Machine learning dislocation density correlations and solute effects in Mg-based alloys

Magnesium alloys, among the lightest structural materials, represent excellent candidates for lightweight applications. However, industrial applications remain limited due to relatively low strength and ductility. Solid solution alloying has been shown to enhance Mg ductility and formability at relatively low concentrations. Zn solutes are significantly cost effective and common. However, the intrinsic mechanisms by which the addition of solutes leads to ductility improvement remain controversial. Here, by using a high throughput analysis of intragranular characteristics through data science approaches, we study the evolution of dislocation density in polycrystalline Mg and also, Mg-Zn alloys. We apply machine learning techniques in comparing electron back-scatter diffraction (EBSD) images of the samples before/after alloying and before/after deformation to extract the strain history of individual grains, and to predict the dislocation density level after alloying and after deformation. Our results are promising given that moderate predictions (coefficient of determination [Formula: see text] ranging from 0.25 to 0.32) are achieved already with a relatively small dataset ([Formula: see text] 5000 sub-millimeter grains).

Path (un)predictability of two interacting cracks in polycarbonate sheets using Digital Image Correlation

Crack propagation is tracked here with Digital Image Correlation analysis in the test case of two cracks propagating in opposite directions in polycarbonate, a material with high ductility and a large Fracture Process Zone (FPZ). Depending on the initial distances between the two crack tips, one may observe different complex crack paths with in particular a regime where the two cracks repel each other prior to being attracted. We show by strain field analysis how this can be understood according to the principle of local symmetry: the propagation is to the direction where the local shear - mode K_II in fracture mechanics language - is zero. Thus the interactions exhibited by the cracks arise from symmetry, from the initial geometry, and from the material properties which induce the FPZ. This complexity makes any long-range prediction of the path(s) impossible.

Boundary lubrication with a liquid crystal monolayer

We study boundary lubrication characteristics of a liquid crystal (LC) monolayer sheared between two crystalline surfaces by nonequilibrium molecular dynamics simulations, using a simplified rigid bead-necklace model of the LC molecules. We consider LC monolayers confined by surfaces with three different atomic structures, subject to different shearing velocities, thus approximating a wide variety of materials and driving conditions. The time dependence of the friction force is studied and correlated with that of the orientational order exhibited by the LC molecules, arising from the competition between the effect of the structure of the confining surfaces and that of the imposed sliding direction. We show that the observed stick-slip events for low shear rates involve order-disorder transitions, and that the LC monolayer no longer has enough time to reorder at high shear rates, resulting in a smooth sliding regime. An irregular stick-slip phase between the regular stick-slip and smooth sliding is observed for intermediate shear rates regardless of the surface structure.

Evolution of grain contacts in a granular sample under creep and stress relaxation

This article deals with the characterization, using an acoustic technique, of the mechanical behavior of a dry dense granular medium under quasistatic loading. Ultrasound propagation through the contact-force network supporting the external load offers a noninvasive probe of the viscoelastic properties of such heterogeneous media. First the response of a glass bead packing is studied in an oedometric configuration during creep and relaxation tests. Quasilogarithmic increases of sound velocities are found in both mechanical tests. A model based on the mechanics of microcontacts between rough grains adequately reproduces our experimental results, especially for the evolution of elastic modulus. Another main experimental finding is that collective grain rearrangements within the packing also play a crucial role at the early stage of creep and relaxation.

Modeling the viscosity and aggregation of suspensions of highly anisotropic nanoparticles

The rheology of nanofiber suspensions is studied solving numerically the Population Balance Equations (PBE). To account for the anisotropic nature of nanofibers, a relation is proposed for their hydrodynamic volume. The suspension viscosity is calculated using the computed aggregate size distributions together with the Krieger-Dougherty constitutive equation. The model is fitted to experimental flow curves for Carbon NanoFibers (CNF) and for NanoFibrillated Cellulose (NFC), giving a first estimation of the microscopic anisotropy parameter, and yielding information on the structural properties and rheology of each system.

