Modeling of hardening and softening processes in Mg alloys

The tensile deformation behavior of a range of supersaturated Mg-Al solid solutions and an as-cast magnesium alloy AM60 has been studied. The Mg-Al alloys were tested at room temperature while the alloy AM60 was tested in the temperature range 293-573 K. The differences in the deformation behavior of the alloys is discussed in terms of hardening and softening processes. In order to identify which processes were active, the stress dependence of the strain-hardening coefficient was assessed using Lukac and Balik's model of hardening and softening. The analysis indicates that hardening involves solid solution hardening and interaction with forest dislocations and non-dislocation obstacles such as second phase particles. Cross slip is not a significant recovery process in the temperature range 293-423 K. At temperatures between 473 and 523 K the analysis suggests that softening is controlled by cross slip and climb of dislocations. At temperatures above 523 K softening seems to be controlled by dynamic recrystallisation. (C) 2004 Elsevier B.V. All rights reserved.

Age hardening of a sintered Al-Cu-Mg-Si-(Sn) alloy

The age hardening response of a sintered Al-3.8 wt% Cu-1.0 wt% Mg-0.70 wt% Si alloy with and without 0.1 wt% Sn was investigated. The sequence of precipitation was characterised using transmission electron microscopy. The ageing response of the sintered Al-Cu-Mg-Si-(Sn) alloy is similar to that of cognate wrought 2xxx series alloys. Peak hardness was associated with a fine, uniform dispersion of lath shaped precipitates, believed to be either the betaor Q phase, oriented along < 010 >. directions and theta' plates lying on {001}(alpha). planes. Natural ageing also resulted in comparable behaviour to that observed in wrought alloys. Porosity in the powder metallurgy alloys did not significantly affect the kinetics of precipitation during artificial ageing. Trace levels of tin, used to aid sintering, slightly reduced the hardening response of the alloy. However, this was compensated for by significant improvements in density and hardness. (c) 2005 Elsevier B.V. All rights reserved.

Bake-hardening of dual-phase steels

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

A mechanistic description of combined hardening and size effects

Mechanistic models based on geometrically necessary dislocations are re-examined in light of recent experiments exhibiting the indentation size effect. A simple method is developed to combine work hardening, solid solution hardening, radiation hardening and size effects. The model is verified by experiments in ionic salt crystals. © 2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

A költségvetési korlát megkeményítése a posztszocialista országokban = Hardening of the budget constraint in the post-socialist countries

A költségvetési korlát megkeményítése nem egyforma mértékben ment végbe minden posztszocialista gazdaságban. Egyes országokban messzire jutottak ebben a tekintetben, másokban viszont alig változott az indulóállapot. A tanulmány áttekinti a költségvetési korlát puhaságának különböző megnyilvánulásait: az állami támogatásokat, a puha adózást, a nem teljesítő bankkölcsönöket, a vállalatközi tartozások felgyülemlését és a kifizetetlen béreket. A jelenséget sokféle tényező okozza, amelyek többnyire együttesen jelentkeznek. Az állami tulajdon fenntartása kedvez a puha költségvetési szindróma megrögződésének, a privatizálás elősegíti a keményítést, de nem elégséges feltétele a kemény korlát érvényesítésének. Ehhez megfelelő politikai, jogi és gazdasági környezetet kell céltudatosan kialakítani. A posztszocialista átmenet kezdetén sokan azt hitték, hogy a hatékony piacgazdaság létrehozásához elegendő lesz megvalósítani a liberalizáció, privatizáció és stabilizáció "szentháromságát". Mára már kiderült, hogy a költségvetési korlát megkeményítése az említett három feladattal egyenrangúan fontos. Ahol ez nem valósul meg (például Oroszország), ott a privatizáció nem hozza meg a várt eredményt. ___________________ The budget constraint has not hardened to equal degrees in the various post-socialist countries. In some of them, a great deal has been done in this respect, while in others there has been hardly any change from the initial state. This study surveys the typical manifestations of softness of the budget constraint, such as state subsidies, soft taxation, non-performing loans, the accumulation of trade arrears between firms, and the build-up of wage arrears. Softness of the budget constraint is caused by several factors that tend to act in combination. Thus retention of state ownership helps to preserve the soft budget-constraint syndrome, while privatization encourages the budget constraint to harden, although it does not form a sufficient condition for it to happen. Purposeful development of the requisite political, legal and economic conditions is also required. It was widely maintained at the outset of the post-socialist transition that the 'Holy Trinity' of liberalization, privatization and stabilization would suffice to produce an efficient market economy. Since then, it has become clear that hardening the budget constraint needs to be given equal priority with these. Otherwise, the effects of privatization will fall short of expectations, as they have in Russia, for example.

