Extrinsic cohesive modelling of dynamic fracture and microbranching instability in brittle materials

Abstract

SUMMARYDynamic crack microbranching processes in brittle materials are investigated by means of a computational fracture mechanics approach using the finite element method with special interface elements and a topological data structure representation. Experiments indicate presence of a limiting crack speed for dynamic crack in brittle materials as well as increasing fracture resistance with crack speed. These phenomena are numerically investigated by means of a cohesive zone model (CZM) to characterize the fracture process. A critical evaluation of intrinsic versus extrinsic CZMs is briefly presented, which highlights the necessity of adopting an extrinsic approach in the current analysis. A novel topologybased data structure is employed to enable fast and robust manipulation of evolving mesh information when extrinsic cohesive elements are inserted adaptively. Compared to intrinsic CZMs, which include an initial hardening segment in the traction-separation curve, extrinsic CZMs involve additional issues both in implementing the procedure and in interpreting simulation results. These include time discontinuity in stress history, fracture pattern dependence on time step control, and numerical energy balance. These issues are investigated in detail through a 'quasi-steady-state' crack propagation problem in polymethylmethacrylate. The simulation results compare reasonably well with experimental observations both globally and locally, and demonstrate certain advantageous features of the extrinsic CZM with respect to the intrinsic CZM.

A one field full discontinuous Galerkin method for Kirchhoff–Love shells applied to fracture mechanics

“…Now the combination between mode I and II is realized in a similar way as achieved by several authors [7,16,[47][48][49][50][51] when considering Cauchy stress tensors for 3D TSL. This method, which was first suggested by Camacho et al [3], and extended a few years later by Ortiz et al [46], considers an effective stress σ eff to detect fracture initialization, with the criteria: σ eff > σ c , and allows for fracture in compression to happen if the shearing stress is sufficiently large,…”

“…This initial slope must tend to infinity to ensure a correct wave propagation in the structure, which leads to some numerical problems [14]. On the other hand, an extrinsic cohesive law, where the cohesive elements are inserted on the fly during the simulation when a fracture criterion is reached [3,7,8,10], requires a very complex implementation [15][16][17] due to the inherent difficulty associated with propagating topological changes in the mesh. As a large number of degree of freedoms (dofs) is needed to obtain a convergence in a fracture problem [7], a parallel implementation can be required to perform large simulations in an admissible computational time, further complicating the implementation.…”

Numerical simulation of dynamic fracture using finite elements with embedded discontinuities

“…We refer among others to Dally (1979), Ravi-Chandar and Knauss (1984a,b), Knauss and Ravi-Chandar (1985), Ramulu and Kobayashi (1985), Fineberg et al (1991), Satoh (1996), Fineberg (1996, 1999), Fineberg and Marder (1999), and references therein, for a discussion of some experimental observations. Numerical simulations of the problem have been reported in Falk et al (2001), Klein et al (2001), Belytschko et al (2003), Zhou and Molinari (2004), Zhou et al (2005), Huespe et al (2006), Song et al (2006), Duarte et al (2007), Karedla and Reddy (2007), Remmers et al (2008), Zhang et al (2007), Zi et al (2007), to mention just a few references employing a variety of different numerical approaches.…”

Study of influence of various loading parameters on crack propagation by using Cohesive Zone Modeling (CZM) approach

“…The cohesive zone model (CZM) has gained a significant importance in the modeling of the crack propagation in solids in recent years [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. The concept of cohesive zone, firstly was conceived by Dugdale et al (1960), Barenblatt et al (1962), Rice et al (1968) etc.…”

“…This work also concerned about the various loading parameters as displacement jump, cohesive energy etc, and analyzed the influence of the cohesive energy on the different type of the 96 Unauthenticated Download Date | 5/11/18 11:30 PM cohesive models. Zhang et al [2] investigated the dynamic failure process in a variety of the materials by incorporating a cohesive zone model into the finite clement scheme. The series of dynamic fracture phenomena, including spontaneous crack initiation, dynamic crack microbranching and crack competition were successfully captured by the CZM simulations in his work.…”