Creep of a fracture line in paper peeling

The slow motion of a crack line is studied via an experiment in which sheets of paper are split into two halves in a "peel-in-nip" (PIN) geometry under a constant load, in creep. The velocity-force relation is exponential. The dynamics of the fracture line exhibits intermittency, or avalanches, which are studied using acoustic emission. The energy statistics is a power law, with the exponent beta ~ 1.8 +/- 0.1. Both the waiting times between subsequent events and the displacement of the fracture line imply complicated stick-slip dynamics. We discuss the correspondence to tensile PIN tests and other similar experiments on in-plane fracture and the theory of creep for elastic manifolds.

1/f noise and avalanche scaling in plastic deformation

We study the intermittency and noise of dislocation systems undergoing shear deformation. Simulations of a simple two-dimensional discrete dislocation dynamics model indicate that the deformation rate exhibits a power spectrum scaling of the type 1/falpha. The noise exponent is far away from a Lorentzian, with alpha approximately 1.5. This result is directly related to the way the durations of avalanches of plastic deformation activity scale with their size.

Complex networks created by aggregation

We study aggregation as a mechanism for the creation of complex networks. In this evolution process vertices merge together, which increases a number of highly connected hubs. We study a range of complex network architectures produced by the aggregation. Fat-tailed (in particular, scale-free) distributions of connections are obtained for both networks with a finite number of vertices and growing networks. We observe a strong variation of a network structure with growing density of connections and find the phase transition of the condensation of edges. Finally, we demonstrate the importance of structural correlations in these networks.

Temporal and spatial persistence of combustion fronts in paper

The spatial and temporal persistence, or first-return distributions are measured for slow-combustion fronts in paper. The stationary temporal and (perhaps less convincingly) spatial persistence exponents agree with the predictions based on the front dynamics, which asymptotically belongs to the Kardar-Parisi-Zhang universality class. The stationary short-range and the transient behavior of the fronts are non-Markovian, and the observed persistence properties thus do not agree with the predictions based on Markovian theory. This deviation is a consequence of additional time and length scales, related to the crossovers to the asymptotic coarse-grained behavior.

Cluster persistence in one-dimensional diffusion-limited cluster-cluster aggregation

The persistence probability, P(C)(t), of a cluster to remain unaggregated is studied in cluster-cluster aggregation, when the diffusion coefficient of a cluster depends on its size s as D(s) approximately s(gamma). In the mean field the problem maps to the survival of three annihilating random walkers with time-dependent noise correlations. For gamma> or =0 the motion of persistent clusters becomes asymptotically irrelevant and the mean-field theory provides a correct description. For gamma<0 the spatial fluctuations remain relevant and the persistence probability is overestimated by the random walk theory. The decay of persistence determines the small size tail of the cluster size distribution. For 0<gamma<2 the distribution is flat and, surprisingly, independent of gamma.

Acoustic emission from paper fracture

We report tensile failure experiments on paper sheets. The acoustic emission energy and the waiting times between acoustic events follow power-law distributions. This remains true while the strain rate is varied by more than 2 orders of magnitude. The energy statistics has the exponent beta approximately 1.25+/-0.10 and the waiting times the exponent tau approximately 1.0+/-0.1, in particular, for the energy roughly independent of the strain rate. These results do not compare well with fracture models, for (brittle) disordered media, which as such exhibit criticality. One reason may be residual stresses, neglected in most theories.

Persistence in cluster-cluster aggregation

Persistence is considered in one-dimensional diffusion-limited cluster-cluster aggregation when the diffusion coefficient of a cluster depends on its size s as D(s) approximately s(gamma). The probabilities that a site has been either empty or covered by a cluster all the time define the empty and filled site persistences. The cluster persistence gives the probability of a cluster remaining intact. The empty site and cluster persistences are universal whereas the filled site depends on the initial concentration. For gamma>0 the universal persistences decay algebraically with the exponent 2/(2-gamma). For the empty site case the exponent remains the same for gamma<0 but the cluster persistence shows a stretched exponential behavior as it is related to the small s behavior of the cluster size distribution. The scaling of the intervals between persistent regions demonstrates the presence of two length scales: the one related to the distances between clusters and that between the persistent regions.

