Bulk Strain Research Articles

Structure, Defects, and Magnetism of Electrospun Hematite Nanofibers Silica-Coated by Atomic Layer Deposition.

In the last years, hematite has been utilized in a plethora of applications. High aspect-ratio nanohematite and hematite/silica core-shell nanostructures are arousing growing interest for applications exploiting their magnetic properties. Atomic layer deposition (ALD) is utilized here to produce SiO2-coated α-Fe2O3 nanofibers (NFs) through two synthetic routes, viz. electrospinning/calcination/ALD or electrospinning/ALD/calcination. The number of ALD cycles (10-100) modulates the coating thickness, while the chosen route controls the final nanostructure. Porous and partially hollow NFs are produced. Their hierarchical structure and the nature and density of the lattice defects and strain are characterized by combining electron microscopy, diffraction, and spectroscopy techniques. The uncoated hematite NFs mostly have surface-related strain, which is attributed to oxygen vacancies/Fe2+ sites. ALD coating causes microstrain release and decrease of surface states. NFs calcined after ALD have extensive bulk strain, which is ascribed to the presence of dislocations throughout the volume of the NF grains. Bulk strain determines the remanent magnetization, whereas both surface and bulk strain influence the coercive field and the thermal behavior across the Morin temperature, including the magnetic memory effect. To the best of the authors' knowledge, the correlation between lattice defects/strain and magnetic properties of SiO2-coated α-Fe2O3 NFs has never been reported before.

Formation of tube-pumice structure under pure shear: Insights from extension tests of solidifying foam

Tube pumice, the bubbles of which are highly elongated in one direction, is a common product of explosive silicic eruptions, especially caldera-forming eruptions. To understand the conditions necessary to generate tube-like bubbles, we performed extensional experiments on polyurethane foam, which experiences vesiculation, deformation, and solidification at room temperature. The strain and strain rate of pure shear deformation were controlled by the pull length and pull rate of the extension, respectively. The shapes of bubbles in the solidified polyurethane foam were analyzed in three dimensions by X-ray computed tomography. The experimental results demonstrate that strain and capillary number control the degree of bubble deformation. Highly deformed (tube-like) bubbles were found in the experiments with large strain and large capillary number. In each experimental sample, there is scatter in the relation between the degrees of bubble deformation and expected capillary numbers, which we interpret to be the result of the inhomogeneous shear field around individual bubbles and bubble coalescence. Despite the large scatter, the average deformation degree is predicted well by the dynamics of a single bubble, where the viscous stress acting on the bubble surface is taken as the product of bulk strain rate and effective viscosity. Using this approach, the average deformation degree of experimental bubbles in each sample was approximately calculated from the deformation model of a single bubble at least in the range of pure shear strain smaller than 1.5. Small bubbles in the samples extended at low viscosities tend to be less elongated than those calculated from the deformation model, due to shape relaxation. The effect of shape relaxation is quantified by a new dimensionless number, i.e., the quench number, which represents the ratio of the timescale of increasing viscosity and shape relaxation. Our experiment suggests that bubble shapes in highly vesicular pumice can be used to analyze their viscosity and strain rate during the elongation process. An analysis of the published data was presented as a test case.

Meso-scale modelling of semi-solid deformation in aluminum foundry alloys: Effects of feeding and microstructure on hot tearing susceptibility

Abstract In the context of hot tearing susceptibility, the semi-solid constitutive behaviour of two commercially important foundry aluminum alloys at high solid fraction has been simulated. The numerical methodology combines solid mechanics, computational fluid dynamics, and microstructure modelling, i.e a meso-scale multi-physics approach. Feedable and un-feedable domains with different microstructures including equiaxed globular, equiaxed dendritic, and combined dendritic and eutectic were developed. Considering that it is the combined effects of a lack of liquid feeding and limited semi-solid ductility that contribute to hot tearing formation, the effect of feeding and mechanical deformation are studied and discussed. The model demonstrates that the microstructure type and the eutectic formation also have a considerable effect on the liquid channels pressure drop and semi-solid bulk stress and strain, and consequently on hot tearing.

