Anelastic Behavior Research Articles

Compressing the memory variables in constant-Q viscoelastic wave propagation via an improved sum-of-exponentials approximation

Earth introduces strong attenuation and dispersion to propagating waves. The time-fractional wave equation with very small fractional exponent, based on Kjartansson's constant-Q theory, is widely recognized in the field of geophysics as a reliable model for frequency-independent Q anelastic behavior. Nonetheless, the numerical resolution of this equation poses considerable challenges due to the requirement of storing a complete time history of wavefields. To address this computational challenge, we present a novel approach: a nearly optimal sum-of-exponentials (SOE) approximation to the Caputo fractional derivative with very small fractional exponent, utilizing the machinery of generalized Gaussian quadrature. This method minimizes the number of memory variables needed to approximate the power attenuation law within a specified error tolerance. We establish a mathematical equivalence between this SOE approximation and the continuous fractional stress-strain relationship, relating it to the generalized Maxwell body model. Furthermore, we prove an improved SOE approximation error bound to thoroughly assess the ability of rheological models to replicate the power attenuation law. Numerical simulations on constant-Q viscoacoustic equation in 3D homogeneous media and variable-order P- and S- viscoelastic wave equations in 3D inhomogeneous media are performed. These simulations demonstrate that our proposed technique accurately captures changes in amplitude and phase resulting from material anelasticity. This advancement provides a significant step towards the practical usage of the time-fractional wave equation in seismic inversion.

A cryogenic forced oscillation apparatus to measure anelasticity of ice.

We have developed a new cryogenic uni-axial forced oscillation apparatus to measure the anelastic behavior of ice by adapting the design of a previous high-precision apparatus for use in low-temperature (<0 °C) conditions. With this new apparatus, Young's modulus and attenuation can be measured over a broad frequency range from 10-4 to 10Hz. We have performed calibration tests with standard materials (steel spring, stainless steel, and acrylic samples) under various conditions to assess the apparatus properties and correct the effects on the obtained raw data. Young's modulus and attenuation for an acrylic sample after all of the data corrections show good agreement with previously published values, demonstrating the validity of the data corrections and reliability of the obtained data. We further obtained a preliminary dataset of Young's modulus and attenuation for an ice polycrystalline sample under small median stress and small stress amplitude. The anelastic response was not strain amplitude-dependent, that is, the response is linear. Moreover, the attenuation data are consistent with the data measured for other polycrystalline materials under similarly small stress conditions in terms of the Maxwell frequency scaling, which is known as a scaling law applicable to linear anelasticity induced by the diffusionally accommodated grain boundary sliding mechanism. Although there is still room for improving the control of testing conditions, we show that the new forced oscillation apparatus is capable of systematic studies on the anelastic properties of ice, the subject of future studies.

Twinning–Detwinning-Dominated Cyclic Deformation Behavior of a High-Strength Mg-Al-Sn-Zn Alloy during Loading Reversals: Experiment and Modeling

The deformation behavior of a high-strength Mg-Al-Sn-Zn alloy under loading reversals has been thoroughly examined through a combination of experimental measurements and crystal plasticity modeling. We focused on an age-treated alloy fortified by distributed Mg2Sn particles and Mg17Al12 precipitates, which underwent two distinct loading cycles: tension-compression-tension (TCT) and compression-tension-compression (CTC), aligned with the extrusion direction (ED). The initial and deformed microstructures of the alloy were analyzed using the electron backscattering diffraction (EBSD) technique. Notably, the alloy displays tensile and compressive yield strengths (YS) of 215 MPa and 160 MPa, respectively, with pronounced anelastic behavior observed during unloading and reverse loading phases. Utilizing the elasto-viscoplastic self-consistent model incorporating a twinning–detwinning scheme (EVPSC-TDT), the cyclic stress–strain responses and resultant textures of the alloy were accurately captured. The predicted alternation between various slip and twinning modes during plastic deformation was used to interpret the observed behaviors. It was found that prismatic &lt;a&gt; slip plays an important role during the plastic deformation of the studied alloy, and its relative activity in tensile loading processes accounts for up to ~66% and ~67% in the TCT and CTC cases, respectively. Moreover, it was discerned that detwinning and twinning behaviors are predominantly governed by stresses within the parent grain, and they can concurrently manifest during the reverse tensile loading phase in the TCT case. After cyclic deformation, the area fractions of residual twins were determined to be 7.51% and 0.93% in the TCT and CTC cases, respectively, which is a result of the varied twinning–detwinning behavior of the alloy in different loading paths.

