Spatiotemporal Thermal Inhomogeneities During Compression of Highly Textured Zirconium

Using a focal plane array infrared camera, the heat generated during large strain compression (at a rate of 1 s⁻¹) is used to study the characteristics of plastic flow for hcp zirconium. Heat generation during plastic flow in a reference material, copper, was seen to develop uniformly both at the lower (40 μm/pixel) and higher (8 μm/pixel) magnifications used in this study. The thermomechanical response of Zr, however, was seen to depend on the loading direction with respect to the specimen texture. Highly textured zirconium compressed along nonbasal oriented grains results in a homogeneous thermal response at both scales. However, compression along basal (0001) oriented grains shows evidence of inhomogeneous deformation at small strains that lead to macroscale localization and failure at large strains. The conversion of plastic work into heat is observed to be a dynamic process, both in the time-dependent nature of the energy conversion, but also in the passage of waves and ‘bursts’ of plastic heating. Basal compression also showed evidence of small scale localization at strains far below macroscale localization, even below 10%. These localizations at the lower strain levels eventually dominate the response, and form the shear band that is responsible for the softening of the macroscopic stress–strain curve.     

Heterogeneity of Plastic Flow of Zirconium Alloys with a Parabolic Law of Strain Hardening

The specific features of plastic–strain macrolocalization at the stage of the parabolic law of strain hardening in samples from industrial zirconium–based alloys are considered. It is shown that in predeformed blanks, zones with a different character of plastic–strain localization are formed. It is also shown that the strain–localization macropattern can be used as a characteristic of the susceptibility of a material to further plastic form–changing, for example, upon tube rolling. The sign of fracture of alloys upon plastic deformation is revealed. The scale effect in the formation of localizedplastic–flow zones is shown and studied.     

Theoretical and experimental study of energy dissipation in the course of strain localization in iron

Plastic strain localization is studied with the use of a high-sensitivity infrared camera. Plastic strain localization in iron is demonstrated to be accompanied by the emergence of heat waves and their propagation over the sample surface. Constitutive equations that describe the energy balance in the material under plastic strains are derived, and the plastic flow of iron is analyzed. The results of research are compared with the data obtained by infrared scanning. The proposed model of strain localization in the form of soliton-like waves (phase triggering waves) is demonstrated to agree with the kinetics of temperature waves characterizing dissipation inherent in the development of plastic deformation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 153–164, January–February, 2009.     

Numerical simulation of plastic-flow localization for simple shear

An algorithm was developed to numerically simulate plastic-flow localization for simple shear of a thermally plastic and viscoplastic material. The algorithm is based on solving the partial differential equations describing continuum flow. The closing equation is the constitutive relation known in the literature as the power law linking the plastic-strain rate to the flow stress, temperature, and accumulated plastic strain. Calculated relations for the time evolution of the shear-band width and the temperature and plastic strains localized in it agree satisfactorily with experimental relations. Good agreement with experimental results is also obtained for the sample temperature distribution at the developed stage of the localization process.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 173–180, January–February, 2005     

Partition of plastic work into heat and stored energy in metals

This study investigates heat generation in metals during plastic deformation. Experiments were designed to measure the partition of plastic work into heat and stored energy during dynamic deformations under adiabatic conditions. A servohydraulic load frame was used to measure mechanical properties at lower strain rates, 10^–3 s^–1 to 1 s^–1. A Kolsky pressure bar was used to determine mechanical properties at strain rates between 10³ s^–1 and 10⁴ s^–1. For dynamic loading, in situ temperature changes were measured using a high-speed HgCdTe photoconductive detector. An aluminum 2024-T3 alloy and -titanium were used to determine the dependence of the fraction of plastic work converted to heat on strain and strain rate. The flow stress and for 2024-T3 aluminum alloy were found to be a function of strain but not strain rate, whereas they were found to be strongly dependent on strain rate for -titanium.     

Simply approximate estimation of local failure position of a free-free slender shell

Dynamic plastic failure characteristics of a space free-free slender shell subjected to intense dynamic loading of suddenly applied pressure unsymmetrical triangle distributed along its span was studied. Both rigid perfectly plastic (r-p-p) analytical method and finite element method based elastic perfectly plastic (e-p-p) material idealization and shell element model were adopted to predict the local failure position in the structure. It was shown that both r-p-p and e-p-p model could estimate a plastic “kink” taking place in the slender shell, which reflects the strain localization of deformation. The comparison for the position of “kink” predicted by using r-p-p and e-p-p methods is found to be reasonable good.     

Dynamic Deformation of Aluminum Alloy AMg–6 at Normal and Higher Temperatures

Dynamic deformation of AMg–6 alloy in uniaxial extension and compression at strain rates of = 190 —1450 sec^–1 at test temperatures of 25 — 250 °C is studied experimentally. A phenomenological constitutive equation that agrees with experimental data is constructed within the framework of the elastoplastic model of a deformable solid.     

