Average Flow Stress Research Articles

Influence of twinning thickness on the mechanical properties of crystalline-amorphous dual-phase CoCrFeNiMn high entropy alloy

This study employs molecular dynamics simulation to investigate the influence of twin thickness on the mechanical properties and plastic deformation mechanisms for crystalline/amorphous dual-phase CoCrFeNiMn high-entropy alloy with varying amorphous layer thicknesses. The results revealed that for a minor amorphous layer thickness (d) of 1 nm, increasing the twin thickness (h) decreased average flow stress and peak stress within the models. It can be attributed to the fact that at smaller h, twin boundaries effectively hinder dislocation motion. However, as h increases, dislocation storage near twin boundaries and subsequent large-scale FCC→HCP phase transformation become more robust, reducing stress. On the other hand, when d thickness increases to 7 nm, stable average flow stress is observed due to thicker shear band formation during plastic deformation. Regardless of whether d was 1 nm or 7 nm, an increase in twin thickness augmented the likelihood of FCC→HCP phase transformation.

Effect of pre-strain on dynamic mechanical properties of Ti-6Cr-5Mo-5V-4Al titanium alloy

Abstract The effect of quasi-static pre-deformation on the dynamic properties of Ti-6Cr-5Mo-5V-4Al titanium alloy was studied. The results revealed that as the pre-tension deformation increased, the average dynamic flow stress was slightly decreased while the dynamic uniform plastic strain and the maximum absorbed energy were improved obviously and the largest value existed when the deformation reached 6.8%. As the pre-tension deformation progressively increased, the dynamic performance exhibited a marked decline. Conversely, with the increase of the pre-compression deformation, the dynamic flow stress experienced a substantial enhancement, but the dynamic uniform plastic and the maximum absorbed energy significantly declined which showed that the pre-compression deformation did harm to the dynamic mechanical properties of Ti-6Cr-5Mo-5V-4Al titanium alloy.

Orientation-related and temperature-dependent continuous grain boundary migration in multi-principal element alloys

Grain boundaries (GBs) significantly affect the mechanical properties of metals and alloys. In this study, we investigated using molecular dynamic simulations the migration behavior of Σ25 (710), Σ5 (310), and Σ37 (750) [001] symmetric tilt GBs in CoCrCuFeNi multi-principal element alloy (MPEA) and Cu samples subjected to shear deformation. In Cu, the migration of the GBs exhibits a coupled migration pattern, consistent with the Cahn model; while in MPEA, the migration pattern varies with GB angle and temperature. Both Σ25 (710) and Σ37 (750) GBs, along with higher temperatures, induce GB roughening and continuous migration in the MPEA samples. Further investigation to the effects of GB angle and temperature was conducted through microstructure evolution tracing and quantitative analysis. A model was developed to describe the temperature-dependent continuous GB migration and average flow stress in MPEA samples with Σ25 (710) or Σ37 (750) GBs. This work can help understand the mechanical behavior of GB in MPEA and provide valuable insights for the development of high-performance materials.

Effect of grain size, temperature, and tensile strain rate on mechanical response of CoCrNi medium-entropy alloys

Grain boundary (GB) strengthening of metallic materials faces limitations as grain sizes are reduced to the nanoscale, primarily due to the transition from the strengthening to the softening effects. Understanding the intrinsic mechanisms behind such pronounced transitions is essential for optimizing the mechanical properties of nanocrystalline (NC) alloys. In this work, the critical grain size responsible for this transition is determined for NC CoCrNi medium-entropy alloys using molecular dynamics simulation, and the underlying mechanisms concerning varying temperatures and strain rates are systematically investigated for the samples with the critical grain size. The transition from Hall-Petch (HP) strengthening to Inverse Hall-Petch (IHP) softening is established by decreasing the average grain sizes from 21 nm to 3 nm. The critical grain size for the current alloys is estimated to be 12 nm, and the underlying deformation mechanisms are illustrated as follows: In the IHP regime, GB-mediated deformation becomes dominant, leading to softening. Conversely, in the HP regime, dislocation slip dominates the deformation mode, contributing to strengthening. It is found that an increase in temperature from 77 K to 1100 K leads to a decrease in the average flow stress and Young's modulus. Meanwhile, the deformation mechanisms change from dislocation slip (77K–700K) to GB-mediated deformation (700 K–1100 K). Furthermore, the underlying mechanisms correlating to the critical strain rate are uncovered. It can be attributed to the shift in deformation mechanisms from dislocation slip at relatively low strain rate regimes (5 × 107 s−1-2 × 109 s−1) to dislocation drag at relatively high strain rate regimes (2 × 109 s−1-5 × 109 s−1). Our atomistic insights into the tensile response of NC CoCrNi may provide a crucial basis for designing superior properties to meet the growing demands of advanced engineering fields.

