The effect of dislocation drag on the stress-strain behavior of F.C.C. metals

The introduction of viscous drag into a simple thermally activated dislocation model for the low temperature plastic deformation of f.c.c. metals leads to some surprising predictions about their stress-strain behavior. One effect of dislocation drag is to produce a region of tensile instability at small strains for any strain rate. At sufficiently high strain rates there is no region of tensile stability. However, computation of a decreased strain for tensile instability at strain rates greater than 10³ s⁻¹, in opposition to experimental measurements, provides evidence that the strong upturn reported for the flow stress of copper is not caused by dislocation drag. The likely explanation is an enhanced rate of dislocation generation.     

Corrosion fatigue mechanisms in b.c.c. stainless steels

The influence of a 3.5% NaCl solution on the cyclic plastic deformation of a b.c.c. Fe-26Cr-1Mo alloy is analysed as a function of the applied electrochemical potential E, taking into account the dislocation behaviour, the formation of microcracks and the evolution of the cyclic corrosion current transients. Three different kinds of damage mechanisms have been pointed out: (i) in the cathodic region (E < −300 mV/SCE), the localization of the hydrogen reduction is favoured when microcracks are mechanically formed. This induces a very marked decrease of the fatigue life at high strain amplitudes, but this deleterious effect is reduced at low strain amplitudes for which the microcrack formation is delayed; (ii) in the passive region for −300 < E < + 500 mV/SCE, the damage mechanisms are related to the localization of the anodic dissolution due to a depassivation-repassivation process. A critical strain rate range ( ∼- 10⁻³ s⁻¹) for which this localization and the corresponding acceleration of the microcrack formation are maximum is encountered; (iii) in the passive region for E > + 500 mV/SCE, the cyclic strain enhances the formation of pits which induce an early formation of microcracks. The study of the microcracking process and its evolution is a key to specify the physical mechanisms by which an aqueous corrosive solution can affect the fatigue life of b.c.c. stainless steels according to the applied electrochemical potential.     

Effects of plasticity on the crack propagation resistance of a metal/ceramic interface

Fracture experiments have been conducted on a gold/sapphire interface. The interface is found to fail by interface separation in a nominally “brittle” manner with a critical strain energy release rate, G_c ≈ 50 Jm⁻², substantially larger than the work of adhesion, W_ad ≈ 0.5 Jm⁻². Evidence of plastic deformation on the gold fracture surface, such as blunting steps and slip steps, suggest that plastic dissipation is the primary contribution to the measured G_c. Calculations suggest that the majority effect occurs in the plastic zone through the crack wake. The interface is also found to be susceptible to slow crack growth.     

The effect of grain size and cross-head velocity on the lower yield strength during inhomogeneous discontinuous yielding in iron and steel

The validity of the relation, \(\underline {Ag} \) , has been checked with experimental results on the lower yield strength, σ _aF of various irons and steels determined at room temperature over wide ranges in cross-head velocity,V _c, and grain boundary intercept or grain diameter,l. Good agreement was found with the proposed relation form ^*=4, wherem ^* is the dislocation velocity-effective stress exponent, and α=1/3. σ _i , the internal stress, ranged between 5000 and 13,000 psi andN ^αθK’ between 4.3×10^?15 and 19.3×10^?15. In the original relation, the value of α was one andK’ was given asK, which was assumed to be a material constant. The modification which became necessary indicates that possibly the density of mobile dislocations and/or the resistance of grain boundaries to propagating Lüder’s bands depend on Lüder’s band velocity and strain. The validity of the relation at very high and very low cross-head velocities or strain rates is discussed. The relation should apply in an intermediate range of cross-head or dislocation velocities wherem ^* should remain constant and should show an apparent decrease at both higher and lower velocities. The basis for this prediction is discussed and results are presented at low strain rates.     

Cast microstructure of Inconel 713C and its dependence on solidification variables

The dependence of cast microstructure of Inconel 713C on solidification variables was investigated over a wide range of local cooling rates, ∈, and thermal gradients in the liquid at the solid-liquid interface,G. The shape of MC carbide particles was found to depend greatly on: 1) theG/R ratio at the solid-liquid interface, whereR is growth rate, through the effect of this ratio on the solid phase,γ _γ , growth morphology. Under planar front growth conditions the carbide particles were octahedral, under cellular growth conditions they were plate-like, elongated along the cellular growth direction, and under dendritic growth conditions they were irregularly shaped; 2) the local cooling rate, ∈, when γ was dendritic, with a transition from octahedral to dendritic with increasing ∈. The size of MC carbide particles was found to be controlled by coarsening and to become finer with increasing ∈. In this alloy the composition of the MC carbide was established as (Nb_0.63Ti_0.31Mo_0.06) C and was practically independent of local cooling rate. Other observations were that the precipitation of γ′ and the formation of nonequilibrium eutectics, such as MC-γ, γ-γ′ or MC-γ-γ′ were suppressed at splat-cooling rates. Also, microsegregation of all alloying elements with the exception of aluminum was normal, with concentration increasing from the dendrite center-line to the dendrite arm boundary. Aluminum behaved in the opposite manner. Within the cooling rate range used herein, this variable had only a slight effect on microsegregation.     

