The limiting speeds of dislocations

The purpose of this article is to show that the limiting speeds of moving dislocations are determined by inertial effects, or by viscous drag, at their cores. Simple expressions for the limiting speeds are derived. The standard idea that the speeds are limited by the inertia of the elastic fields, accompanied by Lorentz contractions, is shown to be flawed because it neglects the angular momentum of a moving dislocation; or, equivalently, because it assumes that the motion is steady if the velocity is constant, but this is not possible because the motion creates plastic deformation. Finally, the standard theory considers the dislocation to be moving in an infinite medium but this is not acceptable, because then both the energy and the mass would then be infinite. This article is based on a presentation given in the symposium entitled “Dynamic Behavior of Materials—Part II”, held during the 1998 Fall TMS/ASM Meeting and Materials Week, October 11–15, 1998, in Rosemont, Illinois, under the auspices of the TMS Mechanical Metallurgy and the ASM Flow and Fracture Committees.     

The motion of multiple height ledges and disconnections in phase transformations

For phase transformations with well-defined terrace planes, interface motion can occur by the motion of ledges or disconnections (ledges with added dislocation character). Symmetry imposes restrictions on the nature of these defects and may lead to the need for multiple height ledges. The structure of the ledge riser can also be variable. These possibilities impose constraints that can influence the motion of the defects and hence affect the rate of phase transformation. Examples of these phenomena are presented for interfaces with differing degrees of lattice matching. This article is based on a presentation made in the symposium “Kinetically Determined Particle Shapes and the Dynamics of Solid:Solid Interfaces,” presented at the October 1996 Fall meeting of TMS/ASM in Cincinnati, Ohio, under the auspices of the ASM Phase Transformations Committee.     

Creep behavior of TiAl alloys with enhanced high-temperature capability

For high-temperature applications, creep strength is of major concern, in addition to oxidation and corrosion resistance, and determines the application range of titanium aluminide alloys in competition with other structural materials. Thus, this work was aimed at identifying mechanisms of creep deformation and microstructural degradation and at developing alloying concepts with respect to an enhanced high-temperature capability. The analysis shows that dislocation climb controls deformation in the range of the intended operation temperatures. Further, complex processes of phase transformations, recrystallization, and microstructural coarsening were observed, which contribute to microstructural degradation and limit component life in long-term service. By alloying with high contents of Nb, both room- and high-temperature strength properties can be improved as Nb increases the activation energy of diffusion and increases the propensity for twinning at ambient temperature. For alloys with enhanced high-temperature capability, microalloying with carbon is also of particular use, because carbide precipitates effectively hinder dislocation motion and are thought to increase microstructural stability. 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.     

Dislocation structure behind a shock front in fcc perfect crystals: Atomistic simulation results

Large-scale molecular dynamics simulations are used to investigate the dislocation structure behind a shock front in perfect fcc crystals. Shock compression in both the 〈100〉 and 〈111〉 directions induces dislocation loop formation via a sequential emission of partial dislocations, but in the 〈100〉 case, this process is arrested after the first partial, resulting in stacking-fault loops. The large mobility of the bounding partial dislocations results in a plastic wave that is always overdriven in the 〈100〉 direction; the leading edges of the partials are traveling with the plastic front, as in the models of Smith and Hornbogen. In contrast, both partials are emitted in 〈111〉 shock compression, resulting in perfect dislocation loops bounded only by thin stacking fault ribbons due to the split partial dislocations. These loops grow more slowly than the plastic shock velocity, so new loops are periodically nucleated at the plastic front, as suggested by Meyers. This article is based on a presentation given in the symposium “Dynamic Deformation: Constitutive Modeling, Grain Size, and Other Effects: In Honor of Prof. Ronald W. Armstrong,” March 2–6, 2003, at the 2003 TMS/ASM Annual Meeting, San Diego, California, under the auspices of the TMS/ASM Joint Mechanical Behavior of Materials Committee.     