Establishing a unified viscoplastic constitutive equation for EA4T steel: Comparative analysis with Arrhenius model

Quasi-static and impact compression experiments were conducted on EA4T steel using a Gleeble-3800 thermal simulation machine. The study aimed to investigate the complex microstructural evolution and thermal deformation behavior of EA4T steel under various experimental conditions, including temperatures ranging from 970 °C to 1170 °C and strain rates ranging from 0.01s−1 to 1s−1. To precisely elucidate these phenomena, we meticulously constructed a unified visco-plastic constitutive model using the internal variable methodology. The model's parameterization was achieved through the effective application of genetic algorithm optimization techniques. Rigorous validation of the model was performed by meticulously comparing its outputs with experimental data, including key metrics such as average grain size, recrystallized fraction, and effective flow stress. In addition,a comparative analysis with the improved Arrhenius model highlights the superior performance of the unified visco-plastic constitutive equation in capturing the intricate microstructural evolution and thermal deformation behavior exhibited by EA4T steel.

The role of phase fraction on the deformation behavior and tensile properties of dual-phase polycrystalline Fe–Ni alloy: A molecular dynamics simulation study

An alloy containing two or more phases with significantly distinct properties may produce a unique combination of high strength and ductility. Fe–Ni alloys processed through the powder metallurgy route form dual-phase structures containing both body- and face-centered cubic phases. The detailed atomic scale microstructural evolution and deformation mechanism of such alloys have not been performed as dual-phase structure materials generate more complex deformation mechanisms than single-phase structure materials. The present study utilizes molecular dynamics simulation to compute the mechanical properties and investigate the deformation mechanism in a dual-phase Fe–Ni alloy with a variable phase fraction of body-centered cubic during a uniaxial tensile test. The results show that phase fraction affects the mechanical properties as well as the deformation behavior. Shear strain distribution and dislocation density provided an explanation for the change in the average flow stress and strengthening mechanism of the dual-phase Fe–Ni alloys. Additionally, the influence of temperature on deformation behavior is investigated. The deformation mechanism at higher temperatures is found to be dislocation slip and grain boundary sliding.

EFFECT OF RANDOM DISTRIBUTION AND SHORT-RANGE ORDERING OF SOLUTES ON THE MECHANICAL PROPERTIES OF NANOCRYSTALLINE Cu–Ag ALLOYS

The effects of solute random distribution (RSS) before relaxation and solute short-range ordering (SRO) after relaxation on the mechanical behavior of nanocrystalline Cu–Ag alloys were analyzed by molecular dynamics simulation. It has been found that the mechanical properties of Cu–Ag alloy mechanics with SRO were better than those of Cu–Ag alloy mechanics with RSS. Specifically, during the whole tensile process, compared with sample #1 with SRO structure, sample #2 with RSS structure has stronger strain–stress response ability, more obvious phase transformation process, and narrower shear strain zone on the grain boundary. Furthermore, when the number of Voronoi seeds is examined concerning the mechanical properties of the nanocrystalline Cu–Ag alloy, it becomes apparent that the average flow stress drops as the quantity of Voronoi seeds increases.

