Nickel Polycrystals Research Articles

Short crack propagation near coherent twin boundaries in nickel-based superalloy

Short crack propagation near a coherent twin boundary in polycrystal nickel alloy is investigated with 3D crystal plasticity extended finite element modelling (CP-XFEM), utilising reconstructed experimentally characterised microstructures and crack path observations. Short 3D cracks at coherent twin boundaries are shown to grow on parallel (111) slip planes at very high rate so as to be an intrinsic part of the nucleation process. This is found to occur predominantly because of the stress states established by twin/parent constraint driven by the local elastic anisotropy. If elastic isotropy is modelled, crack growth is found to be non-planar and inclined to the twin boundary. The twin/parent twist angle is also found to influence local stress state, such that the actual 60° twist angle gives rise to the highest local stresses, preferential crack nucleation and rapid growth parallel to the twin boundary, and the deviations from 60° change the crack morphology and rate of growth.

Influence of tessellation morphology on ultrasonic scattering.

Material properties, such as hardness, yield strength, and ductility, depend on the microstructure of the material. If the microstructural organization can be quantified nondestructively, for example, with ultrasonic scattering techniques, then it may be possible to predict the mechanical performance of a component. Three-dimensional digital microstructures have been increasingly used to investigate the scattering of mechanical waves within a numerical framework. These synthetic microstructures can be generated using different tessellation algorithms that result in different grain shapes. In this study, the variation of ultrasonic scattering is calculated for microstructures of different morphologies for a nickel polycrystal. The ultrasonic properties are calculated for the Voronoi, Laguerre tessellations, and voxel-based synthetic microstructures created by DREAM.3D. The results show that the differences in the two-point statistics and ultrasonic attenuation for different morphologies become more significant at wider size distributions and higher frequencies.

The grain size effect on strain hardening and necking instability revisited from the dislocation density evolution approach

Revisiting the classical topic of the strain hardening behaviour from a perspective of the analytical model based on the evolution of dislocation density with strain, we extended the capacity of the single internal variable model towards predicting necking instability and re-examined the grain size dependence of the flow stress. An excellent agreement is observed between the model predictions of the necking strain and stress and the results of tensile testing of nickel polycrystals with grain sizes varied from sub-micrometres to hundred micrometres. The pivotal significance of the dynamic recovery in the occurrence of necking has been analysed and emphasised in the context of the discussion on the effect of grain size on flow stress. The most interesting corollary of the analysis made is that not only the simple modelling of the dislocation density evolution, which can be traced back from the very early stage of plastic flow in materials with different grain sizes, can be used for realistic approximation of the stress-strain behaviour during homogeneous deformation under constant plastic strain rate, but also for predicting the onset of necking instability with high confidence.

Effect of crystal structure of nickel substrates on interfacial behaviors in Sn/Ni soldered joints

The effects of crystal structure of Nickel on the interfacial phase and growth mechanism were clarified in Sn/Ni soldered joints by using polycrystal nickel and single crystal nickel substrate. It was found that the intermetallic compounds (IMCs) phase, Ni3Sn4, was formed at the interface of Sn/polycrystal nickel joints; while, it changed into NiSn4 when using single crystal nickel substrate. At the following thermal aging process, Ni3Sn4 and NiSn4 exhibited different behaviors: Ni3Sn4 grew faster than NiSn4 showing a much thicker layer. Kinetics analysis indicated that different diffusion mechanisms governed the IMCs layer growth, namely Ni3Sn4 was controlled by diffusion of the reaction elements, whereas NiSn4 was controlled by reaction rate.

