Dislocation Mean Free Path Research Articles

Synergistic interaction behavior of deformation mechanisms in a new metastable β-Ti alloy with high strain hardening rate

The present study successfully designed a novel metastable β titanium alloy, Ti–8.8Cr–1.9Sn, exhibiting exceptionally high strain-hardening rate (∼2.4 GPa) as well as significant total elongation (∼48.2 %). Detailed analysis of the microstructure revealed that the successive activation of primary mechanical twins and primary SIM α" within β phases, along with secondary mechanical twins and secondary SIM α" within twinning zones during deformation, which results in a highly intricate network of deformation microstructures. Meanwhile, during deformation the microstructure undergoes dynamic refinement through the continuous occurrence of mechanical twinning and phase transformations, leading to a reduction in dislocation mean free path, thereby enhancing the strain-hardening rate. Importantly, the microstructural heterogeneity is formed due to generation of numerous heterogeneous interfaces, including β/α'', β/twin, α''/twin as well as twin/twinnano, thereby inducing additional HDI hardening resulting from the formation of GNDs for accommodating strain gradients near these interfaces. Furthermore, the relative mobile dislocation density ρm/ρm0 is significantly high during deformation, due to a reduced exhaustion rate and a high nucleation rate of mobile dislocations. The values of activation volume Va and V∗ typically range from 1b3–100b3, indicating the occurrence of cross-slip and dislocation nucleation. The interaction and accumulation between GNDs and mobile dislocations further contribute to the improvement of strain hardening rate. Therefore, the synergistic interaction activities of multiple deformation mechanisms lead to enhanced strain-hardening rate along with the large plasticity.

Achieving superior strength-ductility balance by tailoring dislocation density and shearable GP zone of extruded Al-Cu-Li alloy

Pre-stretching is commonly employed to accelerate ageing precipitation kinetics in wrought Al-Cu-Li alloys, but uneven precipitation resulting from dislocation pile-ups often degrades ductility. Herein, the strength and ductility of extruded Al-Cu-Li alloy are significantly improved through a novel thermomechanical treatment, involving pre-ageing and pre-stretching, followed by low-temperature interrupted ageing. A superior balance between high yield strength (∼ 657 MPa) and good ductility (elongation to fracture of ∼ 13.5 %) is obtained, with elongation increased by 105 % compared to the conventional T8 temper, while maintaining a respectable yield strength. Microstructure analysis reveals that dense Guinier–Preston (GP) zones induced by pre-ageing effectively dissipate energy from dislocation sliding, resulting in a uniform dislocation configuration even at 8 % pre-stretching. However, the GP zone density is greatly reduced due to their dissolution following pre-stretching. Upon interrupted ageing, the reprecipitation of GP zones forms a homogeneous mixture of δ′, GP zones, and T1 phases. This combination alleviates local stress concentrations and lengthens the dislocation mean free path during tensile testing by shearing the GP zones at multiple sites, thereby improving ductility. Simultaneously, T1 precipitates strengthen the alloy by pinning dislocations and promoting dislocation cross-slip, improving work hardening capacity. The dissolution of GP zones also redistributes the Cu atoms within the matrix, further enhancing the intrinsic ductility of the Al matrix. These findings offer valuable insights for developing high-performance wrought Al-Cu-Li alloys.

Excellent strength-ductility synergy assisted by dislocation dipole-induced plasticity in Co-free precipitate-strengthened medium-entropy alloy

