Intragranular Stress Research Articles

Stress Analysis by Kossel Microdiffraction on a Nickel-Based Single Crystal Superalloy during an <i>In Situ</i> Tensile Test – Comparison with Classical X-Ray Diffraction

A Kossel microdiffraction experimental set up is under development inside a Scanning Electron Microscope (SEM) in order to determine the crystallographic orientation as well as the inter- and intragranular strains and stresses. An area of about one cubic micrometer can be analysed using the microscope probe, which enables to study different kinds of elements such as a grain boundary, a crack, a microelectronic component, etc. The diffraction pattern is recorded by a high resolution Charge-Coupled Device (CCD) camera. The crystallographic orientation, the lattice parameters and the elastic strain tensor of the probed area are deduced from the pattern indexation using a homemade software. The purpose of this paper is to report some results achieved up to now to estimate the reliability of the Kossel microdiffraction technique.

In-Situ Neutron Diffraction Study of the Bauschinger Effect in B2 Structured CoZr

A combination of in-situ neutron diffraction and elastoplastic self-consistent (EPSC) modeling have been used to elucidate the role played by intergranular stresses in the Bauschinger effect in B2 structured CoZr at room temperature and 423 K (150 °C). It is shown that, when insufficient slip modes are present to accommodate arbitrary strains, the large intergranular stresses built up due to inhomogeneous plastic deformation are responsible for the observed Bauschinger effect. Upon the onset of secondary deformation mechanism(s), the stresses are more uniformly distributed among the grains and the influence of intergranular stresses on the Bauschinger effect diminishes. On the other hand, it is speculated that the contribution of intragranular (dislocation-based) stresses is responsible for the persistent Bauschinger effect past the transition point. Similar results are obtained at both room temperature and 423 K (150 °C), and while the yield strength decreases with temperature, the high-temperature stress-strain curve progressively becomes harder than the room temperature one. In light of this, the previously characterized yield strength anomaly in CoZr has been re-examined.

Yield stress of duplex stainless steel specimens estimated using a compound Hall–Petch equation

In this study, the 0.2% yield stress of duplex stainless steel was evaluated using a compound Hall–Petch equation. The compound Hall–Petch equation was derived from four types of duplex stainless steel, which contained 0.2–64.4 wt% δ-ferrite phase, had different chemical compositions and were annealed at different temperatures. Intragranular yield stress was measured with an ultra-microhardness tester and evaluated with the yield stress model proposed by Dao et al. Grain size, volume fraction and texture were monitored by electron backscattering diffraction measurement. The kγ constant in the compound equation for duplex stainless steel agrees well with that for γ-phase SUS316L steel in the temperature range of 1323–1473 K. The derived compound Hall–Petch equation predicts that the yield stress will be in good agreement with the experimental results for the Cr, Mn, Si, Ni and N solid-solution states. We find that the intragranular yield stress of the δ-phase of duplex stainless steel is rather sensitive to the chemical composition and annealing conditions, which is attributed to the size misfit parameter.

Simulation of micromechanical behavior of polycrystals: finite elements versus fast Fourier transforms

In this work, we compare finite element and fast Fourier transform approaches for the prediction of the micromechanical behavior of polycrystals. Both approaches are full-field approaches and use the same visco-plastic single crystal constitutive law. We investigate the texture and the heterogeneity of the inter- and intragranular stress and strain fields obtained from the two models. Additionally, we also look into their computational performance. Two cases—rolling of aluminum and wire drawing of tungsten—are used to evaluate the predictions of the two models. Results from both the models are similar, when large grain distortions do not occur in the polycrystal. The finite element simulations were found to be highly computationally intensive, in comparison with the fast Fourier transform simulations.Figure 9 was corrected in this article on the 25 August 2009. The corrected electronic version is identical to the print version.

