In-plane Elastic Strain Research Articles

Electric Control of the Magnetic Domains in Artificial Magnetoelectric Composite Heterostructure

Magnetic force microscopy (MFM) has been used to probe the influence of an in situ applied in-plane elastic strains and/or magnetic field on the static magnetic configuration of a 530 nm magnetostrictive FeCuNbSiB thin film. The film shows a typical magnetic stripe domain configuration with 180 nm magnetic domain width presenting its magnetic moments oriented perpendicularly to the film plane. The in-plane strain was induced via the application of a voltage in a piezoelectric (PE) actuator on which the film/substrate system was glued. The FeCuNbSiB film was deposited onto a compliant polyimide substrate (Kapton) in order to avoid clamping effects that can lead to low transmission of strains from the actuator to the film/substrate system. The instrumental setup was modified with a custom-built electromagnet for performing in situ MFM experiments under the application of an in-plane magnetic field. We could compare the strain-mediated effect upon the magnetic domain configuration with the effect of an applied magnetic field. This paper clearly shows a better-defined electric field/strain control of the local domain magnetization (size and orientation). The efficient coupling between the magnetostrictive properties of the FeCuNbSiB film and the PE ones of the actuators allows a complete switching of the out-of-plane domain magnetization toward an in-plane homogeneous magnetic one. This magnetoelectric heterostructure can thus open the way for new devices allowing the electric control of the magnetic information at the nanoscale level.

Variational formulation, asymptotic analysis, and finite element simulation of wrinkling phenomena in modified plate equations modeling biofilms growing on agar substrates

The expansion of a bacterial biofilm on an agar substrate is modeled as a system of Föppl–von Kármán equations modified to include growth and coupling to a viscoelastic substrate. Analysis shows that wrinkles appear on the biofilm as a result of growth incompatibility and their frequency increases due to interaction with the agar layer. Simple cases of homogeneous radial and azimuthal growth are approximated by cone and corona solutions of the Monge–Ampère equation that are corrected by corner and boundary layers. A weak formulation of the problem allows us to express in-plane elastic strains and Airy potential solely in terms of the vertical displacement. We have developed a numerical method based on finite elements and simulated biofilm deformation for wide spectra of different growths. For heterogeneous growth, we find wrinkled patterns that are combinations of cones and coronas.

Simultaneous Operando Measurements of the Local Temperature, State of Charge, and Strain inside a Commercial Lithium-Ion Battery Pouch Cell

A high energy X-ray diffraction technique is employed in a new way to make operando through-thickness measurements inside a large format commercial Li-ion pouch cell. The technique, which has a sub-mm in-plane spatial resolution, simultaneously determines the local temperature, the local state of charge of both electrodes (as opposed to the global average state of charge determined electrochemically), and the local in-plane elastic strain in the current collectors, all without embedding any intrusive sensors that alter battery behavior. As both thermal strain and mechanical strain develop during the charge-discharge cycling of the pouch cell, a novel approach developed herein makes it possible to separate them, allowing for measurement of the local temperature inside the battery. The operando experiment reveals that the temperature inside the cell is substantially higher than the external temperature. We propose that mechanical strain is due primarily to load transfer from the electrode to the current collector during lithiation, allowing determination of the local binder. Detailed local SOC mapping illustrates non-uniform degradation of the battery pouch cell. The possibility for 3D measurements is proposed. We believe that this new approach can provide critically needed data for validation of detailed models of processes inside commercial pouch cells.

Property control by elastic strain engineering: Application to graphene

Various carbon nanostructures, including graphene, are of great interest nowadays for many applications. It has been shown that graphene has unique physical and mechanical properties and its properties can be controlled by the applied strain. The objective of the present paper is to describe several physical properties of graphene that can be controlled by means of elastic strain engineering. The space of in-plane elastic strain components is divided into regions with different structural configurations and physical properties of graphene. It is shown that a gap in the phonon density of states is observed when graphene is strained close to the appearance of ripples. Sound velocities of unstrained graphene do not depend on the propagation direction but application of strain, apart hydrostatic tension, makes graphene elastically anisotropic. The orientation, amplitude and wavelength of unidirectional ripples in graphene can be controlled by a change in the components of the applied strain.