Precipitation strengthening is one of the most effective approaches for developing advanced structural materials with outstanding strength-ductility combinations. However, most compositional designs of precipitate-strengthened HEAs/MEAs compromise the cost-property tradeoff owing to the addition of expensive Co element. In this study, a Co-free FeCrNi-based precipitate-strengthened medium entropy alloy (denoted as Al0.2Cr0.9FeNi2.2Ti0.2) with a near-equiatomic FeCrNi matrix and a high content (∼ 35 %) L12 nanoprecipitates was designed using a mixing strategy. The microstructural features, mechanical performance, deformation substructure evolution, and strengthening mechanisms were systematically investigated using EBSD, TEM, and APT. Tensile tests indicated that the current alloy aged within a moderate temperature range achieved an exceptional strength-ductility combination compared to existing Co-containing and Co-free HEAs/MEAs. Particularly, the alloy aged at 700 ℃ (denoted as 700A) demonstrated a high ultimate tensile strength of 1606 MPa and a large ductility of 25 %, benefiting from both precipitation hardening and an unusual strain-hardening sustainability. Such anomalous strain-hardening sustainability can be attributed to the dislocation dipole-induced plasticity. High-density dislocation dipoles can simultaneously provide additional strain hardening by reducing the dislocation mean free path and enhance plastic deformation compatibility by acting as stress delocalization origins, thereby contributing to excellent strength-ductility synergy. These findings will not only open a new door for the future development of high-performance Co-free precipitate-strengthened HEAs/MEAs, but also deepen the understanding of the work-hardening mechanisms in these alloys.

Achieving back-stress strengthening at high temperature via heterogeneous distribution of nano TiBw in titanium alloy by electron beam powder bed fusion

Back-stress strengthening has been proven to be an effective strategy in breaking the room temperature strength–ductility dilemma in hetero-structural metals matrix composite materials (MMC). However, back-stress is difficult to achieve at high temperature because of grain boundary softening, grain boundary sliding, dislocation annihilation and grain rotation. Here, back-stress strengthening is exploited to improve the high temperature tensile properties of Ti-6Al-4 V (TC4) alloy by precipitating a heterogeneous distribution of nano TiB whiskers (TiBw). In this work, the rapid solidification associated with electron beam powder bed fusion (EB-PBF) generates heterogeneous in-situ nano TiBw at both grain boundaries and grain interiors. The nano-TiBw on the grain boundaries (GB nano-TiBw) not only refines the grains but can also pin the grain boundaries. The intragranular nano TiBw (IG nano-TiBw) significantly reduces the dislocation mean free path, inhibit dislocation movement, and dramatically enhances the dislocation storage density. Meanwhile, specimens are strengthened by high-density < a + c > dislocations induced by the precipitated nano TiBw. The heterogeneous distribution of nano TiBw achieved a 50 °C increase in the service temperature of TC4 alloy while also increasing stability. This strategy provides a new perspective for further improving the high-temperature mechanical properties of titanium alloys.

Remarkable contribution of stress-induced martensitic transformation to strain-hardening behavior in Ti−Mo-based metastable β-titanium alloys

The role of stress-induced β → α″ martensitic transformation in contributing to the exceptional strain-hardening behavior of a Ti-11Mo (wt. %) model alloy was studied. The results reveal that the α″-martensite plates, undergoing relatively high transformation strains upon formation, act as effective barriers against dislocation motion. As deformation proceeds, the progressive generation of these plates dynamically reduces the dislocation mean free path (dynamic Hall-Petch effect), while simultaneously encouraging the accumulation of dislocations. These dual effects substantially enhance the flow stress with increasing strain, thereby resulting in remarkable strain-hardenability, a crucial factor for maintaining excellent ductility. This study presents innovative experimental evidence elucidating the mechanism of the transformation-induced plasticity effect in metastable β-titanium alloys, while also offering insights for designing novel alloys with superior strain-hardenability and ductility.

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.

Thermal activation and dislocation dynamics in Ti–6Al–4V alloy

The tensile stress relaxation behaviour is experimentally investigated for Ti–6Al–4V alloy across a temperature range of −60, −30, 20, 120, and 230 °C. Interestingly, the results revealed that the alloy exhibited the lowest resistance to stress relaxation at 20 °C, i.e., room temperature. This resistance was found to increase with both increasing and decreasing test temperatures. The apparent activation volume values, which indicate the dislocation mean free path, increase with strain due to a decrease in activable dislocation segments. Furthermore, these values were found to be proportional to the test temperature, resulting from higher dislocation mobility at moderate temperatures (230 °C and 120 °C) than at lower temperatures. Our experimental and analysis results indicate that dislocation-mediated plastic deformation predominates in all tested temperature conditions. However, the transition from planar to wavy dislocation configuration, observed through Transmission Electron Microscopy (TEM) between temperatures of −30 and 20 °C, along with the change in activation volume, suggests a critical temperature at which dislocation mechanism changes in the Ti–6Al–4V alloy. A rapid exhaustion of a substantial amount of mobile dislocation density, which significantly contributes to time-dependent deformation was observed at 230 °C. These findings provide valuable insights into the mechanisms underlying the stress relaxation behaviour of Ti–6Al–4V alloy at different operational temperatures, offering practical implications for improved alloy design and manufacturing processes.

