Load partitioning between ferrite and cementite during elasto-plastic deformation of an ultrahigh-carbon steel

An ultrahigh-carbon steel was heat-treated to form an in situ composite consisting of a fine-grained ferritic matrix with 34 vol.% submicron spheroidized cementite particles. Volume-averaged lattice elastic strains for various crystallographic planes of the α-Fe and Fe₃C phases were measured by synchrotron X-ray diffraction for a range of uniaxial tensile stresses up to 1 GPa. In the elastic range of steel deformation, no load transfer occurs between matrix and particles because both phases have nearly equivalent elastic properties. In the steel plastic range after Lüders band propagation, marked load transfer takes place from the ductile α-Fe matrix to the elastic Fe₃C particles. Reasonable agreement is achieved between phase lattice strains as experimentally measured and as computed using finite-element modeling.     

Stress–strain relationship between ferrite and martensite in a dual-phase steel studied by in situ neutron diffraction and crystal plasticity theories

The stress–strain relationship between ferrite and martensite phases in the commercial dual-phase DP980 steel was studied using in situ neutron diffraction and the crystal plasticity finite element method (CPFEM). The phase identification method based on the image quality of electron backscatter diffraction and a filtering process was used to obtain information concerning individual crystallographic orientations for ferrite and martensite phases in DP980 steel. The (2 0 0) and (2 1 1) lattice strains of ferrite and martensite phases were measured along the loading and transverse directions as a function of macroscopic stress using in situ neutron diffraction. A CPFEM based on representative volume elements (RVE) was applied to determine the microscopic hardening parameters for each phase by fitting the measured macroscopic stress and measured (2 0 0) and (2 1 1) lattice strains. The microscopic hardening parameters for each phase successfully captured the influence of the crystallographic orientation of the ferrite phase on the localization of shear strain and the behavior of ductile failure in RVE of the unit cell during uniaxial tension.     

Effect of texture on load partitioning in Ti-6Al-4V

Neutron diffraction has been used to characterize the evolution of residual elastic strain in grains with different orientations due to room temperature plastic deformation in two plate product forms of Ti–6Al–4V. The evolution of lattice strains has been rationalized using a two-phase elastic–plastic self-consistent model using only the texture difference between the two product forms. It is found that the elastic properties of both the bulk and individual orientations can be reproduced quite satisfactorily, with a C′ modulus of the β phase of 15 GPa. The residual microstrains produced are generally greater in the unidirectionally rolled material than the cross-rolled, but are smaller than in Ti-834. The residual strains accumulated in the (0 0 0 2) orientation are near-zero, which can only be reproduced in the modelling by assuming a critical resolved shear stress for 〈c + a〉 slip only 1.5× that for 〈a〉 slip, compared to the 3× factor found for isolated single crystals. The implications of this for our understanding of deformation in these materials are discussed.     

Study of internal lattice strain distributions in stainless steel using a full-field elasto-viscoplastic formulation based on fast Fourier transforms

In this work, the evolution of internal lattice strains in face-centered cubic stainless steel under uniaxial tension is studied using a recently developed full-field elasto-viscoplastic formulation based on fast Fourier transforms. The shape of the diffraction peaks is simulated, and the predicted lattice strains (peak shift and broadening) are compared with the experimental measurements obtained by in situ tensile neutron diffraction. Detailed analysis of the lattice strain distributions reveal that {1 0 0} and {1 1 0} transverse families exhibit a bimodal nature, and that transverse lattice strains are more sensitive to local grain interactions compared with longitudinal lattice strains. A comparison with the results of a mean-field formulation indicates that type III (intragranular) stresses play a much larger role than type II (intergranular) stresses in diffraction peak broadening.     

