Understanding ductility or brittleness of monolithic bulk metallic glasses (BMGs) requires detailed knowledge of the amorphous structure. The medium range order (MRO) of ductile Pd$_{40}$Ni$_{40}$P$_{20}$ and brittle Zr$_{52.5}$Cu$_{17.9}$Ni$_{14.6}$Al$_{10}$Ti$_5$ (Vit105) was characterized prior to and after notched 3-point bending tests using variable-resolution fuctuation electron microscopy. Here we show the presence of a second larger MRO correlation length in the ductile material which is not present in the brittle material. A comparison with literature suggests that the larger correlation length accounts for larger shear transformation zones (STZs) which increase the heterogeneity. This enables an easier shear band formation and thus explains the difference in deformability.
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…
We perform a large-scale statistical analysis (> 2000 independent simulations) of the elongation and rupture of gold nanowires, probing the validity and scope of the recently proposed ductile-to-brittle transition that occurs with increasing nanowire length [Wu et. al., Nano Lett., 12, 910-914 (2012)]. To facilitate a high-throughput simulation approach, we implement the second-moment approximation to the tight-binding (TB-SMA) potential within HOOMD-Blue, a molecular dynamics package which runs on massively parallel graphics processing units (GPUs). In a statistical sense, we find that the na…
Molecular dynamics simulations have been performed to understand the influence of temperature on the tensile deformation and fracture behavior of $<$111$>$ BCC Fe nanowires. The simulations have been carried out at different temperatures in the range 10-1000 K employing a constant strain rate of $1\times$ $10^8$ $s^{-1}$. The results indicate that at low temperatures (10-375 K), the nanowires yield through the nucleation of a sharp crack and fails in brittle manner. On the other hand, nucleation of multiple 1/2$<$111$>$ dislocations at yielding followed by significant plastic deformation leadi…
We introduce a lattice model able to describe damage and yielding in heterogeneous materials ranging from brittle to ductile ones. Ductile fracture surfaces, obtained when the system breaks once the strain is completely localized, are shown to correspond to minimum energy surfaces. The similarity of the resulting fracture paths to the limits of brittle fracture or minimum energy surfaces is quantified. The model exhibits a smooth transition from brittleness to ductility. The dynamics of yielding exhibits avalanches with a power-law distribution.
The fracture properties of as-cast TiVNbTa, a refractory high-entropy alloy (RHEA), were investigated using four-point bending tests from -139C to 20C under a strain-rate of 10-3 s-1. From those tests and fractography, the conditional fracture toughness values and the brittle-to-ductile transition temperature were obtained. The brittle-to-ductile transition temperature was between -47C to -27C, which gives an estimated activation energy value of 0.52+-0.09 eV for the alloy. This study provides a preliminary understanding of the nature of dislocation motion in a relatively ductile RHEA.
The fracture behavior of brittle and ductile materials can be strongly influenced by thermal fluctuations, especially in micro- and nano-devices as well as in rubberlike and biological materials. However, temperature effects, in particular on the brittle-to-ductile transition, still require a deeper theoretical investigation. As a step in this direction we propose a theory, based on equilibrium statistical mechanics, able to describe the temperature dependent brittle fracture and brittle-to-ductile transition in prototypical discrete systems consisting in a lattice with breakable elements. Con…
Tearing a thin sheet by forcing a rigid object through it leads to complex crack morphologies; a single oscillatory crack arises when a tool is driven laterally through a brittle sheet, while two diverging cracks and a series of concertina-like folds forms when a tool is forced laterally through a ductile sheet. On the other hand, forcing an object perpendicularly through the sheet leads to radial petal-like tears in both ductile and brittle materials. To understand these different regimes we use a combination of experiments, simulations and simple theories. In particular, we describe the tran…
Recent computational and laboratory experiments have shown that the brittle-ductile transitions in metallic glasses such as Vitreloy1 are strongly sensitive to the initial effective disorder (or "fictive") temperature. Glasses with lower effective temperatures are weak and brittle; those with higher effective temperatures are strong and ductile. The analysis of this phenomenon presented here examines the onset of fracture at the tip of a slightly rounded notch as predicted by the shear-transformation-zone (STZ) theory of spatially varying plastic deformation. The central ingredient of this ana…
