arXiv subjects

Daniel Bonamy

Publications and source records attributed to Daniel Bonamy.

At least 19 recordsLinked to original sources

arXiv2024

Size-dependency and lattice-discreetness effect on fracture toughness in 2D crystals under antiplanar loading

Fracture toughness is the material property characterizing resistance to failure. Predicting its value from the solid structure at the atomistic scale remains elusive, even in the simplest situations of brittle fracture. We report here numerical simulations of crack propagation in two-dimensional fuse networks of different periodic geometries, which are electrical analogs of bidimensional brittle crystals under antiplanar loading. Fracture energy is determined from Griffith's analysis of energy balance during crack propagation, and fracture toughness is determined from fits of the displacement fields with Williams' asymptotic solutions. Significant size dependencies are evidenced in small lattices, with fracture energy and fracture toughness both converging algebraically with system size toward well-defined material-constant values in the limit of infinite system size. The convergence speed depends on the loading conditions and is faster when the symmetry of the considered lattice increases. The material constants at infinity obey Irwin's relation and properly define the material resistance to failure. Their values are approached up to $\sim$ 15 % using the recent analytical method proposed in Nguyen and Bonamy (Phys Rev Lett 123:205503, 2019). Nevertheless, the deviation remains finite and does not vanish when the system size goes to infinity. We finally show that this deviation is a consequence of the lattice discreetness and decreases when the super-singular terms of Williams' solutions (absent in a continuum medium but present here due to lattice discreetness) are taken into account.

cond-mat.soft↗

arXiv2022

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 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.

cond-mat.soft↗

arXiv2020

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 spatio-temporal 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.

cond-mat.stat-mech↗

arXiv2020

Role of particle aggregation on the structure of dried colloidal silica layers

The process of colloidal drying gives way to particle self-assembly in numerous elds including photonics or biotechnology. Yet, the mechanisms and conditions driving the nal particle arrangement in dry colloidal layers remain elusive. Here, we examine how the drying rate selects the nanostructure of thick dried layers in four dierent 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 ($\sim$ 0.65) whereas amorphous arrangements can be observed in layers with either low (down to $\sim$ 0.53) or high ($\sim$ 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 diusion 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.

cond-mat.soft↗

arXiv2020

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. This analysis opens a new way to control 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.

cond-mat.stat-mech↗

arXiv2019

Role of crystal lattice structure in predicting fracture toughness

We examine the atomistic scale dependence of 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.

cond-mat.mtrl-sci↗

arXiv2019

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.

cond-mat.soft↗

arXiv2019

Seismic-like organization of avalanches in a driven long-range elastic string as a paradigm of brittle cracks

Very often damage and fracture in heterogeneous materials exhibit bursty dynamics made of successive impulse-like events which form characteristic aftershock sequences obeying specific scaling laws initially derived in seismology: Gutenberg-Richter law, productivity law, B\r{a}th's law and Omori-Utsu law. We show here how these laws naturally arise in the model of the long-range elastic depinning interface used as a paradigm to model crack propagation in heterogeneous media. We unravel the specific conditions required to observe this seismic-like organization in the crack propagation problem. Beyond failure problems, the results extend to a variety of situations described by models of the same universality class: contact line motion in the wetting problem or domain wall motion in dirty ferromagnet, to name a few.

cond-mat.stat-mech↗

arXiv2018

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 analyzed 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 with the depinning of an elastic interface. Finally, the overall time-size organization of the events are characterized to shed light on the mechanisms underlying the scaling laws observed in seismology.

cond-mat.stat-mech↗

arXiv2018

Highly porous layers of silica nano-spheres sintered by drying: Scaling up of the elastic properties from 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 explicitely 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, 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.

cond-mat.soft↗

arXiv2018

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.

cond-mat.stat-mech↗

arXiv2017

Dynamics of cracks in disordered materials

Predicting when rupture occurs or cracks progress is a major challenge in numerous elds of industrial, societal and geophysical importance. It remains largely unsolved: Stress enhancement at cracks and defects, indeed, makes the macroscale dynamics extremely sensitive to the microscale material disorder. This results in giant statistical uctuations and non-trivial behaviors upon upscaling dicult to assess via the continuum approaches of engineering. These issues are examined here. We will see: How linear elastic fracture mechanics sidetracks the diculty by reducing the problem to that of the propagation of a single crack in an eective material free of defects, How slow cracks sometimes display jerky dynamics, with sudden violent events incompatible with the previous approach, and how some paradigms of statistical physics can explain it, How abnormally fast cracks sometimes emerge due to the formation of microcracks at very small scales.