A Finite Element to Perform 3D Shakedown Analysis for Limited Kinematic Hardening Materials

The use of the Design by Analysis (DBA) route is a modern trend in pressure vessel and piping international codes in mechanical engineering. However, to apply the DBA to structures under variable mechanical and thermal loads, it is necessary to assure that the plastic collapse modes, alternate plasticity and incremental collapse (with instantaneous plastic collapse as a particular case), be precluded. The tool available to achieve this target is the shakedown theory. Unfortunately, the practical numerical applications of the shakedown theory result in very large nonlinear optimization problems with nonlinear constraints. Precise, robust and efficient algorithms and finite elements to solve this problem in finite dimension has been a more recent achievements. However, to solve real problems in an industrial level, it is necessary also to consider more realistic material properties as well as to accomplish 3D analysis. Limited kinematic hardening, is a typical property of the usual steels and it should be considered in realistic applications. In this paper, a new finite element with internal thermodynamical variables to model kinematic hardening materials is developed and tested. This element is a mixed ten nodes tetrahedron and through an appropriate change of variables is possible to embed it in a shakedown analysis software developed by Zouain and co-workers for elastic ideally-plastic materials, and then use it to perform 3D shakedown analysis in cases with limited kinematic hardening materials

The Influence of Limited Kinematic Hardening in Shakedown Analysis

The use of the Design by Analysis concept is a trend in modern pressure vessel and piping calculations. DBA flexibility allow us to deal with unexpected configurations detected at in-service inspections. It is also important, in life extension calculations, when deviations of the original standard hypotesis adopted initially in Design by Formula, can happen. To apply the DBA to structures under variable mechanic and thermal loads, it is necessary that, alternate plasticity and incremental collapse (with instantaneous plastic collapse as a particular case), be precluded. These are two basic failure modes considered by ASME or European Standards in DBA. The shakedown theory is the tool available to achieve this goal. In order to apply it, is necessary only the range of the variable loads and the material properties. Precise, robust and efficient algorithms to solve the very large nonlinear optimization problems generated in numerical applications of the shakedown theory is a recent achievement. Zouain and co-workers developed one of these algorithms for elastic ideally-plastic materials. But, it is necessary to consider more realistic material properties in real practical applications. This paper shows an enhancement of this algorithm to dealing with limited kinematic hardening, a typical property of the usual steels. This is done using internal thermodynamic variables. A discrete algorithm is obtained using a plane stress, mixed finite element, with internal variable. An example, a beam encased in an end, under constant axial force and variable moment is presented to show the importance of considering the limited kinematic hardening in a shakedown analysis.

Shakedown Analysis Considering Limited Kinematic Hardening Materials

In design or safety assessment of mechanical structures, the use of the Design by Analysis (DBA) route is a modern trend. However, for making possible to apply DBA to structures under variable loads, two basic failure modes considered by ASME or European Standards must be precluded. Those modes are the alternate plasticity and incremental collapse (with instantaneous plastic collapse as a particular case). Shakedown theory is a tool that permit us to assure that those kinds of failures will be avoided. However, in practical applications, very large nonlinear optimization problems are generated. Due to this facts, only in recent years have been possible to obtain algorithms sufficiently accurate, robust and efficient, for dealing with this class of problems. In this paper, one of these shakedown algorithms, developed for dealing with elastic ideally-plastic structures, is enhanced to include limited kinematic hardening, a more realistic material behavior. This is done in the continuous model by using internal thermodynamic variables. A corresponding discrete model is obtained using an axisymmetric mixed finite element with an internal variable. A thick wall sphere, under variable thermal and pressure loads, is used in an example to show the importance of considering the limited kinematic hardening in the shakedown calculations

Compressive behaviour of nanocrystallilne Mg-5%Al alloys

Magnesium alloys are attracting increasing research interests due to their low density, high specific strength and good mechineability and availability as compared to other structural materials. However, the deformation and failure mechanisms of nanocrystalline Mg alloys have not been well understood. In this work, the deformation behavior of nanocrystalline Mg-5% Al alloys was investigated using compression test, with a focus on the effects of grain size. The average grain size of the Mg-Al alloy was changed from 13 µm to 50 nm via mechanical milling. The results showed that grain size had a significant influence on the yield stress and ductility of the Mg alloys, and the materials exhibited increased strain rate sensitivity with decrease of grain size. The deformation mechanisms were also strongly dependent with the grain sizes.

