Effect of architecture disorder on the elastic response of two-dimensional lattice materials.

We examine how disordering joint position influences the linear elastic behavior of lattice materials via numerical simulations in two-dimensional beam networks. Three distinct initial crystalline geometries are selected as representative of mechanically isotropic materials with low connectivity, mechanically isotropic materials with high connectivity, and mechanically anisotropic materials with intermediate connectivity. Introducing disorder generates spatial fluctuations in the elasticity tensor at the local (joint) scale. Proper coarse-graining reveals a well-defined continuum-level scale elasticity tensor. Increasing disorder aids in making initially anisotropic materials more isotropic. The disorder impact on the material stiffness depends on the lattice connectivity: Increasing the disorder softens lattices with high connectivity and stiffens those with low connectivity, without modifying the scaling between elastic modulus and density (linear scaling for high connectivity and cubic scaling for low connectivity). Introducing disorder in lattices with intermediate fixed connectivity reveals both scaling: the linear scaling occurs for low density, the cubic one at high density, and the crossover density increases with disorder. Contrary to classical formulations, this work demonstrates that connectivity is not the sole parameter governing elastic modulus scaling. It offers a promising route to access novel mechanical properties in lattice materials via disordering the architectures.

Controlling crackling dynamics by triggering low-intensity avalanches.

We examine the effect of small, spatially localized excitations applied periodically in different manners, on the crackling dynamics of a brittle crack driven slowly in a heterogeneous solid. When properly adjusted, these excitations are observed to radically modify avalanche statistics and considerably limit the magnitude of the largest events. Surprisingly, this does not require information on the front loading state at the time of excitation; applying it either at a random location or at the most loaded point gives the same results. Subsequently, we unravel how the excitation amplitude, spatial extent, and frequency govern the effect. We find that the excitation efficiency is ruled by a single reduced parameter, namely the injected power per unit front length; the suppression of extreme avalanches is maximum at a well-defined optimal value of this control parameter. analysis opens another way to control the largest events in crackling dynamics. Beyond fracture problems, it may be relevant for crackling systems described by models of the same universality class, such as the wetting of heterogeneous substrates or magnetic walls in amorphous magnets.

Dynamic crack growth along heterogeneous planar interfaces: Interaction with unidimensional strips.

We examine theoretically and numerically fast propagation of a tensile crack along unidimensional strips with periodically evolving toughness. In such dynamic fracture regimes, crack front waves form and transport front disturbances along the crack edge at speed less than the Rayleigh wave speed and depending on the crack speed. In this configuration, standing front waves dictate the spatiotemporal evolution of the local crack front speed, which takes a specific scaling form. Analytical examination of both the short-time and long-time limits of the problem reveals the parameter dependency with strip wavelength, toughness contrast and overall fracture speed. Implications and generalization to unidimensional strips of arbitrary shape are lastly discussed.

Role of particle aggregation in the structure of dried colloidal silica layers.

The process of colloidal drying gives way to particle self-assembly in numerous fields including photonics or biotechnology. Yet, the mechanisms and conditions driving the final particle arrangement in dry colloidal layers remain elusive. Here, we examine how the drying rate selects the nanostructure of thick dried layers in four different suspensions of silica nanospheres. Depending on particle size and dispersity, either an amorphous arrangement, a crystalline arrangement, or a rate-dependent amorphous-to-crystalline transition occurs at the drying surface. Amorphous arrangements are observed in the two most polydisperse suspensions while crystallinity occurs when dispersity is lower. Counter-intuitively in the latter case, a higher drying rate favors ordering of the particles. To complement these measurements and to take stock of the bulk properties of the layer, tests on the layer porosity were undertaken. For all suspensions studied herein, faster drying yields denser dry layers. Crystalline surface arrangement implies large bulk volume fraction (∼0.65) whereas amorphous arrangements can be observed in layers with either low (down to ∼0.53) or high (∼0.65) volume fraction. Lastly, we demonstrate via targeted additional experiments and SAXS measurements, that the packing structure of the layers is mainly driven by the formation of aggregates and their subsequent packing, and not by the competition between Brownian diffusion and convection. This highlights that a second dimensionless ratio in addition to the Peclet number should be taken into account, namely the aggregation over evaporation timescale.

How heat controls fracture: the thermodynamics of creeping and avalanching cracks.