Investigating the relationship between grain orientation and surface height changes in nickel polycrystals under tensile plastic deformation

This paper investigates the effect of the grain orientation on the surface roughening of nickel polycrystals undergoing plastic tensile deformation. Both experimental and simulation work was carried out. In the experiments, we measured the surface topography at different strain levels. The surface topography images were analyzed to classify individual grains as either rising or sinking. In simulations, we utilized a Crystal Plasticity Finite Element model that embeds a grain in an isotropic sample. This arrangement ensures that only the grain orientation of the embedded grain influences the grain surface topography. The average surface height of the grain was then calculated to classify its behavior to be rising or sinking. Both experiment and simulation results show that the grains with the loading direction close to the 〈001〉 and 〈111〉 lattice orientations tend to sink. For the rest of the grain orientations, the loading direction orientation, and thus the Schmid or Taylor factor, cannot uniquely determine whether the grain rises or sinks. A parametric study revealed that a grain's average surface height is contributed by the plastic deformation of the most stressed slip systems along the direction normal to the surface.

Low-Cycle Fatigue Properties of ECAPed and Heat-Treated Nickel Polycrystals

Low-Cycle Fatigue Properties of ECAPed and Heat-Treated Nickel Polycrystals

Molecular Dynamics Simulation of Crack Propagation in Nanoscale Polycrystal Nickel Based on Different Strain Rates

Based on the strain rates of 2 × 108 s−1 and 2 × 1010 s−1, molecular dynamics simulation was conducted so as to study mechanisms of crack propagation in nanoscale polycrystal nickel. The strain rate has an important effect on the mechanism of crack propagation in nanoscale polycrystal nickel. In the case of a higher strain rate, local non-3D-crystalline atoms are induced and Lomer-Cottrell locks are formed, which plays a critical role in crack initiation and propagation. Orientation difference between adjacent grains leads to the slipping of dislocations along the different directions, which results in the initiation of a void near the triple junction of grain boundaries and further contributes to accelerating the crack propagation.

Kocks-Mecking analysis of the size effects on the mechanical behavior of nickel polycrystals

In this article, the Kocks-Mecking formalism is employed to analyze the grain size and thickness effects which modify the mechanical behavior of nickel polycrystals. To this aim, a two-internal variable Kocks-Mecking model, based on the evolution of forest and mobile dislocation densities, is numerically optimized using a wide experimental database of tensile curves of nickel polycrystals already published. The original model has been modified to take into account the grain size contribution to strain hardening in addition to the conventional dislocation production and annihilation terms. Using this improved model, the tensile curves of samples with different grain sizes, thicknesses and number of grains across the thickness are well reproduced. By means of an analysis of the model parameters, i.e. dislocation mean free path, cross-slip rate and dislocation densities, the strain mechanisms of nickel polycrystals are investigated as a function of their microstructural characteristics. For specimens with few grains across the thickness, the rate of dislocation annihilation is increased which, in turn, decreases the forest dislocation density and stress level. These results show, first, that the well-known Kocks-Mecking model is able to reproduce size effect and, second, confirm previous assumptions about the mechanical behavior of miniaturized samples. Eventually, the modeling of the mechanical behavior for samples concerned by miniaturization taking into account the surface effect contribution is discussed.

Crack nucleation using combined crystal plasticity modelling, high-resolution digital image correlation and high-resolution electron backscatter diffraction in a superalloy containing non-metallic inclusions under fatigue.

A crystal plasticity finite-element model, which explicitly and directly represents the complex microstructures of a non-metallic agglomerate inclusion within polycrystal nickel alloy, has been developed to study the mechanistic basis of fatigue crack nucleation. The methodology is to use the crystal plasticity model in conjunction with direct measurement at the microscale using high (angular) resolution-electron backscatter diffraction (HR-EBSD) and high (spatial) resolution-digital image correlation (HR-DIC) strain measurement techniques. Experimentally, this sample has been subjected to heat treatment leading to the establishment of residual (elastic) strains local to the agglomerate and subsequently loaded under conditions of low cyclic fatigue. The full thermal and mechanical loading history was reproduced within the model. HR-EBSD and HR-DIC elastic and total strain measurements demonstrate qualitative and quantitative agreement with crystal plasticity results. Crack nucleation by interfacial decohesion at the nickel matrix/agglomerate inclusion boundaries is observed experimentally, and systematic modelling studies enable the mechanistic basis of the nucleation to be established. A number of fatigue crack nucleation indicators are also assessed against the experimental results. Decohesion was found to be driven by interface tensile normal stress alone, and the interfacial strength was determined to be in the range of 1270–1480 MPa.

