On the basis of energy conservation law an without utilizing Linear Fracture Mechanics (LFM) postulates the equation of a real-structure material elastic-plastic fracture has been derived. With the help of this equation the force and energy criteria of Non-linear Fracture Mechanics (NLFM) have been found. These criteria constitute the basis of modern strength analysis of machineparts and structures made of real-structure materials. $K_{lc}$ dependence on ultimate strength limit, yield limit and impact toughness has been established and experimentally confirmed for a number of steels
In this review article we consider the crack growth resistance ofmicrometer and submicrometer sized samples from the fracture mechanics point of view. Standard fracture mechanics test procedures were developed for macroscale samples, and reduction of the specimen dimensions by three to five orders of magnitude has severe consequences. This concerns the interpretation of results obtained by micro and nanomechanics, as well as the life time and failure prediction of micro and nano devices. We discuss the relevant fracture mechanics length scales and their relation to the material specific struct…
We extend the model-free data-driven paradigm for rate-independent fracture mechanics proposed in Carrara et al. (2020), Data-driven Fracture Mechanics, Comp. Meth. App. Mech. Eng., 372 to rate-dependent fracture and sub-critical fatigue. The problem is formulated by combining the balance governing equations stemming from variational principles with a set of data points that encodes the fracture constitutive behavior of the material. The solution is found as the data point that best satisfies the meta-stability condition as given by the variational procedure and following a distance minimizati…
Rapid progress in additive manufacturing methods has created a new class of ultralight and strong architected metamaterials that resemble periodic truss structures. The mechanical performance of these metamaterials with a very large number of unit cells is ultimately limited by their tolerance to damage and defects, but an understanding of this sensitivity has remained elusive. Using a stretching-dominated micro-architecture and metamaterial specimens comprising millions of unit-cells we show that not only is the stress intensity factor, as used in conventional elastic fracture mechanics, insu…
The concept of the diode is usually applied to electronic and thermal devices but very rarely for mechanical ones. A recently proposed fracture rectification effect in polymer-based structures with triangular voids defects has motivated us to test these ideas at the nanoscale using graphene membranes. Using fully-atomistic reactive molecular dynamics simulations we showed that robust rectification-like effects exist. The fracture can be 'guided' to easier propagate along one specific direction than its opposite. We also observed that there is an optimal value for the spacing between each void …
In terms of nonlinear material fracture mechanics, the real (discrete)-structure material fracture model has been developed. The model rests on the demonstration of the fact that crack resistance $K_{1c}=2σ\sqrt l$ and fracture toughness are $G_{1c}=J_{1c}=2σl$ obtained on the basis of energy conservation law and derived without linear material fracture mechanics assumptions can be respectively taken as force and energy criteria for non-linear fracture mechanics. It is shown that $G_{1c}=K_{1c}^2/E$ is the energy criterion of linear fracture mechanics of material and it is sufficiently less th…
In this work, we developed a bond-based cohesive peridynamics model (CPDM) and apply it to simulate inelastic fracture by using the meso-scale Xu-Needleman cohesive potential . By doing so, we have successfully developed a bond-based cohesive continuum mechanics model with intrinsic stress/strain measures as well as consistent and built-in macro-scale constitutive relations. The main novelties of this work are: (1) We have shown that the cohesive stress of the proposed nonlocal cohesive continuum mechanics model is exactly the same as the nonlocal peridynamic stress; (2) For the first time, we…
La(Fe,Mn,Si)13 alloys are a promising material family for magnetic refrigeration. Challenges associated with their structural integrity during device assembly and operation requires deep understanding of the mechanical properties. Here we developed a workflow to quantitatively study the fracture properties of La(Fe,Mn,Si)13 plates used in magnetic cooling devices. We employed microstructural characterisation, optical examination of defects, and four-point bending tests of samples with known defect sizes to evaluate their mechanical performance. We established the residual strength curve which …
The topologies of existing interface elements used to discretize cohesive cracks are such that they can be used to compute the relative displacements (displacement discontinuities) of two opposing segments (in 2D) or of two opposing facets (in 3D) belonging to the opposite crack faces and enforce the cohesive traction-separation relation. In the present work we propose a novel type of interface element for fracture mechanics sharing some analogies with the node-to-segment (in 2D) and with the node-to-surface (in 3D) contact elements. The displacement gap of a node belonging to the finite eleme…
