Relationship between anelastic and nonlinear viscoplastic behavior of 316 stainless steel at low homologous temperature

At low homologous temperature the plastic strain rate seems to be controlled largely by dislocation glide friction. However, since a sizeable fraction of the applied stress σ is dissipated in overcoming the strong barriers due to dislocation tangles generated by strain hardening, only a portion of the applied stress is actually expended against the frictional resistance. A recent model for this process, proposed by Hart, includes the role of dislocation pile-ups at the strong barriers. The pile-ups provide a mechanism for producing the internal back stress that reflects the barrier penetration stress. They also appear in the deformation as a stored anelastic strain component. The resultant behavior at low temperature and high stress is similar to that proposed by Gupta and Li. The same model also predicts an anelastic behavior at low stress. Measurements at both high and low stress levels on 316 Stainless Steel have now shown that the predictions of the model are quantitatively consistent at both stress levels.     

Plastic deformation of an iron-modified titanium trialuminide alloy

Mechanical properties and dislocation structures have been studied from room temperature to 700°C in a titanium trialuminide alloy modified to the composition Al₅Ti₂Fe. In compression the material shows extensive ductility with the yield stress increasing above 300–400°C, but in bend testing it is very brittle. At low temperatures undissociated 〈110〉 dislocations are mobile and deformation is controlled by Peierls effects and by extensive work hardening. At intermediate temperatures many dislocations dissociate into mobile superdislocations giving rise to serrations in the stress-strain curve; undissociated segments appear immobile because of a solute-associated core relaxation. At high temperatures dislocations are dissociated as superdislocations, mobile on both octahedral and cube planes, with cross slip between these planes bringing about high temperature strengthening. The low ductility in bend testing may be related to the high work hardening as well as the intrinsic cleavage weakness of the material.     

Peierls-nabarro plastic deformation in the presence of solute clusters

Solid solution strengthening and weakening in bcc alloys is modeled by a double kink nucleation and lateral motion process in the presence of solute atoms. Classical size or modulus interactions are incorporated into a Peierls-Nabarro dislocation model. The solute atoms are arranged in specified clusters to emphasize the orientation dependence of various superposition effects. A model which fixed the line shape to the pure metal form is shown to be of considerable utility. Nearest and next-nearest neighbor solute-dislocation interactions are responsible for a substantial portion of the changes in the activation energies, but their effects must be reevaluated due to the breakdown of the classical model at such short range. The classical model is not capable of explaining the experimentally observed strengthening, even when nearest and next-nearest neighbor solutes are considered.     

The dependence of activation enthalpy on stress in shear processes

In a typical shear process, the applied stress τ_a presses a dislocation against a barrier. As the stress increases, the dislocation moves up the barrier, and the activation enthalpy necessarily decreases. This predicted decrease of activation enthalpy with increasing stress is confirmed by the observations of Kisel [Physica status solidi (a), 36, 297 (1976)] on edge dislocations in NaCl. However, for screw dislocations Kisel observes an increase of activation enthalpy with applied shear stress, in the same range of stresses. This behaviour can be explained by a model in which edge and screw dislocations surmount localized obstacles by processes with activation volumes V_e and V_s, and travel between obstacles with a speed proportional to τ, if the inequalities kT/V_s >τ_a >kT/V_e are satisfied.     

Influence of Grain Size and Age-Hardening on Dislocation Pile-Ups and Tensile Fracture for a Ti-AI Alloy

In an aged Ti-8.6 wt pct Al alloy macroscopic embrittlement occurs with increasing grain size and degree of age hardening. The influence of the grain sizeL on the true fracture strain can be described by εF ∼L-¹ Tensile crack nucleation is caused microscopically by strong dislocation pile-ups which crack the grain boundaries. Using transmission electron microscopy and equations from the dislocation theory, an experimental method was developed to determine quantitatively the shear stress concentrations at the grain boundaries which are produced by the dislocation pile-ups and cause crack nucleation. The experimental results show that for all investigated grain sizes and degrees of age hardening a critical local stress t* _C ≈ 38 GPa leads to crack nucleation. Based on this result equations were derived which describe the combined influence of grain size and age hardening on the true fracture strain and on the true fracture stress. These equations show a good agreement with the tensile test results.     

Effects of the Peierls stress on the transition from power law creep to Harper-Dorn creep

Using extensive data on metals, ceramics and silicates, it is demonstrated that power law dislocation creep transits to Harper-Dorn creep at the Peierls stress of a crystal. This transition at such a stress level is perhaps induced by the dislocation density being dependent upon the applied stress in power law creep but determined by the Peierls stress in Harper-Dorn creep.     

