Local Strain Heterogeneities Research Articles

Elastic and magnetoelastic relaxation behaviour of multiferroic (ferromagnetic + ferroelectric + ferroelastic) Pb(Fe0.5Nb0.5)O3 perovskite

Resonant Ultrasound Spectroscopy has been used to characterize elastic and anelastic anomalies in a polycrystalline sample of multiferroic Pb(Fe0.5Nb0.5)O3 (PFN). Elastic softening begins at ~550 K, which is close to the Burns temperature marking the development of dynamical polar nanoregions. A small increase in acoustic loss at ~425 K coincides with the value of T* reported for polar nanoregions starting to acquire a static or quasi-static component. Softening of the shear modulus by ~30–35% through ~395–320 K, together with a peak in acoustic loss, is due to classical strain/order parameter coupling through the cubic → tetragonal → monoclinic transition sequence of ferroelectric/ferroelastic transitions. A plateau of high acoustic loss below ~320 K is due to the mobility under stress of a ferroelastic microstructure but, instead of the typical effects of freezing of twin wall motion at some low temperature, there is a steady decrease in loss and increase in elastic stiffness below ~85 K. This is attributed to freezing of a succession of strain-coupled defects with a range of relaxation times and is consistent with a report in the literature that PFN develops a tweed microstructure over a wide temperature interval. No overt anomaly was observed near the expected Néel point, ~145 K, consistent with weak/absent spin/lattice coupling but heat capacity measurements showed that the antiferromagnetic transition is actually smeared out or suppressed. Instead, the sample is weakly ferromagnetic up to ~560 K, though it has not been possible to exclude definitively the possibility that this could be due to some magnetic impurity. Overall, evidence from the RUS data is of a permeating influence of static and dynamic strain relaxation effects which are attributed to local strain heterogeneity on a mesoscopic length scale. These, in turn, must have a role in determining the magnetic properties and multiferroic character of PFN.

Deformation-induced spatiotemporal fluctuation, evolution and localization of strain fields in a bulk metallic glass

Deformation behavior and local strain evolutions upon loading and unloading of a bulk metallic glass (BMG) were systematically investigated by in situ digital image correlation (DIC). Distinct fluctuations and irreversible local strains were observed before the onset of macroscopic yielding. Statistical analysis shows that these fluctuations might be related to intrinsic structural heterogeneities, and that the evolution history and characteristics of local strain fields play an important role in the subsequent initiation of shear bands. Effects of sample size, pre-strain, and loading conditions were systematically analyzed in terms of the probability distributions of the resulting local strain fields. It is found that a higher degree of local shear strain heterogeneity corresponds to a more ductile stress–strain curve. Implications of these findings are discussed for the design of new materials.

Effect of the Microstructure on the Fatigue Strength of a TiAl Intermetallic Alloy Produced by Additive Manufacturing

ABSTRACTIn this work we examine a Ti-48Al-2Cr-2Nb alloy obtained with an additive manufacturing technique by Electron Beam Melting (EBM) by conducting monotonic and cyclic loading experiments both on tension and compression samples for investigating the influence of the microstructure in strain accumulation process by fatigue loading. The residual strain maps corresponding to different applied stress levels, number of cycles and microstructures are obtained through the use of high-resolution Digital Image Correlation (DIC). The strain maps were overlaid with the images of the microstructure and detailed analyses were performed to investigate the features of the microstructure where high local strain heterogeneities arise. Such experiments, conducted ex-situ at room temperature, allow to characterize the effect of different microstructures on the strain accumulation process, and to clearly identify the role of the microstructural features of this TiAl intermetallic alloy on the fatigue initiation process.

