Anelastic Strain Research Articles

Microscopic origin of shear banding as a localized driven glass transition in compressed colloidal pillars.

Here we report on compression experiments of colloidal pillars in which the evolution of a shear band can be followed at the particle level during deformation. Quasistatic deformation results in dilation and anisotropic changes in coordination in a localized band of material. Additionally, a transition from solid- to liquidlike mechanical response accompanies the structural change in the band, as evidenced by saturation of the packing fraction at the glass transition point, a diminishing ability to host anelastic strains, and a rapid decay in the long-range strain correlations. Overall, our results suggest that shear banding quantitatively resembles a localized, driven glass transition.

Strain perceptibility of elements on the diffusion in Zr-based amorphous alloys

With the discovery of bulk metallic glasses (BMGs), there has been considerable interest in understanding their mechanical behavior. In spite of these previous observations on the relation between plastic deformation of metallic glasses and their diffusion behavior, a detailed understanding on the diffusion of BMGs is still unexplored. We evaluated the contribution of deformation-induced structural transformations (elastic, anelastic, viscoplastic or viscoelastic responsive and plastic strain) on the diffusion of Zr-based bulk metallic glasses in as-cast, elastostatically stressed and plastically deformed states. Experimental investigations of the diffusion process and the elemental distributions in the glassy alloy were performed following plastic deformation by multiple cold rolling and elastostatic cyclic compression, respectively. We compared the vacancy model and the transition state model to verify the diffusion mechanism in the deformed bulk metallic glass. The diffusion of tracer atoms, i.e., Fe, in the bulk metallic glass is affected by viscoelastic responsive strain governing the transition-state model. In contrast, the diffusion of constituent atoms, i.e., Ti, Zr, in the bulk metallic glass is dominantly affected by plastic strain governing the vacancy model. The results reveal that the diffusion behavior of bulk glassy alloys can be changed by variation of the constituent elements and applying different strain modes upon deformation.

Stress-state differences between sedimentary cover and basement of the Songliao Basin, NE China: In-situ stress measurements at 6–7 km depth of an ICDP Scientific Drilling borehole (SK-II)

The stress state down to the basement within sedimentary basins yet remains poorly understood. The anelastic strain recovery (ASR) method was employed to measure the stress state in the SK-II borehole in the Songliao Basin, Northeast China. The results show that the stress state differs significantly between the sedimentary cover and basement. In the sedimentary cover (6296–6335 m), the maximum principal stress σ1 is nearly vertical, which is in the normal faulting stress regime dominated by gravitation, in accordance with the normal faults observed on seismic reflection profiles within the sedimentary cover. In contrast, the basement (6646–6846 m) shows that σ1 is nearly horizontal, suggesting a strike-slip or reverse-faulting regime. The stress state of the basement is close to the reasonable stress condition for the Eurasian Plate far from a western Pacific plate subduction zone and consistent with the focal mechanisms of earthquakes (7–15 km) in the vicinity of ICDP SK-II borehole. The difference of stress state may imply that the far-field stress generated by the western Pacific plate has limited effects on the sedimentary cover, an increase in thickness correlates with an increasing influence of tectonic stress with depth.

A viscoelastic integral formulation and numerical implementation of an isotropic constitutive model of saline ice

This work develops a multiaxial numerical implementation of a constitutive model of saline ice which is based on dislocation processes and grain boundary relaxation. The model includes contributions from the elastic, anelastic (time-dependent recoverable), and viscous (time-dependent non-recoverable) straining mechanisms. The anelastic strain model is formulated using a creep compliance tensor and a hereditary integral formulation. The incremental form of the constitutive model is derived and its implementation into finite element software is discussed. We compare our model to multiple experimental data sets including cyclic sinusoidal and creep loading. We find that our model compares well with the experimental data and is able to capture the mechanical behavior of ice across multiple temperatures, loading frequencies, stresses, and timescales.

