Anelastic Deformation Research Articles

Fast relaxation in metallic glasses studied by measurements of the internal friction at high frequencies

We performed high-frequency (0.4–1.7 MHz) measurements of the internal friction (IF) on 14 bulk metallic glasses (MGs). It is found that 12 of these MGs display relaxation IF peaks at temperatures ≈ 400–500 K, which are weakly affected by heat treatment within the amorphous state. The corresponding relaxation time is about 0.3 μs. This fast relaxation is reported for the first time in the literature. The apparent activation enthalpy for 4 MGs is determined. It is shown that if measured at a low frequency of 1 Hz, these IF peaks would appear near room temperature or by 30–50 K below it. Thus, the IF peaks found in the present investigation are direct analogues of low-temperature/low-frequency β′- and/or γ-relaxations described in the literature. It is argued that the origin of these IF peaks is related to the relaxation of structural defects similar to dumbbell interstitials, which are frozen in solid glass from the liquid state upon melt quenching. These defects can be considered as elastic dipoles and their re-orientation in the applied stress provides anelastic deformation and corresponding IF peak. After correction for temperature dependence of the shear modulus, the true activation enthalpy (0.62–1.08 eV) and activation entropy (4 ≤ΔS∕kB≤15) for defect re-orientation are determined.

Continuum kinematics with incompatible-compatible decomposition.

We present a framework for the kinematics of a material body undergoing anelastic deformation. For such processes, the material structure of the body, as reflected by the geometric structure given to the set of body points, changes. The setting we propose may be relevant to phenomena such as plasticity, fracture, discontinuities and non-injectivity of the deformations. In this framework, we construct an unambiguous decomposition into incompatible and compatible factors that includes the standard elastic-plastic decomposition in plasticity. This article is part of the theme issue 'Foundational issues, analysis and geometry in continuum mechanics'.

Anti-Hertz bulging of actuated liquid crystal elastomers

We consider the ‘anti-Hertz’ elastic problem of inverse indentation, which happens when the surface of an elastic material is pressed down with a plate with a round hole to form a bulge. This classical problem takes on a new life when a polydomain nematic liquid crystal elastomer is used. In this case, the nematic director aligns with the leading principal direction of local stress distribution created by bulging. When the deformed material is crosslinked a second time, this alignment pattern and the resulting permanent protrusion are preserved as pressure is removed, creating a bulge that can be reversibly actuated from a flat surface upon cooling. Experimentally, we also observe a dimple ring around the bulge and a punt (indentation) underneath it at the bottom. Theoretically, we model the deformation by coupling linear elastic and anelastic deformations using non-monotonic nematic elasticity and the singular stress-order relation of the polydomain-monodomain transition. The theory is in excellent agreement with the experiments, and predicts the emergence of all observed features.

Probing pre-serration deformation in Zr-based bulk metallic glass via nanoindentation testing

Bulk metallic glasses (BMG) are promising candidates for structural applications. However, they exhibit catastrophic failure, and the detection of their incipient plastic response remains unclear. In this study, we investigated the incipient plastic deformation behavior in Zr50Cu40Al10 at% bulk metallic glass via nanoindentation testing. An original and validated analytical layout, which is based on the load-over-displacement versus the displacement P/h-h plot, facilitates the analysis of any unstable deformation mode in the loading segment of the nanoindentation test. A certain anelastic deformation was detected definitely prior to the first serration that is conventionally recognized as a plasticity initiation. This result clearly indicates the presence of a precursor phenomenon to incipient plasticity before the first serration in BMG.

Непружність та демпфуюча здатність магнію і сплавів Mg—Al в умовах циклічного високоамплітудного навантаження