Strain heterogeneity and magnetoelastic behaviour of nanocrystalline half-doped La, Ca manganite, La0.5Ca0.5MnO3

Elastic and anelastic properties of La0.5Ca0.5MnO3 determined by resonant ultrasound spectroscopy in the frequency range ∼100–1200 kHz have been used to evaluate the role of grain size in determining the competition between ferromagnetism and Jahn–Teller/charge order of manganites which show colossal magneto resistance. At crystallite sizes of ∼75 and ∼135 nm the dominant feature is softening of the shear modulus as the charge order transition point, Tco (∼225 K), is approached from above and below, matching the form of softening seen previously in samples with ‘bulk’ properties. This is consistent with a bilinear dominant strain/order parameter coupling, which occurs between the tetragonal shear strain and the Jahn–Teller order parameter. At crystallite sizes of ∼34 and ∼42 nm the charge ordered phase is suppressed but there is still softening of the shear modulus, with a minimum near Tco. This indicates that some degree of pseudoproper ferroelastic behaviour is retained. The primary cause of the suppresion of the charge ordered structure in nanocrystalline samples is therefore considered to be due to suppression of macroscopic strain, even though MnO6 octahedra must develop some Jahn–Teller distortions on a local length scale. This mechanism for stabilizing ferromagnetism differs from imposition of either an external magnetic field or a homogeneous external strain field (from a substrate), and is likely to lead both to local strain heterogeneity within the nanocrystallites and to different tilting of octahedra within the orthorhombic structure. An additional first order transition occurs near 40 K in all samples and appears to involve some very small strain contrast between two ferromagnetic structures.

Strain Accumulation in TiAl Intermetallics via High-resolution Digital Image Correlation (DIC)

Novel manufacturing process are more and more used to produce advanced structural materials such as the gamma titanium aluminide alloys (γ-TiAl). In this work we examine a Ti-48Al-2Cr-2Nb alloy obtained with an additive manufacturing technique by Electron Beam Melting (EBM) by conducting monotonic and cyclic loading experiments both on tension and compression samples to investigate the influence of the microstructure in strain accumulation process by fatigue loading. The residual strain maps corresponding to different applied stress levels, number of cycles and microstructures are obtained through the use of high- resolution Digital Image Correlation (DIC). The strain maps were overlaid with the images of the microstructure and detailed analyses were performed to investigate the features of the microstructure where high local strain heterogeneities arise. Such experiments, conducted ex-situ at room temperature, allow to characterize the effect of different microstructures on the strain accumulation process, providing additional information into the effect of the lamellar and equiaxed grains and also to capture the evolution of the local deformation process for TiAl. The measure of the residual strains provides further information on the role of the intermetallic phases on the fatigue behavior of γ-TiAl alloys. The comparison with the strain accumulation in fully lamellar microstructure with larger grain size permits to highlight the influence of the position of grain boundaries and the orientation of the lamellae for the onset of fatigue cracking. The analysis and comparison of the strain maps provide information for the selection of the microstructural parameters during material design (i.e. grain size and lamellar grains volume fraction).

Local structural disorder and its influence on the average global structure and polar properties in Na0.5Bi0.5TiO3

Na${}_{0.5}$Bi${}_{0.5}$TiO${}_{3}$ (NBT) and its derivatives have prompted a great surge in interest owing to their potential as lead-free piezoelectrics. In spite of five decades since its discovery, there is still a lack of clarity on crucial issues such as the origin of significant dielectric relaxation at room temperature, structural factors influencing its depoling, and the status of the recently proposed monoclinic ($Cc$) structure vis-\`a-vis the nanosized structural heterogeneities. In this work, these issues are resolved by comparative analysis of local and global structures on poled and unpoled NBT specimens using electron, x-ray, and neutron diffraction in conjunction with first-principles calculation, dielectric, ferroelectric, and piezoelectric measurements. The reported global monoclinic ($Cc$) distortion is shown not to correspond to the thermodynamic equilibrium state at room temperature. The global monocliniclike appearance rather owes its origin to the presence of local structural and strain heterogeneities. Poling removes the structural inhomogeneities and establishes a long-range rhombohedral distortion. In the process the system gets irreversibly transformed from a nonergodic relaxor to a normal ferroelectric state. The thermal depoling is shown to be associated with the onset of incompatible in-phase tilted octahedral regions in the field-stabilized long range rhombohedral distortion.