Assessment of phenomenological models for Indentation Size Effect (ISE) through physically based dislocation density evolution

The depth dependent hardness, referred to as indentation size effect (ISE) has gained considerable attention. ISE is attributed to the strain gradient caused by the inhomogeneous strain distribution beneath the indenter tip. The depth dependence of hardness is phenomenologically accounted using an appropriate length scale parameter. The Unified model is one such model that is built on Nix–Gao’s model and focuses on integrating various length scale parameters resulting from both microstructural and geometrical effects. One aspect of the current work is to assess the applicability of the Unified model to a material like bulk Nickel with a history of cold work. Also, the physics of ISE in metals can be related to the dislocation mean free path influenced by strengthening mechanisms. Past attempts are scarce to quantify the ISE through the microstructure variables. In the present work, an attempt has been made to simulate the nanoindentation test using a dislocation density based constitutive model. The objective of this study is to establish a correlation between the equivalent plastic strain resulting from deep depth indentation (which does not exhibit a size effect) and an equivalent dislocation density. The dislocation density here serves as a state variable that describes the microstructure-dependent mechanical behaviour. The modified KME, a dislocation density-based model, is incorporated as a user subroutine in a commercial finite element solver. It has been proven to accurately predict the indentation behaviour at substantially large depths, which aligns well with the predictions of the Unified model or experimental observations. The good correlation between the value of effective dislocation density and equivalent plastic strain in the plastic zone underneath the indenter assures to extend the use of dislocation density as a state variable to predict ISE.

Tensile and micro-compression behaviour of AISI 316L austenitic stainless steel single crystals at 20 °C and 300 °C: Experiments, modelling and simulations

The mechanical behaviour of 316L stainless steel single crystal is characterised at room temperature and 300°C. Elasticity moduli at room temperature are obtained with resonant ultrasound spectroscopy. Their dependence on temperature is calibrated with molecular dynamics simulations. The plastic behaviour is characterised by tensile tests on millimetre-sized single crystal specimens and compression tests on micrometre-sized single crystal specimens. A constitutive model of crystal plasticity based on dislocation density hardening at finite strains is developed and implemented in an open-source material subroutine compatible with several finite element (FE) and fast Fourier transform (FFT) solvers. Tensile curves at room temperature and 300°C are used to calibrate the interaction coefficients for self and coplanar dislocation interactions. The dislocation mean free path for obstacle dislocations and the annihilation distance are also calibrated. The calibrated model predicts tensile curves in excellent agreement with experimental data. In addition, the predicted plastic strain fields are in good agreement with the experimental fields obtained by digital image correlation. Semi-quantitative agreement between simulation and experimental data is obtained for micro-compression tests without further calibration of the model. Finally, an extension to polycrystals with grain size effects is finally proposed. The predicted strain hardening behaviour is compared with experimental data on stainless steel polycrystals.