It was shown that a material fatigue fracture diagram can be viewed as a locus of points with $σ$ and $\sqrt l$ coordinates' product equal to $K_{1c}/2$, and $σ$ and $l$ product -- to $G_{1c}/2$, where $K_{1c}$ and $G_{1c}$ are non-linear fracture mechanics force and energy criteria. It was established that the average number of interatomic bonds destroyed within one alternate stress $\nabla_{1cs}$ cycle is directly proportional to $σ$ that is twice as large as a peak value of $σ^a$. It was found that low-cycle fatigue is characterized by $σ>σ_{0.2}$ and $σ_{1cs}> 1$, high-cycle fatigue -- by …
We investigate the influence of gradient-enhanced dislocation hardening on the mechanics of notch-induced failure. The role of geometrically necessary dislocations (GNDs) in enhancing cracking is assessed by means of a mechanism-based strain gradient plasticity theory. Both stationary and propagating cracks from notch-like defects are investigated through the finite element method. A cohesive zone formulation incorporating monotonic and cyclic damage contributions is employed to address both loading conditions. Computations are performed for a very wide range of length scale parameters and num…
We investigated through fully atomistic molecular dynamics simulations, the mechanical behavior (compressive and tensile) and energy absorption properties of two families (primitive (P688 and P8bal) and gyroid (G688 and G8bal)) of carbon-based schwarzites. Our results show that all schwarzites can be compressed (with almost total elastic recovery) without fracture to more than 50%, one of them can be even remarkably compressed up to 80%. One of the structures (G8bal) presents negative Poisson's ratio value (auxetic behavior). The crush force efficiency, the stroke efficiency and the specific e…
When a frictional interface is subject to a localized shear load, it is often (experimentally) observed that local slip events initiate at the stress concentration and propagate over parts of the interface by arresting naturally before reaching the edge. We develop a theoretical model based on linear elastic fracture mechanics to describe the propagation of such precursory slip. The model's prediction of precursor lengths as a function of external load is in good quantitative agreement with laboratory experiments as well as with dynamic simulations, and provides thereby evidence to recognize f…
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…
The fundamental problem of friction in the presence of macroscopic adhesion, as in soft bodies, is receiving interest from many experimentalists. Since the first fracture mechanics `purely brittle' model of Savkoor and Briggs, models have been proposed where the mixed mode toughness is interpreted with phenomenological fitting coefficients introducing weaker coupling between modes than expected by the "purely brittle" model. We compare here two such previously proposed models and introduce a third one to show that the transition to sliding is very sensitive to the form of the mixed-mode model.…
We study a planar thin brittle beam subject to elastic deformations and cracks described in terms of a nonlinear Griffith energy functional acting on $SBV$ deformations of the beam. In particular we consider the case in which elastic bulk contributions due to finite bending of the beam are comparable to the surface energy which is necessary to completely break the beam into several large pieces. In the limit of vanishing aspect ratio we rigorously derive an effective Griffith-Euler-Bernoulli functional which acts on piecewise $W^{2,2}$ regular curves representing the midline of the beam. The e…
The dynamics of materials failure is one of the most critical phenomena in a range of scientific and engineering fields, from healthcare to structural materials to transportation. In this paper we propose a specially designed deep neural network, DyFraNet, which can predict dynamic fracture behaviors by identifying a complete history of fracture propagation - from cracking onset, as a crack grows through the material, modeled as a series of frames evolving over time and dependent on each other. Furthermore, this model can not only forecast future fracture processes but also backcast to elucida…
Many people are aware of the theory of elastic fracture originated by AA Griffith, and although Griffith used the theorem of minimum potential energy most people seem unaware of the broader implications of this theorem. If it is set within its classical mechanics roots, it is clear that it is a restricted form of a Lagrangian. In advanced texts on fracture cracks are treated as dynamic entities, and the role of stress waves is clearly articulated. However, in most non-advanced texts on fracture and fatigue the role of stress waves are either not included or not emphasised, often leading to a p…
This work investigated how the structure size affects the quasi-static and fatigue behaviors of graphene polymer nanocomposites, a topic that has been often overlooked. The results showed that both quasi-static and fatigue failure of these materials scale nonlinearly with the structure size due to the presence of a significant Fracture Process Zone (FPZ) ahead of the crack tip induced by graphene nanomodification. Such a complicated size effect and scaling in either quasi-static or fatigue scenario cannot be described by the Linear Elastic Fracture Mechanics (LEFM), but can be well captured by…