Preliminary characterization of anelastic effects in the flexure mechanism for a new Kibble balance at NIST

A new Kibble balance is being built at the National Institute of Standards and Technology (NIST). For the first time in one of the highly accurate versions of this type of balance, a single passive flexure mechanism is used for both modes of operation: the weighing mode and the velocity mode. The mechanism is at the core of the new balance design as it represents a paradigm shift for NIST away from using knife edge-based balance mechanisms, which exhibit hysteresis in the measurement procedure of the weighing mode. Mechanical hysteresis may be a limiting factor in the performance of highly accurate Kibble balances approaching single digit nanonewton repeatability on a nominal 100g mass, as targeted in this work. Flexure-based mechanisms are known to have very good static hysteresis when used as a null detector. However, for larger and especially longer lasting deformations, flexures are known to exhibit anelastic drift. We seek to characterize, and ideally compensate for, this anelastic behavior after deflections during the velocity mode to enable a 10−8 accurate Kibble balance-measurement on a nominal 100g mass artifact with a single flexure-based balance mechanism. A measurement of the anelastic after-effect after static excitation hints that the apparatus produced a result for anelastic relaxation comparable to previously published work. Furthermore, a series of oscillatory displacements similar to those occurring in a velocity mode of a Kibble balance measurement are imposed upon the flexure mechanism and show a significant anelastic relaxation torque resulting in multiple micronewton of force relaxation. The amplitude of this force relaxation could be reduced by counterbending the flexures before performing a force measurement.

Ultrabroad distribution of multiple anelasticities in O-doped refractory multiprincipal element alloys

The Snoek anelastic internal friction (IF) peak due to stress-induced dipole ordering associated with interstitial atoms was well observed in IF curves of single-principal element alloys (SPEAs) as early as in the 1950s, however, its behavior remains elusive in multi-principal element alloys (MPEAs) to date. Here the temperature-dependent IF spectra of NbTiV0.5Zr refractory MPEAs with varying O contents were presented, and the analysis of these data indicates that for O-doped NbTiV0.5Zr MPEAs, the O addition triggers two anelastic IF peaks (the PO1 and PO2), corresponding to the O-Snoek-type relaxation in random solid solution (RSS) and local chemical ordering (LCO) structures, respectively. The half-peak width of the PO1 is 2–3 times broader than that for SPEAs, associated with the wide O migration energy barrier distribution in MPEAs. These phenomena show a striking contrast to the single and narrow Snoek-type peak observed for SPEAs. Our analysis further reveals an approximate linear correlation between the half-peak width of the Snoek-type peak and the mixing entropy. The introduction of O also shifts grain boundary relaxation peaks (PG) towards higher temperatures. Interestingly, high-temperature anomalous modulus changes were observed for the first time in TiV-based lightweight refractory MPEAs, which is suggested to be originated from the order reduction of the body-centered cubic (bcc) structure at elevated temperatures. Moreover, the 1 at.%O doped NbTiV0.5Zr MPEA with a favorable balance between the peak heights of the PO2 and PG, exhibits outstanding specific yield stress (SYS) among refractory MPEAs while maintaining an elongation as high as 20 %. This work provides not only a bridge between the anelastic behavior of SPEAs and MPEAs for upcoming studies and theories concerning bcc MPEAs with interstitial atoms, but contributes to the holistic design of bcc MPEAs with high strength and excellent ductility.

Enhanced Mechanical and Electromechanical Properties of Compositionally Complex Zirconia Zr1-x(Gd1/5Pr1/5Nd1/5Sm1/5Y1/5)xO2-δ Ceramics.

