Lattice Strain Evolution Research Articles

Assessment of X-ray diffraction and crystal plasticity lattice strain evolutions under biaxial loading

A methodology to simulate X-ray diffraction lattice strains using crystal plasticity, replicating in-situ synchrotron experimental measurements during the deformation of a low-carbon steel, has been developed. Uniquely, the model calculated lattice strains for full Debye–Scherrer diffraction rings, providing the in-plane lattice strain distributions determined from crystal plasticity. Thus, a direct method of comparison between experimental and crystal plasticity results becomes possible. The model considered two forms of hardening whilst subjecting the material to two dissimilar proportional strain-paths; uniaxial and balanced biaxial deformation. Both deformation paths showed influence on resulting lattice strain distributions which were also found to depend upon texture. Biaxial straining led to a stronger dependence on the material's hardening behaviour and this was attributed to the higher rate of work hardening seen under biaxial compared to uniaxial straining. However, biaxial deformation showed quite isotropic lattice strains distribution, irrespective of initial texture or hardening. Quantitatively, good agreement between the computed and experimentally determined lattice strain distributions was obtained for each strain path. This success demonstrates the possibility of calibrating crystal plasticity model parameters using such methodologies, or simply to provide insight into the governing mechanisms in polycrystal deformation.

Strain hardening in Fe–16Mn–10Al–0.86C–5Ni high specific strength steel

We report a detailed study of the strain hardening behavior of a Fe–16Mn–10Al–0.86C–5Ni (weight percent) high specific strength (i.e. yield strength-to-mass density ratio) steel (HSSS) during uniaxial tensile deformation. The dual-phase (γ-austenite and B2 intermetallic compound) HSSS possesses high yield strength of 1.2–1.4 GPa and uniform elongation of 18–34%. The tensile deformation of the HSSS exhibits an initial yield-peak, followed by a transient characterized by an up-turn of the strain hardening rate. Using synchrotron based high-energy in situ X-ray diffraction, the evolution of lattice strains in both the γ and B2 phases was monitored, which has disclosed an explicit elasto-plastic transition through load transfer and strain partitioning between the two phases followed by co-deformation. The unloading-reloading tests revealed the Bauschinger effect: during unloading yield in γ occurs even when the applied load is still in tension. The extraordinary strain hardening rate can be attributed to the high back stresses that arise from the strain incompatibility caused by the microstructural heterogeneity in the HSSS.

Stress transfer during different deformation stages in a nano-precipitate-strengthened Ni-Ti shape memory alloy

Understanding the role of fine coherent precipitates in the micromechanical behavior of precipitate-strengthened shape memory alloys (SMAs), which still remains a mystery heretofore, is of crucial importance to the design of advanced SMAs with optimal functional and mechanical properties. Here, we investigate the lattice strain evolution of, and the stress partition between the nanoscale Ni4Ti3 precipitates and the matrix in a precipitate-strengthened Ni-Ti SMA during different deformation stages by in-situ synchrotron high-energy X-ray diffraction technique. We found that, during R-phase reorientation and stress-induced martensitic transformation, which both involve the shear deformation process, the lattice strain of the nanoscale precipitates drastically increases by a magnitude of 0.5%, which corresponds to an abrupt increase of ∼520 MPa in internal stress. This indicates that stress repartition occurs and most of the stress is transferred to the precipitates during the shear deformation of the matrix. It is further revealed that the nanoscale precipitates which only have a low volume fraction bear a considerable amount of applied stress during all deformation stages investigated, implying that the nanoscale precipitates play an important role in the deformation behavior of the precipitate-strengthened Ni-Ti SMAs.

Investigation of thermal aging effects on the tensile properties of Alloy 617 by in-situ synchrotron wide-angle X-ray scattering

The nickel-base Alloy 617 has been considered as the lead candidate structural material for the intermediate heat exchanger (IHX) of the Very-High-Temperature Reactor (VHTR). In order to assess the long-term performance of Alloy 617, thermal aging experiments up to 10,000h in duration were performed at 1000°C. Subsequently, in-situ synchrotron wide-angle X-ray scattering (WAXS) tensile tests were carried out at ambient temperature. M23C6 carbides were identified as the primary precipitates, while a smaller amount of M6C was also observed. The aging effects were quantified in several aspects: (1) macroscopic tensile properties, (2) volume fraction of the M23C6 phase, (3) the lattice strain evolution of both the matrix and the M23C6 precipitates, and (4) the dislocation density evolution during plastic deformation. The property–microstructure relationship is described with a focus on the evolution of the M23C6 phase. For aging up to 3000h, the yield strength (YS) and ultimate tensile strength (UTS) showed little variation, with average values being 454MPa and 787MPa, respectively. At 10,000h, the YS and UTS reduced to 380MPa and 720MPa, respectively. The reduction in YS and UTS is mainly due to the coarsening of the M23C6 precipitates. After long term aging, the volume fraction of the M23C6 phase reached a plateau and its maximum internal stress was reduced, implying that under large internal stresses the carbides were more susceptible to fracture or decohesion from the matrix. Finally, the calculated dislocation densities were in good agreement with transmission electron microscopy (TEM) measurements. The square roots of the dislocation densities and the true stresses displayed typical linear behavior and no significant change was observed in the alloys in different aging conditions.

