Stress Relaxation Mechanism Research Articles

Viscoelastic Relaxation of Polymerized Ionic Liquid and Lithium Salt Mixtures: Effect of Salt Concentration

Polymerized ionic liquids (PILs) doped with lithium salts have recently attracted research interests as the polymer component in lithium-ion batteries because of their high ionic mobilities and lithium-ion transference numbers. To date, although the ion transport mechanism in lithium-doped PILs has been considerably studied, the role of lithium salts on the dynamics of PIL chains remains poorly understood. Herein, we examine the thermal and rheological behaviors of the mixture of poly(1-butyl-3-vinylimidazolium bis(trifluoromethanesulfonyl)imide (PC4-TFSI)/lithium TFSI (LiTFSI) in order to clarify the effect of the addition of LiTFSI. We show that the glass transition temperature Tg and the entanglement density decrease with the increase in LiTFSI concentration . These results indicate that LiTFSI acts as a plasticizer for PC4-TFSI. Comparison of the frequency dependence of the complex modulus under the iso-frictional condition reveals that the addition of LiTFSI does not modify the stress relaxation mechanism of PC4-TFSI, including its characteristic time scale. This suggests that the doped LiTFSI, component that can be carrier ions, is not so firmly bound to the polymer chain as it modifies the chain dynamics. In addition, a broadening of the loss modulus spectrum in the glass region occurs at high . This change in the spectrum can be caused by the responses of free TFSI and/or coordination complexes of Li and TFSI. Our detailed rheological analysis can extract the information of the dynamical features for PIL/salt mixtures and may provide helpful knowledge for the control of mechanical properties and ion mobilities in PILs.

Relaxation Mechanisms and Strain-Controlled Oxygen Vacancies in Epitaxial SrMnO3 Films.

SrMnO3 has a rich epitaxial strain-dependent ferroic phase diagram, in which a variety of magnetic orderings, even ferroelectricity, and thus multiferroicity, are accessible by gradually modifying the strain. Different relaxation processes, though, including the presence of strain-induced oxygen vacancies, can severely curtail the possibility of stabilizing these ferroic phases. Here, we report on a thorough investigation of the strain relaxation mechanisms in SrMnO3 films grown on several substrates imposing varying degrees of strain from slightly compressive (−0.39%) to largely tensile ≈+3.8%. First, we determine the strain dependency of the critical thickness (tc) below which pseudomorphic growth is obtained. Second, the mechanisms of stress relaxation are elucidated, revealing that misfit dislocations and stacking faults accommodate the strain above tc. Yet, even for films thicker than tc, the atomic monolayers below tc are proved to remain fully coherent. Therefore, multiferroicity may also emerge even in films that appear to be partially relaxed. Last, we demonstrate that fully coherent films with the same thickness present a lower oxygen content for increasing tensile mismatch with the substrate. This behavior proves the coupling between the formation of oxygen vacancies and epitaxial strain, in agreement with first-principles calculations, enabling the strain control of the Mn3+/Mn4+ ratio, which strongly affects the magnetic and electrical properties. However, the presence of oxygen vacancies/Mn3+ cations reduces the effective epitaxial strain in the SrMnO3 films and, thus, the accessibility to the strain-induced multiferroic phase.

Length-scale-dependent stress relief mechanisms in indium at high homologous temperatures.

Nanoindentation and electron microscopy have been used to examine the length-scale-dependent stress relaxation mechanisms in well-annealed, high-purity indium at a homologous temperature of 0.69. The experimental methods, analysis, and observations serve as a stepping stone in identifying the stress relaxation mechanisms enabling the formation and growth of metallic dendrites originating at the buried interface between a metallic anode and a solid electrolyte separator. Indium’s load–displacement data are found to be very similar to that of high-purity lithium. Residual hardness impressions show two distinct surface morphologies. Based on these morphologies, the measured hardness, and the estimated pile-up volume, it is proposed that residual impressions exhibiting significant pile-up are the result of deformation dominated by interface diffusion. Alternatively, impressions with no significant pile-up are taken to be the result of shear-driven dislocation glide. An analytical model is presented to rationalize the pile-up profile using interface diffusion.