For Mg—Al alloys with magnesium content from 0 to 9%, measurements of anelastic deformation, damping capacity, and twinning start stresses were carried out. The method of cyclic loading under tension for a wide range of oscillations amplitudes with precision fixation of displacement was used. A method for determination of the start twinning deformation point σ0,002tw under conditions of cyclic loading is proposed, This stress characterizes the beginning of the inverse twinning stage, when the anelastic strain is 2∙10-5. Characteristics of σ0,002tw for technical magnesium and its alloys with aluminum in a wide range of plastic deformation are determined. An insignificant linear increase of σ0,002tw with increasing deformation was established for all Mg—Al alloys. The start twinning deformation point increases with increasing aluminum concentration. For low-alloy alloys with a solid-solution strengthening mechanism, the stress at the beginning of twinning increases insignificantly. For highly alloyed alloys, a significant increase of σ0,002tw stress is observed. It is established that repeated loading within the hysteresis loop to stresses. which is less than the maximum and is not accompanied by additional plastic deformation. If the level of applied stresses during repeated loading reaches the maximum value, the amount of plastic deformation after unloading increases. The addition in εpl gradually decreases with the rise of cycles number. The dependences of inelastic deformation and dissipated energy on the previous deformation degree for all investigated magnesium alloys demonstrate an extreme character. The growth of these characteristics is observed only in the initial part of the load to the residual deformation of 1—2%. With a further increase in deformation, the tendency to anelasticity and the damping capacity decrease. For the dependences dissipatson energy vs amplitude of loob stress, the maximum of dissipation energy is observed under the condition when the stress reaches a critical value, which corresponds to the beginning of prismatic or pyramidal sliding. Keywords: Mg—Al alloys, quasi-static cyclic loading, hysteresis loops, dissipation energy, damping capacity, elasticity, anelasticity, twinning start point.

Manufacturing and deformation behavior of alumina and zirconia helical springs at room temperature

AbstractCeramic helical springs with identical dimensions were produced by hard machining from alumina, alumina toughened zirconia (ATZ), and tetragonal zirconia polycrystals (TZP) stabilized with different oxides. According to the results of the spring constant determination under deformation rates of 3 mm/min, the deformation behavior of all ceramic springs obeys to Hook's law. However, variation of the deformation rate, tests under constant load, and spring recovery behavior revealed differences in the deformation behavior of alumina, TZP, and ATZ springs. Alumina springs exhibited time‐independent deformation in all tests. In contrast, anelastic deformation at room temperature was demonstrated in all springs containing TZP. This deformation is completely reversible over a period of several days. Anelastic behavior is particularly pronounced in Y‐TZP springs, whereas Ce‐TZP springs exhibit comparatively very low but still reliably detectable anelasticity. Oxygen vacancies in the TZP ceramic are considered the most likely explanation for the anelastic behavior of TZP springs at room temperature.

Damping Analysis of High Damping MgO/Mg Composites in Anelastic and Microplastic Deformation

In this study, MgO/Mg composites were prepared using direct melt oxidation to verify the effects of elastic deformation and microplastic deformation on the damping properties. It was found that the composites have high damping properties at a certain strain amplitude, which indicated that the damping properties of the magnesium matrix were effectively enhanced by the in situ-synthesized oxide particle. In addition, other damping mechanisms different from the G–L dislocation damping mechanism exist in MgO/Mg composites, i.e., the damping mechanism of the microplastic deformation, leading to a model of microplastic deformation damping established and its mechanistic analysis.

Structural rejuvenation of a well-aged metallic glass

Rejuvenation of glassy structures in general is characterized by the exothermic enthalpy prior to the glass transition. In the present work, we find that this situation is not applicable to a heavily-aged Zr-based metallic glass that rejuvenates by anelastic deformation before yield. Instead, its rejuvenation can be precisely captured by the low-temperature boson heat capacity peak as well as the effective enthalpy change with the glass-to-liquid transition. These results demonstrate that a structurally stable glass could rejuvenate by decreasing mechanical stability of its basin of potential energy landscape, but without changing the basin's energy level. The underlying mechanism points toward the redistribution of the atomic free volume with a constant system-averaged value. We further find that the rejuvenation limit of this glass is its steady-flow state with self-similar inherent structures at both short- and long-time scales. Our findings refresh the understanding of glass rejuvenation and suggest that the boson peak is a better probe for the structural rejuvenation of glasses.

Ultrasonic-promoted defect activation and structural rejuvenation in a La-based metallic glass

Ultrasonic-assistant rejuvenation in a La-based metallic glass was demonstrated by means of nanoindentation for the first time. A more pronounced nanoindentation creep behavior along with mechanical softening was detected. It is proposed to be associated with the activation of flow defects with long characteristic relaxation time at a low loading rate and short characteristic relaxation time at a high loading rate during anelastic deformation process based on the Maxwell-Voigt model. Such rejuvenation behavior also leads to an unstable plastic flow and a relatively low energy barrier for atomic diffusion during the fast growth process of crystalline phases accompanied with the reduced glass transition and crystallization temperatures. Our studies might provide insights into the microscopic deformation mechanism of glassy materials, which could help in seeking the novel applications of amorphous alloys such as ultrasonic-assistant cold joining or molding.