Evolution of orientation distributions of γ and γ′ phases during creep deformation of Ni-base single crystal superalloys

The evolution of orientation distributions of γ and γ′ phases in crept Ni-base single crystal superalloys have been investigated by theoretical calculations with elastic–plastic models and by experiments. As creep deformation proceeds, the crystallographic orientation distributions for both phases are broadened as a result of the waving of the raft structure, which occurs to reduce the total mechanical energy. The broadening of the orientation distribution occurs in such a way that the 0 0 1 pole broadens isotropically while the h k 0 poles broaden preferentially along the 〈0 0 1〉 directions. Since the extent of the broadening increases almost linearly with the number of creep deformation, the measurement of the broadening by X-ray diffraction can be utilized in non-destructive methods to predict the lifetime of Ni-base superalloys.     

Load partitioning in honeycomb-like silicon carbide aluminum alloy composites

A 50/50 vol.% Al/SiC composite was made via melt infiltration of an aluminum alloy into a porous beech wood-derived SiC preform. The honeycomb-like composite microstructure consisted of an interconnected SiC phase surrounding discrete Al “fibers” aligned in the growth direction of the beech wood. High energy synchrotron X-ray diffraction was used to measure the volume averaged lattice strains in both the SiC and Al phases during in situ compressive loading up to an applied stress of ?530 MPa. Load transfer from the Al to the SiC was observed, and the Al yielded at an applied stress of above ?213 MPa. The elastic behavior of the composite was modeled with both an isostrain rule of mixtures calculation and variational bounds for the effective elastic modulus. Furthermore, calculations of the von Mises effective stress of the SiC and Al phases showed that the wood-derived SiC was a more effective reinforcement than either SiC particle- or whisker-reinforced composites.     

Nonpolar ZnO film growth and mechanism for anisotropic in-plane strain relaxation

Using high-resolution transmission electron microscopy (HRTEM) and X-ray diffraction, we investigated the strain relaxation mechanisms for nonpolar (1 1 ?2 0) a-plane ZnO epitaxy on (1 ?1 0 2) r-plane sapphire, where the in-plane misfit ranges from ?1.5% for the [0 0 0 1]ZnO6[1 ?1 0 ?1]sapphire to ?18.3% for the [?1 1 0 0]ZnO6[?1 ?1 2 0]sapphire direction. For the large misfit [?1 1 0 0]ZnO direction the misfit strains are fully relaxed at the growth temperature, and only thermal misfit and defect strains, which cannot be relaxed fully by slip dislocations, remain on cooling. For the small misfit direction, lattice misfit is not fully relaxed at the growth temperature. As a result, additive unrelaxed lattice and thermal misfit and defect strains contribute to the measured strain. Our X-ray diffraction measurements of lattice parameters show that the anisotropic in-plane biaxial strain leads to a distortion of the hexagonal symmetry of the ZnO basal plane. Based on the anisotropic strain relaxation observed along the orthogonal in-plane [?1 1 0 0] and [0 0 0 1]ZnO stress directions and our HRTEM investigations of the interface, we show that the plastic relaxation occurring in the small misfit direction [0 0 0 1]ZnO by dislocation nucleation is incomplete. These results are consistent with the domain-matching paradigm of a complete strain relaxation for large misfits and a difficulty in relaxing the film strain for small misfits.     

Shape memory behavior of high strength NiTiHfPd polycrystalline alloys

Systematic characterization of the shape memory properties of a quaternary Ni_45.3–Ti_29.7–Hf₂₀–Pd₅ (at.%) polycrystalline alloy was performed in compression after selected aging treatments. Precipitation characteristics were revealed by transmission electron microscopy. The effects of aging temperature and time on transformation temperatures, recoverable and residual strains, and temperature and stress hystereses were determined by differential scanning calorimetry, constant-load thermal cycling experiments and isothermal strain cycling (superelasticity) tests. The crystal structure and lattice parameters of the transforming phases were determined from X-ray diffraction analysis. It was revealed that precipitation hardening significantly improved the shape memory properties of the NiTiHfPd alloy. Under optimum aging conditions, shape memory strains of up to 4% under 1 GPa were possible, and superelasticity experiments resulted in full strain recovery without any plastic deformation, even at stress levels as high as 2 GPa. The NiTiHfPd polycrystalline alloy exhibited very high damping capacity/absorbed energy (30–34 J cm^?3) and work output (30–35 J cm^?3), which were attributed to the ability to operate at high stress levels without significant plastic deformation and to a high mechanical hysteresis (>900 MPa) at temperatures ranging from 20 °C to 80 °C.     

