Steep Strain Gradients Research Articles

Micro-mechanisms of anisotropic deformation in the presence of notch in commercially pure Titanium: An in-situ study with CPFEM simulations

This study investigates the impact of notch severity and initial texture on the micro-mechanisms during low strain deformation in commercially pure Titanium, exploiting in-situ electron back scatter diffraction (EBSD) experiments and crystal plasticity finite element model (CPFEM). In-situ tests were performed at different strain steps of un-notched and notched samples of transverse direction (TD) and rolling direction (RD) orientations. CPFEM, based on initial EBSD microstructures, predicted profuse prismatic slip traces and early activation of prismatic slip in notched sample, with RD orientation exhibiting higher activity. Further, CPFEM results revealed early activation of high CRSS slip systems as well as evidence of early twin activity at notch tip due to severely localized plastic deformation and steep strain gradient, as observed by GND maps causing higher stress at grain boundaries. At the notch tip, digital images correlation (DIC) at microscale indicated strain localization at 45∘ and 90∘ to the tensile axis for TD and RD orientations, respectively. Furthermore, 2.5D and 3D CPFEM confirmed distinct strain patterns at notch tip: TD orientation exhibited combined basal and prismatic slip influences, while RD orientation displayed dominant prismatic slip systems at localized strain. The model also successfully predicted anisotropic surface roughness, contributing to early necking in RD orientation.

A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel

In this study, we employ a physics-based crystal plasticity finite element method (CPFEM) approach to study the microstructural response of DP600 steel to various loading types. With the pursued approach, it is possible link microstructural changes in the dual phase (DP) steel to its macroscopic response in a convenient and efficient manner. Microstructural data were acquired first from experimental work via the electron backscattered diffraction (EBSD) method. DP crystallographic features were then fed to a numerical hybrid calculation subroutine combining a comprehensive physics-based crystal plasticity scheme for ferrite along with an isotropic plasticity scheme for martensite defined on a single-layer representative volume element (RVE). The developed single-layer 3D mode, while allowing for high computational efficiency, can capture the stress/strain distribution, revealing the microscopic features of the deformation process including the physical evolution of the dislocation density, retexturing, and morphology. The single-layer RVE physics-based method employed herein establishes the strong correlation between morphology, dislocation density and deformation response of the material under various loading types. Specifically, findings reveal that the tendency of the ferrite phase neighboring the martensite regions in the DP steel to retexture is much more profound than pure ferrite when subjected to the same loading conditions, pointing out to the steep strain gradients in the former component. Martensite phase facilitates considerable heterogeneity in the stress and strain distribution, increases the misorientation polarization as well as leading to local strain hardening in the neighboring ferrite volume that stem from profound increase in spatial dislocation density. Stress-strain curves under various loading schemes are simulated and discussed in the light of the experimental findings in literature, revealing the dependence of the microstructural evolution on the loading type.

Fatigue Crack Growth in a Monocrystal and Its Similarity to Short-Crack Propagation in a Polycrystal of Nickel

Short fatigue cracks in polycrystalline materials are very important from both practical and basic aspects, yet they are very difficult to observe. Therefore, it is suggested to emulate some properties of short cracks with long fatigue cracks in monocrystals. Indeed, such experiments in pure nickel crystals prove that the three peculiar properties of short fatigue cracks in polycrystalline metals are observed in long cracks in monocrystals, i.e., a lower threshold of the stress intensity factor (ΔKI)th, a higher crack propagation rate at low ΔKI regimes, and the fact that different cracks exhibit different growth behaviors. The fatigue experiments in monocrystals reveal interesting details of the slip activity at the front of fatigue cracks, including a selection rule for the active slip systems above and below the crack, the slip behavior under conditions of steep strain gradients, and the activation of a new slip system.

