Understanding the fracture toughness (resistance) of glasses is a fundamental problem of prime theoretical and practical importance. Here we theoretically study its dependence on the loading rate, the age (history) of the glass and the notch radius $ρ$. Reduced-dimensionality analysis suggests that the notch fracture toughness results from a competition between the initial, age- and history-dependent, plastic relaxation timescale $τ^{pl}_0$ and an effective loading timescale $τ^{ext}(\dot{K}_I,ρ)$, where $\dot{K}_I$ is the tensile stress-intensity-factor rate. The toughness is predicted to scale with $\sqrtρ$ independently of $ξ\!\equiv\!τ^{ext}\!/τ^{pl}_0$ for $ξ\!\ll\! 1$, to scale as $T\sqrtρ\,\log(ξ)$ for $ξ\!\gg\!1$ (related to thermal activation, where $T$ is the temperature) and to feature a non-monotonic behavior in the crossover region $ξ\!\sim\!{\cal O}(1)$ (related to plastic yielding dynamics). These predictions are verified using novel 2D computations, providing a unified picture of the notch fracture toughness of glasses. The theory highlights the importance of timescales competition and far from steady-state elasto-viscoplastic dynamics for understanding the toughness, and shows that the latter varies quite significantly with the glass age (history) and applied loading rate. Experimental support for bulk metallic glasses is presented.
In this work a novel methodology for fracture toughness characterization by means of the small punch test (SPT) is presented. Notched specimens are employed and fracture resistance is assessed through a critical value of the notch mouth displacement {δ^SPT}. Finite element simulations and interrupted experiments are used to track the evolution of {δ^SPT} as a function of the punch displacement. The onset of crack propagation is identified by means of a ductile damage model and the outcome is compared to the crack tip opening displacement estimated from conventional tests at crack initiation. T…
Fracture toughness $K_{IC}$ plays an important role in materials design. Along with numerous experimental methods to measure fracture toughness of materials, its understanding and theoretical prediction is very important. However, theoretical prediction of fracture toughness is challenging. By investigating the correlation between fracture toughness and elastic properties of materials, we have constructed a fracture toughness model for covalent and ionic crystals. Furthermore, by introducing an enhancement factor, which is determined by the density of states at the Fermi level and atomic elect…
We investigate dynamic fracture of heterogeneous materials experimentally by measuring displacement fields as a rupture propagates through a periodic array of obstacles of controlled fracture energy. Our measurements demonstrate the applicability of the classical equation of motion of cracks at a discontinuity of fracture energy: the crack speed jumps at the entrance and exit of an obstacle, as predicted by the crack-tip energy balance within the brittle fracture framework. The speed jump amplitude is governed by the fracture energy contrast and by the combination of rate-dependency of fractur…
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…
Understanding, predicting and eventually improving the resistance to fracture of silicate materials is of primary importance to design new glasses that would be tougher, while retaining their transparency. However, the atomic mechanism of the fracture in amorphous silicate materials is still a topic of debate. In particular, there is some controversy about the existence of ductility at the nano-scale during the crack propagation. Here, we present simulations of the fracture of three archetypical silicate glasses using molecular dynamics. We show that the methodology that is used provide realis…
Quantitative understanding of the fracture toughness of metallic glasses, including the associated ductile-to-brittle transitions, is not yet available. Here we use a simple model of plastic deformation in glasses, coupled to an advanced Eulerian level set formulation for solving complex free boundary problems, to calculate the fracture toughness of metallic glasses as a function of the degree of structural relaxation corresponding to different annealing times near the glass temperature. Our main result indicates the existence of an elasto-plastic crack tip instability for sufficiently relaxed…
Three dimensional calculations of ductile crack growth under mode I plane strain, small scale yielding conditions are carried out using an elastic-viscoplastic constitutive relation for a progres- sively cavitating plastic solid with two populations of void nucleating second phase particles. Full field solutions are obtained for three dimensional material microstructures characterized by ran- dom distributions of void nucleating particles. Crack growth resistance curves and fracture surface roughness statistics are calculated using standard procedures. The range of void nucleating particle vol…
The fracture toughness of Al/SiC nanolaminates with different layer thicknesses (in the range 10 to 100 nm) was measured by means of micropillar splitting and bending of a notched beam. The crack plane was perpendicular to the layers in the former while notched beams with the notch parallel and perpendicular to the layers were milled in the latter. It was found that crack propagation parallel to the layers took place along the metal-ceramic interfaces and the toughness increased with the layer thickness due to the contribution of the plastic deformation of the Al layers. Crack propagation perp…