A New Paradigm for Designing High-Fracture-Energy Steels

The steels used for structural and other applications ideally should have both high strength and high toughness. Most high-strength steels contain substantial carbon content that gives poor weldability and toughness. A theoretical study is presented that was inspired by the early work of Weertman on the effect that single or clusters of solute atoms with slightly different atom sizes have on dislocation configurations in metals. This is of particular interest for metals with high Peierls stress. Misfit centers that are coherent and coplanar in body-centered cubic (bcc) metals can provide sufficient twisting of nearby screw dislocations to reduce the Peierls stress locally and to give improved dislocation mobility and hence better toughness at low temperatures. Therefore, the theory predicts that such nanoscale misfit centers in low-carbon steels can give both precipitation hardening and improved ductility and fracture toughness. To explore the validity of this theory, we measured the Charpy impact fracture energy as a function of temperature for a series of low-carbon Cu-precipitation-strengthened steels. Results show that an addition of 0.94 to 1.49 wt pct Cu and other accompanying elements results in steels with high Charpy impact energies down to cryogenic temperatures (198 K [–75 °C]) with no distinct ductile-to-brittle transition. The addition of 0.1 wt pct Ti results in an additional increase in impact toughness, with Charpy impact fracture energies ranging from 358 J (machine limit) at 248 K (–25 °C) to almost 200 J at 198 K (–75 °C). Extending this concept of using coherent and coplanar misfit centers to decrease the Peierls stress locally to other than bcc iron-based systems suggests an intriguing possibility of developing ductile hexagonal close-packed alloys and intermetallics.     

Dislocation dynamics in niobium-oxygen

The dislocation velocity-stress exponentm has been calculated from measurements of the strain rate sensitivity of the effective stress τ for single crystals of niobium-oxygen solid solutions which exhibit alloy softening. The values ofm evaluated at small plastic strains are found to be a sensitive function of temperature and oxygen concentration. Analysis of these results in terms of Peierls-Nabarro and dislocation-interstitial solute hardening mechanisms infers the latter is rate controlling. Furthermore, alloy softening is best interpreted in terms of the effects which solute interaction processes have on the thermally activated hardening caused by oxygen. Formerly Graduate Assistant, Division of Metallurgy Formerly Graduate Assistant, Division of Metallurgy Formerly Graduate Assistant, Division of Metallurgy     

Temperature-dependent void-sheet fracture in Al-Cu-Mg-Ag-Zr

Previous research showed that tensile fracture strain increases as temperature increases for AA2519 with Mg and Ag additions, because the void-sheet coalescence stage of microvoid fracture is retarded. The present work characterizes intravoid-strain localization (ISL) between primary voids at large constituents and secondary-void nucleation at small dispersoids, two mechanisms that may govern the temperature dependence of void sheeting. Most dispersoids nucleate secondary voids in an ISL band at 25 °C, promoting further localization, while dispersoid-void nucleation at 150 °C is greatly reduced. Increased strain-rate hardening with increasing temperature does not cause this behavior. Rather, a stress relaxation model predicts that flow stress and strain hardening decrease with increasing temperature or decreasing strain rate due to a transition from dislocation accumulation to diffusional relaxation around dispersoids. This transition to softening causes a sharp increase in the model-predicted applied plastic strain necessary for dispersoid/matrix interface decohesion. This reduced secondary-void nucleation and reduced ISL at elevated temperature explain retarded void sheeting and increased fracture strain.     

Work-hardening and recovery mechanisms in gamma-based titanium aluminides

The work-hardening mechanisms in two-phase γ-titanium aluminide alloys were characterized in terms of the glide obstacles determining the velocity and slip path of dislocations, utilizing transmission electron microscopy (TEM) observations and thermodynamic-glide parameters. There was clear evidence that short-range obstacles in the form of dislocation debris and dipoles were produced during plastic deformation at room temperature. These dislocation obstacles contributed significantly to work hardening. The observed strong strain hardening arose from long-range elastic dislocation interactions and the production of dipole and debris defects. The thermal stability of these deformation-induced defects was assessed by isothermal and isochronal annealing. The results indicated that the dipole and debris defects were relatively unstable upon annealing at moderately high temperatures, which led to significant recovery of work hardening. This article is based on a presentation made in the symposium entitled “Fundamentals of Structural Intermetallics,” presented at the 2002 TMS Annual Meeting, February 21–27, 2002, in Seattle, Washington, under the auspices of the ASM and TMS Joint Committee on Mechanical Behavior of Materials.     

