Inhomogeneous ordered states and translational nature of the gauge group in the landau continuum theory: I. General analysis

A phenomenological continuum theory of phase transitions to a global inhomogeneous state of a crystal must take into account the compensating fields that represent the fields of stresses caused by dislocations appearing at the boundaries between local homogeneous regions. These compensating fields, which are introduced in order to satisfy the condition of invariance of the Landau potential with respect to the operation of translation, enter into the theory via extended derivatives of the local order parameters with respect to macroscopic coordinates of the local homogeneous regions in the crystal. Because of this extension of derivatives, the theory of phase transitions to an inhomogeneous state must include the theory of elasticity, in which a potential of the stress field induced by the phase transition is proportional to the compensating field magnitude. The Kröner equation, which describes the state of dislocations induced by spatially inhomogeneous ordering, appears in this theory as a result of minimization of the Landau potential with respect to the compensating fields.     

Numerical simulation of deformation and fracture of a material with a polysilazane-based coating

The paper studies the localization of plastic deformation and fracture in a material with a porous coating. A dynamic boundary value problem in the plane strain formulation is solved. The numerical simulation is performed by the finite difference method. The composite structure corresponds to the experimentally observed one and is specified explicitly in the calculation. A generation procedure of the initial finite-difference grid is developed to describe the coating structure with adjustable porosity and geometry of the substrate-coating interface. Constitutive equations for the steel substrate include an elastic-plastic model of an isotropically hardening material. The ceramic coating is described by a brittle fracture model on the basis of the Huber criterion which accounts for crack nucleation in triaxial tension zones. It is shown that the specific character of deformation and fracture of the studied composite results from the presence of local tensile regions in the vicinity of pores and along the coating-substrate interface, in both tension and compression of the coated material. The interrelation between inhomogeneous plastic flow in the steel substrate and crack propagation in the coating is studied.     

Nonlinear response and avalanche behavior in metallic glasses

The response to different stress amplitudes at temperatures below the glass transition temperature is analyzed by mechanical oscillatory excitation of Pd₄₀Ni₄₀P₂₀ metallic glass samples in single cantilever bending geometry. While low amplitude oscillatory excitations are commonly used in mechanical spectroscopy to probe the relaxation spectrum, in this work the response to comparably high amplitudes is investigated. The strain response of the material is well below the critical yield stress even for highest stress amplitudes, implying the expectation of a linear relation between stress and strain according to Hooke’s Law. However, a deviation from the linear behavior is evident, which is analyzed in terms of temperature dependence and influence of the applied stress amplitude by two different approaches of evaluation. The nonlinear approach is based on a nonlinear expansion of the stress-strain-relation, assuming an intrinsic nonlinear character of the shear or elastic modulus. The degree of nonlinearity is extracted by a period-by-period Fourier-analysis and connected to nonlinear coefficients, describing the intensity of nonlinearity at the fundamental and higher harmonic frequencies. The characteristic timescale to adapt to a significant change in stress amplitude in terms of a recovery timescale to a steady state value is connected to the structural relaxation time of the material, suggesting a connection between the observed nonlinearity and primary relaxation processes. The second approach of evaluation is termed the incremental analysis and relates the observed response behavior to avalanches, which occur due to the activation and correlation of local microstructural rearrangements. These rearrangements are connected with shear transformation zones and correspond to localized plastic events, which are superimposed on the linear response behavior of the material.     

Local zone wise elastic and plastic properties of electron beam welded Ti–6Al–4V alloy using digital image correlation technique: A comparative study between uniform stress and virtual fields method

