Model-free isoconversion methods are the most reliable methods for the calculation of activation energies of thermally activated reactions. A large number of these isoconversion methods have been ...proposed in the literature. A classification of these methods is proposed. Type A methods such as Friedman methods make no mathematical approximations, and Type B methods, such as the generalised Kissinger equation, apply a range of approximations for the temperature integral. The accuracy of these methods is investigated, by deriving expressions for the main sources of error which includes the inaccuracy in reaction rate measurement, approximations for the temperature integral and inaccuracies in determination of temperature for equivalent fraction transformed. Both highly inaccurate and highly accurate Type B methods are identified. In cases where some uncertainty over baselines of the thermal analysis data exists or where accuracy of determination of transformation rates is limited, type B methods will often be more accurate than type A methods.
In metals that are heavily cold deformed, for instance by a severe plastic deformation process, significant strengthening is caused by the high density of defects such as grain boundaries and ...dislocations. In this work a model for volume-averaged dislocation and grain boundary (GB) creation is used to show that unless significant annihilation of defects post deformation occurs, the dislocation densities and GB densities in the deformed material are closely correlated. The dislocation strengthening effect thus shows a strong correlation with GB strengthening, and correlation of strength or hardness with d−1/2, where d is the grain size, as in a Hall-Petch type plot, can not be taken as an indication that GB strengthening dominates. Instead, in many SPD processed metals and alloys, dislocation strengthening is the dominant strengthening effect, even though a Hall-Petch type plot shows a good linear correlation.
An expanded model for the thermodynamics of co-clusters and their strengthening is presented and applied to predict co-cluster formation and strengthening in Al–Mg–Si alloys. The models were tested ...against data on a wide range of Al–Mg–Si alloys aged at room temperature. The strengthening due to co-clusters is well predicted. The formation of co-clusters was studied in an Al–0.5at.% Mg–1at.% Si alloy using three-dimensional atom probe analysis. The results correspond well with the model. It is shown that in general (short-range) order strengthening due to co-clusters will be the main strengthening mechanism in these alloys. Apart from the co-clusters, Si clusters also form, but due to their low enthalpy of formation they contribute little to the strength.
The present study contains a critical review of work on the formation of precipitates and intermetallic phases in dilute precipitation hardening Al-Cu-Mg based alloys with and without Li additions. ...Although many suggestions for the existence of pre-precipitates in Al-Cu-Mg alloys with a Cu/Mg atomic ratio close to 1 have been made, a critical review reveals that evidence exists for only two truly distinct ones. The precipitation sequence is best represented as: supersaturated solid solution→co-clusters→GPB2/S"→S where clusters are predominantly Cu-Mg co-clusters (also termed GPB or GPB I zones), GPB2/S" is an orthorhombic phase that is coherent with the matrix (probable composition Al
10
Cu
3
Mg
3
) for which both the term GPB2 and S" have been used, and S phase is the equilibrium Al
2
CuMg phase. GPB2/S" can co-exist with S phase before the completion of the formation of S phase. It is further mostly accepted that the crystal structure of S' (Al
2
CuMg) is identical to the equilibrium S phase (Al
2
CuMg). The Perlitz and Westgren model for S phase is viewed to be the most accepted structure. 3DAP analysis showed that Cu-Mg clusters form within a short time of natural and artificial aging. Cu-Mg clusters and S phase contribute to the first and second stage hardening during aging. In Al-Cu alloys, the θ phase (Al
2
Cu) has I4/mcm structure with a=0.607 nm and c=0.487 nm, and θ' phase has a tetragonal structure and a=0.404 nm, c=0.58 nm, the space group is I4m2. Gerold's model for θ" (or GPII) appears to be favourable in terms of free energy, and is consistent with most experimental data. The transformation from GPI to GPII (or θ") seems continuous, and as Cu atoms will not tend to cluster together or cluster with vacancies, the precipitation sequence can thus be captured as: supersaturated solid solution→θ" (Al
3
Cu)→θ' (Al
2
Cu)→θ(Al
2
Cu). The Ω phase (Al
2
Cu) has been variously proposed as monoclinic, orthorhombic, hexagonal and tetragonal distorted θphase structures. It has been shown that Ω phase forms initially on {111}
Al
with c=0.935 nm and on further aging, the c lattice parameter changes continuously to 0.848 nm, to become identical to the orthorhombic structure proposed by Knowles and Stobbs (a=0.496 nm, b=0.858 nm and c=0.848 nm). Other models are either wrong (for example, monoclinic and hexagonal) or refer to a transition phase (for example, the Garg and Howe model with c=0.858 in a converted orthorhombic structure). For Al-Li-Cu-Mg alloys, the L1
2
ordered metastable δ' (Al
3
Li) phase has been observed by many researchers. The Huang and Ardell model for T
1
phase (space group P6/mmm, a=0.496 nm and c=0.935 nm), appears more likely than other proposed structures. Other proposed structures are perhaps due to the T
1
phase forming by the dissociation of ½ dislocations into ⅙ Shockley partials bounding a region of intrinsic stacking fault, in which copper and lithium enrichment of the fault produces a thin layer of the T
1
phase.
