Influence of ageing on the low cycle fatigue behaviour of an Al–Mg–Si alloy

Abstract

The low cycle fatigue (LCF) performance of AA6063 Al–Mg–Si alloy at under-aged (UA), peak-aged (PA) and over-aged (OA) conditions has been examined to understand the micromechanism of fatigue and the associated dynamic structural changes in this alloy. The LCF behaviour of the differently aged AA6063 alloys has been studied at strain amplitudes ranging between 0.2 and 1.0% under strain control mode. The UA state exhibits pronounced cyclic hardening unlike the PA and the OA states at strain amplitudes greater than 0.4%. The PA and the OA states show hardening only for a few cycles followed by prolonged softening. Characterisations of the micro- and the sub-structural alterations due to LCF establish that the phenomenon of dynamic precipitation results in cyclic hardening the UA alloy. The softening of PA alloy occurs due to shearing of precipitates and that in the OA alloy takes place owing to reversibility of slip by the formation and annihilation of the Orowan loops around the β (Mg₂Si) precipitates. Analyses of the hysteresis loops reveal Masing, nearly-Masing and non-Masing behaviour in the UA, OA and PA states, respectively. Analyses of the asymmetry factor of the hysteresis loops assist to infer that the Masing behaviour in the UA alloy is due to dislocation–dislocation interactions, whereas the nearly-Masing behaviour in the OA alloy and the non-Masing behaviour in the PA alloy are the consequence of varying degrees of dislocation–precipitate interactions associated with inhomogeneous deformation.     

Fatigue in precipitation hardened materials: a three-dimensional discrete dislocation dynamics modelling of the early cycles

Three-dimensional dislocation dynamics (DD) fatigue simulations in precipitation hardened metals is a major challenge in terms of numerical development. Several precipitate configurations have been investigated with an original treatment of precipitate–dislocation interactions and a parallelized DD code. In grains containing single-sized shearable particles (r _p?=?160?nm), strain is localized in clear bands where the precipitates are totally sheared-off. The fatigue behaviour involves an initial hardening followed by severe cyclic softening and significant surface slip irreversibility. In the presence of large single-sized particles (r _p?=?400?nm), the persistent slip band (PSB) structure is accompanied by highly reversible surface displacements. Slip dispersion originates from Orowan loops that have little effect on the mechanical response. The mechanical behaviour of a bimodal distribution is intermediate between the two above cases with the above microstructural features coexisting within the same grain. Unlike in the monomodal large-particle case, where all the particles retain their initial strength, some of the large particles of the bimodal distribution undergo a significant strength reduction.     

Discrete dislocation simulations of precipitation hardening in superalloys

The low-temperature yield stress of a nickel-based superalloy, containing up to 40% Ni₃A1 precipitates (γ′), is calculated by discrete dislocation simulations. A pair of screw or 60°(a/2) ?110? dislocation glides under external stress across a {111} plane of γ phase, intersected by a random distribution of either spherical or cubic γ′ precipitates. The stress is raised until the dislocations can cut or bow round all the obstacles. In this paper the emphasis is on the cutting regime which is prevalent when the precipitates are small and/or have low antiphase-boundary (APB) energies. From a large number of simulations in the cutting regime, the effects of size, shape, volume fraction and APB energy are found to be as follows: The yield stress is proportional to the square root of the volume fraction of γ′. The yield stress depends weakly on the precipitate size in the size range 20–400?nm, for APB energies of 150, 250 and 320?mJ?m^?2. The yield stress depends linearly on the APB energy for APB energies up to 320?mJ?m^?2 in the size range 50–200?nm. At a precipitate size of 100?nm, cubes are weaker obstacles than equivalent spheres by about 25% for an APB energy of 320?mJ?m^?2; however, the shape effect on strengthening decreases with decreasing APB energy and decreasing precipitate size. When a coherency stress (from a lattice parameter mismatch of 0.3%) is added, the yield stress increases by about 10%. When solid-solution strenthening is added, it is potent when the solute is in the γ matrix, but much less potent when the solute is in γ′. When the γ′ precipitates are larger than 400?nm across and the APB energy greater than 250?mJ?m^?2, significant Orowan looping occurs. The yield stress drops inversely as the precipitate size and becomes insensitive to the APB energy but sensitive to the shear modulus. Many of these results from the full simulations differ from the analytical models of strengthening in superalloys but they can be rationalized from the results of simulations on simple homogenized precipitate structures.     