Delving into the intrinsic co-relation between microstructure and mechanical behaviour of fine-/ultrafine-grained TWIP steels via TEM and in-situ EBSD observation

To illustrate the microstructural factors of grain refinement for enhancing mechanical properties, the fine-/ultrafine-grained TWIP steels with a product of strength and elongation of ∼71 GPa·% were first prepared by combining rolling and stress relief annealing. Subsequently, the evolution of dislocations, stacking faults, and associated substructures of the fine-/ultrafine-grained TWIP steels was analysed by using in-situ EBSD tensile tests and TEM characterisation of the interrupted strain experiments. The results reveal that the excellent mechanical properties of the TWIP steels are attributed to dislocations and associated dislocation cells, dislocation walls, dislocation tangles, stacking faults and associated Lomer-Cottrell locks (LCs), nano-twins, primary and secondary twins and their interactions during plastic deformation. The density of geometrically necessary dislocations (GNDs) was evaluated based on the modified Ashby's model and compared with experimental results, indicating that grain size heterogeneity can promote the accumulation of GNDs, which facilitates the generation of subgrains and new boundaries to reduce the mean free path (MFP) of dislocations, thus enhancing strain hardening. Meanwhile, the interaction of lamellar primary and secondary twins in fine grains and the generation of stacking faults and nano-twins in ultrafine grains at higher strains can further promote strain hardening to elevate strength. Furthermore, the effects of grain orientation and grain size on the activation and evolution of dislocations and twins were elucidated. In ultrafine grains, twinning is strongly inhibited due to the elevated critical shear stress for twinning, resulting in more stacking faults and nano-twins, but fewer dislocation cells. The present work contributes to an in-depth understanding of the mechanical properties of fine-/ultrafine-grained materials to exploit their potential for industrial applications.

Effect of thermal ageing on the deformation behaviour of ferrite and austenite in a duplex stainless steel: Micropillar characterisation and dislocation density modelling

The deformation behaviour of the austenitic and ferritic phases in an aged duplex stainless steel is investigated experimentally and numerically. The effect of the ferritic phase’s spinoidal decomposition during thermal ageing on the mechanical behaviour of the alloy is studied through micropillar compression tests on the individual single crystal phases before and after ageing, and APT and TEM investigations of the decomposed ferrite and corresponding dislocation structures. Dislocation density-based crystal plasticity models are formulated for the austenitic and ferritic phases, and calibrated from the measured micropillars responses.A considerably higher and more homogeneously distributed initial dislocation density is observed in the austenite, resulting in a more homogeneous deformation of the austenitic micropillars than the ferritic ones. The spinoidal decomposition of the ferrite leads to a considerable increase of its initial flow stress. The strengthening effect of thermal ageing and the resulting localised deformation response of the aged ferritic micropillars are correctly described by the crystal plasticity results, which required a higher initial obstacle (dislocations + inter-phases of the newly formed α′ domains) density to dislocation motion. Moreover, a strong size effect was observed on the behaviour of the as-received and aged austenitic and as-received ferritic micropillars, but not in the aged ferritic ones. Such contrasting behaviour originates from the fact that, for the size sensitive cases, the dislocation mean free path is controlled by the mean micropillar diameter, whereas in the aged ferrite micropillars, it is by the ∼ 5 nm wide Cr-rich domains within the spinoidal decomposed ferrite.

Nanotwining induced by tensile fatigue and dynamic impact of laser powder bed fusion additively manufactured CoCrFeNi high-entropy alloy

The laser powder bed fusion (L-PBF) additively manufactured CoCrFeNi high-entropy alloy (HEA), with face-centered cubic (FCC) crystal structure, demonstrates better comprehensive mechanical properties in the building direction (BD). Loading quasi-static, dynamic fatigue, and dynamic separated Hopkinson press bar (SHPB) impact stress conditions along the BD of the L-PBF processed HEA exhibit intriguing microstructural evolution characteristics. The L-PBF generates hierarchical dislocation grids containing numerous cell substructures within the HEA FCC grains, impeding dislocation motion during deformation and improving the strength. When subjected to dynamic fatigue loading, the dislocation grids restrict the mean free path of dislocations and thus trigger the activation of abundant stacking faults. Hence, numerous nanotwins form near the end of the fatigue life. Multiple twinning systems can also be activated under dynamic high-speed impact loading. Especially at a low temperature of 77 K, the stacking fault energy of the CoCrFeNi HEA decreases, resulting in increased activation of nanotwins, exhibiting exceptional toughness and resistance to dynamic loads. Additional twin boundaries also impede dislocation movement for the strain hardening. These findings hold valuable implications for the study of additively manufactured HEA parts working in extreme environments.

