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Cochran JO, Callaghan GL, Caven MJG, Fielding SM. Slow Fatigue and Highly Delayed Yielding via Shear Banding in Oscillatory Shear. PHYSICAL REVIEW LETTERS 2024; 132:168202. [PMID: 38701472 DOI: 10.1103/physrevlett.132.168202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2022] [Revised: 11/21/2023] [Accepted: 03/15/2024] [Indexed: 05/05/2024]
Abstract
We study theoretically the dynamical process of yielding in cyclically sheared amorphous materials, within a thermal elastoplastic model and the soft glassy rheology model. Within both models we find an initially slow accumulation, over many cycles after the inception of shear, of low levels of damage in the form strain heterogeneity across the sample. This slow fatigue then suddenly gives way to catastrophic yielding and material failure. Strong strain localization in the form of shear banding is key to the failure mechanism. We characterize in detail the dependence of the number of cycles N^{*} before failure on the amplitude of imposed strain, the working temperature, and the degree to which the sample is annealed prior to shear. We discuss our finding with reference to existing experiments and particle simulations, and suggest new ones to test our predictions.
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Affiliation(s)
- James O Cochran
- Department of Physics, Durham University, Science Laboratories, South Road, Durham DH1 3LE, United Kingdom
| | - Grace L Callaghan
- Department of Physics, Durham University, Science Laboratories, South Road, Durham DH1 3LE, United Kingdom
| | - Miles J G Caven
- Department of Physics, Durham University, Science Laboratories, South Road, Durham DH1 3LE, United Kingdom
| | - Suzanne M Fielding
- Department of Physics, Durham University, Science Laboratories, South Road, Durham DH1 3LE, United Kingdom
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2
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Agoritsas E, Barés J. Loss of memory of an elastic line on its way to limit cycles. Phys Rev E 2024; 109:L042901. [PMID: 38755875 DOI: 10.1103/physreve.109.l042901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2023] [Accepted: 03/10/2024] [Indexed: 05/18/2024]
Abstract
Oscillatory-driven amorphous materials forget their initial configuration and converge to limit cycles. Here we investigate this memory loss under a nonquasistatic drive in a minimal model system, with quenched disorder and memory encoded in a spatial pattern, where oscillating protocols are formally replaced by a positive-velocity drive. We consider an elastic line driven athermally in a quenched disorder with biperiodic boundary conditions and tunable system size, thus controlling the area swept by the line per cycle as would the oscillation amplitude. The convergence to disorder-dependent limit cycle is strongly coupled to the nature of its velocity dynamics depending on system size. Based on the corresponding phase diagram, we propose a generic scenario for memory formation in disordered systems under finite driving rate.
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Affiliation(s)
- Elisabeth Agoritsas
- Department of Quantum Matter Physics (DQMP), University of Geneva, Quai Ernest-Ansermet 24, CH-1211 Geneva, Switzerland
| | - Jonathan Barés
- Laboratoire de Mécanique et Génie Civil (LMGC), UMR 5508 CNRS-University Montpellier, 34095 Montpellier, France
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3
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Minogue D, Eskildsen MR, Reichhardt C, Reichhardt CJO. Reversible, irreversible, and mixed regimes for periodically driven disks in random obstacle arrays. Phys Rev E 2024; 109:044905. [PMID: 38755905 DOI: 10.1103/physreve.109.044905] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2024] [Accepted: 03/27/2024] [Indexed: 05/18/2024]
Abstract
We examine an assembly of repulsive disks interacting with a random obstacle array under a periodic drive and find a transition from reversible to irreversible dynamics as a function of drive amplitude or disk density. At low densities and drives, the system rapidly forms a reversible state where the disks return to their exact positions at the end of each cycle. In contrast, at high amplitudes or high densities, the system enters an irreversible state where the disks exhibit normal diffusion. Between these two regimes, there can be an intermediate irreversible state where most of the system is reversible, but localized irreversible regions are present that are prevented from spreading through the system due to a screening effect from the obstacles. We also find states that we term "combinatorial reversible states" in which the disks return to their original positions after multiple driving cycles. In these states, individual disks exchange positions but form the same configurations during the subcycles of the larger reversible cycle.
