Knut Marthinsen

Modeling the evolution in microstructure and properties during plastic deformation of f.c.c.-metals and alloys – an approach towards a unified model

Abstract A new approach to the modeling of work hardening during plastic deformation of f.c.c.-metals and alloys has been recently proposed by the present authors. The model is based on a statistical approach to the problem of athermal storage of dislocations. By combining the solution for the dislocation storage problem with models for dynamic recovery of network dislocations and sub-boundary structures, a general internal state variable description is obtained. The model includes effects due to variations in: (i) stacking fault energy, (ii) grain size, (iii) solid solution content, and (iv) particle size and volume fraction. The result is a work hardening model, which in principle is capable of providing the stress–strain behavior for a given metal or solid solution alloy under condition ranging from deformation in the ambient temperature range to high temperature creep. It will be demonstrated that the model predictions, in terms of microstructure evolution and associated properties, in general, are in good agreement with experimental observations.

On the mechanisms of dynamic recovery

Abstract The annihilation of dislocations in dynamic recovery is analyzed in terms of reactions between mobile dislocations and dislocations stored in a Frank network. An extended model is presented comprising spontaneous dislocation collapse reactions and annihilation by dipole climb collapse.

Magnesium: Comparison of density functional theory calculations with electron and x-ray diffraction experiments

Accurate experimental structure factors for Mg have been measured and compared with density functional theory (DFT) to test some commonly used functionals and self-interaction correction (SIC) schemes. Low order structure factors, free of extinction and on absolute scale, were measured accurately by quantitative convergent beam electron diffraction. In addition, a complete set of structure factors up to sin θ/λ=1.6 A−1 was measured by x-ray diffraction at 10 K. The DFT calculations were performed using the full potential linearized augmented plane wave method. It was found that the agreement with experiment increases when going from the local density approximation (LDA) to the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhofer and further to the GGA of Engel and Vosko. Applying the SIC of Perdew and Zunger to the core states for LDA does not improve the agreement with theory, while applying the SIC of Lundin and Eriksson results in a significantly improved agreement. This implies that the main source of error in the LDA functional comes from the description of the core densities. Using the functional which agrees best with experiment, a non-nuclear maximum is established in the calculated electron density of beryllium but not of magnesium.Accurate experimental structure factors for Mg have been measured and compared with density functional theory (DFT) to test some commonly used functionals and self-interaction correction (SIC) schemes. Low order structure factors, free of extinction and on absolute scale, were measured accurately by quantitative convergent beam electron diffraction. In addition, a complete set of structure factors up to sin θ/λ=1.6 A−1 was measured by x-ray diffraction at 10 K. The DFT calculations were performed using the full potential linearized augmented plane wave method. It was found that the agreement with experiment increases when going from the local density approximation (LDA) to the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhofer and further to the GGA of Engel and Vosko. Applying the SIC of Perdew and Zunger to the core states for LDA does not improve the agreement with theory, while applying the SIC of Lundin and Eriksson results in a significantly improved agreement. This implies t...

HRTEM study of the effect of deformation on the early precipitation behaviour in an AA6060 Al–Mg–Si alloy

The effect of 10% pre-ageing deformation on the early precipitation behaviour in an AA6060 Al–Mg–Si alloy aged 10 min at 190°C was investigated by high-resolution transmission electron microscopy (HRTEM) in ⟨100⟩Al projections. The precipitate nucleation was heterogeneous since all precipitates were found to grow on dislocation lines. The pre-ageing deformation suppresses growth of Gunier–Preston zones and β″ phase. The resulting precipitates are still largely coherent with the aluminium matrix. They appear with two main morphologies; one consists of independent, small cross-sections arising from needles with disordered β′ and B′ structures. The other morphology is a much more continuous decoration where precipitates have elongated and conjoined cross-sections and where a particular precipitate phase could not be determined. All precipitates in this work were found to contain a common near-hexagonal sub-cell (SC) with projected bases a = b ≈ 0.4 nm. This strongly indicates that they are built over the same Si network, which recently has been demonstrated to exist in all precipitates in the Al–Mg–Si(–Cu) system. For the discrete morphology type the network has one hexagonal base vector parallel to or very near a ⟨510⟩Al direction. For the continuous type, one base vector falls along a ⟨100⟩Al direction. This orientation of the network is different from previous studies of ternary Al–Mg–Si alloys and must be a direct consequence of the deformation.