Quasi-static spherical/cylindrical cavity expansion in a medium with an arbitrary equation of state and a shear strength plasticity envelope

This paper presents a new analytical quasi-static spherical/cylindrical cavity-expansion model for a medium that is described by an arbitrary (non-linear) equation of state ("pressure - bulk strain" relationship) and a shear strength plasticity envelope (principal stress difference vs. pressure relationship). The paper presents the formulae for determination of the cavity pressure and the corresponding stresses variations in the radial direction.A unified solution is presented for a general compressible elastic-plastic or an elastic-cracked-plastic medium that is described by any nonlinear equation of state and shear strength plasticity envelope.The solution of the problem is based on an analytical relationship that is developed for the ratio between the elastic-plastic interface coordinate and the cavity radius for the examined problem. The derived formulae for the variation of the stresses with the radial coordinate depend on this ratio. The formulation is characterized by special features, for example the cavity boundary condition is not necessarily pressure but may be the boundary displacement, which is more suitable for the model implementation in interaction problems.From the general present model, different special cases may be obtained, such as linear equation of state and linear shear strength envelope, locked hydrostat, or for an incompressible material.Comparisons of the analytical model with available results and known solutions of particular cases, for both spherical and cylindrical cavity expansion problems, show excellent agreement.

Variation in permeability during CO2–CH4 displacement in coal seams: Part 1 – Experimental insights

The injection of CO2 into deep coal seams can improve the recovery of CH4 and contribute to the geological sequestration of CO2. To reveal the controlling factors associated with CO2 displacing CH4, experiments were conducted to simulate the process under different confining pressures (8, 12, 16, and 20 MPa) and CO2 injection pressures (1–6 MPa). The results show that coal can adsorb more CO2 than CH4. However, the permeability of CH4 is greater than that of CO2 under inlet gas pressures of 1–5 MPa. For CH4 saturated coals, the CH4 desorption volume is higher under CO2 displacing conditions compared to pure CH4 desorption processes under the same pressures. The coal adsorbed CO2 decreases under high pore and confining pressures, indicating the displacement results may be better in shallow buried coals. The axial, radial, and bulk strains of coal show steady, sharp, and then slow declining trends with decreasing pore pressures, and the inflection points generally occur at 5.25 and 3.25 MPa. Meanwhile, the strain in three directions decreases exponentially with the increase of effective stress, and the radial strain is higher than the axial strain under each confining pressure. With the combined influences of effective stress, matrix swelling/shrinkage, and gas slippage, the permeability decreases first and then increases with the decrease of pore pressure. With the decrease of pore pressure and the increase of confining pressure, the combined influence of the three factors on coal permeability gradually weakens. The results would be beneficial for controlling the injection process and permeability variation predicting during CO2 sequestration and the replacement of CH4 in coals at different burial depths.

Fracture and Weakening of Jammed Subduction Shear Zones, Leading to the Generation of Slow Slip Events

AbstractGeodetic data have revealed that parts of subduction interfaces creep steadily or transiently. Transient slow slip events (SSEs) are typically interpreted as aseismic frictional sliding. However, SSEs may also occur via mixed viscobrittle deformation, as observed in shear zones containing mixtures (mélange) of strong fractured clasts embedded in a weak viscobrittle matrix. We test the hypothesis that creep in a subduction mélange occurs through distributed matrix deformation, where flow is intermittently impeded by load‐bearing clast networks (jamming). Our numerical models demonstrate that bulk mélange rheology can be dominated by the strong clasts in the absence of fracturing, while at high driving stresses or low frictional strength, clast fracturing redistributes deformation into the matrix, leading to high bulk strain rates. Because mélange stress is heterogeneous, fracturing of clasts occurs throughout jammed mélange when the driving stresses are only ∼20% of the clast yield strength. The effective rheology of jammed mélange can be characterized by a logarithmic dependence of stress on strain rate, which is used to explore strain rate transients caused by temporal variation in clast friction. Clasts must weaken significantly (∼75%) in order to increase strain rate by 8 times. Spring‐block slider models with a more idealized viscobrittle rheology also demonstrate that strain rate transients can be generated when rate‐and‐state friction is incorporated. We outline a model where high bulk strain rates are generated when pervasive fracturing occurs, but further slip is limited by viscous processes. Incorporating such viscous damping into models may widen the conditions under which SSEs can occur while preventing development of seismic slip.