Overview no. 49: On the mechanisms for the electroplastic effect in metals

The effects of high density d.c. current pulses (10³ A/mm² for 60 μs) on the flow stress of a number of polycrystalline metals (Al, Cu, Ni, Fe, Nb, W and Ti) tested in uniaxial tension at 300 K were investigated with the objective of determining the mechanisms responsible for the concurrent load drops. Both reversible and irreversible (plastic) strains contributed to the load drops. The major component of the reversible strain was the thermal expansion due to Joule heating; skin, pinch, and magnetostrictive effects were of less importance. An analysis of the plastic strain contribution to the load drops suggested that it resulted from the enhancement of dislocation mobility due to the action of drift electrons. Employing the thermally activated plastic flow concept, the electron wind “push” coefficient B_ew could be determined for Al and Cu and was found to be of the order of 10⁴ dyn-s/cm², in accord with Roschupkin et al.'s theory. This value is in accord with the dislocation damping constant B determined by other techniques at ~300 K; it is however about an order of magnitude larger than is normally expected for the electron drag coefficient B_e. In addition to the force exerted on dislocations by an electron wind, the analysis indicated that drift electrons also have a significant effect on one or more of the other parameters of the thermally-activated rate equation. Because of test machine inertia effects, oscillations in the load occurred as it dropped in response to a current pulse. A clear resolution of the influence of the oscillations on the results could not however be made, because of the small plastic strains involved (Δϵ_p ≈ 10⁻⁴) and the limited accuracy of the thermal activation parameters employed in the analysis.     

The Impact of Strain Reversal on Microstructure Evolution and Orientation Relationships in Ti-6Al-4V with an Initial Alpha Colony Microstructure

The effect of forward and reverse torsion on flow behavior and microstructure evolution, particularly dynamic and static spheroidization, on Ti-6Al-4V with an alpha lamella colony microstructure was studied. Testing was undertaken sub beta transus [1088 K (815 °C)] at strain rates of either 0.05 or 0.5 s^?1. Quantitative metallography and electron back scatter diffraction has identified that a critical monotonic strain (ε _c) in the range of 0.3 to 0.6 is required to initiate rapid dynamic spheroidization of the alpha lamella. For material deformed to strains below ε _c and then reversed to a zero net strain the orientation relationships between alpha colonies are close to ideal Burgers, enabling prior beta grains to be fully reconstructed. Material deformed to strains greater than ε _c and reversed lose Burgers and no beta reconstruction is possible, suggesting ε _c is the strain required to generate break-up of lamella. Static spheroidization is, however, sensitive to strain path around ε _c. Annealing at 1088 K (815 °C) for 4 hours for material subjected to 0.25 forward + 0.25 forward strain produces 48 pct spheroidized grains while material with 0.25 forward + 0.25 reverse strain has 10 pct spheroidization. This is believed to be a direct consequence of different levels of the stored energy between these two strain paths.     

An Epitaxial Model for Heterogeneous Nucleation on Potent Substrates

In this article, we present an epitaxial model for heterogeneous nucleation on potent substrates. It is proposed that heterogeneous nucleation of the solid phase (S) on a potent substrate (N) occurs by epitaxial growth of a pseudomorphic solid (PS) layer on the substrate surface under a critical undercooling (ΔT _c). The PS layer with a coherent PS/N interface mimics the atomic arrangement of the substrate, giving rise to a linear increase of misfit strain energy with layer thickness. At a critical thickness (h _c), elastic strain energy reaches a critical level, at which point, misfit dislocations are created to release the elastic strain energy in the PS layer. This converts the strained PS layer to a strainless solid (S), and changes the initial coherent PS/N interface into a semicoherent S/N interface. Beyond this critical thickness, further growth will be strainless, and solidification enters the growth stage. It is shown analytically that the lattice misfit (f) between the solid and the substrate has a strong influence on both h _c and ΔT _c; h _c decreases; and ΔT _c increases with increasing lattice misfit. This epitaxial nucleation model will be used to explain qualitatively the generally accepted experimental findings on grain refinement in the literature and to analyze the general approaches to effective grain refinement.     

