The effect of fine precipitate particles on the creep behaviour of ferritic model steels – III. Model calculations

With the findings of the preceding part II a model is established which considers dislocation and diffusion creep and which is used to simulate the creep behaviour of alloys with grain and particle coarsening during creep. It is found that the structure changes during creep give rise to a complex stress – strain rate dependence and to additional transition fields in the corresponding deformation maps which is of importance for the interpretation of practical long-term creep results.     

The cyclic deformation and fatigue behaviour of the low carbon steel SAE 1045 in the temperature regime of dynamic strain ageing

The cyclic deformation behaviour of normalized SAE 1045 steel (german steel grade Ck 45) has been investigated over a range of temperatures between 20 and 375°C. Special attention has been paid to the effects of dynamic strain ageing, which are most pronounced around 300°C. Different types of deformation tests (tension tests, incremental step tests, and constant amplitude cyclic deformation tests under stress control with a stress amplitude of 400 MPa as well as under plastic strain control with a plastic strain amplitude of 0.5%) were carried out to observe the influence of temperature on the macroscopic mechanical behaviour. These tests were followed by TEM studies on microstructural features. In the temperature range of maximum dynamic strain ageing, the material was found to show maximum strength in unidirectional as well as in cyclic deformation tests. While the fatigue life is maximum at the temperature of maximum dynamic strain ageing in stress-controlled tests, it is minimum in plastic strain controlled tests. At the temperature of maximum dynamic strain ageing around 300°C, the dislocations are arranged in dense dislocation tangles and parallel dislocation walls, whereas at room and at higher temperatures (375°C) mainly dislocation cell structures are observed.     

Evolution of dislocation densities and the critical conditions for the Portevin-Le Châtelier effect

A model is proposed for the critical strains associated with the Portevin-Le Châtelier effect (PLC) in terms of the strain dependence of the densities of mobile and forest dislocations. The classical critical condition for the onset of the PLC effect, viz. that of vanishing of the strain rate sensitivity of flow stress under the influence of dynamic strain aging is reexamined. The analysis takes into account the strain dependence of a key quantity: the elementary strain produced when all mobile dislocations perform a successful thermally activated step through the forest obstacles. This elementary strain is estimated by studying a system of coupled differential equations for the evolution of the two densities. Results are obtained in semi-quantitative form and compared with available data. It is shown that the following effects are consistently explained: the occurrence of critical strains for the onset and termination of jerky flow, occasional observation of two PLC regimes within the same deformation curve, the behaviour of the critical strains at high strain rates and low temperatures and, possibly, the particular behaviour exhibited by some alloys at low strain rates and high temperatures. Consequences for the “friction” and “forest” models of dynamic strain aging are discussed.     

Theory of flow localisation due to dynamic strain ageing

The localisation of plastic flow due to dynamic strain ageing is evaluated taking into account transient behaviour associated with the time dependence of the solute composition at mobile dislocations. A constitutive flow equation is defined which includes the local solute composition as an implicit state variable. Linear perturbation theory is employed to define an instability strain above which strain localisation occurs. The instability strain is found to be greater than the strain required for a negative steady state strain rate sensitivity of the flow stress. Both linear theory and numerical simulation show that strain localisation is characterised by sinusoidal strain and strain rate oscillations of increasing amplitude, leading to deformation band formation. The strain required for observable strain localisation is shown to depend on specimen uniformity and experimental technique. The results of the analysis are in agreement with experimental measurements in Fe-C and Au-Cu alloys.     

Analysis on the critical strain associated with the onset of portevin-Lecatelier effect of substitutional F.C.C. alloys

Flow instability of substitutional f.c.c. alloys, which is a common feature of the Portevin-LeChatelier effect, usually develops after a critical strain is reached. With ∈. and T as the tensile strain rate and deformation temperature, respectively, the Arrhenius equation that ∈. ∝ ∈_c^α exp (−Q/kT) is obeyed in numerous systems. Rationalization of the critical strain exponent, α, based on the conventional Cottrell model is not in agreement with empirical data. A proper modification regards ∈_c as related to some critical mobile dislocation density in which the local vacancy enrichment near dislocation core region is considered. Dislocation interception should also play a role in affecting the average dislocation velocity. The rationalization based on the above concepts reveals a correct grain size dependence.     