Insights From Micromechanical Modeling of Intact Rock Failure: Event Characteristics, Stress Drops, and Force Networks

AbstractWe use a bonded‐particle method to investigate event characteristics, b values, internal force distributions, and stress drops in triaxial deformation tests. We simulate brittle through ductile deformation regimes. We find the following: (1) Event rates are proportional to anelastic axial strain: (i) significant and accelerating events rates only occur near peak stress (brittle deformation); (ii) event rates gradually increase until the anelastic strain plateaus (ductile deformation). (2) b value patterns show a systematic decrease when approaching peak stress, after which (i) they increase again (brittle case) or (ii) reach a constant minimum (ductile case). A decrease in b values is indicative of progressive internal damage, with an increasing event rate. (3) Weak‐ and strong‐force networks exist within the sample. Macrofailure of the sample occurs due to collapse of the strong‐force network. Acoustic emissions predominantly occur (i) within the weak‐force network allowing for tensile crack opening and closing despite the large compressive external stresses, and (ii) in areas with the largest spatial force gradients, close to the strong‐force networks. All internal compressive and extensional normal forces display exponential distributions despite uniform boundary stresses. (4) Stress drops of the largest events are inversely proportional to peak stress; the largest stress drops occur for brittle failure, progressively approaching a zero magnitude for ductile deformation. The systemic correlations between b values, the number of acoustic emissions, and stress drops with the maximum principal stress may offer opportunities to invert for changes in the stress state from these remote observables during earthquake cycles.

Activation volume details from nonlinear anelastic deformation of a metallic glass

At high stress, the viscosity of a metallic glass is non-Newtonian, and therefore the rate of anelastic stress relaxation is not linear in the applied stress. In this regime, one can obtain information on the details of the activation volume that are not accessible in the linear regime. While bending in the nonlinear regime introduces a complicated stress state, it offers great stability for noninstrumented measurements over many orders of magnitude of time. We have developed a method of controlled sample bending to a strain of up to ∼0.0155 for Al86.8Ni3.7Y9.5 metallic glass. Significant nonlinearity of the anelastic strain in the stress was observed, which is mainly associated with the largest and slowest shear transformation zones involved not reaching mechanical equilibrium at the end of the constraining period. Combining nonlinear kinetics under constraint and zero bending moment after constraint removal, the volume of the largest shear transformation zones and the transformation shear strain were obtained independently for the inherent state—their most likely values are 4.8 × 10−28 m3 and 0.18, respectively.

Evolution of anelastic behaviour and twinning in cyclic loading of extruded magnesium alloy ZM21

In this study, the cyclic response of the wrought magnesium alloy ZM21 is investigated. The microstructure of the original extruded bar consists of equiaxed grains with a grain size range of 15–18 μm. The anelasticity was measured using a method in which the elastic modulus in every loop is obtained by calculating the slope of lines fitted to the loading and unloading parts of the curves. The cyclic test for ZM21 shows that the anelastic strain increases with the strain, reaching its maximum between 2-4% applied strain and then levels off. The anelastic strain reaches a maximum between 2-4% at which point the fraction of extension twins also reaches a maximum. Twins were separated from their parent grains in order to quantify twin evolution during cyclic loading. Overall, it was found that most of the twins observed are extension twins up to 8% accumulative strain. Beyond 8% strain, exhaustion of 90% of extension twins occurred and contraction twins appeared in the microstructure. Moreover, double twins were identified after a strain of 8%. These twins were composed of extension twins and contraction twins which can contribute to softening. Such softening can result in the reduction of uniform elongation in tension for the cyclic loading in comparison with the monotonic loading. It was possible for the material to sustain continued straining without failure to over double this value, that is, 15%.

Anelastic reorganisation of fibre-reinforced biological tissues

In this work, we contribute to the study of the structural reorganisation of biological tissues in response to mechanical stimuli. We specialise our investigation to a class of hydrated soft tissues, whose internal structure features reinforcing fibres. These are oriented statistically within the tissue, and their pattern of orientation is such that, at each material point, the tissue is anisotropic. From its natural, stress-free state, the tissue can be distorted anelastically into a global reference configuration, and then deformed under the action of external mechanical loads. The anelastic distortions are responsible for changing irreversibly the internal structure of the tissue, which, in the present context, occurs through both the rearrangement of the bonds among the tissue cells and the deformation-driven reorientation of the fibres. The anelastic strains, in addition, are assumed to model the onset and evolution of microcracks in the tissue, which may be triggered by the mechanical loads applied to the tissue in the case of traumatic events, or diseases. For our purposes, we formulate an anisotropic model of remodelling and we consider a fully isotropic model of structural reorganisation for comparison, with the aim to study if, how, and to what extent the evolution of anelastic distortions is influenced by the tissue’s anisotropy.

