Deformation Mechanism Map Research Articles

A Deformation Mechanism Map for the 1.23Cr-1.2Mo-0.26V Rotor Steel and Its Verification Using Neural Networks

A deformation mechanism map is constructed for the 1.23Cr-1.2Mo-0.26V rotor steel as a function of temperature, stress, and strain rate using published creep test results and the current understanding of time dependent deformation mechanisms operative in complex engineering alloys. Instead of diffusional creep, grain boundary sliding (GBS) accommodated by different deformation processes is considered dominant at lower strain rates. The GBS dominated region is further sub-divided into two parts, where GBS is accommodated by wedge type cracking at temperatures below 0.5T/Tm and the accommodation process changes to creep cavitation at temperatures above 0.5T/Tm. The map is verified using experimental data and artificial neural network modeling. The proposed artificial neural network model is capable of predicting the dominance of different deformation mechanisms in 1.23Cr-1.2Mo-0.26V steel over a wide range of stress and temperature. This modeling procedure can potentially be used to construct or expand deformation mechanism maps for other engineering alloys.

Evaluating the Flow Properties of Ultrafine-Grained Materials

Processing through the application of severe plastic deformation (SPD) provides an opportunity for achieving significant grain refinement, typically to the submicrometer or even the nanometer level. If these small grains are reasonably stable at elevated temperatures, it is possible to achieve excellent superplastic capabilities at very rapid strain rates. Recent developments on the flow properties of ultrafine-grained materials are examined and it is shown that the flow mechanisms can be readily depicted using deformation mechanism maps. Examples of maps are presented for materials processed by SPD techniques.

Achieving superplasticity in ultrafine-grained metals

Superplasticity refers to the ability of some materials to pull out to exceptionally high elongations prior to failure. It is now well established that superplastic flow requires both a high testing temperature and a small grain size that is typically less than ∼10μm The processing of ultrafine-grained metals with submicrometer grain sizes through the application of severe plastic deformation (SPD) provides an opportunity for achieving excellent superplastic properties in bulk metals provided these small grains are reasonably stable at elevated temperatures. There have been numerous recent developments in the production of superplastic flow in metals processed by SPD and these developments are reviewed in this report. The analysis shows there is an excellent potential for achieving high superplastic elongations in metals processed by SPD, these high elongations often occur at very high strain rates and, in addition, the behaviour of these metals is consistent with the predictions from deformation mechanism maps.

The origin and geophysical implications of a weak C-type olivine fabric in the Xugou ultrahigh pressure garnet peridotite

We report here a comprehensive investigation of mineral chemistry, water content and deformation features (including the crystallographic preferred orientation and dislocation substructures of olivine) of the Xugou garnet peridotite from the southern Sulu ultrahigh pressure (UHP) terrane. Our results suggest: (1) the Xugou garnet peridotite was equilibrated and deformed at high pressure (4.8–6.6 GPa) and relatively low temperature (810–930 °C) conditions. (2) In contrast to the pronounced shape-preferred orientations of olivine, pyroxene and garnet, electron backscattered diffraction (EBSD) measurements show a weak C-type fabric in olivine, a strong (100)[001] fabric in clinopyroxene and orthopyroxene and a nearly random fabric in garnet, respectively. The deformation mechanism map suggests a dominant deformation mechanism of dislocation-accommodated grain boundary sliding (DisGBS) in olivine. (3) The trivial amount of water in olivine (15±10 ppm), orthopyroxene (21±17 ppm), clinopyroxene (64±48 ppm) and garnet (dry) correspond to a water-poor deformation condition. We proposed that the C-type olivine fabric was generated by a dominant DisGBS with some contribution from diffusion creep at elevated pressures. Calculated seismic properties of the peridotite show the fastest P-wave velocity and the fast polarization direction of S-waves are oriented normal to the foliation plane and perpendicular to the lineation in the foliation plane, indicating that the C-type olivine fabric could also be a candidate to explain the observed strike-parallel faster S-wave polarization near trenches and in collisional orogenic belts.

