Superplasticity and Grain Boundaries in Ultrafine-Grained Materials

Peter M. Burgess, Anatoly I. Pshenichnyuk

• Publisher: Woodhead Publishing
• Year: 2011
• ISBN:
  9780857093837
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

Superplasticity is a state in which solid crystalline materials, such as some fine-grained metals, are deformed well beyond their usual breaking point. The phenomenon is of importance in processes such as superplastic forming which allows the manufacture of complex, high-quality components in such areas as aerospace and biomedical engineering.Superplasticity and grain boundaries in ultrafine-grained materials discusses a number of problems associated with grain boundaries in metallic polycrystalline materials. The role of grain boundaries in processes such as grain boundary diffusion, relaxation and grain growth is investigated. The authors explore the formation and evolution of the microstructure, texture and ensembles of grain boundaries in materials produced by severe plastic deformation.Written by two leading experts in the field, Superplasticity and grain boundaries in ultrafine-grained materials significantly advances our understanding of this important phenomenon and will be an important reference work for metallurgists and those involved in superplastic forming processes.

• Discusses significant problems associated with grain boundaries in polycrystals incorporating structural superplasticity and grain boundary sliding
• Assesses the role of grain boundaries in processes such as grain boundary diffusion, relaxation and grain growth
• Explores the formation and evolution of the microstructure, texture and ensembles of grain boundaries in materials produced by severe plastic deformation

1

Structural Superplasticity of Polycrystalline Materials

1.1 Structural levels, spatial scales and description levels

The physical processes accompanying plastic deformation of polycrystalline materials are reduced to the nucleation, propagation and interaction of point (vacancies, impurity atoms), linear (dislocations, disclinations), planar (grain boundaries, interfacial boundaries) and volume (cracks, pores) defects of the crystal structure [1]. The attempts for the classification of different physical processes taking place with the participation of the above defects lead unavoidably to the considerations of the structural levels of deformation [2] and the characteristic spatial scales [3]. In the classification proposed by V.I. Vladimirov [4] there are spatial scales, defining micro- (

₂ < 10^{− 7}–10^{− 6} cm), meso- (

₁ ~ 10^{− 6}–10^{− 3} cm) and macrolevels (

₀ > 10^{− 3}–10^{− 1} cm). Accepting that this classification is conditional and incomplete, Vladimirov proposes to define for polycrystals an additional scale given by the mean grain size. In a later study [5], Vladimirov introduces a five-level model whose characteristic scales are determined by the quantities divisible by the previously introduced scale

₂ and the mean grain size. However, even this classification is not universal: for the given conditions, some scale levels are absorbed by others. As mentioned justifiably in a study by Khannanov [6], in a general case there is an entire set of scales λ_i (i = 1, 2,…, n).

Better results were obtained using the classification based on the concept of the representative volume which determines the size of the spatial averaging region in which the structural special features of the objects of the lower scale level are characterised by a specific set of integral characteristics and the objects themselves are structureless formations [7]. This approach automatically assumes that every description level has its own set of collective variables which are defined unambiguously by the resultant structural formations. The spatial scales are not specified a priori and they form the characteristic lengths of the resultant structures. Thus, the main priority is the concept of the description level and the scales are determined by the content of a specific investigation.

The investigation of the physical processes taking place with participation of defects are carried out on three description levels, depending on the given task. The microlevel is characterised by the determination of the individual properties and special features of the behaviour of every defect: appropriate collective variables – the coordinates and atomic momenta. The interaction of the atoms is defined by the interatomic potential. Undoubtedly, this description is unnecessary in the investigation of the mechanical properties of solids because its response to the external mechanical effect is determined by the collective behaviour of the previously mentioned crystal structure defects, i.e., by interactions in ensembles of defects and their individual response to the external effect. However, the laws of interaction of defects (roughly speaking, the paired potential) can be determined only on the basis of analysis of their atomic configuration. For example, the molecular static methods can be used to determine the perturbation of the lattice in the vicinity of a vacancy, an impurity atom, a dislocation core or a grain boundary. The calculated displacements of the atom from the equilibrium positions corresponding to the nodes of a regular lattice can be used to determine the excess energy and the characteristic length of the field of elastic perturbations in the lattice for any type of defect. The molecular dynamic methods can be used to calculate the vibrational spectra of new lattice configurations and, consequently, determine the special features of their behaviour at different temperatures. After fulfilling this program, we transfer to the next description level.