Deformation behaviours of coarse-grained and nanocrystalline Mg-5wt% Al alloys

Magnesium alloys have been of growing interest to various engineering applications, such as the automobile, aerospace, communication and computer industries due to their low density, high specific strength, good machineability and availability as compared with other structural materials. However, most Mg alloys suffer from poor plasticity due to their Hexagonal Close Packed structure. Grain refinement has been proved to be an effective method to enhance the strength and alter the ductility of the materials. Several methods have been proposed to produce materials with nanocrystalline grain structures. So far, most of the research work on nanocrystalline materials has been carried out on Face-Centered Cubic and Body-Centered Cubic metals. However, there has been little investigation of nanocrystalline Mg alloys. In this study, bulk coarse-grained and nanocrystalline Mg alloys were fabricated by a mechanical alloying method. The mixed powder of Mg chips and Al powder was mechanically milled under argon atmosphere for different durations of 0 hours (MA0), 10 hours (MA10), 20 hours (MA20), 30 hours (MA30) and 40 hours (MA40), followed by compaction and sintering. Then the sintered billets were hot-extruded into metallic rods with a 7 mm diameter. The obtained Mg alloys have a nominal composition of Mg–5wt% Al, with grain sizes ranging from 13 μm down to 50 nm, depending on the milling durations. The microstructure characterization and evolution after deformation were carried out by means of Optical microscopy, X-Ray Diffraction, Scanning Electron Microscopy, Transmission Electron Microscopy, Scanning Probe Microscopy and Neutron Diffraction techniques. Nanoindentaion, compression and micro-compression tests on micro-pillars were used to study the size effects on the mechanical behaviour of the Mg alloys. Two kinds of size effects on the mechanical behaviours and deformation mechanisms were investigated: grain size effect and sample size effect. The nanoindentation tests were composed of constant strain rate, constant loading rate and indentation creep tests. The normally reported indentation size effect in single crystal and coarse-grained crystals was observed in both the coarse-grained and nanocrystalline Mg alloys. Since the indentation size effect is correlated to the Geometrically Necessary Dislocations under the indenter to accommodate the plastic deformation, the good agreement between the experimental results and the Indentation Size Effect model indicated that, in the current nanocrystalline MA20 and MA30, the dislocation plasticity was still the dominant deformation mechanism. Significant hardness enhancement with decreasing grain size, down to 58 nm, was found in the nanocrystalline Mg alloys. Further reduction of grain size would lead to a drop in the hardness values. The failure of grain refinement strengthening with the relatively high strain rate sensitivity of nanocrystalline Mg alloys suggested a change in the deformation mechanism. Indentation creep tests showed that the stress exponent was dependent on the loading rate during the loading section of the indentation, which was related to the dislocation structures before the creep starts. The influence of grain size on the mechanical behaviour and strength of extruded coarse-grained and nanocrystalline Mg alloys were investigated using uniaxial compression tests. The macroscopic response of the Mg alloys transited from strain hardening to strain softening behaviour, with grain size reduced from 13 ìm to 50 nm. The strain hardening was related to the twinning induced hardening and dislocation hardening effect, while the strain softening was attributed to the localized deformation in the nanocrystalline grains. The tension–compression yield asymmetry was noticed in the nanocrystalline region, demonstrating the twinning effect in the ultra-fine-grained and nanocrystalline region. The relationship k tensions < k compression failed in the nanocrystalline Mg alloys; this was attributed to the twofold effect of grain size on twinning. The nanocrystalline Mg alloys were found to exhibit increased strain rate sensitivity with decreasing grain size, with strain rate ranging from 0.0001/s to 0.01/s. Strain rate sensitivity of coarse-grained MA0 was increased by more than 10 times in MA40. The Hall-Petch relationship broke down at a critical grain size in the nanocrystalline region. The breakdown of the Hall-Petch relationship and the increased strain rate sensitivity were due to the localized dislocation activities (generalization and annihilation at grain boundaries) and the more significant contribution from grain boundary mediated mechanisms. In the micro-compression tests, the sample size effects on the mechanical behaviours were studied on MA0, MA20 and MA40 micro-pillars. In contrast to the bulk samples under compression, the stress-strain curves of MA0 and MA20 micro-pillars were characterized with a number of discrete strain burst events separated by nearly elastic strain segments. Unlike MA0 and MA20, the stress-strain curves of MA40 micro-pillars were smooth, without obvious strain bursts. The deformation mechanisms of the MA0 and MA20 micro-pillars under micro-compression tests were considered to be initially dominated by deformation twinning, followed by dislocation mechanisms. For MA40 pillars, the deformation mechanisms were believed to be localized dislocation activities and grain boundary related mechanisms. The strain hardening behaviours of the micro-pillars suggested that the grain boundaries in the nanocrystalline micro-pillars would reduce the source (nucleation sources for twins/dislocations) starvation hardening effect. The power law relationship of the yield strength on pillar dimensions in MA0, MA20 supported the fact that the twinning mechanism was correlated to the pre-existing defects, which can promote the nucleation of the twins. Then, we provided a latitudinal comparison of the results and conclusions derived from the different techniques used for testing the coarse-grained and nanocrystalline Mg alloy; this helps to better understand the deformation mechanisms of the Mg alloys as a whole. At the end, we summarized the thesis and highlighted the conclusions, contributions, innovations and outcomes of the research. Finally, it outlined recommendations for future work.

