M.J. Starink

A new method for the derivation of activation energies from experiments performed at constant heating rate

The Ozawa, Kissinger and Boswell isoconversion methods for obtaining activation energies, Ea, from experiments performed at constant heating rate belong to one group of methods. It is shown that from these three methods the Kissinger method is generally the most accurate. Based on the analysis of the approximation errors made in this group of methods, a new isoconversion method is obtained, which takes the form: InβT1.8f = − AEakBTf + constant where A = 1.0070 − 1.2 10−5 Ea (Ea in kJ/mol), β is the heating rate and Tf is the temperature at a fixed amount transformed. Hence, similar to Ozawa, Boswell and Kissingers methods it is based on obtaining the slope of a logarithmic function containing the heating rate vs. 1T. The new method is shown to be significantly more accurate than the others.

A Model for the Yield Strength of Overaged Al-Zn-Mg-Cu Alloys

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).

On the meaning of the impingement parameter in kinetic equations for nucleation and growth reactions

AbstractIf certain preconditions are met, the Johnson-Mehl-Avrami-Kolmogorov (JMAK) kinetic equation is exactly accurate for nucleation and growth reactions with linear growth and is, at least, a good approximation for nucleation and growth reactions with parabolic growth. These preconditions include randomly distributed product phases, isotropic growth and constant equilibrium state. Mechanisms causing deviations from these preconditions include: capillarity effect, vacancy annihilation, blocking due to anisotropic growth. It is shown that deviations lead to a modification of the overall transformation, which can be approximated well by a single equation:

β′ and β precipitation in an Al–Mg alloy studied by DSC and TEM

\alpha = 1 - \left[ {\frac{{\left\langle {k\left\langle T \right\rangle t} \right\rangle ^{n_s } }}{{\eta _i }} + 1} \right]^{ - \eta _i }

Effect of self-accommodation on α/α boundary populations in pure titanium

where α is the fraction transformed, ηi is the impingement parameter, ns and k(T) are parameters that depend on growth geometry and growth rate. The factors which influence the impingement parameter are discussed.

Kinetic equations for diffusion-controlled precipitation reactions

Abstract To provide an understanding of how compositional variations affect the characteristics of coarse intermetallic particles in 7000 aluminium alloys, three Al-Zn-Mg-Cu-Zr alloy plates with different zinc, magnesium, and copper contents have been studied by optical microscopy based image analysis, scanning electron microscopy SEM, energy dispersive X-ray spectroscopy EDS, and differential scanning calorimetry DSC. These coarse intermetallic particles are detrimental, especially to the toughness of the alloy. Experimental observations have been interpreted successfully on the basis of the phase diagram and the temperature dependent S phase solvus, derived in turn on the basis of the regular solution model. The temperature dependent S phase solvus indicates that some compositions in the composition windows of 7050 and 7x75 type alloys will give rise to the detrimental S phase, which cannot be dissolved during solution treatment. Also, the T phase has been analysed and conditions for its formation and dissolution are discussed. It is shown that the present results can produce useful information on alloy design and thermomechanical processing via microstructural control.

An analysis method for nucleation and growth controlled reactions at constant heating rate

Precipitation in Al–16 at.%Mg is investigated by differential scanning calorimetry (DSC) and transmission electron microscopy (TEM). The shape of the β′ formation DSC effect is interpreted with a novel theory and the curves obtained on the basis of this new theory fit well to the experimental curves. The s parameter derived from these fits, which is akin to the Avrami parameter n appearing in the Johnson–Mehl–Avrami–Kolmogorov model, is larger than 2.5, indicating that β′ precipitation is an autocatalytic process. TEM showed the abundant presence of defects (mostly dislocation loops) but no evidence of nucleation of β′ precipitates on these defects. The enthalpies of formation of the β and β′ phases are derived as 15.7 and 11.5 kJ per mol Mg, respectively.

Estimation of dislocation densities in cold rolled Al-Mg-Cu-Mn alloys by combination of yield strength data, EBSD and strength models

The microstructural evolution during low temperature ageing of two commercial purity alloys (Al–1.2Cu–1.2Mg–0.2Mn and Al–1.9Cu–1.6Mg–0.2Mn at.%) was investigated. The initial stage of hardening in these alloys is very rapid, with the alloys nearly doubling in hardness during 20 h ageing at room temperature. The microstructural evolution during this stage of hardening was investigated using differential scanning calorimetry (DSC), isothermal calorimetry and three–dimensional atom probe analysis (3DAP). It is found that, during the hardening, a substantial exothermic heat evolution occurs and that the only microstructural change involves the formation of Cu–Mg co–clusters. The kinetics of cluster formation is analysed and the magnitude of the hardening is discussed on the basis of a model incorporating solid solution hardening and modulus hardening originating from the difference in modulus between Al and clusters.