Dislocation-density-related constitutive model and its applicability to cyclic deformation and damage behavior of 316LN SS at 823 K

In the present investigation, an in-depth understanding of the relationship between dislocation kinetics and cyclic plasticity, along with the description of yield asymmetry behavior during loading and unloading in nuclear grade 316LN austenitic stainless steel at 823 K, was examined by employing a constitutive framework using the evolution of physically-based internal-state variables. The formulation encompassed a set of first-order simultaneous differential equations that governed the evolution of dislocation density, mean free path of dislocations, and back stress. These variables were interdependent with the power law which described the kinetics of plastic strain rate. The evolution equations were numerically integrated, and the simulated data were fitted to the experimental data up to stabilized cycle at a temperature of 823 K and total strain amplitudes of ±0.004, ±0.006, ±0.008 and ± 0.010. The predicted cyclic stress response as a function of the cyclic number displayed the continuous cyclic hardening from the first cycle to the initiation of stabilized cycle. Further, good agreement between the predicted and experimental hysteresis loops was found at different cycle numbers. The predicted dislocation density and tensile peak values of back/effective stress increased with cyclic hardening and approached the value of saturation at the stabilized cycle. On the other hand, a rapid decrease in mean free path with cycle number was noticed. An increase in total strain amplitude resulted in a systematic increase in dislocation density, peak stress, back stress and effective stress. At the total strain amplitudes above ±0.006, the predicted higher rates of dislocation accumulation and annihilation, and the faster evolution rate of back stress towards saturation led to the development of stable dislocation substructure configurations with a clear distinction between dislocation high/low dense regions. Furthermore, the applicability of the model was extended by including an empirical relationship between the damage variable and cycle number within the power law, thereby enabling predictions of the cyclic stress-strain response beyond the stabilized cycle.

The coupled effects of grain boundary strengthening and Orowan strengthening examined by dislocation dynamics simulations

DD simulations are performed to unravel the coupled effects between grain boundary strengthening and Orowan strengthening. With the simulations of a plastically-deformed grain embedded in elastic matrix, the internal stresses associated with inter- and intragranular obstacles are quantified. First, plastic yielding is controlled by the length of dislocation sources. Then, in plastic deformation, the stress contribution of bypassing mechanism increases significantly with the size and number of precipitates, while the stress contribution of geometrically necessary dislocations at grain boundaries slightly decreases. Compared with regular spatial distribution of precipitates, random distribution induces a higher strengthening effect by reducing the dislocation mobility. Simulations of four-grain aggregates involving grain refinement and precipitation are systematically investigated. The volume fraction of precipitates is the key factor controlling the Orowan strengthening in addition to the grain size effect. A generalized Hall–Petch equation based on the mean free path of dislocations is proposed. At low strain, a relatively uniform internal stress field is found inside the aggregates with weak stress concentrations around grain boundaries and precipitates. The underlying mechanisms identified in this work are essential for understanding the plastic behavior of precipitate-strengthened polycrystals.

Achieving excellent mechanical properties in a dual-phase FeCrNi medium entropy alloy through athermal transformations and dislocation structures

In this study, a face-centered cubic (FCC) + body-centered cubic (BCC) dual-phase Fe40Cr40Ni20 (at.%) medium-entropy alloy (MEA) with outstanding mechanical properties was developed. Deformation and strain-hardening mechanisms of the MEA were investigated using a transmission electron microscope. In the FCC phase, dislocation slip was the main deformation mechanism, and twinning appeared at the high-stress stage. Dislocation tangle induced by multi-slip positively contributed to the improvement of strain hardening ability. In the BCC phase, deformation mainly depended on dislocation slip, stress-induced martensitic transformation, and twinning. ω particles resulting from martensitic transformation strongly inhibited dislocation motion. Deformation twins and dislocation structures enhanced the strain-hardening ability by reducing the dislocation mean free path. The BCC/FCC interface also contributed to strain hardening ability by hindering the dislocation movement. The combined action of multiple mechanisms led to the high strain-hardening rate of the MEA.