The mechanical properties of the stoichiometric B2 $β$-phase of NiAl are well established, however the effect of off-stoichiometric composition on the fracture toughness has not yet been systematically studied over the entire composition range of 40-50% Al. Here we use microbending tests on notched cantilever beams FIB-milled from NiAl single crystals with an aluminized as well as an oxidation-induced composition gradient to determine the influence of the Al concentration on the mechanical properties. The fracture toughness is maximal for the stoichiometric composition. It decreases with incre…
Toughness describes the ability of a material to resist fracture or crack propagation. It is demonstrated here that fracture toughness of a material can be asymmetric, i.e., the resistance of a medium to a crack propagating from right to left can be significantly different from that to a crack propagating from left to right. Such asymmetry is unknown in natural materials, but we show that it can be built into artificial materials through the proper control of microstructure. This paves the way for control of crack paths and direction, where fracture -- when unavoidable -- can be guided through…
This is a reply to the correspondence of Prof. Robert Ritchie: "On the fracture toughness of bioinspired ceramic materials", submitted to Nature Materials, which discusses the fracture toughness values of the following papers: Bouville, F., Maire, E., Meille, S., Van de Moortèle, B., Stevenson, A. J., & Deville, S. (2014). Strong, tough and stiff bioinspired ceramics from brittle constituents. Nature Materials, 13(5), 508-514 and Le Ferrand, H., Bouville, F., Niebel, T. P., & Studart, A. R. (2015). Magnetically assisted slip casting of bioinspired heterogeneous composites. Nature Materials, 14…
This paper describes an attempt to construct a first-principles theory of the fracture toughness of crystalline solids. It is based on the thermodynamic dislocation theory (TDT), which starts with the assertion that dislocations in solids must obey the second law of thermodynamics. A second starting assumption is that fracture is initiated when the tip of a notch is driven to undergo a sharpening instability. The results of this analysis are developed in comparison with measurements by Gumbsch and colleagues of the notch toughness of both predeformed and non-predeformed tungsten crystals. The …
Connecting bond switching to fracture toughness of calcium aluminosilicate glasses
Aalborg University（奥尔堡大学）；The Hong Kong Polytechnic University（香港理工大学）；Shanghai Jiao Tong University（上海交通大学）；Univ Rennes, CNRS, IPR (Institut de Physique de Rennes)（雷恩大学，法国国家科学研究中心，雷恩物理研究所）；CNRS（法国国家科学研究中心）
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, an…
Delamination is one of the major concerns for carbon fiber reinforced polymer (CFRP) composites. Improving fracture toughness reduces delamination and allows for the creation of multifunctional CFRP. In this study, polyaniline (PANI) coated graphene nanoplatelets (GNP) are introduced in the interlaminar region of CFRP pre-preg with the aid of environmentally friendly thermoplastic polymer, polyvinylpyrrolidone (PVP). The GNP content is varied as 1, 3, and 5% by weight with respect to PVP. The improvements in the fracture toughness are investigated using a double cantilever beam test. An improv…
Fracture is the ultimate source of failure of amorphous carbon (a-C) films, however it is challenging to measure fracture properties of a-C from nano-indentation tests and results of reported experiments are not consistent. Here, we use atomic-scale simulations to make quantitative and mechanistic predictions on fracture of a-C. Systematic large-scale K-field controlled atomic-scale simulations of crack propagation are performed for a-C samples with densities of $ρ=2.5, \, 3.0 \, \text{ and } 3.5~\text{g/cm}^{3}$ created by liquid quenches for a range of quench rates $\dot{T}_q = 10 - 1000~\te…
Superlattice (SL) thin films composed of refractory ceramics unite extremely high hardness and enhanced fracture toughness; a material combination often being mutually exclusive. While the hardness enhancement obtained whentwo materials form a superlattice is well described by existing models based on dislocation mobility, the underlying mechanisms behind the increase in fracture toughness are yet to be unraveled. Here we provide a model based on linear elasticity theory to predict the fracture toughness enhancement in (semi-)epitaxial nanolayers due to coherency stresses and formation of misf…
Sandwich specimens were prepared by firing a thin inter-layer of porous La0.6Sr0.4Co0.2Fe0.8O3-d (LSCF) to bond a thin tetragonal yttria-stabilised zirconia (YSZ) beam to a thick YSZ substrate. Fracture of the joint was evaluated by introducing a wedge between the two YSZ adherands so that the stored energy in the thin YSZ cantilever beam drives a stable crack in the adhesive bond and allows the critical energy release rate for crack extension (fracture toughness) to be measured. The crack path in most specimens showed a mixture of adhesive failure (at the YSZ-LSCF interface) and cohesive fail…
