Achieving high strength and high ductility in nanostructured metals: Experiment and modelling

Engineering nanostructures in metallic materials such as nanograins and nanotwins can promote plastic performance significantly. Nano/ultrafine-grained metals embedded in coarse grains called bimodal metals and nanotwinned polycrystalline metals have been proved to possess extensively improved yield strength whilst keeping good ductility. This paper will present an experimental study on nanostructured stainless steel prepared by surface mechanical attrition treatment (SMAT) with surface impacts of lower strain rate (10 s^?1–10³ s^?1) and higher strain rate (10⁴ s^?1–10⁵ s^?1). Microstructure transition has been observed from the original γ-austenite coarse grains to α′-martensite nanograins with bimodal grain size distribution for lower strain rates to nanotwins in the ultrafine/coarse grained austenite phase for higher strain rates. Meanwhile, we will further address the mechanism-based plastic models to describe the yield strength, strain hardening and ductility in nanostructured metals with bimodal grain size distribution and nanotwinned polycrystalline metals. The proposed theoretical models can comprehensively describe the plastic deformation in these two kinds of nanostructured metals and excellent agreement is achieved between the numerical and experimental results. These models can be utilized to optimize the strength and ductility in nanostructured metals by controlling the size and distribution of nanostructures.     

SIMULATIONS OF MECHANICAL BEHAVIOR OF POLYCRYSTALLINE COPPER WITH NANO-TWINS

Mechanical behavior and microstructure evolution of polycrystalline copper with nano-twins were investigated in the present work by finite element simulations. The fracture of grain boundaries are described by a cohesive interface constitutive model based on the strain gradient plasticity theory. A systematic study of the strength and ductility for different grain sizes and twin lamellae distributions is performed. The results show that the material strength and ductility strongly depend on the grain size and the distribution of twin lamellae microstructures in the polycrystalline copper.     

纳米孪晶和梯度纳米结构金属强韧特性研究进展

金属材料在航空、航天工业以及民用工业等领域具有广泛的应用,如何获取同时具备高强度和良好塑性的金属材料一直是材料、物理、力学等不同学科长期以来亟待解决的难题.传统的强化方法包括应变强化、固溶强化、相变强化、晶粒细化强化和第二相弥散强化等,均会使材料的韧性或塑性降低.近年来,实验研究发现通过界面设计和微结构调控来可以制备出高强高韧的金属材料,认为位错与各类界面的相互作用、以及微结构优化对应力集中的削弱是材料强化和韧化的主要原因.根据已有实验观察,人们通过原子尺度方法定量分析高强高韧金属材料的变形机理,揭示其强化和韧化机制;同时,发展出基于变形机理的理论模型和有限元方法定量描述高强高韧金属的力学行为.论文将重点介绍纳米孪晶金属和梯度纳米结构金属的强韧特性研究进展,并对新型纳米结构金属材料的强韧特性优化进行展望.     

Plastic flow stability of nanotwinned Cu foils

The plastic flow stability of nanotwinned Cu foils was investigated via room temperature rolling. Nanotwinned Cu, with an average twin thickness of 5 nm, exhibited stable plastic flow without shear localization or fracture, even at thickness reduction of over 50%. The retention of {1 1 1} fiber texture after rolling indicates insignificant out-of-plane rotation of the columnar grains and is interpreted in terms of a symmetric slip model. No significant change in the average twin lamellae thickness was seen even at thickness reduction of over 50%, suggesting that some twin boundaries were annihilated during deformation. The annihilation of very thin twins is a consequence of migration of twin boundaries due to the glide of twinning dislocations (disconnections) in the twin plane. The work hardening after rolling is correlated with the dislocation storage at twin boundaries.     

Effect of microstructure on the nucleation of deformation twins in polycrystalline high-purity magnesium: A multi-scale modeling study

A multi-scale, theoretical study of twin nucleation from grain boundaries in polycrystalline hexagonal close packed (hcp) metals is presented. A key element in the model is a probability theory for the nucleation of deformation twins based on the idea that twins originate from a statistical distribution of defects in the grain boundaries and are activated by local stresses at the grain boundaries. In this work, this theory is integrated into a crystal plasticity constitutive model in order to study the influence of these statistical effects on the microstructural evolution of the polycrystal, such as texture and twin volume fraction. Recently, a statistical analysis of exceptionally large data sets of {101?2} deformation twins was conducted for high-purity Mg (Beyerlein et al., 2010a). To demonstrate the significantly enhanced accuracy of the present model over those employing more conventional, deterministic approaches to twin activation, the model is applied to the case of {101?2} twinning in Mg to quantitatively interpret the many statistical features reported for these twins (e.g., variant selection, thickness, numbers per grain) and their relationship to crystallographic grain orientation, grain size, and grain boundary misorientation angle. Notably the model explains the weak relationship observed between crystal orientation and twin variant selection and the strong correlation found between grain size and the number of twins formed per grain. The predictions suggest that stress fluctuations generated at grain boundaries are responsible for experimentally observed dispersions in twin variant selection.     