Joining of materials using welding results in the formation of material zones with varying microstructure across the weld. Extraction of the mechanical properties of those individual heterogeneous zones are important in designing components and structures comprised of welds. In this study, the zone wise local extraction of the elastic and plastic properties of an electron beam welded Ti–6Al–4V titanium alloy has been carried out using both the uniform stress method (USM) and the virtual fields method (VFM) involving digital image correlation (DIC) technique. The surface strain field obtained using DIC technique from a transverse weld specimen tensile testing is used for extracting the zone wise strain evolution. Initially, using uniform stress assumption, zone wise full range stress–strain curves are extracted. In USM methodology, the elastic and plastic material models are fitted to the zone wise stress–strain curves and required parameters are extracted from it. But inherent disadvantage is lot of images need to be processed for the parameter extraction. Recently, VFM is gaining lot of popularity in characterization domain as it is robust, accurate and faster. VFM is based on the principle of virtual work where, the weak form of local equilibrium equations and kinematically admissible virtual displacement fields are utilized for parameter extraction. Hollomon׳s power law is used here as the hardening rule. Young׳s modulus, Poisson׳s ratio, yield stress, strength coefficient and strain hardening exponent are the parameters extracted zone wise using both USM and VFM. A Vicker׳s microhardness measurement is also conducted across the weld zone towards mapping the strength behavior. Fusion zone has reported higher yield strength, strength coefficient and Poisson׳s ratio. Young׳s modulus value is found decreasing from base metal towards the fusion zone. The trend observed in parameter variation across the weld zone obtained by both USM and VFM compares very well. Due to various advantages associated with VFM technique it is generally recommended for parameter extraction.     

Plastic Strain Localization and Its Stages in Al-Mg Alloys

The paper describes an experimental technique based on the use of a Vic-3D contactless digital optical system and digital image correlation for research in the mechanical behavior of a solid and its plastic deformation with space-time inhomogeneities. Using this technique, we analyze the evolution of inhomogeneous strain and local strain rate fields in AMg2m alloy at constant uniaxial tension rates. The analysis reveals quasi-periodic strain field homogenization in jerky flow: alternating phases of active local plastic flow (shear banding) and macroscale strain levelling. Also analyzed are the parameters of localized microscale plastic flow such as the height and width of shear bands, their velocity, and coefficient of plastic strain inhomogeneity. From a series of mechanical tests, the influence of the specimen geometry and loading rate on these parameters is estimated.     

Some effects of inhomogeneous strain on surface properties of metals: I. Flat surface

Jelium model calculations using the many electron formalism and a parameterized charge density distribution have been used to evaluate the change in surface energy, barrier height and work function due to the presence of a tensile and compressive strain gradient at the surface of Cs, Rb, K and Na. The method is useful for short range strain fields (? 4–5 atom spacings), but not for larger fields. The surface energy change due to inhomogeneous strain is almost twice as large as that due to homogeneous strain. The work function changes due to inhomogeneous strain are ~10–10² times larger than those due to homogeneous strains. The results are of considerable importance to general fracture and stress corrosion cracking studies.     

A numerical study of the mechanical behavior at contact between particles of dissimilar elastic–ideally plastic materials

In the present study contact between elastic–ideally plastic dissimilar spheres are investigated in detail. The investigation is based on numerical methods and in particular the finite element method. The numerical results presented are discussed with respect to correlation of global contact properties as well as the behavior of local field variables such as contact pressure distribution and the evolution of the effective plastic strain. Large deformation effects are accounted for and discussed in detail. The constitutive behavior is described by classical Mises plasticity. It is shown that correlation of the dissimilar contact problem can be accurately achieved based on the Johnson contact parameter with the representative stress chosen as the yield stress of the softer material.     

Influence of low temperatures on the fracture micromechanism of materials with bcc and fcc lattice structures under single loading conditions

General regularities of the influence of the local stress state of a material on the plastic zone formation at the crack tip and the fracture micromechanism of materials with bcc and fcc lattice structures under single loading (static, impact, high-speed pulsed) conditions have been established. Schemes of plastic zone formation under plane strain, plane stress, and in the transient region from plane strain to plane stress are proposed.     