Work-hardening stages and deformation mechanism maps during tensile deformation of commercially pure titanium

Commercially pure titanium was tensile tested at different strain rates between 2.2×10−4s−1 and 6.7×10−1s−1 to characterize the strain rate dependence of plastic deformation and the dominating deformation mechanisms. From true stress-true plastic strain curves, three distinct work-hardening stages are identified. The work-hardening rate decreases linearly with increasing flow stress for all three stages and the work-hardening rate is the controlling factor for the transition between the different stages and mechanisms. During the initial stage (at lowest stresses) plastic deformation is carried mainly by dislocation slip, in the following stage (for moderate stresses), an abundance of 64.6∘〈1¯010〉 twin boundaries form indicating the dominance of {112¯2}〈1¯1¯23〉 compression twinning. During the last stage before the onset of necking, additional 84.8∘〈112¯0〉 twin boundaries are detected caused by {101¯2}〈101¯1〉 tensile twinning. Based on the microstructural findings and the strain rate sensitivity, deformation mechanism maps are constructed.

The many facets of deformation mechanism mapping and the application to nanostructured materials

Abstract

Superplasticity, flow and fracture mechanism in an Al–12.7Si–0.7Mg alloy

The superplastic behavior of an Al–12.7mass%Si–0.7mass%Mg alloy was investigated under different conditions. Reasonable superplastic elongations were achieved in the fine-grained (9.1μm) Al–Si–Mg alloy at temperatures ranging from 733 to 793K at initial strain rates ranging from 1.67×10–4 to 1.67×10–3s−1. A maximum elongation to failure of 379% was demonstrated with a strain rate sensitivity, m, of 0.52 and an activation energy for flow, Q, of 156.7KJ/mol at 793K at an initial strain rate of 1.67×10–4s−1, which is close to the lattice diffusion activation energy of aluminum. The dislocation activity within Al grains indicated that intragranular slip is the accommodation mechanism of grain boundary sliding. EBSD (Electron Backscatter Diffraction) results revealed that most grain boundaries were high angle boundaries and therefore indicated that boundary sliding and grain rotation occurred during deformation. A deformation mechanism map was plotted for the Al–Si–Mg alloy at 793K and it is shown that the experimental datum points are in excellent agreement with the predictions of the map. Most cavities were formed around silicon particles and the cavity formation mechanism was proposed. The observation on the fracture surface revealed the presence of filaments. The filament quantity or density increased with increasing testing temperature, which can be interpreted by the transition of dislocation viscous glide creep to grain boundary sliding mechanism at elevated temperatures. The formation of filaments was related to the deformation mechanisms and the lattice diffusion at elevated temperatures. The superplastic fracture in the Al–Si–Mg alloy exhibited a diffuse necking and was a pseudo-brittle fracture. The fracture mechanism was intergranular fracture.

The significance of grain boundary sliding in the superplastic Zn–22 % Al alloy processed by ECAP

A Zn–22 % Al eutectoid alloy was processed by equal-channel angular pressing (ECAP) to reduce the grain size to ~0.8 μm. Tensile testing at 473 K showed superplastic characteristics with a maximum elongation of ~2230 % at a strain rate of 1.0 × 10−2 s−1. The significance of grain boundary sliding (GBS) was evaluated by measuring sliding offsets at adjacent grains from the displacements of surface marker lines in samples pulled to elongations of 30 % at a series of different strain rates. The highest sliding contribution was recorded under testing conditions corresponding to the maximum superplastic ductility. There were relatively large offsets at the Zn–Zn and Zn–Al interfaces, but smaller offsets at the Al–Al interfaces. Analysis shows the results are affected by the presence of agglomerates of similar grains which are present after ECAP processing and specifically by the increased fraction of Al–Al boundaries. The experimental results are in excellent agreement with the predictions of a deformation mechanism map depicting the flow behavior in the Zn–22 % Al alloy, and the results confirm the importance of GBS as the dominant mechanism of flow in superplasticity after processing by ECAP.