Grain size,strain rate,and temperature dependence of flow stress in ultra-fine grained and nanocrystalline Cu and Al: Synthesis,experiment, and constitutive modeling

For the first time, high quality bulk nanocrystalline (nc) fcc metals, with least amounts of imperfections, exhibiting high strength and ductility at room and different temperatures, under quasi-static and dynamic types of loading, were prepared and a comprehensive study on their post-yield mechanical properties was performed. This investigation included study of the effect of temperature on stress–strain responses of mechanically milled bulk nc Cu and Al. The samples after preparation through mechanical milling and consolidation processes were subjected to uniaxial compressive loading at quasi-static and dynamic strain rates of 10⁻² s⁻¹ and 1840–3105 s⁻¹, respectively, at temperatures ranging from 223 to 523 K. In both materials strong dependency of flow stress to temperature was observed; this dependency was rather more pronounced when the materials were tested at the quasi-static strain rate. Further, a new grain size and temperature dependent viscoplastic phenomenological constitutive equation, Khan–Liang–Farrokh (KLF) model was developed based on the Khan–Huang–Liang (KHL) constitutive equation. The model was featured to correlate different characteristic behaviors of polycrystalline materials in the plastic regime, as the result of grain refinement. In addition, the viscoplastic responses of bulk Cu and Al of different grain sizes (from sub-micron to nanometer range), and those from bulk nc Cu and Al at different strain rates (quasi-static to dynamic), recently published (21 and 22), were simulated using the newly developed equation. The results confirmed reasonable capability of the developed model to correlate a wide spectrum of the viscoplastic responses of these fcc metals.     

An investigation of the combined size and rate effects on the mechanical responses of FCC metals

The molecular dynamics (MD) simulations are performed with single-crystal copper blocks under simple shear to investigate the size and strain rate effects on the mechanical responses of face-centered cubic (fcc) metals. It is shown that the yield stress decreases with the specimen size and increases with the strain rate. Based on the theory of dislocation nucleation, a modified power law is proposed to predict the scaled behavior of fcc metals, which agrees well with the numerical and experimental data ranging from nanoscale to macro-scale. In the MD simulations with different strain rates, a critical strain rate exists for each single-crystal copper block of given size, below which the yield stress is nearly insensitive to the strain rate. A hyper-surface is therefore formulated to describe the combined size and strain rate effects on the plastic yield strength of fcc metals. The preliminary results presented in this paper demonstrate the potential of the proposed simple procedure for engineering design at various spatial and temporal scales.     

High Strain Rate Torsion Properties of Ultrafine-Grained Aluminum

Mechanical properties of most metallic materials can be improved by reducing their grain size. One of the methods used to reduce the grain size even to the nanometer level is the severe plastic deformation processing. Equal Channel Angular Pressing (ECAP) is one of the most promising severe plastic deformation processes for the nanocrystallization of ductile metals. Nanocrystalline and ultrafine grained metals usually have significantly higher strength properties but lower tensile ductility compared to the coarse grained metals. In this work, the torsion properties of ECAP processed ultrafine grained pure 1070 aluminum were studied in a wide range of strain rates using both servohydraulic materials testing machines and Hopkinson Split Bar techniques. The material exhibits extremely high ductility in torsion and the specimens did not fail even after 300% of strain. Pronounced yield point behavior was observed at strain rates 500 s⁻¹ and higher, whereas at lower strain rates the yielding was continuous. The material showed slight strain softening at the strain rate of 10⁻⁴ s⁻¹, almost ideally plastic behavior at strain rates between 10⁻³ s⁻¹ and 500 s⁻¹, and slight but increasing strain hardening at strain rates higher than that. The tests were monitored using digital cameras, and the strain distributions on the surface of the specimens were calculated using digital image correlation. The strain in the specimen localized very rapidly after yielding at all strain rates, and the localization lead to the development of a shear band. At high strain rates the shear band developed faster than at low strain rates.     

A first-principles measure for the twinnability of FCC metals

Twinnability is the property describing the ease with which a metal plastically deforms by twinning relative to deforming by dislocation-mediated slip. In this paper a theoretical measure for twinnability in face-centered-cubic (fcc) metals is obtained through homogenization of a recently introduced criterion for deformation twinning (DT) at a crack tip in a single crystal. The DT criterion quantifies the competition between slip and twinning at the crack tip as a function of crack orientation and applied loading. The twinnability of bulk material is obtained by constructing a representative volume element of the material as a polycrystal containing a distribution of microcracks and integrating the DT criterion over all possible grain and microcrack orientations. The resulting integral expression depends weakly on Poisson's ratio and significantly on three interfacial energies: the stacking-fault energy, the unstable-stacking energy and the unstable-twinning energy. All these four quantities can be computed from first principles. The weak dependence on Poisson's ratio is exploited to derive a simple and accurate closed-form approximation for twinnability which clarifies its dependence on the remaining material parameters. To validate the new measure, the twinnability of eight pure fcc metals is computed using parameters obtained from quantum-mechanical tight-binding calculations. The ranking of these materials according to their theoretical twinnability agrees with the available experimental evidence, including the low incidence of DT in Al, and predicts that Pd should twin as easily as Cu.     