Relationship between Work Hardening Behaviour and Deformation Structure in Ni‐free High Nitrogen Austenitic Stainless Steels

The work hardening behaviour of high nitrogen austenitic steel (HNS) depends not only on the nitrogen content but also on the addition of substitutional alloying elements such as Mn and Ni, although the effect of nitrogen content has been considered to be a main factor controlling the work hardening rate in HNS. In this study, two kinds of high nitrogen austenitic steels containing nearly 1 mass‐% of nitrogen with and without Mn (Fe‐25%Cr‐1.1%N and Fe‐21%Cr‐0.9%N‐23%Mn alloys) were tensile‐tested and their work hardening behaviour was investigated for the purpose of clarifying the effect of Mn on the work hardening behaviour. Then the results were related to the change in deformation substructure. In the Fe‐25Cr‐1.1N alloy, the work hardening rate kept high until fracture occurred, while in the Fe‐21Cr‐0.9N‐23Mn alloy it tended to decrease gradually with tensile deformation in the high strain region. It was concluded that the difference in work hardening behaviour between both alloys is attributed to the change in dislocation substructure from planar dislocation array to dislocation cell by the addition of Mn.     

Serrated yielding in AISI 316 stainless steel

Serrated yielding behaviour of a type AISI 316 stainless steel is investigated in the temperature range 300–923 K. Detailed observations have been made on the effect of prior ageing in the temperature range (823–1323 K) for different periods of time on the serrated yielding behaviour at 923 K. Two temperature regions with different activation energies have been identified for serrated flow. The mechanism for serrated flow in the low temperature region (∼ 523–623 K) is the diffusion of interstitial solute to dislocation while substitutional solutes like Cr is responsible for serrated yielding at high temperature region. Certain time-temperature combination of ageing is found to eliminate serrated yielding at 923 K. Results also support the role of grain boundaries as preferred sites for dynamic strain ageing in austenitic stainless steels as previously suggested.     

Finite‐Element Implementation of a Self‐consistent Texture Model with a Hardening Law Based on Dislocation Densities

A self‐consistent texture model is implemented in the finite‐element code ABAQUS/Explicit®. Hardening of the slip systems is described by evolution laws for dislocation densities, and the Bauschinger effect is included. With these ingredients the cold rolling of an IF‐steel is simulated and the evolution of texture and anisotropy is examined. The use of the dislocation based hardening law is found to have a significant effect on the evolution of the anisotropic yield surface, but only very little influence on the texture. Furthermore, the hardening model is used to investigate the evolution of dislocation densities in differently oriented grains during plane strain compression. It is found that the dislocation density varies greatly depending on orientation, an observation which can help to explain the orientation dependence of recrystallization.     

The thermally activated dislocation motion in neutron irradiated iron-nickel alloys

Polycrystalline samples of iron-nickel alloys with various interstitial impurity levels were irradiated to a fluence of 1.6 × 10¹⁹ n/cm² (E > 1 MeV). The temperature and strain rate dependence of the yield stress of the alloys have been investigated in the temperature range of 77 to 580°K. The activation parameters have also been evaluated and used to identify the rate controlling mechanisms of the dislocation motion. It was observed that above 300°K the thermally activated dislocation motion over the neutron-produced obstacles is the rate controlling mechanism for the irradiated samples. This observation is in agreement with a prediction made by Arsenault. The effect of post-irradiation annealing on the temperature dependence of the yield stress becomes significant above 400°K; therefore, by the single strain rate change tests there is no way to determine the athermal stress for the irradiated samples. The motion of double kinks in dislocations over the Peierls’ stress hill is the lower temperature rate controlling mechanism before and after neutron irradiation.     