Creep Mechanism in Several Grades of Aluminum at Low Temperatures

Creep tests were performed at less than 0.4 Tm (Tm is the melting temperature) for 99.999, 99.57 and 99.52% aluminum with several grain sizes in the range of 50­330µm. These Al materials show remarkable creep behavior with an apparent activation energy (Q )o f 30kJ/mol, a stress exponent of 4, and a grain-size exponent of zero, and with a larger creep rate with increasing purity. These parameters resemble those of conventional dislocation creep, which is rate-controlled by the usual diffusion processes, except for the extra-low Q value. This means that a non-diffusional process affects the steady state deformation in this temperature region. Transmission electron microscopy revealed the development of a cell structure in the steady state and dislocations without any tangles in the cell interiors. Therefore, because the ratecontrolling process could not occur inside of the cells, dislocation annihilation occurred through cross slip around the cell walls. According to these creep parameters and microstructural observations, the observed creep region is suggested to be a new creep region occurring through a non-diffusional process within the existing deformation mechanism map of Al at less than 0.4 Tm. [doi:10.2320/matertrans.L-M2013833]

A deformation mechanism map for polycrystals modeled using strain gradient plasticity and interfaces that slide and separate

Small scale strain gradient plasticity is coupled with a model of grain boundaries that take into account the energetic state of a plastically strained boundary and the slip and separation between neighboring grains. A microstructure of hexagonal grains is investigated using a plane strain finite element model. The results show that three different microstructural deformation mechanisms can be identified. The standard plasticity case in which the material behaves as expected from coarse grained experiments, the nonlocal plasticity region where size of the microstructure compared to some intrinsic length scale enhances the yield stress and a third mechanism, active only in very fine grained microstructures, where the grains deform mainly in relative sliding and separation.

A mechanism-based framework for the numerical analysis of creep in zircaloy-4

A deformation-mechanism map has been developed for unirradiated zircaloy-4 based on the creep data available from the literature of the last 35years. These data have been analyzed to identify different creep mechanisms, based on the forms of the relationships between stress, temperature and strain rate. This identification allowed the activation energies and other associated creep parameters to be derived for each mechanism. The creep parameters were used to construct a deformation-mechanism map for zircaloy-4 that shows the conditions under which different mechanisms are dominant. This information provides an important tool for assessing the effects of stress and temperature in design, especially when extrapolating to different regimes. As an example of how this information might be used in a numerical analysis for design purposes, a novel mechanism-based creep framework was implemented within a finite-element code. Although the framework was developed specifically for zircaloy-4, it provides a general example of how mechanism-based creep laws can be implemented into finite-element analyses. This approach allows the creep of complex geometries to be analyzed rigorously, with the dominant deformation mechanisms being identified and evolving automatically in response to the local temperatures and stresses.

Fractal Analysis of Magnetite Grains – Implications for Interpreting Deformation Mechanism

Abstract In the present study, the grain size (d) and shape of 225 magnetite grains, that crystallized at T>600°C in a syntectonic granite (Godhra Granite, India) are evaluated and implications of data to decipher deformation mechanism of magnetite are discussed. Fractal (ruler) dimension (D) analysis of magnetite grains is performed and it is demonstrated that they show fractal behaviour. Smaller magnetite grains tend to be more serrated than the larger ones, which is manifested in the higher fractal (ruler) dimension (D) of the former. Assuming a natural strain rate ranging between 10-10 s-1 and 10-14 s-1, the grain size data fall dominantly in the dislocation creep field of the existing deformation mechanism map of magnetite for 630°C. However, SEM-EBSD studies reveal that subgrains are absent in the magnetite grains and they did not undergo dislocation creep. Thus it is inferred that the shape of magnetite grains was not controlled by dislocation creep. It is concluded that the higher serration and increased fractal dimension of finer magnetite grains implies the importance of diffusion creep as an important deformation mechanism at high-T for magnetite in polymineralic rocks.

