Grain Boundary Affected Zone Research Articles

Crystal plasticity framework related to size effect: From single crystal parameters to polycrystalline mechanical properties

Size effect has a significant influence on the accuracy of two key factors of parameters and models in crystal plasticity simulation. This study introduces a parameter identification method that considers the indentation size effect, determining the initial slip resistance of IN625 alloy. Based on the identified parameters and utilizing the integral point traversal method, a grain boundary affected zone (GBAZ), whose strength field related to the distance to the grain boundary (GB) is introduced into the polycrystalline microstructure to represent the hindering effect of GBs on dislocations. This method effectively predicts the Hall-Petch effect and strain hardening behavior of IN625 alloy. The research reveals that dislocation pile-ups primarily concentrate in small grain clusters within the material. In fine-grained microstructures, a large volume fraction of GBs promotes dislocation pile-ups, reducing the mean free path of dislocations, leading to an increase in dislocation multiplication rate, and consequently, enhancing the strain hardening rate. An increase in GBAZ thickness results in a large stress level within the material, accompanied by a decrease in the homogeneity of stress distribution. However, the sensitivity of strain to GBAZ thickness is found to be low. The method proposed in this work holds significant applicative relevance in parameter calibration and prediction the mechanical properties of polycrystalline materials.

Molecular dynamics study on the mechanical properties of nanocrystalline Ni-W alloys with bimodal structure

In order to study the effects of coarse grain size and Ni content on the mechanical properties, the molecular dynamics (MD) simulation of nanocrystalline (NC) Ni-W alloys with bimodal structure is carried out. The bimodal NC Ni-W alloys samples are established by embedding coarse grain into the fine grain matrix. The solute Ni atoms in the alloys are segregated in the grain boundary affected zone (GBAZ) through severe plastic deformation (SPD). The uniaxial tensile simulation of the samples shows that the coarse grain size and Ni content have obvious effects on the mechanical properties of bimodal NC Ni-W alloys. The dislocation activities and deformation mechanism of the NC Ni-W alloys are discussed in detail by observing the atomic configurations and strain evolutions diagrams obtained by MD simulation. At the same time, the phenomenon of Hall-Petch relationship and inverse Hall-Petch relationship is also observed in the research process.

Structural modelling and quantitative analysis of mechanical gradient in CNT/Al composites

Carbon nanotube-reinforced aluminium normally considered to be composed of Carbon nanotube (CNT) free grain interior (GI) and CNT containing grain boundary affected zone (GBAZ). Research works showed that the property of GI varies with the distance from the boundary. To better understand the influence of this mechanical heterogeneity, we introduced a transition zone (TZ) to emphasise the mechanical heterogeneity of the GI. A dislocation-based plastic strain constitutive model was used to analyse the mechanical response, and the simulation results fit well with the experimental result. Moreover, the TZ thickness with a large simulation influence was found, and its strengthening mechanism, the influence of TZ thickness on the macroscopic mechanical response, geometrically necessary dislocation distribution were discussed in this study.

Strengthening effect of rhenium on different substitution positions of tungsten nanofilm at high temperature: DFT and molecular dynamics simulation

Tungsten-rhenium (W-Re) alloys have excellent high-temperature properties due to the solution strengthening of Re. However, the best strengthening position of Re in W-Re alloy at high temperature is not clear. Therefore, the effects of Re on the high-temperature properties of nano-polycrystalline W-Re film were carried out by using molecular dynamics (MD) simulation and density functional theory (DFT). Our calculated results show that Re atoms at all doping positions can increase the strength and plasticity of the W matrix, the yield strength increased from 18.81 GPa to a maximum of 22.14 GPa, and the yield strain increased from 4.06% to a maximum of 5.46%, because the deformation of the GBAZ increased, resulting in higher plastic hardening and Re changes the directionality of valence electron transfer of W atoms. Among all enhancement sites, the grain boundary affected zone (GBAZ) solid solution (Re atoms distribute in the GBAZ, and there is no Re atom in the grain interior) has the best effect on the yield strength, but based on such model when Re atoms’ amount in the grain interior (GI) increased, the yield strength decreased, and the yield strain slightly improved. It is because a contraction force toward the GI is generated when Re dissolves in it, which weakens the strengthening effect of GBAZ solid solution on GBs. In contrast, the GB strengthening energy increases while the bond length at the GBs decreases when more Re atoms dissolve in the GBAZ. Furthermore, the voids in GBs are significantly reduced, and more voids can be held in GBs during the tensile process. The study is helpful to understand the strengthening mechanism of W-Re alloys.

