Elastoplastic Interaction Research Articles

On intergranular interaction and the crystallographic mechanism of plastically deformed polycrystalline metals

Taylor principle prevailing currently has been proved to be effective only when grains or grain clusters are deformed in a rigid environment, which disagrees with the reality. Grains realize their plastic deformation in elastoplastic environment, and the equilibrium of intergranular stress and strain need to be reached simultaneously and naturally. The intergranular reaction stress (RS) during deformation can be calculated according to Hooke’s law and the yield stress should be the up-limit of the RS. The combinations of constant external stress and changing RS in RS theory induce alternate activation of deformation systems including slips and twinning with different work hardening rates, while grain orientations and inhomogeneous distribution of external stress have important influence. Some additional deformation systems near the boundaries need to be locally activated when the reduced stress up-limits are reached frequently, to balance the intergranular stress and strain incompatibilities in elastoplastic way. Based on the simpler RS theory, the simulation results of rolling texture on aluminium, low carbon steel, austenite stainless steel, titanium are very close to the reality, indicating that the intergranular elastoplastic interactions and the corresponding crystallographic behaviours of plastic deformation have been reasonably and quantitatively described, therefore, Taylor principle becomes no more necessary.

Finite element solution for static and dynamic interactions of cylindrical rigid objects and unsaturated granular soils

By employing a mortar-type contact algorithm, we develop a theoretical and numerical framework for elastoplastic interaction of unsaturated granular soils with a rigid cylindrical object in both static and dynamic analyses. The elastoplastic response is modelled with a constitutive model based on the effective stress concept for unsaturated soils. The constitutive model offers the ability to simulate the effect of stress-induced anisotropy on the plastic response. Several numerical examples are provided for verification purposes and sensitivity analysis, demonstrating the capabilities of the presented framework.

Elucidating the Effect of Bimodal Grain Size Distribution on Plasticity and Fracture Behavior of Polycrystalline Materials

The refinement of grains in a polycrystalline material leads to an increase in strength but as a counterpart to a decrease in elongation to fracture. Different routes are proposed in the literature to try to overpass this strength-ductility dilemma, based on the combination of grains with highly contrasted sizes. In the simplest concept, coarse grains are used to provide relaxation locations for the highly stressed fine grains. In this work, a model bimodal polycrystalline system with a single coarse grain embedded in a matrix of fine grains is considered. Numerical full-field micro-mechanical analyses are performed to characterize the impact of this coarse grain on the stress-strain constitutive behavior of the polycrystal: the effect on plasticity is assessed by means of crystal plasticity finite element modeling [B. Flipon, C. Keller, L. Garcia de la Cruz, E. Hug and F. Barbe, Tensile properties of spark plasma sintered AISI 316L stainless steel with unimodal and bimodal grain size distributions, Mater. Sci. Eng. A 729 (2018) 248–256] while the effect on intergranular fracture behavior is studied by using boundary element modeling [I. Benedetti and V. Gulizzi, A grain-scale model for high-cycle fatigue degradation in polycrystalline materials, Int. J. Fract. 116 (2018) 90–105]. The analysis of the computational results, compared to the experimentally characterized tensile properties of a bimodal 316L stainless steel, suggests that the elasto-plastic interactions taking place prior to micro-cracking may play an important role in the mechanics of fracture of this steel.