Effect of stress path on the miniaturization size effect for nickel polycrystals

The mechanical behavior of metallic materials deeply depends on the size of samples. For specimen dimensions decreasing from a few millimeters to a few micrometers, the general observed trend is a softening of the mechanical behavior in tension which affects the stress level and the strain hardening. The objective of this work is to provide new experimental results in order to analyze the miniaturization size effects for various stress paths without strain gradients across the thickness of the samples. To this aim, experimental tensile tests, large tensile tests and shear tests have been performed on Ni sheets with various grain sizes. Results show that the miniaturization softening is affected by triaxiality, the larger is this parameter, the lower is the mechanical softening. These features seem to be linked to surface effects which are larger for low triaxiality stress paths. From an industrial point of view, it is hence possible to improve the forming of microparts using suitable stress paths.

Size effect on flow stress in uniaxial compression of pure nickel cylinders with a few grains across thickness

Uniaxial compression tests were carried out on pure nickel polycrystals with constant thickness (t) of 1.0mm and various grain sizes (d). Experimental results show that flow stress does not decrease with grain size continuously according to Hall–Petch law. For specimens with fewer grains across the thickness (t/d less than about 9), the Hall–Petch law is not valid anymore and even an inverse Hall–Petch effect occurs as the t/d ratio decreases from 6.2 to 3.5. The size effects on flow stress were analyzed considering boundary conditions, including free surfaces and constrained external boundaries. Then a model considering both free surface weakening and external boundary strengthening effects was proposed. The competition of free surface weakening and external boundary strengthening effects results in the flow stress size effects in micro-compression. There is a good agreement between the experimental and analytical results.

Diffraction post-processing of 3D dislocation dynamics simulations for direct comparison with micro-beam Laue experiments

We present a method of computing lattice rotations and elastic strains due to 3D dislocation structures discretised into straight segments. Combined with ray-tracing, it enables virtual scattering experiments where X-ray diffraction patterns that would arise from such dislocation structures are simulated. We demonstrate the diffraction post-processing of a Frank–Read source simulated using the ParaDiS discrete dislocation dynamics code. This simulation is compared to experimental synchrotron X-ray micro-beam Laue diffraction measurements of a single grain within a deformed nickel polycrystal. The simulated pattern captures the experimentally observed anisotropic broadening of Laue reflections and illustrates that heterogeneous and anisotropic lattice (re)orientation effects dominate the peak shape.

Lattice strain evolution in a high volume fraction polycrystal nickel superalloy

Lattice strain evolution is measured by neutron diffractrometry during tensile testing of a high volume fraction polycrystal nickel superalloy. The intergranular strains reveal anisotropic deformation, with the {2 0 0} plane being least stiff and the {1 1 1} being the stiffest. Initial plasticity is due to yielding of the {2 2 0}. Deconvolution of the {2 0 0} and {2 2 0} doublets reveals co-deformation of γ and γ ′ phases during plasticity. Comparisons are drawn with low and medium volume fraction superalloys.

