A continuum model of crack propagation is presented and discussed. We obtain steady state solutions with a self-consistently selected propagation velocity and shape of the crack, provided that elastodynamic and viscoelastic effects are taken into account. Two different mechanism of crack propagation, a first order phase transition and surface diffusion are considered, and we discuss different loading modes. The arising free boundary problems are solved by phase field methods and a sharp interface approach using a multipole expansion technique.
New monolayer 2D carbon structures, namely qHPC60 and qTPC60, were recently synthesized by covalently bonding C60 polymers. Here, we carried out Reactive (ReaxFF) molecular dynamics simulations to study the thermodynamic stability and fracture patterns of qHPC60 and qTPC60. Our results showed that these structures present similar thermal stability, with sublimation points of 3898K and 3965K, respectively. qHPC60 and qTPC60 undergo an abrupt structural transition becoming totally fractured after a critical strain threshold. The crack propagation is linear (non-linear) for qHPC60 (qTPC60). The e…
Femtosecond laser written patterns at the surface of brittle materials may show a regenerative random transition from self-organized to disordered structures. Here, we show that this random intermittent behaviour carries relevant fracture statistics information, such as the so-called Weibull parameters. Furthermore, we draw a phenomenological analogy with idle and busy periods arising in queueing systems that we used to establish that these successive laser generated cycles are statistically independent. Based on this analogy and together with microscopic observations, we propose an experiment…
In spite of the apparent similarity of micro-branching instabilities in different brittle materials, we propose that the physics determining the typical length- and time-scales characterizing the post-instability patterns differ greatly from material to material. We offer a scaling theory connecting the pattern characteristics to material properties (like molecular weight) in brittle plastics like PMMA, and stress the fundamental differences with patterns in glass which are crucially influenced by 3-dimensional dynamics. In both cases the present ab-initio theoretical models are still too far …
On the Thermomechanical Properties and Fracture Patterns of the Novel Nonbenzenoid Carbon Allotrope (Biphenylene Network): A Reactive Molecular Dynamics Study
Slow crack propagation in ductile, and in certain brittle materials, appears to take place via the nucleation of voids ahead of the crack tip due to plastic yields, followed by the coalescence of these voids. Post mortem analysis of the resulting fracture surfaces of ductile and brittle materials on the $μ$m-mm and the nm scales respectively, reveals self-affine cracks with anomalous scaling exponent $ζ\approx 0.8$ in 3-dimensions and $ζ\approx 0.65$ in 2-dimensions. In this paper we present an analytic theory based on the method of iterated conformal maps aimed at modelling the void formation…
We study the geometrical characteristic of quasi-static fractures in disordered media, using iterated conformal maps to determine the evolution of the fracture pattern. This method allows an efficient and accurate solution of the Lamé equations without resorting to lattice models. Typical fracture patterns exhibit increased ramification due to the increase of the stress at the tips. We find the roughness exponent of the experimentally relevant backbone of the fracture pattern; it crosses over from about 0.5 for small scales to about 0.75 for large scales, in excellent agreement with experiment…
The Maximum Energy Dissipation Principle (MEDP) for dynamics fracture, far from equilibrium, proposed by Slepyan was modified. This modification includes a decoupling between the injected and dissipated energy by adding of a time delay and a description of the ruggedness produced by dissipation patterns. A time delayed energy conservation equation is deduced and dynamical equations that describe the dynamical system evolution were obtained in analogous way to the Slepyan's calculations. The conditions for the rising of the instability process were presented by a bifurcation map. These results …
