Publisher Summary This chapter describes the material failure by coalescence of microscopic voids. The voids nucleate mainly at second phase particles, by decohesion of the particle-matrix interface or by particle fracture, and subsequently the voids grow because of plastic straining of the surrounding material. The growth of voids to coalescence by plastic yielding of the surrounding material involves so large geometry changes that finite strain formulations of the field equations are a necessary tool. A convected coordinate formulation of the governing equations is used. Convected coordinates are introduced, which serve as particle labels. The convected coordinate net can be visualized as being inscribed on the body in the reference state and deforming with the material. It is found that after nucleation, cavities elongate along the major tensile axis and that two neighboring cavities coalesce when their length has grown to the order of magnitude of their spacing. This local failure occurs by the development of slip planes between the cavities or simply necking of the ligament. A detailed micromechanical study of shear band bifurcation that accounts for the interaction between neighboring voids and the strongly nonhomogeneous stress distributions around each void has been carried out, and are also elaborated in this chapter.

Material Failure by Void Growth to Coalescence

Bulk metal working processes are carried out at elevated temperatures where the occurrence of simultaneous softening processes would enable the imposition of large strains in a single step or multi...

Modelling of hot deformation for microstructural control

Theoretical concepts of sintering were originally based upon ideas of the discrete nature of particulate media. However, the actual sintering kinetics of particulate bodies are determined not only by the properties of the particles themselves and the nature of their local interaction with each other, but also by macroscopic factors. Among them are externally applied forces, kinematic constraints (e.g. adhesion of the sample's end face and furnace surface), and inhomogeneity of properties in the volume under investigation (e.g. inhomogeneity of initial density distribution created during preliminary forming operations). Insufficient treatment of the questions enumerated above was one of the basic reasons hindering the use of sintering theory. A promising approach is connected with the use of continuum mechanics, which has been successfully applied to the analysis of compaction of porous bodies. This approach is based upon the theories of plastic and nonlinear-viscous deformation of porous bodies. Similar ideas have recently been embodied in a continuum theory of sintering. The main results of the application of this theory for the solution of certain technological problems of sintering are introduced including their thermo–mechanical aspects.

Theory of sintering: from discrete to continuum

In recent years, processing maps are being used to design hot working schedules for making near-net shapes in a wide variety of materials. In this paper, the results obtained on the characterization of hot working behavior of titanium and its alloys using the approach of processing maps are described. In commercial purity α titanium, dynamic recrystallization (DRX) domain occurs at 775°C and 0.001 s−1 with an efficiency of power dissipation [2m/(m+1) where m is the strain rate sensitivity of flow stress] of 43%. The DRX domain shifts to higher strain rates when the interstitial impurity content is lowered. In the near-α and α-β alloys like IMI 685, Ti–6Al–4V, the preform microstructure has a significant influence on the processing maps. For example, in the transformed β (Widmanstatten) preform microstructures, these alloys exhibit a domain of spheroidization at lower temperature and a domain of β superplasticity at higher temperatures, both occurring at slow strain rates. These domains merge at the β transus because of the occurrence of damage processes which lower the tensile ductility. On the other hand, processing maps on alloys with equiaxed preform microstructure exhibit a clear superplasticity domain in the α-β range and the β phase undergoes DRX with a power dissipation efficiency of ≈45–55%. Titanium materials in general, exhibit wide flow instability regimes due to adiabatic shear bands formation at higher strain rates and hence careful process design has to be adopted for successful forging and microstructural control.

