Strain Rate Amplitude Research Articles

Real-Data Testing of Distributed Acoustic Sensing for Offshore Earthquake Early Warning

Abstract We present a real-data test for offshore earthquake early warning (EEW) with distributed acoustic sensing (DAS) by transforming submarine fiber-optic cable into a dense seismic array. First, we constrain earthquake locations using the arrival-time information recorded by the DAS array. Second, with site effects along the cable calibrated using an independent earthquake, we estimate earthquake magnitudes directly from strain rate amplitudes by applying a scaling relation transferred from onshore DAS arrays. Our results indicate that using this single 50 km offshore DAS array can offer ∼3 s improvement in the alert time of EEW compared to onshore seismic stations. Furthermore, we simulate and demonstrate that multiple DAS arrays extending toward the trench placed along the coast can uniformly improve alert times along a subduction zone by more than 5 s.

Low cycle fatigue behavior of 316LN stainless steel: Effects of temperature, strain rate and strain amplitude

Continuous and interrupted LCF tests were conducted to reveal the effects of temperature, strain rate and strain amplitude on the LCF behavior of a nitrogen-alloyed 316LN stainless steel. The cyclic hardening and softening behavior at high and low strain amplitudes were elaborately elucidated based on the method of stress decomposition and characterization of dislocation configuration evolution. In addition, the dominant damage mechanism responsible for the different cracking modes under various loading conditions was determined based on the observations of fracture surface and secondary cracks on the longitudinal section.

Numerical Modeling of the Capsular Ligament Failure for the C2-C3 Segment in the Case of a Frontal Impact

The cervical spine is a complex anatomical structure that mainly stabilizes the head and protects the spinal cord. Injuries of the cervical spine often occur during falls or road accidents and are particularly serious since they generate strong threats of paralysis and death. It should be noted that the ligaments provide cervical stability but their stabilization in case of injury is not yet well investigated. In this context, the objective of the present work is to study the failure of the ligaments by developing a bio-faithful numerical model while using a more realistic geometry of the spinal components and behavior laws that take into account the effect of strain rate and motion amplitudes. In order to validate the results of the study, we conducted a comparison with previous literature studies. It has been found that damage is often supported by intervertebral discs, anterior longitudinal ligaments (ALL) and capsular ligaments (CL) in the case of frontal impact. Indeed, the highest stresses are concentrated in the annulus fibrosus and the capsular ligaments. In this study, we tested the effect of ligament tears on disc behavior, where it was found that the stress rate increased by approximately 6%. The effect of capsular ligament tear orientation was also examined. The obtained results show that the most dangerous inclination was downward at an angle of 45°.

On the Comparison of Records from Standard and Engineered Fiber Optic Cables at Etna Volcano (Italy)

Distributed Dynamic Strain Sensing (DDSS), also known as Distributed Acoustic Sensing (DAS), is becoming a popular tool in array seismology. A new generation of engineered fibers is being developed to improve sensitivity and reduce the noise floor in comparison to standard fibers, which are conventionally used in telecommunication networks. Nevertheless, standard fibers already have extensive coverage around the Earth's surface, so it motivates the use of the existing infrastructure in DDSS surveys to avoid costs and logistics. In this study, we compare DDSS data from stack instances of standard multi-fiber cable with DDSS data from a co-located single-fiber engineered cable. Both cables were buried in an area located 2.5 km NE from the craters of Mt. Etna. We analyze how stacking can improve signal quality. Our findings indicate that the stack of DDSS records from five standard fiber instances, each 1.5 km long, can reduce optical noise of up to 20%. We also present an algorithm to correct artifacts in the time series that stem from dynamic range saturation. Although stacking is able to reduce optical noise, it is not sufficient for restoring the strain-rate amplitude from saturated signals in standard fiber DDSS. Nevertheless, the algorithm can restore the strain-rate amplitude from saturated DDSS signals of the engineered fiber, allowing us to exceed the dynamic range of the record. We present measurement strategies to increase the dynamic range and avoid saturation.