We carried out fully-atomistic reactive molecular dynamics simulations to study the elastic properties and fracture patterns of transition metal dichalcogenide (TMD) MoX2 (X=S, Se, Te) membranes, in their 2H and 1T phases, within the framework of the Stillinger-Weber potential. Results showed that the fracture mechanism of these membranes occurs through a fast crack propagation followed by their abrupt rupture into moieties. As a general trend, the translated arrangement of the chalcogen atoms in the 1T phase contributes to diminishing their structural stability when contrasted with the 2H one…
Fracture in quasi-statically driven systems is studied by means of a discrete spring-block model. Developed from close comparison with desiccation experiments, it describes crack formation induced by friction on a substrate. The model produces cellular, hierarchical patterns of cracks, characterized by a mean fragment size linear in the layer thickness, in agreement with experiments. The selection of a stationary fragment size is explained by exploiting the correlations prior to cracking. A scaling behavior associated with the thickness and substrate coupling, derived and confirmed by simulati…
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 ultra-fast 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 spatio-temporal microcracking dynamics, with micrometer / nanose…
Graphene nanowiggles (GNW) are graphene-based nanostructures obtained by making alternated regular cuts in pristine graphene nanoribbons. GNW were recently synthesized and it was demonstrated that they exhibit tunable electronic and magnetic properties by just varying their shape. Here, we have investigated the mechanical properties and fracture patterns of a large number of GNW of different shapes and sizes using fully atomistic reactive molecular dynamics simulations. Our results show that the GNW mechanical properties are strongly dependent on its shape and size and, as a general trend narr…
Recently, a new two-dimensional carbon allotrope called pentagraphene (PG) was proposed. PG exhibits mechanical and electronic interesting properties, including typical band gap values of semiconducting materials. PG has a Cairo-tiling-like 2D lattice of non coplanar pentagons and its mechanical properties have not been yet fully investigated. In this work, we combined density functional theory (DFT) calculations and reactive molecular dynamics (MD) simulations to investigate the mechanical properties and fracture patterns of PG membranes under tensile strain. We show that PG membranes can hol…
Exploring the Elastic Properties and Fracture Patterns of Me-Graphene Monolayers and Nanotubes through Reactive Molecular Dynamics Simulations
University of Brasília（巴西利亚大学）；Federal Institute of Education, Science and Technology of Piauí – IFPI（皮奥伊联邦教育、科学和技术学院）；Applied Physics Department, “Gleb Wataghin” Institute of Physics - IFGW, University of Campinas – UNICAMP（坎皮纳斯大学格莱布·瓦塔金物理研究所应用物理系）；Department of Physics, Federal University of Piauí（皮奥伊联邦大学物理系）；Center for Computing in Engineering & Sciences, Unicamp（坎皮纳斯大学工程与科学计算中心）；University of Brasília, Institute of Physics（巴西利亚大学物理研究所）
Mechanical failure of an ideal crystal is dictated either by an elastic instability or a soft-mode instability. We show that the ideal strength measurement of graphene based on nano-indentation experiments \cite{lee2008measurement, lee2013high}, however, indicates an anomaly: the inferred strain beneath the diamond indenter at the failure load is anomalously large compared to the fracture strain predicted by soft-mode analysis or acoustic analysis. Here we present a systematic investigation - based on multi-scale modeling combining the results of continuum, atomistic, and quantum calculations;…
A study of crack patterns in laponite films of different thickness is presented. Two cracking regimes are observed. The earlier with a higher rate of desiccation and shrinking has predominantly four-fold vertices in the crack network, while the later regime has less volume shrinking and forms mainly three-fold vertices. The pattern shows a self-similarity under coarse-graining. The graph of area covered by the cracks versus minimum crack-width resolved, scales with the film thickness. Curves representing crack area for different thickness can thus be made to collapse onto a single curve.
