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Statistics of internal stress fluctuations in dislocated crystals and relevance to density-based dislocation dynamics models
A statistical analysis of internal stress fluctuations, defined as the difference between the local mean stress and stress on dislocations, is presented for deforming crystals with 3D discrete dislocation systems. Dislocation realizations are generated using dislocation dynamics simulations and the associated stress field is computed as a superposition of a regularized stress field of dislocation lines within the domain of the solution and a complementary stress field computed via a finite-element boundary value problem. The internal stress fluctuations of interest are defined by an ensemble of the difference between the stress on dislocation lines and the local mean field stress in the crystal. The latter is established in a piecewise fashion over small voxels in the crystal thus allowing the difference between the local average stress and stress on segments to be easily estimated. The results show that the Schmid stress (resolved shear stress) and Escaig stress fluctuations on various slip systems sampled over a random set of points follow a Cauchy (Lorentz) distribution at all strain levels, with the amplitude and width of the distribution being dependent on the strain. Finally, the implications of the Schmid and Escaig internal stress fluctuations are discussed from the points of view of dislocation cross-slip and the dislocation motion in continuum dislocation dynamics.
An in-situ study of low thermal expansion and internal stress evolution in FeMn alloys
The mechanism of low thermal expansion phenomenon in antiferromagnetic FeMn alloys needs to be revealed. In this work, the evolution of lattice thermal expansion and internal stress in FeMn alloys was investigated by in-situ synchrotron X-ray diffraction during thermal cycling. Preceding the martensitic transformation, the coefficient of lattice thermal expansion (CLTE) decreased and the full width at half maximum (FWHM) of the diffraction peaks broadened abnormally. The evolution of the lattice thermal expansion and the FWHM were both reversible and isotropic. The additional reflection spots around the fundamental diffraction spots in the electron diffraction patterns of austenite and the dispersed nano-scale martensite embryos in austenite observed in the dark field TEM images proves the existence of premartensitic transformation. Finally, similar phenomena were found in FeMn Invar alloy, which indicate that the Invar effect is closely related to the internal stress evolution caused by premartensitic transformation.
Evolution of texture and internal stresses within polycrystalline rock salt using in situ 3D synchrotron computed tomography and 3D X-ray diffraction
Over time rock salt caverns have been extensively used as reliable repositories for hazardous waste such as nuclear waste, oil or compressed gases. Undisturbed rock salt deposits in nature are usually impermeable and have very low porosity. However, rock salt formations under excavation stresses can develop crack networks, which increase their porosities; and in the case of a connected crack network within the media, rock salt may become permeable. Although the relationship between the permeability of rock salt and the applied stresses has been reported in the literature, a microscopic study that investigates the properties influencing this relationship, such as the evolution of texture and internal stresses, has yet to be conducted. This study employs in situ 3D synchrotron micro-computed tomography and 3D X-ray diffraction (3DXRD) on two small-scale polycrystalline rock salt specimens to investigate the evolution of the texture and internal stresses within the specimens. The 3DXRD technique measures the 3D crystal structure and lattice strains within rock salt grains. The specimens were prepared under 1D compression conditions and have shown an initial {111} preferred texture, a dominant {110}$\langle1\bar{1}0\rangle$ slip system and no fully connected crack network. The {111} preferred texture under the unconfined compression experiment became stronger, while the {111}$\langle1\bar{1}0\rangle$ slip system became more prominent. The specimens did not have a fully connected crack network until applied axial stresses reached about 30 MPa, at a point where the impermeability of the material becomes compromised due to the development of multiple major cracks.
Estimating Internal Stress of an Alteration Layer Formed on Corroded Boroaluminosilicate Glass through Spectroscopic Ellipsometry Analysis
Aqueous corrosion of glass may result in the formation of an alteration layer in the glass surface of which chemical composition and network structure are different from those of the bulk glass. Since corrosion occurs far below the glass-transition temperature, the alteration layer cannot fully relax to the new structure with the lowest possible energy. Molecular dynamics simulations suggested that such a network will contain highly strained chemical bonds, which can be manifested as a stress in the alteration layer. Common techniques to measure stress in thin films or surface layers were found inadequate for thick monolithic glass samples corroded in water. Here, we explored the use of spectroscopic ellipsometry to test the presence of internal stress in the alteration layer formed by aqueous corrosion of glass. Furthermore, a procedure for analyses of spectroscopic ellipsometry data to determine birefringence in the alteration layer was developed. Findings with the established fitting procedure suggested that a stress builds up in the corroded surface layer of a boroaluminosilicate glass if there is a change in relative humidity, pH, or electrolyte concentration of the environment to which the glass surface is exposed. A similar process may occur in other types of glass, and it may affect the surface properties of corroded glass objects.