Analysis of Fatigue Damage Accumulation in TiAl Intermetallics

In this work, a Ti-48Al-2Cr-2Nb alloy obtained with a additive manufacturing technique by electron beam melting (EBM) has been examined by conducting high cycle fatigue tests both with plain specimens and with specimens with artificially introduced defects with the objective of studying the growth behavior of small cracks. A consistent model for predicting the fatigue endurance strength of specimens with artificial defects is proposed, based on the Kitagawa diagram and taking into account of the presence of inherent microstructural features of the studied intermetallic alloy. Thus, the origin of fatigue failures due to intermetallic phases and orientation of lamellar colonies was investigated by means of micromechanical analysis through the use of high-resolution Digital Image Correlation (DIC). The local strain heterogeneities were measured out of the load frame by means of an optical microscope at high magnifications. The strain maps were then overlaid with the images of the microstructure and detailed analyses were performed to investigate the features of the microstructure where high local strain heterogeneities arise. High local residual plastic strains were measured inside lamellar colonies, which are detected as the precursor to fatigue crack initiation. The measure of the residual strains also provides further information on the role of the intermetallic phases on the fatigue behaviour of γ-TiAl alloys.

In-Situ Mechanical Testing for Characterizing Strain Localization During Deformation at Elevated Temperatures

An experimental methodology has been developed to characterize local strain heterogeneities in alloys via in-situ scanning electron microscope (SEM) based mechanical testing. Quantitative measurements of local strains as a function of grain orientation, morphology and neighborhood are crucial for mechanistic understanding and validation of crystal plasticity models. This study focuses on the technical challenges associated with performing creep tests at elevated temperatures ≤700°C in an SEM. Samples of nickel-based superalloy Rene 104 were used for this study, but the technique is applicable to testing of any metal samples at elevated temperature. Electron beam lithography was employed to produce a suitable surface speckle pattern of hafnium oxide to facilitate full field displacement measure- ments using a commercial software package. The speckle pattern proved to have good thermal stability and provided excellent contrast for image acquisition using secondary electron imaging at elevated temperature. The speckle pattern and microscope magnification were optimized to obtain the resolution necessary to discern strain localizations within grain interiors and along grain boundaries. Minimum strain resolution due to SEM image distortions was determined prior to tensile testing, and image integration methods were utilized to minimize imaging artifacts. Limitations due to the present specimen heating method and potential solutions to these limitations are also addressed.

Localized deformation as a key precursor to initiation of intergranular stress corrosion cracking of austenitic stainless steels employed in nuclear power plants

Cold-work has been associated with the occurrence of intergranular cracking of stainless steels employed in light water reactors. This study examined the deformation behavior of AISI 304, AISI 347 and a higher stacking fault energy model alloy subjected to bulk cold-work and (for 347) surface deformation. Deformation microstructures of the materials were examined and correlated with their particular mechanical response under different conditions of temperature, strain rate and degree of prior cold-work. Select slow-strain rate tensile tests in autoclaves enabled the role of local strain heterogeneity in crack initiation in pressurized water reactor environments to be considered. The high stacking fault energy material exhibited uniform strain hardening, even at sub-zero temperatures, while the commercial stainless steels showed significant heterogeneity in their strain response. Surface treatments introduced local cold-work, which had a clear effect on the surface roughness and hardness, and on near-surface residual stress profiles. Autoclave tests led to transgranular surface cracking for a circumferentially ground surface, and intergranular crack initiation for a polished surface.