Modelling of porphyroclasts in simple shear and the role of stress variations at grain boundaries

Grain-scale numerical experiments involving simple shear of a two-phase non-linear viscous material are described and compared with mineral fish or lozenge-shaped porphyroclasts, such as muscovite. Two types of 2D models are considered; either a single elongate grain or two parallel elongate grains, in both cases supported by a weaker polygonal grain matrix. The relative viscosities of the contrasting grain structures were systematically varied, allowing us to observe the effects of non-linear viscous rheology on the resulting microstructure and flow patterns. The results show that the finite rotation of the hard elongate grain was similar within any one experiment, but was largely influenced by viscosity contrast, the geometry of the model and the imposed shear strain. Models involving single elongate hard grains show increasing instability at their ends and less strain compatibility with the deforming matrix grains, as the viscosity contrast is increased. In the paired grain models the greatest variation in the matrix grain microstructure is seen in the region where the two hard grains are oriented at a high-angle to the direction of shear. Finally, we consider the changes in intragranular stress by comparing microstructural observations using different viscosities with the distribution of stress in space and during progressive shear. In the plane approximately parallel to the maximum principal stress direction ( σ 1), a localised change of stress occurs across and along the interface between the hard and soft grains. Variations in the mean stress at these boundaries are directly attributable to changes in the minimum principal stress. We propose that with shear strains greater than γ = 2 it is the minimum principal stress that can control diffusion processes at the grain boundary rather than mean stress. In conclusion we suggest that our models have the potential for providing useful insights into why metamorphic reactions can occur at the interface between a porphyroclast and matrix at high shear strains and how stress distribution can control the initiations of such reactions.

Elastic anisotropy and yield surface estimates of polycrystals

Homogenization estimates based on the self-consistent scheme are customarily used to describe the plastic yielding of polycrystals. Such estimates of the initial micro yield surface of a polycrystal depend on the morphologic and crystallographic textures, the slip system geometry, the corresponding critical resolved shear stresses and the single crystal elastic anisotropy. The usual approach relies on a rather crude description of the stress field induced by the local elastic anisotropy. This deficiency is addressed and a new concept, i.e. a “probability” yield surface is proposed. Based on a statistical description of the local fields, the latter makes use of the average and the standard deviation of the resolved shear stress on the different slip systems within a given crystalline orientation. By comparing the homogenization estimates with full-field results, it is shown that the self-consistent scheme does not present intrinsic shortcomings regarding the prediction of the micro yield stress of polycrystals with anisotropic elastic constitutive behaviour. On the contrary, it delivers realistic estimates if the local field fluctuations are taken into account in the yield criterion. The quantitative results obtained for cubic elasticity show a strong influence of the intragranular stress heterogeneity on the estimate of the micro yield stress.

Sensitivity to grain discretization of the simulated crystal stress distributions in FCC polycrystals

An elastoviscoplastic finite element model of aluminum alloys is used to compare mechanical response among meshes formed with several different grain shapes. Tetrahedral elements are used to form grains of cubic, rhombic dodecahedral and truncated octahedral shape. The influence of the grain shape on the aggregate response is examined in terms of the stress variation and the aggregate elastic moduli. While elastic anisotropy in the bulk material is not found to be dependent on grain shape, consistent trends are observed in intragranular and intergranular stress distributions across these mesh definitions.

On the evolution of cyclic deformation microstructure during relaxation test in austenitic stainless steel at 823K

The evolution of cyclic patterns during relaxation time has been studied in terms of long-range internal stresses and effective stress evolution as a function of time at 823 K. The main features are the decrease of intra-granular back stress in relation to dipole annihilation promoted by self-diffusion and a decrease of inter-granular back stress which results in a homogenization of dislocation distribution in all the grains. Moreover, the static aging leads to an increase of the athermal component of the effective stress in association with the hardening effect of solution segregation on dislocation junctions.

