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Results are presented for work on stress-strain relationships in silicon ribbon. Calculations of stress fields, dislocation desities, and buckling were made; uniaxial tensile tests were made on silicon at 1150 C; and dislocation motion studies were performed.
An investigation of the fatigue crack growth (FCG) behavior of PWA 1480 single crystal nickel base superalloy was conducted. Typical Paris region behavior was observed above a delta K of 8 MPa sq rt of m. However, below that stress intensity range, the alloy exhibited highly unusual behavior. This behavior consisted of a region where the crack growth rate became essentially independent of the applied stress intensity. The transition in the FCG behavior was related to a change in the observed crack growth mechanisms. In the Paris region, fatigue failure occurred along (111) facets; however, at the lower stress intensities, (001) fatigue failure was observed. A mechanism was proposed, based on barriers to dislocation motion, to explain the changes in the observed FCG behavior. The FCG data were also evaluated in terms of a recently proposed stress intensity parameter, K sub rss. This parameter, based on the resolved shear stresses on the slip planes, quantified the crack driving force as well as the mode I delta K, and at the same time was also able to predict the microscopic crack path under different stress states.
An investigation of the fatigue crack growth (FCG) behavior of PWA 1480 single crystal nickel base superalloy was conducted. Typical Paris region behavior was observed above a delta K of 8 MPa sq rt of m. However, below that stress intensity range, the alloy exhibited highly unusual behavior. This behavior consisted of a region where the crack growth rate became essentially independent of the applied stress intensity. The transition in the FCG behavior was related to a change in the observed crack growth mechanisms. In the Paris region, fatigue failure occurred along (111) facets; however, at the lower stress intensities, (001) fatigue failure was observed. A mechanism was proposed, based on barriers to dislocation motion, to explain the changes in the observed FCG behavior. The FCG data were also evaluated in terms of a recently proposed stress intensity parameter, K sub rss. This parameter, based on the resolved shear stresses on the slip planes, quantified the crack driving force as well as the mode I delta K, and at the same time was also able to predict the microscopic crack path under different stress states.
The creep behavior of single crystals of gamma-prime and gamma alloys were investigated and compared to the response of two-phase superalloys tested previously. High temperature deformation in the gamma alloys was characteristic of a climb-controlled mechanism, whereas the gamma-prime based materials exhibited glide-controlled creep behavior. The superalloys were much more creep resistant than their constituent phases, which indicates the importance of the gamma/gamma-prime interface as a barrier for dislocation motion during creep.
Specific forms for both the Gibb's and the complementary dissipation potentials were chosen such that a complete potential based multiaxial, isothermal, viscoplastic model was obtained. This model in general possesses three internal state variables (two scalars associated with dislocation density and one tensor associated with dislocation motion) both thermal and dynamic recovery mechanisms, and nonlinear kinematic hardening. This general model, although possessing associated flow and evolutionary laws, is shown to emulate three distinct classes of theories found in the literature, by modification of the driving threshold function F. A parametric study was performed on a specialized nondimensional multiaxial form containing only a single tensorial internal state variable (i.e., internal stress). The study was conducted with the idea of examining the impact of including a strain-induced recovery mechanism and the compliance operator, derived from the Gibb's potential, on the uniaxial and multiaxial response. One important finding was that inclusion of strain recovery provided the needed flexibility in modeling stress-strain and creep response of metals at low homologous temperatures, without adversely affecting the high temperature response. Furthermore, for nonproportional loading paths, the inclusion of the compliance operator had a significant influence on the multiaxial response, but had no influence on either uniaxial or proportional load histories.