Flow stress behavior of porous FVS0812 aluminum alloy during hot-compression

The hot deformation behavior of porous FVS0812 aluminum alloy prepared by spray deposition was studied by means of compression tests on a Gleeble 1500 machine. The samples were hot compressed at temperatures ranging from 573 K to 773 K under various true strain rates of 10⁻⁴–10⁰ s⁻¹. The deformation behaviors are characterized by a significant strain hardening during hot-compression due to the progressive compaction of the pores with increasing compressive strain. A revised formula describing the relationships of the flow stress, strain rate and temperature of the porous alloy at elevated temperatures is proposed by compensation of strain. The theoretical predictions are compared with experimental results, which show good agreement.     

A dislocation density based crystal plasticity finite element model: Application to a two-phase polycrystalline HCP/BCC composites

We present a multiscale model for anisotropic, elasto-plastic, rate- and temperature-sensitive deformation of polycrystalline aggregates to large plastic strains. The model accounts for a dislocation-based hardening law for multiple slip modes and links a single-crystal to a polycrystalline response using a crystal plasticity finite element based homogenization. It is capable of predicting local stress and strain fields based on evolving microstructure including the explicit evolution of dislocation density and crystallographic grain reorientation. We apply the model to simulate monotonic mechanical response of a hexagonal close-packed metal, zirconium (Zr), and a body-centered cubic metal, niobium (Nb), and study the texture evolution and deformation mechanisms in a two-phase Zr/Nb layered composite under severe plastic deformation. The model predicts well the texture in both co-deforming phases to very large plastic strains. In addition, it offers insights into the active slip systems underlying texture evolution, indicating that the observed textures develop by a combination of prismatic, pyramidal, and anomalous basal slip in Zr and primarily {110}〈111〉 slip and secondly {112}〈111〉 slip in Nb.     

Giant faults in deformed Gum Metal

We have experimentally characterized and theoretically described plastic flow localization in Gum Metal, a special titanium alloy with high strength, low Young’s modulus, excellent cold workability and low resistance to shear in certain crystallographic planes. The electron transmission microscopy experiments demonstrate that plastic flow is localized in giant faults – macroscopic planar defects carrying very large plastic strains (thousand percent or more) – in deformed Gum Metal. Also, regions with highly inhomogeneous elastic strains and varying crystal lattice orientation are experimentally observed in the vicinity of giant faults. A theoretical model is suggested describing the generation of giant faults as a process resulting from generation and evolution of nanodisturbances (nanoscopic planar areas of local shear) in Gum Metal. It is shown that giant faults can effectively nucleate and evolve in Gum Metal, and their intersection with grain boundaries produces both elastic strain accumulation and inhomogeneities of crystal lattice orientation. This behavior of giant faults is expected to be essential for excellent cold ductility of high-strength Gum Metal.     

Plastic Incompressibility of Anisotropic Material

Some characteristics of an initially anisotropic aluminum alloy are investigated. The coefficients of transverse elastoplastic and plastic strain are calculated. It is established that the coefficients of transverse plastic strain are much different from 0.5 in directions that are not in the plane of isotropy. It is also shown that the material is plastically incompressible. The possibility of using Hill’s theory of flow with isotropic hardening to describe the inelastic behavior of the material is examinedThe study was partially sponsored by the State Fund for Basic Research of the Ministry of Education and Science of Ukraine (Grant No. 01.07/00010).__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 3, pp. 38–45, March 2005.     

新型铝锡硅合金高温塑性变形流变应力的研究

采用高温等温压缩变形方法,在温度为373-673K范围和应变速率为0.001-1.0s^-1范围内,测定了新型Al-10Sn-4Si合金的流变应力曲线,结果表明,该合金为正应变速率敏感材料并且具有稳态流变特征;稳态流变应力随变形速率的增加而增大,随变形温度的升高而降低,通过回归分析,建立了该合金高温塑性变形时稳态流变应力的半经验方程,这种稳态流变特征与动态回复、动态再结晶及局部晶界粘滞性流动行为有关,受热激活过程控制。     

Plastic deformation localization in commercial Zr-base alloys

The issues concerning the localization of plastic deformation in commercial Zr alloys used in the nuclear power industry are addressed. The possible types of deformation localization pictures corresponding with the respective stages of plastic flow are described. These are shown to be various kinds of self-excited wave processes of plastic flow. The dislocation structure of the material occurring within and in between the nuclei of localized deformation is investigated. The use of the self-excited wave patterns of plastic flow localization as an additional source of information on the mechanical properties of metals and alloys is substantiated.     