Study on the relaxation mechanism of residual stress in SiCp/6061Al composites based on the surface modification of reinforcement

The effect of reinforcement surface modification on the residual stress (RS) in 35vo l%SiCp/6061Al composites was studied, and the experimental conclusions were verified by finite element analysis. The results show that after the SiC particles were modified by pickling, ultrasonic stirring and high-temperature oxidation (1100 ℃/6 h), the composite has the lowest RS, which was only 1.1 MPa. Microstructure and phase composition of 35vo l%SiCp/6061Al composites have been examined by Scanning Electron Microscope (SEM) and X-Ray Diffraction (XRD). It was found that the reinforcement surface modification was beneficial to promote the improvement of interface bonding state, and the diffraction peaks of Si element have been significantly enhanced. Additionally, the formed Al-Si-SiC interphase has a higher interface adhesion work, which effectively reduced the concentration degree of RS. An interface-phase model based on the surface morphology of real SiC particles was established. The simulation results show that the RS was mainly concentrated in the sharp corners of reinforcement, and the stress level is relatively high. When the sharp corners were eliminated, the stress level gradually decreases. When the Al-Si-SiC interphase was formed, the stress level in SiCp/6061Al composites decreases significantly. The results of finite element simulation and experimental measurement were relatively consistent.

Understanding and eliminating thermo-mechanically induced radial cracks in fully metallized through-glass via (TGV) substrates

This work aims to understand and eliminate the formation of thermo-mechanically induced radial cracks in copper (Cu) metallized through-glass via (TGV) substrates made of Corning® high purity fused silica (HPFS® fused silica), after subjection to 420 °C annealing treatment. Radial cracks were found to be formed in Cu TGV substrate during the heating step of annealing treatment process, caused by high stress buildup resulting from the large mismatch in the coefficient of thermal expansion (CTE) between the HPFS® fused silica substrate and the Cu metallization. From analytical studies, high tensile circumferential stresses were found to be the main stress component that is responsible for the formation of radial cracks during heating. From experimental studies, it was found that radial crack formation was exponentially dependent on the applied heating rate, and that faster heating rate increased the probability for their formation. However, a crack-free metallized TGV substrate was achieved when heating rates ≤6.5 °C/min was applied, thus, eliminating radial crack formation. Radial crack elimination was attributed to the significant activation of stress relaxation mechanisms in the Cu. This was confirmed by the measurement of an inverse dependence of Cu protrusion with the applied heating rate. Additionally, the Cu protrusion data confirms that the leading stress relaxation mechanisms in the Cu TGV were grain boundary sliding (GBS), plastic deformation and Coble diffusional creep.

Characterization of the strain-rate–dependent mechanical response of single cell–cell junctions

Cell-cell adhesions are often subjected to mechanical strains of different rates and magnitudes in normal tissue function. However, the rate-dependent mechanical behavior of individual cell-cell adhesions has not been fully characterized due to the lack of proper experimental techniques and therefore remains elusive. This is particularly true under large strain conditions, which may potentially lead to cell-cell adhesion dissociation and ultimately tissue fracture. In this study, we designed and fabricated a single-cell adhesion micro tensile tester (SCAµTT) using two-photon polymerization and performed displacement-controlled tensile tests of individual pairs of adherent epithelial cells with a mature cell-cell adhesion. Straining the cytoskeleton-cell adhesion complex system reveals a passive shear-thinning viscoelastic behavior and a rate-dependent active stress-relaxation mechanism mediated by cytoskeleton growth. Under low strain rates, stress relaxation mediated by the cytoskeleton can effectively relax junctional stress buildup and prevent adhesion bond rupture. Cadherin bond dissociation also exhibits rate-dependent strengthening, in which increased strain rate results in elevated stress levels at which cadherin bonds fail. This bond dissociation becomes a synchronized catastrophic event that leads to junction fracture at high strain rates. Even at high strain rates, a single cell-cell junction displays a remarkable tensile strength to sustain a strain as much as 200% before complete junction rupture. Collectively, the platform and the biophysical understandings in this study are expected to build a foundation for the mechanistic investigation of the adaptive viscoelasticity of the cell-cell junction.