An Accurate Method for Shape Retrieval and Displacement Measurement Using Bi-Prism-Based Single Lens 3D Digital Image Correlation

The bi-prism-based single lens 3D digital image correlation (BSL 3D DIC) technique is a 3D DIC method developed in recent years. The BSL 3D DIC is able to reconstruct the morphology of an object and track its 3D displacements using only a single camera, which significantly improves the integration level of the 3D DIC system and simplifies the system calibration process. In this paper, a novel and practical shape retrieval method is proposed to improve the measurement accuracy of the BSL 3D DIC technique and expand its applicability to strain measurement. The proposed method is based on a geometrical optics analysis using the reverse ray tracing method, which is performed in 3D space and takes into account the possible model errors induced by the system misalignment and the lens distortion. Experimental results demonstrate that the proposed method suffers from only a small error in morphology reconstruction (less than 0.3 %) and is able to measure the in-plane elastic strains with an accuracy of 95 μe.

Magnetic domain-wall motion study under an electric field in a Finemet® thin film on flexible substrate

Influence of applied in-plane elastic strains on the static magnetic configuration of a 530 nm magnetostrictive FeCuNbSiB thin film. The in-plane strains are induced via the application of a voltage to a piezoelectric actuator on which the film/substrate system was glued. A quantitative characterization of the voltage dependence of the induced-strain at the surface of the film was performed using a digital image correlation technique. MFM images at remanence (H=0 Oe and U=0 V) clearly reveal the presence of weak stripe domains. The effect of the voltage-induced strain shows the existence of a threshold value above, which the break of the stripe configuration set in. For a maximum strain of exx~0.5*10-3 we succeed in destabilizing the stripes configuration helping the setting up of a complete homogeneous magnetic pattern.

Phase-field simulation of strain-induced domain switching in magnetic thin films

The strain-induced magnetic domain switching in epitaxial CoFe2O4 (CFO) thin films was studied using phase-field method. In particular, we investigated the domain switching from an initial in-plane direction to out-of-plane under the action of in-plane elastic strains. An abrupt switching feature is observed for a single-domain film while the switching of a multidomain CFO thin film is gradual. Typical magnetic domain structures as a result of the biaxial isotropic in-plane strains are presented.

Creep in α-Al 2O 3 thermally grown on β-NiAl and NiAlPt alloys

We have measured creep relaxation in α-Al 2O 3, thermally grown on stoichiometric β-NiAl, and on β- and γ'-phase alloys of Ni–Al–Pt at temperatures between 950–1100 °C. Creep was monitored using in-situ measurements of strain relaxation in the oxide following the sudden imposition of a stress. A stress was imposed by abruptly changing the sample temperature, exploiting the thermal expansion difference between oxide and substrate. The in-plane elastic strain was obtained using a sin 2ψ X-ray diffraction technique exploiting synchrotron radiation. For oxides grown on β-NiAl and Ni–Al–Pt samples, we found that strain relaxation rates are comparable to those observed in fine grained α-Al 2O 3 bulk ceramics, when bulk results are extrapolated to the lower temperatures examined here. When Hf was added to the Ni–Al–Pt alloy, creep rates in the thermally grown oxide were substantially slowed. Creep rates at stress levels of 100 MPa, or less, are proportional to σ n , with n ≤ 2, consistent with a diffusional creep mechanism.

Creep in protective α-Al2O3 thermally grown on β-NiAl

The authors report systematic measurements of creep relaxation in α-Al2O3, thermally grown in air on (100) single crystals of stoichiometric β-NiAl, at temperatures between 950 and 1100°C. Creep was monitored using time dependent in situ measurements of strain relaxation in the oxide following imposition of a stress resulting from a sudden temperature change. The in-plane elastic strain was obtained using a sin2ψ x-ray diffraction technique exploiting synchrotron radiation. The authors found that strain relaxation rates were comparable to those observed in fine grained α-Al2O3 ceramics when the latter results were extrapolated to the lower temperatures examined here. Creep rates at stress levels of 100MPa, or less, are proportional to σn, with n⩽2, consistent with a diffusional creep mechanism.