Precipitation in solution-treated aluminium–4 wt% copper under cyclic strain

Solution-treated Al–4 wt% Cu was strain-cycled at ambient temperature and above, and the precipitation and deformation behaviours investigated by TEM. Anomalously rapid growth of precipitates appears to have been facilitated by a vacancy super-saturation generated by cyclic strain and the presence of continually refreshed dislocation density to provide heterogeneous nucleation sites. Crystallographic texture appears to be responsible for latent hardening in specimens tested at room temperature. Increasing temperatures lead to a gradual hardening throughout life due to precipitation. Specimens machined at 45° from the rolling direction, which exhibit rapid precipitation hardening, show greater texture hardening due to increased axial stress required to cut precipitates in specimens. In the temperature range 100–200°C, precipitation of Θ″ is suppressed by cyclic strain, and precipitation of Θ′ promoted. The rapid growth of precipitates generated by cyclic strain operates with diminishing effect at higher temperatures due to faster recovery of non-equilibrium vacancy concentrations. Θ′ precipitates generated under cyclic strain are smaller and more finely dispersed than those produced via quench-ageing due to heterogeneous nucleation on dislocations and possess a low aspect ratio and rounded edges of the broad faces caused by the introduction of ledges into the growing precipitates by dislocation cutting. Frequency effects indicate that dislocation action is responsible for the observed reduction in aspect ratio. Accelerated formation of grain-boundary precipitates appears partially responsible for rapid inter-granular fatigue failure at elevated temperatures, resulting in coexistent fatigue striations and ductile dimples on the fracture surface.     

Scanning transmission electron microscopy investigation of an Al–Mg–Si–Ge–Cu alloy

Precipitation in a Mg-rich Al–Mg–Si–Ge–Cu alloy was investigated using aberration-corrected high-angle annular dark-field scanning transmission electron microscopy. The precipitates were needle or lath shaped with the longest dimension parallel to ?001?_Al. The precipitates had no repeating unit cell when viewed along this direction. However, the precipitate structure in projection consisted of a hexagonal network of mixed Si and Ge columns, with Mg, Al, and Cu columns occupying specific sites in between the network columns. The Cu columns appeared with the same local arrangement of atomic columns as in Al–Mg–Si–Cu precipitates, and the Cu-free regions consisted of structural units with Mg and Al at specific sites. These structural units were often arranged in a locally ordered fashion, and in some cases the projected structure possessed and overall point symmetry. The amount of strain on the surrounding matrix was found to vary depending on the width of the precipitate cross section.     

A method to predict the orientation relationship,interface planes and morphology between a crystalline precipitate and matrix. Part I. Approach

A model based on the near-coincidence of diffraction intensity weighted reciprocal-lattice spots is proposed to determine preferred orientation relationships between two crystalline phases. The preferred orientation is found by minimizing the three-dimensional lattice mismatch, i.e. by maximizing the total overlapping intensity, between the diffraction spots of two crystals. The procedure is biased towards matching reciprocal lattice sites with high structure-factor values, which is physically equivalent to matching planes of high atomic density. In contrast to previous reciprocal-lattice models, including the diffraction intensity in the present method makes it sensitive to the types of atoms in (chemistry of) crystals. The preferred orientation relationship is then used to identify the orientations of low-energy interfaces using a Δ g approach. A Voronoi (or Wigner–Seitz) construction based on the Δ g values is further used to qualitatively estimate the equilibrium shape of the precipitate in the matrix. The model was tested by performing calculations on hypothetical Au–Cu crystals to investigate the effects of chemistry and fcc truncated-octahedral precipitates in fcc matrices in Al–Ag, Al–Xe and Al–Pb alloys. The present model has the ability to sample the entire orientation space and rationalize and compare alternate orientation relationships in a reasonable timeframe, thereby providing insight into the formation of precipitate orientation relationships and shapes.     

Anomalous mechanical characteristics of Au/Cu nanocomposite processed by Cu electroplating

An Au/Cu nanocomposite is produced by electroplating Cu on a nanoporous Au, and its mechanical characteristics are investigated by hardness tests. The Au/Cu nanocomposite showed a lower hardness and a lower elastic modulus than the nanoporous Au. Furthermore, annealing caused the nanocomposite to harden twice. Large lattice strains in the Au lattice for the nanocomposite were observed by high-resolution transmission electron microscopy. Also, first-principle calculations showed that lattice strains induce the decreased elastic modulus. Therefore, both the inverse mixing behaviour and the hardening via annealing are suggested to be related to the large lattice strains.     

