Finite element formulation for modelling large deformations in elasto‐viscoplastic polycrystals

Anisotropic, elasto‐viscoplastic behaviour in polycrystalline materials is modelled using a new, updated Lagrangian formulation based on a three‐field form of the Hu‐Washizu variational principle to create a stable finite element method in the context of nearly incompressible behaviour. The meso‐scale is characterized by a representative volume element, which contains grains governed by single crystal behaviour. A new, fully implicit, two‐level, backward Euler integration scheme together with an efficient finite element formulation, including consistent linearization, is presented. The proposed finite element model is capable of predicting non‐homogeneous meso‐fields, which, for example, may impact subsequent recrystallization. Finally, simple deformations involving an aluminium alloy are considered in order to demonstrate the algorithm. Copyright © 2004 John Wiley & Sons, Ltd.     

Elastic and transport properties in polycrystals of cracked grains: Cross-property relations and microstructure

Some arguments of Bristow (1960) concerning the effects of cracks on elastic and transport (i.e., electrical or thermal conduction) properties of cold-worked metals are reexamined. The discussion is posed in terms of a modern understanding of bounds and estimates for physical properties of polycrystals - in contrast to Bristow’s approach using simple mixture theory. One type of specialized result emphasized here is the cross-property estimates and bounds that can be obtained using the methods presented. Our results ultimately agree with those of Bristow, i.e., confirming that microcracking is not likely to be the main cause of the observed elastic behavior of cold-worked metals. However, it also becomes clear that the mixture theory approach to the analysis is too simple and that crack-crack interactions are necessary for proper quantitative study of Bristow’s problem.     

Modelling of interfacial viscoplastic slip coupled to damage in a polycrystalline microstructure

The mesomechanics behavior of a polycrystalline microstructure subjected to creep and constant strain rate loadings is investigated. The analysis is based on a Voronoi polygonization strategy for the generation of grains, that are bonded to each other via interfaces along the grain boundaries. A new constitutive model is proposed for the rate-dependent debonding along these interfaces, whereby damage is kinetically coupled to viscoplastic slip and dilatation. The paper may be viewed as generalizing the rate-independent model used in Cannmo et al. (1995).     

Pressure-shear impact and the dynamic viscoplastic response of metals

Pressure-shear plate impact experiments are used to investigate the viscoplastic response of metals at shear strain rates ranging from 10⁵ s⁻¹ to 10⁷ s⁻¹. Flat specimens with thicknesses between 300 μm and 3 μm are sandwiched between two hard, parallel plates that are inclined relative to their direction of approach. Nominal stresses and strains in the specimens are determined from elastic wave profiles monitored at the rear surface of one of the hard plates. Results are reviewed for two fcc metals: commercially pure aluminum and an aluminum alloy. New results are presented for bcc high purity iron, a high strength steel alloy and vapor deposited aluminum. For commercially pure aluminum the flow stress increases strongly with strain rate as strain rate increases from 10⁴ s⁻¹ to 10⁵ s⁻¹. At strain rates above 10⁵ s⁻¹ the flow stress, based on results for thin vapor-deposited aluminum specimens, increases strongly, but less than linearly, with increasing strain rate until it saturates at strain rates between 10⁶ s⁻¹ and 10⁷ s⁻¹. Preliminary results for high purity alpha-iron indicate that the flow stress increases smoothly over eleven decades of strain rate, and faster than logarithmically for strain rates from 10² s⁻¹ to greater than 10⁶ s⁻¹. In contrast, for a high strength steel alloy the flow stress depends only weakly on the strain rate, even at strain rates at high as 10⁵ s⁻¹. Such contrasting behavior is attributed to differences in the relative importance of viscous glide and thermal activation as rate controlling mechanisms for dislocation motion in the various metals. Numerical studies indicate that experiments performed at the highest strain rates on the thinnest specimens are not adiabatic, thus requiring a full thermal-mechanical analysis in order to interpret the data.     