In-Situ observation on microfracture behavior ahead of the crack tip in 63Sn37Pb solder alloy

in-situ transmission electron microscopy (TEM) tensile tests on as-cast and aged 63Sn37Pb solder alloys were conducted, and the fracture behavior in nanometer scale ahead of the crack tip was inspected and discussed. Results show that the fracture was completed by connecting the discontinuous cracks or voids. Dislocation behavior was concentrated along the grain boundaries for as-cast samples, and displayed mainly as dislocation climb. The crack was intergranular dominated under the lower strain rate. While remarkable mutual dislocation emission was detected in the aged solder. Transgranular cracks were dominant in the fractured area, and they propagated by linking up with the nanometer scale cracks ahead of the crack tips under the effective promotion of the inverse dislocation emission. At the same time, the partial interphase or intergranular cracks in the thinned area were also found. Under this condition, a new critical stress intensity factor K _c ^′ to define the mutual dislocation emission was proposed.     

In-Situ observation on microfracture behavior ahead of the crack tip in 63Sn37Pb solder alloy

in-situ transmission electron microscopy (TEM) tensile tests on as-cast and aged 63Sn37Pb solder alloys were conducted, and the fracture behavior in nanometer scale ahead of the crack tip was inspected and discussed. Results show that the fracture was completed by connecting the discontinuous cracks or voids. Dislocation behavior was concentrated along the grain boundaries for as-cast samples, and displayed mainly as dislocation climb. The crack was intergranular dominated under the lower strain rate. While remarkable mutual dislocation emission was detected in the aged solder. Transgranular cracks were dominant in the fractured area, and they propagated by linking up with the nanometer scale cracks ahead of the crack tips under the effective promotion of the inverse dislocation emission. At the same time, the partial interphase or intergranular cracks in the thinned area were also found. Under this condition, a new critical stress intensity factorK _c ^′ to define the mutual dislocation emission was proposed.     

Overview no. 50: Cleavage-limited maximum strength of work-hardened b.c.c. polycrystals

b.c.c. metals and alloys maintain a non-decaying work-hardening rate up to very high plastic strains when deformed monotonically at low temperatures (T < 0.3 T_M), specially by axisymmetric elongation (wire drawing). This fact seems to offer the possibility of production of strong metallic filaments which are tougher than other fibre reinforcing materials. However, b.c.c. metals being prone to cleave, their rising stress-strain curves could be trimmed by brittle failure beyond some point. This paper studies such contingency and shows that two failure modes are possible: a microscopic-type failure, when the flow stress meets the (strain-dependent) tensile cleavage stress, σ_f^T, and, for large strains, a macroscopic-type failure when the critical stress intensity factor (also strain-dependent) is reached for cracks associated to inclusions or for crack-like surface defects. From the rather limited information gathered on the evolution of the brittle failure stress with strain it is deduced that σ_f^T is mainly controlled by the instantaneous—strain-induced—grain size and that it will rarely limit the b.c.c. wire strength directly. On the contrary, macroscopic-type failures can constitute the absolute strength limit for alloys with very high workhardening rate. Guidelines to further improve such strength limit arise from the present overview.     

Critical Strengths for Slip Events in Nanocrystalline Metals: Predictions of Quantized Crystal Plasticity Simulations

This article studies how the monotonic and cyclic stress-strain response of nanocrystalline (NC) metals is affected by the grain-to-grain distribution of critical strengths (τ _c ) for slip events, as well as plastic predeformation (ε _pre ^p ). This is accomplished via finite element simulations that capture large jumps in plastic strain from dislocation slip events—a process referred to as quantized crystal plasticity (QCP).[1] The QCP simulations show that τ _c and ε _pre ^p significantly alter the monotonic and cyclic response at small strain, but only τ _c affects the response at large strain. These features are exploited to systematically infer the τ _c and ε _pre ^p characteristics that best fit experimental data for electrodeposited (ED) NC Ni. Key outcomes are the following: (1) the τ _c distribution is truncated, with an abrupt onset of slip events at a critical stress; (2) ε _pre ^p  = −0.4 pct, signifying precompression; (3) there is reverse slip bias, meaning that reverse slip events are easier than forward events; and (4) highly inhomogeneous residual stress states can be enhanced or reduced by tensile deformation, depending on ε _pre ^p .     

