Dislocation dynamics in cyclic plastic deformation

The paper presents a theoretical investigation of the slip avalanches (so-called strain bursts) which occur in single-glide-orientated face-centered cubic or hexagonal close-packed metals during stress-amplitude-controlled cyclic plastic deformation. The study is based on a model of the dynamics of dislocations that has been developed in a companion paper (Part I). It is shown that this model allows for a quantitative treatment of the strain-burst phenomenon. In particular, the scaling relations between different strain-burst-characteristic parameters which have been found by experiment are connected to the evolution of the dislocation microstructure and thus find a natural explanation.     

Avalanches and scaling in plastic deformation

Plastic deformation of crystalline materials is a complex nonhomogeneous process characterized by avalanches in the motion of dislocations. We study the evolution of dislocation loops using an analytically solvable phase-field model of dislocations for ductile single crystals during monotonic loading. The distribution of dislocation loop sizes is given by P(A) approximately A-sigma, with sigma=1.8+/-0.1. The exponent is in agreement with those found in acoustic emission experiments. This model also predicts a range of macroscopic behaviors in agreement with observation, including hardening with monotonic loading, and a maximum in the acoustic emission signal at the onset of yielding.     

Two-threshold model for scaling laws of noninteracting snow avalanches

The sizes of snow slab failure that trigger snow avalanches are power-law distributed. Such a power-law probability distribution function has also been proposed to characterize different landslide types. In order to understand this scaling for gravity-driven systems, we introduce a two-threshold 2D cellular automaton, in which failure occurs irreversibly. Taking snow slab avalanches as a model system, we find that the sizes of the largest avalanches just preceding the lattice system breakdown are power-law distributed. By tuning the maximum value of the ratio of the two failure thresholds our model reproduces the range of power-law exponents observed for land, rock, or snow avalanches. We suggest this control parameter represents the material cohesion anisotropy.     

Scaling and complex avalanche dynamics in the Abelian sandpile model

We study the two-dimensional Abelian Sandpile Model on a squarelattice of linear size L. We introduce the notion of avalanche’sfine structure and compare the behavior of avalanches and waves oftoppling. We show that according to the degree of complexity inthe fine structure of avalanches, which is a direct consequence ofthe intricate superposition of the boundaries of successive waves,avalanches fall into two different categories. We propose scalingansätz for these avalanche types and verify them numerically.We find that while the first type of avalanches (α) has a simplescaling behavior, the second complex type (β) is characterized by anavalanche-size dependent scaling exponent. In particular, we define an exponent γto characterize the conditional probability distribution functions for these typesof avalanches and show that γ _α = 0.42, while 0.7 ≤ γ _β ≤ 1.0depending on the avalanche size. This distinction provides aframework within which one can understand the lack of aconsistent scaling behavior in this model, and directly addresses thelong-standing puzzle of finite-size scaling in the Abelian sandpile model.     

Scaling of waves in the bak-tang-wiesenfeld sandpile model

We study probability distributions of waves of topplings in the Bak-Tang-Wiesenfeld model on hypercubic lattices for dimensions D>/=2. Waves represent relaxation processes which do not contain multiple toppling events. We investigate bulk and boundary waves by means of their correspondence to spanning trees, and by extensive numerical simulations. While the scaling behavior of avalanches is complex and usually not governed by simple scaling laws, we show that the probability distributions for waves display clear power-law asymptotic behavior in perfect agreement with the analytical predictions. Critical exponents are obtained for the distributions of radius, area, and duration of bulk and boundary waves. Relations between them and fractal dimensions of waves are derived. We confirm that the upper critical dimension D(u) of the model is 4, and calculate logarithmic corrections to the scaling behavior of waves in D=4. In addition, we present analytical estimates for bulk avalanches in dimensions D>/=4 and simulation data for avalanches in D相似文献   

Localization of stretching strain in doped carbon γ-Fe single crystals

The evolution of local strain during stretching of high-manganese carbon austenite was studied. The ordered patterns of strain localization proved to be closely related to the stages in the stress-strain curve. The results of this study are compared with analogous data for chromium-nickel nitrogen austenite single crystals. The velocity of self-consistent motion of the sites where plastic strain during stretching of γ-Fe single crystals is nonuniform was determined as a function of the strain hardening coefficient and deformation mechanism.     

Strain Avalanches in Microsized Single Crystals:A Theoretical Study of the Relation between the Avalanche Size and Duration

Single crystal micropillars deform via a sequence of discrete strain avalanches,observed as displacement jumps or stress drops.Here we develop a simple crystal plasticity model to provide a quantitative expression of the relation between avalanche duration and avalanche size.It is found that the avalanche durations in scale with the averaged avalanche sizes only hold for those larger magnitudes.We show that the theoretical predictions are capable of capturing the essential aspects of scaling behaviors from micro-compression tests.     