Compressive behaviour of nanocrystalline Mg-5Al alloys

Magnesium alloys are attracting increasing research interests due to their low density, high specific strength, good machinability and availability as compared to other structural materials. However, the deformation and failure mechanisms of nanocrystalline (nc) Mg alloys have not been well understood. In this work, the deformation behaviour of nc Mg-5Al alloys was investigated using compression test, with focus on the effects of grain size. The average grain size of the Mg- Al alloy was changed from 13 to 50 nm via mechanical milling. The results showed that grain size had a significant influence on the yield stress and ductility of the Mg alloys, and the materials exhibited increased strain rate sensitivity with a decrease in grain size. The deformation mechanisms were also strongly dependent on the grain sizes.

Power-law viscous materials for analogue experiments: New data on the rheology of highly-filled silicone polymers

The selection of appropriate analogue materials is a central consideration in the design of realistic physical models. We investigate the rheology of highly-filled silicone polymers in order to find materials with a power-law strain-rate softening rheology suitable for modelling rock deformation by dislocation creep and report the rheological properties of the materials as functions of the filler content. The mixtures exhibit strain-rate softening behaviour but with increasing amounts of filler become strain-dependent. For the strain-independent viscous materials, flow laws are presented while for strain-dependent materials the relative importance of strain and strain rate softening/hardening is reported. If the stress or strain rate is above a threshold value some highly-filled silicone polymers may be considered linear visco-elastic (strain independent) and power-law strain-rate softening. The power-law exponent can be raised from 1 to ~3 by using mixtures of high-viscosity silicone and plasticine. However, the need for high shear strain rates to obtain the power-law rheology imposes some restrictions on the usage of such materials for geodynamic modelling. Two simple shear experiments are presented that use Newtonian and power-law strain-rate softening materials. The results demonstrate how materials with power-law rheology result in better strain localization in analogue experiments.

The analogue shear zone : from rheology to associated geometry

The geometry of ductile strain localization phenomena is related to the rheology of the deformed rocks. Both qualitative and quantitative rheological properties of natural rocks have been estimated from finite field structures such as folds and shear zones. We apply physical modelling to investigate the relationship between rheology and the temporal evolution of the width and transversal strain distribution in shear zones, both of which have been used previously as rheological proxies. Geologically relevant materials with well-characterized rheological properties (Newtonian, strain hardening, strain softening, Mohr-Coulomb) are deformed in a shear box and observed with Particle Imaging Velocimetry (PIV). It is shown that the width and strain distribution histories in model shear zones display characteristic finite responses related to material properties as predicted by previous studies. Application of the results to natural shear zones in the field is discussed. An investigation of the impact of 3D boundary conditions in the experiments demonstrates that quantitative methods for estimating rheology from finite natural structures must take these into account carefully.

Evaluation of plastic deformation ability of Cu/Ni/W metallic multilayers

Plastic deformation behavior of Cu/Ni/Wmetallicmultilayers with individual layer thickness ranging from 5 nm to 300 nm is investigated by nanoindentation testing. The experimental results reveal that the composite still exhibits indentation-induced plastic deformation instability and the loss of strain hardening ability at the nanometer scale even if the composite contains two kinds of layer interfaces (face centered cubic(FCC)/FCC and FCC/ body centered cubic) simultaneously. Plastic deformation behavior of the nanolayered material was evaluated and analyzed.