Analysis of accelerated creep under constant sustaining load for austenitic stainless steels

The effect of stress on creep rate of austenitic stainless steels of type 347 and 316 was studied by applying the differential test technique. It was found that the creep rate could be expressed as follows, whereB ₁ is a material constant depending on temperature,a ₁ anda _o are constants, and σ is the real stress. Considering the increase in real stress during creep process due to void formation and to the decrease in cross sectional area of the specimen, integrating the above equation yields the following creep curve, 1 $$ \in = \in _m + \frac{1}{{n_o \left( {c_o + 1} \right)}}ln\frac{1}{{1 - n_o \left( {c_o + 1} \right) \in _m (t - t_{_m } )}}$$ where ∈ is the creep strain at a given time (t), ∈_m is the minimum creep rate, ∈_m andt _m are the strain and time, respectively, at the minimum creep rate,n _o is a constant, andc _o is the material constant relating to the void formation. This equation agrees very well with the experimental creep curve.     

Effects of Yb-doping on flux pinning properties in YBa2Cu3O7-δ

The effects of Yb-doping on the critical current density (J_c) and the critical temperature (T_c) in YBa₂Cu₃O_7-δ (YBCO) were investigated. Rietveld refinements of X-ray diffraction showed that Yb³⁺ ions had partly substituted Y sites in YBCO and the unit cell volume V decreased monotonically as x increasing. Although T_c almost had no change with increasing Yb-concentration, the increase of J_c occurred as a field was applied and displayed a maximum at x=0.08. We argued that the formation of nanometric inhomogeneity may lead to the enhancement of pinning force.     

Effects of cooling rate and γ′ morphology on creep and stress-rupture properties of a powder metallurgy superalloy

The 650 °C creep and stress-rupture (S/R) behavior of powder metallurgy (PM) RENé 95 alloy was investigated under various cooling rates from two subsolvus solution temperatures. The cooling conditions were chosen to alter the morphology of the cooling γ′ (γ′_c), which constituted a high volume fraction (≃0.85) of all γ′ precipitates. The dispersion characteristics of γ _c ^′ changed from very fine at the highest cooling rate to progressively coarser with reduced cooling rate. At small γ _c ^′ (≃0.05 μm), a marked increase in creep and S/R resistance was observed, whereas at larger γ _c ^′ (≃0.1 μm), a marked decrease was observed. Also, for a givenγ _c ^′ size, both properties benefited from a higher solution temperature. The change in properties with the size of γ _c ^′ was associated with a change in deformation mechanism. The operative mechanism was essentially determined by the mean surface-to-surface spacing(l _s ) of the γ _c ^′ precipitates. Atl _s > 0.05 μm, the Orowan mechanism of dislocation expansion and looping became favorable, which led to higher primary creep strain and steady-state rate and also reduced S/R life. Atl _s < 0.05 μm, dislocation motion was significantly restricted, and the low dislocation density and inadequate dislocation sources were responsible for greatly suppressed primary creep strain and steady-state rate, and in some cases, for an incubation period in the creep curve. In addition, the S/R life increased significantly at lowl _s . Atl _s ≃ 0.05 μm, a mixed mode of deformation was observed due to inherent distribution of particle spacing in the structure, and this gave rise to intermediate creep and S/R resistance. Formerly Manager, Research and Development Department, Cameron Forge Company.     

Modelling of the nucleation temperature of the f.c.c. phase competing with glass formation in Cu-Ti alloys

The observed occurrence of a metastable f.c.c. phase competing with glass formation, and also occurring partially with metallic glass, in Cu-Ti alloys subjected to pulsed laser irradiation has been modelled in terms of both thermodynamic and kinetic parameters. The driving free energy ΔG_v for the formation of the f.c.c. phase from supercooled liquid alloys can be shown to be the result of a shallow T₀ curve extending from the Cu side of the phase diagram and laying substantially above the glass transition temperature (T_g) at all compositions. The dependence of the nucleation temperature T_n upon the cooling rate Ṫ has been modelled for conditions related to substrate epitaxy and also for nucleation in the bulk supercooled liquid. In the former case, when suitable assumptions are made about the values of interfacial energy (γ) and activation energy for diffusion (Q), it has been shown that T_n is profoundly depressed with increasing Ṫ for Ṫ values exceeding 10⁹K/s, the effect being m the middle of the phase diagram, as observed experimentally. When Ṫ is about 10¹⁰K/s, T_n, is depressed below T_g over a wide range of compositions, approximately in agreement with the observed glass formation range in the Cn-Ti system. Considerations of possible bulk nucleation (homogeneous or heterogeneous) indicate that the nucleation temperature associated with this type of nucleation must be above the nucleation temperature for substrate-related nucleation. The estimated growth times of the f.c.c. microcrystals competing with glass formation are of the order of microseconds. Combined with the growth velocities (ifν_c), which are of the order of meters/sec, they account for the very small average size (100 Å) of the experimentally observed microcrystals. The actual growth velocities may be smaller than the speed (ν_τ) with which the temperature isotherms traverse the resolidifying zone. A model of growth is proposed which accounts for the observed mixture of f.c.c. crystals and metallic glass in the re-solidified zone.     

