Polycrystalline Model Research Articles

Mechanical behavior of polycrystals: Coupled in situ DIC-EBSD analysis of pure copper under tensile test

Understanding the mechanisms at the microstructure scale is of great importance for modeling the behavior of materials at different scales. To this end, digital image correlation (DIC) is an effective measurement method for evaluating the strains generated by various loading conditions. The objective of this paper is to describe the experimental setup and the use of high resolution digital image correlation (HRDIC) during in situ Scanning Electron Microscope (SEM) tests in order to provide a coupling between polycrystalline modeling and experiment in the near future. The HRDIC technique is used to evaluate the tensile behavior of a pure copper polycrystal at room temperature. Several magnitudes are investigated in order to discuss the representativeness of the results with respect to the macroscopic scale. The selected image correlation parameters are discussed regarding the ability of the technique to define inter- and intra- granular strain heterogeneities. Finally, based on EBSD analyzes, the impact of grain orientation on the mechanical behavior is discussed. The Schmid factor, calculated from a macroscopic stress, appears to be the determining factor concerning the orientation of the location bands. On the other hand, it is not sufficient to define the mean strains in the grains.

Revealing the Origin of Heterogeneous Phase Transition and Deformation Behavior in Au-Ag-Cu-Based Multicomponent Alloys

Local chemical heterogeneity of highly-concentrated multicomponent alloys has drawn much attention as it can produce novel material behaviors and remarkable properties. In Au-Ag-Cu-based multicomponent alloys, phase separation and ordering have long been recognized to correlate with grain boundaries (GBs), but there is still a lack of atomic-scale understanding of the heterogeneous phase transition and how the microstructures respond to deformation. In this paper, a joint experimental and theoretical study was conducted on a medium-entropy polycrystalline model alloy, which is a representative Au-Ag-Cu-based multicomponent alloy with important applications in fields such as photocatalyst and micro-/nano-electromechanical systems. The GB regions are observed to preferentially nucleate two-phase lamellar structures, which are softer than grain interiors featuring short-range-order and modulated morphologies. First-principles calculations suggest the GB segregation of Ag and depletion of Cu are energetically favorable, consequently creating compositions that facilitate phase separation and impede ordering. Calculations of elasticity-based mechanical properties, stacking fault and surface energies reveal the GB lamellar structures are intrinsically soft with heterogeneous deformation capabilities. Furthermore, design strategies based on GB segregation engineering and tuning the dual-phase compositions are proposed to control heterogeneities. The results provide new insights into GB segregation, phase nucleation precursor and mechanical properties of noble-metal multicomponent alloys.

A Constitutive Model for Polycrystalline U–Nb Alloy Considering Multiple Phase Transition

AbstractThis study proposes a thermomechanical constitutive model for the shape memory effect of U–12.8 at.% Nb (U–Nb) alloy. The phenomenological model uses two variables for transformation. A transitional evolution function based on dissipative force is constructed, which removes the consistency condition. This improvement leads to a natural smoothness of all transitions, without any specifically defined hardening function. In addition, hysteresis is a natural result of the same reference force being converted forward and backward, and defining two different mixing energies is not necessary. The effect of strain rate is captured in the same frame by a function of the transition coefficient. This paper designs a robust and efficient numerical algorithm for the ordinary differential equation system. The model is validated by several special load cases. The simulation results are then compared with previous experimental data in the paper.