Granular solid dynamics with eutaraxy and hysteresis

The dynamics of grain fabrics is captured by means of a hidden state variable , named eutaraxy, which quantifies the propensity for a heat-like micro-seismicity due to disturbing actions. Its increase by driving and decrease by halting are captured by an evolution equation with switch functions. The specific elastic energy depends on the elastic strain and the void ratio so that a Coulomb condition and a maximal void ratio denote critical points. The rate-independent evolution equation of the elastic strain tensor implies a micro-seismically activated relaxation. Monotonous deformations lead to a hypoplastic response, and thereafter isochoric ones tend to steady states . The hysteresis of repeated reversals, which requires rate-independence and stability, is captured without further parameters, and likewise the accumulation of anelastic strain by cycles with small amplitudes. The parameters are physically defined and can be calibrated by means of triaxial tests. Limitations and possible extensions are outlined.

Fast, accurate solutions for 3D strain volumes in a heterogeneous half space

Deformation in the Earth displays many degrees of localization. The mechanics of faulting can be well represented by slip on a 2D surface discretized in piecewise linear boundary elements. Distributed anelastic deformation associated with fluid flow, magma transfer, or viscoelastic relaxation can be approximated by anelastic strain discretized in 3D volume elements. The stress, traction, and displacement kernels for these elements form the basis of forward and inverse modeling of Earth's deformation during the seismic cycle, volcanic unrest or hydrologic change. While there are a number of techniques for computing these kernels for 2D fault surfaces, the techniques for 3D strain volumes are less developed. To improve the models of Earth's deformation, we extend previous work to numerically calculate these kernels for 3D strain volumes in a heterogeneous half space. The model provides high-precision displacement and stress for all these cases in a self-consistent manner. We exploit the adaptive multi-grid elastic solver implemented in the software Gamra (Landry and Barbot, 2016) to compute the deformation induced by boundary and volume elements with high numerical efficency. We demonstrate the correctness of the method with analytic tests. We illustrate the performance by computing a large-scale model of postseismic deformation for the 2015 Mw 7.8 Gorkha, Nepal earthquake with heterogeneous material properties. The open-source, freely available software can be useful for the calculation of elasto-static Green's functions for localized and distributed deformation in a heterogeneous Earth.

Microscopic characterization of structural relaxation and cryogenic rejuvenation in metallic glasses

Plasticity improvement in metallic glasses resulting from cycling treatment between room and liquid nitrogen temperature has been reported and attributed to rejuvenation due to a non-uniform thermal expansion coefficient. However, the detailed microscopic effect is still unclear. The present study focuses on the microscopic effect of room-temperature ageing and cryogenic cycling. La70Cu15Al15 and La70Ni15Al15 metallic glasses were subjected to varying ageing times, after which some were also cryogenically cycled. Quasi-static anelastic relaxation measurements were then employed to characterize the time-constant spectra over seven orders of magnitude. The overall anelastic strain decreases with increasing ageing time, but is not noticeably affected by cryogenic cycling. On the other hand, while ageing also causes an increase in characteristic time constants, cycling reverses this effect. The new details shed light on the effect of structural relaxation and rejuvenation on the properties of shear transformation zones.

Modeling of nonlinear response in loading-unloading tests for fibrous composites under tension and compression

Loading-unloading tests on unidirectional HTS40/PA6 carbon/polyamide laminates are performed in this study to identify the nature of off-axis nonlinear deformation of fibrous composites under tension and compression. Experimental results reveal the involved residual strain (plastic strain) and hysteresis loop during loading and unloading, and their dependence on stress level, fiber orientation, and tension or compression mode. The hysteresis behavior is assumed to be induced by a component of strain, which is considered as anelastic strain. This strain is recoverable like elastic deformation but dissipates work like plastic deformation. An approach is developed to predict the tension-compression asymmetry in plastic strain and anelastic strain, as well as the dependence of asymmetry on stress level and fiber orientation. The proposed approach is a modification of a strength differential model that considers the nonlinear deformation completely as plastic strain for monotonic tests. Predicted off-axis loading-unloading responses of unidirectional laminates are compared with the experimental results. The modified model is found to be effective for adequately describing the tension-compression asymmetry not only in plastic strain but also in complex nonlinear hysteresis behavior.

