Gradient nanostructures exhibit superior combination of strength and ductility compared with homogeneous counterparts. However, their practical performance is often limited by the poor thermal stability and restricted strain hardening capability of nanograined layers, as well as severe stress concentration at the fine-coarse grain transition zone, which typically leads to premature failure. Here, we overcome these limitations by introducing a thermomechanical-coupled incremental sheet forming strategy to engineer an oxide-mediated dual-gradient structure in a 316L austenitic stainless steel. During processing, the coupled high compressive stress and intense thermal exposure transform the inherent Cr-passivation film into dispersed nano-oxides penetrating ∼30 µm in depth. Detailed microstructural characterizations reveal a dual-gradient structure, consisting of a grain-size gradient (spanning from ∼40 nm at the surface to ∼20 µm in the core), and a “butterfly-like” dislocation-density gradient (with peak in the mid-layer), both driven by the cyclic thermomechanical gradients. Importantly, these dispersed nano-oxides play a dual and synergistic role: they stabilize the nanograined surface against thermal coarsening during processing, while counterintuitively acting as effective dislocation pinning sites upon plastic strain, thereby enabling sustained strain hardening in the strongest surface layer. In parallel, high-angular resolution EBSD (HR-EBSD) analyses suggest the presence of dense dislocation dipoles in the mid-layers, which mitigate strain concentration in the hard-soft transition regions. As a result, the engineered dual-gradient structure exhibits exceptional strain hardening capability that surpasses the conventional hetero-deformation-induced (HDI) strengthening regime, achieving an ultimate tensile strength approaching 1 GPa together with tensile ductility exceeding 40%. This work provides a new strategy for exploiting the intrinsic Cr-passivation film as a source for in-situ nano-oxide engineering, providing a simple yet powerful route toward simultaneously achieving ultra-high strength, sustained strain hardening, and large ductility without complex alloy design or external particle additions.

The fabrication of Fe/Al laminated thin-walled composites by incremental sheet forming (ISF) is promising for lightweight structural applications but is severely limited by deformation incompatibility and weak interfacial bonding caused by the large mismatch in thermophysical properties between Fe and Al. This work presents a hybrid incremental sheet forming (HISF) strategy incorporating an aluminum powder interlayer is proposed to ensure stable forming while simultaneously enhancing interfacial strength. The adaptive flow and densification of Al powder accommodate local deformation and enable in-situ solid-state bonding, with favorable forming performance maintained, an interfacial shear strength of 108.45 ± 6.26 MPa was obtained, exceeding previously reported values by 15%~20%. The enhanced interfacial strength during dynamic sheet-powder joining process originates from the multiscale heterogeneous structures, which involves macroscale surface texturing and ultrafine grain gradients. A heterogeneous structure of intermetallic compound (IMC) composed of columnar Al13Fe4, elliptical Al13Fe4 and Al8Fe2Si phases is achieved, where the elliptical Al13Fe4 phases act as plug-like reinforcements pinned into the Al matrix. Additionally, the cooperative deformation capability between Fe and Al is improved by cyclic thermo high stress and Fe side grain gradient effect, further improving the interfacial strength. The bonding and strengthening mechanisms of Fe/Al laminated thin-walled composites are revealed in this work, offering a new pathway for the effective fabrication of high-performance Fe-Al composite parts.

The roll forming process effectively reduces sheet metal springback through multi-pass local plastic strain accumulation and residual stress reconstruction. This paper extends previous work that developed a generalized anisotropic distortional hardening (G-ADH) model based on the associated flow rule. Considering the relationship of shear stress and uniaxial tension stress for 1.8GPa steel, the analytical Poly6-I is used. To accurately predict springback in ultra-high strength sheet in nonlinear loading path, the G-ADH model with Young's modulus degradation is used. For comparison, the Chaboche model is also used to predict the loading-reverse loading curves. The results show that the G‑ADH model offers greater flexibility and higher accuracy than the Chaboche model. To further verify the validity of these models, the springback obtained from cold roll‑forming experiments on U‑shaped sections of 1.8GPa steel is employed. The experimental and numerical results demonstrate that, regardless of the presence of side rolls, the “G-ADH + Poly6-I” model considering Young's modulus exhibits high consistency with experimental data in predicting springback with relative errors below 1.5%, which is attributed to simultaneous description of reverse-loading hardening and degradation of the unloading modulus. The springback differs at different profiles perpendicular to the sheet length direction, which originates from the inconsistency in the extent of the local plastic deformation zones. Lower springback is observed during the forming process that includes side rolls. This study reveals the correlation between the springback amplitude and the accumulation of equivalent plastic strains under low stress during U rolling forming of 1.8GPa steel, providing an accurate numerical tool for predicting and reducing springback of ultra-high strength alloys under bending-unloading-reverse bending deformation paths.