When considering grinding of minerals, scaling effect induces competition between plastic deformation and fracture in brittle solids. The competition can be sketched by a critical size of the material, which characterizes the ductile-brittle transition. A first approach using Vickers indentation gives a good approximation of the critical size through an extrapolation from the macroscopic to the microscopic scales. Nanoindentation tests confirm this experimental value. According to the grain size compared to the indent size, it can reasonably be said that the mode of damage is deformation-induc…
Understanding the fracture toughness of glasses is of prime importance for science and technology. We study it here using extensive atomistic simulations in which the interaction potential, glass transition cooling rate and loading geometry are systematically varied, mimicking a broad range of experimentally accessible properties. Glasses' nonequilibrium mechanical disorder is quantified through $A_{\rm g}$, the dimensionless prefactor of the universal spectrum of nonphononic excitations, which measures the abundance of soft glassy defects that affect plastic deformability. We show that while …
We conisder the brittle versus ductile behavior of aluminum in the framework of the Peierls-model analysis of dislocation emission from a crack tip. To this end, we perform first-principles quantum mechanical calculations for the unstable stacking energy $γ_{us}$ of aluminum along the Shockley partial slip route. Our calculations are based on density functional theory and the local density approximation and include full atomic and volume relaxation. We find that in aluminum $γ_{us} = 0.224$ J/m$^2$. Within the Peierls-model analysis, this value would predict a brittle solid which poses an inte…
In ordinary solids, material disorder is known to increase the size of the process zone in which stress concentrates at the crack tip, causing a transition from localized to diffuse failure. Here, we report experiments on disordered 2D lattices, derived from frictional particle packings, in which the mean coordination number $\langle z \rangle$ of the underlying network provides a similar control. Our experiments show that tuning the connectivity of the network provides access to a range of behaviors from brittle to ductile failure. We elucidate the cooperative origins of this transition using…
We study two closely related, nonlinear models of a viscoplastic solid. These models capture essential features of plasticity over a wide range of strain rates and applied stresses. They exhibit inelastic strain relaxation and steady flow above a well defined yield stress. In this paper, we describe a first step in exploring the implications of these models for theories of fracture and related phenomena. We consider a one dimensional problem of decohesion from a substrate of a membrane that obeys the viscoplastic constitutive equations that we have constructed. We find that, quite generally, w…
Fracture in aluminum alloys with precipitates involves at least two mechanisms, namely, ductile fracture of the aluminum-rich matrix and brittle fracture of the precipitates. In this work, a coupled crystal plasticity-phase field model for mixed ductile-brittle failure modes is formulated and used to investigate the effect of precipitate morphology and size distribution on damage evolution in aluminum alloys. A thermodynamically consistent framework for elastic and plastic work dissipation in the fracture process zone is used to formulate the coupled constitutive behavior for brittle and ducti…
Temperature-activated dislocation avalanches signaling brittle-to-ductile transition in BCC micropillars
School of Mechanics & Engineering Science, Shanghai University（上海大学力学与工程科学学院）；Department of Mechanical & Aerospace Engineering, University of Miami（迈阿密大学机械与航空航天工程系）；School of Physics, Sun Yat-sen University（中山大学物理学院）；Department of Mechanical & Aerospace Engineering, University of California Los Angeles（加州大学洛杉矶分校机械与航空航天工程系）
Magneto-plasticity occurs when a weak magnetic field alters material plasticity and offers a viable solution to enhance ductile-mode cutting of brittle materials. This study demonstrates the susceptibility of non-magnetic single-crystal calcium fluoride (CaF2) to the magneto-plastic effect. The influence of magneto-plasticity on CaF2 was confirmed in micro-deformation tests under a weak magnetic field of 20 mT. The surface pile-up effect was weakened by 10-15 nm along with an enlarged plastic zone and suppressed crack propagation under the influence of the magnetic field. Micro-cutting tests a…
Molecular-dynamics simulations of fracture in metallic glass-like systems are observed to undergo embrittlement due to a small change in interatomic potential. This change in fracture toughness, however, is not accompanied by a corresponding change in flow stress. Theories of brittle fracture proposed by Freund and Hutchinson indicate that strain rate sensitivity is the controling physical parameter in these cases. A recent theory of viscoplasticity in this class of solids by Falk and Langer further suggests that the change in strain rate sensitivity corresponds to a change in the susceptibili…
A Mesoscale Model for Interface-Mediated Plasticity: Investigation of Ductile and Brittle Fracture
City University of Hong Kong（香港城市大学）；University of California, Los Angeles（加州大学洛杉矶分校）；The University of Hong Kong（香港大学）；University of Birmingham（伯明翰大学）