Phase-field simulation of the coupled evolutions of grain and twin boundaries in nanotwinned polycrystals

Nanotwinned polycrystals exhibit an excellent strength-ductility combination due to nanoscale twins and grains. However, nanotwin-assisted grain coarsening under mechanical loading reported in recent experiments may result in strength drop based on the Hall-Petch law. In this paper, a phase-field model is developed to investigate the effect of coupled evolutions of twin and grain boundaries on nanotwin-assisted grain growth. The simulation result demonstrates that there are three pathways for coupled motions of twin and grain boundaries in a bicrystal under the applied loading, dependent on the amplitude of applied loading and misorientation of the bicrystal. It reveals that a large misorientation angle and a large applied stress promote the twinning-driven grain boundary migration. The resultant twin-assisted grain coarsening is confirmed in the simulations for the microstructural evolutions in twinned and un-twinned polycrystals under a high applied stress.     

高速冲击表面处理对金属材料力学性能和组织结构的影响

高速冲击表面处理过程中的应变率对金属材料的宏观力学性能和微观组织结构都具有重要影响。根据当前应变率效应的研究成果,从宏观与微观相结合的角度出发,综述了高速冲击表面处理过程中应变率对金属材料强度和塑性的影响规律,并重点阐述了不同应变率下金属材料内部微观组织结构的演变规律,主要包括晶粒结构、绝热剪切带、相变、位错组态和析出相以及变形孪晶等。此外,还分析了组织结构随应变率的演化和微观变形机制的转变对材料力学性能的强化和弱化机理。最后,对高速冲击表面处理梯度组织的变形特点进行了总结。提出了不同组织结构对材料性能影响的综合效应模型,以期为应变率效应的深入研究奠定基础。     

Size effects on the martensitic phase transformation of NiTi nanograins

The analysis of nanocrystalline NiTi by transmission electron microscopy (TEM) shows that the martensitic transformation proceeds by the formation of atomic-scale twins. Grains of a size less than about 50 nm do not transform to martensite even upon large undercooling. A systematic investigation of these phenomena was carried out elucidating the influence of the grain size on the energy barrier of the transformation. Based on the experiment, nanograins were modeled as spherical inclusions containing (0 0 1) compound twinned martensite. Decomposition of the transformation strains of the inclusions into a shear eigenstrain and a normal eigenstrain facilitates the analytical calculation of shear and normal strain energies in dependence of grain size, twin layer width and elastic properties. Stresses were computed analytically for special cases, otherwise numerically. The shear stresses that alternate from twin layer to twin layer are concentrated at the grain boundaries causing a contribution to the strain energy scaling with the surface area of the inclusion, whereas the strain energy induced by the normal components of the transformation strain and the temperature dependent chemical free energy scale with the volume of the inclusion. In the nanograins these different energy contributions were calculated which allow to predict a critical grain size below which the martensitic transformation becomes unlikely. Finally, the experimental result of the atomic-scale twinning can be explained by analytical calculations that account for the transformation-opposing contributions of the shear strain and the twin boundary energy of the twin-banded morphology of martensitic nanograins.     

A variational multiscale constitutive model for nanocrystalline materials

This paper presents a variational multi-scale constitutive model in the finite deformation regime capable of capturing the mechanical behavior of nanocrystalline (nc) fcc metals. The nc-material is modeled as a two-phase material consisting of a grain interior phase and a grain boundary effected zone (GBAZ). A rate-independent isotropic porous plasticity model is employed to describe the GBAZ, whereas a crystal-plasticity model which accounts for the transition from partial dislocation to full dislocation mediated plasticity is employed for the grain interior. The constitutive models of both phases are formulated in a small strain framework and extended to finite deformation by use of logarithmic and exponential mappings. Assuming the rule of mixtures, the overall behavior of a given grain is obtained via volume averaging. The scale transition from a single grain to a polycrystal is achieved by Taylor-type homogenization where a log-normal grain size distribution is assumed. It is shown that the proposed model is able to capture the inverse Hall-Petch effect, i.e., loss of strength with grain size refinement. Finally, the predictive capability of the model is validated against experimental results on nanocrystalline copper and nickel.     

