Dislocation Dynamics Simulations

The transmission of an incoming dislocation through a symmetrical low-angle tilt grain boundary (GB) is studied for {110}<111> slip systems in body-centered cubic metals using discrete dislocation dynamics (DD) simulations. The transmission resistance is quantified in terms of the different types of interactions between the incoming and GB dislocations. Five different dislocation interaction types are considered: collinear, mixed-symmetrical junction, mixed-asymmetrical junction, edge junction, and coplanar. Mixed-symmetrical junction formation events are found not only to cause a strong resistance against the incident dislocation penetration, but also to transform the symmetrical low-angle tilt GB into a hexagonal network (a general low-angle GB). The interactions between the incident dislocation and the GB dislocations can form an array of <100> dislocations (binary junctions) in non-coplanar interactions, or a single <100> dislocation in coplanar interaction. We study how the transmission resistance depends on the mobility of h100i dislocations. <100> dislocations have usually been treated as immobile in DD simulations. In this work, we discuss and implement the mobility law for 100 dislocations. As an example, we report how the mobility of 100 dislocations affects the equilibrium configuration of a ternary dislocation interaction.

We present a multiscale dislocation density-based constitutive model for the strain-hardening behavior in twinning-induced plasticity (TWIP) steels. The approach is a physics-based strain rate- and temperature-sensitive model which reflects microstructural investigations of twins and dislocation structures in TWIP steels. One distinct advantage of the approach is that the model parameters, some of which are derived by ab initio predictions, are physics-based and known within an order of magnitude. This allows more complex microstructural information to be included in the model without losing the ability to identify reasonable initial values and bounds for all parameters.
Dislocation cells, grain size and twin volume fraction evolution are included. Particular attention is placed on the mechanism by
which new deformation twins are nucleated, and a new formulation for the critical twinning stress is presented. Various temperatures were included in the parameter optimization process. Dissipative heating is also considered. The use of physically justified parameters enables the identification of a universal parameter set for the example of an Fe–22Mn–0.6C TWIP steel.

Creep of single-crystal superalloys is governed by dislocation glide, climb, reactions and annihilation. Discrete three-dimensional (3D) dislocation dynamics (DDD) simulations are used to study the evolution of the dislocation substructure in a gamma/gamma' microstructure of a single-crystal superalloy for different climb rates and loading conditions. A hybrid mobility law for glide and climb is used to map the interactions of dislocations with gamma' cubes. The focus is on the early stages of creep, where dislocation plasticity is confined to narrow gamma channels. With enhancing climb mobility, the creep strain increases, even if the applied resolved shear stress is below the critical stress required for squeezing dislocations into the gamma channels. The simulated creep microstructure consists of long dislocations and a network near the corners of the c0 precipitate in the low-stress regime. In the high-stress regime, dislocations squeeze into the gamma channels, where they deposit dislocation segments at the gamma/gamma' interfaces. These observations are in good agreement with experimentally observed dislocation structures that form during high-temperature and low-stress creep.

We use a physically-based crystal plasticity model to predict the yield strength of body-centered cubic (bcc) tungsten single crystals subjected to uniaxial loading. Our model captures the thermally-activated character of screw dislocation motion and full non-Schmid effects, both of which are known to play critical roles in bcc plasticity. The model uses atomistic calculations as the sole source of constitutive information, with no parameter fitting of any kind to experimental data. Our results are in excellent agreement with experimental measurements of the yield stress as a function of temperature for a number of loading orientations. The validated methodology is employed to calculate the temperature and strain-rate dependence of the yield strength for 231 crystallographic orientations within the standard stereographic triangle. We extract the strain-rate sensitivity of W crystals at different temperatures, and finish with the calculation of yield surfaces under biaxial loading conditions that can be used to define effective yield criteria for engineering design models.

