Quasi-static Deformation Process Research Articles

A novel discrete coordinate approach to modelling nonlinear structural instability problems with material damage

A novel analytical framework for the inclusion of active damaging processes in a structural stability analysis is presented. The framework considers quasi-static deformation processes and is formulated in terms of a discrete coordinate approach, employing an extended total potential energy functional, where the current damage state is expressed in terms of geometric configuration and applied loading. Within the current framework, an efficient analysis of structures prone to buckling instability and material damage is enabled particularly where damage initiates once structural instability has been triggered. Composite panels with multiple damage mechanisms (e.g. delaminations, matrix cracks) are studied to showcase its application.

Extraordinary effect of the δ phase on the electrically-assisted deformation responses of a Ni-based superalloy

The effect of the δ phase (Ni3Nb) on the electrically-assisted (EA) deformation responses, particularly stress, elongation and dislocation distribution, of the Ni-based superalloy is still unknown up to now, though it is clear as nonnegligible on the quasi-static and hot deformation processes. Therefore, the effect of the δ phase during the electrically-assisted tension were experimentally investigated and analyzed with comparison to that in the hot tension process. Generally, the δ phase existing in the Ni-based superalloy always causes the reduction of flow softening and elongation during cold and the initial stage of hot tension processes. What is distinct, the δ phase promotes the flow softening effect and elongation during the EA tension. In addition, the dislocation-free ring around the δ phase was firstly observed during the EA tension. The mechanism of these macro and micro extraordinary phenomena is concluded as that the δ phase causes serious lattice distortion and dislocation pile-up around itself, which leads to an extremely high temperature due to the local Joule heating effect. The faster elimination of dislocation pile-up in the local area because of the local higher temperature results in the dislocation-free ring phenomenon and the significant improvement of flow softening effect and elongation.

Viscoplasticity with frictional contact and rapid growth

We consider a problem in the inelastic deformation theory with a quasistatic deformation process of the gradient‐monotone type. We assume that the body has contact with a rigid foundation: the body moves on the foundation with friction. The frictional contact is modelled by a velocity‐dependent dissipation functional. This makes an evolution problem with two nonlinear monotone operators. We consider the gradient‐monotone inelastic constitutive function with a rapid growth at infinity. This leads us to a nonreflexive Orlicz space as an operational base. The frictional dissipation potential brings about a minimalization problem in this nonreflexive Orlicz space. Copyright © 2016 John Wiley & Sons, Ltd.

Study on Surface Asperity Flattening in Cold Quasi-Static Uniaxial Planar Compression by Crystal Plasticity Finite Element Method

In order to study the surface asperity flattening in a quasi-static cold uniaxial planar compression, the experimental results of atomic force microscope and electron backscattered diffraction have been employed in a rate-dependent crystal plasticity model to analyze this process. The simulation results show a good agreement with the experimental results: in this quasi-static deformation process, lubrication can hinder the surface asperity flattening process even under very low deformation rate. However, due to the limitation of the model and some parameters, the simulation results cannot predict all the properties in detail such as S orientation {123} , and the maximum stress in sample compressed without lubrication. In addition, the experimental results show, with an increase in gauged reduction, the development of Taylor factor, and CSL boundaries show certain tendencies. Under the same gauged reduction, friction can increase the Taylor factor and Σ = 7.

Vertex dynamics simulations of viscosity-dependent deformation during tissue morphogenesis.