Effect of TM (TM=Fe, Mn, Cr) alloying on the high temperature properties and strengthening mechanism of Cf/Al composites

In this paper, the Cf/pure Al composite and the Cf/Al–Fe–Mg–Si composite were prepared by pressure infiltration method, and the microstructure and high temperature mechanical properties of these two kinds of composites were studied. The main interface phase of the Cf/pure Al composite is Al4C3, while in the Cf/Al–Fe–Mg–Si composite, a new type of Fe-rich phase containing Al, Fe, Mn, Cr, Si and other elements with a body-centered cubic structure calibrated by TEM diffraction pattens is discovered, whose lattice constant is 1.39 nm. Results of high temperature bending tests and researches of microstructure demonstrated that, the bending strength of the Cf/Al–Fe–Mg–Si composite decreased first at room temperature to 200 °C, due to re-dissolution of nano-precipitates. Afterwards, the bending strength increased under the combined action of the stress relaxation mechanism, the crack deflection mechanism and the high temperature strengthening mechanism of the Fe-rich phase at a temperature range in 200 °C–400 °C, and reached about 880 MPa at 400 °C, which demonstrated better high temperature mechanical properties than that of the Cf/pure Al composite. The results indicated that the formation of high-temperature stable precipitates through TM alloying can effectively increase the ultimate service temperature of Cf/Al composites. The work in this paper is of great significance in the design and preparation of Cf/Al composites with excellent high-temperature properties.

Heat dissipation and acoustic emission features of titanium alloys in cyclic deformation mode

The present work unveils the features of heat dissipation and acoustic emission accompanying the fatigue crack growth in a titanium alloy (Ti-0.8Al-0.8Mn and Ti Grade 2) using the compact tension and Charpy V-notch specimens. The quantitative measurements of the heat dissipation rate were carried out by an original heat flux sensor. The obtained results reveal that there exist two appreciably different stages of the crack propagation within the stable Paris regime. Relationships between the crack growth rate and the heat dissipation rate are proposed for both stages. The application of the non-supervised clustering algorithm to the continuously recorded acoustic emission signal helped to identify two dominant mechanisms of stress relaxation that occur ahead of the crack tip—mechanical twinning and crack opening. The correlation between the acoustic emission energy and heat dissipation was found to be a harbinger of the approaching transition from stable to unstable crack growth.

Misfit Stresses Due to a Cylindrical Dilatational Inclusion of Annular-Sector Cross-Section in an Infinite Elastic Medium

An elastic model for a cylindrical dilatational inclusion of annular-sector cross-section in an infinite elastic medium is considered. The stress fields are found in a closed analytical form and are illustrated by stress maps. Specific features in the stress distribution are revealed and discussed in detail. It is shown that the stress magnitude can be so high that various mechanisms of stress relaxation can be activated.

Coupled Large-Strain Mechanochemical Theory for Solid-State Reaction With Application to Oxidation

Oxidation is still perceived as a significant challenge in various industrial applications, e.g., pressurized water reactors and gas-turbines. One of the hurdles in understanding oxidation is its coupled multi-physics nature, i.e., the coupling between mechanics, chemical reaction, change in the microstructure, and diffusion. Here, a general large-strain mechano-chemical theory is developed to model the anisotropic reaction/compositional strain in the solid-state chemical reaction. The anisotropic strain leads to a unique stress relaxation mechanism, which is in agreement with existing experimental studies. This novel stress-relaxation is achieved by introducing a kinetic relationship between deviatoric compositional and reaction deformation rate and the deviatoric Cauchy stress. Also, a new chemical potential, including the deviatoric stress, is derived. The new model shows that mechanical stress alters the chemical equilibrium constant through reaction-induced deviatoric stress. Finally, the developed mathematical framework is used to study the aluminum's oxidation for model verification.