Anelastic deformation in the lower crust and its implications for tectonic dynamics in Kyushu, Southwest Japan

Most of the seismicity in inland Kyushu, southwest Japan occur in the localized intraplate shear zones which are Beppu-Shimabara Graben (BSG) and left-lateral shear zone (LSZ). One of the largest fault systems in Japan (Median Tectonic Line—MTL), and subduction zone of the Philippine Sea Plate also exist near Kyushu. These suggest that the island arc, such as Kyushu has a complex deformation process. This study estimated the anelastic strain rate in the lower crust and the interplate coupling rate via inversion analysis using Global Navigation Satellite System data to elucidate the seismotectonics. Deformation in the lower crust and interplate coupling were modeled by cuboid volumetric sources and a back slip model, respectively. To stabilize the solution, a L2 regularization constraint was applied to the anelastic strain rate. Further, constraints on direction and smoothing to the slip deficit rate were applied. These strength of the constraints were determined via the minimum value of the Akaike Bayesian information criterion. The analyses showed that the anelastic strain rate of the BSG and LSZ was ∼0.6 ×10−6 yr−1, and BSG was related to MTL activity. The findings also suggest that this anelastic deformation in the lower crust created a stress concentration zone in the upper crust of BSG and LSZ, with a stress change rate of ∼6–10 kPa·yr−1. The value is consistent with the stress drop and recurrence interval of regional earthquakes, suggesting that the seismicity around BSG and LSZ is strongly influenced by anelastic deformation in the lower crust. It is also suggested that BSG and LSZ development is influenced by slab rollback, and a subducting ridge. Lastly, a comparison between the deviatoric stress field estimated using focal mechanisms and the anelastic strain rate suggests the existence of a shear zone consisting of weak faults south of BSG.

Delayed elasticity of metallic glasses: Loading time and temperature dependences of the anelastic relaxation

One of the hallmarks of disordered matter is the large amplitude of the anelastic deformation, i.e., the fraction of reversible deformation that is not instantaneously recovered after the release of load but is delayed in time. In this paper, this delayed elasticity is studied for the glass-forming ${\mathrm{Zr}}_{46.25}{\mathrm{Ti}}_{8.25}{\mathrm{Cu}}_{7.5}{\mathrm{Ni}}_{10}{\mathrm{Be}}_{27.5}$ alloy by means of stress step and recovery experiments. Even at high temperatures, not far from the glass transition, the delayed elasticity can recover an important fraction of the deformation and endure for a long time. Analyzing the effects of loading time and waiting time on the strain evolution, we reveal the presence of an anelastic response with a timescale dependent on loading time and an invariant shape, which indicates the presence of a distribution of reversible relaxation modes following a ${\ensuremath{\tau}}^{\ensuremath{-}n}$ law with exponent $n$ between 0.5 and 1. The underlying distribution of energy barriers activated at different temperatures is accordingly shape invariant. Moreover, we found that a distribution of reversible modes corresponding to the high-frequency side of the $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{relaxation}$ peak can reproduce the experimental results. The results establish a direct link between the dynamical spectrum and the distribution of activation energies, revealing the origin of the transient creep and anelastic recovery behaviors of metallic glasses.

On the direct and reverse multiplicative decompositions of deformation gradient in nonlinear anisotropic anelasticity

In this paper we discuss nonlinear anisotropic anelasticity formulated based on the two multiplicative decompositions F=FeFa and F=FaFe. Using the Bilby–Kröner–Lee decomposition F=FeFa one can define a Riemannian material manifold (the natural configuration of an anelastic body) whose metric explicitly depends on the anelastic deformation Fa. We call this the global material intermediate configuration. Deformation is a map from this Riemannian manifold to the flat ambient space. Using the reverse decomposition F=FaFe, the reference configuration is a (flat) submanifold of the Euclidean ambient space, while the global intermediate configuration is a Riemannian manifold whose metric explicitly depends on the elastic deformation Fe. We call this the global spatial intermediate configuration. We show that the direct F=FeFa and reverse F=FaFe decompositions correspond to the same anelastic motion if and only if Fe and Fe are equal up to local isometries of the reference configuration. We discuss the constitutive equations of anisotropic anelastic solids in terms of both intermediate configurations. It is shown that the two descriptions of anelasticity are equivalent in the sense that the Cauchy stresses calculated using them are identical. We note that, unlike isotropic solids, for an anisotropic solid the material metric is not sufficient for describing the constitutive behavior of the solid; the energy function explicitly depends on Fa (or Fa) through the structural tensors.

