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A new quantum action-based theory, Dynamic Quantized Fracture Mechanics (DQFM), is presented that modifies continuum-based dynamic fracture mechanics. The crack propagation is assumed as quantized in both space and time. The static limit case corresponds to Quantized Fracture Mechanics (QFM), that we have recently developed to predict the strength of nanostructures.
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We extend the model-free data-driven paradigm for rate-independent fracture mechanics proposed in Carrara et al. (2020), Data-driven Fracture Mechanics, Comp. Meth. App. Mech. Eng., 372 to rate-dependent fracture and sub-critical fatigue. The problem is formulated by combining the balance governing equations stemming from variational principles with a set of data points that encodes the fracture constitutive behavior of the material. The solution is found as the data point that best satisfies the meta-stability condition as given by the variational procedure and following a distance minimization approach based on closest-point-projection. The approach is tested on different setups adopting different types of rate-dependent fracture and fatigue models affected or not by white noise.
Ebert et al. [Phys. Rev. Lett. 77, 3827 (1996)] have fractured icosahedral Al-Mn-Pd single crystals in ultrahigh vacuum and have investigated the cleavage planes in-situ by scanning tunneling microscopy (STM). Globular patterns in the STM-images were interpreted as clusters of atoms. These are significant structural units of quasicrystals. The experiments of Ebert et al. imply that they are also stable physical entities, a property controversially discussed currently. For a clarification we performed the first large scale fracture simulations on three-dimensional complex binary systems. We studied the propagation of mode I cracks in an icosahedral model quasicrystal by molecular dynamics techniques at low temperature. In particular we examined how the shape of the cleavage plane is influenced by the clusters inherent in the model and how it depends on the plane structure. Brittle fracture with no indication of dislocation activity is observed. The crack surfaces are rough on the scale of the clusters, but exhibit constant average heights for orientations perpendicular to high symmetry axes. From detailed analyses of the fractured samples we conclude that both, the plane structure and the clusters, strongly influence dynamic fracture in quasicrystals and that the clusters therefore have to be regarded as physical entities.
We present a new data-driven paradigm for variational brittle fracture mechanics. The fracture-related material modeling assumptions are removed and the governing equations stemming from variational principles are combined with a set of discrete data points, leading to a model-free data-driven method of solution. The solution at a given load step is identified as the point within the data set that best satisfies either the Kuhn-Tucker conditions stemming from the variational fracture problem or global minimization of a suitable energy functional, leading to data-driven counterparts of both the local and the global minimization approaches of variational fracture mechanics. Both formulations are tested on different test configurations with and without noise and for Griffith and R-curve type fracture behavior.
The orthorhombic boride crystal family XYB$_{14}$, where X and Y are metal atoms, plays a critical role in a unique class of superhard compounds, yet there have been no studies aimed at understanding the origin of the mechanical strength of this compound. We present here the results from a comprehensive investigation into the fracture strength of the archetypal AlLiB$_{14}$ crystal. First-principles, textit{ab initio}, methods are used to determine the ideal brittle cleavage strength for several high-symmetry orientations. The elastic tensor and the orientation-dependent Youngs modulus are calculated. From these results the lower bound fracture strength of AlLiB$_{14}$ is predicted to be between 29 and 31 GPa, which is near the measured hardness reported in the literature. These results indicate that the intrinsic strength of AlLiB$_{14}$ is limited by the interatomic B--B bonds that span between the B layers.
We present a stochastic modeling framework for atomistic propagation of a Mode I surface crack, with atoms interacting according to the Lennard-Jones interatomic potential at zero temperature. Specifically, we invoke the Cauchy-Born rule and the maximum entropy principle to infer probability distributions for the parameters of the interatomic potential. We then study how uncertainties in the parameters propagate to the quantities of interest relevant to crack propagation, namely, the critical stress intensity factor and the lattice trapping range. For our numerical investigation, we rely on an automated version of the so-called numerical-continuation enhanced flexible boundary (NCFlex) algorithm.
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