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Microscopic and macroscopic numerical simulation on interaction between stress wave and flaw
Abstract
The finite element program LS-DYNA3D and the molecular dynamic method were applied to investigate the plastic zone formation, evolution process and the consequent dynamic failure behaviors under the dynamic tensile loading in a metal sheet with a preset flaw at macroscopic and microscopic levels, respectively. The calculated results show that the formation of the plastic zone stems from the stress wave-flaw and stress wave-stress wave interactions. The macroscopic and microscopic simulations represent the similar physical characteristics: the crack initiates at the front of the flaw boundary, then connects with the flaw and eventually leads to the global failure.
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Molecular dynamics simulations in three-dimensional copper are performed to quantify the void coalescence process leading to fracture. The correlated growth of the voids during their linking is investigated both in terms of the onset of coalescence and the ensuing dynamical interactions through the rate of reduction of the distance between the voids and the directional growth of the voids. The critical intervoid ligament distance marking the onset of coalescence is shown to be approximately one void radius in both measures.
A dull crack model, with a circular curve on the tip, was investigated. An elastic solution without crack was taken in the periphery of the crack tip, the line field analysis method was adopted and a method for computing plastic zone forward crack tip was proposed. For a circular disk with radial crack uniformly subjected to tension in outer circular boundary, the relation between size of plastic zone forward crack tip and curvature radio of crack tip was obtained. It is concluded that the relationship between size of plastic zone forward crack tip and curvature radio of crack tip exists, if the size of plastic zone forward crack tip keeps as a constant, the uniform tension in out circular boundary is inverse proportional to the square of outer radius. The former conclusion indicates that there exists limitation when size of plastic zone forward crack tip is regarded as criterion of unstable expanding of a crack, and the latter shows the size effect of strength of a body with crack: strength of a body with crack is inverse proportional to the square of line dimension size.
Edge dislocation emissions from Mode I, Mode II and mixed-mode crack tips along multiple inclined slip planes are simulated, and plastic zones as well as dislocation-free zones are obtained. It is found that the shape of the Mode II plastic zone is quite different from that obtained based on von Mises yielding criterion and is consists of three parts, in which the biggest one locates in front of the crack tip. For Mode I crack, however, a similar plastic zone is obtained. Under the same magnitudes of applied stress, the plastic zone of Mode II crack is much larger than that of Mode I crack, and the plastic zone of a mixed-mode crack is mainly affected by the Mode II component. Dislocation-free zones exist around all types of crack tips, which have similar shapes as the corresponding plastic zones.
By means of the explicit nonlinear dynamic finite element computer code LS-DYNA, the nucleation and growth of void in aluminum with a preexisting flaw under plate impact loading have been investigated. The results are as follows: firstly, the void nucleation occurs from the boundary of the preexisting flaw and the ductile matrix, and once the voids have been nucleated, they grow linearly through the localized plastic deformation; secondly, the growth rate of void radius increases linearly with the shock loading amplitude; thirdly, the yield strength and the size of the preexisting flaw have an obvious influence on the relative growth rate of void; finally, if the threshold stress of the void growth is set as 3.5 times of the yield strength, the simulation results agree reasonably well with the theoretical results, which is helpful for the further understanding of the void growth dynamic behavior.
Edge dislocation emissions from a Mode I crack tip along multiple inclined slip planes are simulated, and plastic zones as well as dislocation-free zones are obtained. It is found that the shape of the mode I plastic zone is similar to that obtained by von Mises or Tresca yielding criterion but leaning forward from the crack tip. The shape of dislocation-free zone is similar to that of plastic zone. With dislocation emission, the plastic zone becomes larger and larger while the dislocation-free zone is getting smaller and smaller. Judged by the strain energy density factor, the crack propagation potential decreases remarkably with dislocation emission. When a dear dislocation-free zone exists, the crack potential propagation direction will keep along the crack surface. However, when the plastic zone is fully developed or the dislocation-free zone is vanished, the crack potential propagation direction may also be changed.
This paper presents a new method to determine the crack-tip plastic zone size (Ry) in the center cracked plate in tension. The maximum crack opening displacement (MCOD) is used to estimate Ry in this method. Based on the series of calculation results by finite element analysis, the explicit expression for the crack-tip plastic zone size versus MCOD is fitted by least square method. The expression enables to eliminate the influences of the yield stress of material, crack geometry, plate sizes and transverse stress. Therefore, the presented method of Ry determined by MCOD is suitable to any center crack finite plate of any material under uniaxial or biaxial tension.