In biological development, multiple cells cooperate to form tissue morphologies based on their mechanical interactions; namely active force generation and passive viscoelastic response. In particular, the dynamic processes of tissue deformations are governed by the viscous properties of the tissues. These properties are spatially inhomogeneous because they depend on the tissue constituents, such as cytoplasm, cytoskeleton, basement membrane and extracellular matrix. The multicellular mechanics of tissue morphogenesis have been investigated in vertex dynamics models. However, conventional models are applicable only to quasi-static deformation processes, which do not account for tissue viscosities. We propose a vertex dynamics model that simulates the viscosity-dependent dynamic deformation processes during tissue morphogenesis. By incorporating local velocity fields into the governing equation of vertex movements, the model turns Galilean invariant. In addition, the viscous properties of tissue components are newly expressed by formulating friction forces on vertices as functions of the relative velocities among the vertices. The advantages of the proposed model are examined by epithelial growth simulations under the employed condition for quasi-static processes. As a result, the epithelial vesicle simulated by the proposed model is linearly elongated with nearly free stress, while that simulated by the conventional model is undulated with compressive residual stress. Therefore, the proposed model is able to reflect the timescale of deformations by satisfying Galilean invariance. Next, the applicability of the proposed model is assessed in epithelial growth simulations of viscous extracellular materials. In this test, the epithelial vesicles are deformed into tubular shapes by oriented cell divisions, and their morphologies are extremely sensitive to extracellular viscosity. Therefore, the dynamic deformations in the proposed model depend on the viscous properties of tissue components. The proposed model will be useful for simulating dynamic deformation processes of tissue morphogenesis depending on viscous properties of various tissue components.

Assessing the Influence of Porosity in the Deformation of Metal–Ceramic Composites

The aim of the paper is to develop the previously formulated model [19, 20] of the polycrystalline composite to include porosity growth at metallic interfaces of metal–ceramic composites (MCCs). Examples of this kind of MCCs are: (1) a two-phase material composed of brittle grains WC joined by the plastic binder Co, which can contain a small degree of porosity introduced during the cooling process [31], (2) TiC–Mo2C hard phase grains surrounded by tough binder phase Ni [12]. This work focuses on the description of the deformation of the MCC material including the modelling of a real material internal structure taking into account porosity growth during the loading. Experimental observations of the WC/Co composite [10] indicate that the majority of the fracture energy of MCC is expended through ductile failure of the plastic binder Co (dimple rupture across the binder or in the binder near the binder/carbide interface). This process is preceded by porosity growth at metallic interfaces and finally leads to inter-granular cracks propagation. This paper presents micromechanical modelling of the MCC response in the case of uniaxial tension of 3-D Representative Volume Element (RVE) with the application of the Finite Element Analysis (FEA). The MCC material includes: elastic grains and inter-granular metallic layers containing technological pores that create its real complex internal structure. The quasi-static deformation process of the material comprises elastic deformation of brittle grains, elasto-plastic deformation of inter-granular layers (of different thickness: 2–4 μm) and additional deformation due to micro-porosity development in the layers. A micro-sample analysis leads to the conclusion that a small amount of technological porosity changes the qualitative behaviour of the MCC including deformation, rotation of grains, roughness, and level of plastic strains.

Acceleration of DEM algorithm for quasistatic processes

AbstractThe discrete element method (particle dynamics) is an invaluable tool for studying the complex behavior of granular matter. Its main shortcoming is its computational intensity, arising from the vast difference between the integration time scale and the observation time scale (similar to molecular dynamics). This problem is particularly acute for macroscopically quasistatic deformation processes. We first provide the proper definition of macroscopically quasistatic processes, on the basis of dimensional analysis, which reveals that the quasistatic nature of a process is size‐dependent. This result sets bounds for application of commonly used method for computational acceleration, based on superficially increased mass of particles. Next, the dimensional analysis of the governing equations motivates the separation of time scales for the numerical integration of rotations and translations. We take advantage of the existence of fast and slow variables (rotations and translations) to develop a two‐timescales algorithm based on the concept of inertial manifolds suggested by Gear and Kevrekidis. The algorithm is tested on a 2D problem with axial strain imposed by rigid plates and pressure on lateral boundaries. The benchmarking against the accurate short‐time step results confirms the accuracy of the new algorithm for the optimal arrangement of short‐ and long‐time steps. The algorithm provides moderate computational acceleration. Copyright © 2010 John Wiley & Sons, Ltd.