Study on Extremely-Low-Cycle Fatigue of Fe–15Mn–10Cr–8Ni–4Si Alloy

The extremely-low-cycle fatigue behavior and post-fatigue microstructure of an Fe–15Mn–10Cr–8Ni–4Si austenitic alloy were investigated under a strain rate and maximum strain amplitude of 0.5%/s and 10%, respectively, in the axial direction. The results can be summarized as follows. (1) A steel damper made of Fe–15Mn–10Cr–8Ni–4Si alloy can withstand approximately 15 swings back even if the structure is distorted by approximately 10% due to a large earthquake. (2) The εpa–Nf relationship of the Fe–15Mn–10Cr–8Ni–4Si alloy demonstrated a linear relationship, and it was confirmed that Manson-Coffin rule holds. (3) Even in an extremely-low-cycle fatigue test with a strain rate of 0.5%/s, the test specimen temperature did not exceed 40°C under all test conditions. Therefore, the ε phase was formed in the fatigue test under all test conditions. (4) Various facets and secondary cracks were observed in the fatigue propagation region of the fracture surface. Accordingly, it was inferred that most of the main cracks propagated at the γ/ε interface and the secondary cracks merged. Consequently, the fatigue crack could not propagate linearly, and the generation of the secondary cracks caused a decrease in the displacement at the tip of the crack when the stress was redistributed, thus extending the fatigue life.

Understanding Effects of Ultrasonic Vibration on Microstructure Evolution in Hot Forming Process via Cellular Automata Method.

Compared with traditional forming technology, ultrasonic vibration-assisted plastic forming technology can improve the forming conditions and obtain better surface quality of the workpiece. However, the mechanism and theory of ultrasonic action have not formed a unified understanding. In this paper, ultrasonic-assisted thermal forming technology is taken as the research object. Through experimental research combined with cellular automata methods, based on the dislocation density model, nucleation and growth model, and dynamic recrystallization growth rule, a theoretical model for microstructure simulation of the ultrasonic-assisted thermal forming process was established. By introducing the ultrasonic energy field into the thermal forming process and correcting thermal activation energy and dynamic recovery coefficient, the reasons for flow stress reduction of 9310 steel and the influence of temperature, strain rate, and vibration amplitude on recrystallization were analyzed from the microscopic scale. The results show that the introduction of ultrasonic vibration reduces the dislocation activation energy, promotes dynamic recrystallization behavior, and finally leads to the reduction of flow stress. With an increase in vibration amplitude, the average grain size decreases faster, the recrystallization volume fraction increases faster, the stress decreases larger, and the ultrasonic softening phenomenon becomes more obvious. Decreasing the strain rate will promote the occurrence of dynamic recrystallization, the volume fraction and average grain size of dynamic recrystallization will increase, and the true stress will decrease.

Strain Rate and Stress Amplitude Effects on the Mechanical Behavior of Carbon Paste Used in the Hall-Héroult Process and Subjected to Cyclic Loadings.

Carbon products such as anodes and ramming paste must have well-defined physical, mechanical, chemical, and electrical properties to perform their functions effectively in the aluminum electrolysis cell. The physical and mechanical properties of these products are assigned during the shaping procedure in which compaction stresses are applied to the green carbon paste. The optimization of the shaping process is crucial to improving the properties of the carbon products and consequently to increasing the energy efficiency and decreasing the greenhouse gas emissions of the Hall–Héroult process. The objective of this study is to experimentally investigate the effect(s) of the strain rate, of the stress maximum amplitude, and of the unloading level on the behavior of a green carbon paste subjected to cyclic loading. To this end, experiments consisting of (1) cyclic compaction tests at different maximum stress amplitudes and strain rates, and (2) cyclic compaction tests with different unloading levels were carried out. The study obtained the following findings about the behavior of carbon paste subjected to cyclic loads. The strain rate in the studied range had no effect either on the evolution of the permanent strain as a function of the cycle number, nor on the shape of the stress–strain hysteresis during the cyclic loading. Moreover, samples of the same density that had been subjected to different maximum stress amplitudes in their loading history did not have the same shape of the stress–strain curve. On the other hand, despite having different densities, samples subjected to the same number of cycles produce the same stress–strain curve during loading even though they were subjected to different maximum stress amplitudes in their loading histories. Finally, the level of unloading during each cycle of a cyclic test proved significant; when the sample was unloaded to a lower level of stress during each cycle, the permanent strain as a function of the cycle number was higher.

