Plastic Flow Processes Research Articles

On elastic modeling of inclusion induced microplasticity in metallic matrices from the dilatating sphere problem

Abstract The plastic flow process around a spherical dilatated inclusion has been previously sketched as a “dislocation shell” emission idealizing patterns of collectively moving prismatic circular loops. This elastic description of relaxation is here reintroduced from the discretization of the continuous plastic solution into elementary plastic deformation fields taken compatible except in a thin leading shell-like zone. The assumptions which yield to the elastic problem of the current equilibrium for n -imbricated hollow spheres with overlapping radii are specified and the provided flow and internal stress fields are compared to those from the continuous plasticity modeling on the one hand, and from a dislocation loop pattern on the other hand.

Numerical modelling of localized fracture of inelastic solids in dynamic loading processes

The main objective of the paper is the investigation of adiabatic shear band localized fracture phenomenon in inelastic solids during dynamic loading processes. This kind of fracture can occur as a result of an adiabatic shear band localization generally attributed to a plastic instability implied by microdamage and thermal softening during dynamic plastic flow processes. By applying ideas of synergetics it can be shown that as a result of instability hierarchies a system is self-organized into a new shear band pattern system. This leads to the conclusion that inelastic solid body considered during the dynamics process becomes a two-phase material system. Particular attention is focussed on attempt to construct a physically and experimentally justified localized fracture theory that relates the kinetics of material failure on the microstructural level to continuum mechanics. The description of the microstructural damage process is based on dynamic experiments with carefully controlled load amplitudes and duration. The microdamage process has been treated as a sequence of nucleation, growth and coalescence of microcracks. The microdamage kinetics interacts with thermal and load changes to make failure of solids a highly rate, temperature and history-dependent, non-linear process. The theory of thermoviscoplasticity is developed within the framework of the rate-type covariance material structure with a finite set of internal state variables. The theory takes into consideration the effects of microdamage mechanism and thermomechanical coupling. The dynamic failure criterion within localized shear band region is proposed. The relaxation time is used as a regularization parameter. Rate dependency (viscosity) allows the spatial differential operator in the governing equations to retain its ellipticity, and the initial-value problem is well-posed. The viscoplastic regularization procedure assures the unconditionally stable integration algorithm by using the finite element method. Particular attention is focused on the well-posedness of the evolution problem (the initial–boundary value problem) as well as on its numerical solutions. Convergence, consistency and stability of the discretized problem are discussed. The Lax equivalence theorem is formulated and conditions under which this theorem is valid are examined. Utilizing the finite element method and ABAQUS system for regularized elasto–viscoplastic model the numerical investigation of the three-dimensional dynamic adiabatic deformation in a particular body at nominal strain rates ranging over 103−104 s−1 is presented. A thin shear band region of finite width which undergoes significant deformation and temperature rise has been determined. Its evolution until occurrence of final fracture has been simulated. Numerical results are compared with available experimental observation data. © 1997 John Wiley & Sons, Ltd.

Plastic deformation viewed as evolution of an active medium

The process of plastic flow in crystalline solids has been viewed as the evolution of an active medium in an open system far from thermodynamic equilibrium. The formation of lattice defects, the localization of strain and its variation in the different stages of flow are shown to be related to emergence and evolution of active media of definite types, the evolution of plastic flow involving propagation of different types of self-excited waves and formation of dissipative structures. The analogy with processes occurring in solids under deformation and with the emergence of structures in chemical and biological systems is discussed. Possible types of waves and observing conditions have been classified.

Localized Fracture in Inelastic Polycrystalline Solids under Dynamic Loading Processes