Elastoplastic interaction of grains in polycrystalline materials

A new method is developed for solving boundary value problems of elastoplastic deformation of polycrystalline materials based on the field-theoretical approach. The boundary value problem for inhomogeneous global strain fields in differential form is transformed into a system of integral equations for mesostrain tensors in grains. In this approach, strain at any point of any grain represented as a superposition of homogeneous macrostrain and contributions of interactions with strain in given grain and all another grains of polycrystalline body . It is shown that the effects of the interaction of strains in polycrystal grains can be described using tensors of the fourth rank. This tensor has 36 independent components. The interactions are additive in nature, that drastically simplifies the solution of some problems, for example, search for extreme microstructures of a polycrystal in which critical localized phenomena arise, such as nucleation of the first plastic slips occur. Constitutive equations of deformation type are used for whole body and separate grains. A model of elastoplastic deformation of single crystals of grains is constructed. The physical mechanisms of plastic deformation are shifts in slip systems of crystals. General expressions are obtained for calculating the secant modules of single crystals for any multiaxial deformation. To solve systems of integral equations for mesostrains in grains the perturbation theory upon intergrains interaction used. Nonlinear systems of equations for plastic strains are solved by the iteration method. The features of the elastoplastic interaction of grains are theoretically investigated. The intensity of the elastoplastic interaction depends on the deformed state of the grains. For two identical grains, the elastoplastic interaction of the pair is several times more intense than the elastic one. In this case, the effect of plastically deformed grain on elastically deformed grain is much higher than the inverse effect. An increase in the intensity of interaction with the development of plastic deformations leads to the effect of homogenization of mesodeformations. Computational experiments were performed using polycrystalline titanium as an example.

Nonlocality of one-dimensional bilinear hardening–softening elastoplastic axial lattices

The static behaviour of an elastoplastic axial lattice is studied in this paper through both discrete and nonlocal continuum analyses. The elastoplastic lattice system is composed of piecewise linear hardening–softening elastoplastic springs connected between each other via nodes, loaded by concentrated tension forces. This inelastic lattice evolution problem is ruled by some difference equations, which are shown to be equivalent to the finite difference formulation of a continuous elastoplastic bar problem under distributed tension load. Exact solutions of this inelastic discrete problem are obtained from the resolution of this piecewise linear difference equations system. Localization of plastic strain in the first elastoplastic spring, connected to the fixed end, is observed in the softening range. A continuous nonlocal elastoplastic theory is then built from the lattice difference equations using a continualization process, based on a rational asymptotic expansion of the associated pseudo-differential operators. The continualized lattice-based model is equivalent to a distributed nonlocal continuous elastoplastic theory coupled to a cohesive elastoplastic model, which is shown to capture efficiently the scale effects of the reference axial lattice. The hardening–softening localization process of the nonlocal elastoplastic continuous model strongly depends on the lattice spacing, which controls the size of the nonlocal length scales. An analogy with the one-dimensional lattice system in bending is also shown. The considered microstructured elastoplastic beam is a Hencky bar-chain connected by elastoplastic rotational springs. It is shown that the length scale calibration of the nonlocal model strongly depends on the degree of the difference equations of each lattice model (namely axial or bending lattice). These preliminary results valid for one-dimensional systems allow possible future developments of new nonlocal elastoplastic models, including two- or even three-dimensional elastoplastic interactions.

Crystal plasticity modeling of the effects of crystal orientation and grain-to-grain interactions on DSA-induced strain localization in Al–Li alloys

We develop a crystal plasticity model to investigate the coupled actions of crystal orientation, grain neighborhood and grain-to-grain elasto-plastic interactions on dynamic strain aging (DSA) and the onset and development of associated plastic strain localization in Al–Li alloys. Considering simple model multilayered microstructures with preferred orientations representative of rolled alloys, the aim is to identify grain orientation couples that can limit dynamic strain aging induced strain localization without compromising the flow stress and strain hardening properties. To this end, a slip system-based formulation of dynamic strain aging is implemented in a crystal plasticity finite element framework. The model validity is first checked with the simulation of a tensile specimen loaded at quasi-static applied strain rate. The introduction of dynamic strain aging allows predicting complex propagation of intense plastic localization bands. We further investigate the influence of crystal orientations on early strain localization in Al–Cu–Li–Mg alloys, by performing simulations representative of the early stage of a Kahn Tear test for single crystals and layered polycrystals. Using experimentally reported crystal orientations for rolled microstructures, the simulation results show that in both single and multilayered crystals, there is a strong influence of dynamic strain aging on localization patterns, as well as a significant orientation dependence. In multilayered crystals, the nature of strain localization can be remarkably modified when stand-alone crystals of a certain orientation are coupled with other orientations: strain localization may intensify or fade away depending on the coupling with neighboring orientations.