Dislocation mechanics-based constitutive equations

A review of constitutive models based on the mechanics of dislocation motion is presented, with focus on the models of Zerilli and Armstrong and the critical influence of Armstrong on their development. The models were intended to be as simple as possible while still reproducing the behavior of real metals. The key feature of these models is their basis in the thermal activation theory propounded by Eyring in the 1930’s. The motion of dislocations is governed by thermal activation over potential barriers produced by obstacles, which may be the crystal lattice itself or other dislocations or defects. Typically, in bcc metals, the dislocation-lattice interaction is predominant, while in fcc metals, the dislocation-dislocation interaction is the most significant. When the dislocation-lattice interaction is predominant, the yield stress is temperature and strain rate sensitive, with essentially athermal strain hardening. When the dislocation-dislocation interaction is predominant, the yield stress is athermal, with a large temperature and rate sensitive strain hardening. In both cases, a significant part of the athermal stress is accounted for by grain size effects, and, in some materials, by the effects of deformation twinning. In addition, some simple strain hardening models are described, starting from a differential equation describing creation and annihilation of mobile dislocations. Finally, an application of thermal activation theory to polymeric materials is described. This article is based on a presentation given in the symposium “Dynamic Deformation: Constitutive Modeling, Grain Size, and Other Effects: In Honor of Prof. Ronald W. Armstrong,” March 2–6, 2003, at the 2003 TMS/ASM Annual Meeting, San Diego, California, under the auspices of the TMS/ASM Joint Mechanical Behavior of Materials Committee.     

Motion of Crystal Particles by the Electromagnetic Vibrations in Mg-Cu-Y Bulk Metallic Glasses

The method for producing Mg-Cu-Y and Fe-Co-B-Si-Nb bulk metallic glasses using electromagnetic vibrations is effective in forming the metallic glass phase. Disappearance or decrement of clusters by the electromagnetic vibrations applied to the liquid state is considered to cause suppression of crystal nucleation, because the electromagnetic vibrations vibrate the clusters vigorously in the melt. The purpose of this study was to investigate motion of the crystal particles by the electromagnetic vibrations in Mg-Cu-Y bulk metallic glasses. The electromagnetic vibration force vibrated the crystal particles or the clusters that become crystal nuclei in the melt, because the electric current for the electromagnetic vibrations concentrates in those. Thus, the electromagnetic vibrations were found to select vibration particles from the melt. Moreover, it was considered that composites for which second phases or other compounds are dispersed into the metallic glass phase or a nanostructure phase can be produced by the electromagnetic vibration process. This article is based on a presentation given in the symposium entitled “Bulk Metallic Glasses IV,” which occurred February 25–March 1, 2007 during the TMS Annual Meeting in Orlando, Florida under the auspices of the TMS/ASM Mechanical Behavior of Materials Committee.     

Grain-size dependence of the flow stress of Cu from millimeters to nanometers

Data in the literature on the effect of grain size (d) from millimeters to nanometers on the flow stress of Cu are evaluated. Three grain-size regimes are identified: regime I, d>∼10⁻⁶ m; regime II, d ≈10⁻⁸ to 10⁻⁶ m; and regime III, d<∼10⁻⁸ m. Grain-size hardening occurs in regimes I and II; grain-size softening occurs in regime III. The deformation structure in regime I consists of dislocation cells; in regime II, the dislocations are mostly restricted to their slip planes; in regime III, computer simulations indicate that dislocations are absent and that deformation occurs by the shearing of grain-boundary atoms. The transition from regime I to II occurs when the dislocation cell size becomes larger than the grain size, and the transition from regime II to III occurs when the dislocation spacing due to elastic interactions becomes larger than the grain size. The rate-controlling mechanism in regime I is concluded to be the intersection of dislocations; in regime II, it is proposed to be grain-boundary shear promoted by the pileup of dislocations; in regime III, it appears to be grain-boundary shear by the applied stress alone. This article is based on a presentation given in the symposium “Dynamic Deformation: Constitutive Modeling, Grain Size, and Other Effects: In Honor of Prof. Ronald W. Armstrong,” March 2–6, 2003, at the 2003 TMS/ASM Annual Meeting, San Diego, California, under the auspices of the TMS/ASM Joint Mechanical Behavior of Materials Committee.     

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.     

Comparison between high and low strain-rate deformation of tantalum

To understand the constitutive behavior of tantalum, compression tests are performed over the range of strain rates from 0.0001/s to 3000/s, and at temperatures from 296 to 1000 K. The flow stress is seen to be representable as the sum of a thermal, an athermal, and a viscous drag component. At high strain rates (3000/s), the thermal component is observed to be expressible in terms of the temperature and the strain rate, whereas the athermal component is independent of these variables. At lower strain rates, however, such a separation of the effects of the strain, strain rate, and temperature on the flow stress is not easily achieved. At high enough temperatures, i.e., temperatures above which the thermal component is essentially zero, viscous drag appears to have a significant effect on the flow stress. This article is based on a presentation given in the symposium entitled “Dynamic Behavior of Materials—Part II,” held during the 1998 Fall TMS/ASM Meeting and Materials Week, October 11–15, 1998, in Rosemont, Illinois, under the auspices of the TMS Mechanical Metallurgy and the ASM Flow and Fracture Committees.     