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 present a model for the thermally activated propagation of cracks in elastic matrices. The propagation is considered as a subcritical phenomenon, the kinetics of which being described by an Arrhenius law. In this law, we take the thermal evolution of the crack front into account, assuming that a portion of the released mechanical energy is transformed into heat in a plastic process zone. We show that such a model leads to a two-phase crack propagation: a first phase at low velocity in which the temperature elevation is of little effect and the propagation is mainly governed by the mechanica…
As a potential building block for the next generation of devices or multifunctional materials that are spreading almost every technology sector, one-dimensional (1D) carbon nanomaterial has received intensive research interests. Recently, a new ultra-thin diamond nanothread (DNT) has joined this palette, which is a 1D structure with poly-benzene sections connected by Stone-Wales (SW) transformation defects. Using large-scale molecular dynamics simulations, we found that this sp3 bonded DNT can transit from a brittle to a ductile characteristic by varying the length of the poly-benzene sections…
This paper presents a framework for modeling failure in quasi-brittle geomaterials under different loading conditions. A micromechanics-based model is proposed in which the field variables are linked to physical mechanisms at the microcrack level: damage is related to the growth of microcracks, while plasticity is related to the frictional sliding of closed microcracks. Consequently, the hardening/softening functions and parameters entering the free energy follow from the definition of a single degradation function and the elastic material properties. The evolution of opening microcracks in te…
Earthquakes are complex phenomena characterized by some fundamental seismic laws. However, under the framework of brittle fracture in disordered material, these universal scaling behaviors, especially for critical exponents, are still far from understood. In this Letter, we study avalanches in compression of a nonbrittle material, the ductile metallic glass foam. In addition to elasticity and disorder, more complex inelastic effects can be also introduced by strain localization in cellular structures. We show that different from brittle fracture, the additional shear-banding interactions resul…
Understanding the strengthening and deformation mechanisms in refractory high-entropy alloys (HEAs), proposed as new high-temperature material, is required for improving their typically insufficient room-temperature ductility. Here, density-functional theory simulations and a continuum mechanics analysis were conducted to systematically investigate the competition between cleavage decohesion and dislocation emission from a crack tip in the body-centered cubic refractory HEAs HfNbTiZr, MoNbTaVW, MoNbTaW, MoNbTiV, and NbTiVZr. This crack-tip competition is evaluated for tensile loading and a tot…
Micro- or minor alloying of metallic glasses is of technological interest. An originally ductile Pd-based monolithic bulk metallic glass (Pd$_{40}$Ni$_{40}$P$_{20}$) was selectively manipulated by additions of Fe or Co. The alloying effects were extreme, showing either exceptional ductility upon Co addition or immediate catastrophic failure upon Fe addition when tested under uniaxial compression or 3-point bending. The amorphous structure was characterized prior to deformation with respect to its medium-range order (MRO) using variable resolution fluctuation electron microscopy (VR-FEM). We ob…
Extreme localization of damage in conventional brittle materials is the source of a host of undesirable effects. We show how artificially engineered metamaterials with all brittle constituents can be designed to ensure that every breakable sub-element fails independently. The main role in the proposed design is played by high contrast composite sub-structure with zero-stiffness, furnishing nonlocal stress redistribution. The ability to de-localize cracking in such nominally brittle systems is revealed by the fact that their continuum description is dominated by the gradient (bending) rather th…
Numerous measurements showed that the crack tip opening angle (CTOA) is nearly constant upon stable ductile fracture in Al alloys which widely used in modern transportation industry. The atomic structure of the very tip of a crack front has remained unknown, however. We have carried out a first-principles density functional theory study to reveal the precise alignment of atoms near the crack tip in single-crystalline Al. The calculations demonstrate that the CTOA increases with the opening displacement, thus the observed constant CTOA in millimeter scale is an entirely plastic effect during du…
Soft amorphous materials are viscoelastic solids ubiquitously found around us, from clays and cementitious pastes to emulsions and physical gels encountered in food or biomedical engineering. Under an external deformation, these materials undergo a noteworthy transition from a solid to a liquid state that reshapes the material microstructure. This yielding transition was the main theme of a workshop held from January 9 to 13, 2023 at the Lorentz Center in Leiden. The manuscript presented here offers a critical perspective on the subject, synthesizing insights from the various brainstorming ses…