Anelasticity in thin-shell nanolattices

In this work, we investigate the anelastic deformation behavior of periodic three-dimensional (3D) nanolattices with extremely thin shell thicknesses using nanoindentation. The results show that the nanolattice continues to deform with time under a constant load. In the case of 30-nm-thick aluminum oxide nanolattices, the anelastic deformation accounts for up to 18.1% of the elastic deformation for a constant load of 500 μN. The nanolattices also exhibit up to 15.7% recovery after unloading. Finite element analysis (FEA) coupled with diffusion of point defects is conducted, which is in qualitative agreement with the experimental results. The anelastic behavior can be attributed to the diffusion of point defects in the presence of a stress gradient and is reversible when the deformation is removed. The FEA model quantifies the evolution of the stress gradient and defect concentration and demonstrates the important role of a wavy tube profile in the diffusion of point defects. The reported anelastic deformation behavior can shed light on time-dependent response of nanolattice materials with implication for energy dissipation applications.

Origin of coseismic anelastic deformation during the 2016 Mw 6.4 Meinong Earthquake, Taiwan

An unexpectedly large uplift of 91 mm was detected by geodetic observations during the rupture of 2016 Mw 6.4 Meinong earthquake, Taiwan, which has been attributed as either a triggered anelastic and hydrologic related deformation from a proposed duplex/mud diapir or a triggered aseismic slip on a proposed backthrust. Here, using both high-rate GNSS and free-field strong motion data, we first estimated the coseismic source model. The locations of high PGV were inferred to explain the unexpected distribution of damaged buildings approximately 25–30 km west of the epicenter. Then, the aseismic surface displacements during the earthquake was differentiated using the coseismic source model. The aseismic extension of 3.8 μstrain is inferred at the unexpectedly large uplift region. Combining with local geology, residual gravity anomaly, seismic tomography, interseismic leveling vertical velocities, coseismic leveling uplifts and proposed Coulomb stress changes, the accelerated mud diapirism during the earthquake triggered by slip on the deep seismogenic fault was identified as the cause of unexpectedly large coseismic uplift.

Rate-dependent nanoindentation creep behavior of a Fe-based amorphous coating

A very thick (∼1 mm) coating of Fe-based amorphous material was applied to a Q235 steel substrate by detonation spraying. The rate-dependent anelastic and viscoplastic deformations of the coating were investigated through nanoindentation creep experiments with loading rates of 0.1∼5 mN s−1; the results were analyzed using the Maxwell-Voigt model with two Kelvin units. Creep deformation in the Fe-based amorphous coating was found to be sensitive to loading rate; the nanohardness, creep-stress exponent, and viscosity lessened with increased loading rate during viscoplastic deformation. The presence of two characteristic peaks in the relaxation-time spectrum shows that the anelastic deformation was related to the activation of two types of defects. Low loading rates promoted the activation of defects in the soft region with long relaxation times; larger loading rates promoted the activation of defects in the hard region with shorter structural relaxation times, allowing plastic deformation. This resulted in lower creep resistance at higher loading rates.

Analysis of the anelastic deformation of high-entropy Pd20Pt20Cu20Ni20P20 metallic glass under stress relaxation and recovery

1 Mechanical response of Pd 20 Pt 20 Cu 20 Ni 20 P 20 high-entropy metallic glass is revealed and characterized through the stress relaxation and recovery process. 2 Stress relaxation during consecutive strain steps can be well described by the Kohlrausch-Williams-Watts (KWW) function. 3 A constitutive model is also applied to analyze in detail the hierarchy of structural and dynamic heterogeneity. The anelastic deformation behavior of Pd 20 Pt 20 Cu 20 Ni 20 P 20 high-entropy metallic glass was probed by monitoring the stress relaxation and recovery processes. The stress relaxation under consecutive strain steps can be described by the Kohlrausch-Williams-Watts (KWW) function. In addition, considering a hierarchy of relaxation processes related to the structural heterogeneity, a constitutive model is proposed in order to describe the whole process of stress relaxation and determine the contribution of different time scales. Moreover, a crossover from stochastic activation to percolation of flow defects with the ultimate strain can be observed during stress relaxation process. The anelastic recovery process after a strain step is studied as a function of the initial strain level and characterized by means of a direct spectrum analysis. The peaks in the recovery time-spectra revealed the evolution of flow defects in Pd 20 Pt 20 Cu 20 Ni 20 P 20 high-entropy metallic glass. The understanding of the atomic free-volume zones effect and the anelastic deformation provides important insight into how atomic structural features affect the deformation behavior of high-entropy metallic glasses, and may provide a new avenue into the improvement of their mechanical properties.