Quantitative analysis of multiple deformation mechanisms in NiCrCoFe high-entropy alloy

Multiple deformation mechanisms were often observed during the deformation processes of high-entropy alloys (HEAs), but the quantitative analysis of the contribution of different deformation mechanisms to the total deformation is few involved. In this work, the multiple deformation mechanisms in NiCoCrFe HEA are studied by molecular dynamics (MD) method. The average flow stress transforms from Hall-Petch (HP) relationship to inverse Hall-Petch (IHP) relationship with grain refinement at critical grain size (dc ≈ 27.31 nm). And the microstructural evolutions of microstructures during the deformation process are revealed by means of the crystal-analysis-tool (CAT). The contributions of various microstructural configurations to the total deformation are systematically studied by means of post-processing metrics. In the strengthening regime, the deformation mechanisms are dominated by stacking fault, grain boundary (GB) activity, and HCP martensitic transformation, accompanied with twinning and dislocation. In the softening regime, the deformation mechanisms are dominated by GB activity and stacking fault. The deformation mechanisms revealed according to the percentages of total strain accommodated by various microstructural configurations is more accurate than their atomic fractions. These results would provide an accurate and deep insight into the multiple deformation mechanisms of HEAs.

Thermally activated intermittent flow in amorphous solids.

Using mean field theory and a mesoscale elastoplastic model, we analyze the steady state shear rheology of thermally activated amorphous solids. At sufficiently high temperature and driving rates, flow is continuous and described by well-established rheological flow laws such as Herschel-Bulkley and logarithmic rate dependence. However, we find that these flow laws change in the regime of intermittent flow, where collective events no longer overlap and serrated flow becomes pronounced. In this regime, we identify a thermal activation stress scale, xa(T,), that wholly captures the effect of driving rate  and temperature T on average flow stress, stress drop (avalanche) size and correlation lengths. Different rheological regimes are summarized in a dynamic phase diagram for the amorphous yielding transition. Theoretical predictions call for a need to re-examine the rheology of very slowly sheared amorphous matter much below the glass transition.

Maintain sort order of grain boundary to investigate the deformation mechanism of CoCuFeNiPd high–entropy alloys

Molecular dynamics simulations of tension tests on CoCuFeNiPd high–entropy alloys (HEAs) are performed to study the effects of grain sizes (d), temperatures, and strain rates on the mechanical properties. After a series of tension simulations with different grain sizes, the Hall – Petch (H–P) and inverse Hall – Petch relationships are discovered. Hall–Petch breakdown is observed at grain size (d) of 10 nm. In the inverse Hall – Petch region, the average flow stress (σ(ε)) decreases from 1.97 to 1.76 (GPa) when grain size is decreased from 10 nm to 4 nm. On the contrary, the average flow stress increased from 1.90 to 1.97 (GPa) as d reduced from 18 nm to 10 nm. The microstructural evolution of the CoCuFeNiPd HEAs model exhibits that the primary deformation process in the H–P relation (d > 10 nm) is dislocation slips. The grain boundaries (GB) prevent dislocation expansion in the H– P relation, causing mechanical strengthening. Meanwhile, the main deformation mechanisms for the inverse H–P (d < 10 nm) are grain rotation and GB migration, decreasing flow stress. In addition, Young's modulus of the HEAs model increases with grain size (d). The yield strength, flow stress, and Young's modulus of HEAs specimens tend to reduce at high temperatures. Additionally, the number dislocation length reduces at high temperatures due to the amorphization phenomenon. The results also showed that Young's modulus and yield strength increase when strain rates rise.

Crystallographic texture effect on statistical microvoid growth in heterogeneous polycrystals

Polycrystalline materials usually exhibit obvious preferred grain orientations (i.e., crystallographic texture) after rolling and heat treatments, leading to a certain crystalline anisotropy. However, most previous studies on microvoid growth generally treated the material as homogeneous isotropic matrix, ignoring the influence of crystallographic texture. In the present work, four typical crystallographic textures of face-centered cubic crystal are considered, including the Cube, Goss, Brass and Copper textures. Afterwards, the texture effect on microvoid growth is systematically studied by crystal plasticity finite element simulation, from a statistical point of view. In addition, the role of loading mode (i.e., uniaxial or biaxial tension) in the texture effect on microvoid growth has also been explored. The results indicate that the crystallographic texture evidently affects the statistical void growth in heterogeneous polycrystals, regardless of the loading mode. Meanwhile, it has been found that the statistical void growth of Cube (resp. Brass) texture is always slower (resp. faster) than that of random grain-orientation case. Furthermore, it is interestingly concluded that for the four considered textures, the trend of statistical void growth (from fast to slow) is well consistent with that of average flow stress (from high to low) at any given strain level, which cannot be captured by the classical Rice-Tracey model. Finally, based on the statistical characteristics of void growth for different textures, a statistical Rice-Tracey model incorporating the texture effect is established. It is demonstrated that this statistical model can well envelop all the dispersed void growth results of different textures for the uniaxial tensile loading.

