Formation of periodic mesoband structures in the tension of polycrystals with long boundaries

A study is made of how the mechanism of plastic deformation of polycrystalline low-carbon steel is a ffected by large-scale interface in the form of long localized regions of remelted material extending in the transverse direction. It is shown theoretically and experimentally that oscillating stress mesoconcentrators develop in the neighborhood of such interfaces and that relaxation of these concentrators results in the formation of periodic mesoband structures in deformable polycrystals. Institute of the Physics of Strength and Materials Science, Siberian Division, Russian Academy of Sciences, Tomsk 634021. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 4, pp. 141–147, July–August, 1998.     

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.     

The effect of ultrasonic treatment on mechanical behavior of titanium and steel specimens

The effect of surface ultrasonic treatment on plastic deformation and mechanical properties of polycrystalline titanium and low-carbon steel specimens under tension was studied. The deformation pattern was investigated using optical, transmission electron, scanning electron and scanning tunneling microscopy. It was shown that the material within hardened surface layers is characterized by ultrafine-grained structure. This structure results in plastic flow localization at different scale levels. Localized deformation meso-bands induce weak work hardening of the material. Plastic flow macro-localization causes a drop of the external deforming stress. The peculiar mechanisms of deformation localization within the specimen surface layer govern formation of a banded dislocation substructure in the bulk of the specimen.     

Ultrasound thermometry in transparent and opaque fluids

We have exploited the temperature dependence of sound velocity to measure the thermal fields in transparent and opaque fluids. A chamber containing glycerol undergoing Rayleigh–Bénard convection was probed with an ultrasound transducer operating in the pulse-echo mode. The times-of-flight for the ultrasound pulse to traverse the fluid at several transducer locations were converted into a temperature profile that is in qualitative agreement with simultaneous thermochromic liquid crystal visualization of the flow pattern. Temperature profiles in a mercury-filled stainless steel chamber have also been obtained, both for quiescent and turbulent flows, thereby validating the ultrasound thermometry concept for opaque fluids as well.     

Explosion Dynamics in Saturated Rocks and Solids

Non-elastic pore deformations and crack propagations are the principal causes of dynamic damage in rocks and soils. In the case of downhole blasting from wellbores, these two mechanisms compete with each other. Therefore, to carry out a mechanical analysis of rock blasting, a sufficiently complete model that takes these various mechanisms into account has to be developed. To address this issue, this paper proposes the use of an elastic–plastic model, which includes a yield condition with a non-associated plastic flow rule, the effects of pore fluid saturation, and a brittle failure criterion under extension. The results presented in this paper describe underground explosions with spherical motion (cavity growth under the internal pressure of detonated gases without leakage into the formation), typical for oil or water reservoirs. The governing equations are written in a Cartesian system of coordinates for the case of spatial dynamic medium deformation. For this case, Cartesian coordinates are more convenient than spherical coordinates because they avoid numerical difficulties connected with the non-divergent terms of the non-linear form of the Biot–Frenkel equations. The numerical method uses the Wilkins approach, which has been generalized for the model described in this paper. The dilatancy of the material during plastic deformation is neglected for simplicity. The numerical results show that, when using typical parameters for relatively “soft” porous skeleton, the plastic flow overcomes the brittle failure. An extension zone only appears near the cavity. The results also show the presence of the two Biot P-waves. The second Biot wave, however, is only seen in the case of an extremely high permeability rock. Furthermore, in the case of the first Biot wave, the saturating liquid and the solid skeleton particles are moving with different velocities in a 100 darcy rock and with the same velocity in a 0.01 darcy rock. Calculated radial particle velocities as a function of the scaled radius are close to measured velocities in rigid dense media but are larger than measured ones in clays. It is suggested that the difference is due to different levels of water saturation, assumed full saturation in the calculation, partial saturation in the experiments.     

A non-associated flow rule for sheet metal forming

An improved model of material behavior is proposed that shows good agreement with experimental data for both yield and plastic strain ratios in uniaxial, equi-biaxial, and plane-strain tension under proportional loading for steel, aluminum and possibly other alloys. This model is based on a non-associated flow rule in which the plastic potential and yield surface functions are defined by quadratic functions of the stress tensor. The plastic potential aspect of the model is identical to that proposed by Hill for a quadratic anisotropic plastic potential defined in terms of measured r values. The new model differs in that the yield surface, although also defined by a quadratic function of the stress tensor, is defined independently of the plastic potential in terms of measured yield stresses. The model is developed and implemented in an FEM code that is based on a convected coordinate system. Since the associated flow rule, which assumes equivalency between the plastic potential and yield functions, is commonly accepted as a valid law in the theory of plastic deformation of most metals, the arguments for the associated flow rule are also discussed.     