Shear localization in dynamic deformation of copper single crystals

Dynamic deformation of copper single crystals, especially of fatigued copper single crystals with different orientations, was conducted on a split-Hopkinson pressure bar apparatus. The strain rates were in the range 2???9?×?10³?s^?1. After dynamic deformation, the adiabatic shear bands (ASBs) were examined in a light microscope and SEM. The width and spacing of ASBs formed under different strain rates in a fatigued copper single crystal were measured and the spacing of ASBs is one-order of magnitude smaller than the theoretical predictions. The possible reasons for the discrepancy were discussed. The critical strains for the ASB formation in four different orientated single crystals at stain rate of about 4?×?10³?s^?1 were determined by examining the post-deformation specimens and dynamic stress–strain curves. It is clearly indicated that the critical strains for the ASB formation are orientation-dependent in copper single crystals. A simple microscopic mechanism for ASB formation in fatigued single crystals was proposed.     

Thermodynamic Analysis of the Contributions from Dislocational Substructures to Deformation Processes in Single Crystals of Nickel

A thermodynamic analysis of deformation mechanisms is performed, based on an experimental study of dislocational substructures that form as a result of the deformation of single crystals of nickel at room temperature. It is shown that in single crystals of pure nickel, strain produces a mainly thermal effect. The most important factors responsible for the accumulation of internal energy are elastic and dislocational components.     

Dynamical and spatial aspects of sandpile cellular automata

The Bak, Tang, and Wiesenfeld cellular automaton is simulated in 1, 2, 3, 4, and 5 dimensions. We define a (new) set of scaling exponents by introducing the concept of conditional expectation values. Scaling relations are derived and checked numerically and the critical dimension is discussed. We address the problem of the mass dimension of the avalanches and find that the avalanches are noncompact for dimensions larger than 2. The scaling of the power spectrum derives from the assumption that the instantaneous dissipation rate of the individual avalanches obeys a simple scaling relation. Primarily, the results of our work show that the flow of sand down the slope does not have a 1/f power spectrum in any dimension, although the model does show clear critical behavior with scaling exponents depending on the dimension. The power spectrum behaves as 1/f ² in all the dimensions considered.     

On the localization of plastic flow under compression of NaCl and KCl crystals

The plastic flow localization patterns for alkali halide crystals under compression are investigated. The main spatiotemporal regularities of the strain localization at the stages of deformation hardening in these single crystals are established. The relation is traced between the orientation of localized strain zones and the crystallography of slip systems of the test specimens at the initial stages of plastic deformation. The velocity of motion of localized strain zones under compression is determined.     

The inhomogeneity of plastic deformation

Considerable local strain differences occur in single crystals as a consequence of slip bands. A significant contribution to this phenomenon is the effect of the deformation rate on the inhomogeneity of its distribution. In polycrystalline materials the plastic deformation is affected by grain boundaries and their vicinity as well as by various orientations of single grains in onephase metals and alloys, and by various component properties in multiphase materials. In some cases it has been possible to describe these phenomena by means of micromechanics. Valuable information has also been acquired by means of three-dimensional stereology.     

Corrections to scaling and probability distribution of avalanches for the stochastic Zhang sandpile model

We study the distributions of dissipative and nondissipative avalanches separately in the stochastic Zhang (SP-Z) sandpile in two dimension. We find that dissipative and nondissipative avalanches obey simple power laws and do not have the logarithmic correction, while the avalanche distributions in the Abelian Manna model should include a logarithmic correction. We use the moment analysis to determine the numerical critical exponents of dissipative and nondissipative avalanches, respectively, and find that they are different from the corresponding values in the Abelian Manna model. All these indicate that the stochastic Zhang model and the Abelian Manna model belong to distinct universality classes, which imply that the Abelian symmetry breaking changes the scaling behavior of the avalanches in the case of the stochastic sandpile model.     

Selective excitation of two-wave structure depending on crystal orientation under shock compression

Single crystals subjected to shock compression exhibit responses with distinct two-wave structures for certain crystal orientations. However, little is known to date regarding how the shock response depends on crystal orientation, and especially why the two-wave structure depends on the crystal orientation. In this work, molecular dynamics simulations of shock compressions in copper single crystals are performed to investigate the orientation dependence of shock responses and the corresponding deformation mechanisms. Four copper single crystals with [001], [011], [012], and [123] crystal orientations along the depth direction are investigated. The [011], [012], and [123] crystal orientations of copper single crystals show distinct two-wave structures in their shock responses, while such a two-wave structure in the shock response is not seen for those orientations having a [001] crystal orientation. The potential causes are analyzed by considering the propagation velocities of both elastic and plastic waves. We develop a technique for identifying twin structures in face-centered cubic crystals and this technique can effectively identify the twin structure. The morphology of shock-induced defects(e.g., dislocations and twins) shows the significant dependence of crystal orientation and the mechanisms behind these are discussed in detail. Finally, the Johnson-Cook constitutive model describing dynamic deformations at high temperatures and high strain rates is used to analyze the relationships between the shock responses and microscopic defects. The predictions of the Johnson-Cook constitutive model are consistent with the results of the molecular dynamics simulations.     

