B. Nageswara Rao

On the development of instability criteria during hotworking with reference to IN 718

Abstract A simple instability condition based on the Ziegler’s continuum principles as applied to large plastic flow, is developed for delineating the regions of unstable metal flow during hot deformation. It can be used for any type of the flow stress versus strain rate curve. This criterion has been validated using the flow stress data of IN 718 with microstructural observations. The optimum hot working conditions for the superalloy IN 718 are suggested based on the instability map.

Instability criteria for hot deformation of materials

Abstract Forming and forging processes are among the oldest and most important materials related technologies. New materials technologies centre on the development and widespread use of thermomechanical processing, particularly for aerospace alloys and concepts of metal workability and formability. Workability refers to the relative ease with which a metal can be shaped through plastic deformation. The term workability is often used interchangeably with the term formability, which is preferred for the shaping of sheet metal parts. However, workability is usually used to refer to the shaping of materials by such bulk deformation processes as forging, extrusion, and rolling. The characterisation of mechanical behaviour of a material by tension testing measures two different types of mechanical property: strength properties (such as yield strength and ultimate tensile strength) and ductility properties (such as percentage elongation and reduction in area). Similarly, the evaluation of workability involves both the measurement of the resistance to deformation (strength) and determination of the extent of possible plastic deformation before fracture (ductility). Therefore, a complete description of the workability of a material is specified by its flow stress dependence on processing variables (for example strain, strain rate, preheat temperature, and die temperature), its failure behaviour, and the metallurgical transformations that characterise the alloy system to which it belongs. However, the major emphasis in workability is on measurement and prediction of limit of deformation before fracture. Therefore, the emphasis in the present review article is on methods for determining the extent of deformation a metal can withstand before cracking or fracture occurs. Flow stress data are essential in the development of constitutive equations and processing maps. One of the requirements for process modelling is a knowledge of the material flow behaviour for defining the deformation maps that delineate ‘safe’ and ‘non-safe’ hot working conditions. These maps show in the processing space (that is on axes of temperature T and strain rate ɛ·) the processing conditions for stable and unstable deformation. The range of T and ɛ· for stable material flow useful in the development of process control algorithms should be obtained from physical quantities, which can be evaluated from the test data. As such there is no unique instability theory existing to delineate the regions of unstable flow during hot deformation which is applicable for all the materials. The designer has to establish a suitable theory on the basis of microstructural observations of the flow localisation in the intended materials. Various existing theories are reviewed for identification of flow instabilities (such as adiabatic shear banding, intercrystalline cracking, prior particle boundary cracking in powder compacts, wedge cracking) during hot deformation of materials, and these theories are verified by considering the flow stress data of IN 718 and the reported microstructural observations from different sources.

On the hot working characteristics of 6061Al-SiC and 6061-Al2O3 particulate reinforced metal matrix composites

Abstract For the development of processing maps, a simple instability condition for assessing the extent of plastic deformation in a workpiece prior to the formation of defects, is derived based on the Zieglers continuum principles. To demonstrate the potential of the instability condition, the published flow stress data of 6061 Al-10 vol.% Al2O3 particulate reinforced metal matrix composite is considered. Instability maps at different strain levels were superimposed while delineating the unstable regions in the processing maps. This takes into account the dependence of strain rate sensitivity and strain hardening coefficient of the material on the plastic instability during hot deformation. The stable and unstable regions in the map are verified with the microstructural observations of the deformed compression specimens as well as the industrial forging trials. To examine its validity, a comparative study is made with the flow localization concept for titanium alloys and titanium aluminides. The standard flow localization concept shows inconsistency in predicting the unstable regions in the processing maps, whereas, the present instability criterion is found to be consistent. Further studies were made on the hot deformation of 6061 Al with varying volume fractions and sizes of SiC particulate reinforcements. The ‘stable’ and ‘unstable’ regions in the processing maps identified from the present instability condition using the measured flow stress data, have been compared with the reported microstructural observations of the deformed compression specimens. It is noted from the processing maps that the domain of instability increases with the increasing volume fraction of the SiC particles. The optimum hot working conditions for these composites are suggested.

On the flow localization concepts in the processing maps of titanium alloy Ti–24Al–20Nb

Abstract Using the test data of Ti–24Al–20Nb with microstructural observations, studies are made to examine the applicability of the flow localization concepts as well as the validity of a simplified metallurgical stability condition previously suggested by Narayana Murty and Nageswara Rao, for delineating the regions of flow instabilities in the processing maps.

Instability map for hot working of 6061 Al-10 vol% metal matrix composite

A simple condition for metallurgical instability, useful in the development of processing maps for analysing high-temperature forming of metals, is suggested following a criterion based on continuum principles as applied to large plastic flow proposed by Ziegler. It can be used for any type of flow stress versus strain rate curve. This criterion has been validated using the flow stress data of a 6061 Al-10 vol% metal matrix composite with microstructural observations. Optimum hot working conditions based on the instability map are suggested for this material.

On the flow localization concepts in the processing maps of IN718

On the basis of microstructural observations in titanium and its alloys, a limit on the workability parameters has been proposed in the literature for flow localization or fracture to occur during hot deformation of materials. In this letter, the fixed limit on the workability parameters is verified by considering the flow stress data and the microstructural observations of IN718.

Development and validation of a processing map for zirconium alloys

For the development of processing maps to zirconium alloys, a simple instability condition based on the Zieglers continuum principles as applied to large plastic flow is extended for delineating the regions of unstable metal flow/occurrence of fracture or defects, utilizing the flow stress data of Zr-2.5Nb-0.5Cu. An attempt is made to fit the measured flow stress data in a constitutive equation, useful in the finite element process models. Instability maps at different strain levels were superimposed while delineating the unstable regions in the processing maps. This phenomenon takes into account the dependence of strain rate sensitivity and strain hardening coefficient of the material on the plastic instability during hot deformation. The applicability of the developed processing map has been examined by comparing with the reported microstructural observations of the deformed compression specimens of various zirconium alloys. It is found that the processing map is practically usable in the real fabrication process for the zirconium alloys.

Large deflections of a cantilever beam subjected to a rotational distributed loading

Large deflection problems of a uniform cantilever beam under a rotational distributed loading are formulated by means of a second order nonlinear integro-differential equation. The problem is numerically solved by considering a uniform rotational distributed load and a linearly varying rotational distributed load along the span of the beam. The details of load deflection curves are presented. Assuming Dirac delta function as a load distribution function along the span of the beam, the present general formulation yields the solution for the problem of a uniform cantilever beam with end rotational concentrated load. The numerical results for this case are found to be in good agreement with existing closed form solutions. As the formulation is general, the problem with nonuniform rotational distributed load of any complexity can be solved following the present numerical procedure which is quite simple, accurate and involves less computational time.

Large deflections of a nonuniform cantilever beam with end rotational load

Large deflection analysis of a cantilever beam under a tip concentrated rotational load governed by a second order nonlinear differential equation is solved with a simple and accurate numerical scheme. The details of load deflection curves for a class of beams having variable cross-section are presented.

Processing maps for hot deformation of α2 aluminide alloy Ti-24Al-11Nb

Using the test data of α2 titanium aluminide alloy Ti-24Al-11Nb with microstructural observations, studies are made to examine the flow localization concepts as well as the simplified metallurgical stability criterion for delineating the regions of flow instabilities in the processing maps. The optimum hot working conditions for the material are suggested.