Deformation of a Half‐Space from Anelastic Strain Confined in a Tetrahedral Volume

Deformation in the lithosphere-asthenosphere system can be accommodated by faulting and plastic flow. However, incorporating structural data in models of distributed deformation still represents a challenge. Here, I present solutions for the displacements and stress in a half-space caused by distributed anelastic strain confined in a tetrahedral volume. These solutions form the basis of curvilinear meshes that can adapt to realistic structural settings, such as a mantle wedge corner, a spherical shell around a magma chamber, or an aquifer. I provide computer programs to evaluate them in the cases of anti-plane strain, in-plane strain, and three-dimensional deformation. These tools may prove useful in the modeling of deformation data in tectonics, volcanology, and hydrology.

Experimental and theoretical studies on mechanical creep of 1–3 piezocomposites

Piezoelectric materials like bulk PZT are often subjected to mechanical creep loads. But being brittle, these undergo premature failure. Hence, piezocomposites are used instead of bulk PZT. Piezocomposites are viscoelastic in nature owing to the presence of a ductile epoxy matrix. In this paper, mechanical creep is studied for 1–3 piezocomposites of different fiber volume fractions under various levels of compressive prestress. Experiments are performed to understand the difference in their electromechanical response. The creep strain is found to increase with the increase in matrix volume fraction and stress level. The creep polarization is observed to decrease with the decrease in fiber volume fraction and stress level. The degradation in the piezocoupling coefficient is observed to be the maximum for the piezocomposite 35% fiber volume fraction and the least for the bulk PZT. This is attributed to the time-dependent permanent re-orientation of ferroelastic domains by 90 $$^\circ $$ during the mechanical creep phenomenon. Finally, a viscoelastic model comprising of two parallel Kelvin–Voigt elements is proposed to capture the creep strain. The creep strain is decomposed into the ferroelastic strain and anelastic strain. Creep polarization is computed from the ferroelastic strain. The model predictions are found to be in agreement with the experimental results.

Mechanical rejuvenation in bulk metallic glass induced by thermo-mechanical creep

Using high energy X-ray diffraction we studied the temperature, stress, and time effect on structural changes in a Zr-based bulk metallic glass induced by thermo-mechanical creep. Pair distribution functions obtained from two-dimensional diffraction patterns show that thermo-mechanical creep induces structural disordering, but only when the stress beyond a threshold is applied. A similar threshold behavior was observed for anelastic strain. We conclude that anelastic creep strain induces rejuvenation, whereas plastic strain does not.

LaAlO3: A substrate material with unusual ferroelastic properties

Twin boundary dynamics in LaAlO3 is associated with non-linear anelasticity. Ultrasonic studies of non-linear twin boundary dynamics between 80 and 520 K show that cooling substrates from temperatures near the ferroelastic transition at 813 K generate three characteristic thermal regimes with different non-linear dynamics. Twin boundaries are initially highly mobile. Anelastic strain amplitudes versus stress are power law distributed with an exponent of 2.5. No de-pinning was found down to elastic strain amplitudes of ε0 ∼ 10−7. The power law is gradually replaced between 370 K and 280 K by few large singularities (jerks) due to massive rearrangements of the domain structure for ε0 larger than ca. 5 × 10−5. At lower temperatures, the domain structure is pinned with well-defined thresholds for de-pinning. The de-pinning is not accompanied by global rearrangements of twin patterns below room temperature. Unexpectedly, the low-temperature critical de-pinning strain amplitude decreases with decreasing temperature, which may indicate an additional, so far unknown phase transition near 40 K.

Characterisation and modelling of in-plane springback in a commercially pure titanium (CP-Ti)

Effective prediction of springback during sheet metal forming is critically important for automotive and aerospace industries, especially when forming metals with high strength-to-weight ratio such as titanium. This requires materials mechanical data during plastic deformation and their dependencies on parameters like strain, strain rate and sample orientation. In this study, springback is quantified experimentally as elastic strain recovery, degradation in Young’s modulus and inelastic strain recovery on unloading in a commercially pure titanium type 50A (CP-Ti-50A). The results show strain rate-dependent anisotropic mechanical behaviours and a degradation in Young’s modulus with increased level of plastic deformation. The level of degradation in Young’s modules increases gradually from 13% for samples parallel to the rolling direction (RD) to 20% for those perpendicular to the RD. A measurable nonlinear strain recovery was also observed on unloading that is orientation dependent. The level of springback is characterised as the sum of elastic recovery and the contributions from both the degradation in Young’s modulus and anelastic strain recovery. It is shown that the Chord modulus can estimate springback with a reasonable accuracy taking into consideration the elastic strain recovery, degradation in Young’s modulus and anelastic strain recovery.

