Onset Of Plastic Flow Research Articles

Analysis of heterogeneous deformation and dislocation dynamics in single crystal micropillars under compression

The size dependent deformation of Cu single crystal micropillars with thickness ranging from 0.2 to 2.5 μm subjected to uniaxial compression is investigated using a Multi-scale Dislocation Dynamics Plasticity (MDDP) approach. MDDP is a hybrid elasto-viscoplastic simulation model which couples discrete dislocation dynamics at the micro-scale (software micro3d) with the macroscopic plastic deformation. Our results show that the deformation field in these micropillars is heterogeneous from the onset of plastic flow and is confined to few deformation bands, leading to the formation of ledges and stress concentrations at the surface of the specimen. Furthermore, the simulation yields a serrated stress–strain behavior consisting of discrete strain bursts that correlates well with experimental observations. The intermittent operation and stagnation of discrete dislocation arms is identified as the prominent mechanism that causes heterogeneous deformation and results in the observed macroscopic strain bursts. We show that the critical stress to bow an average maximum dislocation arm, whose length changes during deformation due to pinning events, is responsible for the observed size dependent response of the single crystals. We also reveal that hardening rates, similar to that shown experimentally, occur under relatively constant dislocation densities and are linked to dislocation stagnation due to the formation of entangled dislocation configuration and pinning sites.

Effect of indenter shapes on inverse materials characterization based on the dual indenters method

Abstract The indentation method is a useful tool for studying the onset of plastic flow and work hardening in small volumes. Several approaches based on either single and dual indenters have been reported to characterise a wide range of materials. In this work, the single and dual indenters approaches, with different indenter types, have been comparatively studied using an inverse finite element modelling program developed based on the Kalman filter method. The effect of indenter shapes on the accuracy and uniqueness of the predicted results, as well as convergence time of the program are systematically analysed by automatically mapping the results with a wide range of initial values.

Characterizing and modeling the tensile deformation of polyethylene: The temperature and crystallinity dependences

For various polyethylenes at ambient and elevated temperatures, tensile deformation was characterized by measurements of true stress-true strain curves at constant strain rates, the determination of the elastic and plastic part of strains, and registrations of the stress relaxation at fixed strains. Some peculiar features show up: (i) The yield point is associated with a drop in the stiffness rather than an onset of plastic flow. (ii) The elasticity reaches a plateau at a temperature and crystallinity invariant critical strain (ɛ H ≈ 0.6). (iii) Moduli as derived from the stretching curve can be strongly modified by viscous forces. A recently introduced model treats the stress as arising from three contributions, rubberlike forces originating from the stretched network of entangled amorphous chains, forces transmitted by the skeleton of crystallites, and viscous forces described by Eyring’s equation. Adjustment of the measured data to the model provides a decomposition of the stress in the three parts and thus allows an analysis of the effects of temperature and crystallinity.

Elastic stability and the onset of plastic flow in accelerated solid plates

For accelerated incompressible, ideal elastoplastic plates of finite thickness with a preformed sinusoidal perturbation at the interface, we investigate the stability behavior encompassing neutral and most-unstable modes, stable oscillatory modes, and the onset of plastic flow. We show that the largest perturbation wavelength that can maximize the growth rate corresponds to a finite thickness plate. For elastically stable configurations, stress gradients that arise as a result of the interfacial disturbance can lead to the formation of counter-rotating particle displacement trajectories that tessellate the extent of the plate. By computing the spatiotemporal evolution of the stress tensor, we are able to construct the boundaries that demarcate the transition from elastically stable oscillatory modes to the onset of plastic flow based on the von Mises yield criterion. Earlier estimates of these boundaries for thick plates differ qualitatively and quantitatively from the present results, in which the common simplifying assumptions of thin-plate theory were not invoked. We show that multimodal solutions are necessary to accurately represent the actual oscillatory behavior of the stress tensor, which in general is not time periodic, that thin-plate bimodal solutions are unable to capture.