Optimal parameter assessment of Solar Photovoltaic module equivalent circuit using a novel enhanced hybrid GWO-SCA algorithm

Solar Photovoltaic (PV) modules provide a reliable and clean electricity source that can suit various applications. Based on the quality and type of crystals, the PV modules are classified as monocrystalline, polycrystalline, and thin film. The improvements on different solar PV modules can be made efficiently with accurate mathematical models, which requires extracting its parameters. This paper suggests a novel enhanced hybrid grey wolf optimizer-sine cosine algorithm (EHGWOSCA) to extract solar PV module parameters. The recommended algorithm is validated on CEC-C06 2019 benchmark functions which contain ten standard functions. The PV module parameter extraction is performed on different kinds of PV modules, namely, monocrystalline type Shell CS6K280M, polycrystalline type Shell S75, and thin-film type Shell ST40. Two well-known models of PV modules are considered with a requirement of 5 parameters and 7 parameters extraction. The proposed algorithm is implemented by minimizing the sum of squared errors at open circuit point, short circuit point, and maximum power point (MPP). The results obtained show that in the Monocrystalline model using the proposed hybrid approach with single diode model, an error is 1.0718E−15, and it is further reduced to 1.3229E−16 with the double diode model. The proposed EHGWOSCA Error in the Polycrystalline model with double diode is 6.1594E−19, and the Thin-film model error is 2.91E−22. The effectiveness of the proposed approach is verified by comparative analysis with other methods available in the literature.

Experimental and Numerical Investigation of Energy Evolution Characteristic of Granite considering the Loading Rate Effect

In order to investigate the loading rate effect of energy evolution in granite, the indoor physical simulation test of single face fast unloading-three directions and five faces stress-vertical continuous loading under different loading rates was conducted using a new true triaxial rockbursttest system. The energy accumulation-dissipation-release characteristics in the process of rock deformation and failure were revealed. Based on the three-dimensional discrete element theory and the polycrystalline modeling technique (randomly generated Voronoi mineral grains), the entire process of rockburst inoculation-occurrence-development, as well as the energy evolution characteristics under true triaxial single face unloading conditions, were studied. The test results indicate that the energy transport and conversion of rock samples under different loading rates exhibit distinct stage characteristics. It can be divided into the initial energy accumulation stage, steady energy accumulation stage, rapid energy dissipation stage, and rapid energy release stage. With a rise in loading rate, the specimen in the process of energy accumulation is accompanied by energy dissipation, more external input energy, and elastic strain energy release amount into the kinetic energy of fragments, resulting in the rockburst phenomenon. As the loading rate increases, the elastic strain energy conversion rate (Ue/U) falls, while the dissipative energy conversion rate (Ud/U) increases. The higher the elastic strain energy conversion rate and the lower the dissipative energy conversion rate, the more serious the rockburst occurs. Numerical simulation results show that the entire process of rockburst inoculation-occurrence-development is successfully simulated using the crystal scale fine model (CSFM) considering the grain mineral composition. The ejection failure process can be divided into four stages, including grains ejection, rock spalling into plates, rock shearing into fragments, and rock fragments ejection. The relationships between the peak strength, elastic strain energy of rock samples, and loading rates are obtained, which is consistent with the laboratory test results. The high rate linear growth of kinetic energy evolution between the two inflection points can provide precursor information for rockburst prediction.

Role of orientational disorder in ZSM-22 in the adsorption of SO2

Computational studies addressing the adsorption of fluids in nanoporous materials mostly use ideal single crystal models of the adsorbent. While a few recent studies have tried to address the effects of inter-crystalline spacing on the adsorption of fluids in polycrystalline models of nanoporous materials, the effects of the orientational disorder (OD) in the polycrystalline adsorbent remain unexplored. Here we report the adsorption of SO2 – an industrially and environmentally important gas – in ZSM-22, a zeolite characterized by straight channel-like pores. The simple pore geometry of ZSM-22 helps us make polycrystalline models of the adsorbent with different degrees of OD. Using grand canonical Monte Carlo (GCMC) simulations, we obtain the adsorption isotherms of SO2 in ZSM-22 with different inter-crystalline spacings and degrees of OD. Introducing inter-crystalline space is found to enhance the adsorption capacity, with a larger inter-crystalline space leading to higher adsorption. Increasing the OD in the adsorbent is found to enhance the adsorption capacity too. However, the effects of OD become weaker when the inter-crystalline space is widened. This weakening of the effect of OD is a result of an interplay between the width of the inter-crystalline space and the strength of guest–guest interactions.