Ordering and the micromechanics of Ti–7Al

The evolution of intergranular lattice strain in the α titanium alloy Ti–7Al wt% was characterised using in situ time-of-flight (TOF) neutron diffraction during room temperature tensile loading. Samples were aged to promote ordering and the formation of nanometre-scale α2 (Ti3Al). On ageing, at 550°C and 625°C, dislocations were observed to travel in pairs, and in planar arrays, which has been attributed to the presence of ordering. A slight change in c/a was observed, from 1.6949 to 1.6945, and a slight increase in the macroscopic modulus. However, no changes were observed in the residual lattice strains, which are the grain-orientation average elastic strains produced by plasticity. Therefore it is inferred that the changes in deformation mechanisms caused by ordering that result in an enhanced vulnerability to dwell fatigue affect primarily the extent of slip localisation. The overall strain distributions between grains in different orientations are not changed.

Lattice Strain and Magnetic Property Evolution of La0.5Sr0.5Mn1−x Co x O3 Synthesized by Solid-State Reaction at Low Temperatures

La0.5Sr0.5Mn1−x Co x O 3 (0 ≤x ≤ 0.3) is obtained by calcining the precursor carbonates in air. The precursor and its calcined products are characterized by X-ray powder diffraction, scanning electron microscopy, and vibrating sample magnetometer. A highly crystallized La 0.5Sr 0.5Mn 1−x Co x O 3 (0 ≤x ≤ 0.3) with a perovskite structure is obtained when the precursor is calcined at 900 ∘C in air for 3 h. The lattice strains of La 0.5Sr 0.5Mn 1−x Co x O 3 increase with the increase of Co content and/or the decrease of Mn content between x = 0 and x = 0.1 at first, then decreases with the increase of Co content. The magnetic properties of La 0.5Sr 0.5Mn 1−x Co x O 3 depend on the composition and measurement temperature. Cobalt substitution can markedly improve the coercivity of La 0.5Sr 0.5Mn 1−x Co x O 3.

The evolution of internal stress and dislocation during tensile deformation in a 9Cr ferritic/martensitic (F/M) ODS steel investigated by high-energy X-rays

An application of high-energy wide angle synchrotron X-ray diffraction to investigate the tensile deformation of 9Cr ferritic/martensitic (F/M) ODS steel is presented. With tensile loading and in-situ X-ray exposure, the lattice strain development of matrix was determined. The lattice strain was found to decrease with increasing temperature, and the difference in Young's modulus of six different reflections at different temperatures reveals the temperature dependence of elastic anisotropy. The mean internal stress was calculated and compared with the applied stress, showing that the strengthening factor increased with increasing temperature, indicating that the oxide nanoparticles have a good strengthening impact at high temperature. The dislocation density and character were also measured during tensile deformation. The dislocation density decreased with increasing of temperature due to the greater mobility of dislocation at high temperature. The dislocation character was determined by best-fit methods for different dislocation average contrasts with various levels of uncertainty. The results shows edge type dislocations dominate the plastic strain at room temperature (RT) and 300 °C, while the screw type dislocations dominate at 600 °C. The dominance of edge character in 9Cr F/M ODS steels at RT and 300 °C is likely due to the pinning effect of nanoparticles for higher mobile edge dislocations when compared with screw dislocations, while the stronger screw type of dislocation structure at 600 °C may be explained by the activated cross slip of screw segments.

Intergranular Strain Evolution in Titanium During Tensile Loading: Neutron Diffraction and Polycrystalline Model

Intergranular strains due to tensile plastic deformation were investigated in a commercially pure Ti. Neutron diffraction has been used to characterize the evolution of residual elastic strain in grains with different crystallographic orientations. Experimental data have been obtained for the macroscopic stress–strain curve and the intergranular strain evolution in the longitudinal and transverse direction relative to the uniaxial loading axis. The elasto-plastic self-consistent (EPSC) approach was used to model the deformation behavior of the studied material. Comparison between the neutron measurements and the model predictions shows that in most cases the EPSC approach can predict the lattice strain evolution and capture the plastic anisotropy observed in the experiments.