Fracture Hits and Hydraulic-Fracture Geometry Characterization Using Low-Frequency Distributed Acoustic Sensing Strain Data

The propagation process and geometry of hydraulic fractures depend on complex interactions among the induced fractures and the pre-existing rock fabric, the heterogeneous rock properties, and the stress state. Accurate characterization of the resulting complex hydraulic-fracture geometry remains challenging. Fiber-optic-based distributed acoustic sensing (DAS) measurements have been used for monitoring hydraulic fracturing in adjacent treatment wells. DAS requires an optical fiber attached to the wellbore to transmit the laser energy into the reservoir. Each section of the fiber scatters a small portion of the laser energy back to a surface sensing unit, which uses interferometry techniques to determine strain changes along with the fiber. DAS data in offset wells fall in the low-frequency bands, which has been proven to be a powerful attribute for the characterization of the geometry of hydraulic fractures. Numerous recently published field examples demonstrate the potential of low-frequency DAS (LF-DAS) data for the detailed characterization of the hydraulic fracture geometry. Understanding the fracture-induced rock deformation associated with LF-DAS signals would be beneficial for the better interpretation of real-time data. However, interpretation of LF-DAS measurement is challenging due to the complexity of the subsurface conditions, in addition to potential unanticipated completion issues such as perforation failure, stage isolation failure, etc. All current research efforts focus on the qualitative interpretation of field data.In this study, we quantified the hydraulic fracture propagation process and described the fracture geometry by developing a geomechanical forward model and a Green’s function-based inversion model for the LF-DAS data interpretation, substantially enhancing the value of the LF-DAS data in the process. The work has a significant transformative potential, involving a tool package with developed forward and inversion models that can provide crucial insights for the optimization of hydraulic-fracturing treatments and reservoir development. Methodology The tool package can be used directly in the field to interpret LF-DAS data and monitor hydraulic fracture propagation. Raw data from the field measurement can be automatically processed. The geomechanics forward model we developed can quantify and analyze the strain-rate response from the LF-DAS measurements based on the 3D displacement discontinuity method. Fracture hits are detected by calculating three 1D features along the channel (location) axis, i.e., the maximum strain rate, the summation of strain rates, and the summation of strain-rate amplitudes. Channels with fracture hits usually exhibit significant peak values of these three features. We proposed general guide-lines for fracture-hit detection based on the quantitative analysis of strain/strain-rate responses during the multistage fracturing treatment. The details of the forward model can be found in Liu et al. (SPE 202482, 204457, AMRA-2020-1426). Additionally, we developed a novel Green’s function-based inversion model to qualify fracture width and height based on the determined fracture hits. The strain field that is estimated from the integration of the strain rates measured by the LF-DAS data along the offset monitoring well is related to the fracture widths through a geomechanics Green’s function. The resulting linear system of equations is solved by the least-square method. Details can be found in Liu et al. (SPE 204158, 205379, 204225).

Fracture-Hit Detection Using LF-DAS Signals Measured during Multifracture Propagation in Unconventional Reservoirs