Processing maps for hot working of titanium alloys

The hot deformation behavior of Ti–6Al–4V with an equiaxed α–β preform microstructure is modeled in the temperature range 750–1100°C and strain rate range 0.0003–100 s−1, for obtaining processing windows and achieving microstructural control during hot working. For this purpose, a processing map has been developed on the basis of flow stress data as a function of temperature, strain rate and strain. The map exhibited two domains: (i) the domain in the α–β phase field is identified to represent fine-grained superplasticity and the peak efficiency of power dissipation occurred at about 825°C/0.0003 s−1. At this temperature, the hot ductility exhibited a sharp peak indicating that the superplasticity process is very sensitive to temperature. The α grain size increased exponentially with increase in temperature in this domain and the variation is similar to the increase in the β volume fraction in this alloy. At the temperature of peak ductility, the volume fraction of β is about 20%, suggesting that sliding of α–α interfaces is primarily responsible for superplasticity while the β phase present at the grain boundary triple junctions restricts grain growth. The apparent activation energy estimated in the α–β superplasticity domain is about 330 kJ mol−1, which is much higher than that for self diffusion in α-titanium. (ii) In the β phase field, the alloy exhibits dynamic recrystallization and the variation of grain size with temperature and strain rate could be correlated with the Zener–Hollomon parameter. The apparent activation energy in this domain is estimated to be 210 kJ mol−1, which is close to that for self diffusion in β. At temperatures around the transus, a ductility peak with unusually high ductility has been observed, which has been attributed to the occurrence of transient superplasticity of β in view of its fine grain size. The material exhibited flow instabilities at strain rates higher than about 1 s−1 and these are manifested as adiabatic shear bands in the α–β regime.

Hot working of commercial Ti–6Al–4V with an equiaxed α–β microstructure: materials modeling considerations

A new method of modeling material behavior which accounts for the dynamic metallurgical processes occurring during hot deformation is presented. The approach in this method is to consider the workpiece as a dissipator of power in the total processing system and to evaluate the dissipated power co-contentJ = ∫o σ e ⋅dσ from the constitutive equation relating the strain rate (e) to the flow stress (σ). The optimum processing conditions of temperature and strain rate are those corresponding to the maximum or peak inJ. It is shown thatJ is related to the strain-rate sensitivity (m) of the material and reaches a maximum value(J max) whenm = 1. The efficiency of the power dissipation(J/J max) through metallurgical processes is shown to be an index of the dynamic behavior of the material and is useful in obtaining a unique combination of temperature and strain rate for processing and also in delineating the regions of internal fracture. In this method of modeling, noa priori knowledge or evaluation of the atomistic mechanisms is required, and the method is effective even when more than one dissipation process occurs, which is particularly advantageous in the hot processing of commercial alloys having complex microstructures. This method has been applied to modeling of the behavior of Ti-6242 during hot forging. The behavior of α+ β andβ preform microstructures has been exam-ined, and the results show that the optimum condition for hot forging of these preforms is obtained at 927 °C (1200 K) and a strain rate of 1CT•3 s•1. Variations in the efficiency of dissipation with temperature and strain rate are correlated with the dynamic microstructural changes occurring in the material.

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Modeling of dynamic material behavior in hot deformation: Forging of Ti-6242

A new yield function for compressible PM materials

Computer-aided design of extrusion dies by metal-flow simulation

Computer-Aided Process Modelling of Hot Forging and Extrusion of Aluminum Alloys

An Al-Fe-Ce alloy has been recently demonstrated to be suitable as a matrix material for a composite conductor with high-purity aluminum filaments which can be used in devices operating at liquid hydrogen temperatures. The alloy is lightweight and has high strength, but just as importantly, its major alloying elements (Fe and Ce) are practically diffusionless in Al. The material was initially synthesized by ALCOA using powder metallurgy. Dynamic recrystallization processes were further developed at the Air Force Materials Laboratory, resulting in a more homogeneous microstructure. This paper describes mainly the results of microstructural, electrical resistivity, and low temperature heat capacity measurements on samples before and after dynamic recrystallization.

J. T. Morgan

Papers

Modeling of dynamic material behavior in hot deformation: Forging of Ti-6242

A new yield function for compressible PM materials

Computer-aided design of extrusion dies by metal-flow simulation

Computer-Aided Process Modelling of Hot Forging and Extrusion of Aluminum Alloys

A New Aluminum-Base Alloy with Potential Cryogenic Applications