Impact of interlamellar spacing and non-pearlitic features on mechanical properties and cyclic damage initiation in near-eutectoid pearlitic steels

The relationship between microstructural characteristics and mechanical properties was investigated for C72 and C82 pearlitic steel rods patented at temperatures between 500 °C and 600 °C using a lead bath. Results revealed a refinement of interlamellar spacing upon reduction of patenting temperature. At the same time, the fraction of grain-boundary ferrite and Widmanstätten ferrite as common non-pearlitic regions was slightly increased, reaching a maximum of nearly 1.3 vol.-% in the case of C72 steel patented at 500 °C. Reduction of patenting temperature was associated with strengthening, as confirmed by tensile, fatigue and hardness tests. The strengthening was explained in terms of the Hall-Petch effect for ferrite due to increase in the boundary area. The Hall-Petch coefficient, obtained by taking the apparent interlamellar spacing as the mean free path of dislocations, was in the range 70–140 MPa.μm12. To some extent, these low values could be related to the low solute interstitial content of pearlitic ferrite. More importantly, the coefficients are underestimated due to the plate-shaped morphology of pearlitic ferrite, which causes the average mean free path of dislocations be longer than the apparent interlamellar spacing. Scanning electron microscopy examinations after interrupted fatigue tests indicated the preferred occurrence of intrusions and extrusions, as precursors to fatigue crack, in the non-pearlitic ferrite. The enhancement of fatigue limit at lower patenting temperatures—in spite of slight increase in the fraction of ferrite—is justified by the stress shielding effect of pearlite and necessity of crack propagation into pearlitic regions for stable crack propagation. In effect, as long as the fraction of non-pearlitic features remains low, the interlamellar spacing of pearlite serves as the most efficient strength-controlling microstructural parameter. Furthermore, due to the preferred growth of fatigue cracks parallel to lamellae and deflection at colony boundaries, the refinement of colonies at reduced patenting temperatures is an additional contribution to the fatigue strength.

Exceptional improvement in the yield strength of AZ61 magnesium alloy via cryo-stretching and its implications on the grain growth during annealing

This study explored the influence of pre-stretching temperature on the microstructural characteristics and deformation behavior of AZ61 magnesium alloy and its implications on grain growth during subsequent annealing. AZ61 alloy was stretched to 5% plastic strain along rolling (RD) and transverse direction (TD) at room (RT) and cryogenic temperature (−150 °C, CT) followed by annealing at 320 °C for 1 h to investigate the twinning and dislocation evolution and its consequent effect on the flow stress, plastic strain and strain hardening rate. Compared to RT-stretched samples, significant improvement in yield stress, strain hardening rate and moderate reduction in elongation to failure were witnessed for CT-stretched samples along RD and TD. The subsequent EBSD analysis revealed the increased fraction of fine {10−12} twins and nucleation of multiple {10−12} twin variants caused by higher local stress concentration at the grain boundaries in CT-stretched samples as manifested by the kernel average misorientation. This higher twin fraction and twin-twin interaction imposed the strengthening by restricting the mean free path of dislocations leading to higher flow stress and strain hardening rate. During annealing of the RT/CT-stretched samples, the residual strain energy and twin boundaries were decreased due to static recovery leading to a coarse-grained twin-free microstructure. Strain induced boundary migration (SIBM) was found to be the predominant mechanism governing the grain growth during annealing via movement of high angle grain boundaries.

Combined strengthening from nanoprecipitates, stacking faults and nano-twins enables a strong and ductile medium-entropy alloy