Strain relaxation dynamics of multiferroic orthorhombic manganites

Resonant ultrasound spectroscopy has been used to characterise strain coupling and relaxation behavior associated with magnetic/magnetoelectric phase transitions in GdMnO3, TbMnO3 and TbMn0.98Fe0.02O3 through their influence on elastic/anelastic properties. Acoustic attenuation ahead of the paramagnetic to colinear-sinusoidal incommensurate antiferromagnetic transition at ∼41 K correlates with anomalies in dielectric properties and is interpreted in terms of Debye-like freezing processes. A loss peak at ∼150 K is related to a steep increase in electrical conductivity with a polaron mechanism. The activation energy, E a, of ≳0.04 eV from a loss peak at ∼80 K is consistent with the existence of a well-defined temperature interval in which the paramagnetic structure is stabilised by local, dynamic correlations of electric and magnetic polarisation that couple with strain and have relaxation times in the vicinity of ∼10−6 s. Comparison with previously published data for Sm0.6Y0.4MnO3 confirms that this pattern may be typical for multiferroic orthorhombic RMnO3 perovskites (R = Gd, Tb, Dy). A frequency-dependent loss peak near 10 K observed for TbMnO3 and TbMn0.98Fe0.02O3, but not for GdMnO3, yielded E a ⩾ ∼0.002 eV and is interpreted as freezing of some magnetoelastic component of the cycloid structure. Small anomalies in elastic properties associated with the incommensurate and cycloidal magnetic transitions confirm results from thermal expansion data that the magnetic order parameters have weak but significant coupling with strain. Even at strain magnitudes of ∼0.1–1‰, polaron-like strain effects are clearly important in defining the development and evolution of magnetoelectric properties in these materials. Strains associated with the cubic–orthorhombic transition due to the combined Jahn–Teller/octahedral tilting transition in the vicinity of 1500 K are 2–3 orders of magnitude greater. It is inevitable that ferroelastic twin walls due to this transition would have significantly different magnetoelectric properties from homogeneous domains due to magnetoelastic coupling with steep strain gradients.

Combining Digital Image Correlation and Acoustic Emission for Monitoring of the Strain Distribution until Yielding during Compression of Bovine Cancellous Bone

In this work, the surface heterogeneity in mechanical compressive strain of cancellous bone was investigated with digital image correlation (DIC). Moreover, the onset and progression of failure was studied by acoustic emission (AE). Cubic cancellous bone specimens, with side of 15 mm, were obtained from bovine femur and kept frozen at -20oC until testing. Specimen strain was analyzed by measuring the change of distance between the platens (crosshead) and via an optical method, by following the strain evolution with a camera. Simultaneously, AE monitoring was performed. The experiments showed that compressive Young’s modulus determined by crosshead strain is underestimated at 23% in comparison to optically determined strain. However, surface strain fields defined by DIC displayed steep strain gradients, which can be attributed to cancellous bone porosity and inhomogeneity. The cumulative number of events for the total AE activity recorded from the sensors showed that the activity started at a mean load level of 36% of the maximum load and indicated the initiation of micro-cracking phenomena. Further experiments, determining 3D strain with μCT apart from surface strain, are necessary to clarify the issue of strain inhomogeneity in cancellous bone.

Towards strength–ductility synergy through the design of heterogeneous nanostructures in metals

Metals can be processed to reach ultra-high strength, but usually at a drastic loss of ductility. Here, we review recent advances in overcoming this tradeoff, by purposely deploying heterogeneous nanostructures in an otherwise single-phase metal. Several structural designs are being explored, including bimodal, harmonic, lamellar, gradient, domain-dispersed, and hierarchical nanostructures. These seemingly distinct tactics share a unifying design principle in that the intentional structural heterogeneities induce non-homogeneous plastic deformation, and the nanometer-scale features dictate steep strain gradients, thereby enhancing strain hardening and consequently uniform tensile ductility at high flow stresses. Moreover, these heterogeneous nanostructures in metals play a role similar to multiple phases in complex alloys, functionally graded materials and composites, sharing common material design and mechanics principles. Our review advocates this broad vision to help guide future innovations towards a synergy between high strength and high ductility, through highlighting several recent designs as well as identifying outstanding challenges and opportunities.