Extinction-free electron diffraction refinement of bonding in SrTiO3

Accurate low-order Fourier coefficients of the crystal potential of SrTiO(3) are measured by quantitative convergent-beam electron diffraction. The accuracy in the corresponding derived X-ray structure factors is about 0.1% for the strong low-order reflections (sin theta/lambda < 0.3 A(-1)). This accuracy is better than for conventional X-ray diffraction and equivalent to the accuracy of the X-ray Pendellosung method. Combination of these structure factors with high-order X-ray diffraction measurements allows accurate bonding information to be obtained from a multipole model fitted to the experimental data. It is shown that Ti-O has a covalent component and that the Sr-O bond is mainly ionic. The role of Ti 3d electrons in Ti-O bonding is also discussed.

Work Hardening Behaviour of Heat-Treatable Al-Mg-Si-Alloys

The work hardening of alloys hardened by precipitate heat treatments depends on the distribution of the precipitate sizes and the solute level left in the metal matrix. A mean field theory for precipitation is first applied for the ageing and subsequently it is coupled to a work hardening model to study the stress-strain responses of age hardened conditions of AA6xxx alloys. The predictions are compared to mechanical experiments and to TEM characterisations.

Modelling the evolution in microstructure and properties during processing of aluminium alloys

Abstract A new work-hardening model for f.c.c. metals and alloys has recently been developed [Prog. Mater. Sci. 41 (1998) 129; Mater. Sci. Forum 331–337 (2000) 1231; Mater. Sci. Technol., 17 (2001) 376–388; K. Marthinsen, E. Nes, K. Nord-Varhaug, B. Ronning, in: J.B. Bilde-Sorensen, et al. (Eds.), Proceedings of the 20th Riso International Symposium on Materials Science: Deformation-induced Microstructures, Analysis and Relation to Properties, Riso National Laboratory, Roskilde, Denmark, 1999, pp. 405–410; Mater. Sci. Eng., submitted for publication]. In the present work this model will be applied to the processing of aluminium alloys, covering conditions typical of both hot deformation (rolling and extrusion) and cold rolling, the emphasis, however, will be on hot deformation. Alloying effects due to solid solution (multi-component systems) as well as particles (constituent particles and dispersoids) will be considered.

A unified microstructural metal plasticity model applied in testing, processing, and forming of aluminium alloys

Abstract Over the last seven years a collection of models has been developed and put together by Nes, Marthinsen and coworkers in what here will be referred to as the Microstructure-based Metal Plasticity model, or in short as the MMP model. An overview of the most important modelling aspects will be given here. The basic mechanisms are related to the way the dislocations are stored and recovered in the lattice and how they affect the flow stress during deformation. The model at its current state is able to predict the microstructure evolution and the corresponding flow stress for the entire temperature range and for large strain rates as well as creep behaviour. The inherited processing-related quantities, such as grain size, solute content of alloying elements, and the texture, are taken into account, including a model for dynamic strain ageing. Anisotropy of the stress tensor is related mainly to the coupling to a texture model accounting for lattice rotations of the grains. However, a new and novel mo...

Factors affecting the strength of P{011}〈566〉-texture after annealing of a cold-rolled Al–Mn–Fe–Si alloy

Elongated coarse P{011}〈566〉-oriented grains are frequently observed after annealing of cold-rolled Al–Mn alloys with a highly supersaturated solid solution level. In this study, important factors affecting the strength of the P-texture component after annealing of a cold-rolled Al–Mn–Fe–Si alloy have been systematically investigated and their influence has been documented. The strength of the P-texture component has been analysed in terms of orientation distribution functions, area fractions and number fractions of P-grains at different conditions using EBSD. The strength of the P-texture is very sensitive to the microchemistry state in terms of the amount of Mn in solid solution (potential for concurrent precipitation) and pre-existing second-phase particles (dispersoids). In conditions of a significant P-texture, decreasing annealing temperature and heating rate, as well as increasing the amount of deformation before annealing, promotes a strengthening of the P-texture component. Detailed analyses clearly show that the strong P-texture is either due to a growth advantage of P-oriented grains at lower annealing temperatures or due to their dominating number fraction at higher temperatures. The differences in terms of P-texture intensity are explained in view of the influence of second-phase particles (dispersoids) on the recrystallization nucleation and growth behaviour.

The effect of boundary spacing on substructure strengthening

Abstract The subgrain size and the spacing of high angle boundaries are important parameters used to describe the microstructure in metals deformed to large strains. How the flow stress depends on the boundary spacing is discussed here and it is argued that the best way this is treated is in the work hardening model developed by Nes and co-workers (Progr. Mater. Sci., 1998, 41, 129 – 193; Mater. Sci. Tech., 2001, 17, 376 – 387; Mater. Sci. Eng., 2002, A 322, 176 – 193). The theoretical arguments given are supported by experimental observations.