Measurement of local strain heterogeneities in superelastic shape memory alloys by digital image correlation

This work is focused on the displacement and strain fields measurement using the Digital Image Correlation (DIC) technique on a superelastic Shape Memory Alloy (SMA) sample submitted to uniaxial tension. The local strain heterogeneities are estimated in a CuAlBe multicrystal with one grain in the thickness and millimetric grain size. Crystallographic orientation of each grain is measured by EBSD technique. Several tests are carried out on the same specimen, in front of a long distance microscope with or without speckle pattern, and at two different magnifications.Evolutions of the martensitic transformation are investigated and analysed in terms of the strain heterogeneities. In copper SMA, the important anisotropy of the elastic moduli tensor involves high intergranular elastic strain heterogeneities. Martensite variants induce steps on the specimen surface. However, the strain fields were measured for greater load levels, when the material runs through the phase transformation. These steps interfere with the speckle patterns and may perturb the correlation process. The challenge was also to apply very fine speckle to analyze the deformation in grains. The study shows that the transformation and strain localizations mainly occur in bands involving the well crystallographic oriented grains with respect to the load direction.

Twin Nucleation by Slip Transfer across Grain Boundaries in Commercial Purity Titanium

The role of strain transfer in the activation of deformation twinning at grain boundaries has been characterized in commercially pure titanium deformed in bending. Two different orientations of a textured polycrystal were deformed in bending and were analyzed using electron backscattered diffraction (EBSD) to determine the active slip and twinning systems in the surface tensile region. Prismatic slip and $$ \left\{ {10\bar{1}2} \right\}\left\langle {\bar{1}011} \right\rangle $$ twinning were the most widely observed deformation modes in both orientations. Nonprismatic slip systems were also activated, most likely to accommodate local strain heterogeneities. A slip-stimulated twin nucleation mechanism was identified for soft/hard grain pairs: dislocation slip in a soft-oriented grain can stimulate twin nucleation in the neighboring hard grain when the slip system is well aligned with the twinning system. This alignment was described by a slip-transfer parameter m′.[24] Twins activated by this mechanism always had the highest m′ value among the six available $$ \left\{ {10\bar{1}2} \right\}\left\langle {\bar{1}011} \right\rangle $$ twinning systems, while the Schmid factor, based on the global (uniaxial tensile) stress state, was a less significant indicator of twin activity. Through slip transfer, deformation twins sometimes formed despite having a very low global Schmid factor. The frequency of slip-stimulated twin nucleation depends strongly on the texture and loading direction in the material. For grain pairs having one grain with a large Schmid factor for twinning, nonparametric statistical analysis confirms that those with a larger m′ are more likely to display slip-stimulated twinning.

Assessment of plastic heterogeneity in grain interaction models using crystal plasticity finite element method

Micromechanical models aimed at simulating deformation textures and resulting plastic anisotropy need to incorporate local plastic strain heterogeneities arising from grain interactions for better predictions. The ALAMEL model [Van Houtte, P., Li, S., Seefeldt, M., Delannay, L. 2005. Deformation texture prediction: from the Taylor model to the advanced Lamel model. Int. J. Plasticity 21, 589–624], is one of the models in which the heterogeneous nature of plastic deformation in metals is introduced by accounting for the influence of a grain boundary on the cooperative deformation of adjacent grains. This is achieved by assuming that neighbouring grains undergo heterogeneous shear rates parallel to the grain boundary. The present article focuses on understanding the plastic deformation fields near the grain boundaries and the influence of grain interaction on intra-grain deformations. Crystal Plasticity Finite Element Method (CPFEM) is employed on a periodic unit cell consisting of four grains discretised into a large number of elements. A refined study of the local variation of strain rates, both along and perpendicular to the grain boundaries permits an assessment of the assumptions made in the ALAMEL model. It is shown that the ALAMEL model imbibes the nature of plastic deformation at the grain boundaries very well. However, near triple junctions, the influence of a third grain induces severe oscillations of the stress tensor, reflecting a singularity. According to CPFEM, such singularity can lead to grain subdivision by the formation of new boundaries originating at the triple junction.