Grain size dependence of microstructure and mechanical properties of nanocrystalline TC4 alloy studied by molecular dynamic simulation

Based on molecular dynamic simulation with tensile loading, the microstructure and tensile strength of TC4 titanium alloy are studied with nanocrystalline model. By varying the grain size while keeping the grain geometry the same, the Hall–Petch relationship is observed for average flow stress with average grain size d>15 nm, where the resistance to intragranular deformation is proportional to d-0.5. For d<15 nm, however, smaller grain size leads to smaller resistance to intergranular deformation in the form of grain boundary migration and diffusion, which leads to inverse Hall–Petch relationship. The analysis of displacement vector reveals the role of grain boundaries in restricting propagation of dislocations such as 13<11‾00>, which is responsible for FCC stacking fault inside HCP grain. In the heat treatment modeling under different temperatures, the fraction of grain boundary atoms decreases and thus the maximum tensile strength increases. On the other hand, the fraction of well-ordered atom increases, which can cause growth of existing grain and nucleation of minor BCC grain from previously grain boundary region before heat treatment.

Calculation of Deformation-Related Quantities in a Hot-Rolling Process

The hot deformation of metal as a nonlinear system is mathematically described by a local linear model associated with the working conditions using a transfer function (TF) in the Laplace domain. Experimental data (true stress vs. true strain curves) are obtained using the established compressive uniaxial deformation test, where experimental conditions (strain rate and temperature) define the working conditions of the local linear TF model, which is intrinsically a function of strain. Based on the TF model, three important physical quantities of the tested metal are determined exactly: the work done per unit deformation, the average flow stress, and the flow-stress derivative with respect to the strain based on a particular TF. The exactly determined quantities, determined as a function of strain, can replace the previously used approximations in some rolling force and torque calculations.

Dynamic compression deformation behavior of laser directed energy deposited α + β duplex titanium alloy with basket-weave morphology

Duplex titanium alloy with basket-weave morphology made by laser directed energy deposition (LDED) technique, has a bright application prospect in the armor protection field attributed to its excellent specific strength and bulletproof performance. In this research, the dynamic compressive deformation mechanisms of LDEDed TC11 titanium alloy under a strain rate of 3000/s are systematically investigated by investigating the dislocation slipping and twinning behavior. Meanwhile, this work gives explanations of the microstructure evolution of subsequent heterogeneous shear localization. The results indicate that TC11 alloy with basket-weave morphology possesses huge improvement in the average dynamic flow stress, uniform plastic strain, and impact absorption energy in contrast to that of titanium alloys with an equiaxed microstructure, which is known as the optimum prepared via traditional forming methods. The loading direction to α laths is largely responsible for slip modes manifestation under dynamic compression, which is illustrated in the unit triangle. When loading along < 0001 > at the vertex of the unit triangle, both basal slip and prismatic slip systems could not be motivated. When loading along directions within the unit triangle, either or both basal slip and prismatic slip systems could be activated, causing α lath twisting, rotation, or even refinement. Meanwhile, the Schmid factors reduction caused by α laths rotation results in the twinning, which will reduce the slip mean free path. During the heterogeneous shear localization, the adiabatic shear bands (ASB) formation finally leads to shear failure. The α laths within the transition zone in ASB are compressed to less than 200 nm in thickness. Ultrafine nanoscale equiaxed grains with few defects in the center zone of ASB are generated under dislocations pile-up and sub-grain rotation.