Crystal Plasticity Modeling of the Effects of Crystal Orientation and Grain-to-Grain Interactions on DSA-Induced Strain Localization in Al-Li Alloys

We develop a crystal plasticity model to investigate the coupled actions of crystal orientation, grain neighborhood and grain-to-grain elasto-plastic interactions on dynamic strain aging and the onset and development of associated plastic strain localization in Al-Li alloys. Considering simple model multilayered microstructures with preferred orientations representative of rolled alloys, the aim is to identify grain orientation couples that can limit dynamic strain aging induced strain localization without compromising the flow stress and strain hardeningproperties. To this end, a slip system-based formulation of dynamic strain aging is implemented in a crystal plasticity finite element framework. The model validity is first checked with the simulation of a tensile specimen loaded at quasi-static applied strain rate. The introduction of dynamic strain aging allows predicting complex propagation of intense plastic localization bands. We further investigate the influence of crystal orientations on early strainlocalization in Al-Cu-Li-Mg alloys, by performing simulations representative of the early stage of a Kahn Tear test for single crystals and layered polycrystals. Using experimentally reported crystal orientations for rolled microstructures, the simulation results show that in both single and multilayered crystals, there is a strong influence of dynamic strain aging on localization patterns, as well as a significant orientation dependence. In multilayered crystals, the nature of strain localization can be remarkably modified when stand-alone crystals of a certain orientation are coupled with other orientations: strain localization may intensify or fades away depending on the coupling with neighboring orientations.

Numerical simulation of elastoplastic contact of heavy-loaded spiroid gears

The paper presents the analysis of heavy-loaded low-speed multi-pair spiroid gears under the effect of elastic contact, bending and shearing, and elastoplastic contact interaction of spiroid gearwheel teeth and spiroid worm threads. The main stages of the developed algorithm for analysis of load distribution and plastic strain of flanks with account of elastic and elastoplastic contact conditions, multi-pair contact and macro-roughnesses on flanks are described in short. At elastoplastic contact the zones of plastic contact on flanks of spiroid gearwheel teeth are determined and the value of plastic strain is analyzed. The flanks of the spiroid gearwheel teeth and worm threads are represented in the algorithm as the set of segments (cells) with coordinates of centers determined with account of the analyzed factors that influence the load distribution in spiroid gearing. These factors are the errors of manufacturing and (or) assembly, micro-roughnesses, and deformations of spiroid gear supports. The paper gives the numerical results of research of the real spiroid gears of gearboxes for pipeline valves (PV) at elastic and elastoplastic contact represented as summary tables and diagrams of contact stress distribution along contact areas and of plastic strain, that show the workability of the algorithm. The presented numerical results of the algorithm functioning are well agreed with the experience of operation of spiroid gears and can be applied for analysis of load-carrying capacity of spiroid gears.

On damping characteristics of frictional hysteresis in pre-sliding range

Frictional hysteresis at relative motion in the pre-sliding range is considered. This effect is characterized by an elasto-plastic interaction, and that on the micro-scale, between two rubbing surfaces in contact that gives rise to nonlinear friction force. The pre-sliding friction force yields hysteresis in displacement. In this study, the damping characteristics of frictional hysteresis are analyzed. It is worth noting that we exclude the viscous damping mechanisms and focus on the pure hysteresis damping to be accounted in the friction modeling. The general properties of pre-sliding friction hysteresis are demonstrated and then compared with the limit case of discontinuous Coulomb friction. Further we consider two advanced dynamic friction models, LuGre and Maxwell-slip, so as demonstrate their damping properties and convergence of the motion system to equilibrium state. Experimental observations of the free motion in pre-sliding range are also shown and discussed.