Stabilized finite element method for viscoplastic flow: formulation with state variable evolution

A stabilized, mixed finite element formulation for modelling viscoplastic flow, which can be used to model approximately steady‐state metal‐forming processes, is presented. The mixed formulation is expressed in terms of the velocity, pressure and state variable fields, where the state variable is used to describe the evolution of the material's resistance to plastic flow. The resulting system of equations has two sources of well‐known instabilities, one due to the incompressibility constraint and one due to the convection‐type state variable equation. Both of these instabilities are handled by adding mesh‐dependent stabilization terms, which are functions of the Euler–Lagrange equations, to the usual Galerkin method. Linearization of the weak form is derived to enable a Newton–Raphson implementation into an object‐oriented finite element framework. A progressive solution strategy is used for improving convergence for highly non‐linear material behaviour, typical for metals. Numerical experiments using the stabilization method with hierarchic shape functions for the velocity, pressure and state variable fields in viscoplastic flow and metal‐forming problems show that the stabilized finite element method is effective and efficient for non‐linear steady forming problems. Finally, the results are discussed and conclusions are inferred. Copyright © 2002 John Wiley & Sons, Ltd.     

Phase and microstructure evolution in Cu-In-Cr alloys

Abstract

Cu-In-Cr ternary alloy specimens were prepared with a metal mould and analysed by OP, EPMA, SEM, etc. The results show that the phase composition of Cu-11In-10Cr (wt-%) ternary alloy in casting microstructure includes Cu solid solution, Cr solid solution and Cu₉In₄ (δ) phase. Cu solid solution has dendritic morphology while Cr solid solution is star or petal shaped and is dispersed. In solidification, the solid/liquid interfaces of Cu solid solution and Cr solid solution are nonfaceted and they form by continuous growth, Cu solid solution forms dendrites under the influence of constitutional supercooling, while Cr solid solution forms equiaxed dendrites owing to the restricted chromium content. Chromium content has an influence on the morphology of Cu solid solution dendrites and Cr solid solution.     

Evaluation of carvedilol-loaded microsponges with nanometric pores using response surface methodology

This study demonstrates the use of factorial design for the preparation of microsponges of carvedilol with nanometric pores using the response surface methodology and to establish the functional relationships between two operating variables of Eudragit RS100 and sucrose. The response variables selected for this study were percent drug entrapment (Y1), time taken to release 35% of drug (Y2), percent drug release after 24?h (Y3), percent dissolution efficiency (DE) (Y4) and the angle of repose (Y5). The overall calculated desirability was found to be 0.8065 for the optimised formulation OF1. The response surface analysis of the desirability function with the independent levels indicated that the overall desirability increases with high levels of Eudragit RS100 and sucrose content. The optimum robust formulation (OF1) contains high levels of Eudragit RS100 (400.0?mg) and sucrose (350.21?mg), satisfying the predetermined constraints and goals of all the selected response variables. The scanning electron microscopy of OF1 indicated the spherical shape of microsponges with numerous pores on the surface. The atomic force microscopic study suggested the presence of nanometric pores on the surface of microsponges which may facilitate the release of the drug. Compatibility studies using the Fourier transform infrared spectroscopy, X-ray diffraction and differential scanning calorimeter indicated the absence of any incompatibility between carvedilol and excipients used to prepare microsponges.     

Deformation behavior and microstructure evolution of titanium alloys with lamellar microstructure in hot working process: A review

Titanium alloys have been widely used in many industrial clusters such as automotive, aerospace and biomedical industries due to their excellent comprehensive properties. In order to obtain fine microstructures and favorable properties, a well-designed multi-step thermomechanical processing(TMP) is critically needed in manufacturing of titanium components. In making of titanium components,subtransus processing is a critical step to breakdown lamellar microstructure to fine-structure in hot working process and thus plays a key role in tailoring the final microstructure and properties. To realize this goal, huge efforts have been made to investigate the mechanisms of microstructure evolution and flow behavior during the subtransus processing. This paper reviews the recent experimental and modelling progresses, which aim to provide some guidelines for the process design and microstructure tailoring for titanium alloy research community. The characteristics of the initial lamellar microstructure are presented, followed by the discussion on microstructure evolution during subtransus processing. The globularization of lamellar α is analyzed in detail from three aspects, i.e., globularization mechanism, heterogeneity and kinetics. The typical features of flow behaviors and the explanations of significant flow softening are then summarized. The recent advances in modelling of microstructure evolution and flow behaviors in the subtransus processing are also articulated. The current tantalized issues and challenges in understanding of the microstructure evolution and flow behaviors of the titanium alloys with lamellar microstructure are presented and specified in future exploration of them.     