Analysis of residual stress distribution characteristics of laser surface hardening based on Voronoi model

The laser surface hardening’s parameters have a direct effect on the residual stress of the matrix. It is important to quantitatively reveal the influence degree of process parameters on the matrix residual stress for the formulation of optimal process. In this paper, a random polycrystalline model of the matrix is established based on the Voronoi method. The grain heterogeneity is introduced according to the nanoindentation results. The divided 7 different grain attributes are randomly assigned to each voronoi cell through a python script. A thermo-mechanical coupling model for the laser quenching process of SUS301L-HT stainless steel considering grain heterogeneity was established. The thermal stress field and temperature field distribution of the single laser surface hardening are calculated with different process parameters. On this basis, the BOX-Behnen Design method was used to establish a response surface model, and the response surface method was combined with the Monte Carlo sampling calculation method to calculate the sensitivity of the process parameters. The calculation results show that the analysis value D of the residual stress is a normally distributed. Laser power and laser scanning speed are the main factors affecting the average residual stress of the grain, and the effects of the two are opposite. The laser scanning speed has a greater influence on the residual stress of the matrix than the laser power.

On the interplay of anisotropy and geometry for polycrystals in single‐slip crystal plasticity

AbstractIn this paper, we investigate a variational polycrystalline model in finite crystal plasticity with one active slip system and rigid elasticity. The task is to determine inner and outer bounds on the domain of the constrained macroscopic elastoplastic energy density, or equivalently, the affine boundary values of a related inhomogeneous differential inclusion problem. A geometry‐independent Taylor inner bound, which we calculate directly, follows from considering constant‐strain solutions to a relaxed problem in combination with well‐known relaxation and convex integration results. On the other hand, we deduce outer bounds from a rank‐one compatibility condition between the affine boundary data and the microscopic strain at the boundary grains. While there are examples of polycrystals for which the two above‐mentioned bounds coincide, we present an explicit construction to prove that the Taylor bound is nonoptimal in general.

Finite Element Analysis of AA 6016-T4 Sheet Metal Forming Operations Using a New Polycrystalline Model

A major challenge in forming polycrystalline aluminum alloy sheets is their strong plastic anisotropy, namely the flow stresses and plastic strains depend on the loading direction. This plastic anisotropy is due to the anisotropy of the constituent crystals and the preferred orientations that they assume in the polycrystalline material i.e. crystallographic texture. Recently, in [1] we developed a single-crystal yield criterion that involves the correct number of anisotropy coefficients such as to satisfy the intrinsic symmetries of the constituent crystals and the condition of yielding insensitivity to hydrostatic pressure. This single-crystal criterion is defined for any stress state. It is shown that a polycrystalline model that uses this single-crystal criterion in conjunction with appropriate homogenization procedures leads to an improved prediction of the plastic anisotropy in macroscopic properties under uniaxial tension and shear loadings for polycrystalline aluminum alloy 6016-T4. Moreover, results of FE simulations of cup forming operations demonstrate the predictive capabilities of this polycrystalline model.

Damage Evolution Simulations via a Coupled Crystal Plasticity and Cohesive Zone Model for Additively Manufactured Austenitic SS 316L DED Components

This study presents a microstructural model applicable to additively manufactured (AM) austenitic SS 316L components fabricated via a direct energy deposition (DED) process. The model is primarily intended to give an understanding of the effect of microscale and mesoscale features, such as grains and melt pool sizes, on the mechanical properties of manufactured components. Based on experimental observations, initial assumptions for the numerical model regarding grain size and melt pool dimensions were considered. Experimental observations based on miniature-sized 316L stainless steel DED-fabricated samples were carried out to shed light on the deformation mechanism of FCC materials at the grain scale. Furthermore, the dependency of latent strain hardening parameters based on the Bassani–Wu hardening model for a single crystal scale is investigated, where the Voronoi tessellation method and probability theory are utilized for the definition of the grain distribution. A hierarchical polycrystalline modeling methodology based on a representative volume element (RVE) with the realistic impact of grain boundaries was adopted for fracture assessment of the AM parts. To qualify the validity of process–structure–property relationships, cohesive zone damage surfaces were used between melt pool boundaries as the predefined initial cracks and the performance of the model is validated based on the experimental observations.