Influences of grain size, temperature, and strain rate on mechanical properties of Al0.3CoCrFeNi high–entropy alloys

This study investigates the mechanical properties and deformation behaviours of Al0.3CoCrFeNi high-entropy alloys (HEA) under tension tests by using molecular dynamics (MD) simulations. The effect of different grain sizes (d), temperatures, and strain rates are examined. By varying the grain size from 4.0 nm to 20.0 nm, the shift from mechanical softening to strengthening was observed for the simulated samples. The result shows that the critical grain size of the inverse Hall – Petch and Hall – Petch regime is 12.0 nm. The average flow stress varies slightly increases from 3.02 to 3.19 GPa (5.3%) with the decrease of grain size from 20.0 to 12.0 nm in the Hall – Petch relation. While in the inverse Hall – Petch regime, the average flow stress significantly reduces from 3.19 to 2.7 GPa (15.3%) with grain size reducing from 12.0 to 4.0 nm. The migration of grain boundary (GB), and the rotation of grains are the dominant deformation mechanism in the inverse Hall – Petch regime. Meanwhile, in the Hall-Petch region, the dislocation activities are the main contribution to the deformation mechanism of polycrystalline. The GB plays as a barrier to hinder the dislocation propagation. Therefore, in the Hall - Petch regime, the fraction of GB increases as the grain size decreases, resulting in higher barrier densities for samples with small grain sizes and thereby causing the flow stress to increase. The result points out that Young's modulus of the HEA specimen increased with an increase of the average d. In addition, the result also shows that the ultimate stress, flow stress, and Young's modulus increase with rising the strain rate or decreasing the temperature.

Uncovering strengthening and softening mechanisms of nano-twinned CoCrFeCuNi high entropy alloys by molecular dynamics simulation

High-entropy alloys (HEAs) break the design concept of traditional alloys and exhibit excellent mechanical properties. However, as a new member of the alloy family in recent years, the dependence of the deformation behavior of the HEAs on alloy composition and twin boundary (TB) is still unclear, and many phenomena urgently need to be revealed. Here, the effects of TB spacing and Ni concentration on the mechanical properties and deformation behavior of the nano-twinned (CoCrFeCu)1−XNiX HEA (nt-HEA) under tensile loading are investigated by molecular dynamics simulation. The results show that with the decrease in TB spacing, the average flow stress of the nt-HEA changes from Hall–Petch strengthening to inverse Hall–Petch softening. When the TB spacing is greater than a critical value, the plastic deformation mechanism is dominated by the slip of partial dislocations. However, when the TB spacing is less than the critical value, the plastic deformation mechanism is transformed into the formation of voids induced by the amorphous phase, which becomes the key factor for the softening of the nt-HEA. It is also found that the mechanical properties of the nt-HEA can also change from strengthening to softening by adjusting Ni concentration, which is closely related to the change of stacking fault energy of the nt-HEA. In addition, the plastic deformation mechanism and voids formation mechanism of the nt-HEA are also discussed in detail.

Mechanical behavior of graphene magnesium matrix composites based on molecular dynamics simulation

Magnesium alloy is regarded as a lightest engineering structural metal material due to its low density, but its wide application is limited due to poor plastic deformation behavior. Therefore, the comprehensive mechanical properties of enhanced magnesium alloy have become a research focus in the material science. Here, the effect of graphene on the deformation behavior and that on the mechanical properties of magnesium under tensile loading are studied by molecular dynamics simulation. The results show that the introduction of graphene can significantly improve the mechanical properties of pure magnesium. Comparing with pure magnesium, the Young's modulus and the first peak stress of the graphene magnesium matrix (GR/Mg) composites are increased by about 27.5% and 36.5% respectively, which is mainly due to the excellent mechanical properties of graphene. The results also indicate that the embedded position of graphene has little effect on the Young's modulus or peak stress of the GR/Mg composites, but it will significantly affect the plastic deformation behavior of the GR/Mg composites after the second peak stress. With the increase of the embedded height of graphene, the average flow stress of the GR/Mg composites first increases in the later stage of plastic deformation. When the embedded height reaches 0.4&lt;i&gt;L&lt;/i&gt;, the average flow stress of the GR/Mg composites reaches a maximum value, and then decreases. This phenomenon of the Gr/Mg composites can be explained by the plastic deformation behavior of the magnesium matrix above and below graphene. The embedded position of graphene has a great influence on the plastic deformation behavior of the upper and lower magnesium matrix of the GR/Mg composites. When the embedded height of graphene is small, the plastic deformation capability of magnesium matrix under graphene is strong and dislocation slip is easy to occur. And when the embedded height of graphene is large, the plastic deformation capabilities of the two parts of magnesium matrix above and below graphene are equal, and their plastic deformation behavior tends to be synchronous. The results show that the plastic deformation behavior of the GR/Mg composite is the same as that of pure magnesium, and the phase transition from HCP to BCC and then to HCP occurs in the process of the plastic deformation. The phase transition mechanism of magnesium matrix is also analyzed in detail. The results of this study have certain theoretical guiding significance in designing the high performance graphene metal matrix composites.