Magnetically controlled microstructure evolution in non-ferromagnetic metals

The microstructure evolution during grain growth in magnetically anisotropic materials can be affected by a magnetic field due to an additional driving force for grain boundary motion which arises from a difference in magnetic free energy density between differently oriented grains. Therefore each grain of a polycrystal, exposed to a magnetic field, is inclined to grow or to shrink by a magnetic force depending on the orientation of the respective grain and its surrounding neighbors with regard to the field direction. A theoretical analysis of the grain growth kinetics in the presence of an external magnetic field reveals that magnetically affected grain growth may result in an orientation distribution that favours grains with a lower magnetic free energy density. As it is experimentally demonstrated on polycrystalline zinc, titanium and zirconium, the crystallographic texture in magnetically anisotropic non-magnetic materials can be effectively changed and controlled by means of annealing in a magnetic field. EBSD-analysis revealed that the observed asymmetrical texture after magnetic annealing is due to a large extent to a significant difference in the number of grains that make up different texture components. The results of computer simulations of magnetically affected grain growth in 2-D polycrystals are in a good agreement with theoretical predictions and experimental findings.     

Role of magnesia and silica in alumina microstructure evolution

The effects of MgO and SiO₂ additive distributions on alumina grain morphology have been characterized using high-resolution imaging secondary ion mass spectrometry (HRI-SIMS). In alumina samples singly-doped with MgO, the concentration of Mg segregated to grain boundaries is independent of grain boundary length for a majority of grain boundaries studied. Mg segregant therefore redistributes from grain boundaries to microstructural sinks, such as pores and/or second phases, during grain coarsening. In samples singly-doped with SiO₂, abnormal grain growth develops and the concentration of Si at grain boundaries is also independent of grain boundary length. Redistribution of segregants is again necessary in this case to maintain constant grain boundary composition. Codoping with Mg/Si > 1 suppresses abnormal grain growth as a result of increased mutual solid solubility of both ions and an associated decrease in grain boundary segregation. Grain growth kinetics for doped aluminas are reconsidered in light of these observations.     

Numerical modelling of pressurized fracture evolution in concrete using zero-thickness interface elements

The development of cracks due to the effect of fluid pressure is a problem that concerns many areas of engineering, ranging from structural to geotechnical or petroleum. Within the context of the Finite Element Method, the authors have recently proposed a formulation for the coupled hydro-mechanical behaviour of zero-thickness interface elements. This formulation has been verified for pre-existing discontinuities (e.g. natural joints, faults in rock). In this paper, the above formulation, complemented with an appropriate fracture mechanics-based constitutive model, is applied to developing cracks in plain concrete. The numerical results are compared with a series of wedge splitting tests available in the literature, performed on concrete specimens under the influence of fluid pressure at the notch and along the propagating crack. A good agreement is obtained in terms of wedge-splitting force vs. crack mouth opening displacement (CMOD), crack and fluid fronts vs. CMOD, and fluid pressure along the crack vs. time. The influence of splitting rate and input fluid pressure is also systematically analyzed.     

Grain microstructure evolution and grain boundary junction engineering

Abstract

The grain microstructure evolution in the course of two dimensional (2D) grain growth is considered in greater detail, taking into account the influence of grain boundary triple junctions. It is shown that there are two limiting regimes of grain growth in polycrystals: the first one is associated with the situation when the kinetics of grain growth are controlled by the motion of grain boundaries, while the second one is defined by the motion of grain boundary triple junctions, i.e. when the mobility of triple junctions determines the kinetics of grain growth. A generalised theory of 2D grain growth including a limited triple junction mobility is presented. The theoretical predictions are compared with results of computer simulations by a virtual vertex model. We introduce a new branch of grain boundary engineering, namely, grain boundary junction engineering that utilises junction properties for microstructure control.     