Elastic–plastic contact force history and response characteristics of circular plate subjected to impact by a projectile

A new elastic–plastic impact–contact model is proposed in this paper. By adopting the principle of minimum acceleration for elastic–plastic continue at finite deformation, and with the aid of finite difference method, the proposed model is applied in the problem of dynamic response of a clamped thin circular plate subjected to a projectile impact centrally. The impact force history and response characteristics of the target plate is studied in detail. The theoretical predictions of the impact force and plate deflection are in good agreements with those of LDA experimental data. Linear expressions of the maximum impact force/transverse deflection versus impact velocity are given on the basis of the theoretical results. The project supported by the National Natural Science Foundation of China (10532020).     

Qualitative Distinctions in the Solutions Based on the Plasticity Theories with the Mohr-Coulomb Yield Criterion

The following two models of the plasticity theory are considered: the model with the Mohr-Coulomb yield criterion and the classical model of the plasticity theory with a yield criterion independent of the mean stress. The deformation problem of a plastic layer enclosed between two rotating plates is studied. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 136–145, November–December, 2005.     

Penetration of a rigid shell into a steel obstacle at moderate impact velocities

The effect of the impact velocity and shape of the head of a rigid shell of caliber 20mm on the depth of its penetration into a thick obstacle made of mild low-carbon steel for impact velocities of up to 600m/sec is studied experimentally. Experimental relations between the penetration depth and the impact velocity are obtained for shells with conical and semispherical heads. It is found that for a penetration depth equal to 1 or 2 calibers, the penetration resistance does not depend on the head shape and is characterized by an average stress equal to 2.98GPa. Institute of Experimental Physics, Sarov 607190. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 38–40, January–February, 2000.     

The influence of flow confinement on the rheological properties of complex fluids

The rheological properties of plastic and viscoplastic complex fluids have been investigated using constant velocity squeeze flow rheometry at small gaps in order to examine the influence of the resulting flow confinement. The fluids investigated were aqueous carbopol suspensions and three commercial products (Tesco English mustard, Tesco value lemon curd and Heinz tomato ketchup (HTK)). The bulk rheological properties were measured using parallel plate rheometry. Rough plates were used to eliminate wall slip in both rheometric configurations. The commercial products are Herschel–Bulkley fluids and, for gaps less than a critical value of ~200 μm, the yield stresses tended to large values. There was a corresponding trend to small values for the flow consistencies except for HTK, which has a negligibly small bulk value. A possible explanation is that the micro-structural correlation lengths of these fluids are of the order of that of the critical separation. The yield stresses of the carbopol suspensions also increased sharply at the critical gap but then decreased gradually with decreasing gap separation. The transition may correspond to the formation of a jammed state with the subsequent plastic flow at smaller gap separations arising from localised shearing.     

Flow in a Porous Matrix with Anisotropic Structure

The flow of a viscous fluid through a porous matrix undergoing only infinitesimal deformation is described in terms of intrinsic variables, namely, the density, velocity and stress occurring in coherent elements of each material. This formulation arises naturally when macroscopic interfaces are conceptually partitioned into area fractions of fluid–fluid, fluid–solid, and solid–solid contact. Such theory has been shown to yield consistent jump conditions of mass, momentum and energy across discontinuities, either internal or an external boundary, unlike the standard mixture theory jump conditions. In the previous formulation, the matrix structure has been considered isotropic; that is, the area fractions are independent of the interface orientation. Here, that is not assumed, so in particular, the cross-section area of a continuous fluid tube depends on its orientation, which influences the directional fluxes, and in turn the directional permeability, anisotropy of the structure. The simplifications for slow viscous flow are examined, and particularly for an isotropic linearly elastic matrix in which area partitioning induces anisotropic elastic response of the mixture. A final specialization to an incompressible fluid and stationary matrix leads to potential flow, and a simple plane flow solution is presented to illustrate the effects of anisotropic permeability.     

超高强度钢AF1410塑性流动特性及其本构关系

在本文中,为揭示超高强度钢AF1410的塑性流动性,并研究其塑性流动本构关系,利用CSS4410电子万能试验机和改进的Hopkinson拉压杆技术,对AF1410钢在温度从100K到600K,应变率从0.001/s到2000/s,塑性应变超过20%的塑性流动特性进行了试验研究。结果表明,拉伸加载下AF1410钢屈服强度低于压缩屈服强度,且随应变率增加,拉压屈服强度差值越来越大;该材料塑性流动应力对应变率敏感性低,而对温度较为敏感;随应变率的提高,该材料拉伸失效应变减小,但温度对失效应变无明显影响。最后基于位错的运动学关系,借助试验数据,获得了AF1410钢的塑性流动物理概念本构模型,并通过与经典J-C模型的结果对比对该物理概念本构模型进行了评估分析,表明该物理概念本构模型在较宽温度和应变率范围能较好的预测AF1410钢的塑性流动应力。     

Determination of plastic strains at notches by image-proceessing methods

An image-processing method was developed to quantitatively extract the level of plastic deformation in metal specimen made of 304 stainless steel under remote tensile loading. The effective strain distribution around the notch tip was obtained and compared with the finite-element results. An exponential decay of the plastic strain concentration with distance from the notch tip was observed. Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

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.     