Compositionally complex oxides (CCOs) or high-entropy oxides (HEOs) are new multielement oxides with unexplored physical and functional properties. In this work, we report fluorite structure-derived compositionally complex zirconia with composition Zr1-x(Gd1/5Pr1/5Nd1/5Sm1/5Y1/5)xO2-δ (x = 0.1 and 0.2) synthesized in solid-state reaction route and sintered via hot pressing at 1350 °C. We explore the evolution of these oxides' structural, microstructural, mechanical, electrical, and electromechanical properties regarding phase separation and sintering mechanisms. Highly dense ceramics are achieved by bimodal mass diffusion, composing nanometric tetragonal and micrometric cubic grains microstructure. The material exhibits an anomalously large electrostriction response exceeding the M33 value of 10-17 m2/V2 at room temperature and viscoelastic properties of primary creep in nanoindentation measurement under fast loading. These findings are strikingly similar to those reported for doped ceria and bismuth oxide derivates, highlighting the presence of a large concentration of point defects linked to structural distortion and anelastic behavior, which are characteristics of nonclassical ionic electrostrictors.

The onset of anelastic behavior in fine-grained synthetic dunite

Micromechanical models suggest that the onset of anelastic relaxation in polycrystalline olivine, critical to interpretation of the seismic wave attenuation and dispersion in the upper mantle, should be a mild dissipation peak caused by elastically accommodated grain-boundary sliding. Such behavior has been tentatively invoked to explain both a short-period shear modulus deficit and a dissipation plateau poorly resolved at 900–700 °C in previous forced-oscillation experiments on fine-grained dunite tested within mild-steel jackets. However, these observations may have been complicated by the austenite to ferrite plus cementite phase transition in the jacket material, compliance associated with interfacial Ni70Fe30 foils, and modeling of the mechanical properties of polycrystalline alumina as control specimen. To investigate the influence of these complications within the experimental setup and provide forced-oscillation data of better quality especially at moderate temperatures, we have conducted further forced-oscillation tests for which we removed the interfacial foils, employed single-crystal sapphire as reference sample, and used alternative jacket materials (stainless steel or copper) which experience no phase transition during the staged cooling. The newly acquired forced-oscillation data, although broadly consistent with the previous results, differ significantly especially in temperature sensitivity, and allow refinement of an appropriate Burgers creep-function model. A mild dissipation peak superimposed on monotonic dissipation background during the onset of anelastic relaxation in dry, melt-free and fine-grained dunite has now been consistently observed at temperatures of ∼950–1050 °C and seismic periods of 1–1000 s. Such a dissipation peak with relaxation strength 0.02 ± 0.01 is attributed to elastically accommodated grain-boundary sliding. The high activation energy (> 600 kJ/mol) of viscoelastic behavior involving both dissipation and related dispersion suggests that grain-boundary diffusion may be limited by interfacial reaction within grain boundaries. The reduced relaxation strength makes it difficult to attribute the oceanic lithosphere-asthenosphere boundary to water-mediated elastically accommodated grain-boundary sliding.

Reliability of quasi-integrable Hamiltonian systems with coupled viscoelastic dampings driven by wideband noises

Viscoelasticity is the time-dependent anelastic behavior of materials, which means the response of a viscoelastic system to a stimulus depends on the instantaneous state and its history. For quasi-integrable Hamiltonian systems with coupled viscoelastic dampings driven by wideband noises, the key to estimate their reliability is how to handle the coupled viscoelastic dampings between different degrees of freedom. In the present paper, the contributions of the coupled viscoelastic dampings are decoupled into elastic restoring forces and viscous dampings by using the generalized harmonic balance technique, and the equivalent quasi-integrable Hamiltonian systems without coupled viscoelastic dampings are obtained. Then by using the stochastic averaging method, the averaged equations for all slowly varying processes of the equivalent systems in both non-resonant and internally resonant cases are derived, which retain the main dynamical characteristics of the equivalent systems. The lower-dimensional backward Kolmogorov (BK) equation for reliability and the Pontryagin equation for the mean first passage time of the equivalent systems are derived. Two examples are worked out in detail to illustrate the application of the proposed procedure. Comparisons of the results obtained by using the proposed method with those from the Monte Carlo simulations of original systems show that the proposed method is well applicable.