The evolution of in-plane magnetic anisotropy in CoFeB/GaAs(001) films annealed at different temperatures

A considerable in-plane uniaxial magnetic anisotropy (UMA) field (Hu ∼ 300 Oe) could be achieved when the amorphous CoFeB film was deposited on the GaAs(001) wafer by magnetron-sputtering after proper etch-annealed procedure. In order to get deep insights into the mechanism of the UMA, the film was annealed at different temperatures and the evolution of the in-plane magnetic anisotropy was investigated carefully. With increasing the annealing temperature (TA), the UMA could be maintained well when TA reached 250°C, but became very weak at 300°C. However, when TA was elevated to 400°C, another UMA (Hu ∼ 130 Oe) was built accompanied with a fourfold magnetic anisotropy with its strength of about 50 Oe. In terms of the magnetic anisotropy evolution along with TA, the anelastic strain, which is thought to be resulted from the interfacial interaction between CoFeB and GaAs, may play a dominant role in producing the enhanced UMA based on the ‘bond-orientational’ anisotropy (BOA) model.

Observation and modeling of loading–unloading hysteresis behavior of unidirectional composites in compression

The loading–unloading hysteresis behavior of unidirectional HTS40/PA6 carbon/polyamide laminates under off-axis compression has been examined both experimentally and constitutively in the present study. Monotonic compressive tests are first performed on unidirectional laminates to identify the basic properties of off-axis deformation. Then, five cycles of compressive loading and unloading tests are carried out with a gradually increasing peak stress for each specimen, followed by testing to failure. Significant nonlinear unloading behavior is observed after the material has been loaded into the nonlinear deformation region, and apparent plastic strain is seen after full unloading. The reloading curve also exhibits nonlinearity and conduces to a slightly open hysteresis loop with unloading. An approach is developed to predict the nonlinear hysteresis behavior of unidirectional composites by assuming an anelastic strain component in the nonlinear compressive deformation. The assumption of anelastic strain is a modification of Sun–Chen’s one-parameter plasticity model that considers the nonlinear deformation completely as plastic strain from monotonic tests. The modified model has been validated by the off-axis loading–unloading test results on unidirectional laminates. Results verify that the model accurately captures not only the plastic strain but also the complex nonlinear hysteresis behavior in the observed off-axis loading–unloading stress–strain curves.

Stress State in the Kumano Basin and in Slope Sediment Determined From Anelastic Strain Recovery: Results From IODP Expedition 338 to the Nankai Trough

AbstractThree‐dimensional, in situ stresses in the Kumano Basin and slope sediment (IODP Sites C0002 and C0022) in the Nankai Trough, southwest Japan, have been determined using the anelastic strain recovery (ASR) of core samples. Two samples taken from Hole C0002J, located in the bottom of the Kumano Basin, indicate that the maximum principal stress, σ1, is vertical. The intermediate principal stress, σ2, is oriented ENE–WSW, parallel to the trench axis. These stress orientations are similar to those obtained using ASR and borehole breakout methods in previous expeditions. In contrast, a sample from the lower section of the slope sediment (Hole C0022B), located beneath the megasplay fault, is characterized by σ1 plunging moderately to the ESE and σ3 oriented near‐horizontally, trending NNE–SSW. The direction of maximum horizontal stress obtained from ASR (WNW–ESE) is similar to that inferred from borehole breakouts in an adjacent hole (NW–SE). Trench‐normal compression and a near‐vertical σ2 are also inferred from focal mechanisms of very‐low‐frequency earthquakes within the Nankai accretionary prism, and from borehole breakouts in the hanging wall of the megasplay fault. These observations suggest that the horizontal compressional regime extends to a shallower level than previously thought, likely due to the shallow portion of the megasplay fault accumulating tectonic stress in response to plate convergence.