Effect of tempering temperature on strain hardening exponent and flow stress curve of 1000 MPa grade steel for construction machinery

To study the effect of tempering temperature on strain hardening exponent and flow stress curve, one kind of 1000 MPa grade low carbon bainitic steel for construction machinery was designed, and the standard uniaxial tensile tests were conducted at room temperature.A new flow stress model, which could predict the flow behavior of the tested steels at different tempering temperatures more efficient-ly, was established.The relationship between mobile dislocation density and strain hardening expo-nent was discussed based on the dislocation-stress relation.Arrhenius equation and an inverse propor-tional function were adopted to describe the mobile dislocation, and two mathematical models were established to describe the relationship between tempering temperature and strain hardening expo-nent.Nonlinear regression analysis was applied to the Arrhenius type model, hence, the activation energy was determined to be 37.6 kJ/mol.Moreover, the square of correlation coefficient was 0.985, which indicated a high reliability between the fitted curve and experimental data.By comparison with the Arrhenius type curve, the general trend of the inverse proportional fitting curve was coincided with the experimental data points except of some fitting errors.Thus, the Arrhenius type model can be adopted to predict the strain hardening exponent at different tempering temperatures.     

Stability of the dislocation substructure of α-titanium against deformation temperature variation in the range 4.2–293 K

The dislocation substructure of polycrystalline α-Ti of commercial purity after tension with the test temperature changed in various sequences between 4.2, 77 and 293 K has been studied by the TEM method. The stability of elements of the substructure characteristic of certain deformation temperatures to the deformation temperature changes has been studied. It has been found that reorientation bands (RB's) arising from predeformation at 293 K during subsequent deformation at 4.2 and 77 K gradually degrade and are subject to fragmentation by low-temperature twins for which they are not insurmountable obstacles. If the temperature is changed in the reverse sequence, formation of RB's is impeded or even suppressed and low-temperature twins become insurmountable obstacles for RB's. Processes of nucleation, development of new substructures and their interaction with initial ones are discussed.     

Constitutive model of the TWIP effect in a polycrystalline high manganese content austenitic steel

The TEM study of our steel with a high manganese content reveals that mechanical twining (TWIP effect) occurs during the deformation at room temperature. Microtwins are organised into parallel stacks and two systems are sequentially activated in each grain. They participate to the deformation and they are strong obstacles for the dislocations and for other twins, leading to the decrease of the effective grain size. Thus, TWIP provides our alloy a very good ductility and a high hardening rate. Our constitutive modelling deduced from a model proposed by Bouaziz and Guelton [4] integrates this typical organisation of microtwins. Twinning is quantified in each grain by the partial volume fraction of twins in each system. A nucleation law for the microtwins is introduced which depends on the local stress and the stress relaxation due to pre‐existing twins. The flow stress is deduced from the dislocation density, which evolves with the dynamical recovery and the decrease of the mean free path (MFP). The MFP takes into account the grain and twin boundaries and the forest dislocations. The strain is calculated by adding the contributions of dislocation glide and twinning accounting the orientation of the grain. To treat the polycristal, the behaviours of different grain orientations are mixed by assuming at each strain step that the increment of elastic energy stored is the same in each grain. The model was successfully applied to describe the mechanical properties of our alloy, for two different grain sizes. Some microstructural parameters are yet fitted. This leads to an insufficient prediction of the evolution of the microstructure. In further developments, we expect to introduce numerical simulation results on local characteristics of microtwins (thickness, critical resolved shear stress for twinning) and experimental results on the rate of twin nucleation.     

Sub-zero Temperature Dependence of Tensile Response of Friction Stir Welded Al-Cu-Li (AA2198) Alloy

Mechanical properties at ambient and cryogenic temperatures of Al-Cu-Li alloy are required for design and fabrication of liquid hydrogen and liquid oxygen tanks of satellite launch vehicles. In the present work, bead-on-sheet, friction stir welding was carried out with three different rotation speeds. The yield and strain hardening behaviors of the welds were evaluated in temperature range of 20 K to 298 K. Both yield stress and strain hardening ability in the specimen increased with decrease in testing temperature. The dependence of yield stress on temperature was modeled on the basis of thermally activated dislocation mobility, while that of strain hardening was modeled on the temperature dependence of dynamic recovery rate parameter. The recovery parameter followed an Arrhenius-type relationship with temperature. The model parameters determined from the experimental data were further used to simulate the stress–strain curves at different sub-zero temperatures for the friction stir welds.