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Affiliation(s)
- D Minogue
- Department of Physics, University of Notre Dame, Notre Dame, Indiana 46656, USA
| | - M R Eskildsen
- Department of Physics, University of Notre Dame, Notre Dame, Indiana 46656, USA
| | - C Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C J O Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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4
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Richard D, Elgailani A, Vandembroucq D, Manning ML, Maloney CE. Mechanical excitation and marginal triggering during avalanches in sheared amorphous solids. Phys Rev E 2023; 107:034902. [PMID: 37072969 DOI: 10.1103/physreve.107.034902] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2022] [Accepted: 02/26/2023] [Indexed: 04/20/2023]
Abstract
We study plastic strain during individual avalanches in overdamped particle-scale molecular dynamics (MD) and mesoscale elastoplastic models (EPM) for amorphous solids sheared in the athermal quasistatic limit. We show that the spatial correlations in plastic activity exhibit a short length scale that grows as t^{3/4} in MD and ballistically in EPM, which is generated by mechanical excitation of nearby sites not necessarily close to their stability thresholds, and a longer lengthscale that grows diffusively for both models and is associated with remote marginally stable sites. These similarities in spatial correlations explain why simple EPMs accurately capture the size distribution of avalanches observed in MD, though the temporal profiles and dynamical critical exponents are quite different.
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Affiliation(s)
- D Richard
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam, Netherlands
- Department of Physics and BioInspired Institute, Syracuse University, Syracuse, New York 13244, USA
- Univiversité Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France
| | - A Elgailani
- Northeastern University, Boston, Massachusetts 02115, USA
| | - D Vandembroucq
- PMMH, CNRS UMR 7636, ESPCI Paris, PSL University, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - M L Manning
- Department of Physics and BioInspired Institute, Syracuse University, Syracuse, New York 13244, USA
| | - C E Maloney
- Northeastern University, Boston, Massachusetts 02115, USA
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5
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Keim NC, Medina D. Mechanical annealing and memories in a disordered solid. SCIENCE ADVANCES 2022; 8:eabo1614. [PMID: 36197976 PMCID: PMC9534499 DOI: 10.1126/sciadv.abo1614] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/19/2022] [Accepted: 08/18/2022] [Indexed: 06/16/2023]
Abstract
Shearing a disordered or amorphous solid for many cycles with a constant strain amplitude can anneal it, relaxing a sample to a steady state that encodes a memory of that amplitude. This steady state also features a remarkable stability to amplitude variations that allows one to read the memory. Here, we shed light on both annealing and memory by considering how to mechanically anneal a sample to have as little memory content as possible. In experiments, we show that a "ring-down" protocol reaches a comparable steady state but with no discernible memories and minimal structural anisotropy. We introduce a method to characterize the population of rearrangements within a sample and show how it connects with the response to amplitude variation and the size of annealing steps. These techniques can be generalized to other forms of glassy matter and a wide array of disordered solids, especially those that yield by flowing homogeneously.
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Affiliation(s)
- Nathan C. Keim
- Department of Physics, Pennsylvania State University, University Park, PA 16802, USA
- Department of Physics, California Polytechnic State University, San Luis Obispo, CA 93407, USA
| | - Dani Medina
- Department of Physics, California Polytechnic State University, San Luis Obispo, CA 93407, USA
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6
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Otsuki M, Hayakawa H. Softening and Residual Loss Modulus of Jammed Grains under Oscillatory Shear in an Absorbing State. PHYSICAL REVIEW LETTERS 2022; 128:208002. [PMID: 35657892 DOI: 10.1103/physrevlett.128.208002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2021] [Revised: 12/26/2021] [Accepted: 04/22/2022] [Indexed: 06/15/2023]
Abstract
From a theoretical study of the mechanical response of jammed materials comprising frictionless and overdamped particles under oscillatory shear, we find that the material becomes soft, and the loss modulus remains nonzero even in an absorbing state where any irreversible plastic deformation does not exist. The trajectories of the particles in this region exhibit hysteresis loops. We succeed in clarifying the origin of the softening of the material and the residual loss modulus with the aid of Fourier analysis. We also clarify the roles of the yielding point in the softening to distinguish the plastic deformation from reversible deformation in the absorbing state.