Prediction of flow stress and textures of AZ31 magnesium alloy at elevated temperature

The viscoplastic behaviour of magnesium alloys at high temperatures leads to highly temperature-dependent mechanical properties. While at high strain rates a notable strain hardening response is observed, at low strain rates the material shows a smooth plastic response with negligible amount of hardening. This complicated behaviour is due to different deformation mechanisms that are active at different strain rate regimes, resulting in different strain rate sensitivity parameters. In this study we show, by utilizing both numerical simulations and experiments, that this behaviour can be predicted by a model that combines two deformation mechanisms, grain boundary sliding mechanism and dislocation glide mechanism. We discuss the importance of each deformation mechanism at different strain rate regimes based on the findings of modelling and experimental results for AZ3 magnesium alloy. By developing a model that includes the above-mentioned two deformation mechanism, the prediction of flow properties is expanded to a wide range of strain rate regimes compared to previous study. The obtained numerical findings for the stress–strain behaviour as well as texture evolution show good agreement with the experimental results.     

Precipitate characterisation in metallic systems by small-angle X-ray or neutron scattering

Small-angle scattering enables the extraction of precise, quantitative information about nano-scale precipitate microstructures. It can be used with X-rays (SAXS) or neutrons (SANS). This paper presents simple methods for extracting information on the precipitate size and volume fraction from SAS spectra. The various possibilities for obtaining precipitate size are reviewed, and the meaning of their differences is discussed. Examples of applications for complex precipitate microstructure measurements are given in the following areas: kinetic in-situ measurements in Fe–Cu and Fe–Nb–C alloys, non-stoichiometric precipitation in an Al–Zn–Mg–Cu alloy studied by anomalous SAXS (ASAXS), and precipitation mapping in weld cross-sections.     

A multiscale gradient-dependent plasticity model for size effects

The mechanical behaviour of polycrystalline material is closely correlated to grain size. In this study, we investigate the size-dependent phenomenon in multi-phase steels using a continuum dislocation dynamic model coupled with viscoplastic self-consistent model. We developed a dislocation-based strain gradient plasticity model and a stress gradient plasticity model, as well as a combined model, resulting in a theory that can predict size effect over a wide range of length scales. Results show that strain gradient plasticity and stress gradient plasticity are complementary rather than competing theories. The stress gradient model is dominant at the initial strain stage, and is much more effective for predicting yield strength than the strain gradient model. For larger deformations, the strain gradient model is dominant and more effective for predicting size-dependent hardening. The numerical results are compared with experimental data and it is found that they have the same trend for the yield stress. Furthermore, the effect of dislocation density at different strain stages is investigated, and the findings show that the Hall–Petch relation holds for the initial strain stage and breaks down for higher strain levels. Finally, a power law to describe the size effect and the transition zone between the strain gradient and stress gradient dominated regions is developed.     

Effects of internal stresses and intermediate phases on the coarsening of coherent precipitates: A phase-field study

Phase stability, topology and size evolution of precipitates are important factors in determining the mechanical properties of crystalline materials. In this article, the Cahn-Hilliard type of phase-field model was coupled to elasticity equations within a mixed-order Galerkin finite element framework to study the coarsening morphology of coherent precipitates. The effects of capillarity, particle size and fraction, compositional strain, and inhomogeneous elasticity on the kinetics and kinematics of coherent precipitates in a binary dual phase crystal admitting a third intermediate stable/meta-stable phase were investigated. The results demonstrated the ability of the model to simulate coarsening under the concomitant action of Ostwald ripening and mismatch elastic strain mechanisms. Using a phenomenological coarsening power law, coarsening rates were determined to depend on precipitate size and volume fraction, compositional strain, and strain mismatch between precipitates and the matrix. Results also showed that the necking incubation time between two neighboring precipitates depends inversely on the precipitate’s initial sizes; however, under fixed volume fraction of precipitates, any increase in the initial sizes of the precipitates mitigates the coarsening. Meanwhile, the compositional strain and the growth of the intermediate stable/meta-stable phase leads to substantial enhancements of precipitate coarsening.     