Numerical Simulation of Dynamic Processes of Elastoplastic Interaction Between Three-Dimensional Heterogeneous Bodies on the Basis of Semi-Analytical Finite Element Method. Part 2. A Study of the Dynamic Deformation of Complex-Shaped Three-Dimensional Structures

Possibilities of the semi-analytical finite element method in the investigation of transient processes of the three-dimensional deformation of heterogeneous bodies of revolution and complex-shaped prismatic bodies by the action of pulsed stressing with allowance for contact interaction zones and nonlinear work of material are shown by calculations of real structures.

Numerical Simulation of Dynamic Processes of Elastoplastic Interaction between Three-Dimensional Heterogeneous Bodies on the basis of Semi-Analytical Finite Element Method. Part 1. Computational Relationships of the Semi-Analytical Finite Element Method and Algorithms for the Study of Transient Processes of Dynamic Deformation of Heterogeneous Prismatic Bodies and Bodies of Revolution

On the basis of a semi-analytical finite element method, an effective approach has been developed for studying transient processes of dynamic deformation of three-dimensional heterogeneous bodies of revolution and prismatic bodies of complex shape and structure by the action of time-and space-varying pulsed stressing with allowance for the plastic properties of the material and time-varying contact interaction conditions. New types of finite elements have been created, on the basis of which computational relationships of the semi-analytical finite element method (SAFEM) for problems of dynamics have been constructed. Modified relationships of the Newmark method have been obtained, which have been formulated for the amplitude subsystems of SAFEM. Effective block iteration algorithms for the solution of large systems of nonlinear equations of SAFEM have been developed and realized.

Measuring the local resistivity by the nanoindentation and force-spectroscopy methods

Methods for measuring the resistivity of materials during elastic and elastoplastic interactions of a current-conducting indenter and a studied sample are described. Analytical methods that describe the dependences of the contact ohmic resistance on the pressure force and the contact stiffness are proposed. The considered models are experimentally tested with a NanoScan scanning nanohardness tester using indenters made of boron-doped diamond single crystals.

МОДЕЛИРОВАНИЕ ГИДРОУПРУГОПЛАСТИЧЕСКОГО ВЗАИМОДЕЙСТВИЯ С ПОМОЩЬЮ ПРОГРАММНОГО КОМПЛЕКСА UPSGOD

The UPSGOD computer codes were tested on problems of elastoplastic interaction. The problems of impact interaction of a liquid-filled plastic container with a rigid obstacle and of the internal explosive loading of a liquid-filled shell are solved. The obtained results are compared with the available experimental and numerical data. Keywords: interaction, contact forces, elastic-plastic deformation, model, detonation, container. &nbsp

A numerical modelling of 3D polycrystal-to-polycrystal diffusive phase transformations involving crystal plasticity

A FE modelling of the elastoplastic interactions occurring within a 3D polycrystal subjected to diffusive phase transformation is proposed. The parent polycrystal is represented by a Voronoi tessellation, where grains differ in shape, size and crystallographic orientation. Grains of the new phase nucleate at favourable sites of the parent polycrystal then grow isotropically, following specific kinetics. This process can result in various product polycrystal morphologies where grains are distinguished by their morphologies and their crystallographic orientations, and have crystalline properties different from those of the parent grains. Application is performed on the austenite-to-ferrite transformation of a low carbon steel, by analysing different basic cases of transformation history with different constitutive modellings. Microplasticity and its related internal stresses are shown to develop during the phase transformations and to affect significantly the elastoplasticity of the product medium.

The Influence of Torsional Moments on the Elastoplastic Interaction Curves of a Symmetrical I Cross-Section~!2009-11-04~!2010-01-18~!2010-03-09~!

The Influence of Torsional Moments on the Elastoplastic Interaction Curves of a Symmetrical I Cross-Section~!2009-11-04~!2010-01-18~!2010-03-09~!