The main objective of the paper is the investigation of adiabatic shear band localized fracture phenomenon in inelastic solids during dynamic loading processes. This kind of fracture can occur as a result of an adiabatic shear band localization generally attributed to a plastic instability implied by micro-damage and thermal softening during dynamic plastic flow processes. The theory of thermoviscoplasticity is developed within a framework of the rate type covariance material structure with a finite set of internal state variables. The theory takes into consideration the effects of micro-damage mechanism and thermomechanical coupling. The micro-damage mechanism has been treated as a sequence of nucleation, growth, and coalesence of microcracks. The micro-damage kinetics interacts with thermal and load changes to make failure of solids a highly rate, temperature, and history dependent, nonlinear process. The dynamic failure criterion within localized shear band region is proposed. The relaxation time is used as a regularization parameter. By assuming that the relaxation time tends to zero, the rate independent micro-damage mechanism is considered. Rate dependency (viscosity) allows the spatial differential operator in the governing equations to retain its ellipticity, and the initial-value problem is well posed. The viscoplastic regularization procedure assures the stable integration algorithm by using the finite element method. Particular attention is focused on the well-posedness of the evolution problem (the initial-boundary value problem), as well as on its numerical solutions. Convergence, consistency, and stability of the discretised problem are discussed. The Lax equivalence theorem is formulated and conditions under which this theorem is valid are examined. Utilizing the finite element method and ABAQUS system for regularized elastoviscoplastic model, the numerical investigation of the three-dimensional dynamic adiabatic deformation in a particular body at nominal strain rates ranging from 10-1-104 s-1 is presented. Three particular examples have been considered; namely, a dynamic adiabatic process for a thin-walled steel tube and dynamic adiabatic and quasi-static processes for a thin steel plate. In each case, a thin shear band region of finite width which undergoes significant deformations and temperature rise has been determined. Its evolution until occurrence of final fracture has been simulated. Numerical results are compared with available experimental observation data.

A self-consistent model for cleavage in the presence of plastic flow

A theory is proposed for cleavage in the presence of plastic flow, in circumstances which do not involve strong viscoplastic retardation of dislocation motion. We build upon recent notions that recognize the large disparity between relevant length scales involved in plastic flow processes around cracks in metals and on metal—ceramic interfaces. The lengths consist of (1) the Burgers vector, (2) the nominal dislocation spacing, (3) the elastic “cell” dimension, and (4) the overall plastic zone size. Of particular interest is the phenomenon of “brittle” crack growth in the presence of pre-existing, apparently mobile, dislocations, which has been observed in several material systems. A continuum elastic—plastic finite element model is utilized that assumes the presence of a dislocation-free strip of elastic material of height D surrounding a crack tip, from which dislocations are assumed not to emit. The parameter D is self-consistently chosen by identifying a maximum equivalent Mises stress in the plastic zone with that predicted by a phenomenological strength law of the type first used by Taylor and Orowan, in which strength varies inversely with nominal dislocation spacing or with cell size, either of which is identified as D in different interpretations of the model. For steady-state crack growth to occur, it is found that the applied energy release rate G must generally be several orders of magnitude larger than the ideal work necessary to separate the interface, at least when D is taken as dislocation spacing. Furthermore, this “shielding” ratio is found to be strongly sensitive to the ideal work of fracture itself, as well as other material properties.

A simple elastic cell model of cleavage fracture in the presence of dislocation plasticity

The current analysis is prompted by the recent recognition that an elastic core embedded about the crack tip in a plastic medium affords a mechanism for cleavage-type crack growth with significant plastic dissipation [Beltz et al., Acta metall. mater., submitted (1995)]. We build upon recent notions that recognize the large disparity between relevant length scales involved in plastic flow processes around cracks in metals and on metal-ceramic interfaces. A simple, continuum-based model that assumes the presence of a dislocation-free core of dimension R c is used. The crack tip is assumed not to emit dislocations. The core size is chosen in a self-consistent manner by identifying a maximum equivalent stress in the plastic zone with that predicted by the phenomenological hardening law having the form σ flow = αEb R c . When the inner elastic stress field is matched with the approximate stress field within the plastic zone, it is found that the applied energy release rate needed to initiate crack extension is several orders of magnitude greater than the ideal work of fracture. This apparent shielding of the crack tip is found to strongly depend on the ideal work of fracture, indicating a possible mechanism for segregation-induced interfacial embrittlement.

On the numerical treatment and analysis of finite deformation ductile single crystal plasticity

This contribution is concerned with the numerical analysis and simulation of instability phenomena such as shearband localization in plastic flow processes within the framework of ductile single (fcc) crystal viscoplasticity. To this end, a family of implicit constitutive algorithms and their implementation are considered in detail. Issues of accuracy and conservation of plastic incompressibility are examined. Moreover, the implementation within an overall Newton-Raphson finite element solution strategy relies on the correct evaluation of the algorithmic tangent moduli which result from linearizing the stress update integrator. Likewise, these algorithmic tangent moduli are employed within the numerical analysis of the spatial localization tensor. Examples demonstrating the performance of the proposed strategy at the local constitutive level as well as at the global structural level are given.