While of paramount importance in material science, the dynamics of cracks still lacks a complete physical explanation. The transition from their slow creep behavior to a fast propagation regime is a notable key, as it leads to full material failure if the size of a fast avalanche reaches that of the system. We here show that a simple thermodynamics approach can actually account for such complex crack dynamics, and in particular for the non-monotonic force-velocity curves commonly observed in mechanical tests on various materials. We consider a thermally activated failure process that is coupled with the production and the diffusion of heat at the fracture tip. In this framework, the rise in temperature only affects the sub-critical crack dynamics and not the mechanical properties of the material. We show that this description can quantitatively reproduce the rupture of two different polymeric materials (namely, the mode I opening of polymethylmethacrylate (PMMA) plates, and the peeling of pressure sensitive adhesive (PSA) tapes), from the very slow to the very fast fracturing regimes, over seven to nine decades of crack propagation velocities. In particular, the fastest regime is obtained with an increase of temperature of thousands of Kelvins, on the molecular scale around the crack tip. Although surprising, such an extreme temperature is actually consistent with different experimental observations that accompany the fast propagation of cracks, namely, fractoluminescence (i.e., the emission of visible light during rupture) and a complex morphology of post-mortem fracture surfaces, which could be due to the sublimation of bubbles.

Role of the Crystal Lattice Structure in Predicting Fracture Toughness.

We examine the atomistic scale dependence of a material's resistance to failure by numerical simulations and analytical analysis in electrical analogs of brittle crystals. We show that fracture toughness depends on the lattice geometry in a way incompatible with Griffith's relationship between fracture and free surface energy. Its value finds its origin in the matching between the continuum displacement field at the engineering scale, and the discrete nature of solids at the atomic scale. The generic asymptotic form taken by this field near the crack tip provides a solution for this matching, and subsequently a way to predict toughness from the atomistic parameters with application to graphene.

Seismiclike organization of avalanches in a driven long-range elastic string as a paradigm of brittle cracks.

Crack growth in heterogeneous materials sometimes exhibits crackling dynamics, made of successive impulselike events with specific scale-invariant time and size organization reminiscent of earthquakes. Here, we examine this dynamics in a model which identifies the crack front with a long-range elastic line driven in a random potential. We demonstrate that, under some circumstances, fracture grows intermittently, via scale-free impulse organized into aftershock sequences obeying the fundamental laws of statistical seismology. We examine the effects of the driving rate and system overall stiffness (unloading factor) onto the scaling exponents and cutoffs associated with the time and size organization. We unravel the specific conditions required to observe a seismiclike organization in the crack propagation problem. Beyond failure problems, implications of these results to other crackling systems are finally discussed.

Crack growth in heterogeneous brittle solids: intermittency, crackling and induced seismicity.

Crack growth is the basic mechanism leading to the failure of brittle materials. Engineering addresses this problem within the framework of continuum mechanics, which links deterministically the crack motion to the applied loading. Such an idealization, however, fails in several situations and in particular cannot capture the highly erratic (earthquake-like) dynamics sometimes observed in slowly fracturing heterogeneous solids. Here, we examine this problem by means of innovative experiments of crack growth in artificial rocks of controlled microstructure. The dynamical events are analysed at both global and local scales, from the time fluctuation of the spatially averaged crack speed and the induced acoustic emission, respectively. Their statistics are characterized and compared with the predictions of a recent approach mapping fracture onset to the depinning of an elastic interface. Finally, the overall time-size organization of the events is characterized to shed light on the mechanisms underlying the scaling laws observed in seismology.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.

Highly porous layers of silica nanospheres sintered by drying: scaling up of the elastic properties of the beads to the macroscopic mechanical properties.

Layers obtained by drying a colloidal dispersion of silica spheres are found to be a good benchmark to test the elastic behaviour of porous media, in the challenging case of high porosities and nano-sized microstructures. Classically used for these systems, Kendall's approach explicitly considers the effect of surface adhesive forces onto the contact area between the particles. This approach provides the Young's modulus using a single adjustable parameter (the adhesion energy) but provides no further information on the tensorial nature and possible anisotropy of elasticity. On the other hand, homogenization approaches (e.g. rule of mixtures, and Eshelby, Mori-Tanaka and self-consistent schemes), based on continuum mechanics and asymptotic analysis, provide the stiffness tensor from the knowledge of the porosity and the elastic constants of the beads. Herein, the self-consistent scheme accurately predicts both bulk and shear moduli, with no adjustable parameter, provided the porosity is less than 35%, for layers composed of particles as small as 15 nm in diameter. Conversely, Kendall's approach is found to predict the Young's modulus over the full porosity range. Moreover, the adhesion energy in Kendall's model has to be adjusted to a value of the order of the fracture energy of the particle material. This suggests that sintering during drying leads to the formation of covalent siloxane bonds between the particles.

Aftershock sequences and seismic-like organization of acoustic events produced by a single propagating crack.