Effects of grain size on dislocation organization and internal stresses developed under tensile loading in fcc metals

The relationship between deformation and dislocation properties has been studied for pure polycrystalline nickel and austenitic stainless steel AISI 316L in stage III. Special care was taken to study statistically the effects of the grain size and grain orientation on dislocation densities and distribution. It is shown that the nature of dislocation cells depends on grain size and crystallographic orientation. The dimensional parameters, which depend on grain size, i.e. the inter-boundary spacing (λ) and boundary thickness (e), define three domains of crystallographic orientation and depend on the grain size. Scaling hypotheses reveal two physical mechanisms which, at this level of plastic strain, are correlated to a specific value of the noise, associated with distribution functions. Similarities between structural parameters and dislocation densities in each phase (walls and inter-walls spacing) are identified and discussed in terms of kinetic equations describing dislocation density evolution and fluctuations of certain physical parameters. This similarity provides physical signification of the scaling distribution obtained on λ and e in terms of a stochastic approach to dislocation distribution. The origin of Hall–Petch behaviour observed at large strain is interpreted in terms of an interaction between inter- and intra-granular long-range internal stresses, which depends on grain size. We conclude that, at high strain, the Hall–Petch phenomenological relationship is a consequence of plastic strain history and strain gradient in grains. From this last point, a length scale arises naturally, which depends on stacking fault energy.

Inter- and Intragranular Stress Determination with Kossel Microdiffraction in a Scanning Electron Microscope

A Kossel microdiffraction experimental set up is under development inside a Scanning Electron Microscope (SEM) in order to determine the crystallographic orientation as well as the inter- and intragranular strains and stresses on the micron scale, using a one cubic micrometer spot. The experimental Kossel line patterns are obtained by way of a CCD camera and are then fully indexed using a home-made simulation program. The so-determined orientation is compared with Electron Back-Scattered Diffraction (EBSD) results, and in-situ tests are performed inside the SEM using a tensile/compressive machine. The aim is to verify a 50MPa stress sensitivity for this technique and to take advantage from this microscope environment to associate microstructure observations (slip lines, particle decohesion, crack initiation) with determined stress analyses.

Tracing Memory in Polycrystalline Ferromagnetic Shape‐Memory Alloys

In situ high-energy X-ray diffraction experiments reveal the influence of various microstresses and grain orientations on the memory effect in polycrystalline Ni2MnGa ferromagnetic shape-memory alloys during phase transformation (see figure). The “memory” of grain orientation and intergranular stress is evident; however, the microscale “memory” is degraded due to the existence of the intragranular stress.

Development of inter- and intragranular stresses during switching of ferroelectric polycrystals

Ferroelectrics are crystalline inorganic materials consisting of domains with different directions of spontaneous polarization. By application of sufficiently high electric fields, these domains can switch into a common direction, thus making the material piezoelectric. Due to ferroelasticity, the domains can be also switched into different states by the application of mechanical stress. In polycrystalline materials, as used in most applications, electric and stress fields interact so as to maintain compatibility. We study the influence of grain-to-grain interactions on the overall and local switching behavior and in particular the induced stresses inside grains and across grain boundaries. The behavior inside each grain is represented by the single-crystal model of [Huber, J.E., Fleck, N.A., Landis, C.M., McMeeking, R.M., 1999. A constitutive model for ferroelectric polycrystals. Journal of the Mechanics and Physics of Solids 47 (8), 1663–1697] and the polycrystal response is obtained through a two-dimensional multi-grain model in which grains are represented individually. We investigate the effect of random grain orientations, both in the plane of consideration and in three directions, and compare plane strain with plane stress conditions. It is found that the overall piezoelectric response under electric loading is not dependent only on the intra- and intergranular stresses in the plane but is also significantly affected by stresses in through-thickness direction.

X-ray diffraction study of effect of deposition conditions on α–β phase transition and stress evolution in sputter-deposited W coatings

Pure W and W–Cu–W trilayer coatings were deposited on an Fe substrate by d.c. magnetron sputtering. The α−β phase evolution, intragranular stress evolution in sputter-deposited W layer were investigated by x-ray diffraction. They are directly related to the film microstructure, density and adhesion. Therefore, control of the film stress and phase component transition is essential for its applications. The phase component transition from β-W to α-W and intragranular stress evolution from tensile to compressive strongly depend on the deposition parameters and can be induced by lowering Ar pressure and rising target power. The compressively stressed films with α-W phase have a dense microstructure and high adhesion to Fe substrate.