Micromechanical modelling of the cyclic stress–strain behaviour of nickel polycrystals

A crystalline elastoplasticity model is proposed to describe the cyclic behaviour of face-centred cubic crystals. It is based on many experimental observations correlating the observed dislocation structures with the orientations of corresponding crystals. The model distinguishes between two families of crystals. The first family gathers crystals for which the tension–compression loading axis is located in the centre of the standard stereographic triangle. These crystals, in which bundle and/or slip band dislocation structures are usually observed, are subjected to single slip deformation. The second family gathers crystals in which labyrinths or wall dislocation structures develop. These crystals are subjected to multiple slip deformation. Crystalline plasticity parameters are adjusted using only the single crystal cyclic stress strain curves measured for one orientation of each of the two families. The relevance of the model is evaluated through finite elements calculations of the uniaxial cyclic deformation of texture-free nickel polycrystals at room temperature. The macroscopic predictions are in reasonable agreement with experimental data concerning both the cyclic stress–strain curve and the hysteresis loops provided either large grain sizes or intermediate to high plastic strains are considered. By construction, the modelling is unable to predict grain size effect observed at low plastic strain. The distributions of the mean grain plastic strains become narrower as the macroscopic plastic strain amplitude increases, which appears consistent with the large scattering in high-cycle fatigue lifetimes usually observed. On the contrary, the distributions of mean grain axial stresses get broader, in agreement with neutron and X-ray diffraction measurement values published in the literature. The influence of the material parameters is then discussed. Finally, the cumulative probability curves of the number of cycles to fatigue microcrack nucleation are deduced and discussed with respect to scattering mentioned previously.

Finite element analysis of the free surface effects on the mechanical behavior of thin nickel polycrystals

The miniaturization of metallic samples has been proved to deeply affect their mechanical properties leading to a softening or a hardening effect depending on the order of the dimension reduction. The objective of this work is to provide new numerical results which explain the softening mechanisms on the mechanical behavior for nickel polycrystals which have been experimentally characterized by the authors in a previous published paper ( Keller et al., 2011). Based on a strain gradient crystalline plasticity model identified for nickel, simulations of tensile tests were performed for samples with different thicknesses and grain sizes. The simulations correctly reproduce the softening effect linked to a decrease in the thickness and in the number of grains across the thickness. The analysis of the plasticity mechanisms shows that the softening is due to surface effects which are discussed in terms of grain orientations, dislocation mean free path and long-range back-stress. The model also predicts a hardening mechanism for further dimension reduction if the samples have only grain boundaries perpendicular to the tensile direction. In this case, the modification of the mechanical behavior is due to strain gradients formation.

Analysis of the internal structure and lattice (mis)orientation in individual grains of deformed CP nickel polycrystals by synchrotron X-ray micro-diffraction and microscopy

Monotonic and cyclic loading of polycrystals causes a complex evolution of the dislocation structure and internal stresses. These phenomena were studied in sheet samples of commercially pure (CP) Ni in heat-treated (large-grained) states. Various microscopy tools were used, namely, scanning electron microscopy (SEM) with electron back-scattered diffraction (EBSD) to image the surface grain structure; Focused Ion Beam (FIB) with channelling contrast to visualise the through-thickness grain arrangement; and synchrotron scanning transmission X-ray microscopy (STXM) to obtain absorption-contrast images. In order to investigate the internal defects and lattice distortion caused by them, synchrotron X-ray diffraction was used in a variety of modes. Reciprocal space mapping (RSM) was used to quantify the amount of lattice re-orientation (rotation) due to plastic deformation. Micro-beam Laue diffraction was used to obtain 2D images containing multiple reflections that undergo “streaking” due to plastic deformation. The combination of reciprocal space mapping and Laue micro-diffraction provided improved insight into the deformation processes within individual grains during plastic deformation. The results are interpreted and discussed in conjunction with dislocation dynamics and finite element modelling of plastic deformation by crystal slip.