Fault reactivation and strain partitioning across the brittle-ductile transition

AbstractThe so-called “brittle-ductile transition” is thought to be the strongest part of the lithosphere, and defines the lower limit of the seismogenic zone. It is characterized not only by a transition from localized to distributed (ductile) deformation, but also by a gradual change in microscale deformation mechanism, from microcracking to crystal plasticity. These two transitions can occur separately under different conditions. The threshold conditions bounding the transitions are expected to control how deformation is partitioned between localized fault slip and bulk ductile deformation. Here, we report results from triaxial deformation experiments on pre-faulted cores of Carrara marble over a range of confining pressures, and determine the relative partitioning of the total deformation between bulk strain and on-fault slip. We find that the transition initiates when fault strength (σf) exceeds the yield stress (σy) of the bulk rock, and terminates when it exceeds its ductile flow stress (σflow). In this domain, yield in the bulk rock occurs first, and fault slip is reactivated as a result of bulk strain hardening. The contribution of fault slip to the total deformation is proportional to the ratio (σf − σy)/(σflow − σy). We propose an updated crustal strength profile extending the localized-ductile transition toward shallower regions where the strength of the crust would be limited by fault friction, but significant proportions of tectonic deformation could be accommodated simultaneously by distributed ductile flow.

Thermo-Mechanical Fatigue Lifetime Assessment of Spheroidal Cast Iron at Different Thermal Constraint Levels

In previous work on the thermo-mechanical fatigue (TMF) of compacted graphite iron (CGI), lifetimes measured under total constraint were confirmed analytically by numerical integration of Paris’ crack-growth law. In current work, the results for CGI are further validated for spheroidal cast iron (SGI), while TMF tests at different constraint levels were additionally performed. The Paris crack-growth law is found to require a different CParis parameter value per distinct constraint level, indicating that Paris’ law does not capture all physical backgrounds of TMF crack growth, such as the effect of constraint level. An adapted version of Paris’ law is developed, designated as the local strain model. The new model considers cyclic plastic strains at the crack tip to control crack growth and is found to predict TMF lifetimes of SGI very well for all constraint levels with a single set of parameters. This includes not only full constraint but also over and partial constraint conditions, as encountered in diesel engine service conditions. The local strain model considers the crack tip to experience a distinct sharpening and blunting stage during each TMF cycle, with separate contributions to crack-tip plasticity, originating from cyclic bulk stresses in the sharpening stage and cyclic plastic bulk strains in the blunting stage.

Grain-scale deformation mechanisms and evolution of porosity in experimentally deformed Boom Clay

Boom Clay is a soft, slightly overconsolidated, uncemented claystone considered as potential host material for a radioactive waste repository in Belgium. We studied the evolution of microfabrics in samples which were shortened to 20% bulk strain in consolidated-undrained (CU) triaxial experiments at effective confining pressures of 0.375, 0.750 and 1.5 MPa, respectively.Results show a geomechanical behavior in agreement with previous studies, with total strain partly localized in shear zones and partly diffuse outside the shear zones. The diffuse strain is accommodated by pore compaction without any discernible microstructural changes compared to the starting material. In the shear zones, pore collapse reduces SEM-visible porosity and further deformation mechanisms within the shear zones are particulate flow (grain boundary sliding), particle rotation and the formation of microcracks. There is no evidence for comminution of quartz and feldspar grains. Strain localization on macro- and mesoscale is governed by viscosity contrasts between harder clasts (e.g. quartz and feldspar) embedded in a soft, porous, phyllosilicate-rich matrix.Our microstructures are comparable to those observed in Boom Clay deformed naturally and in the excavation damaged zone of the underground research facility. This suggests that our results are representative of Boom Clay's geomechanical behavior at the microscale.

Strain and damage sensing of polymer bonded mock energetics via piezoresistivity from carbon nanotube networks

The strain and damage sensing abilities of randomly oriented multi-walled carbon nanotube (MWCNT) networks dispersed in the polymer binder of polymer bonded energetics are experimentally investigated. Monoclinic sugar crystals acting as mock energetics and aluminum powder acting as metallic fuel were added to simulate a fuel-oxidizer combination commonly used in the aerospace industry. MWCNTs were added to polydimethylsiloxane (PDMS), an elastomeric polymer binder, and hybrid mock energetics were fabricated. Four different material compositions were characterized based on the stress–strain response under monotonic uniaxial tension and compression to failure tests, allowing for the assessment of the effects of MWCNTs and aluminum powder on the average bulk elastic modulus, peak stress, and strain to failure. Along with mechanical loading, the piezoresistive response i.e. the change in resistance and reactance as a function of applied strain, was measured in both the elastic and failure regimes of the mechanical response for each material system. Gauge factors were calculated in three distinct regions of elastic behavior, microscale, and macroscale damage demonstrating the MWCNT network’s ability to sense strain, microscale damage, and macroscale fracture of mock energetic materials. Results observed herein demonstrate valid structural health monitoring applications for embedded carbon nanotube sensing networks in elastomer-based energetics experiencing significantly higher strain levels than prior proofs of concept with epoxy-based material systems.