The problem of crack pattern formation due to thermal shock loading at the surface of half-space is solved numerically using two-dimensional boundary element method. The results of numerical simulations with 100-200 random simultaneously growing and interacting cracks are used to obtain scaling relations for crack length and spacing. The numerical results predict that such process of pattern formation with quasi-static crack growth is not stable and at some point the excess energy leads to unstable propagation of one of the longest crack. The onset of instability has also been determined from …
A meso-scale analysis is performed to determine the fracture process zone of concrete subjected to uniaxial tension. The meso-structure of concrete is idealised as stiff aggregates embedded in a soft matrix and separated by weak interfaces. The mechanical response of the matrix, the inclusions and the interface between the matrix and the inclusions is modelled by a discrete lattice approach. The inelastic response of the lattice elements is described by a damage approach, which corresponds to a continuous reduction of the stiffness of the springs. The fracture process in uniaxial tension is ap…
Dynamic fracture in a wide class of materials reveals "fracture energy" $Γ$ much larger than the expected nominal surface energy due to the formation of two fresh surfaces. Moreover, the fracture energy depends on the crack velocity, $Γ=Γ(v)$. We show that a simple dynamical theory of visco-plasticity coupled to asymptotic pure linear-elasticity provides a possible explanation to the above phenomena. The theory predicts tip blunting characterized by a dynamically determined crack tip radius of curvature. In addition, we demonstrate velocity selection for cracks in fixed-grip strip geometry acc…
Thermal fracture is prevalent in many engineering problems and is one of the most devastating defects in metal additive manufacturing. Due to the interactive underlying physics involved, the computational simulation of such a process is challenging. In this work, we propose a thermo-mechanical phase-field fracture model, which is based on a thermodynamically consistent derivation. The influence of different coupling terms such as damage-informed thermomechanics and heat conduction and temperature-dependent fracture properties, as well as different phase-field fracture formulations, are discuss…
Experiments in quasi 2-dimensional geometry (Hele Shaw cells) in which a fluid is injected into a visco-elastic medium (foam, clay or associating-polymers) show patterns akin to fracture in brittle materials, very different from standard Laplacian growth patterns of viscous fingering. An analytic theory is lacking since a pre-requisite to describing the fracture of elastic material is the solution of the bi-Laplace rather than the Laplace equation. In this Letter we close this gap, offering a theory of bi-Laplacian growth patterns based on the method of iterated conformal maps.
We prepared thin layers of amorphous silicon by deposition of a liquid-phase polysilane precurser on glass substrate. Raman scattering provides evidence for residual tensile stress in the silicon, which is evaluated quantitatively. Under treatment with hydrofluoric acid, this stress leads to spiral cracks in the silicon. We explain the process of crack formation and examine this phenomenon both analytically and numerically, the latter with the finite element method (FEM). The FEM yields the geometry correction factor for such spiral cracks in terms of the Griffith criterion. This allows for th…
Fracture mechanics is crucial for many fields of engineering, as precisely predicting failure of structures and parts is required for efficient designs. The simulation of failure processes is, from a mechanical and a numerical point of view, challenging, especially for inhomogeneous materials, where the microstructure influences crack initiation and propagation and leads to complex crack patterns. The phase field method for fracture is a promising approach to encounter such materials since it is able to describe complex fracture phenomena like crack kinking, branching and coalescence. Moreover…
Long-term durability is a major obstacle limiting the widespread use of lithium ion batteries (LIBs) in heavy-duty applications and others demanding extended lifetime. As one of the root causes of degradation and failure of battery performance, the electrode failure mechanisms are still unknown. Here, we reveal the fundamental fracture mechanisms of single-crystal silicon electrodes over extended lithiation/delithiation cycles, using electrochemical testing, microstructure characterization, fracture mechanics, and finite element analysis. Anisotropic lithium invasion causes crack initiation pe…
Moiré patterns can lead to fundamentally new electronic behavior when formed between two atomic lattices slightly shifted with respect to each other. A solid is however not just characterized by the atomic lattice, but also by charge or magnetic excitations that do not need to be commensurate to the lattice. This raises the question if one can obtain a moiré by combining periodic electronic modulations and the atomic lattice. Here we report on the discovery of a one-dimensional charge density wave (1D-CDW) which is a moiré pattern between the atomic lattice and a hot spot for electronic scatte…