SummaryLow-frequency distributed acoustic sensing (LF-DAS) data are a powerful attribute to detect fracture hits and characterize fracture geometry during multistage hydraulic fracturing treatments in unconventional reservoirs. The DAS data in low-frequency bands linearly correlate with strain and strain rate induced by dynamic fracture propagation. Due to the complexity of multiple-fracture propagation in unconventional reservoirs, the measured signals from different wells exhibit various characteristics. Mechanisms causing the differences are not well understood, which makes the interpretation of real LF-DAS data and detection of fracture hits very challenging. Hence, it is necessary to relate the observed strain/strain-rate signatures to specific fracture patterns based on the physical model of rock deformation during fracture propagation and to quantitatively characterize signatures surrounding fracture hits. In this study, we have applied our in-house fracture propagation model to simulate simultaneous multiple-fracture propagation as well as fracture-induced strain and strain-rate responses along an offset monitor well. Then a general guideline for fracture-hit detection is proposed based on quantitative analysis of strain/strain-rate responses during multiple-fracture propagation. Finally, a set of field examples are presented to demonstrate the potential of LF-DAS data on hydraulic fracturing monitoring.During multiple-fracture propagation, a “heart-shaped” zone with positive strain rates may be identified for each fracture before the fracture hit. Immediately after the fracture encounters the monitor well, part of the fiber within the fracture path keeps being extended, while the fiber sections off the path become compressed. Three 1D features along the channel (location) axis are designed to detect fracture hits. The features are maximum strain rate, the summation of strain rates, and summation of strain-rate amplitudes. Channels with fracture hits usually exhibit significant peak values of the three features. However, the characteristic signatures can be less detectable when the gauge length is close to the cluster spacing. Connections between fracture-hit locations and cluster perforations clearly reflect the fracture propagation direction. The field examples illustrate the complexity of real LF-DAS signals and demonstrate the adequacy of the proposed guideline for fracture-hit detection with multicluster completion. The fractures propagate nearly perpendicular to the horizontal wellbore in this unconventional shale formation. In addition, four to five fractures out of eight perforation clusters can propagate 396.24 m (1,300 ft) and hit the monitor well, and the “heel-biased” fracture pattern is observed (fractures that do not hit the monitor well are usually close to the toe side). Fracturing fluid leaking off into the previous stage can also be diagnosed, which could negatively affect the completion efficiency.

Large amplitude oscillatory rheology of silica and cellulose nanocrystals filled natural rubber compounds

Nanoparticles reinforce rubbers and enhance Payne effect for the compounds experiencing large amplitude oscillatory shear deformation. Herein the effects of silica and cellulose nanocrystals on the Payne effect of natural rubber compounds are investigated by stress decomposition methods for clarifying the elastic and viscous nonlinearities varying with filler content and composition. The Payne effect is in general characterized by intercycle strain softening and shear thinning behaviors and intracycle hardening and thinning behaviors at high strain (strain rate) amplitudes while the filler influences the behaviors markedly at intermediate strain (rate) amplitudes. Especially, the addition of cellulose nanocrystals in the silica filled compounds improves the elastic nonlinearity and greatly weakens the viscous nonlinearity, providing a perspective on understanding the Payne effect for manufacturing high-performance rubber materials.

Environmentally assisted fatigue behavior of 308L weld metal in borated and lithiated high-temperature water

Environmentally assisted fatigue (EAF) tests in borated and lithiated high-temperature water were conducted to investigate the effect of dissolved oxygen (DO), strain rate and strain amplitude on fatigue life of 308L weld metal. It was found that fatigue lives were comparable in 0.005 ppm DO and 0.1 ppm DO water, and decreased slightly with decreasing the strain rate from 0.04%/s to 0.004%/s. The EAF effects were more pronounced at low strain amplitudes. The EAF cracking mechanisms involved with dendrite boundary orientation relative to cyclic stress axis and δ-ferrite in 308L weld metal are discussed.

Indigenous Design and Development of Split Hopkinson Pressure Bar (SHPB) test setup for characterization of materials at high strain rates

This paper presents design and development of split Hopkinson pressure bar (SHPB) indigenously for testing of different materials at high deformation rate. SHPB is capable to measure the deformation rate 100s-1 to 2,000s-1, by maintaining the uniform and uni-axial stress in the samples. SHPB apparatus consist of the mechanical components, support structure, bars supports and the incident and transmission bars, striker bar, gas gun, piston and rod assembly. The momentum trap system is used to absorb the energy in the form of friction and heat. All components are designed, manufactured, calibrated and assembled to test the samples. Results obtained at high deformation rates are used to characterize samples of different materials by converting in the form of strain, strain rate and stress amplitude in samples.