Single crystal superalloys have become increasingly popular for turbine blade and vane applications due to their high strength, and creep and fatigue resistance at elevated temperatures. The crystallographic orientation of a single crystal material greatly affects its material properties, including elastic modulus, shear modulus, and ductility. These directional properties, along with the type of loading and temperature, dictate an anisotropic response in the yield strength, creep resistance, creep rupture ductility, fatigue resistance, etc. A significant amount of research has been conducted to determine the material properties in the <001> orientation, yet the material properties deviating from the <001> orientation have not been assessed for all cases. Based on the desired application and design criteria, a crystal orientation is selected to yield the maximum properties. Currently, single crystal manufacturing is able to control the primary crystallographic orientation within 15 of the target orientation, which is an acceptable deviation to meet both performance and cost guidelines; the secondary orientation is rarely specified. A common experiment is the standard load-controlled tensile test, in which specimens with different orientations can be loaded to observe the material response. The deformation behavior of single-crystal materials under tension and compression is known to be a function of not only material orientation, but also of varying microdeformation (i.e. dislocation) mechanisms. The underlying dislocation motion causes deformation via slip, and affects the activation of specific slip systems based on load and orientation. The slip can be analyzed by observing the visible traces left on the surface of the specimen from the slip activity within the single crystal material. The goal of this thesis was to predict the slip systems activated in three-dimensional stress fields of a notched tensile specimen, as a function of crystal orientation, using finite element analysis without addressing microstructural deformation mechanisms that govern their activation. Out of three orientations tested, the specimen with a [110] load orientation and a [001] growth direction had the lowest maximum resolved shear stress; this specimen orientation appears to be the best design candidate for a tensile application.
During the 2001-2002 award period, we performed research on Pt/Ti/bare 6H-SiC and bare 4H-SiC interfaces in order to identify their electronic properties as a function of surface preparation. The overall aim of this work is to optimize the electronic properties of metal contacts to SiC as well as the active SiC material itself as a function of surface preparation and subsequent processing. Initially, this work has involved identifying bare surface, subsurface, and metal induced gap states at the metal-SiC contact and correlating energies and densities of deep levels with Schottky barrier heights. We used low energy electron-excited nanoluminescence (LEEN) spectroscopy, X-ray photoemission spectroscopy (XPS), and Secondary Ion Mass Spectrometry (SIMS) in order to correlate electronic states and energy bands with chemical composition, bonding, and crystal structure. A major development has been the discovery of polytype transformations that occur in 4H-SiC under standard microelectronic process conditions used to fabricate SiC devices. Our results are consistent with the stacking fault generation, defect formation, and consequent degradation of SiC recently reported for state-of-the-art ABB commercial diodes under localized electrical stress. Our results highlight the importance of -optimizing process conditions and material properties - anneal times, temperatures and doping to control such structural changes within epitaxial SiC layers. Thus far, we have established threshold times and temperatures beyond which 4H-SiC exhibits 3C-SiC transformation bands for a subset of dopant concentrations and process conditions. On the basis of this temperature time behavior, we have been able to establish an activation energy of approximately 2.5 eV for polytype transformation and dislocation motion. Work continues to establish the fundamental mechanisms underlying the polytype changes and its dependence on material parameters.
While previously published experimental results have shown that the step-free (0 0 0 1) 4H-SiC mesa growth surface uniquely enables radical improvement of 3C-SiC and 2H-AlN/GaN heteroepitaxial film quality (greater than 100-fold reduction in extended defect densities), important aspects of the step-free mesa heterofilm growth processes and resulting electronic device benefits remain to be more fully elucidated. This paper reviews and updates recent ongoing studies of 3C-SiC and 2H-AlN/GaN heteroepilayers grown on top of 4H-SiC mesas. For both 3C-SiC and AlN/GaN films nucleated on 4H-SiC mesas rendered completely free of atomic-scale surface steps, TEM studies reveal that relaxation of heterofilm strain arising from in-plane film/substrate lattice constant mismatch occurs in a remarkably benign manner that avoids formation of threading dislocations in the heteroepilayer. In particular, relaxation appears to occur via nucleation and inward lateral glide of near-interfacial dislocation half-loops from the mesa sidewalls. Preliminary studies of homojunction diodes implemented in 3C-SiC and AlN/GaN heterolayers demonstrate improved electrical performance compared with much more defective heterofilms grown on neighbouring stepped 4H-SiC mesas. Recombination-enhanced dislocation motion known to degrade forward-biased 4H-SiC bipolar diodes has been completely absent from our initial studies of 3C-SiC diodes, including diodes implemented on defective 3C-SiC heterolayers grown on stepped 4H-SiC mesas.