Necking evolution of Ti6Al4V titanium alloy under high-temperature tension at low strain rates is a typical non-uniform deformation with significant strain-rate gradients. Accurately predicting this process contributes to revealing materials’ flow behavior during non-uniform and large plastic deformation. In this work, tensile tests conducted at 700 °C and microstructure characterization indicate that the flow behavior of Ti6Al4V exhibits pronounced strain-rate sensitivity and dynamic recrystallization-induced strain softening. Employing a hybrid experimental-numerical strategy, a physically based model is validated as an effective approach for extrapolating post-necking flow stress curves. Subsequently, two phenomenological models are calibrated using these flow stress curves. By deriving the stress updating algorithms in an implicit finite element method, three visco-plastic models are utilized to simulate tension processes with necking evolution. The results suggest that the physically based model predicts tensile necking processes more accurately compared to phenomenological models, despite using similar flow stress curves. The necking evolution simulated by phenomenological models is notably retarded due to the lack of strain-rate history effects. In contrast, the physically based model, which records the strain-rate history, predicts lower flow stress in the necking center but higher flow stress in regions farther from the center, thereby promoting necking localization. Besides, large time increments in simulations fail to capture strain-rate gradients in necking regions, and a recommended time increment is provided to ensure stable simulations of necking evolution.

Electrically-assisted forming (EAF) offers a promising solution for processing difficult-to-form metal foils. Nevertheless, how size effect and current interact during non-uniform plastic deformation is not fully clarified. This study investigates the influence of current on the strain gradient effect through experimental and computational methods. The forming angle decreases gradually with increasing current, as demonstrated by a series of electrically-assisted microbending tests on Ti65 titanium alloy foils. A mechanism-based strain gradient plasticity (SGP) model incorporating current effects is proposed. The model is further employed to quantify the current-induced variation of the material length scale. The strengthening contribution induced by geometrically necessary dislocations follows a non-monotonic trend with the increasing current. It rises initially but diminishes slightly beyond a critical thermal/current condition. The electrically-assisted roll forming process of the semi-hexagonal corrugated sheet is further investigated. Analyzing this process requires concurrently considering both the SGP effect and the non-uniform Joule heating induced by the current. Accordingly, an equivalent heat generation model is developed based on a simplified resistance framework. Coupling this thermal model with the current-dependent SGP theory enables accurate prediction of forming angles of the corrugated sheets. This modeling framework overcomes the oversimplified isothermal assumption in previous EAF simulations, and serves as a generalizable approach for EAF simulations of diverse thin-walled components.

Laminated sheet metal parts comprise two or more substrate sheet metals to leverage the respective performance advantages, yielding superior overall performance with wider application prospects compared to single-layer parts. However, traditional manufacturing methods for sequentially bonding and forming extend development cycle time with poor part performance. In the present work, a novel hybrid manufacturing method synchronizing incremental sheet forming with friction stir additive manufacturing for laminated sheet metal parts is proposed. Through experiments, microstructural characterization and mechanical testing, the influence of process parameters on the mechanical properties and microstructure of heterogeneous materials are investigated. Inspired by biological structure, multiple heterogeneous structures are introduced to enhance the mechanical properties and bonding performance, including dual-gradient grain and bimodal grain structures in material matrix and interlocking corrugated texture at the Steel/Al interface. The dual-gradient grain structure from surface to interior of steel matrix reflects a transition from grain refinement to dynamic recrystallisation. The coarse grains in bimodal structure of aluminum matrix underwent severe plastic deformation with significant precipitation behavior and the ultrafine grains exhibit recrystallisation behavior along with numerous stacking faults. It is also found that the average misorientation value in the corrugated interface is markedly higher than those in material matrix, along with abundant dislocations and twin structures within interfacial compound layer. Both yield strength and shearing strength of laminated sheet materials significantly increase with rising pre-strain and interface corrugation, reaching 437 MPa and 112 MPa at a pre-strain of 0.30 and corrugated amplitude of 10 mu m, respectively and encompassing those of laminated materials by conventional processes reported. This work reveals a fundamental mechanism that heterostructure-induced stress partitioning contributes to the synergistic enhancement of mechanical property and interfacial bonding, with the contribution rate of back stress reaching 76% of yield stress. Finally, case studies demonstrate the proposed process realizes integrated forming-bondingadditive manufacturing of laminated sheet metal parts with short cycle time, enabling the in-situ engineering of multi-scale heterogeneous structures to simultaneously improve strength and bonding performances.