Single-phase face-centered cubic (fcc) alloys typically exhibit remarkable strain-hardening capability and large ductility but possess low yield strength. Conventional strengthening strategies inevitably lead to the loss of ductility. Here, an Nb alloyed CrCoNi-based medium-entropy alloy with a superb yield strength of ∼1.82 GPa, an ultimate tensile strength of ∼1.94 GPa, and good ductility of ∼24 % at 93 K is designed through the combined strengthening from nanoprecipitates, stacking faults, and nano-twins. The cold-rolling is employed to introduce high-density stacking faults and nano-twins, while subsequent low-temperature annealing generates numerous Nb-rich γ″ nanoprecipitates in the fcc matrix. The combined effects of precipitation strengthening, stacking fault- and nanotwin-induced strengthening contribute to an increase in flow stress to surpass the critical stress for the formation of stacking faults and deformation twinning. Moreover, the precipitation of high-density Nb-rich γ″ nanoprecipitates reduces the stacking fault energy of the fcc matrix. Therefore, the precipitation of γ″ nanoprecipitates produces more stacking faults and nano-twins during tensile deformation. The formation of stacking faults and nano-twins in turn, by dynamically introducing high-density interfaces for reducing the mean free path of dislocations, generates a high strain-hardening rate, thus high ultimate tensile strength and large ductility. More importantly, the coherent interfaces between γ′′ nanoprecipitates and the fcc matrix facilitate the transmission of stacking faults and nano-twins across the γ′′ nanoprecipitates. This mechanism could relieve the stress/strain concentrations at interfaces that could otherwise lead to premature crack initiation. This kind of combined strengthening from nanoprecipitates, stacking faults, and nano-twins provides a new avenue to further enhance the strength of nano-twinned materials or precipitation-strengthened materials while maintaining good ductility.

A discrete dislocation dynamics model of creep in polycrystals

The dislocation creep represents high temperature plastic deformation of metallic materials. However, the subject is usually approached with constitutive and phenomenological formulations. The notable exceptions are the recent use of numerical modeling. For example, single-crystal discrete dislocation dynamics (DDD) has been adopted to involve dislocation glide and climb together with diffusion of vacancies. This naturally provides a physics-based framework for dislocation creep. However, the existing model(s) are limited to single crystals and hence are limited in scope. This study extended a single crystal dislocation creep model into polycrystalline ensemble. This was then used to simulate steady state creep rate (ε˙) with respect to creep stress (σ), temperature (T) and grain size (d) in polycrystalline aluminum. Our virtual experiments showed an Arrhenius relationship between ε˙ and T, and a power law scaling with σ. Further, our simulations also revealed a power law increase in ε˙ with d. This is striking, as available experimental data indicate both grain size dependence as well as independence. The answer to this apparent contradiction also emerged from our numerical simulations. It was shown that ε˙ is controlled by interactions of dislocations with static obstacles and grain boundaries. Dominance of static obstacles, in particular, significantly diminished the grain size effect. The role of dislocation mean free path on the pinning and dislocation creep behavior of polycrystalline metallic material was thus mechanistically established.

Effect of grain size on critical twinning stress and work hardening behavior in the equiatomic CrMnFeCoNi high-entropy alloy

While the impact of grain boundary strengthening on dislocation slip is particularly effective in the equiatomic CrMnFeCoNi high-entropy alloy (HEA), its effect on deformation twinning remains unclear. To better understand how a grain size reduction affects the onset of deformation twinning and the work hardening behavior of the CrMnFeCoNi HEA, chemically homogeneous, nearly untextured, and single-phase face-centered cubic alloys with different grain sizes were investigated. Tensile tests were performed at 293 and 77 K and interrupted at different strains followed by systematic transmission electron microscopy observations. In all cases, deformation twinning occurs above a critical stress that is independent of temperature. This uniaxial twinning stress decreases from ∼785 to ∼615 MPa when the grain size increases from 6 to 242 µm, respectively, following the Hall-Petch equation. The resistance of the grain boundaries against slip and twinning is found to be nearly identical (Hall-Petch slope: ∼500 MPa·µm1/2) but the twinning stress extrapolated to infinite grain size (592 ± 30 MPa) is larger than the uniaxial friction stress against dislocation glide at 293 and 77 K (130 and 320 MPa, respectively). Deformation twinning at 77 K is found to sustain a high work hardening rate when it is triggered in a plastic regime dominated by planar glide of dislocations. In contrast, it does not significantly contribute to the work hardening rate at 293 K when dislocation cells have already formed and the dislocation mean free path is smaller than the mean twin spacing.