A new method to introduce grain size-dependence in classical crystal plasticity constitutive model is developed by considering the resistance to dislocation motion in the grain boundary influence region as equivalent to that of a work hardening. A general framework for the size-dependent constitutive model is derived by implementing this method on a core and mantle model. The work hardening, equivalent to grain boundary effect, is realized by introducing a fictitious, pre-existing, plastic strain grain boundary influence region (mantle) following the principles of classical crystal plasticity. This fictitious plastic strain, in effect, increases the yield strength and decreases the initial hardening coefficient of the grain. With the thickness of grain boundary influence region and the distribution of introduced plastic strain remaining the same, the grain boundary effect increased as the grain size becomes smaller. A simplified model that considers the grain boundary effect on a grain average sense is also developed under this general framework. Implementation of this general framework to the specific cases of crystal plasticity constitutive models is demonstrated by considering the case of power law flow rule and hyperbolic-secant hardening rule. Finally, the grain size-dependent constitutive model is validated by comparing the predicted stress-strain behavior of polycrystal samples with different average grain sizes under uniaxial loading with the experimental results.
Discrete dislocation dynamics (DDD) is a widely employed computational method to study plasticity at the mesoscale that connects the motion of dislocation lines to the macroscopic response of crystalline materials. However, the computational cost of DDD simulations remains a bottleneck that limits its range of applicability. Here, we introduce a new DDD-GNN framework in which the expensive time-integration of dislocation motion is entirely substituted by a graph neural network (GNN) model trained on DDD trajectories. As a first application, we demonstrate the feasibility and potential of our method on a simple yet relevant model of a dislocation line gliding through an array of obstacles. We show that the DDD-GNN model is stable and reproduces very well unseen ground-truth DDD simulation responses for a range of straining rates and obstacle densities, without the need to explicitly compute nodal forces or dislocation mobilities during time-integration. Our approach opens new promising avenues to accelerate DDD simulations and to incorporate more complex dislocation motion behaviors.
Here, the motion of line defects (dislocations) has been studied for more than 60 years, but the maximum speed at which they can move is unresolved. Recent models and atomistic simulations predict the existence of a limiting velocity of dislocation motion between the transonic and subsonic ranges at which the self-energy of dislocation diverges, though they do not deny the possibility of the transonic dislocations. We used femtosecond x-ray radiography to track ultrafast dislocation motion in shock-compressed single-crystal diamond. By visualizing stacking faults extending faster than the slowest sound wave speed of diamond, we show the evidence of partial dislocations at their leading edge moving transonically. Understanding the upper limit of dislocation mobility in crystals is essential to accurately model, predict, and control the mechanical properties of materials under extreme conditions.
Mean-stress effects on fatigue life are critical in isothermal and thermomechanically loaded materials and composites. Unfortunately, existing mean-stress life-prediction methods do not incorporate physical fatigue damage mechanisms. An objective is to examine the relation between mean-stress induced damage (as measured by acoustic emission) and existing life-prediction methods. Acoustic emission instrumentation has indicated that, as with static yielding, fatigue damage results from dislocation buildup and motion until dislocation saturation is reached, after which void formation and coalescence predominate. Correlation of damage processes with similar mechanisms under monotonic loading led to a reinterpretation of Goodman diagrams for 40 alloys and a modification of Morrow's formulation for life prediction under mean stresses. Further testing, using acoustic emission to monitor dislocation dynamics, can generate data for developing a more general model for fatigue under mean stress.
It has been noted that the crack propagation exponent p for most metals usually varies between values of 2 and 4, and that the motion of dislocations plays an important part in determining the exponent p. Attention is presently given to the significance of the exponent p in terms of the motion of dislocations, in view of the theory of thermally activated plastic flow and the cumulative plastic strain concept for a failure criterion.
A major challenge in advancing nuclear materials for next-generation fission and proposed fusion reactors is to comprehensively understand the formation of irradiation-induced defects. Here it is essential to correlate the evolution of irradiation-induced defects and the degradation of mechanical properties, as they collectively dictate the material's lifespan and ensure nuclear safety. Scanning transmission electron microscopy (STEM) based techniques have emerged as indispensable tools for irradiation-induced defect characterization, offering high spatial resolution imaging and chemical analysis, such as electron energy loss spectroscopy (EELS) and energy dispersive X-ray spectroscopy (EDXS). These techniques have been effectively used to obtain an atomic-scale view of the defect structure. Recent advances in electron microscopy, particularly in 4D-STEM, offer detailed insight into microstructural evolution by capturing full 2D diffraction patterns at every pixel position. Using high-speed direct electron detectors, this technology generates a four-dimensional dataset, overcoming the limitations of traditional STEM imaging.