Accurately predicting and controlling machining-induced residual stress is essential for high-precision manufacture of complex TC4 components, especially for multi-pass precision milling with significant microstructure evolution and size effect, which undermine the accuracy of predicting residual stress. Furthermore, once the thickness of each tooth is generally smaller the tool edge radius under milling, the size effect is enhanced under the minimum uncut chip thickness (MUCT). In the present work, an analytical model for predicting residual stress in multi-pass precision milling was established by considering size effect under two synergistic pathways. Grain refinement and geometrically necessary dislocations (GND) induced by preceding pass were incorporated in the proposed model as initial condition, while the primary shear zone governed by MUCT was set as boundary condition. A finite element model was established to compute MUCT and predict residual stress. Multi-pass milling experiments validate the analytical and numerical simulation results. Analytical and experimental investigations indicate that machined subsurface develops pronounced strain gradients and a sharp increase in GND density, which increases stress magnitude and residual stress-affected depth in subsequent passes. Analytical results reveal that size effect affects the dynamics of material flow, an average prediction error for residual stress decreased by 27.65% compared with models without considering size effect. Similarly, incorporation of the size effect causes the depth of maximum compressive residual stress to increase from 1.5 mu m in the first pass to 2.4 mu m and 3.3 mu m in the subsequent passes, indicating a substantially deeper stress-affected zone than that predicted without the size effect. Numerical simulation validates the determined MUCT, yielding a 22.93% reduction in the average relative prediction error compared with the model neglecting size effect. The established model resolves residual stress superposition and size effect in milling by integrating microstructural evolution and MUCT, providing a theoretical foundation for toolpath-controlled industrial applications.

The Mg-4Y-3RE (WE43) magnesium alloy possesses high specific strength, excellent shock absorption, strong electromagnetic shielding, and recyclability. However, the oxidation and defects often happen during conventional welding. Solid-state diffusion bonding in a near-vacuum environment enables high-reliability joints by minimizing these issues. It is difficult to obtain high bonding joint strength due to the limitation of various factors. This work systematically investigates the effects of temperature, time, pressure, and surface roughness on the diffusion-bonded joint quality of WE43 magnesium alloy through a phased optimization strategy. The optimal parameter combination is optimized. The results demonstrate that the joint interface achieves a shear strength of 179.9 ± 3.9 MPa and a bonding ratio of 94.14 % when the minimal plastic deformation is ensured. Microstructural characterization reveals that recrystallization, precipitates evolution and elemental diffusion effects collectively promote metallurgical bonding at the interface. Subsequent solution treatment at 525 °C for 8 h and aging at 250 °C for 16 h, the shear strength significantly increases to 229.5 ± 5.2 MPa, which represents the highest value in comparable reported studies. This research provides theoretical foundations and technical references for solid-state bonding processes of high-strength magnesium alloys.

Premature interfacial failure in Fe/Al heterogeneous thin-walled components remains a critical challenge during conventional joining-before-forming processes due to severe plastic incompatibility. To address this, an interfacial joining and strengthening strategy based on Hybrid Incremental Sheet Forming (HISF) is proposed. This novel approach integrates a corrugated interface geometry with a steel-side grain-size gradient (CGI) under a cyclic micro-plastic loading scheme. By employing Molecular Dynamics (MD) simulations alongside macroscopic shear tests and microstructural characterizations, the shear response and defect evolution across the Fe/Al interface are elucidated. The findings reveal that the CGI strategy effectively alleviates interfacial stress concentration and promotes directional atomic diffusion. This promotes a transition in the dominant failure mode from interface-dominated brittle debonding to Al matrix-dominated ductile fracture, simultaneously enhancing shear strength and deformation compatibility. Based on these mechanisms, a semi-empirical shear strength model was established, providing mechanistic insight for the interfacial design and forming-path optimization of high-performance heterogeneous metal components.