A composite theoretical model for the thermal conductivity of nanocrystalline materials

In order to study the thermal conductivity of nanocrystalline (NC) materials, a two-phase composite model consisting of grain interior (GI) regarded as an ordered crystal phase and plastically softer grain boundary-affected zone (GBAZ) phase was presented. The effects of GI and GBAZ on thermal conduction were considered, respectively. In this work, time independent Schrodinger’s wave equation (TISWE) was used to study the carriers’ transmission in a crystal particle, through which we can get the thermal conductivity of the GBAZ. The thermal conductivity of GI was calculated based on a kinetic theory. The whole effective grain thermal conductivity was simulated by a modified formula for composite materials. The results showed that as the grain size decreases to 80 nm, it has a strong size effect, and the thermal conductivity decreases with the decreasing of grain size.

A phenomenological variational multiscale constitutive model for intergranular failure in nanocrystalline materials

We present a variational multiscale constitutive model that accounts for intergranular failure in nanocrystalline fcc metals due to void growth and coalescence in the grain boundary region. Following previous work by the authors, a nanocrystalline material is modeled as a two-phase material consisting of a grain interior phase and a grain boundary affected zone (GBAZ). A crystal plasticity model that accounts for the transition from partial dislocation to full dislocation mediated plasticity is used for the grain interior. Isotropic porous plasticity model with further extension to account for failure due to the void coalescence was used for the GBAZ. The extended model contains all the deformation phases, i.e. elastic deformation, plastic deformation including deviatoric and volumetric plasticity (void growth) followed by damage initiation and evolution due to void coalescence. Parametric studies have been performed to assess the model's dependence on the different input parameters. The model is then validated against uniaxial loading experiments for different materials. Lastly we show the model's ability to predict the damage and fracture of a dog-bone shaped specimen as observed experimentally.

The effects of the finest grains on the mechanical behaviours of nanocrystalline materials

This article proposes a new constitutive model to account for effects of the finest grains, with sizes ranging from 2 to 4 nm, on the mechanical behaviours of nanocrystalline (NC) materials. In this model, the normal nanograins (ranging from 20 to 100 nm) were treated as though they were composed of a grain interior (GI) and a grain boundary (GB) affected zone (GBAZ). The finest grains were considered to be part of the GBAZ, denoted as super triple junctions (STJs). For the initial plastic deformation stage of the NC materials, a phenomenological constitutive equation was suggested to predict the deformation behaviours of the GBAZ. The formation of GB dislocation (GBD) pileups provides dramatic strain hardening in deformed NC materials and thereby enhances their ductility. Then, the constitutive equations to describe the plastic deformation of the GI and the GBAZ lattice region were established. In this stage, the GBAZ are already saturated with GBD pileups, and GI deformation is the dominant mechanism. Finally, the mechanical model for the NC materials with the finest grains was built using the self-consistent method, and an overall moderate “work hardening,” sustained over a long range of plastic strain, was predicted. The effects of TJs/STJs on the deformation mechanism were quantitatively analysed. The analysis demonstrated that the existence of the finest grains will simultaneously lead to good strength and good ductility.

Constitutive modeling of strain rate effects in nanocrystalline and ultrafine grained polycrystals

We present a variational two-phase constitutive model capable of capturing the enhanced rate sensitivity in nanocrystalline (nc) and ultrafine-grained (ufg) fcc metals. The nc/ufg-material consists of a grain interior phase and a grain boundary affected zone (GBAZ). The behavior of the GBAZ is described by a rate-dependent isotropic porous plasticity model, whereas a rate-independent crystal-plasticity model which accounts for the transition from partial dislocation to full dislocation mediated plasticity is employed for the grain interior. The scale bridging from a single grain to a polycrystal is done by a Taylor-type homogenization. It is shown that the enhanced rate sensitivity caused by the grain size refinement is successfully captured by the proposed model.

A micro-continuum model for the creep behavior of complex nanocrystalline materials

A nanocrystalline material which has an average grain size of less than 100 nm is characterized with a significant portion of atoms residing in the grain boundaries or in the grain-boundary affected zone (GBAZ), while nanocrystalline materials with a more complex structure may contain additional strengthening nanoparticles or nano pores. In this article we develop a micro-continuum model to capture the creep response of such a complex nanocrystalline system. We make use of the concept of a three-phase composite with the GBAZ serving as the matrix, and grain interiors and dispresed particles (or voids) as two distinct types of inclusions. Both the grain interior and the GB zone are capable of undergoing the rate-dependent plastic deformation, but the strengthening nanoparticles or pores are taken to deform only elastically. During deformation the porosity will continue to evolve; its evolution is also addressed. In addition, the effect of temperature on the overall creep response is also accounted for. Several important features of creep characteristics in light of grain size, and nanoparticle and nanopore concentrations, are illustrated, and it is also demonstrated that the calculated results are in reasonable agreement with available experimental data.