The evolution of an ensemble of defects in the field of external stresses is investigated on the mesolevel using the characteristics of the defects determined on the microlevel. Instead of indicating the position of every vacancy and the appropriate dilation field, the spatial distribution of vacancies and the appropriate elastic fields are introduced. Their kinetic properties are determined by the diffusion coefficient derived on the lower structural level. The impurity atoms are also described in a similar manner. The dislocation on this description level can be treated as an elastic string with a specific energy of unit length and appropriate field of elastic perturbations, defining the interaction of the dislocation with other defects. The kinetic properties of the dislocations in the field of external stresses are determined by the sliding and climbing speeds. The ensembles of the dislocations can be investigated in discrete or continuous formalism in relation to the specific content of the investigation. If the previous description level requires operation with a small number of defects (the number of atoms of different type) and with the astronomically large number of variables (the coordinates and atomic momenta), we now have a slightly larger number of objects (defects of all types) and an incomparably smaller number of collective variables: spatial-time densities of vacancy distribution, dislocations (generally speaking, tensor distribution), grains (according to size), grain boundaries (with respect to disorientation). Complete information on these quantities enables us to determine the deformation response of the microvolume to the external effect. On this description level, the material is still principally structural and is characterised by steep spatial gradients of the deformation response.

The spatial scale of the macrolevel is determined as the minimum size of the averaging region starting at which the deformation response is given only by the external loading conditions. This description is principally structureless and is characterised by the classic tensors of the mechanics of deformed solids.

At present, the investigations of the characteristics of the crystal structure defects on the microlevel can be regarded as almost completed to the extent sufficient for the requirements of plasticity physics. The main difficulty is the presence of considerable non-linearities and of self-organisation processes, determined by these non-linearities, in the ensembles of the defects. For example, the intrinsic energy of a dislocation ensemble at the given dislocation density is proportional to the first degree of density, and the interaction energy with the longrange effect taken into account is proportional to the second degree of density. The latter circumstance results in a faster transition to the non-linear regime in comparison with, for example, dense gases for which the interaction energy increases with increase of the density at a considerably lower rate because of the short range of their potential. The interaction of the dislocations of different slip systems at low dislocation densities can be ignored with a high degree of accuracy and it is sufficient to examine only their interaction with other crystal structure defects (mostly with grain boundaries and with forming dislocation clusters). At high temperatures the structure of the grain boundary can change as a result of the spreading of lattice dislocations. Beginning at some level of dislocation density, the interactions in the ensemble become controlling and the system is converted to a highly non-linear system. This results in the formation of greatly differing spatial dislocation structures (dipoles, polygonisation walls, dislocation networks, clusters, substructures, etc). This field in materials science is referred to as physical mesomechanics and is being developed by the Tomsk scientific school [8]. These processes are detected in loading of the materials with a large mean grain size and determine the wide range of different physical situations (from the stages of strain hardening to recrystallisation processes). Although these most complicated processes are difficult to formalise, so that we still have no physical theory of plasticity (and dynamic recrystallisation), the transition to the macrolevel of description for materials with a large mean grain size without additional attempts is ensured using the so-called Taylor model. The efficiency of the model in the investigated situation is determined by the frequently verified experimental fact: in deformation of the material with a large mean grain size the deformation of the grains repeats the deformation of the specimen as a whole. In other words, the representative volume is given by the mean grain size and the transition to the macrolevel is ensured by averaging of the accurately determined region. In fact, the problem of developing the physical theory of plasticity of coarse-grained materials is reduced to the correct description of the processes on the mesolevel [9].

A slightly different situation is encountered when investigating the superplasticity phenomenon. It is well known that one of the conditions of realisation of this phenomenon is the application of the material with a relatively small mean grain size. The density of the lattice dislocations in the volume of the grain does not reach high values, deformation processes are not accompanied by the transition to the non-linear evolution regime and it is sufficient to examine only the interaction of lattice dislocations with the grain boundaries. In addition, the experiments show that intragranular deformation during superplastic deformation is an accommodation process which accompanies the main deformation mechanism – grain boundary sliding. Thus, in comparison with the classic plasticity of coarse-grained materials, the mesolevel of superplastic deformat...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Introduction
• Chapter 1: Structural Superplasticity of Polycrystalline Materials
• Chapter 2: Characteristics of Grain Boundary Ensembles
• Chapter 3: Orientation-Distributed Parameters of the Polycrystalline Structure
• Chapter 4: Experimental Investigations of Grain Boundary Ensembles in Polycrystals
• Chapter 5: Grain Boundary Sliding in Metallic bi- and Tricrystals
• Chapter 6: Percolation Mechanism of Deformation Processes in Ultrafine-Grained Polycrystals
• Chapter 7: Percolation Processes in a Network of Grain Boundaries in Ultrafine-Grained Materials
• Chapter 8: Microstructure and Grain Boundary Ensembles in Ultrafine-Grained Materials
• Chapter 9: Grain Boundary Processes in Ultrafine-Grained Nickel and Nanonickel
• Chapter 10: Duration of the Stable Flow Stage in Superplastic Deformation
• Chapter 11: Derivation of Constitutive Equations in Multicomponent Loading Conditions
• Conclusion
• Index