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Affiliation(s)
- Michio Otsuki
- Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawaoiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
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7
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Parley JT, Sastry S, Sollich P. Mean-Field Theory of Yielding under Oscillatory Shear. PHYSICAL REVIEW LETTERS 2022; 128:198001. [PMID: 35622036 DOI: 10.1103/physrevlett.128.198001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2022] [Accepted: 04/13/2022] [Indexed: 06/15/2023]
Abstract
We study a mean field elastoplastic model, embedded within a disordered landscape of local yield barriers, to shed light on the behavior of athermal amorphous solids subject to oscillatory shear. We show that the model presents a genuine dynamical transition between an elastic and a yielded state, and qualitatively reproduces the dependence on the initial degree of annealing found in particle simulations. For initial conditions prepared below the analytically derived threshold energy, we observe a nontrivial, nonmonotonic approach to the yielded state. The timescale diverges as one approaches the yielding point from above, which we identify with the fatigue limit. We finally discuss the connections to brittle yielding under uniform shear.
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Affiliation(s)
- Jack T Parley
- Institut für Theoretische Physik, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Srikanth Sastry
- Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkar Campus, 560064 Bengaluru, India
| | - Peter Sollich
- Institut für Theoretische Physik, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany and Department of Mathematics, King's College London, London WC2R 2LS, United Kingdom
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8
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szulc A, Mungan M, Regev I. Cooperative effects driving the multi-periodic dynamics of cyclically sheared amorphous solids. J Chem Phys 2022; 156:164506. [DOI: 10.1063/5.0087164] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
When subject to cyclic forcing, amorphous solids can reach periodic, repetitive states, where the system behaves plastically, but the particles return to their initial positions after one or more forcing cycles, where the latter response is called multi-periodic. It is known that plasticity in amorphous materials is mediated by local rearrangements called ``soft spots' or ``shear transformation zones'.Experiments and simulations indicate that soft spots can be modeled as hysteretic two-state entities interacting via quadrupolar displacement fields generated when they switch states and that these interactions can give rise to multi-periodic behavior. However, how interactions facilitate multi-periodicity is unknown. Here we show, using a model of random interacting two-state systems and molecular dynamics simulations, that multi-periodicity arises from oscillations in the magnitudes of the switching field of soft spots which cause soft spots to be active during some forcing cycles and idle during others. We demonstrate that these oscillations result from cooperative effects facilitated by the frustrated interactions between the soft spots. The presence of such mechanisms has implications for manipulating memory in frustrated hysteretic systems.
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Affiliation(s)
- asaf szulc
- Department of Physics, Ben-Gurion University of the Negev, Israel
| | - Muhittin Mungan
- Rheinische Friedrich Wilhelms Universität Bonn Institute of Applied Mathematics, Germany
| | - Ido Regev
- Solar energy and environmental physics, Ben-Gurion University of the Negev - Sede Boqer Campus, Israel
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9
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Bhaumik H, Foffi G, Sastry S. Avalanches, Clusters, and Structural Change in Cyclically Sheared Silica Glass. PHYSICAL REVIEW LETTERS 2022; 128:098001. [PMID: 35302798 DOI: 10.1103/physrevlett.128.098001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2021] [Revised: 01/14/2022] [Accepted: 02/09/2022] [Indexed: 06/14/2023]
Abstract
We investigate avalanches and clusters associated with plastic rearrangements and the nature of structural change in the prototypical strong glass, silica, computationally. We perform a detailed analysis of avalanches, and of spatially disconnected clusters that constitute them, for a wide range of system sizes. Although qualitative aspects of yielding in silica are similar to other glasses, the statistics of clusters exhibits significant differences, which we associate with differences in local structure. Across the yielding transition, anomalous structural change and densification, associated with a suppression of tetrahedral order, is observed to accompany strain localization.