Superplastic deformation and microstructure evolution in PM IN-100 superalloy

The superplastic deformation behaviour of PM IN-100 alloys consolidated by hot isostatic pressing (HIP) was investigated in compression tests at temperatures between 1323 and 1373K. The microstructural changes were observed using scanning electron microscopy. In the high strain rate region, grain refinement occurs due to dynamic recrystallization, resulting in the work softening type stress-strain curves. At low strain rates, grain growth occurs during deformation corresponding to work hardening. The strain rate sensitivity index,m, reaches a maximum value (m = 0.6) at the optimum strain rate which depends on the test temperature. The grain size dependence coefficient,p, was determined to be 2.0. The activation energy for deformation was 348kJ mol^–1. The rate-controlling mechanism of superplasticity in as HI Ped IN-100 seems to be the grain-boundary sliding controlled by volume diffusion rather than grain-boundary diffusion.     

Essential work of fracture and viscoplastic response of a carbon black-filled thermoplastic elastomer

Observations are reported on a carbon black-filled thermoplastic elastomer in uniaxial cyclic tensile tests with various maximum strains and double-edge-notched-tensile (DENT) tests with various ligament widths at ambient temperature. It is shown that the stress-strain diagrams in DENT tests measured relatively far away from the ligament coincide with those in tensile cyclic tests on un-notched samples. To describe the viscoplastic response of un-notched specimens, constitutive equations are derived, and adjustable parameters are found by fitting the experimental data. It is demonstrated how the energy stored in a DENT sample under tension can be accounted for in calculations of the specific essential work of fracture.     

An experimental method to validate viscoplastic constitutive equations in the dynamic response of plates

In the present paper measured and simulated vibrations of viscoplastic plates under impulsive loadings are compared to each other. The aim is to determine how accurately the measured deformations can be calculated by the chosen constitutive and structural theories. A first-order shear deformation shell theory assuming small strains and moderate rotations as well as viscoplastic laws are used. In the experimental part of this study short time measurement techniques are applied to shock tubes in order to record fast loading processes and plate deformations.     

Cu-Cr-Zr-Y合金动态再结晶及微观组织演化

通过在Gleeble-1500D热模拟试验机上进行高温等温压缩试验,对Cu-0.4Cr-0.15Zr-0.04Y合金在应变速率为0.001~10s-1、变形温度为650~850℃、最大变形程度为50%条件下的流变应力行为进行了研究。分析了该合金在高温变形时的流变应力和应变速率及变形温度之间的关系,并研究了在热压缩过程中组织的变化。结果表明,热模拟试验中,应变速率和变形温度的变化强烈地影响合金流变应力的大小,流变应力随变形温度升高而下降,随应变速率提高而增大。从应变速率、流变应力和温度的相关性,得出了该合金高温热压缩变形时的应力指数(n)、应力参数(α)、结构因子(A)、热变形激活能(Q)和流变应力方程,变形温度对合金动态再结晶行为有强烈影响。     

Texture and microstructure evolution in ultrafine-grained AZ31 processed by EX-ECAP

Extruded AZ31 alloy was processed by equal channel angular pressing (ECAP) up to 12 passes at 180 °C following route B_c, i.e. rotating the sample 90° between individual passes. Microstructure evolution was investigated using EBSD and TEM, as a function of strain imposed by ECAP. The first ECAP pass resulted in the formation of a new texture component which relates to the bimodal grain structure observed in this specimen. The grains larger than 10 μm show the orientation changes corresponding to the ECAP shear, which is characterised by the rotation of the basal poles by approximately 40° from the initial orientation. The fine grains with the average size of 1 μm maintain the initial orientation. The character of the bimodal grain structure and the distinct texture components between large and small grains remained unchanged up to 4 ECAP passes. Further ECAP pressing to 8 and 12 passes leads to a grain refinement through the whole sample volume and the orientation changes of all grains corresponding to the ECAP shear.     

3-D Simulation of hot forming and microstructure evolution

Stretch rolling is used for the production of a preform for subsequent die-forging of a connecting rod. A fully three-dimensional thermo-mechanically coupled FEM-simulation of a five-pass stretch rolling process has been performed. The influence was studied of various thermal and mechanical boundary conditions on the spatial strain and temperature fields developing. The results for the parameters strain, strain rate and temperature are used to predict the austenite grain size during the hot forming process by use of established recrystallization models. The calculated grain sizes are compared with those of formed components showing good agreement between experiment and numerical prediction.