Ø. Grong

Modelling of the age hardening behaviour of Al-Mg-Si alloys

Abstract In the present investigation a special control volume formulation of the classical precipitation model for coupled nucleation, growth and coarsening has been adopted to describe the evolution of the particle size distribution with time during thermal processing of Al–Mg–Si alloys. The analysis includes both isothermal and non-isothermal transformation behaviour. Well established dislocation theory is then used to evaluate the resulting change in hardness or yield strength at room temperature, based on a consideration of the intrinsic resistance to dislocation motion due to solute atoms and particles, respectively following heat treatment. The model is validated by comparison with experimental microstructure data obtained from transmission electron microscope examinations and hardness measurements, covering a broad range in the experimental conditions. It is concluded that the model is sufficiently relevant and comprehensive to be used as a tool for predicting the response of Al–Mg–Si alloys to thermal processing, and some examples are given towards the end.

Modelling of non-isothermal transformations in alloys containing a particle distribution

Abstract A framework for modelling coupled nucleation, growth and coarsening in diluted alloys is presented, based on the method of finite differences. According to the assumptions, the particle distribution is divided into a series of discrete size classes, each represented by a control volume. By applying a standard procedure for discretization of the governing evolution equation, the flux of particles in and out of the control volumes can be calculated at each time step during thermal cycling. The essential features of the model are illustrated in various numerical examples and case studies, where the memory of a past process step is likely to have an effect on the overall transformation behaviour. These include simulation of up-quenching and linear heating of age hardening Al–Mg–Si alloys under idealized conditions, assuming spherical particles with uniform thermodynamic properties.

Microstructural modelling in metals processing

Abstract Modelling of microstructure evolution has long been part of physical metallurgy, both in the laboratory and in industry. Until recently, however, physically-based modelling was limited to idealised alloys under controlled laboratory conditions, while the complexity of industrial processing of commercial alloys necessitated empirical approaches. The advent of powerful computing facilities, and in particular the rapid growth in application of the finite element method to metals processing, has stimulated new research with the aim of bringing the two areas together. The present review describes progress in this rapidly expanding field. The preliminary review in Section 1 illustrates the potential of integrating microstructural modelling with the very detailed process histories which are available from modern finite element analyses. The ‘internal state variable’ approach is identified as a particularly appropriate method to reach the objective of providing useful predictive capability in industrial processing, within the scope of personal computers. The general method, and its simplification for single parameter models in which the microstructure evolution may be treated as an ‘isokinetic’ reaction, are outlined in Section 2 . The paper then presents internal state variable formulations for a range of thermal problems, as temperature-controlled processes dominate. These are solid-state diffusional transformations (precipitate dissolution, nucleation and growth, and coarsening) in Section 3 ; solidification and subsequent solid-state phase transformations in Section 4 ; and grain growth in Section 5 . Case studies are presented for each problem, illustrating the applicability of the approach to industrially relevant processing of commercial alloys. Examples range from casting, to cooling after hot forming, to heat treatment and welding. Bringing together this range of phenomena and processes in one review makes two specific points: (a) the state variable formulation offers a robust modelling framework, in which real non-isothermal process histories may be readily linked to fundamental isothermal theories of microstructure evolution, (b) depending on the problem, different levels of approximation can be accepted without invalidating the results, but the modeller needs to exercise critical judgement to find the optimum level of complexity. Finally in Section 6 , a number of examples are presented in which state variable models have been fully integrated with finite element analyses, with two examples from welding and one from casting. These case studies demonstrate that significant opportunities now exist for enhancing industrial processing capabilities. At the same time, the underlying microstructural modelling provides a renewed stimulus for improving scientific understanding of some of the classical problems of physical metallurgy.

Modelling of precipitation reactions in industrial processing

Abstract The present investigation is concerned with modelling of diffusion-controlled precipitation reactions in industrial processing, with particular emphasis on heat treatment. In the first part of the paper the components of the model are outlined and constitutive equations presented which allow the fraction transformed to be calculated as a function of time and temperature. The model uses a combination of chemical thermodynamics and kinetic theory to describe the microstructure evolution, with the particular feature of writing the Avrami equation in a differential form. In general, the solution of the differential equation requires stepwise integration in temperature-time space over a predetermined thermal cycle, but the mathematical treatment can largely be simplified if the additivity condition pertaining to an isokinetic reaction is satisfied. The theory is thus generic in the sense that it can be adopted to a wide spectrum of materials and heat treatment conditions, ranging from low and high alloy steels to aluminium alloys. In the second part of the paper this formalism has been applied to describe the quench sensitivity of AA6082 extrusions. The process model takes into account the thermal history of the base material and allows calculation of the peak strength following artificial ageing for a wide range of cooling conditions. The results show that the peak strength is both a function of the alloy composition, the homogenizing conditions and the cooling rate through the critical temperature range for β′-Mg 2 Si precipitation, in agreement with general experience. It is concluded that the existing theoretical framework is sufficiently comprehensive to serve as a tool for alloy design and optimization of cooling schedules for AlMgSi extrusions and an illustration of this is given towards the end of the paper.

