjusts the mesh such that the crack path is perpendicular to the nodal force of the paired nodes. The constitutive theory of the material is formulated based on large strain plasticity with return mapping algorithm. Notice that small strain elasticity is a special case of large strain plasticity. Hence we can verify our numerical results with those in linear elastic fracture mechanics. It is found that (1) the magnitude of crack tip stress decreases when large strain, instead of small strain, is considered; (2) node releasing method is adequate to determine the critical stress intensity factor with very high accuracy; (3) node releasing method enables one to simulate the fracture phenomenon with no initial crack—therefore ideally a simple tension test is sufficient to determine the critical energy release rate of a material; (4) crack speed asymptotically approaches to Rayleigh wave speed in case of elasticity, mode I, plain stress, and fixed grip; (5) crack speed asymptotically approaches to approximately half of Rayleigh wave speed if plasticity is considered; (6) plasticity affects the direction of crack propagation. REFERENCE [1] Freund, L.B. Dynamic Fracture Mechanics. Cambridge University Press: New York, 1990.