cond-mat.soft↗

arXiv2016

Euler-like modelling of dense granular flows: application to a rotating drum

General conservation equations are derived for 2D dense granular flows from the Euler equation within the Boussinesq approximation. In steady flows, the 2D fields of granular temperature, vorticity and stream function are shown to be encoded in two scalar functions only. We checked such prediction on steady surface flows in a rotating drum simulated through the Non-Smooth Contact Dynamics method. This result is non trivial because granular flows are dissipative and therefore not necessarily compatible with Euler equation. Finally, we briefly discuss some possible ways to predict theoretically these two functions using statistical mechanics.

cond-mat.stat-mech↗

arXiv2016

Role of evaporation rate on the particle organization and crack patterns obtained by drying a colloidal layer

-- A scientific hurdle in manufacturing solid films by drying colloidal layers is preventing them from fracturing. This paper examines how the drying rate of colloidal liquids influences the particle packing at the nanoscale in correlation with the crack patterns observed at the macroscale. Increasing the drying rate results in more ordered, denser solid structures, and the dried samples have more cracks.Yet, introducing a holding period (at a prescribed point) during the drying protocol results in a more disordered solid structure with significantly less cracks. To interpret these observations, this paper conjectures that a longer drying protocol favors the formation of aggregates. It is further argued that the number and size of the aggregates increase as the drying rate decreases. This results in the formation of a more disordered, porous film from the viewpoint of the particle packing, and a more resistant film, i.e. less cracks, from the macroscale viewpoint.

cond-mat.soft↗

arXiv2015

Atomic-scale avalanche along a dislocation in a random alloy

The propagation of dislocations in random crystals is evidenced to be governed by atomic-scale avalanches whose the extension in space and the time intermittency characterizingly diverge at the critical threshold. Our work is the very first atomic-scale evidence that the paradigm of second order phase transitions applies to the depinning of elastic interfaces in random media.

cond-mat.mtrl-sci↗

arXiv2015

Effect of the porosity on the fracture surface roughness of sintered materials: From anisotropic to isotropic self-affine scaling

To unravel how the microstructure affects the fracture surface roughness in heterogeneous brittle solids like rocks or ceramics, we characterized the roughness statistics of post-mortem fracture surfaces in home-made materials of adjustable microstructure length-scale and porosity, obtained by sintering monodisperse polystyrene beads. Beyond the characteristic size of disorder, the roughness profiles are found to exhibit self-affine scaling features evolving with porosity. Starting from a null value and increasing the porosity, we quantitatively modify the self-affine scaling properties from anisotropic (at low porosity) to isotropic (for porosity larger than 10 %).

cond-mat.mtrl-sci↗

arXiv2014

Fluctuations of global energy release and crackling in nominally brittle heterogeneous fracture

The temporal evolution of mechanical energy and spatially-averaged crack speed are both monitored in slowly fracturing artificial rocks. Both signals display an irregular burst-like dynamics, with power-law distributed fluctuations spanning a broad range of scales. Yet, the elastic power released at each time step is proportional to the global velocity all along the process, which enables defining a material-constant fracture energy. We characterize the intermittent dynamics by computing the burst statistics. This latter displays the scale-free features signature of crackling dynamics, in qualitative but not quantitative agreement with the depinning interface models derived for fracture problems. The possible sources of discrepancies are pointed out and discussed.

cond-mat.stat-mech↗

arXiv2013

Crackling vs. continuum-like dynamics in brittle failure

We study how the loading rate, specimen geometry and microstructural texture select the dynamics of a crack moving through an heterogeneous elastic material in the quasi-static approximation. We find a transition, fully controlled by two dimensionless variables, between dynamics ruled by continuum fracture mechanics and crackling dynamics. Selection of the latter by the loading, microstructure and specimen parameters is formulated in terms of scaling laws on the power spectrum of crack velocity. This analysis defines the experimental conditions required to observe crackling in fracture. Beyond failure problems, the results extend to a variety of situations described by models of the same universality class, e.g. the dynamics in wetting or of domain walls in amorphous ferromagnets.

cond-mat.stat-mech↗