Measurement of stress using synchrotron x-rays

Stress analysis in polycrystalline materials reveals that stress can vary considerably amongdifferent subpopulations of grains. Samples of MgO and mixtures of MgO and spinel havebeen studied. After the onset of plastic flow, stronger grains or orientations will supportmore stress than the weaker grains. A grain to grain fabric develops that enables this stresspartitioning. The stress partitioning and the resulting fabric can invalidate staticmeasurements of elastic moduli. However, high temperature flow mechanisms reveal a moreisotropic strength behaviour resulting in a more uniform variation of stress withorientation.

The flow stress behavior of OFHC polycrystalline copper

The flow stress behavior of OFHC polycrystalline copper was evaluated using cold-rolled and equal channel angular extruded materials. Prior to tensile testing at room temperature, the specimens were heat treated to obtain grain sizes ranging from 3 to 60 μm. The flow stress, when correlated with the square root of true strain, is associated with four stages of hardening. These stages, in terms of increasing strain, are attributed to: (1) dislocation source activation, possibly at annealing twin boundaries during the onset of plastic flow, (2) dislocation slip and cross slip, (3) constriction of the screw dislocation partials for cross slip continuation, and (4) dislocation annihilation and saturation as interpreted through dynamic recovery. The tensile properties and analyses are supported by observations and measurements from orientation imaging and transmission electron microscopy.

Electron microscopy observations of twin-twin intersections in a particle hardened copper-titanium alloy

The authors have recently reported electron microscopy (CTEM and HREM) observations of mechanical twinning in age hardened copper-titanium alloys containing a fine dispersion of the metastable Cu{sub 4}Ti ({beta}{prime}; D1{sub a}) phase ({approx}15 vol%). These particle hardened alloys are known to twin profusely and it has been suggested that single crystals of Cu-Ti-Al alloys containing coherent Cu{sub 4}Ti (D1{sub a}) particles yield by twinning at the onset of plastic flow. In this short paper conventional (CTEM) and high-resolution (HREM) electron microscopy observations of twin/twin intersections in the precipitation hardened two-phase copper-titanium alloys are reported. These results will suggest that the mechanisms governing shear accommodation in obstacle twins remain to be elucidated.

High-Temperature Plasticity of the β-phase in Nearly-Equiatomic Nickel-Titanium Alloys

Plastic behaviour of the β nickel-titanium alloys with nearly-equiatomic compositions, Ti-49.5, 50.0 and 50.5 mol%Ni, has been studied. The alloys were highly ductile due to dislocation glide at temperatures where the β-phase was in equilibrium. The ductility became largest at the lowest temperature in the stability range of the β-phase. The strain-rate vs. flow stress relations of easy-glide deformation in tensile testing and steady-state creep deformation satisfied the power law. Both of the deformations are associated with the dislocation glide which are likely to be controlled by the Peierls mechanism. A yield drop at the onset of plastic flow appeared only in the tensile deformation of Ti-50.5 mol%Ni, but not in Ti-49.5 and 50.0 mol%Ni alloys. Excess nickel atoms would exist as antistructure defects, which might be responsible for the yield point phenomena.

Mechanical and Thermal Stability of Heavily Drawn Pearlitic Steel Wire

AbstractHaving interlamellar spacings on the nanometer scale, there is no doubt about considering heavily drawn pearlitic steel wire as a nano-layered material. This extremely fine structure is of great technical importance: indeed, as the interlamellar distance determines the onset of plastic flow, the wire can be brought to a tensile strength beyond 4000 MPa and is therefore one of the strongest materials on the market nowadays.At extremely large strains (well beyond ε = 4) and/or at moderate temperatures, the pearlitic steel loses its strength. Several possible failure mechanisms, like fragmentation of the cementite or thermal and strain-induced cementite dissolution, are put forward, but until now, there is no definite understanding of the really active mechanism.In the present work, the calorimetric differential scanning technique, in combination with thermopower measurements and the high-resolution atomic force microscopy, have turned out to be most promising tools to reveal some of the mechanisms that are responsible for the degradation of the lamellar aggregate.