The maximum normal tensile stress at a shallow notch is used elsewhere to define a threshold level for the initiation of delayed hydride cracking at blunt notches in the pressure tubes of CANDUTM nuclear reactors. A simple method, based on a modified Neuber's solution, combined with the slip-line theory, is proposed to estimate the maximum tensile stress and the plastic zone size at a shallow notch under plane strain conditions. The applicability of the method is expected to be limited to non-workhardening materials having a high Young's modulus. Good agreement is found between the results of this simple method and finite element calculations applied to a cold-worked Zr-2·5Nb pressure tube material.
Based on stress field equations and Hill yield criterion, the crack tip plastic zone is determined for orthotropic materials and isotropic materials under small-scale yielding condition. An analytical solution to calculating the crack tip plastic zone in plane stress states is presented. The shape and size of the plastic zone are analyzed under different loading conditions. The obtained results show that the crack tip plastic zones present “butterfly-like” shapes, and the elastic–plastic boundary is smooth. The size of the plastic zone for orthotropic composites is less at the crack tip for various loading conditions, compared with the case of isotropic materials. Crack inclination angle and loading conditions affect greatly the size and shape of crack tip plastic zone. The mode I crack has a crucial effect on the plastic zone for mixed mode case in plane stress state. The plastic zone for pure mode I crack and pure mode II crack have a symmetrical distribution to the initial crack plane.
The theories for crack initiation orientation under biaxial loading based on the singular elastic field may become inaccurate as the crack tip plasticity increases. In this study, a criterion based on the relative minimum plastic zone radius (MPZR) is investigated for prediction of fatigue crack initiation angles. The MPZR criterion is applied to inclined surface crack specimens and through-crack specimens under mixed mode loading, and its performance is compared with those of the maximum tensile stress theory (MTS) and the minimum strain energy density theory (MSED). It is found that the MPZR criterion provides somewhat better overall prediction of the crack initiation angle than the MTS and MSED theories. The approach is also applied to predict crack initiation under mixed monotonic loading for through-crack specimens. The MPZR criterion is found to give conservative results, while the MTS criterion yields best correlation.
We investigate the microscopic mechanisms of void growth in polycrystalline copper undergoing triaxial expansion at a large, constant strain rate: a process central to the initial phase of dynamic fracture. Void nucleation, growth, interaction and coalescence are studied using atomistic simulations. The influence of pre-existing microstructure on the void growth is characterized both for nucleation and for growth. These processes are found to be in agreement with the general features of void distributions observed in experiment. We also examine some of the microscopic mechanisms of plasticity associated with void growth.
The process of fracture in ductile metals involves the nucleation, growth, and linking of voids. This process takes place both at the low rates involved in typical engineering applications and at the high rates associated with dynamic fracture processes such as spallation. Here we study the growth of a void in a single crystal at high rates using molecular dynamics (MD) based on Finnis-Sinclair interatomic potentials for the body-centred cubic (bcc) metals V, Nb, Mo, Ta, and W. The use of the Finnis-Sinclair potential enables the study of plasticity associated with void growth at the atomic level at room temperature and strain rates from 10^9/s down to 10^6/s and systems as large as 128 million atoms. The atomistic systems are observed to undergo a transition from twinning at the higher end of this range to dislocation flow at the lower end. We analyze the simulations for the specific mechanisms of plasticity associated with void growth as dislocation loops are punched out to accommodate the growing void. We also analyse the process of nucleation and growth of voids in simulations of nanocrystalline Ta expanding at different strain rates. We comment on differences in the plasticity associated with void growth in the bcc metals compared to earlier studies in face-centred cubic (fcc) metals. Comment: 24 pages, 12 figures
We give a quantified reasoning and description of the perplexity for evaluating language models using the concept of entropy in information theory: The smaller the entropy of the language estimated by the language model is, the more precise the language model is; an interpolated model based on two (n-1)-gram models is better than the (n-1)-gram component models, but not a n-gram model. We also explore the methods to estimating the entropy of Chinese using language models.