Microstructural instabilities: dislocation substructures with pronounced mechanical effects

Microstructure evolution is largely dominated by the internal stress fields that appear upon the appearance of inhomogeneous structures in a material. The hardening behaviour of metals physically originates from such a complex microstructure evolution. As deformation proceeds, statistically homogeneous distributions of dislocations in grains become unstable, which constitutes the driving force for the development of a pronounced dislocation substructure. The dislocation structure already appears at early stages of deformation due to the statistical trapping of dislocations. Cell walls contain dislocation dipoles and multipoles with high dislocation densities and enclose cell-interior regions with a considerably smaller dislocation density. The presence and evolution of such a dislocation arrangement in the material influence the mechanical response of the material and is commonly associated with the transient hardening after strain path changes. This contribution introduces a micromechanical continuum model of the dislocation cell structure based on the physics of the dislocation interactions. The approximation of the internal stress field in such a microstructure and the impact on the macroscopic mechanical response are the main items investigated here.     

Internal stresses in the model of hard and soft regions

The simple composite model of material with inhomogeneous dislocation structure is extended to provide information on strain response to stress changes in steady-state creep. This extension enables us, therefore, to simulate the so-called dip-test technique and to calculate operationally defined internal stress. It is shown that this internal stress corresponds to the back stress acting in soft regions. The model is also convenient for the calculation of strain transients.     

Substructure formation in high-strength dispersely strengthened alloys

Conclusions Analysis of new experimental laws of plastic flow observed in high-strength alloys with dispersional strengthening (such as the formation of substructure with high crystal-lattice curvature, high-temperature localization of deformation from the earliest stages, with reorientation of the localized-shear zones and the adjacent undeformed structural elements) leads to the conclusion that deformational point defects play an important role in the realization of collective deformational modes in the high-strength state.In conditions of high nonequilibrium concentration, deformational point defects, first, permit the inclusion of quasi-viscous diffusional mechanisms of crystal-lattice reorientation by point-defect drift in the local fields of high inhomogeneous stress and, second, by facilitating dislocational deformation mechanisms, may lead to local weakening of the shear zones, localization of the plastic flow, and stability loss, in particular, as a result of mutually consistent autocatalytic defect multiplication.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 81–92, March, 1991.     

Effect of Martensite Volume Fraction on Strain Partitioning Behavior of Dual Phase Steel

Monotonic deformation behavior of ferrite-martensite dual phase steels with martensite volume of 13-43% have been analyzed in the current investigation using micromechanics based finite element simulation on representative volume elements. The effects of martensite volume fraction on the strain partitioning behavior between soft ferrite matrix and hard martensite islands in dual phase steels during tensile deformation have been investigated. As a consequence of strain incompatibility between hard martensite and soft ferrite phases, inhomogeneous deformation and finally deformation localization occur during tensile deformation. Restricted local deformation in ferrite phase caused by the adjacent martensite islands triggers the local stress triaxiality development. As the martensite volume fraction increases, the local deformation restrictions in ferrite phase also increases and which results in higher stress triaxiality development. Similarly the strain partitioning behavior between ferrite matrix and martensite island is also influenced by the volume fraction of martensite. The strain partitioning coefficient increases with increasing martensite volume fraction.     

Finite strain stress fields near the tip of an interface crack between a soft incompressible elastic material and a rigid substrate

We present a numerical study of finite strain stress fields near the tip of an interface crack between a rigid substrate and an incompressible hyperelastic solid using the finite element method (FEM). The finite element (FE) simulations make use of a remeshing scheme to overcome mesh distortion. Analyses are carried out by assuming that the crack tip is either pinned, i.e., the elastic material is perfectly bonded (no slip) to the rigid substrate, or the crack lies on a frictionless interface. We focus on a material which hardens exponentially. To explore the effect of geometric constraint on the near tip stress fields, simulations are carried out under plane stress and plane strain conditions. For both the frictionless interface and the pinned crack under plane stress deformation, we found that the true stress field directly ahead of the crack tip is dominated by the normal opening stress and the crack face opens up smoothly. This is also true for an interface crack along a frictionless boundary in plane strain deformation. However, for a pinned interface crack under plane strain deformation, the true opening normal stress is found to be lower than the shear stress and the transverse normal stress. Also, the crack opening profile for a pinned crack under plane strain deformation is completely different from those seen in plane stress and in plane strain (frictionless interface). The crack face flips over and the tip angle is almost tangential to the interface. Our results suggest that interface friction can play a very important role in interfacial fracture of soft materials on hard substrates.     