Deformation behavior of 4;Mo alloys

Five polycrystalline nickel-molybdenum single-phase alloys (up to 10 at.% Mo) and pure nickel (INCO 270) were tested in compression at two temperatures. The molybdenum solutes contribute not only an additive friction stress, but also a multiplicative effect on the strain-hardening rate. This multiplicative effect is interpreted in terms of an influence of mobile solutes on the dislocation/dislocation interaction strength. Solute mobility was evidenced by the occurrence of static strain aging and of a strain-rate sensitivity that has a negative contribution. The total rate sensitivity, however, remained positive and jerky flow was not observed.     

Study on the Deformation Behavior of Mg-3.6% Er Magnesium Alloy

The deformation behaviour of a casting Mg-3.6% Er magnesium alloy after T6 treatment was studied in tensile tests from room temperature to 450 ℃ under different strain rates ranging from 1.0 ×10^-4 to 6.0 × 10^-3 S^-1 Obtained local plateau in the temperature dependence of the ultimate strength （σb） and yield strength （σ0.2） under constant strain rate indicated the presence of dynamic strain ageing （DSA）. Serrated flow was observed at the temperature of 200, 250, and 300 ℃. The observed negative strain rate sensitivity suggested that the serrated flow behavior arose from DSA. The temperature and strain rate dependence of the critical strain for the onset of serrated flow was analyzed using a phenomenological DSA equation, and the apparent activation energy Q for the serrated flow was obtained by calculation.     

Constant structure creep in metals after stress reduction in steady state stage

Constant structure creep in several metals and alloys was investigated in structures corresponding to the steady state creep conditions. Results were interpreted by means of the back stress concept. In accord with postulates of the strain transient dip test technique, the residual effective stress is considered the controlling stress for dislocation glide. The suggested interpretation of constant structure creep data allows to obtain some information about parameters of the dislocation kinetics in the steady state creep. From the interpretation, a pronounced applied stress dependence of the mobile dislocation density as well as a specific relation between the activation area and the effective stress in steady state creep under various creep conditions result.     

Influence of changing strain rate on microstructure during hot deformation

Hot plane strain compression tests have been carried out on a ferritic stainless steel, commercial purity aluminium and an aluminium 1% magnesium alloy under conditions of constant strain rate and with strain rate changed in a controlled manner from one constant value to another. At constant strain rate, subgrain size and dislocation density inside subgrains are related to flow stress in the manner observed previously on other materials. During and after changes in strain rate, subgrain size and dislocation density are not uniquely related to flow stress. Significant strain intervals after a strain rate change are required to establish the new equilibrium subgrain size. For the alloys, these strain intervals are larger when strain rate is increased than when it is decreased. The opposite is found for the commercial aluminium. This difference in behaviour is explained In terms of the relative rates of glide and climb of dislocations.     

Cyclic strain induced precipitation in a solution treated aluminium alloy

Cyclic mechanical tests were carried out on specimens of an Al-Mg-Si alloy, 6351, in the solution treated condition and the behaviour compared to that of an Al-Mg alloy, 5182. Both showed marked cyclic hardening typical of non precipitation hardened aluminium alloys. In the 5182 alloy, this hardening has been attributed to dislocation pinning by solute atoms. Differences in mechanical behaviour were observed which suggested that hardening of the 6351 alloy may be due to a cyclic strain induced precipitation hardening effect rather than solute atom pinning. Using a previously described weak beam technique, evidence was found for precipitate formation on dislocations in the cycled 6351 alloy. The evolution of the microstructure during cycling was different in the two alloys. In the 6351 alloy, the dislocation density reached a maximum and then decreased with further cycling even though hardening continued to occur. This was attributed to progressive deactivation of dislocation sources whilst normal annihilation reactions continued to occur among the mobile dislocations.     

