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A linear relationship between mobile dislocation density and creep strain has generally been assumed in various models of creep in Ni-base superalloys. No stress or temperature dependence is assumed in such relationships. The current study aims to verify this relationship by use of an X-ray rocking curve-based method on DS GTD111™, a directionally solidified (DS) nickel-base turbine blade alloy. A new measurement scheme tailored for such large-grained, DS alloys using simultaneous tilt–twist methodology is outlined. Multiple test sets of DS GTD111™, creep tested under varying boundary conditions, were measured using this technique. The resulting rocking curve full-width-half-maxima (square root of the dislocation density) were found to correlate to creep strain by a simple linear transfer function with no systematic dependence on stress or temperature. As a validation case, application of this transfer function is demonstrated for long-term test data.

According to Eshelby&rsquo, s theory, inelastically inhomogeneous inclusions in a metallic matrix give rise to a distribution of internal stresses. In the case of particle strengthened materials, such as nickel base superalloys, the presence and evolution of this back-stress leads to various observable effects, such as primary creep, back-flow upon loading, and memory of prior deformation. This article presents the background of the concept of back-stress and how it applies to the scenario of creep. A derivation of an evolution equation for back-stress in the context of primary creep is also presented. The results from neutron diffraction with in-situ creep experiments on directionally solidified nickel superalloys are presented in order to demonstrate the validity of the proposed equation and the corollaries derived therefrom.

This paper outlines a microstructure-based model relating gamma prime microstructure and grain size of Ni-base alloys to their creep behavior. The ability of the model to explain creep of multiple superalloys with a single equation and parameter set is demonstrated. The only parameters that are changed from alloy to alloy are related to the gamma prime characteristics and grain size. This model also allows prediction of creep performance as a function of heat treatment and explains some apparently contradictory data from the literature.

This article outlines the work being carried out at GE Global Research, Bangalore in the area of creep modeling and remaining life assessment of ferritic steels and superalloys. Fundamental insights into the commonalities and differences between creep behavior of these two classes of materials are discussed. It is shown that these basic insights offer ways to develop physics based models that can enable confident extrapolation to regimes well outside the range of calibration. Methods to measure creep damage (non-cavity damage) are also discussed. It is shown that these methods when applied in conjunction with the physics based models can enable accurate remaining life assessment of high temperature components.

This article presents the findings of recent studies on creep of advanced 9-10% Cr ferritic steels. It is shown that the obstacles that fundamentally control creep in these steels are nano-scale MX carbonitrides whose time dependent coarsening leads to weakening. The second crucial factor in creep strengthening is the subgrain structure that results from martensitic transformation. The boundaries in this structure produce a back-stress through an anelastic bowing mechanism. A quantitative model that takes these microstructural features into account is shown to be able to predict the long-term creep behavior of ferritic steels.

A new approach to dislocation creep is proposed based on a reappraisal of diffusion controlled glide as outlined by Hirth and Lothe. It is argued that creep may be viewed as a process of thermally activated release of dislocations from pinning centers and the latter could be dislocation related features such as nodes, kinks and jogs or nanoscale particles with incoherent interfaces. It is shown that the proposed approach is able to explain the creep behavior of materials that represent both these classes. It is shown that, contrary to extant theories, superalloys and pure metals fall within the first class while ferritic steels represent the second class of materials. A simple equation relating creep rate to stress is derived to describe the creep behavior as per the above philosophy and is shown to represent the creep data of a vast range of materials. The proposed equation obviates the need for the traditional power law approaches to creep with arbitrary exponents of stress. The applicability of the basic constitutive equation developed here to modeling of the creep strain vs. time behavior is demonstrated by combining it with equations from the damage mechanics philosophy. It is shown that the creep data of GTD111, a typical γ′ strengthened Ni-base superalloy, are predicted well by this equation set.

The key microstructural features that control creep in advanced 9–10%Cr steels are elucidated. Conclusive evidence for the presence and coarsening of nano-scale MX carbonitrides which contribute to the long-term stability of these materials is presented. It is also shown that subgrain structures resulting from the martensitic transformation contribute to the basic strength by generating internal stresses through an anelastic bowing mechanism. Kinetic equations that describe the evolution of these microstructural features with time and strain, derived from exhaustive experimental measurements for two steels, are incorporated into a creep equation set based on the damage mechanics philosophy. It is shown that the anomalously high activation energy reported in the literature for creep of ferritic steels can be traced to the fact that temperature dependence of subgrain growth had been ignored hitherto. This model is shown to be able to predict creep data for two steels accurately up to tens of thousands of hours over which data are available.

