Orowan Theory Research Articles

Coarsening Kinetics of Y2O3 Dispersoid in New Grade of Fe-Al-Cr-Based ODS Alloy

Oxide dispersion strengthened (ODS) alloys with a high content of Al are candidate materials for extreme high temperature applications such as turbine blades and other components working at temperatures significantly above 1000 °C. While oxidation kinetics of Fe–Al ODS steels is frequently studied, the stability and growth kinetics of strengthening oxide dispersion is a rarely studied topic. The Fe-10Al-4Cr-4Y2O3 is an experimental material, fabricated at IPM by powder metallurgy route and contains much higher volume fraction of Y2O3 than similar materials. Stability and growth kinetics of Y2O3 particles of our material are studied on 24 samples aged for 0.5, 1, 2, 4, 8, 16, 32 and 72 h at 1200 °C, 1300 °C and 1400 °C. The sizes of at least 600 individual Y2O3 particles are measured on each sample to obtain extensive statistical analysis of the particle growth. The average particle size coarsens from 28.6 ± 0.7 nm to 36.9 ± 0.9 nm in 1200 °C series and to 81.4 ± 5.6 nm in 1400 °C series. The evaluated activation energy of coarsening of Y2O3 particles is 274 ± 65 kJ. The effects of particle coarsening on mechanical properties is demonstrated by HV measurements, which is in very good agreement with the Orowan theory.

Super-high-strength and formable medium Mn steel manufactured by warm rolling process

In this paper, we demonstrate the design and manufacture of super-high strength medium Mn steel with good ductility, via the combination of warm rolling and V alloying. This new strategy could produce not only the extensive precipitation of fine VC particles in both ferrite and austenite but also the bimodal size distribution of retained austenite (RA) grains. A substantial increase of yield strength up to 650 MPa was achieved after the intercritical annealing of this V-alloyed medium Mn steel without deteriorating ductility; whereas the calculated precipitation strengthening using the classical Ashby–Orowan theory is no more than 400 MPa. Quantifying possible strengthening mechanisms revealed that dislocation strengthening should make an additional contribution because recovery in austenite could be strongly retarded by the nanosized precipitates. In this V-alloyed steel, the coarse RA grains firstly transformed to martensite during yielding at the much higher stress threshold, followed by a significant work hardening due to dislocations multiplication, twinning-induced-plasticity (TWIP) and transformation-induced-plasticity (TRIP) in the ultrafine RA grains. The best combination of strength and ductility included 1.5 GPa ultimate tensile strength and 28% total elongation. This was achieved due to the sustainable TRIP and TWIP effects in the later straining stage resulting from the ultrafine austenite grains, the latter were reversely transformed from the recrystallized ferrite grains.

The blocking effects of interphase precipitation on dislocations’ movement in Ti-bearing micro-alloyed steels

The effects of interphase precipitation and random dispersive precipitation on dislocations’ movement in ferrite grains and nano-mechanical properties have been investigated by using an in-situ nano-mechanical tester. Through the analyses of load–depth curves, nano-hardness was measured to be 4.19GPa for interphase precipitation and 3.90GPa for random dispersive precipitation, respectively. Plateaus are formed in the early stages of load–depth curves for specimens with interphase precipitates, while no plateaus can be observed for specimens with random dispersive precipitates. Mechanism for the interaction between dislocations and precipitates has been established by using Ashby–Orowan theory, which is believed to have been caused by the blockage of parallel precipitates on dislocations, resulting in the drop of applied stress to generate plateaus in load–depth curves.

OS0314 結晶塑性モデルによるMg板の圧延解析手法に関する検討

To simulate texture development during actual rolling process of magnesium sheet, rolling analysis was performed using two numerical methods with application of crystal plasticity model. First, the explicit finite element method DYNA3D is used for simulation of symmetric rolling process. Then, strain distribution was calculated by Orowan theory. Analysis by homogenization method was performed using the strain distribution. As a result, it was confirmed that the analysis by homogenization method considering shear strain is valid.

Orowan strengthening effect on the nanoindentation hardness of the ferrite matrix in microalloyed steels

Although it is well known that there is a significant contribution of precipitation strengthening to the strength of structural steels, it is difficult to experimentally separate the precipitation contribution from the overall strength due to the complex nature of steel microstructures. In this study, the contribution of precipitation strengthening to the matrix strength of ferrite in steel was experimentally investigated through nanoindentation tests. Nanoindentation hardness values of the ferrite matrix in precipitates-containing steels were greater than those in precipitate-free steels, which may be due to the Orowan strengthening mechanism based on the interaction between precipitates and dislocations. To better understand the precipitation strengthening contribution, interparticle spacing values of precipitates were calculated for each microalloyed steel and used for the analysis of hardness change. It was revealed that the trend of nanoindentation hardness change with variation in interparticle spacing corroborated the expectation based on classic Orowan theory.