Nontraditional Mechanical Alloying by the Controlled Plastic Deformation, Flow and Fracture Processes (<I>Overview</I>)

Two aspects of nontraditional mechanical alloying are considered as one of the most promising solid-state materials processing : direct net-shaping into bulk materials from element constituent powders through the combined secondary processing to MA, and, precise description and understanding of mechanically mixing and refinement processes. Through the experimental studies on our developed mechanical alloying in some systems of materials, two key issues are found to promote the above two directions into further advancement. Those are the preclustering or premixing effect induced by MA on the secondary processing and the effect of controlled plastic flow and failure on the mechanical alloying. With respect to the former issue, MA combined with the shock reactive synthesis is developed to demonstrate that the intermetallic compound should be synthesized in the solid-state reaction from the MAed precursor. On the latter, elasto-plastic super-large deformation analysis is applied to the powder compaction and extrusion process in the repeated loading for nontraditional mechanical alloying to show that the refinement process in MA should be attributed to the large configuration change of powders including their plastic failure into fragments.

Instability phenomena and adiabatic shear band localization in thermoplastic flow processes

The main objective of the paper is the development of the viscoplastic regularization procedure valid for a broad class of thermodynamic plastic flow processes in damaged solids. The additional aim is to investigate instability phenomena and adiabatic shear band localization criteria when spatial covariance, thermomechanical coupling, strain induced anisostropy and micro-damage softening effects are taken into consideration. This investigation is based on an analysis of acceleration waves and takes advantage of a notion of the instantaneous adiabatic acoustic tensor. In the first part of the paper the formulation of an inelastic flow process is given and particular attention is focussed on the thermomechanical coupling effects. The thermodynamic theory of elastic-viscoplastic damaged solids is presented within a framework of the rate type covariance material structure with a finite set of the internal state variables. A notion of covariance is understood in the sense of invariance under an arbitrary spatial diffeomorphism. Rate sensitivity effect is introduced by the assumption of the viscoplastic overstress conception. A notion of a relaxation time has been used to control the description of mechanical as well as thermal disturbances. By the assumption that the mechanical relaxation time is equal to zero the thermo-elastic-plastic (rate independent) response of the damaged material is accomplished. In the second part of the paper the existence of a solution to the initial-boundary value problem is examined and its stability property is investigated based on the application of nonlinear semi-group methods and an analysis of continuity of evolution operators. For an adiabatic process the investigation of acceleration waves is given. The determination of eigenvalues of the appropriate acoustic tensor is presented. This helps to assess the well-posedness of the initial-value problems which describe the thermodynamic plastic flow processes. Differences for two constitutive assumptions, namely for rate dependent and rate independent responses, are examined. In the case of an adiabatic process and elastic-viscoplastic response of a material the conditions for the existence, uniqueness and well-posedness of the initial value problem have been investigated. Criteria for adiabatic shear band localization of plastic deformation are obtained by assuming that some eigenvalue of the instantaneous adiabatic acoustic tensor for rate independent response is equal to zero. Several particular cases of the constitutive model have been considered.

Fluid-melt-rock interaction in mafic eclogites and coesite-bearing metasediments: Constraints on volatile recycling during subduction

The question as to whether the metasomatizing-slab agent needed to form island-arc magmas is an aqueous fluid or a hydrous melt requires a knowledge of fluid-melt-rock interaction during high-pressure low-temperature metamorphism. In the Western Alps, typical “anhydrous” mafic eclogites (Monviso Massif) and coesite-bearing metasediments (Dora-Maira Massif) have experienced a prograde P- T path characteristic of a mature (cold) subduction zone. Microstructural, petrologic, geochemical and fluid inclusion studies show that fluid flow was limited during eclogite and high-grade blueschist facies metamorphism. Most of the fluids were driven off the rocks at pressures lower than 1 and 1.6 GPa, respectively. With increasing pressure and temperature, the remaining fluid phase was released during crystal plastic flow processes or devolatilisation reactions but retain the host rocks to form veins, partial melts or dense hydrous silicates. Tectonic erosion at modern convergent margins delivers large amounts of terrigenous sediments (KMASH system) in subduction zones. In contrast to the basalt and peridotite systems, the KMASH system is characterized by a wide range of pressure-sensitive reactions which allow the reconstruction of dehydration/hydration depths in the subducted slab. Independently of the thermal structure of subduction zones, terrigenous sediments will begin to melt at pressures < 2 GPa. The melt phase can absorb tremendeous quantities of water and represent major sinks for devolatilisation fluids. Dense hydrous silicates will form in any subducted sediments at all depths. These silicates can store significant amount of water in their structure. In the subducted oceanic crust and upper mantle, heterogeneous distribution of fluids inherited from hydrothermal alteration at mid-ocean ridges will cause contemporaneous dehydration and hydration reactions on a local scale rather than large-scale fluid infiltration in the overlying mantle wedge. The situation where a cold, competent and fluid-rich subducted slab is bounded above by a hot, relatively weak and anhydrous material is likely to act against buoyant rise of devolatilisation fluids by forcing the fluids to flow downwards. At sub-arc depths (50 ± 10 to 80 150 km ) and for any geothermal gradient, continuous internal buffering of volatile activities will retain the fluid phase in the slab. This is in contrast with shallow, sub-forearc depths (20 to 50 ± 10 km), where tectonic vein arrays, localized thrust faults, serpentine diapirs, mud volcanoes and boninite magmas attest to the release of large volume of fluids into the overriding mantle wedge.