Effect of microporosity and loading condition on fatigue life of A356 casting alloys

This study quantitatively describes the mutual contributions of microporosity and loading conditions (i.e. strain rate and stress amplitude) on the fatigue properties of low-pressure die-cast A356 alloy, in terms of the defect susceptibility coefficient of fatigue life to microporosity variation under various loading conditions. A fatigue test is conducted in high-cycle axial fatigue mode with a variation of strain rate, applying different loading frequencies (0.3–30 Hz) in a stress ratio of R = - 1.0. Computational topography (CT) analysis and scanning-electron microscope (SEM) fractographic observations were performed to evaluate the size and distribution of micro-voids. The overall dependence of fatigue life on microporosity variation can be linearly described as an exponential form of the defect susceptibility coefficient of fatigue life to the microporosity variation, with the maximum fatigue life achievable in a defect-free condition. The contribution of microporosity to fatigue life becomes insensitive as the strain rate increases at given stress amplitudes, whereas it becomes more dominant with the increase of stress amplitude at a given strain rate. Even though the existence of micro-voids inside a material fundamentally influences major stress concentrations and the origins of fatigue-crack propagation, its practical contribution to fatigue life by the variation of strain rate and stress amplitude is intimately related to the stress concentration by position at the near-circumference of the specimen, rather than the nominal variation of load-carrying capacity by the size and area fraction of micro-voids.

Effect of strain rate on fatigue property of A356 aluminium casting alloys containing pre-existing micro-voids

This study aims to investigate the dependence of fatigue life on strain rate variations by loading frequency, and simultaneously, to evaluate the mutual relation between the strain rate and microporosity on the fatigue property in terms of the defect susceptibility of fatigue life to microporosity variation. The test specimen was prepared from the rim section of an automotive wheel fabricated by low-pressure die-casting on an A356 alloy. The high-cycle fatigue test was carried out in a strain rate range corresponding to the frequency range of 0.3–30 Hz at a stress ratio of R = −1. The strain rate increased to a two-order interval from 10−2 to 100 s−1 as the loading frequency increased from 0.3 Hz to 30 Hz. The nominal fatigue strength coefficient and exponent decreased from 754 MPa and 0.18 to 293 MPa and 0.09, respectively, with increasing strain rate. The fatigue life in low-stress amplitude slightly increased with the strain rate, while it remarkably decreased with the strain rate as the stress amplitude increased. This is because the elastic/plastic strain component ratio (Δεe/Δεp) decreased upon increasing the plastic strain component, accompanied by increasing strain rate. The plastic strain component was remarkably increased with the strain rate and stress amplitude, and decreased by the strain-hardening effect on the lapse of fatigue cycle, even though the elastic strain component remained at a constant level, depending mainly upon the stress amplitude. Additionally, the contribution of microporosity to the variation of fatigue life was underestimated as the strain rate increased, and became more sensitive with the variation of the elastic/plastic strain component in the fatigue cycle as the stress amplitude increased. The main propagation path of fatigue cracks is changed from a mixed mode of the cracking failure by the damage evolution of eutectic Si particle and the matrix penetration by shear deformation of matrix region, to a cracking failure mode where the damage evolution of eutectic Si particles dominated as the strain rate increased.

Mechanical and electrical behaviors of self-sensing nanocomposite-based MWCNTs material when subjected to twist shear load

For the industrial applications of self-sensing multi-walled carbon nanotubes (MWCNTs)/polymers nanocomposites, it is very important to investigate their behavior under complex experimental conditions, such as the torsion twist test. In this study, self-sensing nanocomposites specimens based on different concentrations of MWCNTs were fabricated by a hot-press technique. The dispersion of MWCNTs in the matrix was examined by scanning electronic microscopy and evaluated by Raman spectra. The results show a good distribution of the MWCNTs inside the matrix, which also was in agreement with the increase of the electrical conductivity when increased the content of the MWCNTs. Additionally; it has been shown throughout this investigation that the piezoresistive properties of MWCNTs/phenolic nanocomposites depend principally on the MWCNTs concentration. A high value of change in resistance was observed for the specimens with low content of the MWCNTs. We also addressed the influence of subjected static and cyclic torsion shear loadings to investigate the influences of MWCNTs content, strain rate and strain amplitude on the strain sensitivity [i.e., gauge factor (GF)] performances. The results show that a wide range of GFs ranging from 0.88 for phenolic with 1.5 wt.% MWCNTs at the strain rate of 0.4 min − 1 to 4.11 for phenolic with 0.5 wt.% MWCNTs at the strain rate of 1.2 min − 1. Therefore, the results obtained here provide good understanding guidelines for the behavior of the nanocomposite-based MWCNTs when subjected to a torsional shear loading and its sensing sensitivity for different strain patterns.