The Corinth Rift Laboratory or an in situ Investigation on Interactions between Fluids and Active Faults

Earthquakes result from the sudden acceleration of a preliminary long-term slow deformation process. The objective of the Corinth Rift Laboratory (CRL) is to investigate in situ this quasistatic deformation process and mechanisms leading to a sudden catastrophic acceleration. Of particular interest is the characterization of the structure of the deforming zones and of the progressive localization of deformation. Special attention is given to the role of fluids but also on the influence of faults on regional fluid flow doi:10.2204/iodp.sd.s01.20.2007

The Corinth Rift Laboratory or an <i>in situ</i> Investigation on Interactions between Fluids and Active Faults

Earthquakes result from the sudden acceleration of a preliminary long-term slow deformation process. The objective of the Corinth Rift Laboratory (CRL) is to investigate <i>in situ</i> this quasistatic deformation process and mechanisms leading to a sudden catastrophic acceleration. Of particular interest is the characterization of the structure of the deforming zones and of the progressive localization of deformation. Special attention is given to the role of fluids but also on the influence of faults on regional fluid flow <br><br> doi:<a href="http://dx.doi.org/10.2204/iodp.sd.s01.20.2007" target="_blank">10.2204/iodp.sd.s01.20.2007</a>

Microstructural and mechanical characterization of Nb-based in situ composites from Nb–Si–Ti ternary system

This study deals with the Nb–niobium silicide-based composites developed by the hot-pressing of Nb–Si–Ti ternary powder mixtures with a fixed Ti addition (6 at.%) and Si content ranging from hypereutectic (11 at.%) to near-eutectic compositions (18 at.%). The effects of Si content, Ti addition and strain rates on the sample microstructural characterization, flexural strength, fracture toughness, quasi-static compressive deformation and failure processes were investigated. It was revealed that the volume fraction of silicides increased with increasing Si content, and most of the Ti atoms dissolved into the niobium silicides to form (Nb,Ti) 5Si 3 solid solutions instead of binary titanium silicides. The experimental evidence showed that a moderate improvement in the flexural strength, fracture toughness and compressive yield stress of the composites was achieved by the addition of Ti. Higher Si additions produced a much more remarkable enhancement in the compressive yield stress and bulk hardness, whereas both the flexural strength and fracture toughness decreased with increasing Si content owing to the existence of residual porosities in the samples. The composites showed remarkable superiority to the arc-melted Nb–Si alloys and monolithic niobium silicides in fracture toughness ( 8.3 – 13.0 MPa m vs. 4.5 MPa m ), where the toughening effect was attributed mainly to crack bridging and crack deflection by the remaining ductile Nb phase. Moreover, quasi-static uniaxial compression tests at strain rates between 10 –5 and 10 –3 s −1 indicated that the deformation behavior and failure processes were significantly affected by Si content and strain rates. The strain-rate-hardening behavior for all the strain rates was observed in the composite materials and the strain-rate sensitivity decreased with increasing Si content. At a lower strain rate, the composite materials with a hypoeutectic Si composition failed with a pseudoplastic response and at an angle of ∼45° off the compressive loading direction. However, in the case of higher strain rate and Si content, the brittle failure in the samples occurred through vertical splitting and spalling of fragments.

Modeling Large-deformation-induced Microflow in Soft Biological Tissues

The homogenization approach to multiscale modeling of soft biological tissues is presented. The homogenized model describes the relationship between the macroscopic hereditary creep behavior and the microflow in a fluid-saturated dual-porous medium at the microscopic level. The micromodel is based on Biot’s system for quasistatic deformation processes, modified for the updated Lagrangian formulation to account for coupling the fluid diffusion through a porous solid undergoing large deformation. Its microstructure is constituted by fluid-filled inclusions embedded in the porous matrix. The tangential stiffness coefficients and the retardation stress for the macromodel are derived for a time-stepping algorithm. Numerical examples are discussed, showing the strong potential of the model for simulations of deformation-driven physiological processes at the microscopic scale.