Localization of plastic deformation in calcium fluoride crystals at elevated temperatures

The strain distribution was experimentally studied in CaF₂ crystals subjected to compression tests along [110] and [112] at a constant strain rate at temperatures T = 373–1253 K. At T > 845 K, the plastic deformation in deformed samples is found to be strongly localized in narrow bands, where the shear strain reaches several hundred percent. The physical deformation conditions are determined under which the plastic flow loses its stability and, as a result, the deformation is localized. The temperature dependence of the critical stress of the transition to a localized flow is found. A scenario is proposed for the nucleation and development of large localized shears during high-temperature deformation of single crystals.     

dc = 4 is the upper critical dimension for the Bak-Sneppen model

Numerical results are presented indicating d(c) = 4 as the upper critical dimension for the Bak-Sneppen evolution model. This finding agrees with previous theoretical arguments, but contradicts a recent Letter [Phys. Rev. Lett. 80, 5746 (1998)] that placed d(c) as high as d = 8. In particular, we find that avalanches are compact for all dimensions d< or =4 and are fractal for d>4. Under those conditions, scaling arguments predict a d(c) = 4, where hyperscaling relations hold for d< or =4. Other properties of avalanches, studied for 1< or =d< or =6, corroborate this result. To this end, an improved numerical algorithm is presented that is based on the equivalent branching process.     

Mechanoluminescence induced by elastic and plastic deformation of coloured alkali halide crystals at fixed strain rates

Mechanoluminescence (ML) emission from coloured alkali halide crystals takes place during their elastic and plastic deformation. The ML emission during the elastic deformation occurs due to the mechanical interaction between dislocation segments and F-centres, and the ML emission during the plastic deformation takes place due to the mechanical interaction between the moving dislocations and F-centres. In the elastic region, the ML intensity increases linearly with the strain or deformation time, and in this case, the saturation region could not be observed because of the beginning of the plastic deformation before the start of the saturation in the ML intensity. In the plastic region, initially the ML intensity also increases linearly with the strain or deformation time, and later on, it attains a saturation value for large deformation. When the deformation is stopped, initially the ML intensity decreases at a fast rate; later on, it decreases at a slow rate. The decay time for the fast decrease of the ML intensity gives the relaxation time of dislocation segments or pinning time of the dislocations, and the decay time of the slow decrease of the ML intensity gives the diffusion time of holes in the crystals. The saturation value of the ML intensity increases linearly with the strain rate and also with the density of F-centres in the crystals. Initially, the saturation value of the ML intensity increases with increasing temperature, and for higher temperatures the ML intensity decreases with increasing temperature. Therefore, the ML intensity is optimum for a particular temperature of the crystals. From the ML measurements, the relaxation time of dislocation segments, pinning time of dislocations, diffusion time of holes and the energy gap between the bottom of the acceptor dislocation band and interacting F-centre level can be determined. Expressions derived for the ML induced by elastic and plastic deformation of coloured alkali halide crystals at fixed strain rates indicates that the ML intensity depends on the strain, strain rate, density of colour centres, size of crystals, temperature, luminescence efficiency, etc. A good agreement is found between the theoretical and experimental results.     

Scaling laws in granular continuous avalanches in a rotating drum

We study the front shape of avalanches produced in a rotating two-dimensional drum partially filled with small glass beads. We focus our work on the study of the length and shape of granular fronts, in particular how they do scale in terms of the physical parameters involved. A single scaling law for the length is found. This scaling law is also relevant for the behavior of the full shape of the fronts. More than 300 different fronts shape, for different values of the parameters collapse into an universal curve.     

Landslides on sandpiles: Some moment relations in one dimension

Several relations between the structure of stable recurrent states and the statistics of avalanches in a one-dimensional sandpile automaton are derived and numerically verified. In particular, it is shown that the average avalanche size is determined by the second rather than the first moment of the distribution of trough distances. The two moments scale differently with system size, which implies multiscaling for the distribution. Moreover, the scaling of edge events (avalanches which fall off the pile) is shown to differ from that of bulk events (avalanches which remain on the pile).