Effect of the random spatial distribution of nuclei on the transformation plasticity in diffusively transforming steel

The γ → α diffusive phase transformations of steels can lead to transformation plasticity (TRIP) if accompanied of an external loading stress or a pre-hardening of the parent phase. The most current approaches of its modelling are based on the Greenwood-Johnson mechanism; they call upon hypotheses (about microstructure morphology, constitutive laws...) which are at the origin of discrepancies between predictions and experimental observations in particular loading cases. Some of these restricting hypotheses can be eliminated with a micromechanical finite elements approach, where the elastoplastic interactions between phases are determined at the micro-scale of a volume element containing hundreds of growing particles (Barbe et al., 2005, 2008). This paper deals with the effect of the spatial distribution of product phase nuclei on the global kinetics and transformation-induced plasticity (TRIP) in the volume element. Two distributions are considered: uniform random and at preferential nucleation sites of a Voronoi tesselation mimicking austenite microstructure.

地盤中に埋め込まれたアルミ製ポールの静的水平載荷実験と解析(構造)

This paper deals with analyses of aluminum poles for reinforcement of old or weak wooden houses due to static lateral loading test. Three-dimensional elasto-plastic Finite Element Method (FEM) analyses were carried out to examine whether the computer analysis could accurately simulate or not results for the elasto-plastic behaviors of aluminum columns buried in soils with different embedment depths due to laterally loading tests. The behaviors were simulated fairly precisely by the elasto-plastic FEM. In addition, impact analyses were made for the horizontal load tests for aluminum poles with actual size buried in a soil to examine the applicability of the three-dimensional FEM. In consequence, the impact behaviors of the aluminum column could be found in consideration of the elasto-plastic interaction between aluminum column and soil.

A comparative study of concentrated plasticity models in dynamic analysis of building structures

Concentrated plasticity (CP) models are frequently used in static and dynamic building analysis and have been implemented in available commercial software. This investigation deals with three different CP-models, a simplified macroelement model (SEM) for a complete building story, a frame element with elasto-plastic interaction hinges (PH), and a frame element with fiber hinges (FB). The objectives of this work are to evaluate the quality of the earthquake responses predicted by these models and to identify important aspects of their implementation and limitations for their use in dynamic analysis. The three elements are tested in a single-story asymmetric plan building and in a three-story steel building. Results show that base shear and global response values are usually computed with better accuracy than interstory deformations and local responses. Besides, the main limitation of elasto-plastic CP models is to control the displacement offsets that result from perfect elasto-plastic behavior. On the other hand, calibration of the SEM-model shows that global responses in steel structures may be computed within 20% error in the mean at a computational cost two orders of magnitude smaller than that of the other CP elements considered. However, the three element models considered lead to increasing levels of accuracy in the dynamic response and their use depends on the refinement of the analysis performed. Copyright © 2005 John Wiley & Sons, Ltd.

Fatigue Life and Traction Modeling of Continuously Variable Transmissions

A model was developed to study the elastohydrodynamics and contact mechanics of toroidal Continuously Variable Transmission (CVT) type contacts. The aim is to predict the fatigue life, traction and efficiency of such contacts with the intention of making optimizations based on design criteria and constraints. A generalized Reynolds equation was developed for isothermal, transient lubrication of elliptical rough contacts with mixed rolling, two-dimensional sliding, and spinning conditions, incorporating any non-Newtonian model, roughness asperity isothermal elastoplastic interactions, and a three-dimensional subsurface stress analysis. The output is in the form of film thickness and traction maps, including contact efficiency, three-dimensional stress fields, and, finally, the predicted fatigue lives of CVT contacts, based on the Ioannides-Harris life model. A parametric study reveals the effect of surface roughness, lubricant bulk temperature, contact ellipticity ratio, slide-roll ratio, and contact load on the fatigue life, traction and contact efficiency of CVTs, and allows for design optimizations based on a compromise between life, traction and efficiency.

Dynamic elastoplastic interaction between an impactor and a spherical shell

Dynamic axisymmetric elastoplastic interaction between a massive body and a simply supported, circular segment of a spherical shell is studied. The problem of determining the contact‐interaction force is formulated for the case of spherical and conical bodies. A nonlinear integral equation is derived for various models of local plastic compression using the equations of equilibrium of a membrane spherical shell written in terms of radial displacement of the shell. Numerical results are presented graphically.