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 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…
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 single lap shear test is widely used to measure the strength of dissimilar welds even though such a test brings limited understanding of the intrinsic weld toughness. The present study proposes a numerical finite element (FE) analysis and experimental characterization of dissimilar joints presenting various microstructures (thickness of the intermetallic layer (IML) and hardness profile). For this purpose, Friction Melt Bonding (FMB) and Friction Stir Welding (FSW) were used to join aluminum AA6061 and Dual Phase steel (DP980). The FE simulations allowed calculating the evolution of the J-…
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 …
The widespread use of sodium aluminosilicate glass in many engineering applications due to its mechanical and optical properties (transparency, dielectric, etc.), has become common in recent years. However, glass, a brittle material, has its vulnerability to fracture. Processes such as heat treatment (heat tempering) or chemical strengthening through ion-exchange have been used to create residual stress profiles on the glass, in a bid to improve its fracture strength. However, failure still occurs, which is mostly catastrophic and expensive to repair. Therefore understanding, predicting, and e…
The effect of substrate was studied using nanoindentation on thin films. Soft films on hard substrate showed more pile up than usual which was attributed to the dislocation pile up at the film substrate interface. The effect of tip blunting on the load depth and hardness plots of nanoindentation was shown. The experimental date of variation of Vickers hardness with film thickness and loads were fitted and new parameters were analyzed. The delaminated area was analyzed using geometrical shapes using optical view of the failure region along with the load displacement Indentation fracture using N…
In a recent contribution, Kumar, Bourdin, Francfort, and Lopez-Pamies (J. Mech. Phys. Solids 142:104027, 2020) have introduced a comprehensive macroscopic phase-field theory for the nucleation and propagation of fracture in linear elastic brittle materials under arbitrary quasistatic loading conditions. The theory can be viewed as a natural generalization of the phase-field approximation of the variational theory of brittle fracture of Francfort and Marigo (J. Mech. Phys. Solids 46:1319--1342, 1998) to account for the material strength at large. This is accomplished by the addition of an exter…
The fracture toughness for a mode I/II crack propagating in a ductile material has been subject to numerous investigations. However, the influence of the material hardening law has received very limited attention, with isotropic hardening being the default choice if cyclic loads are absent. The present work extends the existing studies of monotonic mode I/II steady-state crack propagation with the goal to compare the predictions from an isotropic hardening model with that of a kinematic hardening model. The work is conducted through a purpose-built steady-state framework that directly delivers…
In this work, the mode I fracture toughness of dissimilar metal-composite adhesive joints is experimentally investigated using the double cantilever beam (DCB) test. The particular joint under study is resulted by the adhesive joining of a thin titanium sheet with a thin carbon fiber reinforced plastic (CFRP) laminate and is envisioned to be implemented in the hybrid laminar flow control system of future aircraft. Four different industrial technologies for the joining of the titanium and CFRP adherents are evaluated/compared; co-bonding with and without adhesive and secondary bonding using eit…
Medium- and high-entropy alloys based on the CrCoNi-system have been shown to display outstanding strength, tensile ductility and fracture toughness (damage-tolerance properties), especially at cryogenic temperatures. Here we examine the JIc and (back-calculated) KJIc fracture toughness values of the face-centered cubic, equiatomic CrCoNi and CrMnFeCoNi alloys at 20 K. At flow stress values of ~1.5 GPa, crack-initiation KJIc toughnesses were found to be exceptionally high, respectively 235 and 415 MPa(square-root)m for CrMnFeCoNi and CrCoNi, with the latter displaying a crack-growth toughness …
Interface-Controlled Defect Engineering in TiN/TaN Superlattices for Enhanced Hardness and Fracture Toughness
Technische Universität Wien（维也纳工业大学）；Plansee (Shanghai) High Performance Material Ltd.（普莱思（上海）高性能材料有限公司）；Guangdong University of Technology（广东工业大学）；RWTH Aachen University（亚琛工业大学）；Austrian Academy of Sciences（奥地利科学院）；Uppsala University（乌普萨拉大学）
In order to design tougher materials, it is crucial to understand the relationship between their composition and their resistance to fracture. To this end, we investigate the fracture toughness of usual sodium silicate glasses (NS) and complex calcium--silicate--hydrates (CSH), the binding phase of cement. Their atomistic structure is described in the framework of the topological constraints theory, or rigidity theory. We report an analogous rigidity transition, driven by pressure in NS and by composition in CSH. Relying both on simulated and available experimental results, we show that optima…