Symmetry rules and strain/order-parameter relationships for coupling between octahedral tilting and cooperative Jahn–Teller transitions in ABX 3 perovskites. II. Application

The structural evolution of selected perovskites containing Jahn-Teller cations has been investigated in the light of a formal analysis of symmetry hierarchies for phase transitions driven by octahedral tilting and Jahn-Teller cooperative distortions. General expressions derived from the strain/order-parameter coupling relationships allowed by symmetry are combined with observed changes in lattice parameters to reveal details of order-parameter evolution and coupling. LuVO3, YbVO3, YVO3 and CeVO3 are representative of systems which develop Jahn-Teller ordering schemes associated with irreducible representations M2+ and R3+ of the space group Pm3m. Tilting of their octahedra is associated with M3+ and R4+. The Pnma (M3+ + R4+ tilting) <--> P2(1)/a (M3+ + R4+ tilting, R3+ Jahn-Teller order) transition below room temperature is close to second order in character. Shear strains which depend primarily on tilt angles show little variation, implying that there is only weak coupling between the tilting and Jahn-Teller order parameters. The subsequent P2(1)/a <--> Pnma (M3+ + R4+ tilting, M2+ Jahn-Teller order) is first order in character, and involves either a reduction in the R4+ tilt angle or a change in the strength of tilt/Jahn-Teller order-parameter coupling. In LaMnO3, the isosymmetric Pnma (M3+ + R4+ tilting) <--> Pnma (M3+ + R4+ tilting, M2+ Jahn-Teller order) transition can be described in terms of a classical first-order transition conforming to a 246 Landau expansion with negative fourth-order coefficients. Strain evolution in Ba-doped samples suggests that the transition becomes second order in character and reveals a new strain relaxation mechanism in LaMnO3 which might be understood in terms of local strain heterogeneities due to the disordering of distorted MnO6 octahedra. Transitions in PrAlO3 and La(0.5)Ba(0.5)CoO3 illustrate the transformation behaviour of systems in which the Jahn-Teller ordering scheme is associated with the irreducible representation Gamma3+. Overall, coupled tilting + Jahn-Teller phase transitions in perovskites conform to mean-field behaviour, consistent with the underlying role of strain in promoting long interaction lengths.

Suppression of strain coupling in perovskiteLa0.6Sr0.1TiO3by cation disorder

An octahedral tilting transition has been investigated in two samples of ${\mathrm{La}}_{0.6}{\mathrm{Sr}}_{0.1}\mathrm{Ti}{\mathrm{O}}_{3}$ by powder neutron diffraction. One (slowly cooled) sample had a degree of cation/vacancy ordering on the $A$ sites and was tetragonal, $P4∕mmm$, at high temperatures. The second (quenched) sample had disordered cations and cubic, $Pm\overline{3}m$, symmetry at high temperatures. On cooling, both underwent the same $R$-point tilting transition at $\ensuremath{\sim}560--570\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, to give symmetry changes $P4∕mmm\ensuremath{\leftrightarrow}Cmmm$ and $Pm\overline{3}m\ensuremath{\leftrightarrow}I4∕mcm$, respectively. From the evolution of the tilt angles, the transition appears to be close to tricritical in both cases. As expected from a Landau expansion in the two order parameters, the transition temperature was found to be only weakly dependent on the degree of cation order. In contrast with the expectation of standard patterns of strain to order parameter coupling, however, the tilted (tetragonal) form of the disordered sample remained metrically cubic, implying that coupling of the tetragonal shear strain with the octahedral tilting was suppressed. It is proposed that cation disordering causes the development of local strain heterogeneities in crystals of ${\mathrm{La}}_{0.6}{\mathrm{Sr}}_{0.1}\mathrm{Ti}{\mathrm{O}}_{3}$ which prevent a coherent, long-range shear strain from developing. Manipulation of the degree of cation order in perovskites with carefully selected compositions might therefore provide a means by which the magnitudes of ferroelastic strains could be engineered according to the requirement of particular applications.