Brittle fractures of inhomogeneous materials like rocks, concrete, or ceramics are of two types: Nominally brittle and driven by the propagation of a single dominant crack or quasi-brittle and resulting from the accumulation of many microcracks. The latter goes along with acoustic noise, whose analysis has revealed that events form aftershock sequences obeying characteristic laws reminiscent of those in seismology. Yet, their origin lacks explanation. Here we show that such a statistical organization is not only specific to the multi-cracking situations of quasi-brittle failure and seismology, but also rules the acoustic events produced by a propagating crack. This simpler situation has permitted us to relate these laws to the overall scale-free distribution of inter-event time and energy and to uncover their selection by the crack speed. These results provide a comprehensive picture of how acoustic events are organized upon material failure in the most fundamental of fracture states: single propagating cracks.

Finite size effect on the structural and magnetic properties of MnAs/GaAs(001) patterned microstructures thin films.

MnAs epitaxial thin films on GaAs(001) single crystalline substrates crystallize at room temperature (RT) in a mixture of two crystalline phases with distinct magnetic properties, organized as stripes along the MnAs [0001] direction. This particular morphology is driven by anisotropic epitaxial strain. We elucidate here the physical mechanisms at the origin of size reduction effect on the MnAs crystalline phase transition. We investigated the structural and magnetic changes in MnAs patterned microstructures (confined geometry) when the lateral dimension is reduced to values close to the periodicity and width of the stripes observed in continuous films. The effects of the microstructure's lateral size, shape and orientation (with respect to the MnAs [Formula: see text] direction) were characterized by local probe synchrotron X-ray diffraction (µ-XRD) using a focused X-ray beam, X-ray Magnetic Circular Dichroïsm - Photo Emission Electron Microscopy (XMCD-PEEM) and Low Energy Electron Microscopy (LEEM). Changes in the transition temperature and the crystalline phase distribution inside the microstructures are evidenced and quantitatively measured. The effect of finite size and strain relaxation on the magnetic domain structure is also discussed. Counter-intuitively, we demonstrate here that below a critical microstructure size, bulk MnAs structural and magnetic properties are restored. To support our observations we developed, tested and validated a model based on the size-dependence of the elastic energy and strain relaxation to explain this phase re-distribution in laterally confined geometry.

Understanding fast macroscale fracture from microcrack post mortem patterns.

Dynamic crack propagation drives catastrophic solid failures. In many amorphous brittle materials, sufficiently fast crack growth involves small-scale, high-frequency microcracking damage localized near the crack tip. The ultrafast dynamics of microcrack nucleation, growth, and coalescence is inaccessible experimentally and fast crack propagation was therefore studied only as a macroscale average. Here, we overcome this limitation in polymethylmethacrylate, the archetype of brittle amorphous materials: We reconstruct the complete spatiotemporal microcracking dynamics, with micrometer/nanosecond resolution, through post mortem analysis of the fracture surfaces. We find that all individual microcracks propagate at the same low, load-independent velocity. Collectively, the main effect of microcracks is not to slow down fracture by increasing the energy required for crack propagation, as commonly believed, but on the contrary to boost the macroscale velocity through an acceleration factor selected on geometric grounds. Our results emphasize the key role of damage-related internal variables in the selection of macroscale fracture dynamics.

Origin and tailoring of the antiferromagnetic domain structure in α-Fe2O3 thin films unraveled by statistical analysis of dichroic spectromicroscopy (x-ray photoemission electron microscopy) images.

The magnetic microstructure and domain wall distribution of antiferromagnetic α-Fe2O3 epitaxial layers is determined by statistical image analyses. Using dichroic spectromicroscopy images, we demonstrate that the domain structure is statistically invariant with thickness and that the antiferromagnetic domain structure of the thin films is inherited from the ferrimagnetic precursor layer one, even after complete transformation into antiferromagnetic α-Fe2O3. We show that modifying the magnetic domain structure of the precursor layer is a genuine way to tune the magnetic domain structure and domain walls of the antiferromagnetic layers.

Transient damage spreading and anomalous scaling in mortar crack surfaces.

The scaling properties of a post-mortem mortar crack surface are investigated. The root mean square of the height fluctuations is found to obey anomalous scaling properties, but with three exponents, two of them characterizing the local roughness ( zeta approximately 0.79 and zetae approximately 0.41 ) and the third one driving the global roughness (zetag approximately 1.60) . The critical exponent zeta approximately 0.79 is conjectured to reflect damage screening occurring for length scales smaller than the process zone size, while the exponent zetae approximately 0.41 characterizes roughness at larger length scales, i.e., at length scales where the material can be considered as linear elastic. Finally, we argue that the global roughness exponent could be material dependent contrary to both local roughness exponents ( zeta approximately 0.8 and zetae approximately 0.4 ) which can be considered as universal.