Effect of crystalline grain structures on the mechanical properties of twinning-induced plasticity steel

In order to improve the mechanical properties of twinning-induced plasticity steel, the grain morphology was tailored by different solidification technologies combined with deformation and heat treatment processing routes. Three typical grain morphologies, i.e., equiaxed, columnar as well as equiaxed/columnar grains were formed, and their mechanical behaviors were comparatively studied. Among the three materials, the equiaxed grain material exhibited the highest strength but the lowest plasticity. Depending on the grain size, the smaller the grain size, the higher the strength, but the lower the elongation. The columnar grain material possessed the most excellent plasticity but the weakest strength.These properties presented a non-monotonic dependence on the dendrite spacing, and the moderate spacing resulted in the optimum combination of strength and plasticity. The equiaxed/columnar grain coexisted material showed interesting properties, i.e., the strength and plasticity were just between those of single grain-shaped materials. The three materials also presented different strain hardening behaviors particularly in the uniform deformation stage. The equiaxed grain material showed a constant strain hardening rate, while the columnar grain and equiaxed/columnar grain materials showed a progressively increasing rate with increasing the true strain.     

Combined grain size, strain rate and loading condition effects on mechanical behavior of nanocrystalline Cu under high strain rates

Molecular dynamics simulations of nanocrys-talline Cu with average grain sizes of 3.1 nm, 6.2 nm, 12.4 nm and 18.6 nm under uniaxial strain and stress tension at strain rates of 10 8 s 1 , 10 9 s 1 and 10 10 s 1 are performed to study the combined grain size, strain rate and loading condition effects on mechanical properties. It is found that the strength of nanocrystalline Cu increases as grain size increases regardless of loading condition. Both the strength and ductility of nanocrystalline Cu increase with strain rate except that there is no monotonic relation between the strength and strain rate for specimens under uniaxial strain loading. Moreover, the strength and ductility of specimens under uniaxial strain loading are lower than those under uniaxial stress loading. The nucleation of voids at grain boundaries and their subsequent growth characterize the failure of specimens under uniaxial strain loading, while grain boundary sliding and necking dominate the failure of specimens under uniaxial stress loading. The rate dependent strength is mainly caused by the dynamic wave effect that limits dislocation motion, while combined twinning and slipping mechanism makes the material more ductile at higher strain rates.     

Confined impinging twin air jets at high Reynolds numbers

An experimental study is carried out to investigate flow characteristics of confined twin jets issuing from the lower surface and impinging normally on the upper surface. Pressure distributions on the impingement and confinement plates were obtained for Reynolds numbers ranging from 30,000 to 50,000, nozzle-to-plate spacing (H/D) in the range of 0.5-4 and jet-to-jet spacing (L/D) in the range of 0.5-2. Smoke-wire technique was used to visualize the flow behavior. The effects of Reynolds number, nozzle-to-plate spacing and jet-to-jet spacing on the flow structure are examined. The subatmospheric regions occur on both impingement and confinement plates at the nozzle-to-plate spacing up to 1 for all studied Reynolds numbers and jet-to-jet spacings in consideration. They lie nearly up to the same radial location at both surfaces and move radially outward from the stagnation points with increasing nozzle-to-plate spacing and jet-to-jet spacing. It is concluded that there exists a relation between the subatmospheric regions and peaks in heat transfer coefficients for low spacings in the impinging jets.     

梯度纳米结构金属力学性能、变形机理和多尺度计算研究进展

近年来,梯度纳米结构金属因其优越的力学性能和独特的塑性变形机理受到广泛关注,已成为材料与力学学科的热点和前沿。本文首先介绍梯度纳米结构金属的强度、塑性、加工硬化和抗疲劳等核心力学性能,以及晶粒长大、塑性应变梯度和几何必需位错等塑性变形机理及其力学研究。其次介绍梯度纳米结构金属的多尺度计算与模拟研究。最后讨论梯度纳米结构金属研究领域存在的挑战。     

Characterization of yielding behavior of polycrystalline metals with single crystal plasticity based on representative characteristic length

Single crystal plasticity based on a representative characteristic length is proposed and introduced into a homogenization approach based on finite element analyses, which are applied to characterization of distinctive yielding behaviors of polycrystalline metals, yield-point elongation, and grain size strengthening. The computational manner for an implicit stress update is derived with the framework of a standard multi-surface plasticity at finite strain, where the evolution of the characteristic lengths are numerically converted from the accumulated slips of all of slip systems by exploiting the mathematical feature of the characteristic length as the intermediate function of the plastic internal variables. Furthermore, a constitutive model for a single crystal reproduces the stress–strain curve divided into three parts. Using two-scale finite element analysis, the macroscopic stress–strain response with yield-point elongation under a situation of low dislocation density is reproduced. Finally, the grain size effect on the yield strength is analyzed with modeling of the grain boundary in the context of the proposed constitutive model and is discussed from both macroscopic and microscopic views.