Phase-field approaches to fracture based on energy minimization principles have been rapidly gaining popularity in recent years, and are particularly well-suited for simulating crack initiation and growth in complex fracture networks. In the phase-field framework, the surface energy associated with crack formation is calculated by evaluating a functional defined in terms of a scalar order parameter and its gradients, which in turn describe the fractures in a diffuse sense following a prescribed regularization length scale. Imposing stationarity of the total energy leads to a coupled system of …
The fracture mechanics was widely employed to explain the crack propagation in the deposition produced by drying colloidal suspension. However, more complex than conventional fracture, those cracks periodically distribute and make up a unique pattern. This still remains mysterious so far. Inspired by the concept of spinodal decomposition, here, we develop the theory to elucidate the spatial arrangement of the cracks, which indicates that the crack pattern is generated by the phase separation of colloidal clusters and water. It concludes that the crack spacing results from the wavelength of the…
We present a novel computational framework to simulate the electromechanical response of self-sensing carbon nanotube (CNT)-based composites experiencing fracture. The computational framework combines electrical-deformation-fracture finite element modelling with a mixed micromechanics formulation. The latter is used to estimate the constitutive properties of CNT-based composites, including the elastic tensor, fracture energy, electrical conductivity, and linear piezoresistive coefficients. These properties are inputted into a coupled electro-structural finite element model, which simulates the…
Patterns on broken surfaces are well-known from everyday experience, but surprisingly, how and why they form are very much open questions. Well-defined facets are commonly observed1-4 along fracture surfaces which are created by slow tensile cracks. As facets appear in amorphous materials5-7, their formation does not reflect microscopic order. Fracture mechanics, however, predict that slow crack fronts should be straight, creating mirror-like surfaces8-13. In contrast, facet-forming fronts propagate simultaneously within different planes separated by steps. It is therefore unclear why steps ar…
Impact craters exist on various solid objects in the planetary system. A simplified analogy of the process of their formation is here analyzed by standard solid state physics and the so called dynamic quantized fracture mechanics. An expression which links the crater volume to the parameters of the impactor and the target is obtained within the two approaches. For low impactor energy, this expression is of the same mathematical form as the one resulting from recent experiments.It is shown that the formation of an impact crater is possible even without heating of the target, if the critical str…
This study presents the formulation, the numerical solution, and the validation of a theoretical framework based on the concept of variable-order mechanics and capable of modeling dynamic fracture in brittle and quasi-brittle solids. More specifically, the reformulation of the elastodynamic problem via variable and fractional order operators enables a unique and extremely powerful approach to model nucleation and propagation of cracks in solids under dynamic loading. The resulting dynamic fracture formulation is fully evolutionary hence enabling the analysis of complex crack patterns without r…
To obtain the probability distribution of 2D crack patterns in mesoscopic regions of a disordered solid, the formalism of Paper I requires that a functional form associating the crack patterns (or states) to their formation energy be developed. The crack states are here defined by an order parameter field representing both the presence and orientation of cracks at each site on a discrete square network. The associated Hamiltonian represents the total work required to lead an uncracked mesovolume into that state as averaged over the initial quenched disorder. The effect of cracks is to create m…
This paper describes a two-dimensional (2D) finite element simulation for fracture and fatigue behaviours of pure alumina microstructures such as those found at hip prostheses. Finite element models are developed using actual Al2O3 microstructures and a bilinear cohesive zone law. Simulation conditions are similar to those found at a slip zone in a dry contact between a femoral head and an acetabular cup of hip prosthesis. Contact stresses are imposed to generate cracks in the models. Magnitudes of imposed stresses are higher than those found at the microscopic scale. Effects of microstructure…
Ti-6Al-4V is a titanium alloy with excellent properties for lightweight applications and its production through Additive Manufacturing processes is attractive for different industrial sectors. In this work, the influence of mechanical properties on the notch fracture resistance of Ti-6Al-4V produced by Selective Laser Melting is numerically investigated. Literature data is used to inform material behaviour. The as-built brittle behaviour is compared to the enhanced ductile response after heat treatment (HT) and hot isostatic pressing (HIP) post-processes. A Phase Field framework is adopted to …