Multiscale discrete dislocation dynamics study of gradient nano-grained materials

Gradient nano-grained (GNG) metals have shown a better strength-ductility combination compared to their homogeneous counterparts. In this paper, the mechanical properties and the related deformation mechanisms of GNG aluminum were investigated using three-dimensional multiscale discrete dislocation dynamics (DDD). GNG polycrystalline models and uniform nano-grained (UNG) counterparts were constructed within a multiscale DDD framework. A dislocation-penetrable grain boundary model based on a coarse-graining approach was adopted to handle the interaction between dislocations and grain boundaries. The simulation results show that the yield stress and strain hardening of the GNG sample is larger than the value calculated by the rule of mixtures, indicating a synergetic strengthening induced by the gradient structure. The associated microstructure evolution demonstrates that dislocations initially activate and glide in the larger grains and then gradually propagate into the smaller grains in the GNG sample, this sequential yielding of layers with different grain sizes generates stress and strain gradients, which is accommodated by geometrically necessary dislocations (GNDs). Moreover, we found that the Bauschinger effect in GNG sample is stronger than those in component UNG samples, suggesting a significant back stress strengthening in the GNG sample during plastic deformation. Finally, a theoretical model is established which successfully describes the Bauschinger effect of GNG and corresponding UNG samples according to the features of dislocation evolution upon unloading. The present study provides insights into the outstanding mechanical property of GNG metals from the view of dislocation dynamics at the submicron scale and offers theoretical guidance for designing strong-and-ductile metals.

Numerical simulation and parameter sensitivity analysis of multi-particle deposition behavior in HVAF spraying

Particle deposition behavior is critical to improve coating quality. Based on the Coupled Eulerian and Lagrangian (CEL) method, a three-dimensional multi-particle random deposition model was established, and grain inhomogeneity was introduced into the TC18 substrate. A polycrystalline model of the microstructure for the sprayed substrate was established by the Voronoi method. The evolution of the temperature, strain and stress fields during particle deposition was revealed, and the formation mechanism of pore defects was also analyzed. The results show that the overall strain of small particles is large, the core strain of large particles is small, and the edge strain is significant. The stress value near the large particles in the coating is large, while the stress at the edge of the coating is relatively small. The stress distribution of the TC18 substrate is similar to the uneven random geometric distribution of grains. On this basis, the response surface model of coating characteristics was established, the influence of process parameters on coating characteristics was analyzed, and the sensitivity of process parameters is determined. This research can provide a basis and guidance for engineering applications in related fields.

Micro-damage evolution under intensive dynamic loading and its influence on constitutive and state equations for nanocrystalline NiTi alloy through molecular dynamics

In this study, to comprehensively reveal the damage mechanisms of NiTi alloys, molecular dynamics (MD) simulations were applied to examine the void evolution process under uniaxial and triaxial intensive dynamic loading. A single-crystal model was first used in the MD simulations. The calculation results revealed that the single-crystal NiTi model exhibited a similar damage response to brittle fracture. The corresponding damage mechanism was the rapid growth and coalescence of voids inside the material. Meanwhile, the defect influence was also examined for the single-crystal model, and the reduction effect of the ultimate stress value due to the stress concentration was analyzed quantitatively by the MD simulations. In addition, a polycrystalline model of NiTi was used in the MD simulations. Compared with the single-crystal model, the polycrystalline model showed an evident plastic stage under uniaxial loading due to dislocation slip. The MD simulation proved that the dislocations accumulated on the grain boundaries, which led to a stress concentration effect on the grain boundaries and sequentially resulted in void generation. However, the propagation and coalescence of voids were hindered by the grain interactions, which resulted in a ductile damage behavior inside the material. Based on this mechanism, the grain size influence was also studied in the MD simulations. It was discovered that the grain size effect in the damage stage resulted in a damage ductility enhancement with the decrease in the average grain size value. Finally, based on the relationships between the stress-strain curve, void fraction, and damage behavior, novel constitutive and state equations were proposed with damage terms to consider the void evolution process during the damage stage. The prediction results showed good agreement with the MD simulation data.