Techniques to characterize dynamics in biomaterials microenvironments: XPCS and microrheology of alginate/PEO-PPO-PEO hydrogels.

Many recent studies have highlighted the timescale for stress relaxation of biomaterials on the microscale as an important factor in regulating a number of cell-material interactions, including cell spreading, proliferation, and differentiation. Relevant timescales on the order of 0.1-100 s have been suggested by several studies. While such timescales are accessible through conventional mechanical rheology, several biomaterials have heterogeneous structures, and stress relaxation mechanisms of the bulk material may not correspond to that experienced in the cellular microenvironment. Here we employ X-ray photon correlation spectroscopy (XPCS) to explore the temperature-dependent dynamics, relaxation time, and microrheology of multicomponent hydrogels comprising of commercial poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO) triblock copolymer F127 and alginate. Previous studies on this system have shown thermoreversible behavior in the bulk oscillatory shear rheology. At physiological temperatures, bulk rheology of these samples shows behavior characteristic of a soft solid, with G' > G'' and no crossover between G' and G'' over the measurable frequency range, indicating a relaxation time >125 s. By contrast, XPCS-based microrheology shows viscoelastic behavior at low frequencies, and XPCS-derived correlation functions show relaxation times ranging from 10-45 s on smaller length scales. Thus, we are able to use XPCS to effectively probe the viscoelasticity and relaxation behavior within the material microenvironments.

Residual Stress Relaxation of DRWDs in OSDs under Constant/Variable Amplitude Cyclic Loading

An orthotropic steel deck (OSD) has a complicated structure, and its fatigue life is mainly determined by various welding details. Fatigue assessment of deck-to-rib welding details (DRWDs) under long-term train loads is an important concern for engineers. Properly assessing the initial residual stress and the mechanism of stress relaxation in DRWDs under long-term external loading is a prerequisite for predicting the fatigue damage and service life of OSDs. In this paper, a finite element analysis method is proposed to calculate the residual stress relaxation in DRWDs of OSDs under constant/variable amplitude cyclic loading. First, experiments on full-size OSD specimens were carried out using the hole drilling strain-gauge method, and the multi-axial distribution characteristics of residual stress on the sub-surface of the deck were obtained. On this basis, a refined residual stress analysis model of DRWDs using thermal-structural sequence coupling analysis and life and death unit technology is established, and the accuracy of the model is verified by the test data. Second, a coupling stress analysis model that considers the welding residual stress and mechanical stress using cyclic plastic constitutive model is established. The combined influence of number of cycles, stress amplitude, and stress ratio on multi-axial residual stress relaxation effect under constant/variable amplitude cyclic loading is investigated. Finally, a release formula of welding residual stress relaxation coefficient is proposed based on the external loading stress amplitude, stress ratio, and material yield stress. The results show that (1) with the increase in the number of loading cycles, the stress decreases until it is stabilized, while the global distribution of welding residual stress remains unchanged. Most of the welding residual stress release (about 95%) occurs in the first cycle; (2) the residual stress relaxation decreases with the increase in stress amplitude and increases linearly with the stress ratio; (3) the residual stress release is controlled by the maximum amplitude stress in the variable amplitude cyclic loading. After the residual stress is released, the stress will not continue to be released if the DRWDs have the same or smaller amplitude loading.