A Three-Dimensional Analytical Solution for Reservoir Expansion, Surface Uplift and Caprock Stress Due to Pressurized Reservoirs

An analytical solution is presented for the displacement, strain and stress of a three-dimensional poro-elastic model with three layers, where the three layers are an underburden, a reservoir with a given fluid pressure, and an overburden. The fluid pressure in the reservoir is assumed symmetrical around the z-axis and represented by a Fourier cosine series. The poro-elastic solution is expressed as a superposition of the solutions for each term in the Fourier series. It is shown that the bulk strain in the reservoir layer is proportional to the fluid pressure and that the bulk strain in the underburden and overburden is zero. Using these properties of the bulk strain, a solution is derived for the three-layer model where the fluid flow and mechanics are fully coupled. A particular aim of the model is to study the surface uplift from a given reservoir pressure. The expansion of the reservoir and the uplift of the surface are studied in terms of the wavelengths in the Fourier representation of the pressure. It is shown that the surface uplift can be written in a similar form to the 1D vertical expansion of the reservoir layer, but where the fluid pressure is based on the Fourier series. It is shown that the amplitudes with average wavelengths longer than 2pi times the thickness of the reservoir give expansion of the reservoir, but average wavelengths much shorter than this limit do not. Similarly, amplitudes with average wavelengths much longer than 2pi times the thickness of the overburden produce surface uplift, but wavelengths much shorter do not. The stress in the overburden, which is generated by the reservoir fluid pressure, is also analysed in terms of the wavelengths. A case is given where the analytical uplift is compared with the results of a numerical simulation and the agreement is excellent.

Coherent X-ray Imaging of CO-Adsorption-Induced Structural Changes in Pt Nanoparticles: Implications for Catalysis

Using coherent X-ray diffraction imaging (CXDI) as an in situ tool, we determined the shape and strain state of a platinum nanoparticle with ≈160 nm diameter supported by a strontium titanate substrate. The experiment was performed at a temperature of 400 K under continuous gas flow conditions of pure Ar and Ar/CO mixtures. The nanoparticle was preselected by scanning electron microscopy (SEM) and postanalyzed by atomic force microscopy (AFM). We obtain a very good agreement between the overall nanoparticle size, shape, and defect structure as determined by CXDI and AFM. In addition, we compare the strain state in the nanoparticle near surface region and its bulk: For pure Ar flow, we find a slight compressive strain in the nanoparticle bulk compared to an expansion in the near surface region. We ascribe the latter to the presence of high index vicinal surfaces. Our analysis suggests that under mixed Ar/CO flow at 400 K reshaping of the nanoparticle occurred. New high index facets developed, leading to a stronger lattice expansion, also propagating into the nanoparticle bulk. Our high-resolution experiments pave the way for future CXDI experiments under operando catalytic reaction conditions.

Strain Pattern Analysis of Mylonites From Sitampundi-Kanjamalai Shear Zone, Thiruchengode, South India

This study aims to investigate the petrography and strain pattern of mylonites from parts of N-S trending Sitampundi-Kanjamalai Shear Zone (SKSZ) around Thiruchengode. The petrographic study indicates the presence of recrystallized quartz, K-feldspar, plagioclase, biotite and some hornblende. The kinematic analysis of Mylonites was done with the help of shear sense indicators such as recrystallized type quartz (quartz ribbon) around the cluster of feldspar, S-C fabric shows dextral shear sense and some sinisterly shear sense in some parts of SASZ which can be considered as a product of partitioning of both strain and vorticity between domains. These all indicates the simple shear extension along E-W direction and the mylonitic foliation shows the pure shear compression along N-S direction. Further the study of bulk strain analysis by Flinn plot method using L and T section of mylonite shows k<1 which lies in the field of flattening zone of finite strain. The kinematic vorticity number is calculated by Rxz/β method which gives the value of 0.36 indicating the general shear. The rigid grain graph shows that the pure shear component is more ­­­­dominant than the simple shear component. The analysis leads to the conclusion that the mylonite has experienced a high temperature shearing of above 700°cat deep crustal level.