A remarkable room-temperature precipitation strengthening method is proposed in this work, which significantly enhances the strength of conventionally un-heat-treatable Al-2.5Mg-0.4Fe sheet. It is found that the combination of severe plastic deformation and cyclic loading triggers the precipitation of abundant ultrafine-grained Al₁₃Fe₄ phases ranging from 100 to 1000 nm at room temperature. With increasing strain of 0.8 and loading cycles of 2000, the Al-2.5Mg-0.4Fe alloy exhibits excellent tensile strength of 480 MPa, far exceeding that by conventional strengthening method. It is indicated that both grain refinement strengthening and precipitation strengthening become more pronounced as plastic strain and cyclic loading increase, dominating the mechanical enhancement. Despite high stacking fault (SF) energy of aluminum alloy, cyclic severe plastic deformation (CSPD) introduces numerous SFs by grain nanocrystallization and Fe atom segregation. Molecular dynamics analysis reveals that the presence of Fe solute atoms significantly promotes the structural transformation under cyclic shear strain. Moreover, the enhanced precipitation strengthening effect through twin refinement is investigated during CSPD, in which the twinned precipitates not only act as strong dislocation barriers to dislocation motion, but also as plasticity carriers to coordinate matrix deformation. This study presents a simple but effective room-temperature strengthening strategy for non-heat-treatable alloys.

Electrically assisted forming (EAF) technologies leverage electroplastic effects induced by electric current passage through metallic materials to enhance the deformation ability of difficult-to-form alloys, such as titanium alloys, which typically require elevated temperature (>700 degrees C) for high-precision forming due to their limited formability at lower temperature. However, microstructure evolution and mechanical response prediction of titanium alloy foils during EAF at elevated temperature remain insufficiently investigated owing to complex interplay between electroplasticity and size effect. In the present study, electrically assisted uniaxial tensile experiments were performed on Ti65 titanium alloy foils with a thickness of 0.1 mm and grain sizes ranging from 7.2 mu m to 22.3 mu m. Experimental results demonstrated that electric current-induced softening and strain rate strengthening exhibit a pronounced size effect. Initial grain size and critical recrystallization strain show an inverse correlation. Dynamic recrystallization (DRX) volume fraction increases significantly with electric current density for fine-grained specimens. But, the effect of current density on DRX process is limited and nonmonotonic for coarse-grained specimens. A physically based constitutive model that integrates size effects with multiple strengthening and softening mechanisms is developed. The proposed model accurately characterizes the flow softening behavior of Ti65 titanium alloy foils with different initial grain sizes across varying electric current densities and strain rates. It is revealed that grain coarsening significantly weakens the contributions of precipitation strengthening and DRX softening on dislocation density evolution. Furthermore, significant flow stress drop due to athermal electroplasticity is calculated based on the proposed model.

The performance of thin-walled components (TWC) in advanced applications is critically governed by the surface characteristics, which encompass both macroscopic morphology and subsurface microstructure. Conventional manufacturing struggles to synergistically tailor the macro and micro aspects in a single process. This study introduces a novel hybrid manufacturing strategy, ISF-M, which can achieve cyclic integration of incremental sheet forming (ISF) and NC milling. By dynamically switching the rotation direction of a bespoke ratchet-shaped tool, alternating cycles of localized plastic deformation and material removal within a single toolpath can be achieved. Experiments demonstrate that ISF-M transcends the capabilities of individual or sequential processes by enabling coordinated control over macro-surface texture and micro-scale grain gradient. It is found that ISF-M process provides a superior capability of generating various surface morphologies that can combine formed, milled and integrated surface textures through designed forming-milling sequences, and the surface morphologies in ISF and ISF-M can be predicted accurately through a proposed model with considerations of geometric relationship and elastic-plastic deformation. Besides, the increasing of milling operation during ISF-M significantly enhances the depth and refinement of ultrafine-grained gradient structure. Finite element analysis reveals that this is attributed to the cyclic shear stress and the intense stress gradient inside surface material under the alternating milling and forming of ISF-M process. Therefore, by combining the characteristics of the iso-material and subtractive-material manufacturing, the new ISF-M method provides an innovative solution for fabricating TWCs with multi-scale structured surface and enhanced mechanical properties in one step.