Charge-density wave phase-slip in niobium triselenide : dislocations and the growth of an, electronic crystal

The analogy is explored between phase-slip in charge-density wave conductors, which brings about the growth and decay of an electronic crystal, and the processes of growth and plastic flow which occur in conventional crystals. The experimental data on NbSe 3 are re-examined, and new measurements of the voltage V ps needed to produce phase-slip at a given rate presented. It is suggested that V ps is determined mainly by the difficulty of inducing dislocation loops in the charge-density wave to climb to the crystal surface, rather than by their difficulty of nucleation

A 2D analytical multiple slip model for continuum texture development and plastic spin

A two-dimensional continuum slip model is presented which accounts in an approximate way for texture development in polycrystalline metals during large strain plastic deformations. The basic kinematic model is that of a rigid–plastic laminated material deforming predominantly by slip along its contact planes. A polycrystalline material is then modelled as a continuum of such laminated components, initially oriented in a random fashion. Texture development, in terms of a continuous laminae orientation distribution function (LODF), is then governed by relatively simple partial differential equations. For stationary plastic flow processes, analytical solutions to these equations are obtained and discussed. Particular emphasis is laid on the predicted macroscopic plastic spin, defined as the weighted average of the slip-induced spin in the laminated components. Results for particular deformation processes are compared with rigorous analyses using a Taylor–Bishop–Hill model for the plastic deformation of cubic polycrystals due to crystallographic slip.

The deformation of CuW laminates

The process of plastic flow in bimetallic laminates of copper and tungsten has been investigated by texture determination, and the mapping of plastic deformation using a grid technique. The results indicate that in the region close to the CuW interface the plastic flow of the matrix is constrained, and the original undeformed texture is retained. The tungsten plates alter the strain path of the copper matrix and influence both the overall texture and the process of flow localization at large strains.

On combined isotropic and kinematic hardening effects in plastic flow processes

Abstract Attention is focused on the description of the combined isotropic and kinematic hardening effects in plastic solids. It has been found that making use of the simple geometrical relation permits us to determine the coefficient in the evolution equation describing the kinematic hardening of the Ziegler type in such a way that the evolution law is consistent with the loading criterion and satisfies the time independence requirement. On the other hand this method leaves room for the identification procedure for the material constants based on available experimental results. General constitutive and evolution equations for plastic solids are formulated. The plastic potential is assumed different than the yield criterion. Simplifications for the associated flow rule are also investigated. A new evolution law for the anisotropic hardening is discussed. This law represents the linear combination of the Prager and Ziegler kinematic hardening rules. Application of the theory developed to the description of the plastic behavior of damaged solids is given. A particular example is considered. The discussion and the interpretation of the isotropic and anisotropic hardening moduli are presented.

The influence of hydrogen on the development of localized plastic deformation in internally nitrided single crystals of iron

It is well known that hydrogen can severely reduce the ductility and toughness of iron and ferrous alloys. Interface embrittlement effects, possibly through reductions in the cohesion of interfaces, and hydrogen induced microstructural damage through, for example, microvoid formation, are documented mechanisms. On the other hand, it has been reported that dissolved hydrogen affects the plastic flow process itself, through interactions with dislocations, and this appears to promote localized plastic deformation which in turn leads to fracture. The purpose of the present study was to make direct use of these background studies to learn more about the possible influences of hydrogen on the localization process. The authors' procedure was to experimentally observe the influence of hydrogen on the deformation and shear band process in ductile single crystals of internally nitrided Fe-Ti-Mn alloys. Dislocation structures involved in the localization process, along with the evolution of stress levels and strain hardening rates as shear bands formed, were documented. These crystals thus offered a good opportunity to study how hydrogen dissolved in this ferrous alloy lattice would influence the development of already well characterized dislocation structures and localization processes. The experiments carried out in the present work essentially paralleled those conducted previously, wheremore » untested crystals from the same material were hydrogen charged as described below. They were subjected to similar mechanical tests and metallographic and electron microscopy study.« less