On tension–compression asymmetry in ultrafine-grained and nanocrystalline metals

We present a physically motivated computational study explaining the tension/compression (T/C) asymmetry phenomenon in nanocrystalline (nc) and ultrafine-grained (ufg) face centered cubic (fcc) metals utilizing a variational constitutive model where the nc-metal is modeled as a two-phase material consisting of a grain interior phase and a grain boundary affected zone (GBAZ). We show that the existence of voids and their growth in GBAZ renders the material pressure sensitivity due to porous plasticity and that the utilized model provides a physically sound mechanism to capture the experimentally observed T/C asymmetry in nc- and ufg-metals.

Strain Gradient Plasticity Theory Based on Dislocation - Controlling Mechanism for Nanocrystalline Materials

Due to their dissimilar properties and different deformation mechanisms between grain interior (GI) and grain boundary affected zone (GBAZ) in the nanocrystalline (NC) materials, a two-phase composite model consisting of GI and GBAZ was developed and adopted to build strain gradient plasticity theory. Comparison between experimental data and model predictions at different grain sizes for NC copper shows that the developed method appears to be capable of describing the strain hardening of NC materials.

Effects of strain gradient on the mechanical behaviors of nanocrystalline materials

For the purpose of evaluating the effects of strain gradient on the mechanical behavior of nanocrystalline (NC) materials, a new composite constitutive model comprised of grain interior (GI) regarded as an ordered crystal phase and plastically softer grain boundary affected zone (GBAZ) phase with respect to strain gradient has been developed. Due to their dissimilar properties and mismatch between the two phases, dislocation-controlling mechanism based on the statistically stored dislocations (SSDs) and geometrically necessary dislocations (GNDs) was analyzed and extended to NC regime to consider the different influences of two parts in the composite model, respectively. A stress–strain relation for strain gradient plasticity was firstly built to predict the effect of grain size on the flow stress. To describe the strain strength quantitatively, a strain-hardened law determined from strain gradient and a nanostructure characteristic length parameter which differed from that of classical strain gradient theory were introduced in detail. It was shown that the strain gradient in NC materials contributes directly to the mechanical behaviors of this sort of materials and cannot be neglected.

Mechanics of creep resistance in nanocrystalline solids

In a nanocrystalline solid a significant portion of atoms resides in the grain boundary and the nearby outer grain. This combined region, known as the grain-boundary affected zone (GBAZ), is plastically softer than the grain interior, and it are the combined contributions of the grain interior and GBAZ that give rise to the overall response. In this spirit a two-phase composite model is developed to study the high-temperature creep resistance of nanocrystalline materials. Here the rate equation of each phase is represented by a power law and the Arrhenius function, but that of the grain interior is further taken to scale with the Hall–Petch relation whereas that of the GBAZ remains independent of grain size. This unified constitutive equation in turn leads to the concept of secant viscosity. Then a homogenization theory is developed by means of a transition from linear viscoelasticity to nonlinear viscoplasticity with the Maxwell viscosity constantly replaced by the secant viscosity. Subsequently a field-fluctuation method is called upon to determine the effective stress of both phases. The developed theory is applied to model the creep behavior of nanocrystalline Cu, NiP alloy, and Ni at various levels of stress, temperature, and grain size, with results that reflect good agreement with available experiments. We then applied the theory to examine the nature of creep resistance as the grain size decreases in the nanometer range in some detail, and it was discovered that creep resistance in the Hall–Petch like plot undergoes a transition from a positive slope to leveled off, and then to a negative slope. The leveled-off value in effect represents the maximum creep resistance that a material can attain, and it is found that this occurs at a critical grain size, d crit, that exists in the nanometer range.