Texture development and plastic anisotropy of B.C.C. strain hardening sheet metals

A Taylor-like polycrystal model is adopted here to investigate the plastic behavior of body centered cubic (b.c.c.) sheet metals under plane-strain compression and the subsequent in-plane biaxial stretching conditions. The <111> pencil glide system is chosen for the slip mechanism for b.c.c. sheet metals. The {110} <111> and {112} <111> slip systems are also considered. Plane-strain compression is used to simulate the cold rolling processes of a low-carbon steel sheet. Based on the polycrystal model, pole figures for the sheet metal after plane-strain compression are obtained and compared with the corresponding experimental results. Also, the simulated plane-strain stress—strain relations are compared with the corresponding experimental results. For the sheet metal subjected to the subsequent in-plane biaxial stretching and shear, plastic potential surfaces are determined at a given small amount of plastic work. With the assumption of the equivalence of the plastic potential and the yield function with normality flow, the yield surfaces based on the simulations for the sheet metal are compared with those based on several phenomenological planar anisotropic yield criteria. The effects of the slip system and the magnitude of plastic work on the shape and size of the yield surfaces are shown. The plastic anisotropy of the sheet metal is investigated in terms of the uniaxial yield stresses in different planar orientations and the corresponding values of the anisotropy parameter R, defined as the ratio of the width plastic strain rate to the through-thickness plastic strain rate under in-plane uniaxial tensile loading. The uniaxial yield stresses and the values of R at different planar orientations from the polycrystal model can be fitted well by a yield function recently proposed by Barlat et al. (1997b).     

Plasticity of a high strength steel alloy

Experimentally determined plastic constitutive equations of the parabolic form (σ − σ_y = β(ε − ε_y)1/2) are presented for a high strength alloy steel. Two deformation moduli β were required to describe the quasistatic compression data, both of which, as well as the point of change, were predicted by a mode index and transition strain structure of a general theory of plasticity. Dynamic strain, duration of impact, and final strain distribution were measured on specimen rods subjected to axial, symmetric, and constant velocity impact. The dynamic yield stress was 16% higher than the quasistatic value. The dynamic response function, deduced from a simple wave propagation theory, was also parabolic and a single deformation modulus, equal to the initial quasistatic value, applied. Thus, it was shown that the form of the quasistatic response function was preserved in dynamic loading, and that the increase of the dynamic stress was due to the increase of the yield stress.     

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.     

Linear stability in the flow of a liquid film concurrent with a gas flow

The two-phase flow of liquid films are often encountered in practice, but the number of theoretical papers devoted to this problem is limited. The problem of the linear stability of a viscous liquid film subjected to a gas flow has been formulated in [1] and, in somewhat different form, in [2]. The linear stability of plane-parallel motion in films has been studied analytically in [1–8] for some limiting cases. The range of validity of the analytic approaches remains an open question. Therefore, an exact numerical analysis of flow stability over a fairly broad range is required. In the present paper a separate solution of the problem for the gas and the liquid is shown to be possible. The Orr-Sommerfeld equation has been integrated numerically, and the results are compared to the results of analytic calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 143–146, January–February, 1976.The author is grateful to É. É. Markovich for directing the work and to V. Ya. Shkadov for his interest in the work and many useful comments.     

Types of Localization of Plastic Deformation and Stages of Loading Diagrams of Metallic Materials with Different Crystalline Structures

Macrolocalization, which accompanies the process of plastic deformation beginning from the yield point and ending by fracture, is determined by the staged character of material-loading diagrams. The evolution of localization patterns in a plastic flow of body-centered cubic vanadium alloy, hexagonal close-packed magnesium alloy, tetragonal tin, and face-centered cubic submicrocrystalline aluminum is analyzed within this concept. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 176–184, March–April, 2006.     

Development of the polymeric split hopkinson bar technique

A compression version of the split Hopkinson bar with pressure bars and a striker, which are made of Plexiglas (a material with low density and velocity of sound) is developed. The technique is designed to determine stress—strain diagrams under high strain rates of highly deformable materials with low density and strength, such as plastics, foams, and rubbers. Dynamic stress—strain curves in compression for spheroplastic, foam plastic, and rubber are presented, which were obtained using the technique developed.     

The characteristics of plastic flow and a physically-based model for 3003 Al–Mn alloy upon a wide range of strain rates and temperatures

The uniaxial compressive responses of 3003 Al–Mn alloy upon strain rates ranging from 0.001/s to about 10⁴/s with initial temperatures from 77 K to 800 K were investigated. Instron servohydraulic testing machine and enhanced split Hopkinson bar facilities have been employed in such uniaxial compressive loading tests. The maximum true strain up to 80% has been achieved. The following observations have been obtained from the experimental results: 1) 3003 Al–Mn alloy presents remarkable ductility and plasticity at low temperatures and high strain rates; 2) its plastic flow stress strongly depends on the applied temperatures and strain rates; 3) the temperature history during deformation strongly affects the microstructure evolution within the material. Finally, paralleled with the systematic experimental investigations, a physically-based model was developed based on the mechanism of dislocation kinetics. The model predictions are compared with the experimental results, and a good agreement has been observed.