Measurement and prediction of strain in individual phases of a 2219Al/TiC/15p-T6 composite during loading

The objective of this study was to compare neutron diffraction measurements of strain in an aluminum titanium carbide MMC with numerical predictions. In particular, the authors focused on the elastic strains in each phase during applied loading and how these strains changed at the onset of plastic flow. During loading of an MMC, the presence of a hard, reinforcing, minority phase can lead to localized or non-homogeneous plastic flow in the matrix. This can modify the pre-existing residual stresses that are introduced during cooling from fabrication temperatures because of mismatch in the thermal expansion coefficients of the constituent phases. By combining experiment and calculation, the authors have investigated the deformation processes.

Regularities of a variation in electrical resistance and deforming stress of ABM-1 alloy and aluminum at 77 K

A resistometric investigation of the onset of plastic flow and the regularities of strain hardening of ABM-1 alloy (Al-Be-Mg) and coarse-grained aluminum at liquid nitrogen temperature is performed. It is shown that plastic flow in the considered materials begins long before the appearance of the yield point. The established regularities of a variation in electrical resistance and deforming stress are explained by the evolution of a structural state characterized by a variation in the coefficient of dislocation interaction.

The validation of the upper-bound elemental technique (UBET) in the prediction of strain distributions in forgings

Many researchers have been developing predictive methods in order to establish the behaviour of metals at the onset of plastic flow and the upper-bound elemental technique (UBET) is a particularly suitable practical method which has been developed by the authors. This paper presents a comparison between the strain distribution predicted by UBET with those obtained by an experimental metallographic technique. It describes an experimental evaluation of strain distributions within a moderately complex axisymmetric forged compoment, using an established microstructural evaluation technique. The resultant analysis is then applied to validate the simulated forging and strain distribution obtained by UBET, for the same component. The potential of the UBET for practical application and academic enhancement is demonstrated thereby.

A Comparative Study of Thermal Conditions at Onset of Plastic Flow in Various Semiconductors

The required thermal conditions for control of thermal stresses during the melt growth of Si, GaAs, InP and CdTe are compared. The results indicate that the low thermal conductivity and CRSS values of the compound semiconductors results in significantly lower values of admissible heat transfer rates in these materials when compared to Si.

Finite Element Analysis of a Layered Elastic Solid in Normal Contact With a Rigid Surface

Based on the finite element method, the elastic contact problem of a layered semi-infinite solid compressed by a rigid surface is solved numerically. The case of a surface layer stiffer than the substrate is considered, and general solutions for the subsurface stress and deformation fields are presented for relatively thin, intermediate, and thick layers. Additionally, the stresses in a compressed homogeneous half-space having the substrate properties have been obtained for comparison. The significance of the layer thickness relative to the size of the half-contact width, the friction coefficient at the contact zone, and the stiffness of the layer are critically examined and the conditions under which the layer is beneficial are addressed. Furthermore, the mechanisms of microcrack initiation at the layer surface or interface, layer debonding, and onset of plastic flow in the layered solid are explained qualitatively, in light of the governing stresses, and the regimes of their prevalence are approximately determined.

Interfacial Stress Singularities at Free Edge of Hybrid Metal Matrix Composites

Novel hybrid-matrix composites with alternating metallic matrices of different plastic flow resistance offer excellent potential for a superior strength and toughness combination than traditional monomatrix composites. The local stress concentrations in this class of composites can be controlled by proper tailoring of the metal matrices. The free edge accentuated stress state which govern inter-matrix interfacial cracking in such hybrid metal matrix composites has been solved. Determined through asymptotic expansion and numerical methods, the local decohesion stress, σθθ, is found to be always positive for far field tensile loading. The power of the stress singularity is found to depend on the ratio of the plastic resistances of the two matrix metals. A larger difference in resistance to onset of plastic flow between the two matrix metals leads to stronger stress singularity. The work hardening behavior of the matrices also affects the power of the stress singularity. At the limit, the interfacial stress becomes nonsingular for non-workhardening matrices. Detailed results of both the power of the stress singularity, and its angular variation have been determined for a range of matrix combinations.