Interface pinning in spontaneous imbibition

Evaporation and gravity induced pinning in spontaneous imbibition are examined within a phase field formalism. Evaporation is introduced via a nonconserving term and gravity through a convective term that constrains the influx of liquid. Their effects are described by dimensionless coupling constants epsilon and g, respectively. From liquid conservation, the early time behavior of the average interface position follows H(t) approximately t1/2 until a crossover time t*(g,epsilon). After that the pinning height Hp(g,epsilon) is approached exponentially in time, in accordance with mean field theory. The statistical roughness of the interface is described by an exponent chi approximately 1.25 at all stages of the rise, but the dynamic length scale controlling roughness crosses over from xi(x) approximately H1/2 to a time independent pinning length scale xi(p)(epsilon,g).

Susceptibility and percolation in two-dimensional random field Ising magnets

The ground-state structure of the two-dimensional random field Ising magnet is studied using exact numerical calculations. First we show that the ferromagnetism, which exists for small system sizes, vanishes with a large excitation at a random field strength-dependent length scale. This breakup length scale L(b) scales exponentially with the squared random field, exp(A/delta(2)). By adding an external field H, we then study the susceptibility in the ground state. If L>L(b), domains melt continuously and the magnetization has a smooth behavior, independent of system size, and the susceptibility decays as L-2. We define a random field strength-dependent critical external field value +/-H(c)(delta) for the up and down spins to form a percolation type of spanning cluster. The percolation transition is in the standard short-range correlated percolation universality class. The mass of the spanning cluster increases with decreasing Delta and the critical external field approaches zero for vanishing random field strength, implying the critical field scaling (for Gaussian disorder) H(c) approximately (delta-delta(c))(delta), where delta(c)=1.65+/-0.05 and delta=2.05+/-0.10. Below Delta(c) the systems should percolate even when H=0. This implies that even for H=0 above L(b) the domains can be fractal at low random fields, such that the largest domain spans the system at low random field strength values and its mass has the fractal dimension of standard percolation D(f)=91/48. The structure of the spanning clusters is studied by defining red clusters, in analogy to the "red sites" of ordinary site percolation. The sizes of red clusters define an extra length scale, independent of L.

Extremal statistics in the energetics of domain walls

We study at T=0 the minimum energy of a domain wall and its gap to the first excited state, concentrating on two-dimensional random-bond Ising magnets. The average gap scales as deltaE1 approximately L(straight theta)f(N(z)), where f(y) approximately [ln y](-1/2), straight theta is the energy fluctuation exponent, L is the length scale, and N(z) is the number of energy valleys. The logarithmic scaling is due to extremal statistics, which is illustrated by mapping the problem into the Kardar-Parisi-Zhang roughening process. It follows that the susceptibility of domain walls also has a logarithmic dependence on the system size.

Intermittence and roughening of periodic elastic media

We analyze intermittence and roughening of an elastic interface or domain wall pinned in a periodic potential, in the presence of random-bond disorder in 1+1 and 2+1 dimensions. Though the ensemble average behavior is smooth, the typical behavior of a large sample is intermittent, and does not self-average to a smooth behavior. Instead, large fluctuations occur in the mean location of the interface and the onset of interface roughening is via an extensive fluctuation which leads to a jump in the roughness of order lambda, the period of the potential. Analytical arguments based on extreme statistics are given for the number of the minima of the periodicity visited by the interface and for the roughening crossover, which is confirmed by extensive exact ground state calculations.

Dynamic scaling in one-dimensional cluster-cluster aggregation

We study the dynamic scaling properties of an aggregation model in which particles obey both diffusive and driven ballistic dynamics. The diffusion constant and the velocity of a cluster of size s follow D(s) approximately s(gamma) and v(s) approximately s(delta), respectively. We determine the dynamic exponent and the phase diagram for the asymptotic aggregation behavior in one dimension in the presence of mixed dynamics. The asymptotic dynamics is dominated by the process that has the largest dynamic exponent with a crossover that is located at delta=gamma-1. The cluster size distributions scale similarly in all cases but the scaling function depends continuously on gamma and delta. For the purely diffusive case the scaling function has a transition from exponential to algebraic behavior at small argument values as gamma changes sign, whereas in the drift dominated case the scaling function always decays exponentially.