     

cyclic deformation of Ni3(Al,Nb) single crystals at ambient and elevated temperatures

In order to study the cyclic deformation of an alloy crystal and the asymmetry in the flow stress of the γ′ phase, Ni₃(Al, Nb) crystals have been cycled in strain control at room temperature, 400 and 700°C. The orientation of the crystals has been a major variable studied. At all temperatures, cyclic hardening has been found considerable and at the two lower temperatures, the asymmetry has been found to follow the predictions of the model by Paidar et al. [Acta metall. 32, 435 (1984)] which is based on the increase of the dislocation friction stress by thermally activated cross slip onto [001] planes. Moreover, TEM observations of the dislocation structures are consistent with the model. At 700°C, a dominance of the tensile stress in the asymmetry was observed rather surprisingly. The model of Paidar et al. does not apply at this high temperature because dislocation climb and cube slip occurs, and no asymmetry is expected. Cracking and life behavior are also reported.     

Assessment of Methods Used in 1D Models for Computing Bed-Load Transport in a Large River: The Danube River in Slovakia

Comprehensive measurements of bed-load sediment transport through a section of the Danube River, located approximately 70?km downstream from Bratislava, Slovakia, are used to assess the accuracy of bed-load formulas implemented in 1D modeling. Depending on water discharge and water level, significant variations in the distribution of bed load across the section were observed. It appeared that, whatever the water discharge, the bed shear stress τ is always close to the estimated critical bed shear stress for the initiation of sediment transport τcr. The discussion focuses on the methods used in 1D models for estimating bed-load transport. Though usually done, the evaluation of bed-load transport using the mean cross-sectional bed shear stress yields unsatisfactory results. It is necessary to use an additional model to distribute the bed shear stress across the section and calculate bed load locally. Bed-load predictors also need to be accurate for τ close to τcr. From that point of view, bed-load formulas based on an exponential decrease of bed-load transport close to τcr appear to be more appropriate than models based on excess bed shear stress. A discussion on the bed-load formula capability to reproduce grain sorting is also provided.     

Mechanisms of cyclic strain hardening in Ni3Al+B single crystals

The evolution of dislocation substructures and their correlation with strees response in Ni₃Al+B single crystals fatigued at room temperature has been studied. Fatigue was conducted at total-strain amplitudes of 0.05–0.2%. Cyclic strain hardening and a tension/compression flow stress asymmetry were observed. The magnitude of stress asymmetry was found to depend on the applied cyclic strain. A dislocation structure composed of jogged superdislocations and superdislocation dipoles was observed. The dislocation dipoles were mainly formed by nonconservative of jogged superdislocations. Dragging of jogs, interaction between dislocations, and impedance of dislocation motion by dislocation dipoles (point defect clusters) are considered to be the major contributors to cyclic strain hardening in Ni₃Al+B single crystals. The separation between superpartial dislocations of a paired superdislocation was found to fluctuate away from the equilibrium spacing during cyclic straining. The extent of the fluctuation became more pronounced as the applied cyclic strain increased. This phenomenon was intimately related to the cyclic-strain dependence of tension/compression flow stress asymmetry found in fatigued Ni₃Al+B single crystals.     

The flow stress of potassium

Experimental results on the flow stress of potassium in the temperature range of 1–30 K are compared with atomistic computer simulation of rigid dislocation motion and of dislocation kink pair generation and migration. Quantitative agreement is demonstrated. Implications for the rate theory and the continuum elastic theory of kink pairs are discussed.     

The effect of impurity interstitials on the lattice resistance to dislocation motion

A computer simulation model was developed to determine the nature of the synergistic effect between the lattice resistance and impurity interstitial atoms to dislocation motion. If the interaction between an impurity interstitial and a screw dislocation in a bcc lattice with a large Peierls barrier is treated in an elastic continuum manner, strengthening will occur. This strengthening occurs at all interstitial concentrations and at all temperatures in the low-temperature region.     

位错滑移运动与运动阻力辨析

对位错在点阵周期场中运动时需要克服的阻力,以及影响阻力大小的因素作了辨析和讨论.含有位错的晶体变形,确定无疑是位错在外力场作用下滑移运动的宏观结果.对位错在完整晶体中运动分析表明,派-纳力对温度十分敏感.一定温度下,位错并非仅处于某一势能水平.即使外力应力小于派纳力,位错也可以通过扭折侧向运动,且由于热起伏造成的能量隆起,进而侧向扩展,使位错更容易运动.