Characterisation of dynamic recrystallisation in nickel using processing map for hot deformation

Abstract

The hot deformation behaviour of polycrystalline nickel has been characterised in the temperature range 750–1200°C and strain rate range 0·0003–100 s^?1 using processing maps developed on the basis of the dynamic materials model. The efficiency of power dissipation, given by [2m/(m+1)], where m is the strain rate sensitivity, is plotted as a function of temperature and strain rate to obtain a processing map. A domain of dynamic recrystallisation has been identified, with a peak efficiency of 31% occurring at 925°C and 1 s^?1. The published results are in agreement with the predictions of the processing map. The variations of efficiency of power dissipation with temperature and strain rate in the dynamic recrystallisation domain are identical to the corresponding variations of hot ductility. The stress–strain curves exhibited a single peak in the dynamic recrystallisation domain, whereas multiple peaks and ‘drooping’ stress–strain curves were observed at lower and higher strain rates, respectively. The results are explained on the basis of a simple model which considers dynamic recrystallisation in terms of rates of interface formation (nucleation) and migration (growth). It is shown that dynamic recrystallisation in nickel is controlled by the rate of nucleation, which is slower than the rate of migration. The rate of nucleation itself depends on the process of thermal recovery by climb, which in turn depends on self-diffusion.

MST/1524     

Dislocation density in carbonyl nickel during sintering

Three different size fractions of carbonyl nickel powder were sintered for 2 h at temperatures of 300 to 940° C. In addition to linear shrinkage measurements, the internal structures of the specimens were examined with X-ray line broadening and in some cases with TEM. The shrinkage of the different fractions was compared with the calculated dislocation densities. The results show that dislocations which originate from the production process are rearranged during the presintering process and are annihilated in a normal coarse powder at the very beginning of the sintering process. Only when the sintering particles are of micron-size or less, do dislocations remain during the sintering process, making it possible for them to contribute to the material transport. The mechanisms by which dislocations can do this are discussed in this paper.     

Superplasticity in a magnesium alloy prepared with bimodal grain size distributions developed by dynamic recrystallisation

In the present work the influence of bimodal grain size distributions on superplastic behavior, of a magnesium alloy, was investigated. Samples with different volume fraction of fine grains have been prepared, and their strain rate-stress relation during superplasticity has been measured. Additionally, the predictions of two deformation models, based on the isostrain and the isostress conditions, were compared with the experimental data. The isostrain model allows the major experimental observations to be readily explained and predicted.     

Linear-non-linear dynamic substructures

The dynamic substructure method is extended to linear and non-linear coupling systems. Only those master co-ordinates with non-linear nature (non-linear co-ordinates) are retained. Other slave co-ordinates relating to the linear part (linear co-ordinates) are eliminated by the dynamic substructure method. The dynamic flexibility matrix associated with the linear co-ordinates is first expanded in terms of the fixed interface natural modes. The condensed dynamic stiffness-matrix associated with the non-linear co-ordinates is formed subsequently. The convergence of the condensed dynamic stiffness matrix with respect to the natural modes can be improved by means of matrix manipulations and Taylor series expansion. To find the steady state solutions, the non-linear responses are expanded into a Fourier series. Responses of the linear co-ordinates are related to the non-linear co-ordinates analytically. To solve for the unknown Fourier coefficients, the harmonic balance method gives a set of non-linear algebraic equations relating the vibrating frequency and the nodal displacement coefficients. A Newtonian algorithm is adopted to solve for the unknown Fourier coefficients iteratively. The computational cost of a non-linear analysis depends heavily on the number of degrees of freedom encountered. In the method, the number of degrees of freedom is kept to a minimum and the computational cost is greatly reduced.     