Anelastic Behaviour of Commercial Die-Cast Magnesium Alloys: Effect of Temperature and Alloy Composition.

The anelastic deformation, resulting from partial reversal of {102} twinning, is studied at room temperature to 150 °C on several commercial die-cast magnesium alloys for the first time. The magnitude of anelastic strain decreases with increasing temperature. For inter-alloy comparison, AZ91 shows the largest maximum anelastic strain, while AM40 and AM60 show similar maximum anelastic strain. The phenomenon is discussed in terms of solid solution softening and hardening of slip planes and how they influence twinning. T5-aged AE44 consistently shows smaller magnitude of anelasticity compared to as-cast AE44, suggesting that the precipitates formed during ageing may decrease the twin-boundary mobility and further suppress untwinning. Presence of anelasticity poses a challenge to yield strength measurement using the conventional 0.2% offset method, and a more accurate and consistent method of using a higher offset strain or a lower modulus is proposed in this study.

Room-temperature oxygen vacancy migration induced reversible phase transformation during the anelastic deformation in CuO

From the mechanical perspectives, the influence of point defects is generally considered at high temperature, especially when the creep deformation dominates. Here, we show the stress-induced reversible oxygen vacancy migration in CuO nanowires at room temperature, causing the unanticipated anelastic deformation. The anelastic strain is associated with the nucleation of oxygen-deficient CuOx phase, which gradually transforms back to CuO after stress releasing, leading to the gradual recovery of the nanowire shape. Detailed analysis reveals an oxygen deficient metastable CuOx phase that has been overlooked in the literatures. Both theoretical and experimental investigations faithfully predict the oxygen vacancy diffusion pathways in CuO. Our finding facilitates a better understanding of the complicated mechanical behaviors in materials, which could also be relevant across multiple scientific disciplines, such as high-temperature superconductivity and solid-state chemistry in Cu-O compounds, etc.

Atomistic understanding of creep and relaxation mechanisms of Cu64Zr36 metallic glass at different temperatures and stress levels

In this paper, the tensile creep behavior of Cu64Zr36 metallic glass (MG) is investigated by molecular dynamics simulations. The effects of stress and temperature on the evolution of activated states during nanoscale creep tests are discussed, the creep failure time is predicted by linear regression analysis and three creep mechanisms are found. The creep mechanisms at the low stress and high temperature regime is dominated by thermally activated atomic diffusional creep; the low temperature and low stress regime is dominated by anelastic deformation and homogeneous activation of elastic events, while the low temperature and high stress regime is governed by local inhomogeneous shear deformation through shear transformation zones (STZs) percolation and embryonic shear band formation. These mechanisms help to further understand the creep behavior and derive an atomistic description of the relationship between the creep behavior and the three mechanisms of mechanical relaxations in MGs: atomic diffusion via cooperative atomic motion or α relaxation, stress-induced STZs activation such as slow β relaxation and anelastic deformation (fast β’ relaxation), respectively.

The nature of yielding and anelasticity in metals

Recent reports in the literature identified pre-yield stress-strain nonlinearity and hysteresis (anelasticity) as occurring in metals at virtually all stresses. These observations raise foundational questions about metal deformation. Does a critical stress exist below which dislocations are immobile? Is there a critical stress for which permanent deformation occurs? Is anelasticity distinct from elasticity and plasticity? To answer such questions, special tensile tests with loading-unloading cycles after various prestrains were performed for 11 commercial sheet alloys: 9 AHSS (advanced high strength steels) and two Mg alloys. A dissipative dislocation bow-out model of anelasticity was derived that closely reproduces the experimental results and is consistent with the evolving experimental picture of anelasticity. Following prestrain, a finite yield stress was found to exist, below which no permanent deformation or hardening occurs. Anelasticity is distinct from elasticity and plasticity: it is recoverable and dissipative; mechanically reversible and thermodynamically irreversible. Corresponding tests of initial loading suggest radically different conclusions. Without prestrain, i.e. without a developed internal stress pattern, plastic deformation occurs near zero stress. A postulate of local and nonlocal interactions accounting for elastic, plastic and anelastic deformation was proposed.