Rapid Fatigue Limit Estimation of Metallic Materials Using Thermography-Based Approach

This work attempts to develop a theoretical model in combination with the representative volume element (RVE) theory for realizing rapid fatigue limit prediction. Within the thermodynamic framework, it is believed that two components, namely anelastic and microplastic behaviors, which correspond to recoverable and non-recoverable microstructural motions, contribute to temperature variation during high-cycle fatigue. Based on this, the constitutive equation of the response relationship between the temperature rise evolution and the stress amplitude of metallic materials can be deduced in combination with the heat balance equation. Meanwhile, a determination approach for the thermographic experimental data for accurate fatigue limit estimation is developed by combining it with a statistical method. Finally, the experimental data of metallic specimens and welded joints were utilized to validate the proposed model, and the results demonstrated great agreement between experimental and predicted data.

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.

A thermodynamically consistent model for hydraulic transients in metallic pipes undergoing elasto-viscoplastic deformations

This work presents an extension of the fluid transient analysis to include the elasto-viscoplastic behavior of the pipe material. A previously developed quasi-2D flow model is employed as a basic framework, and the pipe’s elasto-viscoplastic behavior is added by considering constitutive equations formulated via an internal variables theory. The resulting governing equations form a non-linear hyperbolic system of partial differential equations whose approximated solutions are obtained by employing the method of characteristics followed by the Newton–Raphson method. The model is thermodynamically consistent, a feature that is consistently detailed in this work to uphold the application of energy-based theoretical analyses of the phenomenon. Taking as reference the transient responses obtained from an experimental installation that simulates an accident, the present approach is found to be fully consistent and valuable for simulating fast hydraulic transients in metallic materials experiencing plastic deformation. By comparing the pressure fluctuations of models with and without elasto-viscoplasticity, more attenuation and dispersion of the pressure responses are found when such behavior is considered. The elasto-viscoplasticity effect on the pressure responses is better understood when the connection between the viscoplastic mechanisms and energy dissipation is exposed. During the fluid transient, the pipe dissipates meaningful amounts of energy that cause a significant alteration in the whole fluid–pipe dynamics. Another numerical example, based on a hypothetical water hammer flow that causes plastic deformation in the pipeline, is also addressed. Such a case puts in evidence that not only the anelastic behavior of the pipe must be taken into account but also that an accurate description of the fluid friction may be significant to portray realistically fluid transient responses. At last, an assessment of the pipe integrity by means of a scalar damage variable theory is carried out to emphasize the application prospects of the present research.

Hysteresis and dichotomous mechanics in cyclic crushing failure of confined freshwater columnar ice

Cyclic crushing experiments with a haversine velocity waveform were performed on passively confined, freshwater columnar ice specimens for a variety of velocities and frequencies. The aim of the experiments was to study the ice deformation and failure behavior in crushing when loaded at a predefined displacement pattern closely resembling the frequency lock-in regime of ice-induced vibrations. The focus of the experiments was on the development of load and ice deformation behavior at the grain and ice specimen scales during each cycle. To this end, the deformation and failure of the ice were observed with crossed-polarized light to highlight the microstructure in-situ during cyclic crushing. It was shown that there are dichotomous mechanical behaviors of the damaged and confined ice during a single crushing cycle: brittle at high velocity and non-brittle at low velocity. At low velocity, ice fracture was interrupted and stress relaxation occurred until the predefined velocity began increasing in the cycle. The stress relaxation in the load was accompanied by stress-optic effects in the ice. It was found that a load peak-velocity hysteresis developed in each crushing cycle: peak loads following the non-brittle behavior were temporarily higher than the peak loads of the brittle behavior. The temporary load peak enhancement tended to increase with increasing duration of stress relaxation, i.e. the peak enhancement tended to increase with decreasing velocity and frequency. Negligible peak enhancement and stress relaxation duration were observed for the highest frequency and mean velocity tested of 2 Hz and 10 mm s−1, respectively. For tests with a minimum velocity of 1 mm s−1, no stress relaxation was observed in the load measurement. Preliminary results from deviating from the haversine velocity waveform by increasing the minimum velocity showed that the stress relaxation duration decreases, but the non-brittle peak load does not decrease. It is speculated that ice anelastic ice behavior could account for the rapid stress relaxation at low velocity. It is unclear what causes the hysteresis, although it is speculated that dynamic strain aging might play a role. The change in ice behavior during the experiments demonstrates a mechanism which develops rapidly and might therefore incite the development of the frequency lock-in regime of ice-induced vibrations of vertically-sided structures.