The results of an analysis of creep deformation in hexagonal and circular honeycomb structures using an elastic–plastic finite element method are reported here. Representative unit cells of transverse sections of the honeycomb structures were subjected to compression loading, with the wall material assumed to undergo creep following a power law of the form e ˙ = K σ n . It is shown that, in spite of using a steady-state law, the honeycomb shows primary and tertiary creep stages, arising from inhomogeneous deformation and geometrical effects, respectively. When the creep law is modified to include work-hardening of the wall material, the onset of the tertiary-like stage is delayed. It is also found that a circular honeycomb is stronger than a hexagonal honeycomb of similar relative density due to constraints within the structure. External constraints, such as those which may arise from friction with external surfaces, are also shown to lead to strengthening by producing triaxial compressive stresses within the cell walls.

This paper reports a novel technique to fabricate hexagonal honeycomb structures. Here, a low-melting coating on stacked circular tubes is used to form liquid bridges at the tube junctions upon heating. The surface tension in these bridges then pulls the curved tube elements continuously to create planar walls, thereby replacing the circular core structures with ones of hexagonal geometry. An analysis of this process explains the rate of evolution of the tube radius based on the flow law of the tube material, the latter being influenced by the penetration of liquid phase along the boundaries of the nickel grains in the tubes.

This article attempts to relate ultrasonic second harmonic generation to dislocation structures in fatigued materials. By focusing on the fact that asymmetric dislocation motion is required to generate the second harmonic, a theoretical derivation of the non-linearity parameter (ratio of the amplitude of second harmonic to square of the amplitude of the fundamental) from dislocation pile-ups is presented. In order to verify the theory, harmonic generation was measured along a failed fatigue sample of DA718, a nickel base superalloy that exhibits planar slip, and consequently dislocation pile-ups. TEM studies along the length of the failed fatigue sample revealed a banded dislocation structure, composed of pile-ups near the fracture zone and a sparse dislocation network closer to the grip region. The non-linearity parameter was found to increase by between 90% and 140% from the grip region to the fracture zone and this correlated well with the calculations based on theoretical expressions derived here. � 2007 Elsevier Ltd. All rights reserved.

FEM analysis was used to study the interactions between die friction, backpressure and strain rate sensitivity during equal channel angular pressing. One of the key findings is that strain rate sensitivity causes strain redistribution, resulting in higher equivalent strains and a substantial component of compression in the workpiece. This compression gives rise to effects such as lift-off of the leading end of the workpiece from the die bottom and improved die fill. Friction has different effects at room and elevated temperatures. While a moderate amount is beneficial at room temperature, friction has a detrimental interaction with strain rate sensitivity at high temperature. Backpressure, though largely beneficial, is shown to have negative effects when combined with friction and a high strain rate sensitivity.

The model of Arzt–Rosler and Wilkinson (ARW) for detachment controlled creep is reanalyzed here. A modified version of this model is presented wherein the expression for activation energy is replaced by one that represents the energy for a single activated step. The modified equation is derived from the well-known analysis of an activation barrier modified by an applied stress. Predictions of strain rate as a function of stress from the new analysis are similar to those of the ARW model.

Much work has been carried out in the general area of hot deformation and more specifically in the understanding and descriptions of the flow response that is observed under conditions that characterise hot deformation. Yet, the issue of the effects of energy dissipated on the metallurgical changes has not been found to be resolved successfully. The systems modelling approach of the dynamic materials model (DMM) has been extended to a study of the stress–strain curve. Definition of a parameter called the energy storage ratio (ESR) enables tracking of the metallurgical processes that underlie the stress–strain curve. It is established that the onset of dynamic recrystallisation corresponds to a constant critical value of the ESR which is independent of strain rate and temperature.

Realistic simulation of metal forming processes requires constitutive equations that describe the behavior of a material under varying process conditions. The equations that have hitherto been developed to address this problem are generally too involved and require the determination of many constants. In this paper, a simple approach based on the representative nature of the work hardening rate, which enables the use of an elementary rate equation in such modelling, is introduced. A prediction methodology based on the concept of fading memory is developed and is found to give good predictions in the case of copper. A mechanistic interpretation of the approach is proposed.

Investigations on nanostructured metallic systems have shown that exceptional property enhancements are potentially achievable through structural refinement to the nano-scale. While dramatic property improvements have been reported on these materials in the past, significant technical challenges exist in processing, as well as in retention of microstructural stability and useful properties at elevated temperatures. This presentation will summarize the key challenges in developing nanostructured metallic systems, and highlight our progress and selected successes in the understanding of structure-property relationships in bulk nanostructures as well as nanostructured multilayered systems. Work in nanoparticle dispersion-strengthened metallic systems will also be highlighted in this presentation.