Dependence of the yield stress of filamentary sodium chloride crystals on the starting dislocation structure

The onset of plastic flow of filamentary NaCl crystals with the simplest types of starting dislocation structure was studied under conditions which completely exclude the effect of stress concentration in the clamps of the microdeformation machine. It was established that the growth dislocations, having an outlet to the side boundaries, do not exclude the appearance of a sharp projection of the flow on the stretching diagram, though they reduce its height. The flow projection remains in samples with traces of microdeformation, formed by random effects during manipulation; in addition, the behavior of the filamentary crystals at the yield stress depends on the nature of these traces.

Mathematical modelling of jointed rock masses : Olofsson, T PhD Thesis, Lulea Univ1985: 42 D, 143P

In this thesis, a theoretical model of the mechanical behaviour of jointed rock masses is developed. An equivalent material approach is used to formulate the constitutive equations, where the structural components, intact rock and joints are assigned continuous material properties. The elastic and inelastic properties of the joints are modelled by an elastoviscoplastic formulation. The model can be used to study general stress and strain paths for both two- and three-dimensional structures based on constitutive equations, i.e., stress strain relations or in finite element codes. The rock mass model using the equivalent material approach can be applied to hard rock masses with several sets of intersecting continuous joints. The theoretical model developed for a single joint can also be used for discrete formulation of joint elements in finite element codes. The intact rock is treated as a linearly elastic material. The elastic behaviour of the joint is modelled with a constant stiffness matrix. The onset of plastic flow is initiated when the normal stress exceeds the normal compressive strength of the joint asperities or the tensile normal strength of the joint, the shear stress, exceeds the cohesive strength and frictional resistance of the joint surface. The normal tensile strength and the cohesion of the joints are assumed to be constant material properties. (Author/TRRL)

A numerical study of localized deformation in bi-crystals

Finite element calculations are presented for a model bi-crystal subjected to tensile loading. The constitutive description used is strain rate dependent and is based, on a finite strain kinematical theory that accounts for lattice and material rotations. Two calculations are described in which the latent hardening is varied. The presence of a grain boundary is shown to promote nonuniform deformation from the very onset of plastic flow and after finite straining localized shear bands are observed to form. Shear band development in the bi-crystals is compared to that in the single crystal calculations of Peirce et al. (1982, 1983). In addition, comparisons are made of shear band formation in strain rate dependent and rate independent single crystal models. In this it is shown that although the connection between localization and loss of ellipticity of the governing equations holds for rate independent models, the process itself does not depend on this when rate dependence is included in the theory. In particular, the rate dependent governing equations remain elliptic in all the examples described here.

Acoustic study of elastic properties, dislocation damping and plasticity of crystals

AbstractThe results of acoustic studies of elasticity and dislocation inelasticity of crystals are presented. Regularities of elastic anisotropy variation with ionicity of bonds in ANB8‐N crystals have been considered. Amplitude dependences of ultrasound damping supply the information on dislocation structure and dislocation — to point defect interaction. Oscillation of dislocations during internal friction measurements are compared to their translation motion at the onset of plastic flow.

Acoustic emission from dislocation motion in precipitation-strengthened alloys

Abstract A model is proposed to explain the effect of precipitation on acoustic emission from dislocation motion in age-hardening systems. The model is based on the hypothesis that a substantial number of dislocations must move rapidly and nearly simultaneously within a small volume of material in order to create detectable acoustic emission. In alloy systems where cross slip is difficult, precipitates, if they are not too strong, can serve as breakable pins and lead to the formation of dislocation avalanches and thereby increase acoustic emission near the onset of plastic flow. In easy cross slip systems, dislocations tend to cross slip around precipitates rather than form pile-ups, so the precipitates do not lead to increased acoustic emission. These considerations do not apply if the pins are Cottrell atmospheres, and high levels of acoustic emission may be observed in either easy or difficult cross slip systems when solute atmospheres provide the pinning. Acoustic emission measurements have been made ...