Unstable flow in martensite and ferrite

It is proposed that unstable plastic flow of iron alloys containing carbon or nitrogen occurs when (? lnν/?τ ^*) _T becomes negative (v is the average velocity of the dislocations andτ ^* the effective stress acting upon them) at the maximum in the force-velocity curve deduced from either the Snoek or the Cottrell steady-state drag model. In addition, a nucleating event is necessary. A model is developed which predicts relationships between the applied stress, the strain rate and the temperature at the onset of unstable flow, and also the activation energy associated with the event. Experiments have been carried out on iron-carbon and iron-nickel-carbon alloys covering a range of carbon concentration in solution. The alloys were either annealed ferrite or martensite and, thus, the extremes of the range of possible dislocation density were examined. Two distinct types of plastic instability were identified: jerky flow, the result of Snoek interaction, and serrated flow due to Cottrell drag. All the qualitative and quantitative features of the phenomenon which were examined were found to be in complete accord with the model. The average velocity of the dislocations as a function of the temperature at the start of unstable flow has been deduced from the model and an estimate of the density of dislocations moving at the time has been made using measured values of the critical strain rate. The strain rate and temperature at which unstable flow disappears were measured as a function of the carbon concentration and the two types of substructure. The data show that an explanation based on the assumption that the phenomenon involved is the same as that producing the Köster internal-friction peak is untenable. An alternative suggestion, based on the relative stability of a Cottrell cloud and a carbide precipitate, is discussed briefly and qualitatively.     

Evaluation of hydrogen-assisted cracking behavior of low-alloy steel in the range 95 °C to 350 °C

In this report, hydrogen-assisted cracking (HAC) behavior of low-alloy steel was evaluated using a constant elongation rate tensile test, and the temperature and crack tip strain rate effects were observed. It was found that temperature dependence of the threshold condition (C _σm ^c ) of HAC above about 100 °C followed the relation C _σm ^c = Kexp(−41,300/Rr) whereK is a constant andT is absolute temperature. The relationship between HAC growth rate and crack tip strain rate was established as almost linear, irrespective of temperature and hydrogen concentration at the crack tip. Hydrogen heat release tests were also performed. From these tests, formation and growth of microcracks which are trap sites of hydrogen were thought to be the mechanism of HAC in the steel. From this mechanism, HAC behavior of the low-alloy steel could be qualitatively explained.     

Internal friction in F.C.C. alloys due to solute drag on dislocations—I. A model for the effect of core diffusion

The internal friction (mechanical loss) behavior of dislocations is studied in a model which, for the first time, considers the substitutional solute mobility in the dislocation core to be higher than in the bulk around it. The parameters investigated include the external stress σ_xy, the solute concentration c₀, the pinning length of the dislocation and the temperature. It is shown that, at low c₀ and high σ_xy, the kinetics of the dislocation motion is determined by the fast diffusion of the solute atoms in the core, while for high c₀ and low σ_xy the diffusion of the atoms far away from the dislocation is rate-limiting. The results are compared with the analytical model of Schoeck and are applied to the alloy system SlSi. New experimental results supporting the model are described in a companion paper (Part II).     

Effect of temperature and shear direction on yield stress by {11\bar 22}〈\overline {11} 23〉 slip in HCP metals23〉 slip in HCP metals

The yield shear stress τ _y due to {11 $\bar 2$ 2}〈 $\overline {11} $ 23〉 second-order pyramidal slip system in cadmium, zinc, and magnesium hcp crystals increased with increasing temperature. This result is interpreted by two thermally activated processes as follows: (1) the dissociation of a (c+a) edge dislocation with a Burgers vector of 1/3〈 $\overline {11} $ 23〉 into a c sessile dislocation and an a glissile basal dislocation, and the subsequent immobilization of the (c+a) edge dislocation; (2) consequently, the double-cross slip of (c+a) screw dislocations must be activated thermally by an increment of applied stress to increase propagation velocity of slip band width. Moreover, τ _y is affected strongly by a direction of applied shear force due to second-order pyramidal slip in zinc as well as in cadmium. The anomalous behaviors of yielding would be caused by the nonsymmetrical core structure of the (c + a) dislocation due to the lattice heterogeneity in hcp metals.