Multiscale modeling of precipitate microstructure evolution

We demonstrate how three "state-of-the-art" techniques may be combined to build a bridge between atomistics and microstructure: (1) first-principles calculations, (2) a mixed-space cluster expansion approach, and (3) the diffuse-interface phase-field model. The first two methods are used to construct the driving forces for a phase-field microstructural model of theta'- Al2Cu precipitates in Al: bulk, interfacial, and elastic energies. This multiscale approach allows one to isolate the physical effects responsible for precipitate microstructure evolution.     

The maximum precipitate density

The Kampmann and Wagner mathematical model of precipitation kinetics is used to investigate the dependence of the maximum precipitate density on precipitation parameters. For the Cu-rich Cu–Co system, a relationship is derived that allows the precipitate/matrix interfacial free energy and the density of nucleation sites to be deduced from measurements of the maximum precipitate density. This relationship is shown to agree very well with published experimental data. A criterion for assessing the suitability of experimental data for analysis by our relationship is proposed and is tested on the available results.     

A phase-field model for elastically anisotropic polycrystalline binary solid solutions

A phase-field model for modeling the diffusional processes in an elastically anisotropic polycrystalline binary solid solution is described. The elastic interactions due to coherency elastic strain are incorporated by solving the mechanical equilibrium equation using an iterative-perturbation scheme taking into account elastic modulus inhomogeneity stemming from different grain orientations. We studied the precipitate interactions among precipitates across a grain boundary and grain boundary segregation–precipitate interactions. It was shown that the local pressure field from one coherent precipitate influences the shape of precipitates in other grains. The local pressure distribution due to primary coherent precipitates near the grain boundary leads to inhomogeneous solute distribution along the grain boundary, resulting in non-uniform distribution of secondary nuclei at the grain boundary.     

Phase-field study for the splitting behaviour of precipitate under applied stress

This paper employs the phase-field method to study the splitting behaviour of a single coherent particle under an applied uniaxiai stress. It finds that the splitting behaviour is greatly influenced by the initial shape of precipitates, the bulk free energy condition, the degree of supersaturation and the ratio of the interfacial energy to the elastic strain energy, etc. The simulated results demonstrate that the aspect ratio of the particle determines whether the splitting can occur and how many split plates can be obtained. The splitting of particle is sensitive to the interracial energy, i.e. the splitting becomes more and more difficult with increasing the ratio of the interracial energy to the elastic strain energy. And increasing the magnitude of the applied stress is favourable to the splitting. The splitting process is also explained from the point of view of the corresponding diffusion potential.     

Strain Directed Assembly of Nanoparticle Arrays Within a Semiconductor

The use of strain to direct the assembly of nanoparticle arrays in a semiconductor is investigated experimentally and theoretically. The process uses crystal strain produced by a surface structure and variations in layer composition to guide the formation of arsenic precipitates in a GaAs-based structure grown at low temperature by molecular beam epitaxy. Remarkable patterning effects, including the formation of single and double one-dimensional arrays with completely clear fields are achieved for particles in the 10-nm size regime at a depth of about 50-nm from the semiconductor surface. Experimental results on the time dependence of the strain patterning indicates that strain controls the late stage of the coarsening process, rather than the precipitate nucleation. Comparison of the observed particle distributions with theoretical calculations of the stress and strain distributions reveals that the precipitates form in regions of maximum strain energy, rather than near extremum points of hydrostatic stress or dilatation strain. It is therefore concluded that the patterning results from modulus differences between the particle and matrix materials rather than from other strain related effects. The results presented here should be useful for extending strain directed assembly to other materials systems and to other configurations of particles.     

High-resolution transmission electron microscopy and tomographic atom probe studies of the hardening precipitation in an Al–Cu–Mg alloy

The hardening precipitation of an Al–Cu–Mg aluminium alloy designed for aeronautics was investigated using high-resolution transmission electron microscopy (HREM) and tomographic atom probe techniques. The observed precipitates clearly belong either to the Guinier–Preston–Bagaryatskii (GPB) zones type or to the so-called S-Al₂CuMg precipitation. We analysed a large number of precipitates in order to obtain statistical information on the precipitation. We focused on the structural and/or chemical composition of the different precipitates. It was found, in particular, that the very numerous GPB zones do not present a single chemical composition. Evidence is also given for the presence of two different kinds of S-precipitate/matrix orientation relationships, strongly linked to the morphology of the precipitate. The structure of the S precipitates was confirmed by direct comparison with simulated HREM images. Particular attention was paid to the nature of the S-precipitate/matrix interfaces.     