A simplified analysis of interface failure under compressive normal stress and monotonic or cyclic shear loading

Interface damage and delamination is usually accompanied by frictional slip at contacting interfaces under compressive normal stress. The present work is concerned with an analysis of progressive interface failure using the cohesive crack model with the critical stress softening and frictional traction present at the contact. Both monotonic and cyclic loadings are considered for anti-plane shear of an elastic plate bonded to a rigid substrate by means of cohesive interface. An analytical solution can be obtained by neglecting the effect of minor shear stress component. The analysis of progressive delamination process revealed three solution types, namely: short, medium and long plate solutions. The long plate solution was obtained under an assumption of quasistatic progressive growth of the delamination zone. In view of snap back response, the quasistatic deformation process cannot be executed by either traction or displacement control. The states of frictional slip accompanied by shake down or incremental failure are distinguished in the case of cyclic loading, related to load amplitude and structural dimensions. The analysis provides a reference solution for numerical treatment of more complex cases. Copyright © 2005 John Wiley & Sons, Ltd.

The Creation Process of Faults in Quasi-static Deformation

We investigated quasi-static deformation processes of granular systems both by experiments and numerical calculations. We simulated the deformation of a regular arrangement of particles using the discrete elements method and found that the initial deformation of the granular system causes the formation of microscopic shear zones through a fingering-like instability of the stress field. These microscopic shear zones propagate as their localized strain increases in magnitude and then evolves into macroscopic faults. The picture of a fingering-like instability is consistent with our experimental results concerning the creation sequence and spacing of faults appearing in a granular system contained in a V-shaped container.

Nature of friction in extrusion process and its effect on material flow

This investigation focuses on simulation of the extrusion process and in particular the effect of the initial billet temperature on friction and its consequences on material flow. The simulation is compared with data obtained from an experimental extrusion press. All the simulations are performed with the implicit finite element codes FORGE2 and FORGE3. The effect of the initial billettemperature on the deformation zone pattern and its consequent effect onfriction using bothnumerical simulationandexperimentalworkare presented.A comparison withexperimentsis made to assess the relative importance ofsome extrusion parameters in the extrusion process and to ensure that the numerical discretisation provided a true simulation of the process. A specific functional relationship to directly measure interfacial friction under conditions approaching those encountered in the quasi-static deformation process is described. The results revealed that the friction factor increases with increase in initial billet temperature and varies from 0.65 at 300 ° C to a 0.91 at 450 ° C after reaching the peak pressure. The dead metal zone is observed to vary in form and has a greater volume at high temperatures. The increase in friction results in an increase of initial extrusion load. The finite element program appears to predict all the major characteristics of the flow observed macroscopically.

Variational inequality formulation for flow theory plasticity

We consider the quasi-static deformation process of an elasto-plastic body, under the assumption of small strains. The elasto-plastic behaviour of the material ss assumed to be governed by the Huber-von Mises yield function with piecewise linear strain hardening (softening). The yield function is written in the terms of the strains, and we define the problem as the system that consists of (a) a variational equation which is the equilibrium condition for the body and (b) a variational inequality expressing the unilateral character of the plastic strain-rate multiplier. An iterative method for solving this nonlinear system, based on an incremental, implicit time integration scheme and on a finite element approximation is proposed. The variational inequality after being discretized using finite elements is solved as a linear complementarity problem. The results of some numerical experiments for a test problem are provided.