Influence of alloying elements on the strain rate and temperature dependence of the flow stress of steels

After a short introduction to the theoretical background of thermally activated glide of dislocations, a constitutive model is presented, which describes the temperature and strain-rate dependence of the flow stress. The properties of this constitutive equation were estimated for several plain carbon steels in normalized conditions, for quenched and tempered low-alloy steels, as well as for some high-strength low-alloy (HSLA) steels based on the temperature dependence and strain-rate sensitivity of the flow stress at temperatures 81 K≤T≤398 K and strain rates 5·10⁻⁵ s⁻¹≤ε≤1·10⁻²s⁻¹. The constitutive equation enables the extrapolation of flow-stress data to higher strain rates (ε<~10 ⁺⁴s⁻¹), which are in good agreement with the results obtained from high strain-rate deformation tests. The influence of solute-alloying elements on the thermal stress, the activation enthalpy, and the constitutive parameters will be discussed. This article is based on a presentation given in the symposium entitled ‘Dynamic Behavior of Materials-Part II,” held during the 1998 Fall TMS/ASM ASM Meeting and Materials Week, October 11–15, 1998, in Rosemont, Illinois, under the auspices of the TMS Mechanical Metallurgy and the ASM Flow and Fracture Committees.     

The role of mobile dislocations in the nucleation of brittle fracture

The development of dislocation substructure has been studied in dual-phase steels using transmission electron microscopy. This substructure has been correlated with the fracture behavior of these steels. The high ductility and impact strength of the dual-phase steels seem dependent on their initial dislocation substructure, in which an important role is played by a/2< 111> screw dislocations, which, when present in a crisscross configuration, can react, forming mobile a< 001> edge dislocations on their intersections. The presence and generation of the mobile a< 001> edge dislocations are considered here as a condition of the quasi-brittle behavior of these steels, and the nucleation of brittle cracks is discussed in terms of interactions between these dislocations. This article is based on a presentation made in the symposium “Quasi-Brittle Fracture” presented during the TMS fall meeting, Cincinnati, OH, October 21-24, 1991, under the auspices of the TMS Mechanical Metallurgy Committee and the ASM/MSD Flow and Fracture Committee.     

Atomistic Simulations of the Plasticity Behavior of Shock-Induced Polycrystalline Nickel

Shock loading single crystalline nickel creates a defected nanostructure dominated by stacking faults and twins. This transformation is caused by a complex interplay between the incident waves, the waves reflected from sample-free surfaces, and the interference between reflected waves. The plasticity behavior of this shock-induced defected nickel was studied using molecular dynamics (MD) simulations. Compared to a perfect single-crystal nickel sample of the same size, the twinned sample has significantly less yield stress in compression, a slightly lower yield stress in tension, and a yield stress about 30 pct higher in shear. Importantly, our simulations reveal the underlying atomistic mechanisms of dislocation nucleation and twin growth. We observe that while strengthening under shear loading involves lattice dislocations cutting through twins, weakening arises from nucleation of dislocations on the twins under tensile and compressive loading. Also, we have discovered precursors to dislocation loop nucleation in these simulations. This article is based on a presentation made in the symposium entitled “Dynamic Behavior of Materials,” which occurred during the TMS Annual Meeting and Exhibition, February 25–March 1, 2007 in Orlando, Florida, under the auspices of The Minerals, Metals and Materials Society, TMS Structural Materials Division, and TMS/ASM Mechanical Behavior of Materials Committee.     

Growth of δ′ on dislocations in a dilute Al-Li alloy

The quantitative results of δ′ growth kinetics on dislocations in an Al-2.27 wt pct Li alloy demonstrate that at temperatures greater than 0.5 of the homologous melting temperature, T _m , volume diffusion is the dominant mechanism. However, a small contribution, approximately one atom in 300, is made by pipe diffusion through the dislocation. This can be established by careful examination of dislocation climb associated with precipitate growth. An analysis based on the δ′ growth kinetics and diffusion equation gives an activation energy of 0.56 eV for Li pipe diffusion. At temperatures <0.5 T _m , δ′ precipitate growth is faster when associated with dislocations, and here, pipe diffusion is necessary to account for the kinetics observed. This article is based on a presentation made in the symposium “Kinetically Determined Particle Shapes and the Dynamics of Solid:Solid Interfaces,” presented at the October 1996 Fall meeting of TMS/ASM in Cincinnati, Ohio, under the auspices of the ASM Phase Transformations Committee.     