Multilevel dynamic substructures

The dynamic substructure method is extended to multilevel (recursive) substructures. The obvious distinction of the two approaches is that the stiffness and mass matrices before condensation are no longer frequency independent. The dynamic stiffness matrix at any substructure level is proved to be a function of the vibrating frequency in terms of some constant matrices which are derivable from the dynamic stiffness matrix at one lower substructure level. The method can accurately predict more modes than the number of degrees of freedom retained. The computational procedure, the generalized inverse iteration, the stationary principle of the system natural frequency and the generalized Rayleigh's quotient are derived for the frequency dependent matrices. Numerical examples are given to illustrate some engineering applications. A transcendental dynamic stiffness matrix can be transformed to a more convenient algebraic form by the present method.     

Damped dynamic substructures

The dynamic substructure method is extended to lightly or heavily damped systems. Both internal and external dampings are considered. The damped dynamic flexibility associated with the slave co-ordinates is first expanded in terms of the damped fixed interface natural modes and the condensed dynamic stiffness associated with the master co-ordinates is formed subsequently. The convergence of the condensed dynamic stiffness with respect to the damped natural modes can be improved by means of the static matrices. Since the dynamic stiffness method is equivalent to the modal synthesis method, the component mode method and Kron's method, the theory presented here is readily applicable to these methods are restricted to symmetric damping matrices.     

Non-conservative dynamic substructures

The dynamic substructure method is extended to non-conservative systems. The substructure fixed-interface flexibility is expressed in its natural modes. The formulation includes conservative and dissipative systems as special cases. To accelerate the convergence with respect to the partial modes, the flexibility is separated into modal contributing and static contributing parts. Inverse iteration is used to find the non-defective systemmodes. The parameters which make the system matrix defective are determined by the Newtonian algorithm and the derivatives of determinants are given explicitly     

Directional recrystallisation in nickel based high temperature alloy

Abstract

The directional recrystallisation during zone annealing of a nickel alloy intended for high temperature use has been investigated. The material was processed from powder, by extrusion and rolling, to produce sheet. Zone annealing of that material led to a very coarse, directional grain structure with a distinctly different preferred orientation to that of the rolled and primary recrystallised material. There was no correlation between the preferred orientations of the large grains and their growth directions. The textures were related by a transformation close to that characteristic of a ∑5 coincident site lattice. It is possible that this represents a rapid growth relationship in the case where the growth is controlled by the dissolution of the coherent γ′ precipitate.

MST/3436     

Dynamic recrystallisation and dynamic precipitation in AA6061 aluminium alloy during hot deformation

Abstract

Deformation behaviour of AA6061 alloy was investigated using uniaxial compression tests at temperatures from 400 to 500°C and strain rates from 0·01 to 1 s^?1. Stress increases to a peak value, then decreases monotonically until reaching a steady state. The dependence of stress on temperature and strain rate was fitted to a sinh-Arrhenius equation and characterised by the Zener–Hollomon parameter with apparent activation energy of 208·3 kJ mol^?1. Grain orientation spread analysis by electron backscattered diffraction indicated dynamic recovery and geometrical dynamic recrystallisation during hot compression. Deformation at a faster strain rate at a given temperature led to finer subgrains, resulting in higher strength. Dynamic precipitation took place concurrently and was strongly dependent on temperature. Precipitation of Q phase was found in the sample deformed at 400°C but none at 500°C. A larger volume fraction of precipitates was observed when samples were compressed at 400°C than at 500°C.     

Evolution of dynamic recrystallisation in AISI 304 stainless steel

Abstract

The nucleation and development of dynamic recrystallisation (DRX) has been studied via hot torsion testing of AISI 304 stainless steel. The DRX behaviour was investigated with microstructural analysis and slope changes of flow stress curves. The characteristics of serrated grain boundaries observed by SEM, electron backscattered diffraction and TEM indicated that the nucleated DRX grain size was similar to that of the bulged part of the original grain boundary. The DRX of the alloy was nucleated and developed by strain induced grain boundary migration and by the necklace mechanism. Before the steady state in the flow curve at 1000 ° C and 0.5 s^-1, the dynamically recrystallised grains did not remain a constant size and gradually grew to the size of fully DRX grains at steady state (30 μm). The calculation of the grain size was based on X _DRX (volume fraction of dynamically recrystallisation) under the assumption that the nucleated DRX grains grow to the steady state continuously. It was found that the calculated grain size of the alloy was good agreement with that of the observed grain size. It is expected that a fine grained steel can be obtained by controlling hot deformation conditions on the basis of newly developed equations for predicting DRX behaviour.     