Isomechanical groups in bulk metallic glasses

Isomechanical groups are, as defined by Frost and Ashby [H.J. Frost and M.F. Ashby, Deformation–Mechanism Maps, Pergamon Press, Oxford, 1982], separate classes of materials that exhibit similar deformation and transport properties when normalised by an appropriate parameter. Fundamentally, this separation results from significant differences in material structure and bonding. Here, such an analysis is applied to 40 bulk metallic glasses (BMGs) grouped into three classes according to their Poisson's ratio, which is known to be an indicator of intrinsic toughness. Through rigorous statistical analysis, it is found that isomechanical groups are present and that they may result from (1) variation in the tendency for directional bonding, and (2) how liquid-like the structure is, which may be characterised by a quantification of local volumetric strain. These results suggest that, although experimentally observed properties from BMGs in different isomechanical groups are all typically considered within the same framework, differences in atomic packing and inter-atomic bonding mean that they should in fact be treated separately. These fundamental differences in bonding and structure may explain the known large variation in the tendency for toughness and plasticity in BMGs.

Using deformation mechanism maps to depict flow processes in superplastic ultrafine-grained materials

Deformation mechanism maps are a very useful tool for displaying deformation mechanisms as a function of the three fundamental parameters of high temperature flow: the applied stress, the testing temperature and the grain size of the material. These maps are used extensively in the field of high temperature creep but there has been very little use with ultrafine-grained (UFG) metals. This article reviews the principles of deformation mechanism maps, presents examples of maps for some representative metals processed by equal-channel angular pressing or high-pressure torsion and then describes a simple procedure for constructing maps for UFG materials.

Advanced Procedures for Long-Term Creep Data Prediction for 2.25 Chromium Steels

A critical review of recent creep studies concluded that traditional approaches such as steady-state behavior, power law equations, and the view that diffusional creep mechanisms are dominant at low stresses should be seriously reconsidered. Specifically, creep strain rate against time curves show that a decaying primary rate leads into an accelerating tertiary stage, giving a minimum rather than a secondary period. Conventional steady-state mechanisms should therefore be abandoned in favor of an understanding of the processes governing strain accumulation and the damage phenomena causing tertiary creep and fracture. Similarly, creep always takes place by dislocation processes, with no change to diffusional creep mechanisms with decreasing stress, negating the concept of deformation mechanism maps. Alternative descriptions are then provided by normalizing the applied stress through the ultimate tensile stress and yield stress at the creep temperature. In this way, the resulting Wilshire equations allow accurate prediction of 100,00 hours of creep data using only property values from tests lasting 5000 hours for a series of 2.25 chromium steels, namely grades 22, 23, and 24.

A True-Stress Creep Model Based on Deformation Mechanisms for Polycrystalline Materials

A true-stress creep model has been developed based on well-recognized deformation mechanisms, i.e., dislocation glide, dislocation climb, and grain boundary sliding. The model provides a physics-based description of the entire creep deformation process with regards to the strain-time history (primary, secondary, and tertiary creep), rupture strain and lifetime, which finds good agreement with experimental observations for Waspaloy. A deformation-mechanism map is constructed for Waspaloy, and a creep failure criterion is defined by the dominant deformation mechanisms leading to intergranular/transgranular fracture. Thus, the model is a self-consistent tool for creep life prediction.