Camage leading to ductile fracture under high strain-rate conditions

Quantitative metallographic studies of damage evolution leading to ductile fracture under high strainrate loading conditions are presented. A model material is considered, namely, leaded brass, which contains a dispersed globular lead phase that acts as void nucleation sites. Interrupted tensile split Hopkinson bar tests have been performed to capture the evolution of porosity and void aspect ratio with deformation at strain rates up to 3000 s⁻¹. Both uniaxial and notched specimen geometries were considered to allow the effects of remote stress triaxiality to be investigated. Plate impact testing has also been performed to investigate the evolution of damage under the intense tensile triaxiality and extremely high rates of deformation (10⁵ s⁻¹) occurring within a spall layer. Quantitative metallographic measurements of damage within deformed specimens are used to assess predictions from a Gursonbased constitutive model implemented within an explicit dynamic finite element code. A stresscontrolled void nucleation treatment is shown to capture the effect of triaxiality on damage initiation for the range of experiments considered. J.P. FOWLER, formerly Research Associate with the Mechanical and Aerospace Engineering Department, Carleton University This article is based on a presentation given in the symposium entiled “Dynamic Behavior of Materials—Part II,” held during the 1998 Fall TMS/ASM Meeting and Materials Week, October 11–15, 1998, in Rosemont, Illinois, under the auspices of the TMS Mechanical Metallurgy and the ASM Flow and Fracture Committees.     

Damage leading to ductile fracture under high strain-rate conditions

Quantitative metallographic studies of damage evolution leading to ductile fracture under high strain-rate loading conditions are presented. A model material is considered, namely, leaded brass, which contains a dispersed globular lead phase that acts as void nucleation sites. Interrupted tensile split Hopkinson bar tests have been performed to capture the evolution of porosity and void aspect ratio with deformation at strain rates up to 3000 s⁻¹. Both uniaxial and notched specimen geometries were considered to allow the effects of remote stress triaxiality to be investigated. Plate impact testing has also been performed to investigate the evolution of damage under the intense tensile triaxiality and extremely high rates of deformation (10⁵ s⁻¹) occurring within a spall layer. Quantitative metallographic measurements of damage within deformed specimens are used to assess predictions from a Gurson-based constitutive model implemented within an explicit dynamic finite element code. A stress-controlled void nucleation treatment is shown to capture the effect of triaxiality on damage initiation for the range of experiments considered. This article is based on a presentation given in the symposium entitled “Dynamic Behavior of Materials—Part II,” held during the 1998 Fall TMS/ASM Meeting and Materials Week, October 11–15, 1998, in Rosemont, Illinois, under the auspices of the TMS Mechanical Metallurgy and the ASM Flow and Fracture Committees.     

Comparison between high and low strain-rate deformation of tantalum

To understand the constitutive behavior of tantalum, compression tests are performed over the range of strain rates from 0.0001/s to 3000/s, and at temperatures from 296 to 1000 K. The flow stress is seen to be representable as the sum of a thermal, an athermal, and a viscous drag component. At high strain rates (3000/s), the thermal component is observed to be expressible in terms of the temperature and the strain rate, whereas the athermal component is independent of these variables. At lower strain rates, however, such a separation of the effects of the strain, strain rate, and temperature on the flow stress is not easily achieved. At high enough temperatures, i.e., temperatures above which the thermal component is essentially zero, viscous drag appears to have a significant effect on the flow stress. was formerly with the Center of Excellence for Advanced Materials, University of California, San Diego. This article is based on a presentation given in the symposium entitled “Dynamic Behavior of Materials—Part II,” held during the 1998 Fall TMS/ASM Meeting and Materials Week, October 11–15, 1998, in Rosemont, Illinois, under the auspices of the TMS Mechanical Metallurgy and the ASM Flow and Fracture Committees.     