Intragranular Particle Residual Stress Strengthening of Al2O3–SiC Nanocomposites

Al2O3/SiC ceramic nanocomposites were fabricated from nanocrystalline Al2O3 (10 nm in diameter) and SiC (15 nm in diameter) powders, and a theoretical model of intragranular particle residual stress strengthening was investigated. The SiC nanoparticles in the Al2O3 grains create a normal compressive stress at the grain boundaries and a tangential tensile stress in the Al2O3 grains, resulting in the “strengthening” of the grain boundaries and “weakening” of the grains. The model gives a good explanation of the experimental results of the authors and others which are difficult to be explained by the existing strengthening models, i.e. the maximum strength is normally achieved at about 5 vol% of SiC particles in the Al2O3–SiC ceramic nanocomposites. According to the model, there exists an optimum amount of SiC for strengthening, below which the grain boundaries are not fully “strengthened” and the fracture is mainly intergranular, above which the grains are “weakened” too much and the fracture is mainly transgranular, and at which the fracture is a mixture of intergranular and transgranular.

Inter- and intragranular stresses in cyclically-deformed 316 stainless steel

Neutron diffraction was used to study residual stresses in cyclically-deformed 316 LN stainless steel. The tension–compression high-cycle fatigue tests were conducted in air with a frequency of 0.2 Hz. Large intergranular stresses were found to develop in the stainless steel as a result of elastic and plastic anisotropy. These intergranular stresses started to decrease when micro-cracks were initiated at the surface and vanished when the sample reached failure. Cyclic loading also led to the development of intragranular stresses, as evidenced by the broadening of the diffraction peaks. Analysis of the orientation dependence of the measured peak widths indicates that the immobile dislocations generated by fatigue deformation are mostly edge rather than screw type.

Evaluation of finite element based analysis of 3D multicrystalline aggregates plasticity: Application to crystal plasticity model identification and the study of stress and strain fields near grain boundaries

Plastic heterogeneities of hexagonal close-packed (HCP) materials are numerically investigated at the grain level. Intensive use of parallel Finite Elements computations enables us to study micro-plasticity of realistic 3D multicrystalline aggregates, including, macroscopic mechanical responses but also average responses in each grain and particularly local stress and strain fields. This paper focuses on three applications of this simulation method. The first part of this paper is devoted to a fine analysis of micro-plasticity of HCP materials. Intergranular but also intragranular stress and strain heterogeneities are described and micro-plasticity patterns are displayed throughout the 3D microstructures. A special attention is paid to the sensitivity of simulations with respect to the mesh discretization, the element interpolation and the geometrical representation of grain boundaries, in terms of macroscopic and local responses. Later, a simplified homogenization method is evaluated, regarding results of the first part. Afterwards, this method is applied with a zirconium alloy to identify a set of coefficients for a single crystal plasticity model. Finally, in order to provide critical information for intergranular damage phenomena (reported in literature for zirconium alloys), the third part provides a statistical analysis of over-stresses at grain boundaries.

The effects of grain size on the cyclic deformation behaviour of polycrystalline nickel

Abstract The present paper reviews experimental results about the effect of grain size on cyclic stress–strain ( Σ as – e pa ) behaviour of high purity (99.99%) nickel material. The effect of grain size ( d ) on cyclic stress–strain behaviour can be described using the classical Hall–Petch relationship: Σ as = Σ 0 ( e pa )+ k ( e pa ) d −1/2 . The parameters k and Σ 0 both depend on the plastic strain amplitude e pa . k increases rapidly for small plastic strains, decreases for high plastic strains and stays lower than the values obtained under tensile loading. This aspect is discussed with guidance from qualitative and quantitative transmission electron microscopy (TEM) observations and stress partitioning in terms of back stress ( X ) and effective stress ( Σ ef ). More precisely, the back stress is partitioned into intra-granular and inter-granular long-range interactions. According to TEM observations, the interpretation of a quasi-plateau in the cyclic stress–strain curve, generally associated with the occurrence of ladder structures is questionable for the smaller grain size (18 μm). The quasi-plateau seems to be associated more with a competition between inter-granular and intra-granular back stresses than with the formation of ladder structures in polycrystalline nickel.