A physical interpretation of softening of pressure-sensitive and anisotropic materials

Several new dynamic models are proposed to explain the mechanical behaviour of softening of pressure-sensitive and anisotropic materials at a macroscopic level. If a pressure-sensitive material is loaded by a force and a variable pressure or an anisotropic material is subjected to a load with a changeable loading direction relative to the material frame, their stress–strain relationships become more complicated. Mechanical behaviours of these stress–strain relationships have to cover the feature concerning the change of pressure or loading direction, i.e. mechanical properties of pressure-sensitive material corresponding to different pressure state or anisotropic material relating to different loading direction will play an important role in deciding their stress–strain relationships. Such shift of material properties due to the variable pressure or loading history may significantly expand the traditional concept of the stability of material deformation, and the second order of plastic work being negative may be a response of stable plastic deformation, which is commonly called softening.     

Description of waves in inhomogeneous domains using Heun’s equation

There are a number of model equations describing electromagnetic, acoustic or quantum waves in inhomogeneous domains and some of them are of the same type from the mathematical point of view. This isomorphism enables us to use a unified approach to solving the corresponding equations. In this paper, the inhomogeneity is represented by a trigonometric spatial distribution of a parameter determining the properties of an inhomogeneous domain. From the point of view of modeling, this trigonometric parameter function can be smoothly connected to neighboring constant-parameter regions. For this type of distribution, exact local solutions of the model equations are represented by the local Heun functions. As the interval for which the solution is sought includes two regular singular points. For this reason, a method is proposed which resolves this problem only based on the local Heun functions. Further, the transfer matrix for the considered inhomogeneous domain is determined by means of the proposed method. As an example of the applicability of the presented solutions the transmission coefficient is calculated for the locally periodic structure which is given by an array of asymmetric barriers.     

Plastic zone boundary and Poisson’s ratio depending on plastic loosening

A more accurate determination of the plastic zone boundary for plane strain and plane stress state is proposed. The plastic zone boundary is determined with regard to plastic loosening, given exact stress distribution and Schleicher yield criterion. The presence of mean normal stress in the Schleicher criterion ensures uniform expansion of the plastic zone. The dependence of Poisson’s ratio and constraint ratio for plastic strain on plastic loosening of material is examined. These parameters peak at the tip or in the immediate vicinity of a stress concentrator and decrease with distance from it. In a small neighborhood of the crack tip, a region is found in which Poisson’s ratio is impossible to determine from the Schleicher criterion. The size of this region is identified with the size of the region of exhausted plasticity.     

Cu刃型扩展位错附近局部应变场的原子模拟研究

通过结合virial应变分析技术的准连续介质多尺度模拟方法研究了金属Cu刃型扩展位错的局部应变场.结果表明在距离位错核心几十纳米的区域内晶体处于小变形状态,virial应变计算结果与弹性理论预测结果符合得相当好,当距离位错核心仅几纳米时,晶格畸变加剧,virial应变极大值出现在扩展位错两端的Shockley分位错芯部.进一步分析表明Shockley分位错芯部严重畸变区大致呈长轴7b1、短轴3b1的椭圆形,其中b1为分位错柏氏矢量的长度.     

Strain hardening in polymer glasses: limitations of network models

Simulations are used to examine the microscopic origins of strain hardening in polymer glasses. While traditional entropic network models can be fit to the total stress, their underlying assumptions are inconsistent with simulation results. There is a substantial energetic contribution to the stress that rises rapidly as segments between entanglements are pulled taut. The thermal component of stress is less sensitive to entanglements, mostly irreversible, and directly related to the rate of local plastic rearrangements. Entangled and unentangled chains show the same strain hardening when plotted against the microscopic chain orientation rather than the macroscopic strain.