Integral sheet metal design via severe plastic deformation – state of the art and future challenges

The innovative forming processes Linear Flow Splitting (LFS) and Linear Bend Splitting (LBS) were developed to facilitate the continuous production of branched profiles with tailored sheet thickness by inducing severe plastic strain. In contrast to most SPD processes the stress state in LFS and LBS is very complex and plastic deformation is confined to limited volumes which results in steep strain gradients and consequently ultrafine grained (UFG) gradient microstructures. Even though the processes have been commercialized, the increased lightweight potential that originates from the local grain refinement remains mostly idle since it is neither fully understood nor easily assessable yet.The present work shows the state of the art for the LFS and LBS processes and compares the microstructures and distribution of mechanical properties for different steels processed with different LFS parameters. The data is used to identify characteristic manufacturing induced properties that are insensitive to processing parameters. Based on the experimental results a material flow model for the processing zone is proposed which is discussed with respect to the current understanding of plasticity at severe strains.

Effect of orientation on plastic deformations of Alloy 617 for VHTR applications

Alloy 617 is considered a primary structure material for building the intermediate heat exchanger (IHX) for the very high temperature reactor (VHTR). In the present work, the effect of orientation of Alloy 617, which may influence the engineering design and performance, was investigated by mechanical tests and associated microstructural analysis. Tensile tests at various temperatures were performed on the specimens at various angles to the rolling plane. The yield strength parabolically dropped once the sampling direction deviated from the rolling plane, whereas the ultimate tensile strength decreased in a linear trend. The mechanical anisotropy reflected by the loss of the transverse strengths exists throughout the range of testing temperatures up to 1000°C. The microstructural analysis revealed that the intrinsic Bauschinger effect, the loss of transverse yield strength, is caused by mechanical fibering in Alloy 617, which is originally induced during hot rolling processing. The results also indicated that the inclusion particles caused steep strain gradients during plastic deformations in Alloy 617, due to the dislocation pileups on the interphase boundaries. The distribution of strained area is orientation dependent and thus caused localized plastic deformations and early fractures in the transverse direction at low temperatures. In addition, it was found that the strained area could be recovered by forming new grains, leading to an oriented dynamic recrystallization (DRX) at high temperatures.

Finite Element Analysis of Stress Concentration Problems Based on Cosserat Continuum Model

In the present work, the Cosserat micro-polar continuum theory is introduced into the FEM numerical model, which is used to simulate the stress concentration problems. The stress concentration phenomena around circular hole, elliptic hole and rhombic hole in plane strain condition, are numerically simulated by two types of Cosserat continuum finite elements of the standard displacement and rotation u4ω4 and u8ω8 based on Dirichlet principle. It is indicated that, compared with the classical continuum finite element, these two Cosserat continuum finite elements can reflect the steep strain gradient and scale effects occurring in the stress concentration problems, and they can weaken the stress concentration and may get consistent solution with actual situation.

Averaging effects of a strain gage

Choosing the right strain gage for a measurement application requires selecting gages with the right characteristics for the job. In general, the strain gage is to be used to measure the strain at the center of the gage, but it inherently underestimates the peak strain when it is mounted in high stress gradient areas. This paper concerns itself with the averaging effects of a strain gage along gage filaments. The approach is unconventional in dealing with the orientation and size of the gage. The results provide insight into the averaging effect and selecting gages for measuring strains in areas of steep strain gradients. Dimensionless curves which can be used to estimate errors as well as enhance hole-drilling method results are presented. Practical recommendations are made for selecting gages for high strain gradient measurements.

Flexure mode flexoelectric piezoelectric composites

We present a flexure mode composite design to generate steep transverse strain gradient to exploit large flexoelectric coefficient μ1122 of (Ba,Sr)TiO3 (BST) ceramics. Very strong direct piezoelectric effect was observed in composites due to the flexoelectricity. In a single unit composite, sharp low frequency (<300 Hz) mechanical resonance leads to high effective d33>2000 pC/N as the result of enhancement of strain gradient at resonance. Giant nonresonance d33 well beyond piezoelectric single crystal about 4350 pC/N was measured at a temperature around Curie temperature of BST ceramic in a six unit three layer composite.