Orientation Selection in ULC Steel during Thermally Activated Phenomena Induced by Cold Deformation

The scope of this work was to study the physical metallurgical behaviour of the microstructure and the texture of ultra low carbon (ULC) steel during cold rolling and subsequent thermally activated phenomena. It was the intention to contribute to the scientific search for the answer to many open questions raised in recent literature. The powerful tool of quantitative texture analysis, together with modern measurement equipment was used for this purpose. At first, a ULC steel was cold rolled to two different rolling reductions and the local strain heterogeneities after the cold rolling were studied. Secondly, crystallographic orientation selection during primary recrystallization was considered both for cold rolled ULC steel and for a Fe-2.8%Si single crystal. The latter was a re-evaluation of the historic growth selection experiment by Ibe and Lücke. Finally, secondary recrystallization in ULC steels was evaluated in terms of oriented nucleation and selective growth.

Crack opening due to deformation twin shear at grain boundaries in near-γ TiAl

Microcrack nucleation has been observed at apparent deformation twin interactions with grain boundaries in a duplex near-gamma TiAl specimen deformed to surface tensile strain of about 1.4%. To prove that these microcracks are a result of twins and not dislocation slip bands, detailed characterization of the surface topography and crystallography associated with the microcracks was conducted and analyzed. Electron backscatter diffraction patterns were used in conjunction with selected area channeling patterns to determine the crystallography near the observed microcracks. Transmission electron microscopy of a selected twin, extracted using a focused ion beam, and atomic force microscopy were used to show that the observed microcracks could only have been caused by local strain heterogeneities caused by twin interactions with grain boundaries and not by dislocation slip bands.

Effect of Inhomogeneous Deformation on the Recrystallization Kinetics of Deformed Metals

In this paper, the Johnson-Mehl-Avrami-Kolmogorov equation, modified by Rollett et al. (1989) to take the heterogeneity of recrystallization into account, was used to derive analytical equations to calculate the instantaneous and average Avrami exponent during the heterogeneous recrystallization process. The model can explain experimental observations, such as a lower exponent than predicted by the JMAK theory and a decreasing exponent with proceeding recrystallization; moreover, by building up a quantitative relationship between local strain variation and heterogeneity of recrystallization kinetics, it can also describe so-far unexplained observations, such as the range of experimentally observed exponents in recrystallization, and the very small effect of temperature and deformation conditions on the Avrami exponent.

Strain and local heterogeneity in the forsterite?fayalite solid solution

Infrared powder-absorption spectra of nine natural and five synthetic olivine samples across the forsterite–fayalite join have been investigated at room temperature in the range 70–1400 cm−1. Variations of peak positions as a function of Fe content are close to linear for those vibrational bands whose trend could be followed across the solid solution. Line-broadening has been quantified by autocorrelation analysis. Positive deviations from linearity of the line-broadening parameter, Δcorr, for groups of bands at low energies are consistent with the existence of local elastic strain heterogeneities at intermediate compositions in the solid solution. It also appears that the structure of forsterite is more homogeneous than Fe-rich olivines in relation to local elastic strain effects. Positive deviations from linearity of the line-broadening parameter for the low-energy regions scale linearly with calorimetric data for the enthalpy of mixing. This close correlation between line-broadening in IR spectra and calorimetric enthalpies of mixing has now been observed for four different binary solid solutions, and there is a further, qualitative correlation with bulk modulus.

Local Strain Heterogeneities after Cold Rolling of an Ultra Low Carbon Steel

Local Strain Heterogeneities after Cold Rolling of an Ultra Low Carbon Steel

Effect of Weave Architecture on Tensile Properties and Local Strain Heterogeneity in Thin‐Sheet C–SiC Composites

Room‐temperature tensile properties were measured for two thin C–SiC composites fabricated from single sheets of carbon fiber fabric with nominally the same weave architecture, but different fiber packing densities. The SiC matrixes were formed by infiltration and pyrolysis of a polymer precursor (allylhydridopolycarbosilane). The tensile properties are related to microstructural characteristics, observed damage mechanisms, and measurements of local strain concentrations by speckle interferometry. Differences are observed between the responses of these thin‐sheet composites and conventional CVI‐matrix composites of larger thickness. Debonding between transverse and longitudinal fiber tows allows significant strains due to straightening of initial wavy fiber tows and leads to local stress concentrations. The strength and elastic modulus are affected by the waviness of the longitudinal tows.