Evaluation of elastic–viscoplastic self-consistent polycrystal plasticity models for zirconium alloys

Our elastic viscoplastic self-consistent (EVPSC) model is improved by including thermal strain to allow study of the behavior of a Zircaloy-2 slab under moderately large strains. The approach of introducing thermal strain effect is similar to the one developed by Turner et al. (1995) and used by Xu et al. (2008a). Various self-consistent schemes (SCSs) of the EVPSC model are then evaluated in terms of the deformation behavior of the material under different uniaxial strain paths. The material parameters for the various models are determined by fitting experimental data from uniaxial tension and compression tests along the normal direction (ND) and from uniaxial tension tests along the rolling direction (RD). The quality of the various SCS predictions is assessed based on comparisons of macroscopic deformation behavior (stress–strain curves and R-values) and microscopic mechanical response (the evolution of lattice strains and texture coefficients) between the predicted and experimental data. It is revealed that the Affine and Meff=0.1 self-consistent models give much better performance than the Secant and Tangent models.

In-situ investigation of the anisotropic mechanical behavior of rolled AA 7020-T6 alloy through lattice strain evolution during uniaxial tension

The texture-induced anisotropic mechanical behavior of a highly textured AA 7020-T6 (maximum orientation density of 29.7 multiple random distribution), was characterized by the lattice strain evolution along rolling direction (RD), 45° to RD and 90° to RD, respectively, under uniaxial tension using high energy X-ray diffraction. The uniaxial tensile tests were done till ultimate tensile strength (UTS), which show different yield strengths (YS), UTS and elongations along the three directions on a macroscopic level. On micromechanical level, the lattice strain evolution explains the correlation between crystallite orientation and different mechanical behavior, leading to the macroscopic anisotropy. In the elastic region, the sample 45° to RD has the lowest lattice plane dependent Young's modulus compared to the other two directions. In the elastic plastic transition region, lattice strain differences among different {hkl} lattice planes are highest for sample 45° to RD and lowest for sample 0° to RD. Moreover, the 45° to RD sample has the lowest lattice dependent YS. In the plastic region, the work hardening behavior of different {hkl} lattice planes in all three directions can be divided into two groups, corresponding to two types of dislocation combinations. However, {200} planes of samples 45° and 90° to RD behave abnormally due to the stress along <110> of the {200} planes and the orientation density of {200} planes parallel and perpendicular to the loading direction (LD).

Effect of Strain Path on Lattice Strain Evolution during Monotonic and Cyclic Tension of Magnesium Alloy

In-situ neutron diffraction has been employed to examine the effect of strain path on lattice strain evolution during monotonic and cyclic tension in an extruded Mg-8.5wt.%Al alloy. In the cyclic tension test, the maximum applied stress increased with cycle number. Lattice strain data were acquired for three grain orientations, characterized by the plane normal to the stress axis. The lattice strain in the hard {10.0} orientation, which is unfavorably oriented for both basal slip and {10.2} extension twinning, evolved linearly throughout both tests during loading and unloading. The {00.2} orientation exhibited significant relaxation associated with {10.2} extension twinning. Coupled with a linear lattice strain unloading behavior, this relaxation led to increasingly compressive residual strains in the {00.2} orientation with increasing cycle number. The {10.1} orientation is favorably oriented for basal slip, and thus showed a soft grain behavior. Microyielding occurred in the monotonic tension test and in all cycles of the cyclic test at an applied stress of ~50 MPa, indicating that strain hardening in this orientation was not completely stable from one cycle to the next. The lattice strain unloading behavior was linear in the {10.1} orientation, leading to a compressive residual strain after every cycle, which, however, did not increase systematically from one cycle to the next as in the {00.2} orientation.

An elasto-plastic self-consistent model with hardening based on dislocation density, twinning and de-twinning: Application to strain path changes in HCP metals

In this work, we develop a polycrystal mean-field constitutive model based on an elastic–plastic self-consistent (EPSC) framework. In this model, we incorporate recently developed subgrain models for dislocation density evolution with thermally activated slip, twin activation via statistical stress fluctuations, reoriented twin domains within the grain and associated stress relaxation, twin boundary hardening, and de-twinning. The model is applied to a systematic set of strain path change tests on pure beryllium (Be). Under the applied deformation conditions, Be deforms by multiple slip modes and deformation twinning and thereby provides a challenging test for model validation. With a single set of material parameters, determined using the flow-stress vs. strain responses during monotonic testing, the model predicts well the evolution of texture, lattice strains, and twinning. With further analysis, we demonstrate the significant influence of internal residual stresses on (1) the flow stress drop when reloading from one path to another, (2) deformation twin activation, (3) de-twinning during a reversal strain path change, and (4) the formation of additional twin variants during a cross-loading sequence. The model presented here can, in principle, be applied to other metals, deforming by multiple slip and twinning modes under a wide range of temperature, strain rate, and strain path conditions.