The competition of grain size and porosity in the viscoplastic response of nanocrystalline solids

Many important processing techniques for nanocrystalline solids, such as ball milling and compaction, are frequently accompanied by the presence of voids in the end products. These voids can apparently lower the yield strength of the material. In order to address the issue of competition between grain size and porosity, we develop an explicit, analytical composite model that allows us to determine the viscoplastic response of a porous, nanocrystalline solid. The development made use of the concept of a three-phase composite comprising of the plastically harder grain interior, plastically softer grain-boundary affected zone (GBAZ), and porosity. A homogenization theory that accounts for the evolution of porosity during plastic flow is established. This establishment is built upon the extension of a linear viscoelastic composite to a non-linear viscoplastic one, in which the viscoplastic behavior of the constituent phases is represented by a unified constitutive law. Then by means of a field fluctuation method, the local strain rates are linked to the applied total strain rate. Such a linkage in turn provides the secant viscosity of the constituent phases at every stage of deformation. In order to test the applicability of the developed theory, we have applied it to model the viscoplastic response of an iron and an iron–copper mixture tested by Khan et al. [Khan, A.S., Zhang, H., Takacs, L., 2000. Mechanical response and modeling of fully compacted nanocrystalline iron and copper. Int. J. Plasticity 16, 1459–1476] and Khan and Zhang [Khan, A.S., Zhang, H., 2000. Mechanically alloyed nanocrystalline iron and copper mixture: behavior and constitutive modeling over a wide range of strain rates. Int. J. Plasticity 16, 1477–1492]. It is demonstrated that the theory is capable of capturing the major features of the tested results at various grain sizes and porosities. Our calculations further point to the change of yield strength in the Hall–Petch plot from an initial increase to level off, and then to decline, at various porosities under a constant strain-rate loading. This in turn brings about the existence of a critical grain size in the nano-meter range at which the material exhibits maximum yield strength. Moreover, this critical grain size tends to move to the left in the Hall–Petch plot as the GBAZ becomes softer.

A secant-viscosity composite model for the strain-rate sensitivity of nanocrystalline materials

In order to address the strain-rate sensitivity of nanocrystalline solids, a secant-viscosity composite model is developed in this article. The microgeometry of the composite is taken to consist of the grain-interior phase and the grain-boundary affected zone (GBAZ) as suggested by Schwaiger et al. [Schwaiger, R., Moser, B., Dao, M., Chollacoop, N., Suresh, S., 2003. Some critical experiments on the strain-rate sensitivity of nanocrystalline nickel. Acta Mater. 51, 5159–5172], while the constituent properties are modeled by a unified viscoplastic constitutive law. The drag stress of the grain interior is assumed to follow the Hall–Petch relation, but that of the GBAZ is independent of grain size, d. Then in terms of the secant viscosity of the constituent phases, the strain-rate sensitivity of the nanocrystalline solid is determined with the help of a linear viscous comparison composite and a field-fluctuation approach. To test the applicability of the developed model, it is applied to predict the strain-rate effect of a nanocrystalline Ni, and the grain-size dependence of its stress–strain relations. Our theoretical calculations indicate that the tensile strength of a nanocrystalline Ni with d = 40 nm is about five times that of a microcrystalline one with d = 10 μm under the same strain rate of ε ˙ = 3 × 10 - 4 s - 1 , and that the nanocrystalline Ni exhibits a much stronger strain-rate effect. These predictions are found to be consistent with the experimental data of Schwaiger et al. Possible grain-size softening with further grain-size reduction such as reported in molecular dynamic simulations is also demonstrated.

Cyclic deformation and dynamic compressive properties of copper bicrystals

Cyclic deformation and dynamic compressive tests of three copper bicrystals were carried out on a Shimadzu servo-hydraulic testing machine and a split Hopkinson pressure bar (SHPB) apparatus respectively. The post-deformation dislocation structures, grain boundary (GB) serrations and adiabatic shear bands (ASBs) were examined using electron channeling contrast (ECC) imaging in a scanning electron microscope (SEM). After cyclic straining the secondary slip bands were activated near the GB forming a GB affected zone (GBAZ). Microstructures beneath it are dislocation labyrinth or irregular persistent slip bands (PSBs). The saturation stress at GBAZ was calculated to be higher than that in the grain interior. In dynamic compression, the formation of ASBs, was found to be promoted by the GB. Dynamic stress–strain curves were compared with each other for single crystals, bicrystals and polycrystals. Microstructures were also characterized with orientation imaging microscopy (OIM) by electron backscattering diffraction (EBSD) technique. It was found that relatively larger lattice rotations occurred across the ASBs than in the other regions, which can be deduced by the localization of simple shear along ASBs. No recrystallization was found in the ASBs or along GBs in the present circumstance.

