The mechanical yielding of amorphous solids under external loading can be broadly classified into ductile and brittle types, depending on whether their macroscopic stress response is smooth or abrupt, respectively. Recently, it has been shown that these two regimes, obtained by tuning the degree of annealing of the system, are separated by a critical point at a finite inherent disorder strength. Here, we demonstrate a transition from brittle yielding to ductile yielding by introducing quenched disorder in the form of randomly pinned particles. The well-annealed samples, which exhibit brittle yielding, undergo a transition to increasingly ductile yielding with increasing pinning concentrations while exhibiting an enhanced stress overshoot. Extensive finite size analysis is performed to demonstrate the critical nature of the transition at a finite pinning concentration and the various scaling exponents obtained are found to be in good agreement with the reported values. Finally, we show a direct correspondence with the shear band width and the critical pining concentration to establish a possible connection between inherent disorder strength and quenched disorder strength due to particle pinning.
We study theoretically the yielding of sheared amorphous materials as a function of increasing levels of initial sample annealing prior to shear, in three widely used constitutive models and three widely studied annealing protocols. In thermal systems we find a gradual progression, with increasing annealing, from smoothly "ductile" yielding, in which the sample remains homogeneous, to abruptly "brittle" yielding, in which it becomes strongly shear banded. This progression arises from an increase with annealing in the size of an overshoot in the underlying stress-strain curve for homogeneous sh…
We study the nonlinear rheology of a novel class of transient networks, made of surfactant micelles of tunable morphology reversibly linked by block copolymers. We couple rheology and time-resolved structural measurements, using synchrotron radiation, to characterize the highly nonlinear viscoelastic regime. We propose the fluctuations of the degree of alignment of the micelles under shear as a probe to identify a fracture process. We show a clear signature of a brittle-to-ductile transition in transient gels, as the morphology of the micelles varies, and provide a parallel between the fractur…
The conditions which determine whether a material behaves in a brittle or ductile fashion on mechanical loading are still elusive and comprise a topic of active research among materials physicists and engineers. In this study, we present results of {\em in silico} mechanical deformation experiments from two very different model solids in two and three dimensions. The first consists of particles interacting with isotropic potentials and the other has strongly direction dependent interactions. We show that in both cases, the excess vibrational density of states is the fundamental quantity which …
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…
In this paper, we study the progressive collapse of 3D framed structures made of reinforced concrete after the sudden loss of a column. The structures are represented by elasto-plastic Euler Bernoulli beams with elongation-rotation failure threshold. We performed simulations using the Discrete Element Method considering inelastic collisions between the structural elements. The results show what collapse initiation and impact-driven propagation mechanisms are activated in structures with different geometric and mechanical features. Namely, we investigate the influence of the cross sectional siz…
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…
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…
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 analyze the failure process of a two-component system with widely different fracture strength in the framework of a fiber bundle model with localized load sharing. A fraction 0\leq α\leq 1 of the bundle is strong and it is represented by unbreakable fibers, while fibers of the weak component have randomly distributed failure strength. Computer simulations revealed that there exists a critical composition α_c which separates two qualitatively different behaviors: below the critical point the failure of the bundle is brittle characterized by an abrupt damage growth within the breakable part o…
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 combine an analytically solvable mean-field elasto-plastic model with molecular dynamics simulations of a generic glass-former to demonstrate that, depending on their preparation protocol, amorphous materials can yield in two qualitatively distinct ways. We show that well-annealed systems yield in a discontinuous brittle way, as metallic and molecular glasses do. Yielding corresponds in this case to a first-order nonequilibrium phase transition. As the degree of annealing decreases, the first-order character becomes weaker and the transition terminates in a second-order critical point in th…
Brittle failure is ubiquitous in amorphous materials that are sufficiently cooled below their glass transition temperature, $T_g$. This catastrophic failure mode is limiting for amorphous materials in many applications, and many fundamental questions surrounding it remain poorly understood. Two challenges that prevent a more fundamental understanding of the transition between a ductile response at temperatures near $T_g$ to brittle failure at lower temperatures are i) a lack of computationally inexpensive molecular models that capture the failure modes observed in experiments and ii) the lack …
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…
Applying constant tensile stress to a piece of amorphous solid results in a slow extension, followed by an eventual rapid mechanical collapse. This "creep" process is of paramount engineering concern, and as such was the subject of study in a variety of materials, for more than a century. Predictive theories for $τ_w$, the expected time of collapse, are lacking, mainly due to its dependence on a bewildering variety of parameters, including temperature, system size, tensile force, but also the detailed microscopic interactions between constituents. The complex dependence of the collapse time on…
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…
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…
Upon loading, amorphous solids can exhibit brittle yielding, with the abrupt formation of macroscopic shear bands leading to fracture, or ductile yielding, with a multitude of plastic events leading to homogeneous flow. It has been recently proposed, and subsequently questioned, that the two regimes are separated by a sharp critical point, as a function of some control parameter characterizing the intrinsic disorder strength and the degree of stability of the solid. In order to resolve this issue, we have performed extensive numerical simulations of athermally driven elasto-plastic models with…
We address the question of why larger, high symmetry crystals are mostly weak, ductile and statistically sub-critical, while smaller crystals with the same symmetry are strong, brittle and super-critical. We link it to another question of why intermittent elasto-plastic deformation of sub-micron crystals features highly unusual size sensitivity of scaling exponents. We use a minimal integer-valued automaton model of crystal plasticity to show that with growing variance of quenched disorder, which can serve in this case as a proxy for increasing size, sub-micron crystals undergo a crossover fro…
Understanding the role played by the microstructure of materials on their macroscopic failure properties is an important challenge in solid mechanics. Indeed, when a crack propagates at a heterogeneous brittle interface, the front is trapped by tougher regions and deforms. This pinning induces non-linearities in the crack propagation problem, even within Linear Elastic Fracture Mechanics theory, and modifies the overall failure properties of the material. For example crack front pinning by tougher places could increase the fracture resistance of multilayer structures, with interesting technolo…