Structural Superplasticity at High Strain Rates of Super Duplex Stainless Steel Fe‐25Cr‐7Ni‐3Mo‐0.3N

The fine‐grained super duplex stainless steel Fe‐25Cr‐7Ni‐3Mo‐0.3N consisting of two phases (δ‐ferrite/austenite) exhibits structural super‐plasticity at higher strain rates of ? ≈ 10^?2s^?1 in the temperature range between 975 and 1100°C. The equiaxed microstructure with an average grain size of was produced by thermomechanical processing. Maximum strain‐rate‐sensitivity exponents of m ≈ 0.5 and elongations to failure of more than 500% were achieved. From thermal activation analysis an activation energy for superplastic flow of Q = 310 ± 20 kJ/mole was derived. The superplastic behaviour at higher strain rates is quantitatively described by a deformation model where grain or interphase boundary sliding is accommodated by sequential steps of dislocation glide and climb. The high strain‐rate‐sensitivity exponent and the observed dislocation density indicate that dislocation climb in the slightly solid solution strengthened austenite is the rate controlling step for superplastic flow. The deformation mechanism reveals that the investigated super duplex stainless steel exhibits superplastic behaviour that is typical for class II solid solution alloys.     

Additive strengthening mechanisms in dispersion hardened polycrystals

Tensile data from polycrystalline samples of copper dispersion strengthened by alumina are analysed. The basis of this analysis is to look at the strain range from 0.05 to 0.20 where the stress-strain curves show a parabolic hardening behaviour and are parallel to one another. The means by which the addition of strength components from various elements of the microstructure and substructure might explain this behaviour are investigated. It is shown that a linear combination of a matrix friction stress, an Orowan bowing stress, a matrix mean stress from the particles and a combined dislocation interaction term can explain this data and also the data from some aluminium-alumina materials. The dislocation interaction term, which dominates, is comprised of terms which cover the pure matrix work hardening, the hardening due to particles and due to the grain boundaries. This term is derived by summing the dislocation density contributions from each of these three sources. The type of additivity suggested here not only gives very good agreement with the stress-strain data but it also uses and is in accord with the experimental measurements of dislocation densities made using transmission electron microscopy.     

Study of Fatigue in Metals Using Ultrasonic Technique

Abstract

An investigation of the basic mechanisms associated with cyclic and fatigue stressing was undertaken employing as a research tool a megacycle frequency internal friction method (ultrasonic wave attenuation). The materials used were plain high-carbon and alloy steels (SAE 1095 and SAE 4340). The behaviour of lattice imperfections, dislocations and interstitial atoms (carbon) in particular, was studied in more detail, since these are reported to have a strong influence on the fatigue characteristics of iron-base alloys.

Initially, static stressing conditions were studied. Using a dislocation loop pinning model, the conditions for the break-away of a dislocation loop from interstitial atoms in annealed and in cold-worked material were investigated. These findings were applied to the experimental results obtained on cyclic stressing and an interpretation is offered in terms of the formation of active dislocation loops and their immobilization by interstitial atoms.

The results are discussed with reference to improving fatigue characteristics of iron-base alloys and a similarity with the work of Mason (19) on non-ferrous metals is noted.     

The kinetics of dislocation climb over hard particles—I. Climb without attractive particle-dislocation interaction

The effect of hard particles of low volume fraction on the creep strength is studied theoretically in a two-part paper. Here in part I, the kinetics of dislocation climb over a particle is modelled assuming that the particle does not exert an attractive force on the dislocation (“non-interacting” particle). The shape of the climbing dislocation is given by a minimum energy condition, which is shown to rule out purely “local” climb (as considered in previous models). A natural power-law dependence of the dislocation velocity on the applied stress, with n ranging from about 3 to 4, is obtained, and only a small threshold stress can be identified. The results appear compatible with the creep behaviour of alloys strengthened by coherent precipitates, but are totally at variance with experimental threshold stress data for materials with incoherent particle dispersions.     

Strain aging and strain hardening in NiC alloys

Two nickel-carbon alloys and pure nickel were investigated by compression in the temperature range where strain aging phenomena occur. The effect of carbon on the dynamic-recovery part of strain hardening is severe, especially at higher temperatures. Static strain aging increases strongly with strain. This dependence persists even when the time and concentration dependence of the aging stress increment have saturated; it can therefore not be due to deformation-generated vacancies. The strain dependence can be well expressed by a linear relation with flow stress, up to the beginning of dynamic recovery, where it saturates. This behavior, as well as dynamic strain-aging results, are very similar to observations in substitutional alloys. It is concluded that vacancies are rarely if ever responsible for the strain dependence of aging phenomena, and that this is instead due to a strong interaction between solute hardening and strain hardening.