Piezoelectric composite based on the enhanced flexoelectric effects

In this study, a piezoelectric composite is fabricated from a Ba0.67Sr0.33TiO3 (BST) composition and air, and measured at room temperature (24°C) where the BST is in its paraelectric centric phase. The charge separation mechanism is flexoelectricity, driven by the strain gradient introduced by the pyramidal boundary shapes of each BST building unit of the composite. In spite of the macro (millimeter) dimensions of the building units that inhibit a steep strain gradient, the composite is sufficiently active to be measured by using a conventional Berlincourt d33 meter. The measured values are in good agreement with expectation from the earlier measured flexoelectric coefficient μ11 of the BST and the finite element simulation results of the strain gradient in the pyramid BST units.

Effect of Rolling Friction on the Development of {111} Texture in A1050 Aluminium Sheets

Commercially pure aluminum (A1050) sheets have been cold- rolled in vacuum, to obtain high friction between rolls and sheet. This cold-rolling in vacuum successfully introduced large shear deformation near the sheet surface. The shear strain is the highest at the sheet surface, and rapidly decreased to zero at the quarter thickness. These high shear strains are sufficient enough to produce {111} and {001} cold- rolling, or shear texture. Conventional cold-rolling texture such as (001) [100], is naturally observed at the mid-thickness. It is confirmed that a high shear strain and probably steep strain gradient through thickness have a sufficient effect on the increase in {111} cold-rolling texture near the sheet surface. {111} cold-rolling texture is proved to be effective in the evolution of {111} recrystallization texture. This development will be discussed based on the cold-rolling texture change.

Relationships between melt-induced rheological transitions and finite strain: Observations from host rock pendants of the Tuolumne Intrusive Suite, Sierra Nevada, California

Finite strain analysis in the northern (Piute Meadow pendant (PMP)) and eastern (Saddlebag Lake pendant (SLP)) host rock pendants of the Tuolumne Intrusive Suite (TIS) reveals plane strain geometries in the pendants and a steep strain gradient in the SLP. Average regional z-axis shortening in both pendants is ca. 43% and increases to ca. 70 and 85% in the SLP within ca. 100 m to the pluton contact. Microstructures in the SLP adjust to increasing temperatures and partial melting near the margin. Beyond the pluton margin, weakly elongate quartz grains with lobate grain boundaries, patchy to sweeping undulose extinction, deformation bands, and incipient subgrains are consistent with low-temperature dislocation creep. Towards the margin, quartz grain boundaries become increasingly irregular and display “chessboard” patterns indicating high-temperature dislocation creep. Grain size is markedly smaller near the margin and despite large finite strain grains do not show evidence for crystal-plastic deformation. Cuspate strain-free interstices are interpreted to mimic former anatectic melt. Outcrop-scale migmatization, coincidence with abruptly increasing finite strain, and microfracturing towards the margin implies that fracture-induced mechanical grain size reduction may have triggered the transition to melt-assisted granular flow, ultimately resulting in drastic rheological weakening.

Flexoelectric effects: Charge separation in insulating solids subjected to elastic strain gradients

After a brief historical introduction this article will present a summary of experimental work carried through at Penn State to explore the flexoelectric coefficients μ ijkl in ferroelectric, incipient ferroelectric and relaxor ferroelectric perovskites. The initial objective was to understand the magnitude of flexoelectricity in these systems to see whether it would be possible to develop a piezoelectric composite containing no piezoelectric element, which nonetheless could have practically useful properties. Recent discussions of the thermodynamic converse effect, ie. the generation of elastic strain by an electric field gradient, now suggest that such composites might be designed to have unique properties such as a direct but no converse effect, or vice-versa, and materials with this character could have important practical application. Present data already suggest that the direct effect may make an important contribution to the properties of epitaxial thin films where mismatch can give rise to very steep elastic strain gradients. Clearly, more work is needed to fully quantify the flexoelectric behavior. It will be important to measure single crystals in the ceramic systems which have been studied and to characterize the converse effect as a check of the measured values