As recently suggested in an interestring and stimulating paper by Menga, Carbone & Dini (MCD), applying fracture mechanics energy concepts for the case of a sliding adhesive contact, imposing also the shear stress is constant at the interface and equal to a material constant (as it seems in experiments), leads to a increase of contact area which instead is never observed. We add that the rigorous MCD theory also predict a size effect and hence a distortion of the JKR curve during sliding which is also not observed in experiments. Finally, a simpler example with the pure mode I contact case, le…
Graphene and some graphene like two dimensional materials; hexagonal boron nitride (hBN) and silicene have unique mechanical properties which severely limit the suitability of conventional theories used for common brittle and ductile materials to predict the fracture response of these materials. This study revealed the fracture response of graphene, hBN and silicene nanosheets under different tiny crack lengths by molecular dynamics (MD) simulations using LAMMPS. The useful strength of these large area two dimensional materials are determined by their fracture toughness. Our study shows a comp…
Stretchable conductors are of crucial relevance for emerging technologies such as wearable electronics, low-invasive bioelectronic implants or soft actuators for robotics. A critical issue for their development regards the understanding of defect formation and fracture of conducting pathways during stress-strain cycles. Here we present a novel atomic force microscopy (AFM) method that provides multichannel images of surface morphology, conductivity, and elastic modulus during sample deformation. To develop the method, we investigate in detail the mechanical interactions between the AFM tip and…
Cement is the most widely used manufacturing material in the world and improving its toughness would allow for the design of slender infrastructure, requiring less material. To this end, we investigate by means of molecular dynamics simulations the fracture of calcium-silicate-hydrate (C-S-H), the binding phase of cement, responsible for its mechanical properties. For the first time, we report values of the fracture toughness, critical energy release rate, and surface energy of C-S-H grains. This allows us to discuss the brittleness of the material at the atomic scale. We show that, at this sc…
In a recent contribution, Shrimali and Lopez-Pamies (2023) have shown that the Griffith criticality condition that governs crack growth in viscoelastic elastomers can be reduced -- from its ordinary form involving a historically elusive loading-history-dependent critical tearing energy $T_c$ -- to a fundamental form that involves exclusively the intrinsic fracture energy $G_c$ of the elastomer. The purpose of this paper is to make use of this fundamental form to explain one of the most distinctive fracture tests for viscoelastic elastomers, the so-called delayed fracture test.
Despite numerous experimental and theoretical investigations of the mechanical behavior of high-capacity Si and Ge Li-ion battery anodes, our basic understanding of swelling-driven fracture in these materials remains limited. Existing theoretical studies have provided insights into elasto-plastic deformations caused by large volume change phase transformations, but have not modeled fracture explicitly beyond Griffith's criterion. Here we use a multi-physics phase-field approach to model self-consistently anisotropic phase transformation, elasto-plastic deformation, and crack initiation and pro…
The effects of shear on energy release rate and mode mixity in a symmetric sandwich beam with isotropic layers and a debond crack at the face sheet/core interface are investigated through a semi-analytic approach based on two-dimensional elasticity and linear elastic fracture mechanics. Semi-analytic expressions are derived for the shear components of energy release rate and mode mixity phase angle which depend on four numerical coefficients derived through accurate finite element analyses. The expressions are combined with earlier results for three-layer configurations subjected to bending-mo…
A continuum model of fracture that describes, in principle, the propagation and interaction of arbitrary distributions of cracks and voids with evolving topology without a fracture criterion is developed. It involves a 'law of motion' for crack-tips, primarily as a kinematical consequence coupled with thermodynamics. Fundamental kinematics endows the crack-tip with a topological charge. This allows the association of a kinematical conservation law for the charge, resulting in a fundamental evolution equation for the crack-tip field, and in turn the crack field. The vectorial crack field degrad…
We consider the effect of differing coefficients of static and dynamic friction coefficients on the behaviour of contacts involving microslip. The classic solutions of Cattaneo and Mindlin are unchanged if the transition in coefficients is abrupt, but if it occurs over some small slip distance, the solution has some mathematical similarities with those governing the normal tractions in adhesive contact problems. In particular, if the transition to dynamic slip occurs over a sufficiently small area, we can identify a `JKR' approximation, where the transition region is condensed to a line. A loc…