Periodic elastic medium in which periodicity is relevant

We analyze, in both (1+1) and (2+1) dimensions, a periodic elastic medium in which the periodicity is such that at long distances the behavior is always in the random-substrate universality class. This contrasts with the models with an additive periodic potential in which, according to the field-theoretic analysis of Bouchaud and Georges and more recently of Emig and Nattermann, the random manifold class dominates at long distances in (1+1) and (2+1) dimensions. The models we use are random-bond Ising interfaces in hypercubic lattices. The exchange constants are random in a slab of size L(d-1)xlambda and these coupling constants are periodically repeated, with a period lambda, along either 10 or 11 [in (1+1) dimensions] and 100 or 111 [in (2+1) dimensions]. Exact ground-state calculations confirm scaling arguments which predict that the surface roughness w behaves as w approximately L(2/3), L<<L(c) and w approximately L(1/2),L>>L(c) with L(c) approximately lambda(3/2) in (1+1) dimensions, and w approximately L0.42,L<<L(c) and w approximately ln(L),L>>L(c) with L(c) approximately lambda(2. 38) in (2+1) dimensions.

Roughening of a propagating planar crack front

A numerical model of the front of a planar crack propagating between two connected elastic plates is investigated. The plates are modeled as square lattices of elastic beams. The plates are connected by similar but breakable beams with a randomly varying stiffness. The crack is driven by pulling both plates at one end in Mode I at a constant rate. We find zeta=1/3, z=4/3, and beta=1/4 for the roughness, dynamical, and growth exponents, respectively, that describe the front behavior. This is similar to continuum limit analyses based on a perturbative stress-intensity treatment of the front [H. Gao and J. R. Rice, J. Appl. Mech. 56, 828 (1989)]. We discuss the differences to recent experiments.

Scaling of interfaces in brittle fracture and perfect plasticity

The roughness properties of two-dimensional fracture surfaces as created by the slow failure of random fuse networks are considered and compared to yield surfaces of perfect plasticity with similar disorder. By studying systems up to a linear size L=350 it is found that in the cases studied the fracture surfaces exhibit self-affine scaling with a roughness exponent close to 2/3, which is asymptotically exactly true for plasticity though finite-size effects are evident for both. The overlap of yield or minimum energy and fracture surfaces with exactly the same disorder configuration is shown to be a decreasing function of the system size and to be of a rather large magnitude for all cases studied. The typical "overlap cluster" length between pairs of such interfaces converges to a constant with increasing L.

Elasticity of Poissonian fiber networks

An effective-medium model is introduced for the elasticity of two-dimensional random fiber networks. These networks are commonly used as basic models of heterogeneous fibrous structures such as paper. Using the exact Poissonian statistics to describe the microscopic geometry of the network, the tensile modulus can be expressed by a single-parameter function. This parameter depends on the network density and fiber dimensions, which relate the macroscopic modulus to the relative importance of axial and bending deformations of the fibers. The model agrees well with simulation results and experimental findings. We also discuss the possible generalizations of the model.

Energy landscapes in random systems, driven interfaces, and wetting

We discuss the zero-temperature susceptibility of elastic manifolds with quenched randomness. It diverges with system size due to low-lying local minima. The distribution of energy gaps is deduced to be constant in the limit of vanishing gaps by comparing numerics with a probabilistic argument. The typical manifold response arises from a level-crossing phenomenon and implies that wetting in random systems begins with a discrete transition. The associated "jump field" scales as <h> approximately L-5/3 and L-2.2 for (1+1) and (2+1) dimensional manifolds with random bond disorder.

Scaling and noise in slow combustion of paper

We present results of high resolution experiments on kinetic roughening of slow combustion fronts in paper, focusing on short length and time scales. Using three different grades of paper, we find that the combustion fronts show apparent spatial and temporal multiscaling at short scales. The scaling exponents decrease as a function of the order of the corresponding correlation functions. The noise affecting the fronts reveals short range temporal and spatial correlations, and non-Gaussian noise amplitudes. Our results imply that the overall behavior of slow combustion fronts cannot be explained by standard theories of kinetic roughening.