Local Finite Element and Experimental Limit Loads of Cracked Piping Elbows Under Opening Bending

: Finite element (FE) and experimental data of cracked, 88.9 mm outside diameter, 5.49 mm thick, short radius, carbon steel piping elbows under displacement controlled, opening bending are reported. Short and long defects with depth-to-thickness ratios ranging from shallow to through-wall, axially or circumferentially centred about the bend crown centreline or intrados respectively, are considered. The FE predicted general deformation mechanisms and overall strain distributions compare well with the experimental observations. Also, the strains agree well with the experimental values away from the defects. However, in the immediate vicinity of the defect, the FE strain data give much more detail about the initiation and spread of plasticity as the loading is increased towards plastic collapse of the component, but specific integration point strain data reveals that the variations are large and that steep strain gradients are evident even within individual elements. This explains the poor comparisons with experimental data in these regions. Using the above type of data, in conjunction with the twice-elastic slope (TES) method for the determination of plastic loads for the cases investigated, it has been shown that values lower than those obtained from similar global measurements (load-displacement plots) are consistently obtained.

Evaluation of strain distribution in freestanding and buried lateral nanostructures

A free-standing lateral nanostructure based on GaAs[001] containing a ${\mathrm{Ga}}_{0.97}{\mathrm{In}}_{0.03}\mathrm{As}$ single quantum well and similar structures after the overgrowth with GaAs and AlAs, respectively, have been investigated by high-resolution x-ray grazing incidence diffraction (GID) and conventional x-ray diffraction (HRXRD). The wire shape of the freestanding structure and the lateral density variation in the overgrown samples, were determined by running scans with constant length of the scattering vector (transverse scans) across the grating truncation rods (GTR's) close to the $(2\ifmmode\bar\else\textasciimacron\fi{}20)$ reflection. The in-plane strain distribution became available crossing the $(220)$ GTR's by a scan in the longitudinal direction. Exploiting the capability of GID for depth resolution, the in-plane strain distribution was analyzed for different values of depth below the sample surface. The strain analysis was completed by HRXRD measurements close to the (004) reflection. The x-ray measurements were interpreted in terms of the distorted wave Born approximation applied for GID geometry. The strain distribution is determined by comparing the measured GTR intensities with the corresponding simulations containing the displacement fields obtained from finite-element calculations. At the freestanding wire structure we find laterally compressive strain of about $\ensuremath{\Delta}{a/a}_{\ensuremath{\Vert}}=\ensuremath{-}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ at the single quantum well (SQW) with a steep strain gradient close to the wire side walls. Both overgrown samples show pronounced lateral strain variation within the overgrown layer, which still appears up to the completely planar surface. Within the SQW the in-plane strain is still compressive after GaAs overgrowth and of similar amount compared to the freestanding grating. The strain is increased by about 30% after overgrowth with AlAs. For both overgrown samples the strain gradient near the wire side walls is reduced, but reaches a maximum close to the SQW. Accompanied by the defect passivation, these findings explain the difference in the energy shift of the photoluminescence line between freestanding and overgrown lateral nanostructures.

Noninvasive photoelastic method to show distribution of strain in the hoof wall of a living horse.

A photoelastic method used for materials testing in industry was adapted to show the distribution of strain through the hoof wall in the living horse. Strain was a change in length per unit length in the material of the loaded hoof wall compared with the unloaded condition. Coloured fringes appeared in the photoelastic plastic where there were differences in strain between adjacent sites (strain gradients) in the hoof. Strain distribution was observed in the shod and unshod hoof wall of the front hooves of 6 sound horses with hooves that appeared 'good' to visual inspection, and one unsound horse with hoof cracks. No significant differences in strains were apparent across the hoof walls of the sound horses when the horses were standing normally. Steep strain gradients were apparent in hooves, associated with defects such as cracks, unstable nail holes, and long toes.