Evolution of Intergranular Stresses in a Martensitic and an Austenitic NiTi Wire During Loading–Unloading Tensile Deformation

In situ synchrotron X-ray diffraction testing was carried out on a martensitic and an austenitic NiTi wire to study the evolution of internal stresses and the stress-induced martensite (SIM) phase transformation during room temperature tensile deformation. From the point of lattice strain evolution, it is concluded that (1) for the martensitic NiTi wire, detwinning of the [011]B19′ type II twins and the {010}B19′ compound twins is responsible for internal strains formed at the early stage of deformation. (2) The measured diffraction moduli of individual martensite families show large elastic anisotropy and strong influences of texture. (3) For the austenitic NiTi wire, internal residual stresses were produced due to transformation-induced plasticity, which is more likely to occur in austenite families that have higher elastic moduli than their associated martensite families. (4) Plastic deformation was observed in the SIM at higher stresses, which largely decreased the lower plateau stresses.

Crystal Plasticity Analysis of Stress Partitioning Mechanisms and Their Microstructural Dependence in Advanced Steels

Two-phase advanced steels have an optimized combination of high yield strength and large elongation strain at failure, as a result of stress partitioning between a hard phase (martensite) and a ductile phase (ferrite or austenite). Provided with strong interfaces between the constituent phases, the failure in the brittle martensite phase will be delayed by the surrounding geometric constraints, while the rule of mixture will dictate a large strength of the composite. To this end, the microstructural design of these composites is imperative especially in terms of the stress partitioning mechanisms among the constituent phases. Based on the characteristic microstructures of dual phase and multilayered steels, two polycrystalline aggregate models are constructed to simulate the microscopic lattice strain evolution of these materials during uniaxial tensile tests. By comparing the lattice strain evolution from crystal plasticity finite element simulations with advanced in situ diffraction measurements in literature, this study investigates the correlations between the material microstructure and the micromechanical interactions on the intergranular and interphase levels. It is found that although the applied stress will be ultimately accommodated by the hard phase and hard grain families, the sequence of the stress partitioning on grain and phase levels can be altered by microstructural designs. Implications of these findings on delaying localized failure are also discussed.

Development of a laboratory-based transmission diffraction technique forin situdeformation studies of Mg alloys

A laboratory-based transmission X-ray diffraction technique was developed to measure elastic lattice strains parallel to the loading direction duringin situtensile deformation. High-quality transmission X-ray diffraction data were acquired in a time frame suitable forin situloading experiments by application of a polycapillary X-ray optic with a conventional laboratory Cu X-ray source. Based on the measurement of two standard reference materials [lanthanum hexaboride (NIST SRM 660b) and silicon (NIST SRM 640c)], precise instrumental alignment and calibration of the transmission diffraction geometry were realized. These results were also confirmed by the equivalent data acquired using the standard Bragg–Brentano measurement geometry. An empirical Caglioti function was employed to describe the instrumental broadening, while an axis of rotation correction was used to measure and correct the specimen displacement from the centre of the goniometer axis. For precise Bragg peak position andhkilintensity information, a line profile fitting methodology was implemented, with Pawley refinement used to measure the sample reference lattice spacings (do(hkil)). It is shown that the relatively large X-ray probe size available (7 × 7 mm) provides a relatively straightforward approach for improving the grain statistics for the study of metal alloys, where grain sizes in excess of 1 µm can become problematic for synchrotron-based measurements. This new laboratory-based capability was applied to study the lattice strain evolution during the elastic–plastic transition in extruded and rolled magnesium alloys. A strain resolution of 2 × 10−4at relatively low 2θ angles (20–65° 2θ) was achieved for thein situtensile deformation studies.In situmeasurement of the elastic lattice strain accommodation with applied stress in the magnesium alloys indicated the activation of dislocation slip and twin deformation mechanisms. Furthermore, measurement of the relative change in the intensity of 0002 and 10\overline 13 was used to quantify {10\overline 12}〈\overline 1011〉 tensile twin onset and growth with applied load.

