A molecular dynamics investigation of rapid fracture mechanics

Abraham, Farid F.; Brodbeck, D.; Rudge, W. E.; Xu, Xiaopeng

doi:10.1016/s0022-5096(96)00103-2

Cited by 126 publications

(56 citation statements)

References 20 publications

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“…We applied this concept of an effective spring constant to a continuous interatomic potential: in particular, to the Lennard-Jones 12:6 potential. The prediction is in agreement with computer simulations [8,9]. …”

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confidence: 86%

“…Abraham et al [8,9] proposed that the onset of the instability can be understood from the point of view of reduced local lattice vibration frequencies due to softening at the crack tip. They noted that the onset of the roughening (the instability) corresponds to the point in the crack tip dynamics where the time it takes the tip to transverse one lattice spacing approximately equals the period of one atomic vibration.…”

Section: Pacs: 6220mkmentioning

confidence: 99%

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Bond-Breaking Relaxation Governs Onset of the Fracture Instability

Abraham¹

2007

TOMECHJ

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Abstract:A dynamic crack will travel in a straight path up to a material-dependent critical speed beyond which its path becomes erratic. Predicting this critical speed and discovering the origin of this instability are two outstanding problems in fracture mechanics. We recently discovered a simple scaling model based on an effective elastic modulus that gives successful predictions for this critical speed. We now show that a simple atomic picture based on broken-bond relaxation at the dynamic crack tip provides an explanation for the origin of the effective elastic modulus. PACS: 62.20.MKIn 1951, Yoffe [1] made the physically intuitive suggestion that mode I crack growth occurs in the direction of maximum asymptotic hoop stress and found the crack speed for the onset for branching to be about 70% of the Rayleigh wave speed c R [2,3]. However, this high speed is rarely observed in experiment [4,5]. An obvious shortcoming in Yoffe's analysis is the assumption of a constant linear elastic response for all deformations. In our recent study of brittle fracture [6], we showed that hyperelasticity, the elasticity at large strain, plays a governing role in the onset of the crack instability from unidirectional motion. We discovered a simple, yet remarkable, scaling based on an effective elastic modulus for our modelled solid (the secant modulus at the stability limit of the bulk solid), which led to successful predictions for the onset speed of the crack instability. We have also applied this scaling to the same-modelled solid with the exception that the crack is constrained to travel unidirectional irrespective of its speed [7]. This allowed the crack to achieve a unique steady-state speed that has a dependence on hyperelasticity. Using our scaling law, we found that the steady-state crack speed scales to a constant value equal to a crack speed of a linear solid with our effective elastic modulus. In this paper, we demonstrate that atomic relaxation of breaking bonds at the crack tip governs these dynamic features of the travelling brittle crack.We summarize our earlier findings. Our simulation model is based on a generalized bilinear force law composed of two spring constants, one associated with small deformations (k 1, r < r on ) and the other associated with large deformations (k 2 , r > r on) . This is shown in Fig. (1a). This model allowed us to investigate the generic effects of hyperelasticity by changing the relative magnitude of the spring constants = k 2 /k 1 and transition distance r on of the potential [in terms of 0 = (r on /r 0 ) -1]. We considered the propagation of a crack in two-dimensional hexagonal lattice geometry. The slab is loaded in mode I with a constant strain rate. The dynamic crack instabilities for the various = k 2 /k 1 are associated with the precipitous drops in crack speed (see Fig. 1b), as indicated by the arrows, and *Address correspondence to this author at the Lawrence Livermore National Laboratory, Livermore, CA 94550, USA; E-mail: abraham4@llnl.gov are a consequence of the crack ...

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confidence: 86%

Section: Pacs: 6220mkmentioning

confidence: 99%

Bond-Breaking Relaxation Governs Onset of the Fracture Instability

Abraham¹

2007

TOMECHJ

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“…The resulting theory is therefore scale independent and applied equally well at all length scales. It has been noted that dynamic growth of cracks within a molecular dynamics simulation exhibit response similar to the continuum model [3,4].…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Experimental Challenges in the Investigation of Dynamic Fracture of Brittle Materials

Ravi‐Chandar

2001

Physical Aspects of Fracture

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“…In contrast to metals, where fracture and deformation can often be described using the embedded atom method (EAM) [12 -17], a proper description of fracture in silicon has proved to be far more difficult [4,8,10,[17][18][19][20][21][22][23][24][25][26][27][28][29]. Early attempts to model fracture in Si used Tersoff's classical potential [30] (in the following referred to as ''Tersoff potential'') and similar formulations [31,32].…”

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confidence: 99%

Multiparadigm Modeling of Dynamical Crack Propagation in Silicon Using a Reactive Force Field

2006

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We report a study of dynamic cracking in a silicon single crystal in which the ReaxFF reactive force field is used for several thousand atoms near the crack tip, while more than 100 000 atoms are described with a nonreactive force field. ReaxFF is completely derived from quantum mechanical calculations of simple silicon systems without any empirical parameters. Our results reproduce experimental observations of fracture in silicon including changes in crack dynamics for different crack orientations.

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A molecular dynamics investigation of rapid fracture mechanics

Cited by 126 publications

References 20 publications

Bond-Breaking Relaxation Governs Onset of the Fracture Instability

Bond-Breaking Relaxation Governs Onset of the Fracture Instability

Experimental Challenges in the Investigation of Dynamic Fracture of Brittle Materials

Multiparadigm Modeling of Dynamical Crack Propagation in Silicon Using a Reactive Force Field

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