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Affiliation(s)
- Himangsu Bhaumik
- Jawaharlal Nehru Center for Advanced Scientific Research, Jakkur Campus, Bengaluru 560064, India
| | - Giuseppe Foffi
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Srikanth Sastry
- Jawaharlal Nehru Center for Advanced Scientific Research, Jakkur Campus, Bengaluru 560064, India
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Reichhardt C, Reichhardt C. Reversible to Irreversible Transitions for Cyclically Driven Particles on Periodic Obstacle Arrays. J Chem Phys 2022; 156:124901. [DOI: 10.1063/5.0087916] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We examine the collective dynamics of disks moving through a square array of obstacles under cyclic square wave driving. Below a critical density we find that system organizes into a reversible state in which the disks return to the same positions at the end of every drive cycle. Above this density, the dynamics are irreversible and the disks do not return to the same positions after each cycle. The critical density depends strongly on the angle θ between the driving direction and a symmetry axis of the obstacle array, with the highest critical densities appearing at commensurate angles such as θ=0{degree sign} and θ=45{degree sign} and the lowest critical densities falling at θ=arctan(0.618), the inverse of the golden ratio, where the flow is the most frustrated. As the density increases, the number of cycles required to reach a reversible state grows as a power law with an exponent near ν=1.36, similar to what is found in periodically driven colloidal and superconducting vortex systems.
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Affiliation(s)
| | - Cynthia Reichhardt
- Theoretical Division, Los Alamos National Laboratory, United States of America
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11
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Liu C, Ferrero EE, Jagla EA, Martens K, Rosso A, Talon L. The Fate of Shear-Oscillated Amorphous Solids. J Chem Phys 2022; 156:104902. [DOI: 10.1063/5.0079460] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Chen Liu
- Columbia University Department of Chemistry, United States of America
| | | | - Eduardo A. Jagla
- Teoria de solidos, Centro Atomico Bariloche, Comision Nacional de Energia Atomica, Argentina
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12
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Mungan M, Sastry S. Metastability as a Mechanism for Yielding in Amorphous Solids under Cyclic Shear. PHYSICAL REVIEW LETTERS 2021; 127:248002. [PMID: 34951789 DOI: 10.1103/physrevlett.127.248002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2021] [Revised: 09/12/2021] [Accepted: 11/16/2021] [Indexed: 06/14/2023]
Abstract
We consider the yielding behavior of amorphous solids under cyclic shear deformation and show that it can be mapped into a random walk in a confining potential with an absorbing boundary. The resulting dynamics is governed by the first passage time into the absorbing state and suffices to capture the essential qualitative features recently observed in atomistic simulations of amorphous solids. Our results provide insight into the mechanism underlying yielding and its robustness. When the possibility of activated escape from absorbing states is added, it leads to a unique determination of a threshold energy and yield strain, suggesting thereby an appealing approach to understanding fatigue failure.
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Affiliation(s)
- Muhittin Mungan
- Institut für angewandte Mathematik, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
| | - Srikanth Sastry
- Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkar Campus, 560064 Bengaluru, India
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13
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Sastry S. Models for the Yielding Behavior of Amorphous Solids. PHYSICAL REVIEW LETTERS 2021; 126:255501. [PMID: 34241520 DOI: 10.1103/physrevlett.126.255501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2020] [Accepted: 05/18/2021] [Indexed: 06/13/2023]
Abstract
Investigations of plastic deformation and yielding of amorphous solids reveal a strong dependence of their yielding behavior on the degree of annealing. Above a threshold degree of annealing, the nature of yielding changes qualitatively, becoming progressively more discontinuous. Theoretical investigations of yielding in amorphous solids have almost exclusively focused on uniform deformation, but cyclic deformation reveals intriguing features that remain uninvestigated. Focusing on athermal cyclic deformation, I investigate a family of models, which reproduce key features observed in simulations, and provide an interpretation for the intriguing presence of a threshold energy.
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Affiliation(s)
- Srikanth Sastry
- Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur Campus, Bengaluru 560064, India
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