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

The modification of lamellar alpha phase in Ti-6A1-4V by hot working was investigated with the aim of controlling morphology (aspect ratio) and final grain size. The effect of strain was studied using forging at 955 °C (1750 °F), followed by annealing at 925 °C (1700 °F) to allow the alpha morphology to adjust. Increasing the deformation from 6.5 pct to 80 pct reduction caused the lamellar alpha morphology to become progressively more equiaxed upon annealing. TEM observations showed that annealing of material deformed to 6.5 pct resulted in recovery of the alpha, without a noticeable change in the morphology, while higher deformation resulted in plate shearing and beta cusp formation. It was found that material with an initial thin alpha plate structure (thickness — 3.4 ώm) breaks up at a lower critical strain than a material with a thicker plate morphology (thickness ≃ 6 μm). The material with thin alpha plates more rapidly forms equiaxed alpha grains separated by beta phase, while the material with a thicker plate structure exhibits more alpha/alpha boundaries after deformation and annealing. The morphology change from alpha lamellae into lower aspect ratio grains was identified to be by a break-up of the alpha lamellae, essentially by a two-step process: a formation of low and high angle alpha/alpha boundaries or shear bands across the alpha plates followed by penetration of beta phase to complete the separation. This break-up takes place during hot deformation and subsequent annealing.

Modification of alpha morphology in Ti-6Al-4V by thermomechanical processing

The hot workability of conventional titanium alloys and titanium aluminides is reviewed. For both alloy classes, the influence of hot working variables and microstructure on failure via fracture or flow-localization controlled processes is summarized. The occurrence of wedge cracking and cavitation during bulk forming of α / β alloys with Widmanstatten microstructures or γ titanium aluminides with lamellar or equiaxed structures, is examined. In particular, the effects of grain size, grain boundary second phases and process variables on failure are presented. Observations and models of flow localization and cavitation processes which lead to failure during low strain rate, superplastic, tensile-type deformation of titanium and titanium aluminide alloys with fine equiaxed structures, are also described. In the area of flow-localization-controlled failure during bulk forming, the occurrence of shear bands and other flow nonuniformities during both conventional and isothermal hot working processes is reviewed. The influence of material properties, such as flow softening rate and strain rate sensitivity and process variables, which lead to temperature and hence flow nonuniformities, is examined. The flow localization concepts are illustrated for several hot working processes.

Hot workability of titanium and titanium aluminide alloys—an overview

In this article, the thermomechanical processing of ingot-metallurgy alpha/beta titanium alloys is summarized, with special emphasis on microstructure evolution and workability considerations. Primary hot working dealing with the conversion of ingot structures to fine-equiaxed wrought structures is addressed. In this regard, the breakdown of lamellar microstructures, the occurrence of cavitation/wedge cracking, and the development of crystallographic texture are described. Secondary processes such as sheet rolling, superplastic forming, and closed-die forging are also reviewed.

The thermomechanical processing of alpha/beta titanium alloys

Inverse analysis for identification of rheological and friction models in metal forming

The stable and unstable plastic flow of Ti-6Al-2Sn-4Zr-2Mo-0.1Si (Ti-6242) has been investigated at temperatures from 816 to 1010 °C (1500 to 1850 °F) and at strain rates from 0.001 to 10 s-1 in order to establish its hot forging characteristics. In hot, isothermal compression, Ti-6242 with an equiaxed a structure deforms stably and has a flow stress which decreases with straining due to adiabatic heating. With a transformed-β microstructure, unstable flow in hot compression is observed and concluded to arise from large degrees of flow softening caused by microstructural modification during deformation and, to a small extent, by adiabatic heating. Both microstructures have a sharp dependence of flow stress on temperature. Using the concepts of thermally-activated processes, it was shown analytically that this dependence is related to the large strain-rate sensitivity of the flow stress exhibited by the alloy. From lateral sidepressing results, the large dependence of flow stress on temperature was surmised to be a major factor leading to the shear bands occurring in nonisothermal forging of the alloy. Shear bands were also observed in isothermal forging. A model was developed to define the effect of material properties such as flow softening rate and strain-rate sensitivity on shear band development and was applied successfully to predict the occurrence of shear bands in isothermal forging.

Deformation and unstable flow in hot forging of Ti-6Ai-2Sn-4Zr-2Mo-0.1Si

The occurrence of shear bands in isothermal, hot forging of metals has been investigated using a variety of experimental and analytical tools. Isothermal sidepressing tests on Ti-6Al-2Sn-4Zr-2Mo-0. 1Si were conducted at a variety of hot working temperatures and deformation rates to develop a data base on the occurrence of shear bands as a function of material properties and processing conditions. An instability criterion was developed, and the tendency to form shear bands was shown to depend strongly on the ratio of the nondimensional work-hardening (or flow-softening) rate to the strain-rate sensitivity of the flow stress. This analysis and supporting experimental data formed the basis for the development of workability maps, which delineate safe regimes for hot working in terms of strain rate and temperature. Employing a sophisticated computer code, an extensive series of simulations was also run for the sidepressing operation to obtain an idea of the detailed process by which shear bands initiate. These simulations were conducted using actual Ti-6242 material properties as well as hypothetical properties which are representative of those of other metals deformed in the hot working regime. From these simulations, predictions of the influence of flow softening and rate sensitivity on flow localization were made and found to be similar to experimental results and predictions obtained from the instability analysis. However, process simulation gave a more complete insight into the initiation and growth stages in the development of shear bands that was not possible using only the instability analysis.

The occurrence of shear bands in isothermal, hot forging

A Numerical Method For Simultaneous Prediction of Metal Flow and Temperatures in Upset Forging of Rings

This paper describes the principles and the application of two mathematical models, developed for predicting the significant variables of the strip rolling process. The first model and the associated computer program ROLING can estimate the roll-separating force and the roll torque. This model includes the most up-to-date analyses of (a) the plastic deformation in the strip, (b) the elastic compression and recovery of the strip before and after rolling, and (c) the elastic deformation of the rolls. The second model and the associated computer program ROLTEM have been developed to simulate the metal flow and temperatures in strip rolling. They consider simultaneous heat generation, heat transport, and heat transfer during rolling using a finite-difference algorithm. The predictions made by the computer programs ROLING and ROLTEM have been compared with existing experimental data. The results indicate that the agreement of theoretical predictions with experimental results is well within acceptable engineering accuracy.

G. D. Lahoti

Papers

Deformation and unstable flow in hot forging of Ti-6Ai-2Sn-4Zr-2Mo-0.1Si

The occurrence of shear bands in isothermal, hot forging

A Numerical Method For Simultaneous Prediction of Metal Flow and Temperatures in Upset Forging of Rings

Computer-Aided Analysis of the Deformations and Temperatures in Strip Rolling

Prediction of Temperature Distributions in Axisymmetric Compression and Torsion