Combined Macro–Micro Modeling for Rolling Force and Microstructure Evolution to Produce Fine Grain Hot Strip in Tandem Hot Strip Rolling

T.M.C.P. (Thermo Mechanical Control Process) has been widely used in the steel industry. We have produced fine grain hot strips industrially through high reduction and low temperature asymmetric rolling which decreases rolling force by generating a cross shear zone.We needed combined macro–micro model to predict rolling force in the finishing train and microstructure evolution of fine grain hot strips. First, deformation analysis model, an asymmetric rolling theory based on numerical analysis using Orowan's theory was proposed. Second, to obtain the material data for the kinetics of microstructure change in the low temperature austenite region, the compression tests were performed and we measured recrystallization ratio by EBSD (Electron back scattering diffraction). Third, microstructure evolution model to formulate the ferrite transformation using the intragranular nucleation was introduced.Accuracy of the new combined macro–micro model for rolling force and microstructure evolution was very excellent and it enabled us to confirm dynamic ferrite transformation occurrence during high reduction low temperature rolling at the actual tandem hot strip mill.

Mathematical modelling for rolling force and microstructure evolution and microstructure controlling with heavy reduction in tandem hot strip rolling

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The influence of tempering on cleavage fracture stress and transition behaviour of bainitic 2.25Cr1Mo steel

The effect of tempering on the mechanical properties and on the cleavage fracture stress of bainitic 2.25Cr1Mo steel was studied in a variety of structures with the Hollomon‐Jaffe parameter M ranging between 18.23 × 103 and 21.70 × 103. The rapid decrease in yield stress and UTS was observed up to value M = 20 × 103. For values M > 20 × 103 the reduction of yield stress and UTS slows down. The cleavage fracture stress continuously decreases with increasing value of M. Concurrently, the changes in dislocation density and in carbide size, morphology and distribution were observed. Various theories of cleavage origin of tempered bainitic microstructures are discussed. The transition temperatures, determined from impact Charpy test, reach minimum at M = 20 × 103. Using Orowan's theory of initiation of the brittle fracture in steels, the minimum of transition temperatures may be explained by the different reduction rates of cleavage fracture stress and yield stress with value of M.

Electrical conductivity versus strength in a precipitation hardened alloy

There is a trade off between electrical conductivity and strength in precipitation hardened alloys. Nordheim's relation relates conductivity to dissolved solute. The Gibbs-Thomson equation relates dissolved solute to particle size. The Orowan theory equation relates particle size and spacing to yield strength. The inter-relations among these equations were determined in a Cu−0.74 wt% Ni−0.14 wt% P alloy. The methodology developed allows predictions of the optimum trade off between strength and conductivity for a particular electron device application of a precipitation hardened alloy in the coarsening regime.

アルミ熱延へのＯｒｏｗａｎ理論の適用

Rolling tests are carried out to confirm if Orowan theory is applicable to hot rolling of aluminum. In some cases using lubricant, sliding friction with low friction coefficients occurs, on the other hand in cases without lubricant sticking friction occurs. On the whole, mixed sliding and sticking friction is dominant in hot rolling of aluminum. For the prediction of rolling force, precise estimation of rolling temperature is necessary, because temperature fall during rolling is over 100°C in some cases. Moreover, precise estimation of mean flow stress is also necessary, because it has variation over 10% even for the same materials according to the small deviation of chemical composition or heating condition in the soaking furnace etc. By considering the above, the calculated rolling force and forward slip agree well with the experimental ones with sufficient accuracy.

Calculation of hardening of the diffusion layer during nitriding of steel

1. We calculated the hardening of the nitrided layer on steel by use of the Mott-Nabarro theory for coherent nitride precipitates and by the Orowan theory for noncoherent precipitates. 2. The existing nitriding technique does not make it possible to obtain the level of hardening of the diffusion layer that is theoretically possible. 3. The methods considered can be used as the basis for optimizing the geometry and morphology of hardening nitride phases precipitated in zones of internal nitriding and also to calculate the composition of Nitralloys.

Effect of non-stoichiometry on wear of ferrite recording heads

VTR ferrite head wear W r against CrO 2 is investigated as a function of δ in single crystals of Ni 0.669 Fe 2.331 O 4+δ . Two kinds of CrO 2 tape are used: one with calendered smooth surface(c-tape) and the other with coarse surface(n-tape). Knoop hardness H k is measured to correlate W r and H k . Although H k increases with δ, W r has a minimum value for the c-tape and a maximum for the n-tape near δ=0. It is concluded from the microscopic observations of the worn surface that the head surface is damaged with brittle fracture in the shape of stripes with a width of about 10 μm due to stress from tape, resulting in wear. It is pointed out that the δ dependence of W r should be decided by the nature of the plastic work in Orowan theory. A modified Orowan theory is proposed in order to understand the crystal geometric dependence of the head surface on W r .