Fracture surfaces provide various types of information about fracture. The fracture toughness $K_{{\rm I}c}$, which represents the resistance to fracture, can be estimated using the three-dimensional (3D) information of a fracture surface, i.e., its roughness. However, this is time-consuming and expensive to obtain the 3D information of a fracture surface; thus, it is desirable to estimate $K_{{\rm I}c}$ from a two-dimensional (2D) image, which can be easily obtained. In recent years, methods of estimating a 3D structure from its 2D image using deep learning have been rapidly developed. In thi…
High-strain-rate shear tests were conducted on a three-layered bonded test piece comprising a central aluminum layer with PMMA resin layers bonded on both sides. Upon calculating the displacement field and the strain field using digital image correlation (DIC), the crack tip was located, and the fracture toughness was evaluated at the Aluminum/PMMA bonding interface. As a result of the DIC, it was possible to determine the process by which 1) the elastic stress wave propagated to the aluminum section, 2) the wave was transmitted to the PMMA section, and 3) the crack developed at the interface.…
We present a computational framework to explore the effect of microstructure and constituent properties upon the fracture toughness of fibre-reinforced polymer composites. To capture microscopic matrix cracking and fibre-matrix debonding, the framework couples the phase field fracture method and a cohesive zone model in the context of the finite element method. Virtual single-notched three point bending tests are conducted. The actual microstructure of the composite is simulated by an embedded cell in the fracture process zone, while the remaining area is homogenised to be an anisotropic elast…
We develop a numerical methodology for the calculation of mode-I R-curves of brittle and elastoplastic lattice materials, and unveil the impact of lattice topology, relative density and constituent material behavior on the toughening response of 2D isotropic lattices. The approach is based on finite element calculations of the J-integral on a single-edge-notch-bend (SENB) specimen, with individual bars modeled as beams having a linear elastic or a power-law elasto-plastic constitutive behavior and a maximum strain-based damage model. Results for three 2D isotropic lattice topologies (triangula…
One might ask why is it important to know the mechanism of fracture in leaves when Mother Nature is doing her job perfectly. I could list the following reasons to address that question: (a) Leaves are natural composite structures, during millions of years of evolution, they have adapted themselves to their surrounding environment and their design is optimized, one can apply the knowledge gained from studying the fracture mechanism of leaves to the development of new composite materials; (b) Other soft tissues like skin and blood vessel have similar structure at some scales and may possess the …
Integral-type nonlocal damage models describe the fracture process zones by regular strain profiles insensitive to the size of finite elements, which is achieved by incorporating weighted spatial averages of certain state variables into the stress-strain equations. However, there is no consensus yet how the influence of boundaries should be taken into account by the averaging procedures. In the present study, nonlocal damage models with different averaging procedures are applied to the modelling of fracture in specimens with various boundary types. Firstly, the nonlocal models are calibrated b…
Ab initio-calculated ideal strength and toughness describe the upper limits for mechanical properties attainable in real systems and can, therefore, be used in selection criteria for materials design. We employ density-functional ab initio molecular dynamics (AIMD) to investigate the mechanical properties of defect-free rocksalt-structure (B1) TiN and B1 Ti1-xAlxN (x = 0.25, 0.5, 0.75) solid solutions subject to [001], [110], and [111] tensile deformation at room temperature. We determine the alloys' ideal strength and toughness, elastic responses, and ability to plastically deform up to fract…
We investigate the role of microstructural bridging on the fracture toughness of composite materials. To achieve this, a new computational framework is presented that integrates phase field fracture and cohesive zone models to simulate fibre breakage, matrix cracking and fibre-matrix debonding. The composite microstructure is represented by an embedded cell at the vicinity of the crack tip, whilst the rest of the sample is modelled as an anisotropic elastic solid. The model is first validated against experimental data of transverse matrix cracking from single-notched three-point bending tests.…
Natural hard composites like human bone possess a combination of strength and toughness that exceeds that of their constituents and of many engineered composites. This augmentation is attributed to their complex hierarchical structure, spanning multiple length scales; in bone, characteristic dimensions range from nanoscale fibrils to microscale lamellae to mesoscale osteons and macroscale organs. The mechanical properties of bone have been studied, with the understanding that the isolated microstructure at micro- and nano-scales gives rise to superior strength compared to that of whole tissue,…