Evolution of the residual stress state in a duplex stainless steel during loading

The evolution of micro- and macrostresses in a duplex stainless steel during loading has been investigated in situ by X-ray diffraction. A 1.5 mm cold-rolled sheet of alloy SAF 2304 solution treated at 1050°C was studied. Owing to differences in the coefficient of thermal expansion between the two phases, compressive residual microstresses were found in the ferritic phase and balancing tensile microstresses in the austenitic phase. The initial microstresses were almost two times higher in the transverse direction compared to the rolling direction. During loading the microstresses increase in the macroscopic elastic regime but start to decrease slightly with increasing load in the macroscopic plastic regime. For instance, the microstresses along the rolling direction in the austenite increase from 60 MPa, at zero applied load, to 110 MPa, at an applied load of 530 MPa. At the applied load of 620 MPa a decrease of the microstress to 90 MPa was observed. During unloading from the plastic regime the microstresses increase by approximately 35 MPa in the direction of applied load but remain constant in the other directions. The initial stress state influences the stress evolution and even after 2.5% plastic strain the main contribution to the microstresses originates from the initial thermal stresses. Finite element simulations show stress variations within one phase and a strong influence of both the elastic and plastic anisotropy of the individual phases on the simulated stress state.     

A method for measuring single-crystal elastic moduli using high-energy X-ray diffraction and a crystal-based finite element model

This paper presents a method – based on high-energy synchrotron X-ray diffraction data and a crystal-based finite element simulation formulation – for understanding grain scale deformation behavior within a polycrystalline aggregate. We illustrate this method by using it to determine the single-crystal elastic moduli of β21s, a body-centered cubic titanium alloy. We employed a polycrystalline sample. Using in situ loading and high-energy X-rays at the Advanced Photon Source beamline 1-ID-C, we measured components of the lattice strain tensor from four individual grains embedded within a polycrystalline specimen. We implemented an optimization routine that minimized the difference between the experiment and simulation lattice strains. Sensitivity coefficients needed in the optimization routine are generated numerically using the finite element model. The elastic moduli that we computed for the β21s are C₁₁ = 110 GPa, C₁₂ = 74 GPa and C₄₄ = 89 GPa. The resulting Zener anisotropic ratio is A = 5.     

Development of intergranular thermal residual stresses in beryllium during cooling from processing temperatures

The intergranular thermal residual stresses in texture-free solid polycrystalline beryllium were determined by comparison of crystallographic lattice parameters in solid and powder samples measured by neutron diffraction during cooling from 800 °C. The internal stresses are not significantly different from zero >575 °C and increase nearly linearly <525 °C. At room temperature, the c axis of an average grain is under ～200 MPa of compressive internal stress, and the a axis is under 100 MPa of tensile stress. For comparison, the stresses have also been calculated using an Eshelby-type polycrystalline model. The measurements and calculations agree very well when temperature dependence of elastic constants is accounted for, and no plastic relaxation is allowed in the model.     

Load partitioning during compressive loading of a Mg/MgB2 composite

A composite, consisting of 68 vol.% superconducting continuous MgB₂ fibers aligned within a ductile Mg matrix, was loaded in uniaxial compression and the volume-averaged lattice strains in the matrix and fiber were measured in situ by synchrotron X-ray diffraction as a function of applied stress. In the elastic range of the composite, both phases exhibit the same strain, indicating that the matrix is transferring load to the fibers according to a simple iso-strain model. In the plastic range of the composite, the matrix is carrying proportionally less load. Plastic load transfer from matrix to fibers is complex due to presence in the fibers of a stiff WB₄ core and of cracks produced during the in situ synthesis of the MgB₂ fibers from B fibers. Also, load transfer behavior was observed to be different in bulk and near-surface regions, indicating that surface measurements are prone to error.     