Stress relaxation behaviors and mechanical properties of precipitation strengthening copper alloys

In order to measure cantilever bending stress of elastic alloys during stress relaxation experiment, a homo-made apparatus has been developed. The mechanical properties and stress relaxation resistances of three high strength copper alloys have been investigated. Considering different experimental conditions, the Cu-Ni-Sn alloys exhibit the optimum stress relaxation resistance. The mechanisms of stress relaxation and precipitation strengthening have been discussed. The hardness is recommended to be a critical parameter which can be used to evaluate the stress relaxation resistance simply. Because the interactions between precipitation particles and dislocations which influence the hardness also affect the dynamic recovery of mobile dislocations during stress relaxation. Finally, two effective methods have been proposed to slow down the stress relaxation in the copper alloys.

Nonlinear dynamics and stages of damage of Ti6Al4V and Ti45Nb titanium alloys in very high cycle fatigue

The paper presents an experimental methodology aimed at evaluating a very-high cycle resource for aviation titanium alloys Vt-6 (Ti6Al4V) and Ti45Nb for medical applications with different microstructures (large-crystal and submicrocrystalline ones). The submicrocrystalline (SMC) state was obtained by an intensive plastic deformation realized in two ways: the three-dimensional forging for Ti45Nb and radial-shear rolling for Ti6Al4V. The experimental program tests high-cycle and very-high-cycle loading (number of cycles 107-109) realized using the in situ determination method of the accumulation of the irreversible fatigue damage by analyzing nonlinear forms of feedback in a closed system ultrasonic fatigue setup. This makes it possible to establish the connection of the microscopic fatigue mechanisms with the model views and consider the stages of the damage development based on the nonlinear kinetics of the defect accumulation under cyclic loading in high- and gigacycle fatigue modes. We established various relations between changes in the amplitude of the second harmonic of vibrations of the free end of the samples with different internal structures, which are associated with the mechanisms of stress relaxation and damage accumulation. The grain size reduction in Ti45Nb alloy by the three-dimensional forging improved the fatigue properties by 1.3-1.5 times, whereas for VT-6 alloy, the radial-shear rolling method could not increase the fatigue properties in the very high cycle fatigue range, which may be caused by the presence of large residual internal stresses. Based on the scale parameters obtained earlier from the fracture surface morphology and the relations established in this work, the kinetic equations for the origin and growth of fatigue cracks in the gigacycle loading range will be constructed. This equation, based on the empirical power parameters related to the structure of the material, will allow us to determine the number of cycles for the origin of an internal crack and its growth to the surface.

Time-dependent uniaxial behavior of rolled magnesium alloy AZ31B at 393 K and room temperature

To address the time-dependent properties of rolled AZ31B alloy, we conducted typical tests of the rate jump, creep, and stress relaxation at room temperature and 393 K. In the rate jump tests, the tensile curve exhibited a strong dependence on the strain rate, whereas compression was totally insensitive to the stress rate at both temperatures. For the creep and stress relaxation test, we observed creep strain and decay stress in the compression, which was weaker than the tensile curve. The plastic viscosity increased at 393 K because the dislocation motion was thermally activated. We then applied thermal activation theory for the repeated stress relaxation tests. The activation volume implies that cross-slip and dislocation nucleation are the operating mechanisms for creep and stress relaxation.

Suppression of Dendritic Growth on Li Negative Electrode for All-Solid-State Rechargeable Battery