Static Unified Inelastic Model: pre- and post-yield dislocation-mediated deformation

Modelling dislocation glide over the initial part of a stress–strain curve of metals received little attention up to now. However, dislocation glide is essential to ones understanding of the fundamental relationship between inelastic deformation and the evolution of the dislocation network structure. Therefore, we present a model of dislocation-driven deformation under static loading conditions.We reproduce repeated cyclic uniaxial tensile tests on Interstitial-Free and Low-Alloy steels. The elastic mechanical behaviour is described by isotropic linear elasticity, pre-yield anelastic mechanical behaviour by a dislocation bow-out model with dissipation, and the post-yield evolution of dislocation network structure by a statistical storage model. We hypothesise that when the local anelastic compliance is lower than the global plastic compliance, deformation is mechanically recoverable, and vice versa. This hypothesis is corroborated with the classical Taylor relation. We report the relation between stable and unstable dislocation glide using this prototypical modelling framework.We find four structural variables, that are based on dislocation physics, to describe the stress–strain curve: total dislocation density, average dislocation segment length, dislocation junction formation rate, and average dislocation junction length. Firstly, we quantify the dislocation network evolution during uniaxial monotonic loading, and verify work-hardening by dislocation junction formation and a Taylor-type equation for flow. Finally, we present a semi-empirical relation for the evolution of the dislocation network structure. Which allows us to: refine the physical interpretation of the Taylor relationship, and rationalise experimental observations on apparent modulus degradation by thermomechanical processing. Both these findings circumvent the limitations of current, physics-based hardening models.

Frequency-dependent P-wave anelasticity due to multiscale (fractal) heterogeneities in rocks

Understanding the effect that multiscale heterogeneities have on the wave responses of rocks at different frequencies is essential in the interpretation of seismic data. In fact, the behaviors of ultrasonic and seismic waves differ because the experiments involve different spatial scales. Then, a solution is to apply a theory that establishes a relation between the wave properties at different frequency bands considering a size range of heterogeneities. To investigate this problem, we have measured the compressional wave (P-wave) anelasticity (velocity and attenuation) of tight reservoir rocks at ultrasonic, sonic and seismic frequencies. The wave behavior as a function of porosity or clay content shows a consistent trend. With increasing confining pressure, the effect of porosity on attenuation decreases, while that of clay content gradually becomes important. To interpret the data, we propose a double-fractal poroelasticity model by incorporating the self-similarity characteristics of cracks and clay minerals. The comparison between the experimental data and model results reveals the fractality of the clay inclusions and cracks, with radii range of [10−6, 10−1.5] m and [10−6, 10−3.1] m, respectively, which is responsible for the anelastic behavior of the waves on a wide frequency band.

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.

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.

The Anelastic Behaviors of Co–Fe–Ni–P Metallic Nano-glasses: Studies on the Viscous Glass–Glass Interfaces

The Anelastic Behaviors of Co–Fe–Ni–P Metallic Nano-glasses: Studies on the Viscous Glass–Glass Interfaces

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.

Probing the Damage Zone at Parkfield

AbstractRocks are heterogeneous materials that exhibit nonlinear elastic (anelastic) behavior at scales ranging from the laboratory to Earth. In the laboratory, typical, complex relationships exist between stress and strain that include hysteresis, finite relaxation times, strain rate, and history dependence. These behaviors are linked to important characteristics such as stress, porosity, permeability, material integrity, and material failure. We adopted a “pump‐probe” type experiment common in laboratory studies, using solid earth tides as the low‐frequency pump and empirical Green's function as the high‐frequency probe. By probing the velocity at different points in the pump cycle, we constrained important information about the strain‐modulus relationship. Near the San Andreas Fault, we observed strongly nonlinear elastic behavior that characterizes the damage zone. We also constrained important aspects of hysteretic behavior that are related to damage properties and possibly pore pressure. Away from the fault, the nonlinear behavior is diminished.