Effect of deformation and external load on the characteristics of martensite transformations and shape-memory effects in alloys based on titanium nickelide

The effect of plastic deformation and external load on the characteristics of shape-memory effects is studied for alloys based on titanium nickelide of nearly equiatomic composition. A nonmonotonic dependence of the characteristic temperatures of martensite transformations on the strain degree of deformation is obtained. This phenomenon is explained in relation to the stages of development of plastic deformation. Optimal loading and deformation conditions for obtaining maximum values of reversible deformation are determined. Russian Medical-Engineering Center, Tomsk 634034. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 175–181, March–April, 1998.     

基于有限元模拟的SUS304奥氏体不锈钢摩擦耦合变形过程的应力分析

采用ANSYS/LS-DYNA软件对SUS 304奥氏体不锈钢薄板的摩擦耦合变形过程进行了数值模拟.采用隐式-显式序列求解法和分段线性塑性材料模型,分析了钢带摩擦耦合变形时的应力分布规律及载荷、下压量和滑动速度等因素对钢带剪应力、主应力及等效应力的影响.结果表明:摩擦耦合变形的试验参数显著影响钢带的应力分布,验证了钢带在低于其屈服强度的应力条件下发生塑性变形的摩擦诱发效应.对奥氏体不锈钢摩擦诱发马氏体转变行为的研究及其摩擦学性能的改善具有一定的指导意义.     

One plasticity model for problems of plastic metal working

Scalar and tensor models of plastic flow of metals extending plasticity theory are considered over a wide range of temperatures and strain rates. Equations are derived using the physico-phenomenological approach based on modern concepts and methods of the physics and mechanics of plastic deformation. For hardening and viscoplastic solids, a new mathematical formulation of the boundary-value plasticity problem taking into account loading history is obtained. Results of testing of the model are given. A numerical finite-element algorithm for the solution of applied problems is described. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 159–169, November–December, 2008.     

Differential constitutive equations of incompressible media with finite deformations

A method is proposed for constructing a system of constitutive equations of an incompressible medium with nonlinear dissipative properties with finite deformations. A scheme of the mechanical behavior of a material is used, in which the points are connected by horizontally aligned elastic, viscous, plastic, and transmission elements. The properties of each element of the scheme are described with the use of known equations of the nonlinear elasticity theory, the theory of nonlinear viscous fluids, and the theory of plastic flow of the material under conditions of finite deformations of the medium. The system of constitutive equations is closed by equations that express the relation between the deformation rate tensor of the material and the deformation rate tensor of the plastic element. Transmission elements are used to take into account a significant difference between macroscopic deformations of the material and deformations of elements of the medium at the structural level. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 158–170, May–June, 2009.     

The role of dissipation and defect energy in variational formulations of problems in strain-gradient plasticity. Part 1: polycrystalline plasticity

A general set of flow laws and associated variational formulations are constructed for small-deformation rate-independent problems in strain-gradient plasticity. The framework is based on the thermodynamically consistent theory due to Gurtin and Anand (J Mech Phys Solids 53:1624–1649, 2005), and includes as variables a set of microstresses which have both energetic and dissipative components. The flow law is of associative type. It is expressed as a normality law with respect to a convex but otherwise arbitrary yield function, or equivalently in terms of the corresponding dissipation function. Two cases studied are, first, an extension of the classical Hill-Mises or J ₂ flow law and second, a form written as a linear sum of the magnitudes of the plastic strain and strain gradient. This latter form is motivated by work of Evans and Hutchinson (Acta Mater 57:1675–1688, 2009) and Nix and Gao (J Mech Phys Solids 46:411–425, 1998), who show that it leads to superior correspondence with experimental results, at least for particular classes of problems. The corresponding yield function is obtained by a duality argument. The variational problem is based on the flow rule expressed in terms of the dissipation function, and the problem is formulated as a variational inequality in the displacement, plastic strain, and hardening parameter. Dissipative components of the microstresses, which are indeterminate, are absent from the formulation. Existence and uniqueness of solutions are investigated for the generalized Hill-Mises and linear-sum dissipation functions, and for various combinations of defect energy. The conditions for well-posedness of the problem depend critically on the choice of dissipation function, and on the presence or otherwise of a defect energy in the plastic strain or plastic strain gradient, and of internal-variable hardening.