Model-free isoconversion methods which use approximations of the temperature integral are generally reliable methods for the calculation of activation energies of thermally activated reactions ...studied during linear heating. These methods generally neglect the temperature integral at the start of the linear heating, I(To). An analytical equation is derived which describes the deviations introduced by this assumption. It is shown that for most reactions encountered this assumption does not have a significant influence on the accuracy of the method. However in cases where To is within about 50 to 70 K of the reaction stage to be investigated and activation energies are relatively low, significant deviations are introduced. It is shown that some of the published thermal analysis work on activation energy analysis of reactions occurring at relatively low temperatures is affected by these deviations. Examples are specific cases of dehydration reactions, cure reactions and cluster formation in Al alloys.
Co-clusters in ternary or higher order metallic alloys are metastable structures involving two or more distinct alloying atoms that retain the structure of the host lattice. A thermodynamic model ...based on a single interaction energy of dissimilar nearest neighbour interaction energy is presented, and a model for the strengthening due to these co-cluster dimers is derived. The model includes a new treatment of (short-range) order strengthening relevant to these co-clusters and further encompasses modulus hardening and chemical hardening. The models are tested against data on a wide range of Al–Cu–Mg alloys treated at temperatures between 20 and 220
°C. Both quantitative calorimetry data on the enthalpy change due to co-cluster formation and strengthening due to co-clusters is predicted well. It is shown that in general (short-range) order strengthening will be the main strengthening mechanism.
Transmission electron microscopy (TEM) and differential scanning calorimetry (DSC) have been used to study S phase precipitation in an Al–4.2 Cu–1.5 Mg–0.6 Mn–0.5 Si (AA2024) and an Al–4.2 Cu–1.5 ...Mg–0.6 Mn–0.08 Si (AA2324) (wt.%) alloy. In DSC experiments on as solution treated samples two distinct exothermic peaks are observed in the range 250–350°C, whereas only one peak is observed in solution treated and subsequently stretched or cold worked samples. Samples heated to 270 and 400°C at a rate of 10°C/min in the DSC have been studied by TEM. The selected area diffraction patterns show that S phase precipitates with the classic orientation relationship form during the lower temperature peak, and for the solution treated samples, the higher temperature peak is caused by the formation of a second type of S phase precipitates which has an orientation relationship that is rotated by ∼4° to the classic one. The effects of Si and cold work on the formation of the second type of S precipitates have been discussed.
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•New accurate model for continuous cooling quench sensitivity of 6xxx Al alloys.•The model considers two consecutive quench induced phases: Mg2Si and B′.•Model contains composition ...dependency and is successfully tested on five alloys.•Model is verified by extensive DSC, SEM, TEM and XRD experiments.•Model predicts enthalpy changes, volume fractions, T6-strength and -hardness.
This work studies the quench-induced precipitation during continuous cooling of five Al–Mg–Si alloys over a wide range of cooling rates of 0.05–2×104K/min using Differential Scanning Calorimetry (DSC), X-ray diffraction, optical- (OM), transmission electron- (TEM) and scanning electron microscopy (SEM) plus hardness testing. The DSC data shows that the cooling reactions are dominated by a high temperature reaction (typically 500°C down to 380°C) and a lower temperature reaction (380°C down to 250°C), and the microstructural analysis shows they are β-Mg2Si phase formation and B′ phase precipitation, respectively. A new, physically-based model is designed to model the precipitation during the quenching as well as the strength after cooling and after subsequent age hardening. After fitting of parameters, the highly efficient model allows to predict accurately the measured quench sensitivity, the volume fractions of quench induced precipitates, enthalpy changes in the quenched sample and hardness values. Thereby the model can be used to optimise alloy and/or process design by exploiting the full age hardening potential of the alloys choosing the appropriate alloy composition and/or cooling process. Moreover, the model can be implemented in FEM tools to predict the mechanical properties of complex parts after cooling.
A model for the yield strength of multi-component alloys is presented and applied to overaged Al–Zn–Mg–Cu alloys (7xxx series). The model is based on an approximation of the strengthening due to ...precipitate bypassing during precipitate coarsening and takes account of ternary and higher order systems. It takes account of the influence of supersaturation on precipitation rates and of volume fraction on coarsening rates, as well crystallographic texture and recrystallisation. The model has been successfully used to fit and predict the yield strength data of 21 Al–Zn–Mg–Cu alloys, with compositions spread over the whole range of commercial alloying compositions, and which were aged for a range of times and temperatures to produce yield strengths ranging from 400 to 600 MPa. All but one of the microstructural and reaction rate parameters in the model are determined on the basis of microstructural data, with one parameter fitted to yield strength data. The resulting accuracy in predicting unseen proof strength data is 14 MPa. In support of the model, microstructures and phase transformations of 7xxx alloys were studied by a range of techniques, including differential scanning calorimetry (DSC), electron backscatter diffraction (EBSD) in an SEM with a field emission gun (FEG-SEM).
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