Nonlinear viscoelasticity of a dilute suspension of Brownian spheroids in oscillatory shear flow

The nonlinear viscoelasticity of a dilute suspension of Brownian spheroids subject to an oscillatory shear deformation is calculated numerically. This is achieved by determining the suspension microstructure, parameterized via the orientation distribution function. Specifically, the long-time periodic orientation distribution function is obtained via a numerical solution to the Fokker–Planck equation by combining a finite-difference approximation in space with a Fourier series in time. From an ensemble average of the particle stresslet, weighted by the orientation distribution function, the entire stress tensor and relevant birefringence parameters, namely, the average orientation angle and linear dichroism, are calculated; this is done over a range of the Weissenberg number (Wi) and the Deborah number (De), or dimensionless strain-rate amplitude and oscillation frequency, respectively. Detailed calculations are presented for prolate spheroids of aspect ratio r=20; however, our methodology is general and can be applied to spheroids of arbitrary aspect ratio. We provide results in four viscoelastic regimes: linear viscoelastic (Wi≪1), quasilinear viscoelastic (Wi>1 and Wi/De≪1), quasisteady viscoelastic (De→0), and finally, the nonlinear viscoelastic regime (Wi ≳ 1 and Wi/De ≳ 1), which is our main emphasis. In this last regime, where the nonlinear and unsteady viscoelasticity of the material is probed, multiple overshoots are observed in the shear stress and first normal stress difference. The mechanistic origin of these overshoots can be understood from the periodic orientation dynamics (i.e., Jeffery orbits) of a particle under steady shear in the absence of Brownian rotation (Wi→∞). This is achieved by simultaneously analyzing the microstructure, shear stress, first normal stress difference, and birefringence parameters specifically at Wi=20 and De=1. For these values of Wi,De, and r, the period of a Jeffery orbit is comparable to the period of an oscillation cycle, allowing sufficient time for a single Jeffery orbit (and subsequent overshoot) to occur during an oscillation cycle. We contrast this behavior to recent work by Khair [J. Fluid. Mech. 791, R5 (2016)] on nearly spherical particles, for which many more overshoots are observed during an oscillation cycle, due to the shorter period of the Jeffery orbit. We briefly provide results for oblate spheroids of aspect ratio r=0.05 and compare to the results for r=20. Finally, we comment on the relevance of the present micro-mechanical analysis to the nonlinear viscoelasticity of other complex fluid materials.

Low cycle fatigue behavior of modified 9Cr-1Mo steel at 300 °C

Low cycle fatigue (LCF) behavior of modified 9Cr–1Mo steel is studied at 300°C, in the domain of dynamic strain aging (DSA), over a wide range of total strain amplitudes (∆εt/2) from ± 0.25% to ± 0.50%, at two different strain rates of 10−2s−1 & 10−3 s−1. Inverse effect of strain rate is observed on LCF behavior that is increase in the cyclic stress response, reduction in fatigue life and decrease in plastic strain amplitude with decrease in strain rate. Irrespective of strain rate and strain amplitude there is cyclic softening till failure. High dislocation density and bowing of dislocations is observed at low strain rate of 10−3s−1. The observed cyclic softening, irrespective of strain amplitude and strain rate, is attributed mainly to recovery of dislocations and formation of cell structure. The increase in the rate of fatigue crack growth at the strain rate of 10−3s−1 is associated with DSA.

