Deformation of Crystals: Connections with Statistical Physics

Sethna, James P.; Bierbaum, Matthew; Dahmen, Karin A.; Goodrich, Carl P.; Greer, Julia R.; Hayden, Lorien X.; Kent-Dobias, Jaron; Lee, Edward D.; Liarte, Danilo B.; Ni, Xiaoyue; Quinn, Katherine N.; Raju, Archishman; Rocklin, D. Zeb; Shekhawat, Ashivni; Zapperi, Stefano

doi:10.1146/annurev-matsci-070115-032036

Cited by 79 publications

(76 citation statements)

References 156 publications

(202 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The distribution of dislocations and grain boundaries and their motion play an important role in materials physics as they determine many material properties and response, especially in polycrystalline and heteroepitaxial systems. A great deal of research has been devoted to the study of such systems to better understand the interplay between the many disparate length scales involved (Rollett et al, 2015, Sethna et al, 2017. Microscopic theories, such as Density Functional Theory and Molecular Dynamics, provide detailed descriptions at the microscopic scale, but are unfortunately restricted to relatively small length and time scales.…”

Section: Introductionmentioning

confidence: 99%

A coarse-grained phase-field crystal model of plastic motion

Salvalaglio¹,

Angheluta²,

Huang³

et al. 2020

Journal of the Mechanics and Physics of Solids

View full text Add to dashboard Cite

The phase-field crystal model in an amplitude equation approximation is shown to provide an accurate description of the deformation field in defected crystalline structures, as well as of dislocation motion. We analyze in detail stress regularization at a dislocation core given by the model, and show how the Burgers vector density can be directly computed from the topological singularities of the phase-field amplitudes. Distortions arising from these amplitudes are then supplemented with non-singular displacements to enforce mechanical equilibrium. This allows for a consistent separation of plastic and elastic time scales in this framework. A finite element method is introduced to solve the combined amplitude and elasticity equations, which is applied to a few prototypical configurations in two spatial dimensions for a crystal of triangular lattice symmetry: i) the stress field induced by an edge dislocation with an analysis of how the amplitude equation regularizes stresses near the dislocation core, ii) the motion of a dislocation dipole as a result of its internal interaction, and iii) the shrinkage of a rotated grain. We compare our results with those given by other extensions of classical elasticity theory, such as strain-gradient elasticity and methods based on the smoothing of Burgers vector densities near defect cores.

show abstract

Section: Introductionmentioning

confidence: 99%

A coarse-grained phase-field crystal model of plastic motion

Salvalaglio¹,

Angheluta²,

Huang³

et al. 2020

Journal of the Mechanics and Physics of Solids

View full text Add to dashboard Cite

show abstract

“…Here, we provide a way that can be used, in principle, to estimate the probability of quenched microstates as a function of material parameters (plastic strain, size, and hardening coefficients). 2 The evidence for quenched disorder in initial defect microstructures has been accumulated through observations of abrupt plastic events or material-crackling noise in a large variety of materials, such as FCC and BCC crystals, [3][4][5][6] amorphous solids 7 and also earthquake geological faults. 8,9 This crackling noise 10 has been commonly explained by random field models 11,12 or interface depinning ones, [13][14][15][16][17][18] where the major component is homogeneous solid elasticity, but also a spatially inhomogeneous and random distribution of local, quenched disorder (typically entering local flow stress information) 4,17,[19][20][21] and the allowed microstates are characterized by its stress and strain and minimize the elastic energy functional.…”

Section: Introductionmentioning

confidence: 99%

“…However, the major concern has been the fact that while homogeneous elastic properties are relatively straightforward to measure and test at virtually any scale, 22 the model distribution of local, quenched disorder is elusive, despite its commonly observed signature response of stochastic plastic bursts. [3][4][5]7 In this paper, we propose a feasible approach to "learn" the quenched disorder distributions directly from load-response timeseries: We argue that the full characteristics of the timeseries may unveil the information on the form of the quenched disorder distribution which is not available through typical temporally local observables (such as abrupt event size/duration). 23 While the major motivation of this work stems from plastic deformation, this method is generally applicable across crackling noise phenomena, defined through timeseries of an applied field (magnetic field, force, stress) and the associated response variable (magnetization, displacement, and strain).…”

Section: Introductionmentioning

confidence: 99%

“…a Uniaxial stress-strain curves have been shown to be increasingly stochastic -with clear bursts-and with higher apparent strength, as the sample/probe volume decreases, in the range where the probed volume has effective diameter 0.5, 10, or 100 μm. [3][4][5]7 The yield stress in such samples ranges from 50 to 500 MPa. (inset): Avalanche bursts, quantified through their strain magnitude S, have been shown to follow power-law distributions with a cutoff that decreases with sample volume.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Learning local, quenched disorder in plasticity and other crackling noise phenomena

Papanikolaou

2018

npj Comput Mater

View full text Add to dashboard Cite

When far from equilibrium, many-body systems display behavior that strongly depends on the initial conditions. A characteristic such example is the phenomenon of plasticity of crystalline and amorphous materials that strongly depends on the material history. In plasticity modeling, the history is captured by a quenched, local and disordered flow stress distribution. While it is this disorder that causes avalanches that are commonly observed during nanoscale plastic deformation, the functional form and scaling properties have remained elusive. In this paper, a generic formalism is developed for deriving local disorder distributions from fieldresponse (e.g., stress/strain) timeseries in models of crackling noise. We demonstrate the efficiency of the method in the hysteretic random-field Ising model and also, models of elastic interface depinning that have been used to model crystalline and amorphous plasticity. We show that the capacity to resolve the quenched disorder distribution improves with the temporal resolution and number of samples.

show abstract

“…Since dislocation energies are strongly coupled to their atomic environment, a more realistic picture taking into account viscoelastic effects suggests that some irreversible local deformation processes even exist at low deformation . In this respect, molecular dynamics (MD) studies appear to be an attractive way to characterize the very local deformation mechanisms in both elastic and plastic regimes, although limited in size (typically tens of nanometers) and time (microseconds).…”

Section: Introductionmentioning

confidence: 99%