On the failure of NiAl bicrystals during laser-induced shock compression

Thin NiAl bicrystals 5 mm in diameter and 150–350 μm thick were tested under laser-induced shock compression to evaluate the material behavior and the effect of localized strain at the grain boundary on the failure of these specimens. Circular NiAl bicrystal samples with random misorientation were grown using a modified Czochralski technique and samples were prepared for shock compression at moderate pressures (<10 GPa). The observed crack patterns on the drive surface as well as the free surface were examined using optical microscopy. Transmission electron microscopy (TEM) of the drive surface as well as in the bulk of one grain was performed on recovered specimens following shock compression. This revealed that a nanocrystalline region with a grain size of 15–20 nm formed on a thin layer at the drive surface following the plasma expansion phase of the laser-induced shock. TEM in the bulk of one grain showed that plastic deformation occurred in a periodic fashion through propagation of dislocation clusters. Cracking on the free surface of the samples revealed a clear grain boundary affected zone (GBAZ) due to scattering of the shock wave and variations in wave speed across the inclined boundary. Damage tended to accumulate in the grain into which the elastic wave refracted. This damage accumulation corresponds well to the regions in which the transmitted waves impinged on the free surface as predicted by elastic scattering models.

Cyclic deformation behavior and intergranular fatigue cracking of a copper bicrystal with a parallel grain boundary

Abstract Cyclic deformation behavior and intergranular fatigue cracking of a [4 9 16]/[4 9 27] copper bicrystal with a grain boundary (GB) parallel to the stress axis were investigated under constant plastic strain control at room temperature in air. It was found that cyclic saturation stresses of the bicrystal increased with increasing strain amplitude, and were higher than the plateau stress of 28–30 MPa, if modified by an orientation factor ΩB of the bicrystal. Surface observations showed that a GB affected zone (GBAZ) with secondary slip formed owing to plastic strain incompatibility near the GB. As cyclic deformation was continued, fatigue cracks always initiated at the intersection sites of persistent slip bands (PSBs) with the GB. Gradually, they linked each other along the GB, leading to intergranular cracking. However, fatigue crack nucleating along slip bands was not observed as intergranular cracking occurred. It is indicated that intergranular fatigue cracking is the major damage mode even though the GB was parallel to the stress axis. Based on the results above, the GB strengthening effect and intergranular fatigue cracking mechanism were discussed in combination with the GBAZ and the interaction between PSBs and GB.

THE ROLE OF STRAIN COMPATIBILITY IN THE CYCLIC DEFORMATION OF COPPER BICRYSTALS

In order to improve our understanding of the link between the cyclic deformation of single crystals and of polycrystalline materials, a study was performed on copper bicrystals. Testing under strain control within the high cycle regime was performed in isoaxial [149] (90° and 180°) twist boundaries and [149]/[001] bicrystals, all with boundaries perpendicular to the tensile axis. A Grain Boundary Affected Zone (GBAZ), where multiple slip dominated, appeared when the boundaries developed compatibility stresses. Experiments showed that the behavior of macroscopically compatible bicrystals, 180° boundaries, is approximately similar to that of a monocrystal, whereas the fatigue responses of the other misorientation show a grain boundary effect, which increases the cyclic stress. The strain in each grain of the [149]/[001] sample was measured separately. The plastic deformation in the adjacent crystals oscillated during initial hardening; finally, the soft grain carried approximately five times the plastic strain of the other grain. © 1997 Acta Metallurgica Inc.

Crystallographic fatigue crack growth in incompatible Aluminum Bicrystals: Its Dependence on Secondary Slip

The secondary slip behavior ahead of crystallographic fatigue cracks and its effect on the crack growth near the grain boundaries (GBs) in $$[12\bar 1]$$ tilt nonsymmetrical aluminum bicrystals under constant cyclic stress amplitude have been systematically examined. The displacement field ahead of short crack tips near the interfaces in two specimens has been measured by using a microfiducial grid technique. It has been observed that the critical persistent slip band (PSB) ahead of a short crack tip near the GB in a middle misoriented bicrystal was able to develop as long as the primary one and resulted in a temporary stage II growth. As a longer crystal- lographic crack grew into the grain boundary affected zone (GBAZ), activation of the critical slip ahead of the crack front and crack branching along the critical PSB occurred in all groups of the aluminum bicrystals, which reveals a crucial role of the critical slip in increasing the crack opening and triggering the slip in the adjacent grain. On the other hand, cross slip became the dominant slip mode ahead of the crystallographic crack front near the GB in a bicrystal of larger misfit angles and drove the crack along the cross PSB, a steep path with a remarkably high growth rate, until it propagated into the GBAZ. The resultant stress on the secondary slip system ahead of a crack front near the interface contributed by the internal stress due to both intergranular and intragranular incompatible strain, as well as the enhanced crack tip stress, has been evaluated and rationalizes the activation of the secondary slip systems.