Introduction All-Solid-State Lithium Battery (ASSLiB) is expected as one of the next-generation batteries to achieve high power and energy density and high safety. Applying the Li metal negative electrode with a high mass capacity and low standard electrode potential to the ASSB system is desirable; however, there is a critical problem of the Li dendritic growth which induces internal short-circuits. The Li dendritic growth is known to proceed even in the voids and cracks of solid electrolytes (SEs). Moreover, because the Li metal electrode is sandwiched between a current collector and SE, high mechanical stress due to volume expansion is applied to the electrode/SE interface during charging. For conventional planer current collectors, Li metal easily penetrates into SE through voids for the relaxation of mechanical stress (Fig. 1a). In contrast, for porous current collectors, the mechanical stress will be reduced because the deposited Li-metal can fill pores. In this study, we investigated the usefulness of an Au-coated membrane filter with micro-size pores as a porous current collector for suppressing the Li dendritic growth (Fig. 1b).1 Experimental A porous current collector was prepared by cutting a commercial membrane filter (Advantec, 16080004) with 8 µm-diameter pores and 7 µm-thickness into a circular shape. Gold or nickel was coated with a sputter coater to give electric conductivity. The gold-coated porous current collector is named as Au-MF, and nickel-coated one is named as Ni-MF.A laboratory-made cell was assembled in an Ar-filled grove box. Li3PS4-glass electrolyte as SE was prepared by mechanical-milling according to ref. 1, and pelletized in a polycarbonate tube. Gold was coated on the negative electrode side of the SE pellet. The SE was put between the porous current collector and Li-In alloy as the counter electrode, followed by pressing to obtain an ASSB cell.All charge/discharge measurements were conducted by galvanostatic technique at 30 ℃. The charge/discharge current density and deposition capacity for evaluating coulombic efficiency were 0.1 mA cm-2 and 0.1 mAh cm-2, respectively. Li deposition behavior in the porous current collectors was investigated by scanning electron microscope (SEM). Results and Discussion Fig. 2(a) shows an SEM image of the Au-MF as prepared. Circular pores with 8 µm in diameter are vertically and sparsely located. After charging at 0.010 mA cm-2 for 10 h, the surface morphology of Au-MF changed like moss (Fig. 2(b)), which means Li was deposited on the surface of Au-MF. When the Ni-MF, in which Ni layer does not form any alloys with Li, was used to charge at the current density of 0.010 mA cm-2 for 10 h, Li deposits were observed only in the pores of Ni-MF and surface morphology did not change (Fig. 2(c)). These results suggest that the Li deposition on Au-MF is due to the Li diffusion in the Au layer on the MF, and the mechanical stress on the Au-MF/SE interface is relaxed by the Li deposition in pores.Fig. 3 shows Coulombic efficiencies of Au-MF, Ni-MF, planer Ni foil and Au-coated Ni-foil as a function of cycle number. The Coulombic efficiency reached to the maximum at the 4th cycle in each case. The Au-MF showed the highest coulombic efficiency of 82 %, while other electrodes showed lower than 80 % values. The charge/discharge curve for the Ni foil and Ni-MF showed the short-circuit at the 8th cycle; however, the Au-MF and the Au-coated Ni foil did not make a short-circuit for 20 cycles. These results indicate Au-MF is superior in coulombic efficiency and the suppression of Li dendritic growth to the other current collectors.We assume the synergetic effect of Au-coating and pores on the current collector. During charging, the electrochemically prepared Li metal diffuses to the pores through the Au layer and fills the pores. This effective filling of the pores with Li metal is essential for suppressing the Li dendritic growth. The Coulombic efficiency depends on the amount of the dead Li, which is formed by interruption of conduction during the dissolution of lithium deposited in dendrite form. Preventing the dendritic growth of Li metal also leads to the increase in the Coulombic efficiency.In conclusion, the Au-coated porous current collector can effectively work for inhibiting the Li dendritic growth. Acknowledgement This work was partially supported by JST ALCA-SPRING. References Shinzo et. al., ACS Appl. Mater. Interfaces (2020), 12, 20, 22798 Figure 1

Influence of Interface Proximity on Precipitation Thermodynamics

The formation of coherent precipitates is often accompanied by large elastic mismatch stresses, which suppress phase separation. We discuss the presence of interfaces as a mechanism for stress relaxation, which can lead to preferred zones of precipitation. In particular, we discuss the proximity of free surfaces and shear-coupled grain boundaries, for which we can obtain a substantial local energy reduction and predict the influence on the local precipitation thermodynamics. The latter case is accompanied by morphological changes of the grain boundary, which are less suitable for large-scale descriptions. For that purpose, we develop an effective description through an elastic softening inside the grain boundary and map the microscopic grain boundary relaxation to a mesoscopic elastic and phase field model, which also allows generalizing the description to multi-phase situations.