In vivo bone strain patterns in the zygomatic arch of macaques and the significance of these patterns for functional interpretations of craniofacial form.

It has been proposed that the mammalian facial skeleton is optimized for countering or dissipating masticatory stress. As optimized load-bearing structures by definition exhibit maximum strength with a minimum amount of material, this hypothesis predicts that during chewing and biting there should be relatively high and near uniform amounts of strain throughout the facial skeleton. If levels of strain in certain areas of the facial skeleton are relatively low during these behaviors, this indicates that the amount of bone mass in these areas could be significantly reduced without resulting in the danger of structural failure due to repeated masticatory loads. Furthermore, and by definition, this indicates that these areas are not optimized for countering masticatory stress, and instead their overall morphology and concentration of bone mass has most likely been selected or influenced mainly by factors unrelated to the dissipation or countering of chewing and biting forces. An analysis of in vivo bone strain along the lateral aspect of the zygomatic arch of macaques indicates the clear absence of a high and near uniform strain environment throughout its extent. Instead, there is a steep strain gradient along the zygomatic arch, with the highest strains along its anterior portion, intermediate strains along its middle portion, and the lowest strains along its posterior portion. These data, in combination with earlier published data (Hylander et al., 1991), indicate that levels of functional strains during chewing and biting are highly variable from one region of the face to the next, and therefore it is unlikely that all facial bones are especially designed so as to minimize bone tissue and maximize strength for countering masticatory loads. Thus, the functional significance of the morphology of certain facial bones need not necessarily bear any important or special relationship to routine and habitual cyclical mechanical loads associated with chewing or biting. Furthermore, the presence of these steep strain gradients within the facial skeleton suggests that the amount of bone mass in the low-strain areas may be largely determined by factors unrelated to processes frequently referred to as "functional adaptation," or conversely, that the "optimal strain environment" of bone varies enormously throughout the facial skeleton (cf., Rubin et al., 1994). Based solely on anatomical considerations, it is likely that the zygomatic arch is bent in both the parasagittal and transverse planes and twisted about its long axis. Due to constraints on rosette position, the strain data are incapable of determining if one or more of these loading conditions predominate. Instead, the strain data simply provide limited support for the possible presence of all of these loading regimes. Finally, as the masseter muscle is concentrated along the anterior portion of the zygomatic arch and as the arch has fixed ends, the largest shearing forces and the largest bending and twisting moments are located along its anterior portion. This in turn explains why the largest strains are found along the anterior portion of the zygomatic arch.

The mechanical or metabolic function of secondary osteonal bone in the monkey macaca fascicularis

Secondary osteonal bone is believed by many to serve a mechanical function, altering the properties arid/or orientation of bone in response to fluctuating mechanical demands or in the prevention and/or repair of fatigue microdamage. Based on this belief, secondary osteons should be concentrated mainly in regions experiencing high peak-strain conditions. Others contend that secondary osteonal bone functions primarily in meeting the body's calcium needs, and should be expected to form principally in low peak-strain regions so as to avoid compromising the mechanical strength of the bone. These two hypotheses were tested by examining the distribution of secondary osteonal bone in both relatively high- and low-strain regions of the macaque face. Previous strain-gauge studies have demonstrated a steep strain gradient in the macaque face, with relatively high peak strains in the anterior portion of the zygomatic arch and in the mandibular corpus. Relatively low peak strains have been found in the posterior portion of the zygomatic arch and supraorbital bar. Results presented here show that in the mature macaques, there is no consistent relation between newly forming secondary osteons (i.e. those labelled with fluorescent dyes) and peak strain levels. From these data it is concluded that, in the non-perturbed adult, either mechanical and metabolic factors contribute equally to the observed pattern or that metabolically driven remodelling is initiated without regard to strain levels. In immature macaques, however, the relation between peak strain levels and secondary osteon density is positive, with a significantly higher density of labelled osteons in the high strain regions. From these data it is concluded that, in immature individuals, mechanical factors are predominantly responsible for the initiation of secondary osteonal remodelling.