The isothermic annealing of bainite

AbstractBainitic high carbon steel has been isothermally annealed in the temperature range, 823–973K, in order to follow changes in structure and mechanical properties. The kinetic data for carbide coarsening were found to be in substantial agreement with the Ostwald ripening theory at the higher annealing temperatures. The observed divergence from the theory at the lower temperatures is attributed to the influence of grain boundary diffusion.The dependence of mechanical properties on structure has been examined in relation to several important models. Good data correlation was found in all cases but agreement with predicted values of slope and intercept constants was found only for the models based on the Orowan theory of hardening.The responses to annealing of upper and lower bainite are substantially different and result in measurable differences in mechanical properties of the two structures after heat treatment. Resume Les auteurs ont fait des recuits isothermes dans la gamme de temperature de 823 a ...

Study of the mechanical properties of alloy 36NKhTYu in relation to the mechanisms underlying the precipitation of the ?' and ? phases

The nature of the dispersion (precipitation) hardening of the alloy 36NKhTYu is examined. It is shown that the increase observed in the resistance of the alloy to the motion of dislocations inside the grains during the continuous precipitation of the γ' phase is due to the presence of long-range order in the hardening particles. In addition to this, there is also a considerable increase in that part of the yield stress which is associated with the grain boundaries; this is because of the precipitation of carbides at grain boundaries and the corresponding sharp increase in slip localization. Overaging is characterized by a reduction in the resistance to the motion of the dislocations inside the grains, and a diminishing influence of the grain boundaries (ultimately to no influence at all). These results are in satisfactory agreement with calculations based on the Orowan theory, and also with the assumption that, as overaging progresses, the range of the dislocations is reduced from a distance equal to the grain size to a distance equal to that separating the particles ofγ′ phase, while localized slip is replaced by uniform slip.

Dispersion strengthening of aluminium-aluminium-oxide products

The true stress-true strain curves at room temperature and at 400°C were determined for various types of aluminium-aluminium-oxide products containing from 0.2 to 4.7 weight per cent of aluminium oxide and manufactured from atomized, high-temperature-oxidized and flake powder. Before testing the products were recrystallized to a grain size large compared with the interparticle spacing. The effect of particles on the initial flow stress and the flow stress for 0.2 % offset at room temperature and at 400°C is in agreement with Orowan's theory. Furthermore the effect of particles on the strainhardening rate at room temperature is great for small strains, but vanishes for large strains (>3%), at which the stress-strain curves of the dispersed products are practically parallel to the curve for aluminium of the same purity as the matrix of the dispersed product (99.5%). At 400°C practically no strain hardening is observed above a plastic strain of 0.2 per cent. The increase in flow stress at room temperature for strain values below 3 per cent was related to the plastic strain by the equation σ−gs oy = k 1ε 1 2 , where σ oy is the initial flow stress and where k 1 increases for increasing volume fraction and decreasing particle size of the dispersed particles. A general expression for k 1 was derived by means of Ashby's expression for the relationship between the dislocation density and the strain in dispersion-strengthened products.

Yielding and Work-Hardening in Ni-ThO2Alloys

Theories of dispersion-phase-strengthening are briefly discussed and then critically examined in the light of experimental evidence obtained with nickel containing a fine dispersion of thoria. The results are in close agreement with Orowan's theory. The work-hardening theory of Fisher, Hart, and Pry, though in qualitative agreement with the experimental results, postulates the formation of concentric dislocation loops around particles of the dispersed phase. Transmission electron micrographs of the nickel-thoria indicate that the formation of prismatic loops near to particles is a more likely process, and this is borne out by analysis of the experimental results.

Dispersed particle hardening of aluminum-copper alloy single crystals

Single crystals were grown in aluminum-copper alloys containing from 3 to 5 per cent copper. These crystals were strained in tension after receiving heat treatments designed to develop CuAl 2 particles of varying sizes and distributions. Values of the critical resolved shear stress were found to be inversely proportional to the mean spacing between particles, in accordance with Orowan's theory. Fisher, Hart and Pry's theory that dislocation rings formed around the particles during deformation make a large contribution to work hardening, has received confirmation from the experimental results on these crystals. While a crystallographically defined critical resolved shear stress was observed, deformation took place mostly by multiple slip, the external characteristics of the deformation being similar to those of polycrystalline material.