Insights from the Lattice-Strain Evolution on Deformation Mechanisms in Metallic-Glass-Matrix Composites

In situ high-energy synchrotron X-ray diffraction experiments and micromechanics-based finite element simulations have been conducted to examine the lattice-strain evolution in metallic-glass-matrix composites (MGMCs) with dendritic crystalline phases dispersed in the metallic-glass matrix. Significant plastic deformation can be observed prior to failure from the macroscopic stress–strain curves in these MGMCs. The entire lattice-strain evolution curves can be divided into elastic–elastic (denoting deformation behavior of matrix and inclusion, respectively), elastic–plastic, and plastic–plastic stages. Characteristics of these three stages are governed by the constitutive laws of the two phases (modeled by free-volume theory and crystal plasticity) and geometric information (crystalline phase morphology and distribution). The load-partitioning mechanisms have been revealed among various crystalline orientations and between the two phases, as determined by slip strain fields in crystalline phase and by strain localizations in matrix. Implications on ductility enhancement of MGMCs are also discussed.

Study of Lattice Strain Evolution in Stainless Steel Under Tension: The Role of Self‐Consistent Plasticity Model

The recently developed large strain elastic visco‐plastic self‐consistent (EVPSC) model, with various popular self‐consistent schemes including the Affine, Meff, Secant, and Tangent, is used to study the lattice strain evolution in a stainless steel under uniaxial tension. The material parameters for the various self‐consistent schemes are fitted to experimental stress and strain curve under uniaxial tension. An assessment of the predictive capability of the self‐consistent schemes is performed based on comparisons of the predicted lattice strain evolutions and in situ neutron diffraction measurements done on the same material. It is found that, among the self‐consistent schemes examined, the self‐consistent schemes with grain interaction stiffness halfway between those of the limiting Secant (stiff) and Tangent (compliant) approximations give the best results.

Characterization of Ball Milled Ni–Al2O3 Nanocomposite Powders

Homogenous Ni–Al2O3 nanocomposite powders with uniform distribution of Al2O3 nanoparticles were obtained through ball milling of Ni and Al2O3 powders for 9 hours. Field emission scanning electron microscopy and X-ray mapping were used to characterize the ball milled powders and Al2O3 nanoparticles’ dispersion, respectively. The evolution of crystallite size and lattice strain in the nanostructured Ni powder was followed through X-ray diffraction. It was found that ball milling led not only to the uniform dispersion of the Al2O3 nanoparticles, but also to the reduction in crystallite size and increase in the lattice strain of the Ni phase. For the composite containing 5 wt.% Al2O3, the increase of milling time from 0 to 9 hours led to a continuous decrease of the crystallite size of the Ni phase from 1120 to 36 nm. For the composite containing 10 wt.% Al2O3, the increase of milling time from 0 to 2 hours augmented the lattice strain of the Ni phase and a further increase of milling time to 9 hours led to its decrease.

Self-consistent Modelling and the Evaluation of Lattice Deformation in a Polycrystalline Austenitic Stainless Steel

Individual anisotropic grains within a polycrystalline material exhibit different micro-mechanical responses for a given applied macroscopic stress, leading to a variation in the meso-scale intragranular lattice strain. Despite various experimental data for the lattice strain evolution measured by neutron diffraction, a physical understanding of how the lattice strain evolves during plastic flow is still incomplete. In this study, a self-consistent model is established, taking into account detailed dislocation kinetics and its influence on different evolution processes of the dislocation distribution on different crystallographic planes of each grain within a polycrystalline material. The model is used to evaluate the micro-mechanical behaviour of F.C.C. polycrystalline austenitic stainless steels. Predictions of the lattice strain developed within individual grains of a polycrystal are compared with experimental results obtained using neutron diffraction. This model captures the major trends in the evolution of the lattice strains and provides an explanation and interpretation of the internal processes that most influence the observed response.

Heterogeneous nucleation and shape transformation of multicomponent metallic nanostructures

To be able to control the functions of engineered multicomponent nanomaterials, a detailed understanding of heterogeneous nucleation at the nanoscale is essential. Here, by using in situ synchrotron X-ray scattering, we show that in the heterogeneous nucleation and growth of Au on Pt or Pt-alloy seeds the heteroepitaxial growth of the Au shell exerts high stress (∼2 GPa) on the seed by forming a core/shell structure in the early stage of the reaction. The development of lattice strain and subsequent strain relaxation, which we show using atomic-resolution transmission electron microscopy to occur through the slip of {111} layers, induces morphological changes from a core/shell to a dumbbell structure, and governs the nucleation and growth kinetics. We also propose a thermodynamic model for the nucleation and growth of dumbbell metallic heteronanostructures.