Grain-size effects on the deformation in nanocrystalline multi-principal element alloy

Multi-principal element alloys (MPEAs) continue to garner great interest due to their potentially remarkable mechanical properties, especially at elevated temperatures for key structural and energy applications. Despite extensive literature examining material properties of MPEAs at various compositions, much less is reported about the role of grain size on the mechanical properties. Here, we examine a representative nanocrystalline BCC refractory MPEA and identify a crossover from a Hall-Petch to inverse-Hall-Petch relation. While the considered MPEA predominantly assumes a single-phase BCC lattice, the presence of grain boundaries imparts amorphous distributions that increase with decreasing grain size (i.e., increasing grain boundary volume fraction). Using molecular dynamics simulations, we find that the average flow stress of the MPEA increases with decreasing average grain size, but below a critical grain size of 23.2 nm the average flow stress decreases. This change in the deformation behavior is driven by the transition from dislocation slip to grain-boundary slip as the predominant mechanism. The crossover to inverse-Hall-Petch regime is correlated to dislocation stacking at the grain boundary when dislocation density reaches a maximum.

Anisotropic deformation behavior of [formula omitted], [formula omitted] and [formula omitted]-textured nanocrystalline titanium

Molecular dynamics (MD) simulation is employed to investigate tensile deformation of 112-0 , 101-0 and 0001 -textured nanocrystalline titanium with average grain size ranging from 4 nm to 48 nm. The grain size and orientation dependent mechanical properties are determined. Average flow stress of 112-0 texture is much higher than that of other textures, which may be induced by the complex twinning-dislocation and dislocation–dislocation interactions involving 101-2〈101-1〉 twinning (TW), basal 〈a〉 and pyramidal 〈c+a〉 slip within this texture. In contrast to this, the easier prismatic 〈a〉 slip acts as the dominant slip mode for the 0001 -textured samples. Plastic deformation of the 101-0 -textured samples is mainly controlled by 112-1〈112-6〉 TW. Grain boundary mediated plasticity (GBMP) is more pronounced in the 101-0 -textured structures, while it is restricted by dislocation pile-ups in the 112-0 -textured structures. Further discussions about effects of grain size on different deformation mechanisms including GBMP, dislocation slip and deformation TW are made. Inparticular, the variation of twin variant number, twin fraction and dislocation number with grain size are quantitatively counted. The detailed analysis of TW nucleation mechanism reveals the emergence of multiple TW nucleation sources with increasing grain size. The current study sheds light on the deformation anisotropy of nanocrystalline titanium, facilitating the optimization design of Ti-based nanostructures.

Criticality in sheared, disordered solids. I. Rate effects in stress and diffusion.

Rate effects in sheared disordered solids are studied using molecular dynamics simulations of binary Lennard-Jones glasses in two and three dimensions. In the quasistatic (QS) regime, systems exhibit critical behavior: the magnitudes of avalanches are power-law distributed with a maximum cutoff that diverges with increasing system size L. With increasing rate, systems move away from the critical yielding point and the average flow stress rises as a power of the strain rate with exponent 1/β, the Herschel-Bulkley exponent. Finite-size scaling collapses of the stress are used to measure β as well as the exponent ν which characterizes the divergence of the correlation length. The stress and kinetic energy per particle experience fluctuations with strain that scale as L^{-d/2}. As the largest avalanche in a system scales as L^{α}, this implies α<d/2. The diffusion rate of particles diverges as a power of decreasing rate before saturating in the QS regime. A scaling theory for the diffusion is derived using the QS avalanche rate distribution and generalized to the finite strain rate regime. This theory is used to collapse curves for different system sizes and confirm β/ν.