While Sc and Zr additions markedly improve the printability and mechanical properties of Al-Mg alloys fabricated via additive manufacturing (AM), the recyclability and sustainability of supersaturated Sc/Zr-containing alloys remain largely unexplored. Here, Al-Mg-Sc-Zr alloys with Sc/Zr contents spanning the AM-relevant compositional range, were prepared by conventional casting and tailored heat treatments to mimic the microstructure-property evolution in recycled Al scraps enriched with Sc and Zr. Dual-scale second phases are identified, comprising micrometer-scale primary Al3(Sc1-x, Zrx) particles and nanoscale L12-Al3(Sc1-x, Zrx) precipitates. Moreover, three distinct primary particles, i.e., Zr-dominated, Sc-dominated and Sc/Zr-enriched are revealed. The associated local strain/stress concentration and geometrically necessary dislocation densities are quantitatively resolved using high-resolution EBSD. A competitive interaction between dual-scale second phases is demonstrated to govern recrystallization, where particle-stimulated nucleation and Zener pinning act antagonistically, leading to non-monotonic dependence of recrystallization and room/high temperature mechanical properties on Sc/Zr contents. These findings establish a quantitative composition-precipitation-property framework for the sustainable design of high-performance Al alloys recycled from AM applications.

Yield criterion with concise parameters and high accuracy has always been recommended for industrial applications. Based on a novel modeling strategy of gradual surface-distortion (GSD), an analytical yield criterion framework is constructed under the associated flow rule, integrating simplicity, generality and flexibility. Derived from structures of SY2009 criterion, R-value and curvature control terms with independent parameter calibration are developed, resulting in yield surface distortion occurring gradually. Three curvature variables are integrated into a single factor through empirical formulas without additional pure shear and plane strain tension experiments. This framework is an eighth-order homogeneous polynomial, with all parameters uniquely determined through a set of mechanical tests conducted under plane stress conditions. Initially, a simplified GSD version is constructed to characterize yield loci of BCC and FCC materials, requiring a minimum of only seven experimental data (T0, T45, T90, TEB, r0, r45, r90). Subsequently, by introducing stresses and R-values in two optional directions, an extended GSD version is proposed to enhance strong anisotropy description. The generality and accuracy of this framework are validated across 19 different materials to predict yield locus, uniaxial stress and Rvalue curves. The results demonstrate that the simplified model almost replicates Yld2000-2d and enables accurate prediction in the evolution of yield locus under anisotropic hardening. For strongly anisotropic materials, the extended model exhibits high prediction accuracy. By using an implicit finite element method, this framework accurately predicts the earing profile in cup drawing of AA3104-H19. Besides, the convexity trust-domain and the generality of curvature variables are discussed.

Metal extrusion printing is a metal additive manufacturing technology based on extrusion molding. This study is based on this method for forming and printing 6061 aluminum alloy composite slurry. Analyzed the extrusion effect of different metal contents. Through multiple experiments, found the optimal extrusion speed, printing speed, and layer height. On this basis, the role of sintering conditions (temperature, rate, and duration) in influencing mechanical properties was further studied. After optimizing the sintering process, the compressive strength of the sintered part obtained was reaching 31.95 MPa, approximately 5.55 times that of before sintering, proving the effectiveness of the process optimization, achieving optimization of the printing and forming process parameters of 6061 aluminum alloy.

The production of aero engine casings requires forming Ti-6Al-4V cylinders with low aspect ratios. Compared to conventional thermal forming, electrically assisted forming demonstrates higher efficiency and leverages non-thermal effects to enhance the plastic deformation ability of Ti-6Al-4V titanium alloy. The electrically assisted differential thermal bulging, combining characteristics of thermal/electrically assisted forming, produces the cylinder components that maintain peak tensile strength among all experimental conditions across 25–350℃ under lower effective currents and forming temperatures. During bulging process design, the finite element methods were performed to optimize electrode quantity and spacing, which aims to alleviate thermal expansion and achieve uniform electrical/thermal distribution. The cylinder components produced via this novel approach exhibit only 40

This study aims to predict the thickness variation of Al3003-H14 square lithium battery shells during multi-stage deep drawing and ironing processes. A modified material model, MAT122_3R_3D_CL_user, was developed by coupling the Hill'48 yield function and Cockcroft & Latham ductile damage criterion through secondary development in LS-DYNA. Anisotropic parameters for MAT122_3R_3D were determined using Lankford coefficients (r0, r45 , r90 ) obtained from uniaxial tensile tests. Numerical simulations with 3D solid elements accurately captured thickness changes and failure positions, which aligned well with experimental results. The causes of thickness deviations, including simplified assumptions for anisotropic coefficients and constant friction condition, were analysed. The proposed model enables optimization of process parameters to prevent excessive thinning or fracture during forming.