Surface energy effect on nonlinear free axial vibration and internal resonances of nanoscale rods

This study aims to investigate effects of the surface energy parameters on the nonlinear axial vibration and internal resonances of nanoscale rods. The surface energy parameters considered are the surface density and the surface Lamé constants. The nonlinear governing equation of motion is derived using the Hamilton's principle which includes the strain energy and the kinetic energy of the nanorod surface and bulk. The strain and kinetic energies of the nanorod bulk are obtained using the classical theory of elasticity and those of the nanorod surface are obtained using the surface elasticity theory. Then, the nonlinear governing equation of motion is solved using the method of multiple scales and natural frequencies are obtained for fixed-fixed and fixed-free boundary conditions. Effects of the surface energy parameters on the frequencies are examined for various cases. It is observed that the type of effect of the surface energy parameters depends on their sign. It is also seen that the type of effect of the surface energy parameters on nonlinear frequencies may become different at higher frequency numbers. The observations of this study can be a useful reference for more accurate design and fabrication of nano-electro-mechanical systems in which rod-shaped nano-structures, carbon nanotubes, play a significant role.

Lubrication effects on magmatic mush dynamics

Silicic magma bodies are formed by repeated injections of mobile magma and reside as a crystal-rich mush. Numerical studies of open-system events have revealed the complexity of mixing and rheological behavior. This is associated with the dilation of the crystal network and the possible occurrence of a lubricated regime. Lubrication forces are hydrodynamic interactions occurring when neighboring crystals have relative motion. The effect of such dissipative forces has not yet been explored in the case of magmatic mush. Here, we investigate the effects of lubrication on mush dynamics and on magma transport. First, we propose scaling relationships to assess the relative importance of the forces controlling the motion of one crystal within a mush by adding lubrication terms into the Basset-Boussinesq-Oseen equation that describes crystal motion in a viscous melt. We then investigate lubrication effects at the macroscopic scale with computational fluid dynamics with discrete element modeling (CFD-DEM) simulations that include these forces. We explore two cases: crystal mush sedimentation and the injection of a crystal-free magma inside a mush. We perform all simulations twice, with and without lubrication forces, and compare the results. At the grain scale, we show that three dimensionless numbers and the crystal content can describe the competition between viscous drag, buoyancy, and lubrication. Two of these numbers (Stokes and Froude numbers) have been previously employed in the context of dilute suspensions. The third is a new form of the Sommerfeld number that measures the importance of lubrication. At the macroscopic scale, simulation pairs (with and without lubrication forces) exhibit very similar behavior when in steady state. The duration of the transient regime preceding steady state, however, is increased when lubrication forces are included. Lubrication causes an apparent bulk strain hardening followed by softening at the initiation of the mush motion. Our results show that lubrication opposes dilation and the initiation of motion within the magmatic mush during this transient phase. Our results highlight the control that the crystal network exerts on magma transport and provide a novel way to evaluate when lubrication matters.

Relating strain hardening moduli in high density polyethylene copolymers to anisotropic molecular deformation using infrared spectroscopic imaging

Understanding and establishing the relationship between the microstructure of high density polyethylene (HDPE) resins and their mechanical behavior is critical in designing new products and catalysts to produce these polymers. Recent advancement in the mid-infrared (IR) spectroscopic imaging techniques combined with intuitive mathematical modelling can provide a powerful tool in solving this industry-wide long-standing challenge. In this work, IR spectral anisotropy methods coupled with the Crystal Tie Mesh (CTM) model were used to examine the effects of various resin architectures (monomodal and bimodal) on the bulk strain hardening moduli in cold drawn HDPE samples. Using a polarized laser for IR imaging, the related stress strain profiles of local strain gradients (100% sample strain) were modelled using a modified Eyring algorithm. A clear correlating trend was found between a resulting structural parameter in this algorithm (β) and the bulk strain hardening moduli for all samples studied. Results show that the more stable the molecular network (e.g., the lamella segments connected via bridging entanglements and tie molecules), the less strain is observed (i.e. higher β values) when a load is applied. The observed structural effects on the β parameter are consistent with previous results obtained using the CTM model that views the system to be a type of cross linked network formed by multiple bridging and entangled tie chains through common crystalline lamella.