Techniques and Applications of the Simulated Pattern Adaptation of Wilkinson’s Method for Advanced Microstructure Analysis and Characterization of Plastic Deformation

Electron Backscatter Diffraction (EBSD) based Orientation Imaging Microscopy (OIM) is used routinely at ~500 materials laboratories worldwide for the characterization and development of diverse crystalline materials. Statistically significant data sets (~107 individual EBSD measurements) can be collected and analyzed within time periods of acceptable beam stability (~105s). However, limitations in angular and spatial resolution have motivated a continued search for more robust EBSD-based methods. Herein is a gathered presentation of advanced techniques in use, intended as a guide to researchers in selecting the most appropriate method for their work. Wilkinson’s method has been shown to increase angular resolution nearly two orders of magnitude to ±0.006°, facilitating measurement of elastic strain, lattice curvature, and dislocation density. A simulated pattern adaptation of Wilkinson’s method extends these measurement capabilities to polycrystalline materials, by avoiding the need for an experimental strain free reference pattern. The angular resolution limit obtained is ~0.04°. Accurate pattern center calibration, essential to the high resolution methods, is accomplished by parallelization of band edges projected onto a sphere centered at the interaction volume. FFT powered cross-correlation functions improve the spatial resolution near grain boundaries and correct for measurement inaccuracies induced by overlapping patterns. To corroborate these claims, exemplary results taken from a wedge-indented nickel single crystal, cold-worked copper polycrystal, and rolled nickel polycrystal are shown.

Intrinsic Effects due to the Reduction of Thickness on the Mechanical Behavior of Nickel Polycrystals

Uniaxial tensile tests were performed on high-purity nickel polycrystals with thicknesses (t) ranging from 12.5 to 3200 μm. The grain size (d) of each sample was set to a value close to 100 μm in order to avoid grain size effects. Experimental results highlight the intrinsic effect of the thickness on the mechanical properties of nickel. For plastic strains higher than 0.01, a strong softening of the flow stress is clearly observed when the t/d ratio decreases from four to one. This critical range is independent of the plastic strain. Transmission electron microscopy (TEM) investigations of dislocation structures were carried out in core and surface regions of samples plastically strained in the second hardening stage. It is shown that the mean dislocation cell diameter obtains values two or three times higher near free surfaces than in core areas for specimens with t/d ratios lying at a range of 1 to 4. This observation can be interpreted in terms of an increase in the mean free path of mobile dislocations in the second hardening stage. The transition between polycrystal and single-crystal behavior for nickel with constant grain size and various thicknesses is, therefore, an intrinsic effect related to progressively stronger surface softening effects.

Parallelized hybrid Monte Carlo simulation of stress-induced texture evolution

A parallelized hybrid Monte Carlo (HMC) methodology is devised to quantify the microstructural evolution of polycrystalline material under elastic loading. The approach combines a time explicit material point method (MPM) for the mechanical stresses with a calibrated Monte Carlo (cMC) model for grain boundary kinetics. The computed elastic stress generates an additional driving force for grain boundary migration. The paradigm is developed, tested, and subsequently used to quantify the effect of elastic stress on the evolution of texture in nickel polycrystals. As expected, elastic loading favors grains which appear softer with respect to the loading direction. The rate of texture evolution is also quantified, and an internal variable rate equation is constructed which predicts the time evolution of the distribution of orientations.

The effect of microstructural representation on simulations of microplastic ratcheting

This paper assesses the sensitivity of cyclic plasticity to microstructure morphology by examining and comparing the microplastic ratcheting behavior of different idealized microstructures (square, hexagonal, tessellated, and digitized from experimental data). This analysis demonstrates the sensitivity of computational accuracy to the various approximations in microstructural representation. The methodology used to perform this study relies on a coupling between microstructural characterization, mechanical testing and numerical simulations to investigate the influence of the microstructure on the purely tensile uniaxial microplastic ratcheting behavior of pure nickel polycrystals. The morphology and deformation behavior of polycrystals were characterized using electron back-scatter diffraction (EBSD), while a finite element model (FEM) of crystal plasticity was used in a computational framework. The predicted cyclic behavior is compared to experimental results both at the macroscopic and microstructural scales. The stress–strain response is less sensitive to the details of the microstructural representation than might be expected with all representations displaying similar macroscopic constitutive response. However, the details of the plastic strain distribution at the microstructural scale and the related estimations of damage mechanics vary substantially from one microstructural representation to another.