As an innovative small-batch forming method, flexible free incremental sheet forming (FFISF) utilizes two auxiliary sheets on both sides of the sheet metal to increase its hydrostatic stress, showing its promising advantages in rapidly fabricating sheet metal part of titanium alloy at room temperature. However, due to the significant springback of titanium alloy and complex deformation states in FFISF such as cyclic loading, bending and through-thickness stresses, accurate simulation of the springback of TC4 titanium alloy after FFISF remains challenging. To address this problem, this work adopts various flow stress equations, kinematic hardening models and anisotropic yield criteria to analyse the influence of constitutive relationship on the simulation accuracy of the springback for U-shaped TC4 parts at room temperature. By comparing simulation results with experimental data, key factors of constitutive models influencing the simulation accuracy are identified and the springback behaviour of TC4 sheet metal by FFISF is further elaborated. Finally, an accurate simulation of the springback after FFISF is achieved by utilizing appropriate constitutive models for TC4 titanium alloys at room temperature. This work offers notable benefits for facilitating the accurate manufacturing of complex titanium components using FFISF at room temperature, therefore expanding the potential of industrial application.

The Mg-4Y-3RE (WE43) magnesium alloy possesses significant advantages such as high specific strength, excellent shock absorption, strong electromagnetic shielding capabilities and recyclability. However, its close-packed hexagonal structure leads to poor plasticity at room temperature, which limits its broader engineering applications. Therefore, superplastic forming at high temperatures is used to manufacture the components from this alloy. This study conducted tensile tests on hot-rolled WE43 rare-earth magnesium alloy with coarse grains at various temperatures and strain rates. The high-temperature superplastic properties were characterized, revealing the intrinsic mechanisms of thermal deformation behavior. The results indicate that the best superplasticity is achieved at 460 °C. This is attributed to the smallest grain size, the weakest texture, and the relatively uniform distribution of the second phase at this temperature. The influence of strain rate on elongation at temperatures among 440 °C∼500 °C is not significant as the impact of strain rate is multifaceted. Meanwhile, the elongation can reach up to 367.7 ± 3.7 % at a strain rate of 0.01s−1, which exhibits the high strain rate superplasticity (HSRS). Under these conditions, the deformation of coarse-grained WE43 rare-earth magnesium alloy is controlled by grain boundary sliding (GBS) and solute drag dislocation creep. Furthermore, the GBS involves deformation coordination mechanisms such as grain boundary diffusion, lattice diffusion, dislocation climbing, and dynamic recrystallization accommodation mechanisms.

A new variant of incremental sheet forming method with two-layer auxiliary sheet under target blank, named as DS-ISF, is developed to induce through-thickness gradient plastic deformation on formed commercial-purity titanium (CP-Ti) panel at room temperature. Gradient plastic deformation induces significant refinement of 18 nm and hardening of 6 GPa, breaking through the limit of structural refining and hardening during traditional SPD. General pattern of structural evolution toward nanoscale involves: generation of T/M lamellae, development of T/M blocks, formation of EDs and UFL structures, and evolution of NL mixed with NE structures. Special attention is paid to the influence of strain gradient on structural refining and hardening below the structural size limit. Formation of NL mixed with NE structure dependents upon longitudinal subdividing and transverse fragmenting mechanisms, which is realized by strain gradient-accumulated high-density GNDs forming extended boundaries with critical misorientation angle of 3.5 degrees. Operating longitudinal subdividing requires a minimum strain gradient of eta(L)=0.25 mu m(-1), while performing transverse fragmenting needs a minimum strain gradient of eta(T)=0.75 mu m(-1). Hardening mechanism below the size limit is analyzed in terms of the linear additivity of boundary strengthening and dislocation strengthening. Refining behavior (d(T), mu m) and hardening behavior (Delta HV, GPa) correlated with strain gradient (eta, mu m(-1)) is quantified by d(T)=0.015/eta and Delta HV=4.8 root eta, respectively.