Effect of scandium and titanium-boron on grain refinement and hot cracking of aluminium alloy 7108

AbstractThe effect of scandium and titanium–boron (Tibor) additions on the solidification behaviour of castings and welds of aluminium alloy 7108 has been investigated. A circular patch test was adopted to evaluate the effects of these elements on the hot cracking suscepti bility of welds made on cast coupons treated with different grain refiner additions. It was observed that grain size, as well as cracking susceptibility, decreased with increasing amounts of scandium and that hot cracking was completely eliminated at scandium additions above 0·25 wt-%. A more pronounced grain refining effect in welds was observed with Tibor and, in addition, no hot cracking was observed with Tibor additions as low as 0·02 wt-%Ti (0·004 wt-%B). Castings, however, were more effectively grain refined with scandium, achieving a finer grain size than with Tibor.

Additivity and isokinetic behaviour in relation to diffusion controlled growth

Additivity and isokinetic behaviour in relation to transformations that involve coupled nucleation and growth have been examined. As a starting point, a numerical solution is presented which takes into account the independent variations of the nucleation and growth rate with temperature and matrix solute content. This solution is later used to check the validity of two analytical models, based on the internal state variable approach and the Avrami equation, respectively. It is concluded that the analytical solutions provide an approximate but adequate description of the overall transformation behaviour during continuous cooling. The latter is particularly true if the evolution equations are calibrated against experimental microstructure data, as frequently done in high-hierarchy models for process simulation.

Additivity and isokinetic behaviour in relation to particle dissolution

Additivity and isokinetic behaviour in relation to particle dissolution have been examined. As a starting point, the analytical time dependent solutions for dissolution of plate-like and spherical precipitates in an infinite matrix have been manipulated and rewritten in a state variable form. The validity of these solutions during continuous heating and cooling is then checked against more exact numerical calculations based on the control volume approach. It is concluded that the state variable formulation, which represents an extension of the isokinetic concept, provides an adequate description of the dissolution process under conditions where these solutions are valid, except in cases where back diffusion leads to transient particle growth. This phenomenon is mainly associated with plate-like precipitates, and has its origin in the development of a negative concentration gradient at the particle/matrix interface during cooling because of a sluggish transport of solute away from the interface and into the adjacent matrix.

Mechanisms of inclusion formation in low alloy steels deoxidised with titanium

Abstract In the present investigation, the conditions for inclusion formation in two Ti deoxidised steels and one Al–Ca deoxidised steel have been examined by means of optical and electron microscopy, in combination with a thermo dynamic analysis of the phase relations involved. It is concluded that the Ti containing inclusions form as a result of a series of reactions occurring in the ladle, during solidification and in the solid state. The important solid state reaction products are MnS, TiN, and MnOTiO2 . The presence of Mn rich compounds at the surface of the inclusions is consistent with the observation of a Mn depleted zone in the surrounding steel matrix. In contrast, the primary inclusions in the Al–Ca deoxidised steel are complex oxysulphides, which are thermodynamically more stable and can therefore form in the liquid state.

High-Temperature Oxidation of Iron and the Decay of Wüstite Studied with in situ ESEM

The oxidation of iron at elevated temperature in pure oxygen and water vapor and the decomposition of wüstite were studied in situ with environmental scanning-electron microscopy (ESEM). Depending on the type of gas atmosphere, iron formed either a porous multi-layer oxide scale with additional growth of oxide whiskers or a compact wüstite scale. The oxidation mechanism of iron is referred to and the results are reviewed on the basis of the available literature. The disintegration of the wüstite scale is followed in situ during cooling in an oxidizing environment. The disproportionation reaction and the observed development of an additional scale morphology is seen to arise from mechanical stresses and nucleation reactions. These results highlight the advantages of in situ techniques.

Factors affecting initiation of pitting corrosion in super martensitic stainless steel weldments

Abstract In the present investigation optical microscopy, in combination with sputtered neutral mass spectrometry (SNMS), has been used to examine the conditions for initiation of pitting corrosion in the heat affected zone (HAZ) of two super martensitic (SM) stainless steel weldments. It is shown that the corrosion resistance depends mainly on the nature of the surface oxide, as determined by the oxygen potential in the shielding gas and the HAZ temperature–time relationship, and less strongly on the underlying microstructure. In the absence of H2S the initiation is associated with spalling of the iron enriched chromium oxide within a narrow region approximately 6 mm from the fusion line, where the contaminated oxide layer is thinnest. As H2S is introduced, the region close to the fusion boundary becomes susceptible to localised corrosion because of the more extensive metal oxidation. Thus, the high temperature oxidation and iron oxide scale formation accompanying the welding operation appear to be the main factors affecting pitting corrosion initiation in SM stainless steel weldments.