This is a physics-based constitutive model of dislocation glide in metals that explicitly accounts for the redistribution of dislocations due to their motion. The model parameterizes the complex microstructure by dislocation densities of edge and screw character, which either occur with monopolar properties, i.e. a single dislocation with positive or negative line sense, or with dipolar properties, i.e. two dislocations of opposite line sense combined. The advantage of the model lies in the description of the dislocation density evolution, which comprises the usual rate equations for dislocation multiplication and annihilation, and formation and dissociation of dislocation dipoles. Additionally, the spatial redistribution of dislocations by slip is explicitly accounted for. This is achieved by introducing an advection term for the dislocation density that turns the evolution equations for the dislocation density from ordinary into partial differential equations. The associated spatial gradients of the dislocation slip render the model nonlocal. The model is applied to wedge indentation in single-crystalline nickel. The simulation results are compared to published experiments (Kysar et al., 2010) in terms of the spatial distribution of lattice rotations and geometrically necessary dislocations. In agreement with experiment, the predicted dislocation fluxes lead to accumulation of geometrically necessary dislocations around a vertical geometrical border with a high orientation gradient below the indenter that is decisive for the overall plastic response. A local model variant without dislocation transport is not able to predict the influence of this geometrical transition zone correctly and is shown to behave markedly softer.

This work investigates the origin of creep dislocations in a Ni-base, single crystal superalloy subject to creep at an intermediate stress and temperature. Employing high angular resolution electron backscatter diffraction (HR-EBSD), electron channeling contrast imaging under controlled diffraction conditions (cECCI) and discrete dislocation dynamics (DDD) modelling, it is shown that low-angle boundariesd-which correspond to dendrite boundaries or their residues after annealingdare not the major sources of creep dislocations. At the onset of creep deformation, they are the only active sources. Creep dislocations are emitted from them and percolate into the dislocation-depleted crystal. However, the percolation is very slow. As creep deformation proceeds, before the boundary-originated dislocations move further than a few micrometers away from their source boundary, individual dislocations that are spread throughout the undeformed microstructure become active and emit avalanches of creep dislocations in boundary-free regions, i.e. regions farther than a few micrometer away from boundaries. Upon their activation, the density of creep dislocations in boundary-free regions soars by two orders of magnitude; and the entire microstructure becomes deluged with creep dislocations. The total area of boundary-free regions is several times the total area of regions covered by boundary-originated creep dislocations. Therefore, the main sources of creep dislocations are not low-angle boundaries but individual, isolated dislocations in boundary-free regions.

The interaction of dislocations with precipitates is an essential strengthening mechanism in metals, as exemplified by the superior high-temperature strength of Ni-base superalloys. Here we use atomistic simulation samples generated from atom probe tomography data of a single crystal superalloy to study the interactions of matrix dislocations with a gamma' precipitate in molecular dynamics simulations. It is shown that the precipitate morphology, in particular its local curvature, and the local chemical composition significantly alter both, the misfit dislocation network which forms at the precipitate interface, and the core structure of the misfit dislocations. Simulated tensile tests reveal the atomic scale details of many experimentally observed dislocation–precipitate interaction mechanisms, which cannot be reproduced by idealized simulation setups with planar interfaces. We thus demonstrate the need to include interface curvature in the study of semicoherent precipitates and introduce as an enabling method atom probe tomography-informed atomistic simulations.

Dislocation glide is a general deformation mode, governing the strength of metals. Via discrete dislocation dynamics and molecular dynamics simulations, we investigate the strain rate and dislocation density dependence of the strength of bulk copper and aluminum single crystals. An analytical relationship between material strength, dislocation density, strain rate and dislocation mobility is proposed, which agrees well with current simulations and published experiments. Results show that material strength displays a decreasing regime (strain rate hardening) and then increasing regime (classical forest hardening) as the dislocation density increases. Accordingly, the strength displays universally, as the strain rate increases, a strain rate-independent regime followed by a strain rate hardening regime. All results are captured by a single scaling function, which relates the scaled strength to a coupling parameter between dislocation density and strain rate. Such coupling parameter also controls the localization of plasticity, fluctuations of dislocation flow and distribution of dislocation velocity.