Precipitation and solute distribution in an interrupted-aged Al–Mg–Si–Cu alloy

Quantitative analysis of the precipitate species and solute distribution was carried out on Al–Mg–Si–Cu alloy 6061 aged to peak hardness using a conventional T6 heat treatment and the so-called T6I6 heat treatments. In this latter, a dwell period at reduced temperature (65°C) is introduced into the T6 ageing cycle (at 177°C or 150°C) which modifies the microstructure and results in the simultaneous improvement of both tensile properties and fracture toughness. Analysis of three-dimensional atom probe data reveals that the superior mechanical properties of the T6I6/177 temper are achieved by a combined effect of a greater consumption of solute atoms by precipitates, an increased number density of fine precipitates and the presence of greater fractions of the effective strengthening precipitates in the final microstructure. Three types of precipitates were found to be characteristic of the peak aged conditions: β′′ precipitates, Guinier–Preston zones and Mg–Si(–Cu) co-clusters. The composition of the strengthening precipitates was found to vary over a wide range for the different heat treatment schedules, corresponding to a variation in the number density of stable nuclei, without any accompanying change in their morphology. All precipitates were found to contain substantial quantities of aluminium. The results also indicate that the strengthening precipitates are preferentially formed from Si-rich nuclei that contain Cu atoms, as opposed to Cu-free nuclei.     

Atomistic multiscale simulations on the anisotropic tensile behaviour of copper-alloyed alpha-iron at different states of thermal ageing

The mechanical behaviour of steels is strongly related to their underlying atomistic structures which evolve during thermal treatment. Cu-alloyed α-Fe undergoes a change in material behaviour during the ageing process, especially at temperatures of above 300°C, where precipitates form on a large time-scale within the α-Fe matrix, yielding first a precipitation strengthening of the material. As the precipitates grow further in time, the material strength decreases again. This complex process is modelled with a multiscale approach, combining Kinetic Monte Carlo (KMC) with Molecular Dynamics (MD) simulations in a sequential way and exploiting the advantages of both methods while simultaneously circumventing their particular disadvantages. The formation of precipitates is modelled on a single-crystal lattice with a diffusion based KMC approach. Transferring selected precipitation states at different ageing times to MD simulations allows the performance of nano tensile tests and the analysis of failure initiation. The anisotropic tensile behaviour is investigated in the [100], [110] and [111] directions, showing monotonically decreasing tensile strengths and deformation strains. Hence precipitation strengthening is mainly due to dislocation–precipitate interactions which are non-existent at small tensile loadings in this scenario. At the point of ductile failure, dislocations are generated at the interfaces between precipitates and the Fe matrix. Straining in the [100] direction, they lie on {110} and {112} glide planes, as expected. With the method presented here, the changes of the anisotropic tensile moduli are related to different states of thermal ageing, i.e., to nucleation, growth and Ostwald ripening of Cu precipitates.     

Aberration-corrected HAADF-STEM investigations of precipitate structures in Al–Mg–Si alloys with low Cu additions

Precipitates in a lean Al–Mg–Si alloy with low Cu addition (~0.10 wt.%) were investigated by aberration-corrected high angle annular dark field scanning transmission electron microscopy (HAADF-STEM). Most precipitates were found to be disordered on the generally ordered network of Si atomic columns which is common for the metastable precipitate structures. Fragments of known metastable precipitates in the Al–Mg–Si–(Cu) alloy system are found in the disordered precipitates. It was revealed that the disordered precipitates arise as a consequence of coexistence of the Si-network. Cu atomic columns are observed to either in-between the Si-network or replacing a Si-network column. In both cases, Cu is the center in a three-fold rotational symmetry on the Si-network. Parts of unit cells of Q′ phase were observed in the ends of a string-type precipitates known to extend along dislocation lines. It is suggested that the string-types form by a growth as extension of the B′/Q′ precipitates initially nucleated along dislocation lines. Alternating Mg and Si columns form a well-ordered interface structure in the disordered Q′ precipitate. It is identical to the interface of the Q′ parts in the string-type precipitate.