Non-linear stress response of non-gap-spanning magnetic chains suspended in a Newtonian fluid under oscillatory shear test: A direct numerical simulation

A direct numerical simulation approach is used to investigate the effective non-linear viscoelastic stress response of non-gap-spanning magnetic chains suspended in a Newtonian fluid. The suspension is confined in a channel and the suspended clusters are formed under the influence of a constant external magnetic field. Large amplitude oscillatory shear (LAOS) tests are conducted to study the non-linear rheology of the system. The effect of inertia on the intensity of non-linearities is discussed for both magnetic and non-magnetic cases. By conducting magnetic sweep tests, the intensity and quality of the non-linear stress response are studied as a function of the strength of the external magnetic field. The Chebyshev expansion of the stress response is used to quantify the non-linear intra-cycle behaviour of the suspension. It is demonstrated that the system shows a strain-softening behaviour while the variation of the dynamic viscosity is highly sensitive to the external magnetic field. In a series of strain sweep tests, the overall non-linear viscoelastic behaviour of the system is also investigated for both a constant frequency and a constant strain-rate amplitude. It is shown that the intra-cycle behaviour of the system is different from its inter-cycle behaviour under LAOS tests.

Nonlinear relaxation modulus via dual-frequency medium amplitude oscillatory shear (MAOS): General framework and case study for a dilute suspension of Brownian spheroids

A framework for determining the first nonlinear relaxation modulus of a viscoelastic fluid from a medium-amplitude oscillatory shear (MAOS) deformation is constructed. Knowledge of this “MAOS relaxation modulus” allows one to predict the weakly nonlinear stress response of a material under an arbitrary transient deformation via a memory integral expansion. Our framework is demonstrated by explicitly determining the MAOS relaxation modulus for a dilute suspension of Brownian spheroids subject to a dual-frequency oscillatory shear flow. Specifically, we first calculate the second normal stress difference for such a deformation from a corotational memory integral expansion. Second, the microstructural stress response of the model system of Brownian spheroids is determined via a regular perturbation expansion of the orientation distribution function at small dimensionless strain-rate amplitude, or Weissenberg number. An analytical expression for the MAOS relaxation modulus is resolved by comparing the second normal stress difference results of the memory integral expansion and microstructural stress calculation. Finally, using the MAOS relaxation modulus, we reconstruct the stress response of the model system for the start-up and cessation of simple shear and uniaxial extension. In summary, our work offers an approach to utilizing medium (and large) amplitude oscillatory shear results to predict stress dynamics of viscoelastic fluids in other transient, nonlinear flows.

Shear banding in large amplitude oscillatory shear (LAOStrain and LAOStress) of polymers and wormlike micelles

We investigate theoretically shear banding in large amplitude oscillatory shear (LAOS) of polymers and wormlike micelles. In LAOStrain we find banding at low frequencies and sufficiently high strain rate amplitudes in fluids for which the underlying constitutive curve of shear stress as a function of shear rate is non-monotonic. This is the direct analogue of quasi steady state banding seen in slow strain rate sweeps along the flow curve. At higher frequencies and sufficiently high strain amplitudes we report a different but related phenomenon, which we call `elastic' shear banding. This is associated with an overshoot in the elastic (Lissajous-Bowditch) curve of stress as a function of strain. We suggest that this may arise widely even in fluids that have a monotonic underlying constitutive curve, and so do not show steady state banding under a steadily applied shear flow. In LAOStress we report banding in fluids that shear thin strongly enough to have either a negatively, or weakly positively, sloping region in the underlying constitutive curve, noting again that fluids in the latter category do not display steady state banding in a steadily applied flow. This banding is triggered in each half cycle as the stress magnitude transits the region of weak slope in an upward direction, such that the fluid effectively yields. Our numerics are performed in the Rolie-poly model of polymeric fluids, but we also provide arguments suggesting that our results should apply more widely. Besides banding in the shear rate profile, which can be measured by velocimetry, we also predict banding in the shear and normal stress components, measurable by birefringence. As a backdrop to understanding the new results on shear banding in LAOS, we also briefly review earlier work on banding in other time-dependent protocols, focusing in particular on shear startup and step stress.