Evaluation of the dynamic explicit/elastoviscoplastic finite-element method in sheet-forming simulation

The application of the dynamic explicit time integration method has been proven to be efficient and robust for sheet-metal forming simulation. However, the sheet stamping operation in the automobile industry is usually a quasi-static process. Therefore, there remain some subjects to investigate, such as the estimation of dynamic effects and the evaluation of numerical schemes of so-called mass scaling, damping scaling and material viscosity scaling. In this paper, these problems are investigated by the approaches of the theoretical formulation and numerical verification. Firstly the principle of virtual power is proposed to interpret the quasi-static deformation process, adopting the Lagrange multiplier method to introduce quasi-static conditions. Next, a discussion is focused on the comparison between the real forming process and the virtual simulation process. The latter employs a high forming speed to reduce the consumptions of computation time. Finally the hemispherical-punch deep-drawing of a square sheet is analyzed using a new dynamic explicit/elasto viscoplastic finite-element program developed by the authors. The numerical results are compared with either the experiments or static explicit/elastoplastic analyses. The suitability of the newly developed program for the quasi-static deformation process is confirmed.

Mechanical Response of Semi-Brittle Ceramics Subjected to Tension-Compression State. Part I: Theoretical Modeling

This article discusses the construction of constitutive equations for the quasi-static deformation process of semi-brittle materials from the onset to the state pre ceding final failure. The simple connection between mesomechanical and phenomenologi cal modelling of damage is possible. The generalization of the damage measurement idea by unloading modulus [31] allows one to follow the whole non-linear unloading process in the multi-axial state of stress, specifying all mechanisms contained in it.

Analyse thermomécanique des lois de comportement par thermographie infrarouge

La connaissance des phenomenes dissipatifs et non dissipatifs associes aux processus quasi-statiques de deformation, represente un atout supplementaire important pour l'elaboration de loi thermomecanique de comportement. On decrit, ici, un dispositif experimental, utilisant les techniques de thermographie infrarouge, et permettant d'observer les phenomenes thermiques et energetiques durant la deformation d'un echantillon en traction simple. Apres avoir rappele la definition du bilan energatique, dans le cas de materiaux elasto-plastiques, on relie la dissipation et l'energie interne bloquee durant l'ecrouissage, aux variables d'etat. La puissance mecanique dissipee est evaluee continument durant l'essai. On utilise pour cela, les images thermiques fournies par la camera infra-rouge. On presente le dispositif experimental, puis successivement, on decrit le modele physique permettant de relier l'energie dissipee aux cartes de temperature de surface ainsi que le protocole d'etalonnage. En fin d'article, on presente quelques resultats obtenus avec plusieurs materiaux et on evoque rapidement leur incidence sur la forme des lois de comportement.

Plane Strain Visioplasticity for Dynamic and Quasi-Static Deformation Processes

The visioplasticity approach is developed to enable the complete stress history of any steady or nonsteady, quasi-static or impact, plane strain plastic deformation process to be determined from a record of the deformation pattern. The velocity field is determined experimentally, and, for dynamic conditions, high-speed photographs are taken of grid patterns marked on the end surface of the specimen. Digitization of the instantaneous grid node positions allows the velocity fields to be obtained at predetermined time intervals throughout the transient deformation period. Hence, the strain-rate, equivalent strain rate, equivalent strain, and finally stress fields can all be obtained. Plane strain upsetting tests, conducted at a speed of 0.1mm/s give results that agree closely with the well-documented “friction hill” type of normal stress distribution for quasi-static rates of strain. However, with a specimen deformed at a speed of 478.54 cm/s the normal stress distribution is radically different exhibiting a saddle-type distribution. The effect of strain rate on the interface and interior stresses will have significant bearing on a number of metal-forming operations.

Aspects of theoretical plasticity at finite deformation and large pressure

A broad theoretical investigation of plasticity in crystalline solids at finite deformation is presented, with primary attention focused upon single crystals and aggregates at large pressure. Nonlinear elastic and nonlinear plastic constitutive relations for cubic crystals undergoing quasistatic deformation processes are studied. An aggregate model is introduced which enables transition to macroscopic behavior, including a prediction of pressure-dependence of yield surfaces in macro-stress space.