Tensile flow stress of ceramic particle-reinforced metal in the presence of particle cracking

A simplified model is proposed to quantify the effect of damage in the form of particle cracking on the elastic and plastic behaviour of particle-reinforced metal matrix composites under uniaxial tensile loading: cracked particles are simply replaced, in a mean-field model, with as much matrix. Pure aluminium reinforced with 44 vol.% alumina particles, tested in tension and unloaded at periodic plastic deformations, is analysed by neutron diffraction during each reloading elastic step, at 30%, 50%, 70% and 90% of the tensile flow stress. The data give the evolution of the elastic matrix strains in the composite and also measure the progress of internal damage by particle cracking. The test gives (i) the evolution of the in situ matrix flow stress, and (ii) the evolution of load partitioning during elastic deformation with increasing composite damage. Predictions of the present model compare favourably with relevant results in the literature, and with results from the present neutron diffraction experiments.     

Crack tip process zone domain switching in a soft lead zirconate titanate ceramic

Non-180° domain switching leads to fracture toughness enhancement in ferroelastic materials. Using a high-energy synchrotron X-ray source and a two-dimensional detector in transmission geometry, non-180° domain switching and crystallographic lattice strains were measured in situ around a crack tip in a soft tetragonal lead zirconate titanate ceramic. At K_I = 0.71 MPa m^1/2 and below the initiation toughness, the process zone size, spatial distribution of preferred domain orientations, and lattice strains near the crack tip are a strong function of direction within the plane of the compact tension specimen. Deviatoric stresses and strains calculated using a finite element model and projected to the same directions measured in diffraction correlate with the measured spatial distributions and directional dependencies. Some preferred orientations remain in the crack wake after the crack has propagated; within the crack wake, the tetragonal 0 0 1 axis has a preferred orientation both perpendicular to the crack face and toward the crack front.     

Phase volume fractions and strain measurements in an ultrafine-grained NiTi shape-memory alloy during tensile loading

An ultrafine-grained pseudoelastic NiTi shape-memory alloy wire with 50.9 at.% Ni was examined using synchrotron X-ray diffraction during in situ uniaxial tensile loading (up to 1 GPa) and unloading. Both macroscopic stress–strain measurements and volume-averaged lattice strains are reported and discussed. The loading behavior is described in terms of elasto-plastic deformation of austenite, emergence of R phase, stress-induced martensitic transformation, and elasto-plastic deformation, grain reorientation and detwinning of martensite. The unloading behavior is described in terms of stress relaxation and reverse plasticity of martensite, reverse transformation of martensite to austenite due to stress relaxation, and stress relaxation of austenite. Microscopically, lattice strains in various crystallographic directions in the austenitic B2, martensitic R, and martensitic B19′ phases are examined during loading and unloading. It is shown that the phase transformation occurs in a localized manner along the gage length at the plateau stress. Phase volume fractions and lattice strains in various crystallographic reflections in the austenite and martensite phases are examined over two transition regions between austenite and martensite, which have a width on the order of the wire diameter. Anisotropic effects observed in various crystallographic reflections of the austenitic phase are also discussed. The results contribute to a better understanding of the tensile loading behavior, both macroscopically and microscopically, of NiTi shape-memory alloys.     