Experimental investigations into Kinetics of recrystallisation of cold rolled nickel

Abstract

The kinetics of recrystallisation of cold rolled nickel (99.98% purity) have been investigated by means of in situ heating in a scanning electron microscope and quantitative post-mortem metallographic examinations as well as microhardness measurements. The specimens were deformed over a wide range of deformation ratio (ε = 0.25–1.12) and isothermally annealed at 455°C. The Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory has been tested, and it has beenfound that measured JMAK exponents (n = 1.3–2.1) are lower than those predicted theoretically and are strongly dependent on deformation ratio. Therefore, it is confirmed that the JMAK theory fails to apply to the recrystallisation of plastically deformed nickel. Two hypotheses, competition between recovery and recrystallisation and non-random distribution of nucleation sites, are discussed to explain the low values of the JMAK exponent.     

Dislocation structures in cyclically deformed nickel polycrystals

The effect of the grain orientation and the plastic strain amplitude _pa on the saturated dislocation structure was studied on individual grains of cyclically deformed nickel polycrystals by means of scanning electron microscopy using the electron back scattering pattern technique and the channelling contrast of back scattered electrons. The main features of the dislocation configuration in a grain were found to be essentially determined by the crystallographic axial orientation of the grain. A labyrinth-like dislocation pattern is typical for grains with axial orientations near [001], a patch pattern exists in grains with a loading axis (LA) near [011] and fragmented dislocation walls are dominant in grains with LA near [ 11]. Grains with axial orientations in the central part of the stereographic standard triangle contain a bundle arrangement of dislocation structures. All four types of dislocation structures, but mostly the bundle type, can occur together with the ladder structure of persistent slip bands. Cell patterns were found to be a result of a modification of the bundle and patch configuration at high deformation amplitudes. The mesoscopic dimensions of the dislocation patterns turned out to depend on _pa in the same way for all grain orientations: while the thickness of regions with high dislocation density is reduced with increasing _pa, the width of regions with low dislocation density remains roughly constant.     

Dislocation structures in nickel during high temperature low cycle fatigue at large cumulative strains

The development of the dislocation arrangement during high temperature low cycle fatigue in nickel polycrystals was investigated. Special attention was paid to dislocation structures in the vicinity of grain boundaries. It was found that a defined cell structure develops during progressing cyclic deformation. The motion of grain boundaries associated with high temperature cyclic deformation leads to a dislocation structure gradient in the wake of the boundaries. These structure gradients are suspected to be prone to setting off nucleation of dynamic recrystallization. Upon strain path changes the fatigued structure was observed to become gradually superimposed by a new cell structure without prior decomposition.     

基于多重多级动力子结构的Lanczos算法

提出利用多重多级子结构技术与Lanczos方法求解超大型复杂结构动力特性的子结构算法。该算法利用子结构周游树技术,分别对每个子结构进行Lanczos迭代,通过累加各个子结构的正交化系数组成全局三对角矩阵,最后求解得到整体结构的特征值。算法能够计算超大型结构特征值和特征向量,计算效率高;消耗计算机资源少,稳定性高。由于考虑了各子结构内部自由度对整体求解的贡献,算法精度得到显著提高,并与不作凝聚的单一整体结构分析具有相同的计算精度,计算结果不受复杂子结构划分方式的限制。数值算例验证了所提出算法的正确与有效性。     

Preparation of polycrystalline nickel diffusion studies

Grain-boundary diffusion experiments in doped NiO specimens require fully dense, fine-grained specimens free from unknown residual impurities' but the preparation of such specimens encounters problems in reducing porosity to sufficiently low levels and in ensuring good bonding and freedom from contamination at the boundaries. Ceramic processing techniques have been investigated experimentally in relation to these factors and it is concluded that suitable high density may be obtained using careful control of processing parameters and of factors such as powder particle size, but that the resultant specimens will not be much use unless particular effort is directed to elimination of the minute traces of insoluble impurity that clog up the boundaries und control their character. Preparation of pure boundaries that exhibit intrinsic behaviour is highlighted as a major materials problem in grain-boundary studies.     