Evaluation of experimental stress–strain dependence in thermally cycled Al thin film on Si(100)

A new method is introduced for the evaluation of experimental stress–strain dependence in thermally cycled thin films. The method is demonstrated on the analysis of an Al thin film on a Si(100) substrate characterized using in situ high-temperature X-ray diffraction 25–450 °C. Diffraction data are used to evaluate in-plane elastic strain in the film as a function of thermal strain originating from the mismatch of thermal expansion coefficients (TECs) between the film and the substrate. The magnitude of the thermal strain is calculated from experimental TECs of the film and the substrate at every measurement temperature. By relating in-plane stresses to thermal strains, an experimental stress–strain dependence for the Al thin film is obtained. The proposed method allows one to identify elastic behavior and to quantify plastic strain in the film. Finally, advantages of the method are discussed in particular its independence from using TECs reported in the literature.

Mixed Mode (K<sub>I</sub>+K<sub>II</sub>) Stress Intensity Factor Measurement by Electronic Speckle Pattern Interferometry and Image Correlation

The surface displacement fields of a fatigue precracked compact tension sample under tensile load were registered by electronic speckle pattern interferometry and image correlation. The in-plane elastic strain fields calculated from the displacement data were used to obtain the first stress invariant, which for the case of plane stress is proportional to the real part of the first complex potential in Muskhelishvili's approach. Solutions for the stress fields around the crack tip, KI and KII were sought in the form of the Fourier series using Muskhelishvili's complex stress functions. The Fourier series coefficients were calculated from the displacement data using multiple point overdeterministic method (MPODM). The nominal and inferred KI values differ by around 10%; this is probably due in part to mixed mode (KII) loading introduced by some degree of misalignment during the experiment.

Measuring the interface stress: Silver/nickel interfaces

Interface stress is a surface thermodynamics quantity associated with the reversible work of elastically straining an internal solid interface. In a multilayered thin film, the combined effect of the interface stress of each interface results in an in-plane biaxial volume stress acting within the layers of the film that is inversely proportional to the bilayer thickness. We calculated the interface stress of an interface between {111} textured Ag and Ni on the basis of direct measurements of the dependence of the in-plane elastic strains on the bilayer thickness. The strains were obtained using transmission x-ray diffraction. Unlike previous studies of this type, we used freestanding films so that there was no need to correct for intrinsic stresses resulting from forces applied by the substrate that can lead to large uncertainties of the calculated interface stress value. Based on the lattice parameters of the bulk, pure elements, an interface stress of −2.02 ± 0.26 N/m was calculated using the x-ray diffraction results from films with bilayer thicknesses greater than 5 nm. This value is somewhat smaller than previous measurements obtained from as-deposited films supported by substrates. For smaller bilayer thicknesses the apparent interface stress becomes smaller in magnitude, possibly due to a loss of layering in the specimens.

Measurement of residual stresses in a multi‐layer explosive welded joint with successive milling technique

AbstractIn the multi‐layer welded joint of titanium‐tantalum (Ti‐5Ta/Ti‐5Ta/Ta/substrate of stainless steel (SUS304) the second layer of plate Ti‐5Ta is 4mm thick, and the third plate Ta is only 1 mm thick. It is almost impossible to measure the stresses near the weld with cutting strip technique. Using a successive milling technique the inplane elastic strain releases normal to the thickness direction are measured. With the finite element method (FEM) inherent strain distribution along thickness z‐direction is evaluated according to the elastic strain releases. Subsequently, assuming that the inherent strains (plastic strains resulting from the welding process) are the initial strains of the FEM analysis for the welded residual stresses, these are used further to evaluate the residual stress distributions along the thickness z‐direction in the multi‐layer explosive welding joint.

Epitaxial strain and the growth of Cu(001) on Fe(001).

In order to study the role of epitaxial strain in stabilizing a body-centered cubic (bcc) modification of Cu, we have made high-resolution, in situ measurements of the in-plane elastic film strain associated with epitaxial growth of Cu(001) on Fe(001). Using grazing-incidence x-ray scattering with synchrotron radiation, we observe in-plane elastic strains in the Cu as large as 7.6% occurring at a coverage of 2 equivalent monolayers. These tensile strains tetragonally distort the face-centered cubic (fcc) Cu lattice, resulting in a body-centered tetragonal structure. A true bcc structure is not observed. As the film grows thicker, the epitaxial strain decays in a continuous, monotonic manner resulting in a slightly strained fcc structure by 10 equivalent monolayers. The observed strain relaxation agrees with equilibrium theory, suggesting that the growth of bcc Cu is contingent upon kinetic barriers to misfit dislocation nucleation and/or movement.