CRSS of γ/γ′ phases from in situ neutron diffraction of a directionally solidified superalloy tension tested at 900 °C

Neutron diffraction was used to monitor elastic strains during in situ tension testing of a directionally solidified (DS) superalloy at 900 °C. Changes in misfit and thermal expansion coefficients of individual phases were obtained. In the γ phase, it is demonstrated that elastic strains saturate at 350 MPa, which is well below the yield strength of the alloy. This is interpreted as the onset of dislocation glide through less stressed vertical channels. The critical resolved shear stress (CRSS) of γ is found to be 143 ± 11 MPa, in agreement with a calculated CRSS that is dominated by Orowan bowing of dislocations through nanoscale-wide γ channels. This provides confirmation of Orowan bowing in plasticity/creep of the γ phase. Implications of CRSS and misfit in a “threshold stress” for creep and rafting are discussed. The CRSS of γ′ is found to be consistent with pairwise penetration of dislocations into γ′.     

Lattice strain evolution during tensile and compressive loading of CP Ti

The micromechanics of textured Grade 1 commercially pure titanium are examined using neutron diffraction, self-consistent modelling and microscopy. It is found that twinning produces greater hardening than slip, that the residual lattice strains produced in the (0 0 0 2) are on the order of 0.001, and that both compression and tension twins are observed for both tensile and compression straining. The critical resolved shear stresses found are consistent with the macroscopic flow curves, lattice strains and textures produced, but are much lower than those found using uncorrected focused ion beam-milled micromechanical testing. The twins observed in axial compression were thicker than those found when compressing in the hoop direction, which is taken to imply that axial compression produced a greater number of twinning dislocations that could result in twin thickening.     

Time-dependent synchrotron X-ray diffraction on the austenite decomposition kinetics in SAE 52100 bearing steel at elevated temperatures under tensile stress

We have studied the decomposition kinetics of the metastable austenite phase present in quenched-and-tempered SAE 52100 steel by in situ high-energy synchrotron X-ray diffraction experiments at elevated temperatures of 200–235 °C under a constant tensile stress. We have observed a continuous decomposition of austenite into ferrite and cementite. The decomposition kinetics is controlled by the long-range diffusion of carbon atoms into the austenite ahead of the moving austenite/ferrite interface. The presence of a tensile stress of 295 MPa favours the carbon diffusion in the remaining austenite, so that the activation energy for the overall process decreases from 138–148 to 82–104 kJ mol^?1. Before the austenite starts to decompose, a significant amount of carbon atoms partition from the surrounding martensite phase into the metastable austenite grains. This carbon partitioning takes place simultaneously with the carbide precipitation due to the over-tempering of the martensite phase. As the austenite decomposition proceeds gradually at a constant temperature and stress, the elastic strain in the remaining austenite grains continuously decreases. Consequently, the remaining austenite grains act as a reinforcement of the ferritic matrix at longer isothermal holding times. The texture evolution in the constituent phases reflects both significant grain rotations and crystal orientation relationships between the parent austenite phase and the newly formed ferritic grains.     

Evidence of variation in slip mode in a polycrystalline nickel-base superalloy with change in temperature from neutron diffraction strain measurements

The deformation mechanisms under tensile loading in a 45 vol.% γ′ polycrystalline nickel-base superalloy have been studied using neutron diffraction at 20 °C, 400 °C, 500 °C, 650 °C and 750 °C with the results interpreted via (self-consistent) polycrystal deformation modelling. The data demonstrate that such experiments are suited to detecting changes of the γ′ slip mode from {1 1 1} to {1 0 0} with increasing temperature. Between room temperature and 500 °C there is load transfer from γ′ to γ, indicating that γ′ is the softer phase. At higher temperatures, opposite load transfer is observed indicating that the γ matrix is softer. At 400 °C and 500 °C, an instantaneous yielding increment of about 2% was observed, after an initial strain of 1.5%. This instantaneous straining coincided with zero lattice misfit between γ and γ′ in the axial direction. Predicted and experimental results of the elastic strain response of the two phases and different grain families showed good agreement at elevated temperatures, while only qualitative agreement was found at 20 °C.