Transmittance predictions for transparent alumina ceramics based on the complete grain size distribution or a single mean grain size replacing the whole distribution

A simple method, based on the equivalent composite model or the dense polycrystalline model, is proposed for predicting the in-line transmittance in ceramics with a grain size distribution of birefringent crystallites. It is shown that the transmittance predictions based on the Rayleigh-Gans approximation are indistinguishable from those based on Mie theory, so that the latter can be replaced by the former. Based on normal distributions of different position and width it is shown that size distributions with smaller mean sizes lead to higher transmittance, whereas the effect of the distribution width on the transmittance is comparatively weak (with the narrowest distribution being the most favorable for high transmittance). The key result of this paper is the fact that for the distributions investigated (normal and log-normal) the transmittance prediction based the whole grain size distribution can be replaced by a transmittance prediction based on the geometric mean of the intensity-weighted distribution.

Dynamic response of polycrystalline high energetic systems: Constitutive modeling and application to impact

This paper presents a new polycrystalline model and Lagrangian computational framework for describing the large-scale thermo-mechanical response of energetic materials under dynamic loadings. In our multi-scale computational polycrystalline framework, at the grain level, the elastic response is modeled using an anisotropic Hooke's law, while the plastic behavior is described with a recently developed quadratic anisotropic single-crystal model that accounts for the intrinsic symmetries associated with the lattice of the constituent crystals. The orientation, plastic strains, and stresses in the individual grains are continuously updated, so the predicted macroscopic scale response takes into account the evolution of the thermo-mechanical state at the meso-scale. First, we illustrate the polycrystalline model capabilities by simulating the response of a pentaerythritol tetranitrate (PETN) polycrystalline high energetic system when subjected to dynamic compression. It is shown that there are strong differences in temperature and stresses between the constituent grains, depending on their relative orientation with respect to the wave direction. Moreover, it is shown that the rise in temperature in certain grains may be well in excess of the macroscopic value. We also present 3D finite element simulations of the impact of a penetrator made of a high-strength steel containing the same polycrystalline PETN system. Insights into the complex interactions between the energetic system and the metallic casing material are provided. Furthermore, it is shown that if the crystallinity is neglected, the predicted temperature rise and the extent of the zone of maximum heating in the energetic system during the impact event differ noticeably from those obtained with our polycrystalline model, which accounts for the crystallinity of the PETN material and the anisotropy in the plastic flow of its constituent crystals.

Modeling of flux-dependent fluence effect on in-reactor deformation in Zr-alloy tubes

Zr-alloy tubes in reactors suffer from harsh thermal-mechanical-irradiation coupling conditions. Abundant modeling efforts have been devoted to predicting in-reactor deformation but the flux-dependent fluence effect was rarely considered. In this work, a polycrystalline model which considers this effect is proposed, by introducing a flux-dependent factor α which characterizes the trend that higher flux results in more accumulated irradiation defects and therefore higher obstruction on dislocation movement. With this model, the flux-dependent anisotropic deformation behaviors as a function of fluence can be well captured. Particularly, a linear relationship between α and flux is revealed from the experimental results in CANDU reactors.