Dynamic strain aging arises from the interaction between solute atoms and matrix dislocations in strained metallic alloy. It initiates jerky dislocation motion and abrupt softening, causing negative strain rate sensitivity. This effect leads to instable flow phenomena at the macroscopic scale, appearing as a serrated stress–strain response and deformation banding. These macroscopic features are referred to as the Portevin–Le Chatelier effect (PLC). Here we study the atomistic origin of dynamic strain aging in an Al-4.8 at.% Mg alloy using atom probe tomography (APT) and transmission electron microscopy (TEM). Samples were prepared from as-cold rolled (90% thickness reduction), stabilized (120 °C, 20 h) and recrystallized sheets (400 C, 10 min), respectively. In the stabilized state, Mg was found to decorate <110> aligned dislocations with up to 12.5 at.%. Tensile tests in combination with thermographic and laser speckle observations were used to map the deformation bands for the site-specific extraction of APT samples from regions inside the PLC bands. We observed an asymmetrical Mg distribution along some of the dislocations, matching model predictions for high dislocation speeds at peak drag stress by Zhang and Curtin. In this case, the Mg distribution is characterized by depletion in the compressive regime above the dislocation slip plane and enrichment in the dilatation region below the slip plane. Mg also depletes in a tail-like form behind fast-moving dislocations, further promoting slip localization.

The early stage of high-temperature low-stress creep in single-crystal superalloys is characterized by the rapid development of interfacial dislocation networks. Although interfacial motion and dynamic recovery of these dislocation networks have long been expected to control the subsequent creep behavior, direct observation and hence in-depth understanding of such processes has not been achieved. Incorporating recent developments of discrete dislocation dynamics models, we simulate interfacial dislocation motion in the channel structures of single-crystal superalloys, and investigate how interfacial dislocation motion and dynamic recovery are affected by interfacial dislocation interactions and lattice misfit. Different types of dislocation interactions are considered: self, collinear, coplanar, Lomer junction, glissile junction, and Hirth junction. The simulation results show that strong dynamic recovery occurs due to the short-range reactions of collinear annihilation and Lomer junction formation. The misfit stress is found to induce and accelerate dynamic recovery of interfacial dislocation networks involving self-interaction and Hirth junction formation, but slow down the steady interfacial motion of coplanar and glissile junction forming dislocation networks. The insights gained from these simulations on high-temperature low-stress creep of single-crystal superalloys are also discussed.

The transmission of an incoming dislocation through a symmetrical low-angle tilt grain boundary (GB) is studied for {110}<111> slip systems in body-centered cubic metals using discrete dislocation dynamics (DD) simulations. The transmission resistance is quantified in terms of the different types of interactions between the incoming and GB dislocations. Five different dislocation interaction types are considered: collinear, mixed-symmetrical junction, mixed-asymmetrical junction, edge junction, and co-planar. Mixed-symmetrical junction formation events are found not only to cause a strong resistance against the incident dislocation penetration, but also to transform the symmetrical low-angle tilt GB into a hexagonal network (a general low-angle GB). The interactions between the incident dislocation and the GB dislocations can form an array of <100> dislocations (binary junctions) in non-co-planar interactions, or a single
<100> dislocation in co-planar interaction. We study how the transmission resistance depends on the mobility of
<100> dislocations. <100> dislocations have usually been treated as immobile in DD simulations. In this work, we discuss and implement the mobility law for <100> dislocations. As an example, we report how the mobility of <100> dislocations affects the equilibrium configuration of a ternary dislocation interaction.

Creep of single-crystal superalloys is governed by dislocation glide, climb, reactions and annihilation. Discrete three-dimensional (3D) dislocation dynamics (DDD) simulations are used to study the evolution of the dislocation substructure in a gamma/ Gamma' microstructure of a single-crystal superalloy for different climb rates and loading conditions.