Experimental investigations on early-age tensile creep of internally cured high strength concrete under different initial stress/strength ratios

High strength concrete (HSC) with high strength and low permeability has been widely utilized in the reinforced concrete structures recently. However, the water-to-cement ratio of HSC is low, marked self-desiccation will occur, and autogenous shrinkage is induced. The autogenous shrinkage causes tensile stress in the restrained concrete, and the tensile creep (TC) counteracts the autogenous shrinkage as a stress relaxation mechanism. Although the TC of internally cured HSC (ICHSC) with super absorbent polymers (SAPs) under fully restrained conditions has been studied, research on the early-age TC of ICHSC under constant tensile loading remains insufficient. Therefore, the effect of initial stress/strength (s/s) ratio (ranged from 20% to 35%, 50%, and 65%) on the TC behavior of ICHSC at early age was experimentally investigated by Temperature Stress Test Machine in this research. Experimental results and corresponding analysis showed that: (1) the early-age basic TC, basic TC coefficient, and specific basic TC of ICHSC at 7 days of loading was 37, 66, 95, and 148 με, 2.26, 2.31, 2.30, and 2.76, and 52, 53, 53, and 72 με/MPa, respectively, and increased as the initial s/s ratio increased; (2) the early-age basic TC rate of ICHSC at 1 day of loading was 0.57, 1.01, 1.70, and 3.04 με/h and increased as the initial s/s ratio increased; (3) the nonlinear basic TC of ICHSC occurred when the initial s/s ratio ranged from 50% to 65%; (4) a prediction model for the TC of ICHSC considering initial s/s ratios was proposed based on Østergaard model.

Strain, stress and stress relaxation in oxidized ZrCuAl-based bulk metallic glass

Surface engineering of Zr51.3Al8.5Cu31.3Ni4Ti4.9 bulk metallic glass (BMG) by gaseous oxidizing below the glass-transition temperature is investigated as a means to introduce compressive residual stress in the surface region. The ZrCuAl-based BMG was exposed to an extremely low oxygen partial pressure of 10−41 bar at 600 K for 60 h. The oxidizing treatment led to the formation of an internal oxidation zone, consisting of finely dispersed nano-crystalline cubic ZrO2 (c-ZrO2), metallic regions inclined with the surface and Cu-hillocks at the surface. The stresses introduced by the volume expansion associated with oxidation were evaluated from i) the lattice strains within c-ZrO2, as determined with an X-ray diffraction (XRD) based method, and ii) strain-relaxation as a response to annular focused ion beam (FIB) milling, as monitored with digital image correlation (DIC). XRD analysis yielded -1.5 GPa (compressive stress) in the nano-crystalline c-ZrO2, while the strain relaxation monitored with FIB-DIC analysis indicated compressive residual stresses of −1.4 GPa in the internal oxidation zone. The strains and stresses determined with the independent measurement methods are discussed. The quantitative macro-strains are discussed in relation to the microstructural features and stress relaxation mechanisms during evolution of the internal oxidation zone.

Concepts of Stress Relaxation and Heterophase Structures in Ferroelectric Solid Solutions of the Perovskite Type

Examples are given of the relaxation of internal mechanical stresses during the formation of heterophase structures in ferroelectric solid solutions 0.86BaTiO3–(0.14 − x)BaZrO3−xCaTiO3 and ((Bi0.5Na0.5)0.94Ba0.06)1−y(K0.5Nd0.5)yTiO3 of the perovskite type. The conditions for elastic matching of monodomain and polydomain ferroelectric phases at x = const or y = const are analyzed. The volume concentrations of these phases are determined under conditions of complete stress relaxation.