Cyclic creep process in AISI 316L stainless steel in terms of dislocation patterns and internal stresses

In order to understand the ratchetting process in polycrystalline stainless steel, a consistent mechanical data base was provided and associated dislocation features were explored by qualitative and quantitative TEM observations. Particular attention was paid to the effect of peak stress ( σ max) and mean stress ( σ m) on the ratchet strain rate. The effect of tensile plastic strain history (peak stress) on cyclic creep was rationalized under the form of three peak stress phases ( R 0, R I and R II) in which the cyclic deformation mechanisms are different. Planar slip, during the cyclic test in phase R 0, led to a high plastic strain reversibility which inhibited cyclic creep. The cyclic creep threshold stress corresponds to a cross-slip activity promoted by a specific long-range internal stress state. Peak stresses which were higher than a threshold stress σ th equal to 230 MPa (stage R I and stage R II) induced the formation of two types of dislocation trapping, namely in dipolar walls and in polarized walls. Only the last type induced cyclic creep. Special attention was paid to the dependence of ratchetting process on the fluctuations of the intergranular and intragranular back stress and their evolution as a function of the number of cycles. Both types of internal stress fluctuations acted to enhance cyclic creep.

Influence of the thermomechanical treatment on the microplastic behaviour of a wrought Al–Zn–Mg–Cu alloy

For plastic deformations smaller than the conventional limit of 0.2% for the yield stress, the so-called microplastic behaviour of a rolled Al–Zn–Mg–Cu alloy is investigated experimentally. Tension and compression responses are compared along the rolling and the transverse directions. The alloy shows an asymmetric response in tension and compression (i.e., compressive stress minus tensile stress for a given absolute plastic strain is non-zero). Moreover, this asymmetry changes sign between the rolling and the transverse directions. The difference between tension to compression is observed to decrease as the conventional limit is approached. The influence of the heterogeneous microstructure of the alloy and the fabrication process on these asymmetries is discussed. Modelling of the material response based on a self-consistent scheme is used to estimate the internal stresses resulting from the thermomechanical treatment, and also to investigate the influence of the heterogeneous elastoplastic behaviour of two types of constitutive grains (recrystallised and unrecrystallised). For a plastic strain smaller than 0.02%, the microplastic behaviour is not well described with the adopted model since the underlying assumption of uniform stress and strain fields per phase is questionable in this initial level of plasticity. However, the model shows that the asymmetries observed at plastic strains ranging from 0.02% to 0.2% are consistent with the intragranular stresses developed during the stretching step.

Grain-size effects on tensile behavior of nickel and AISI 316L stainless steel

The aim of this work is to provide experimental results to understand the grain-size effects on tensile hardening of fcc polycrystalline materials. The contribution of grain size on hardening rate is discussed in terms of backstress (X) and effective-stress (Σ ef) evolutions in the different hardening stages. Based on this stress partition, the origin of the classical Hall-Petch relationship is clarified at the different levels of microstructural heterogeneities. If the backstresses and effective stresses verified the Hall-Petch formulation, however, the effective stress is less dependent on grain size than the backstress. The grain-size effect on short-range internal stresses (effective stress) is well explained in terms of a mean path length using classical dislocation modeling. The backstress dependence on grain size seems to be mainly the result of intergranular plastic-strain incompatibilities in relation with the formation of a grain-boundary layer in stage I. In others stages (higher plastic strain), the interactions between intergranular and intragranular long-range internal stresses have been illustrated. The degree of these interactions remains unclear.