Strain-induced self-organization of steps and islands in SiGe/Si multilayer films

It has recently been recognized that “stress management” may become a unique way of fabricating nanostructures, because structural self-assembly and self-organization can be strongly influenced by strain. In this article, we review recent studies of growth and ordering processes in multilayer films of alternating Si and SiGe layers with nanometer-layer spacing. The formation of ordered arrays, superlattices of step bunches, and three-dimensional (3-D) islands that exhibit remarkable spatial and size uniformity and very good long-range order, are demonstrated. Theoretical analyses and simulations based on elastic models are discussed to elucidate the lattice strain-induced formation and self-organization processes. The self-organized steps and 3-D islands provide a possible route for fabricating novel devices based on quantum wires and quantum dots. This article is based on a presentation made in the symposium “Kinetically Determined Particle Shapes and the Dynamics of Solid:Solid Interfaces,” presented at the October 1996 Fall meeting of TMS/ASM in Cincinnati, Ohio, under the auspices of the ASM Phase Transformations Committee.     

Influence of alloying elements on the strain rate and temperature dependence of the flow stress of steels

After a short introduction to the theoretical background of thermally activated glide of dislocations, a constitutive model is presented, which describes the temperature and strain-rate dependence of the flow stress. The properties of this constitutive equation were estimated for several plain carbon steels in normalized conditions, for quenched and tempered low-alloy steels, as well as for some high-strength low-alloy (HSLA) steels based on the temperature dependence and strain-rate sensitivity of the flow stress at temperatures 81 K≤T≤398 K and strain rates 5 · 10⁻⁵ s⁻¹≤ε≤1 · 10⁻² s⁻¹. The constitutive equation enables the extrapolation of flow-stress data to higher strain rates (ε≲10⁺⁴ s⁻¹), which are in good agreement with the results obtained from high strain-rate deformation tests. The influence of solute-alloying elements on the thermal stress, the activation enthalpy, and the constitutive parameters will be discussed. This article is based on a presentation given in the symposium entitled “Dynamic Behavior of Materials-Part II,” held during the 1998 Fall TMS/ASM Meeting and Materials Week, October 11–15, 1998, in Rosemont, Illinois, under the auspices of the TMS Mechanical Metallurgy and the ASM Flow and Fracture Committees.     

Quantitative description of damage evolution in ductile fracture of tantalum

Dynamic ductile fracture has been studied through incipient spallation experiments on two grades of tantalum. A commercially pure Ta material incipiently spalled at 252 m/s, a highly pure Ta material incipiently spalled at 246 m/s, and a highly pure Ta material preshocked at 250 m/s and incipiently spalled at 246 m/s were used. Microstructural parameters of the fracture process such as porosity, void-size distributions, and void aspect ratios have been quantified using image analysis and optical profilometry techniques. The commercially pure Ta, the highly pure Ta preshocked prior to spall, and the annealed high-purity Ta exhibited 27, 16.6, and 5.5 pct porosity, respectively. The void-size distribution observed in all three tests was adequately represented by either a log-normal or a linear combination of a log-normal and a Weibull distribution function. At least 80 pct of the aspect ratios observed in all three tests were adequately represented by a gamma distribution function. This article is based on a presentation given in the symposium entitled “Dynamic Behavior of Materials—Part II,” held during the 1998 Fall TMS/ASM Meeting and Materials Week, October 11–15, 1998, in Rosemont, Illinois, under the auspices of the TMS Mechanical Metallurgy and the ASM Flow and Fracture Committees.     

Simulation of shear plugging through thin plates using the GRIM eulerian hydrocode

Ballistic experiments have been performed using aluminum spheres against 10-mm rolled homogenous armour (RHA), MARS270, MARS300, and titanium alloy plates to investigate the influence of the plugging mechanism on material properties. The experiments have measured the threshold for plug mass and velocity as well as the recovered aluminum sphere mass over a range of velocities. Some of the experiments have been simulated using the in-house second generation Eulerian hydrocode GRIM. The calculations feature advanced material algorithms derived from interrupted tensile testing techniques and a triaxial failure model derived from notched tensile tests over a range of strain rates and temperatures. The effect of mesh resolution on the results has been investigated and understood. The simulation results illustrate the importance of the constitutive model in the shear localization process and the subsequent plugging phenomena. The stress triaxiality is seen as the dominant feature in controlling the onset and subsequent propagation of the crack leading to the shear plug. The simulations have demonstrated that accurate numerics coupled with accurate constitutive and fracture algorithms can successfully reproduce the observed experimental features. However, extrapolation of the fracture data leads to the simulations overpredicting the plug damage. The reasons for this are discussed. This article is based on a presentation given in the symposium entitled “Dynamic Behavior of Materials—Part II,” held during the 1998 Fall TMS/ASM Meeting and Materials Week, October 11–15, 1998, in Rosemont, Illinois, under the auspices of the TMS Mechanical Metallurgy and the ASM Flow and Fracture Committees.