Deformation Mechanism Maps for Al-Cu-Mg Alloys Micro-Alloyed with Tin

High temperature deformation behavior of Al–5.9%Cu–0.5%Mg alloy and Al–5.9%Cu–0.5%Mg alloy containing 0.06 wt.% of Sn was studied by hot compression tests at various temperatures and strain rates. Addition of trace amounts of Sn into the Al–Cu–Mg alloy system resulted in a significant increase of flow stress for all conditions of temperature and strain rate. 100% and 89% of the flow stress values during hot deformation could be predicted within ± 10% deviation values for the aluminum alloys with and without Sn content, respectively, by artificial neural network (ANN) modeling. From the deformation mechanism maps and microstructural investigation, the safe process regimes for hot working of the base alloy was identified to be at (i) very low strain rate (< 0.003 s−1) at temperature < 450 °C, and (ii) high temperature (> 400 °C) with strain rate > 0.02 s−1. For the micro-alloyed alloy, it was at low strain rates (< 0.01 s-1) for the entire temperature range studied. Flow softening for both alloys was observed to be at low strain rates and was identified to be due to dynamic recrystallization (DRX). The metallurgical instability during deformation was identified due to shear band formation and/or inter-crystalline cracking.

Physics based Prognostics of Solder Joints in Avionics

Applicability of a physics based prognostics approach for solder joints using microstructural damage models is investigated. A modified deformation mechanism map for the solder alloys is introduced where grain boundary sliding (GBS) plays a dominant role during creep deformation. The high homologous temperature of solder as well as the combined thermal-vibration cycling experienced during typical operating missions necessitates the use of a combined creep-fatigue failure approach. In this work, a PCB consisting of a heat generating chip with Ball-Grid Array (BGA) solder joints is considered for avionics application. A prognostics based Life Cycle Management approach was used to perform the mission analysis, FEA, thermal-mechanical stress analysis and damage accumulation analysis. The remaining useful life (RUL) is predicted for different rupture strains. The uniqueness of this approach lies in the use of microstructure based damage models and consideration of both material and mission variability to predict the RUL under actual usage. The life critical nodes were observed near the junction of the solder joints with the substrate due to high disparities in their coefficients of thermal expansion. In addition, the probabilistic analysis was also performed by randomly varying the grain size and fitting a two-parameter Weibull distribution to the failure data. The model calibration and the results show some practical trends that need to be verified through future experimentation. The simulation results demonstrate the viability of using a physics-based approach for the prognosis of solder joint failures in avionics.

Developing superplasticity and a deformation mechanism map for the Zn–Al eutectoid alloy processed by high-pressure torsion

A Zn–22% Al eutectoid alloy was processed by high-pressure torsion (HPT) for 1, 3 and 5 turns at room temperature to produce an ultrafine grain size of ∼350 nm. Tensile testing at a temperature of 473 K gave excellent superplastic properties with elongations to failure up to a maximum of 1800% at an imposed strain rate of 1.0 × 10 −1 s −1: this is within the range of high strain rate superplasticity and represents the highest elongation recorded to date for a specimen processed by HPT. It is shown that the experimental data are in excellent agreement with a deformation mechanism map constructed for a temperature of 473 K.

Reconstructing the pyrite deformation mechanism map

Deformation mechanism maps are important tools to understand how minerals deform across a range of pressure, temperature and strain rate conditions. Recent studies have suggested that the current deformation mechanism map for pyrite is in need of revision, with plastic deformation evident over a much wider range of conditions than it proposes. This study uses stress–strain data from experimentally deformed pyrite, combined with electron backscatter diffraction (EBSD) results from a range of experimental and natural samples to construct a revised pyrite deformation mechanism map. This map corresponds to polycrystalline pyrite with a grain size of ~ 35 μm and suggests the onset of crystal plasticity at geological strain rates (~ 10 − 12 –10 − 16 s − 1 ) occurs at temperatures as low as ~ 260 °C. The revised mechanism map is based upon all available data, experimental data for pyrite are limited and acquired at geologically unreasonable, fast strain rates (10 − 4 –10 − 5 s − 1 ), and strain rates for the naturally deformed samples can only be estimated. Therefore, considerable extrapolation is required and whilst this revised map is an improvement upon the existing map, it should still only be considered a ‘guide’ to the potential deformation mechanisms, which may operate across a range of P–T conditions in polycrystalline pyrite-rich ores.