Recursive grain remapping scheme for phase‐field models of additive manufacturing

AbstractThe phase‐field method is an attractive tool in modeling microstructural evolution due to rapid solidification under additive manufacturing conditions, but typical polycrystalline models are prone to grain coalescence. Grain tracking and remapping schemes can eliminate artificial coalescence and increase the number of grains and crystallographic orientations that may be considered in a simulation, but previous tracking and remapping schemes may not efficiently capture the complex grain morphologies that form during additive manufacturing. A new recursive scheme is derived from a binary tree of axis‐aligned bounding boxes that can efficiently represent columnar and irregularly shaped grains. We demonstrate the power of this approach by simulating microstructures with hundreds to thousands of grains and quantify the reduction in the number of order parameters required to represent the microstructure. The new scheme leads to orders of magnitude fewer computational resources as compared to the naïve paradigm of one grain per order parameter, and also offers a substantial improvement over algorithms derived from bounding spheres.

Polycrystalline simulations of in-reactor deformation of recrystallized Zircaloy-4 tubes: Fast Fourier Transform computations and mean-field self-consistent model

Fuel cladding and structural components made of zirconium alloys, used in light and heavy water nuclear reactors, exhibit, during normal operation, significant in-reactor deformation. Fast Fourier Transform (FFT) simulations have been conducted on large grain aggregates to simulate the in-reactor behavior of recrystallized Zircaloy-4. Original constitutive equations have been proposed to account, at the microscopic scale, for thermal creep, irradiation creep and irradiation induced growth. The evolution of irradiation defects with irradiation is taken into account, especially to deduce the local growth strain. A good description of the in-reactor behavior is obtained with irradiation defects evolution consistent with Transmission Electron Microscopy observations. The FFT simulations are compared to a self-consistent model. A good agreement is obtained when the behavior is linear (irradiation creep and growth) while the nonlinear response (thermal creep) is underestimated by the self-consistent model. The FFT simulations are also compared to the lower-bound model which neglects the interactions between grains. The lower-bound model underestimates the growth strain proving the importance of using an accurate polycrystalline model to predict the growth strain from the knowledge of the irradiation defect evolution.

A molecular dynamics study on the cyclic plastic deformation mechanism of Al–Mg alloys

The deformation mechanism and hardening law of single-crystal and polycrystalline Al–Mg alloy materials during the cyclic loading deformation process of different paths are studied herein according to the principle of molecular dynamics. An analysis of the single-crystal simulation results indicates that the Bauschinger effect decreases with the increase of strain. The cyclic loading leads to dislocation locking and other obstacles, which, in turn, lead to hardening of the material. After that, the force generated by the accumulated strain moves the dislocation obstacle and causes the material to soften. Based on the Voronoi polygon method, polycrystalline models with different grain sizes are established, and the plastic deformation mechanism of these models under cyclic loading is analyzed. The results show that the critical grain size of the direct and inverse Hall–Petch relationship exists in the Al–Mg alloy. When the grain size is below this value, grain rotation and grain boundary sliding become the main deformation mechanisms of the small polycrystalline grains. Dislocation blockage remains an important factor in the hardening of polycrystalline materials, while the aggregation of solute atoms at the grain boundaries is another contributing factor.

Numerical Investigation into the Influence of Grain Orientation Distribution on the Local and Global Elastic-Plastic Behaviour of Polycrystalline Nickel-Based Superalloy INC-738 LC

Polycrystalline nickel-based superalloys tend to have large grains within component areas where high loads are dominant during operation. Due to these large grains, caused by the manufacturing and cooling process, the orientation of each grain becomes highly important, since it influences the elastic and plastic behaviour of the material. With the usage of the open source codes NEPER and FEPX, polycrystalline models of Inconel 738 LC were generated and their elastic and crystal plasticity behaviour simulated in dependence of different orientation distributions under uniaxial loading. Orientation distributions close to the [100] direction showed the lowest Young’s moduli as well as the highest elastic strains before yielding, as expected. Orientations close to the [5¯89] direction, showed the lowest elastic strains and therefore first plastic deformation under strain loading due to the highest shear stress in the slip systems caused by the interaction of Young’s modulus and the Schmid factor.