Effect of recrystallisation on microstructural evolution and mechanical properties of single crystal nickel base superalloy CMSX-2 Part 1 - Microstructural evolution during recrystallisation of single crystal

Abstract

Nickel base superalloy CMSX - 2 single crystal bars were shot peened to induce surface residual stresses. Partial solutionising at 1300 ° C revealed a relationship between dissolution of the γ ′ phase into the matrix and recrystallisation. Recrystallisation occurred with dissolution of γ ′ phase in the dendritic core at 1300 ° C. Recrystallisation had preferentially begun at the dendritic core exposed at the shot peened surface and then gradually proceeded to the interdendritic regions. Phases more resistant to dissolution such as the coarse γ ′ particles and the γ - γ ′ eutectic phase in the interdendritic region dissolved into the matrix with recrystallisation, even at 1300 ° C, which is lower than the solutionising temperature of the alloy. Residual stresses assisted dissolution of the existing phases. The recrystallised grains grew preferentially in the dendritic core where rapid dissolution of γ ′ phase occurred. The growth of the recrystallised grains was impeded by the coarse γ ′ particles and the γ - γ ′ eutectic phase in the interdendritic region. Full solutionising of the shot peened specimens resulted in well developed recrystallised grains at the surface.     

Modelling of dynamic recrystallisation kinetics in austenitic stainless and hypereutectoid steels

Abstract

Two important parameters for dynamic recrystallisation can be derived from changes in the strain hardening rate: the critical strain for initiation of dynamic recrystallisation and the point of maximum softening. In the present work, these values are determined from stress–strain data obtained by compression testing over the range of 900–1100°C. The resulting strains are used to derive a kinetic model of dynamic recrystallisation for two materials: 304 austenitic stainless steel and a hypereutectoid plain carbon steel. The values of the mechanical parameters used to define the proposed model are confirmed with the aid of metallographic analysis of the recrystallised microstructures.     

Microstructural changes of polycrystalline nickel during high-temperature deformation at ambient and high pressures

The microstructures of polycrystalline nickel, deformed in compression at temperatures of 1000–1500 K at high pressure (1500 MPa) and at ambient (0.1 MPa) pressure, were compared. Dynamic recrystallization and strain-induced grain growth were observed to occur during creep tests at both pressure levels. Our experimental results at ambient pressure are in good agreement with Sandstrom and Lagneborg's theory on dynamic recrystallization. However, high-pressure application considerably retarded recrystallization and grain-growth kinetics. This behaviour was attributed to an increase in the activation energy for grainboundary migration at high pressure.     

An investigation of grain-boundary plane crystallography in polycrystalline nickel

An investigation has been carried out to measure and categorize the grain-boundary plane indices of boundaries in pure nickel. Coincidence site lattices (excluding = 3s) were found to be either asymmetrical tilt boundaries with high indices, or have irrational boundary planes. For the =3s, almost half were asymmetrical tilt boundaries displaced from the 111/111 symmetrical tilt boundary on the 110 zone. Such boundaries have low energies compared to other =3s. The 211/211 incoherent twin was not observed, which was explained on the basis of its higher energy compared to other boundaries on the 110 zone. The results are compared and contrasted with previous data, where boundaries abutted the specimen surface during annealing, which is not the case for the present data. Comments are made with respect to the relationship between macroscopic and atomic-level boundary geometry and implications of the results for grain-boundary properties.