Rate-dependent deformation and Poisson’s effect in porous titanium

Dynamic and quasi-static compression experiments are conducted on a high-density porous titanium with in situ X-ray imaging to characterize its deformation dynamics. The porous titanium exhibits higher strain-rate sensitivity than full-density titanium. Strain field mapping indicates that compaction bands are narrower and denser under dynamic loading, leading to a more homogeneous strain distribution and thus a higher flow stress. The mean Poisson’s ratio for dynamic loading is 15% lower than that for quasi-static loading at the same bulk strain, as a result of local inertial confinement which also contributes to the rate hardening of porous titanium.

Wear of Dies of Bulk Straining According to Criteria of Low-Cycle Fatigue and Plastic Crushing

Cyclically changing thermomechanical loads causing the stress–strain state of dies are part of the crushing mechanism of surface and crack propagation in stress concentration zones. In order to evaluate the maximum stresses causing the critical strains of a die, a mathematical model is developed making it possible to predict the durability of a die’s working parts. The durability of punches and matrixes is estimated by the average number of loading cycles up to the breakdown of the tool according to the criteria of low-cycle strength and plastic crushing.

On Boussinesq-type models for long longitudinal waves in elastic rods

In this paper we revisit the derivations of model equations describing long nonlinear longitudinal bulk strain waves in elastic rods within the scope of the Murnaghan model in order to derive a Boussinesq-type model, and extend these derivations to include axially symmetric loading on the lateral boundary surface, and longitudinal pre-stretch. We systematically derive two forced Boussinesq-type models from the full equations of motion and non-zero surface boundary conditions, utilising the presence of two small parameters characterising the smallness of the wave amplitude and the long wavelength compared to the radius of the waveguide. We compare the basic dynamical properties of both models (linear dispersion curves and solitary wave solutions). We also briefly describe the laboratory experiments on generation of bulk strain solitary waves in the Ioffe Institute, and suggest that this generation process can be modelled using the derived equations.

Effects of heat release and imposed bulk strain on alignment of strain rate eigenvectors in turbulent premixed flames

The impact of combustion heat release and bulk compressive strain on local alignment between the flame front normal and strain rate eigenvectors (principal strain rates) are investigated using simultaneous laser-induced fluorescence imaging of OH and tomographic particle image velocimetry in turbulent premixed CH4/O2/N2 counterflow flames with Karlovitz numbers (Ka) of 1.3 and 2.7. The bulk strain rate imposed by the counterflow introduces a preferential alignment of the most compressive principal strain rate, s3, with the flame normal, n. Dilatation induced by heat release acts as a competing mechanism that promotes the alignment of the most extensive principal strain rate, s1, with n. In the counterflow flames, the preferential s3-n alignment prevails and remains dominant across the entire flame. This alignment stands in stark contrast to observations from previous studies in turbulent Bunsen flames or flames in isotropic turbulence, indicating the significance of bulk strain rate in determining local strain-flame alignment. The effects of increasing turbulence intensity on strain rate-flame front alignment are twofold; on the one hand, turbulence diminishes the s3-n preferential alignment that is associated with the bulk strain field by increasing flame surface wrinkling and reducing the tendency of the flame front normal and s3-eigenvectors to align with the axis of the counterflow. On the other hand, turbulence reduces the impact of heat release and enhances preferential s3-n alignment approximately 1 mm ahead of the flame front, reflecting the characteristic alignment of compressive strain and scalar gradients in turbulent non-reacting flows. The effects of bulk strain are also observed in strain rate alignment statistics based on the fluctuating velocity fields, although the impact is less pronounced than for the statistics based on the full velocity fields.As a result of this complex interplay between heat release, turbulence, and bulk strain rate, the flame-tangential strain rate is on average extensive, and the flame-normal strain rate is dominantly compressive except for an approximately 0.8 mm wide region near the flame front where it is extensive due to dilatation. The compressive bulk strain in the counterflow was also shown to compress the length scales over which the strain rate and its alignment are affected by flame heat release. The present finding is important for developing turbulent flame models to accommodate the effect of bulk strain rate that is inherently associated with practical burner geometries, and the length scale dependence of the bulk strain effect could be a consideration for determining the cutoff scale in the context of large-eddy simulations.