Transformation steps of microstructures in photodeposited films of a-Se

Amorphous selenium (a-Se) colloid particles have been directly photodeposited onto insulating substrates. Scanning Electron Microscopy (SEM) supported by kinetic adsorption measurements reveals the origin of the photodeposition process. The studies show that film formation occurs through a sequence of particle precipitation, growth, and photoadsorption. A plastic flow and coalescence process creates a continuous monolayer before a fast deposition rate of Se on the deposited materials commences. Surface forces seem to have an important role in the creation of the morphological structures of the adsorbed particles.

On evolution laws of anisotropic damage

This paper is focused on the development of evolution laws of anisotropic damage. Material damage in the form of microcracks and microcavities leading to macro-mechanical property variations is modelled phenomenologically with some distortion and blurring of fine details, arguing that the extent of material property changes may serve as an appropriate, indirect measure of damage. The experimentally observed phenomenon of damage hardening is also described. The well-established thermodynamic theories of irreversible processes are then appealed for deriving constitutive equations of the materials suffering from progressive deterioration, together with a new hypothesis of energy equivalence instead of the restrictive hypothesis of strain or deformation equivalence hitherto proposed. Thermodynamic conjugate force of the damage variable, the “damage energy release rate”, is deduced in analytical form by assuming that the energy involved in the plastic flow and damaging processes can be uncoupled. Evolution laws of anisotropic damage are established following the concept of a damage surface in the space of affinities as well as the principle of maximum damage dissipation. An important outcome of the investigation is the identification of a new damage characteristic tensor J which can accurately describe the anisotropic nature of damage growth and yet is simple with only one unknown parameter to be determined from a standard tension test.

Simulation of Flow Wear in Boundary Lubrication Using a Vickers Identation Method

The process of plastic flow of asperities in boundary-lubricated sliding contact was observed at successive intervals using scanning electron microscopy, and the Vickers indentation method was introduced to simulate the observed process. The characteristics of plastic flow of asperities during sliding contact could be estimated quantitatively by the Vickers indentation method. The Vickers indentation method showed that, below a contact pressure of 40 MPa, the flow rate increased in proportion to the contact pressure, and above 40 MPa, it became almost constant at 4.5 μm/104 passes. With the increase in the sliding velocity from 0.25 to 1.09 m/s, the flow rate decreased from 2.4 to 0.3 μml;m/104 passes.

Plastic flow process of surface layers in flow wear under boundary lubricated conditions

The process of filmy wear debris generation in boundary lubrication was observed successively using scanning electron microscopy. On the rough surface, the contact occurred alternatively between higher asperities and filmy wear debris was generated as a result of the accumulation of plastic flow of surface layers of deformed asperities. The following two types of plastic flow were observed: forward plastic flow; side plastic flow. On the smooth surface, filmy wear debris was generated as a result of side plastic flow accompanying ploughing. In this way, the wear type, which was controlled by the plastic flow of asperities and the generated filmy wear debris, was named “flow wear” in this paper. The particle sizes of filmy wear debris, which were estimated in flow wear, were less than 15 μm and dependent on the surface roughness.

Dislocation glide motion in 6H SiC single crystals subjected to high-temperature deformation

Abstract SiC single crystals of 6H polytype were plastically deformed by uniaxial compression at a constant strain rate at temperatures between 1100 and 1800°C, and their critical resolved shear stress τc and strain-rate sensitivity were measured as a function of temperature. The flow rate [ydot] was found to be expressible in the form [ydot] (τc − τi) n exp (−U/kT), where the activation energy U, the stress exponent n and the stress τi were evaluated to be 3·4 ± 0·7 eV, 3·1 ± 0·4 and 3 MPa, respectively. The present study indicates that plastic strain of the SiC crystals under the present deformation conditions was due to dislocation glide motion on the basal slip system. The motion also appears to have been the rate-controlling process of plastic flow. It is concluded through quantitative reasoning that, in the temperature range studied, the basal dislocation motion is dominated by the Peierls mechanism rather than by the solution-hardening mechanism.