Here this work aims at a quantitative and mechanistic understanding of the dynamic process of the phonon-dislocation interaction in PbTe/PbSe (001) heterostructures using the Concurrent Atomistic-Continuum (CAC) method as the simulation tool. The misfit dislocation network and the atomic-scale dislocation core structure obtained in the simulations are found to agree reasonably well with the experimental observations of the PbTe/PbSe (001) interface. Through visualizing the dynamic interaction between phonons and dislocations, as well as quantifying the dislocation vibration amplitude, the phonon energy transmission, and the thermal resistance of the misfit interfaces, this work has illustrated and quantified two mechanisms for phonon-dislocation interaction: (1) phonon scattering by the strain field of dislocations, and (2) phonon scattering by dislocations that vibrate via the local modes of a dislocation network; the latter, leads to resonant phonon-dislocation interaction, which is manifested as local maxima of out-of-phase vibration of the atoms on the two sides of the slip plane, leading to local minima of the energy transmission in the heterostructure that contains one interface. The local vibrational modes are found to be excited only by shear stress induced by transverse phonons. Among various resonant modes, the one with the lowest frequency has the strongest effect. This work has also demonstrated the collective motion of dislocations under ultrafast phonon pulses. In addition, the dynamic properties of the misfit dislocation network localized within one interface are found to be significantly altered by the presence of misfit dislocations at other interfaces, thus further confirming the cooperative dynamic nature of the motion of dislocations and phonons.
Many elementary deformation processes in metals involve the motion of dislocations. The planes of glide and specific processes dislocations prefer depend heavily on their atomic core structures. Atomistic simulations are desirable for dislocation modeling but their application to even sub-micron scale problems is in general computationally costly. Accordingly, continuum-based approaches, such as the phase-field microelasticity, phase-field dislocation dynamics (PFDD), generalized Peierls–Nabarro (GPN) models, and the concurrent atomistic–continuum (CAC) method, have attracted increasing attention in the field of dislocation modeling because they well represent both short-range cores interactions and long-range stress fields of dislocations. To better understand their similarities and differences, it is useful to compare these methods in the context of benchmark simulations and predictions. In this paper, we apply the CAC method and different PFDD variants – one of them is equivalent to a GPN model – to simulate an extended (i.e., dissociated) dislocation in Al with initially pure edge or pure screw character in terms of the disregistry. CAC and discrete forms of PFDD are also employed to calculate the Peierls stress. By conducting comprehensive convergence studies, we quantify the dependence of these measures on time/grid resolution and simulation cell size. Several important but often overlooked differences between PFDD/GPN variants are clarified. In conclusion, our work sheds light on the advantages and limitations of each method, as well as the path towards enabling them to effectively model complex dislocation processes at larger length scales.
An investigation was undertaken to determine if the size and modulus interaction of a solute atom with a screw dislocation and the modulus interaction with an edge dislocation contributed to strengthening, in addition to the size interaction with an edge dislocation. The results indicate that the size interaction between solute atom and an edge dislocation accounts for most of the solid solution strengthening in f.c.c. alloys. The contribution to the yield stress from the modulus interaction with an edge dislocation is less than 15%. The interaction between a solute atom and a screw dislocation is much less than that between a solute atom and an edge dislocation.
We report a number of recent Molecular Dynamics (MD) simulations have demonstrated that screw dislocations in face centred cubic (fcc) metals can achieve stable steady state motion above the lowest shear wave speed (v shear ) which is parallel to their direction of motion (often referred to as transonic motion). This is in direct contrast to classical continuum analyses which predict a divergence in the elastic energy of the host material at a crystal geometry dependent ‘critical’ velocity v crit . Within this work, we first demonstrate through analytic analyses that the elastic energy of the host material diverges at a dislocation velocity (v crit ) which is greater than v shear , i.e. v crit >v shear . We argue that it is this latter derived velocity (v crit ) which separates ‘subsonic’ and ‘supersonic’ regimes of dislocation motion in the analytic solution. In addition to our analyses, we also present a comprehensive suite of MD simulation results of steady state screw dislocation motion for a range of stresses and several cubic metals at both cryogenic and room temperatures. At room temperature, both our independent MD simulations and the earlier works find stable screw dislocation motion only below our derived v crit . Nonetheless, in real-world polycrystalline materials v crit cannot be interpreted as a hard limit for subsonic dislocation motion. In fact, at very low temperatures our MD simulations of Cu at 10 Kelvin confirm a recent claim in the literature that true ‘supersonic’ screw dislocations with dislocation velocities v>v crit are possible at very low temperatures.