The toughness of a polymer material can increase significantly if two networks are combined into one material. This toughening effect is a consequence of a transition from a brittle to a ductile failure response. Although this transition and the accompanying toughening effect have been demonstrated in hydrogels first, the concept has been proven effective in elastomers and in macroscopic composites as well. This suggests that the transition is not caused by a specific molecular architecture, but rather by a general physical principle related to the mechanical interplay between two interpenetra…
Amorphous solids display a ductile to brittle transition as the kinetic stability of the quiescent glass is increased, which leads to a material failure controlled by the sudden emergence of a macroscopic shear band in quasi-static protocols. We numerically study how finite deformation rates influence ductile and brittle yielding behaviors using model glasses in two and three spatial dimensions. We find that a finite shear rate systematically enhances the stress overshoot of poorly-annealed systems, without necessarily producing shear bands. For well-annealed systems, the non-equilibrium disco…
We use atomistic computer simulations to provide a microscopic description of the brittle failure of amorphous materials, and we assess the role of rare events and quenched disorder. We argue that brittle yielding originates at rare soft regions, similarly to Griffiths effects in disordered systems. We numerically demonstrate how localized plastic events in such soft regions trigger macroscopic failure via the propagation of a shear band. This physical picture, which no longer holds in poorly annealed ductile materials, allows us to discuss the role of finite size effects in brittle yielding a…
Fatigue fracture in ductile materials, e. g. metals, is caused by cyclic plasticity. Especially regarding the high numbers of load cycles, plastic material models resolving the full loading path are computationally very demanding. Herein, a model with particularly small computational effort is presented. It provides a macroscopic, phenomenological description of fatigue fracture by combining the phase-field method for brittle fracture with a classic durability concept. A local lifetime variable is obtained, which degrades the fracture resistance progressively. By deriving the stress-strain pat…
High strength and high toughness are usually mutually exclusive in engineering materials. Improving the toughness of strong but brittle materials like ceramics thus relies on the introduction of a metallic or polymeric ductile phase to dissipate energy, which conversely decreases the strength, stiffness, and the ability to operate at high temperature. In many natural materials, toughness is achieved through a combination of multiple mechanisms operating at different length scales but such structures have been extremely difficult to replicate. Building upon such biological structures, we demons…
Cracking the case: fluctuations enhance ductility in refractory alloys
École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Laboratory of materials design and simulation (MADES), Institute of Materials, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院材料研究所材料设计与模拟实验室）；National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院新型材料计算设计与发现国家中心）；EMPA - Swiss Federal Laboratories for Materials Science and Technology（瑞士联邦材料科学与技术研究院）；Laboratory for Multiscale Modeling in Mechanics (LAMMM), Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院机械工程学院多尺度力学建模实验室）；School of Engineering, Brown University, Providence, RI 02906 USA（布朗大学工程学院）
Unveiling the Puzzle of Brittleness in Single Crystal Iridium
College of Materials Science and Engineering（湖南大学材料科学与工程学院）；Hunan University（斯科尔科沃科学技术研究所）；Skolkovo Institute of Science and Technology（苏州实验室）；Suzhou Laboratory
An atomistic understanding of annealing embrittlement is a longstanding issue for metallic glasses, which is still lacking due to the insurmountable gap between the thermal history of atomic models and laboratory-made samples. Here, based on a thermal-cycling annealing method that can vary the effective quenching rate over ten orders of magnitude, we perform an atomistic study of the ductile-brittle transition in a ternary model metallic glass, which can be keyed to the annealing embrittlement in bulk metallic glasses. We reveal that thermal annealing can effectively obliterate thermally activ…
The mechanical response of graphene nano-ribbon under tensile loading has been investigated using atomistic simulation. Lattice symmetry dependence of elastic properties are found, which fits prediction from Cauchy-Born rule well. Concurrent brittle and ductile behaviors are observed in the failure process at elastic limit, which dominates at low and high temperature respectively. In addition, the free edges of finite width ribbon help to activate bond-flip events and initialize ductile behavior.
This study presents experimental and computational analyses of the phase composition and mechanical behavior of a functionally graded material (FGM) grading from 100 vol% 304L stainless steel (SS304L) to 100 vol% Ni-20Cr (NiCr) in 10 vol% increments. The mechanical behavior of the FGM was evaluated by extracting tensile specimens from SS304L-rich and NiCr-rich regions of the FGM, with the former behaving in a ductile manner and the latter being relatively brittle. The brittle response of the NiCr-rich sample was explained by the presence of the eutectic FCC+BCC phase in this sample, as identif…
The influence of shock-wave-loading profile on the failure processes in a brittle material has been investigated. Tungsten heavy alloy (WHA) specimens have been subjected to two shock-wave loading profiles with a similar peak stress of 15.4 GPa but different pulse durations. Contrary to the strong dependence of strength on wave profile observed in ductile metals, for WHA, specimens subjected to different loading profiles exhibited similar spall strength and damage evolution morphology. Post-mortem examination of recovered samples revealed that dynamic failure for both loading profiles is domin…
Widespread processes in nature and technology are governed by the dynamical transition whereby a material in an initially solid-like state then yields plastically. Major unresolved questions concern whether any material will yield smoothly and gradually (ductile behaviour) or fail abruptly and catastrophically (brittle behaviour); the roles of sample annealing, disorder and shear band formation in the onset of yielding and failure; and, most importantly from a practical viewpoint, whether any impending catastrophic failure can be anticipated before it happens. We address these questions by stu…
In this paper we present a thermodynamically consistent material model which is capable of modelling ductile-to brittle failure mode transition in ductile material undergoing deformations at high strain rates, and demonstrate the performance of the model in a numerical study using a fully coupled thermal-structural finite element analysis of a notched aluminium alloy specimen loaded in cyclic tension. The model is based on an objective representation of the deformation and stress measures and on a rate type constitutive equations. It does not only complies with the principles of material model…
Typical empirical bond-order potentials are short ranged and give ductile instead of brittle behavior for materials such as crystalline silicon or diamond. Screening functions can be used to increase the range of these potentials. We outline a general procedure to combine screening functions with bond-order potentials that does not require to refit any of the potential's properties. We use this approach to modify Tersoff's [Phys. Rev. B 39, 5566 (1989)], Erhart & Albe's [Phys. Rev. B 71, 35211 (2005)] and Kumagai et al.'s [Comp. Mater. Sci. 39, 457 (2007)] Si, C and Si-C potentials. The result…
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…
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…
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…
Our goal is to unravel the mechanisms that lead to failure of a ductile two-phase material - that consists of a ductile soft phase and a relatively brittle hard phase. An idealized microstructural model is used to study damage propagation systematically and transparently. The analysis uncovers distinct microstructural features around early voids, whereby regions of the hard phase are aligned with the tensile axis and regions of the soft phase are aligned with the shear directions. These features are consistently found in regions exhibiting damage propagation, whereby the damage remains initiat…
We have developed a new material for neutron shielding applications where space is restricted. W$_2$B is an excellent attenuator of neutrons and gamma-rays, due to the combined gamma attenuation of W and neutron absorption of B. However, its low fracture toughness (~3.5 MPa$\cdot$m$^{0.5}$) and high melting point (2670 °C) prevent the fabrication of large fully-dense monolithic parts with adequate mechanical properties. Here we meet these challenges by combining W$_2$B with a minor fraction (43 vol.%) of metallic W. The material was produced by reaction sintering W and BN powders. The mechanic…
The fracture process of commercially pure titanium was visualized in model materials containing artificial holes. These model materials were fabricated using a femtosecond laser coupled with a diffusion bonding technique to obtain voids in the interior of titanium samples. Changes in void dimensions during in-situ straining were recorded in three dimensions using x-ray computed tomography. Void growth obtained experimentally was compared with the Rice and Tracey model which predicted well the average void growth. A large scatter in void growth data was explained by differences in grain orienta…