Precipitation of calcium–alumino–silicate–hydrate gels: The role of the internal stress
Concrete gains its strength from the precipitation of a calcium–alumino–silicate–hydrate (C–A–S–H) colloidal gel, which acts as its binding phase. However, despite concrete’s ubiquity in the building environment, the atomic-scale mechanism of C–A–S–H precipitation is still unclear. Here, we use reactive molecular dynamics simulations to model the early-age precipitation of a C–A–S–H gel. We find that, upon gelation, silicate and aluminate precursors condensate and polymerize to form an aluminosilicate gel network. Notably, we demonstrate that the gelation reaction is driven by the existence of a mismatch of atomic-level internal stress between Si and Al polytopes, which are initially experiencing some local tension and compression, respectively. The polymerization of Si and Al polytopes enables the release of these competitive stresses.
Irradiation-induced internal stresses in polycrystalline α -uranium: a mesoscale mechanical approach
Not Available
Chemo-Mechanical Model for Internal Stress Impact on Lithium Dendrite Growth.
Abstract not provided.
StressNet - Deep learning to predict stress with fracture propagation in brittle materials
Abstract Catastrophic failure in brittle materials is often due to the rapid growth and coalescence of cracks aided by high internal stresses. Hence, accurate prediction of maximum internal stress is critical to predicting time to failure and improving the fracture resistance and reliability of materials. Existing high-fidelity methods, such as the Finite-Discrete Element Model (FDEM), are limited by their high computational cost. Therefore, to reduce computational cost while preserving accuracy, a deep learning model, StressNet, is proposed to predict the entire sequence of maximum internal stress based on fracture propagation and the initial stress data. More specifically, the Temporal Independent Convolutional Neural Network (TI-CNN) is designed to capture the spatial features of fractures like fracture path and spall regions, and the Bidirectional Long Short-term Memory (Bi-LSTM) Network is adapted to capture the temporal features. By fusing these features, the evolution in time of the maximum internal stress can be accurately predicted. Moreover, an adaptive loss function is designed by dynamically integrating the Mean Squared Error (MSE) and the Mean Absolute Percentage Error (MAPE), to reflect the fluctuations in maximum internal stress. After training, the proposed model is able to compute accurate multi-step predictions of maximum internal stress in approximately 20 seconds, as compared to the FDEM run time of 4 h, with an average MAPE of 2% relative to test data.
New Mechanism for Yield Point Phenomena
Yield point phenomena (YPP) are widely attributed to discrete dislocation locking by solute atmospheres. An alternate YPP mechanism was recently suggested by simulations of Ta single crystals without any influence of solutes or discrete dislocations. The general meso-scale (GM) simulations consist of crystal plasticity (CP) plus accounting for internal stresses of geometrically necessary dislocation content. GM predicted the YPP while CP did not, suggesting a novel internal stress mechanism. The predicted YPP varied with crystal orientation and boundary conditions, contrary to expectations for a solute mechanism. The internal stress mechanism was probed by experimentally deforming oligocrystal Ta samples and comparing the results with independent GM simulations. Strain distributions of the experiments were observed with high-resolution digital image correlation. A YPP stress–strain response occurred in the 0–2% strain range in agreement with GM predictions. Shear bands appeared concurrent with the YPP stress–strain perturbation in agreement with GM predictions. At higher strains, the shear bands grew at progressively slower rates in agreement with GM predictions. It was concluded that the internal stress mechanism can account for the existence of YPP in a wide variety of materials including ones where interstitial-dislocation interactions and dislocation transient avalanches are improbable. Furthermore, the internal stress mechanism is a CP analog of various micro-scale mechanisms of discrete dislocations such as pile-up or bow-out. It may operate concurrently with strain aging, or either mechanism may operate alone. A suggestion was made for a future experiment to answer this question.
Dislocation Patterning in Deforming Crystals: Theory, Computational Predictions and Validation (Final Technical Report)
This project was awarded for an initial period of three years, followed by a no-cost extension for one year and a funded one-year renewal. During the first four years, the project focused on investigating the role of dislocation reactions and dislocation correlation in dislocation patterning in FCC metals. During the fifth year, the scope of research was expanded to investigate the effects of composition inhomogeneity on the mesoscale plastic response of Body-Centered Cubic (BCC) alloys. In addition to its impact on metal hardening during deformation, dislocation patterning provides the microstructure information required to understand phenomena like fracture and recrystallization in metals. The Continuum Dislocation Dynamics (CDD) framework was the methodology used during the first four years, followed by the use of Discrete Dislocation Dynamics (DDD) during the fifth year. CDD is a density-based formalism of dislocation dynamics in which the plastic deformation of crystals is predicted together with the mesoscale dislocation patterns by tracking the space-time evolution of dislocations as driven by the applied stress, short-range and long-range interactions of dislocations, and cross slip. CDD is a crystal mechanics approach in which the plastic constitutive part is replaced with the equations of dislocation dynamics, which is driven by the internal stress via a mobility laws, while the evolution of the density gives the eigenstrain required to update the internal stress itself. The governing equations are thus those of crystal mechanics cast as an eigenstrain problem and those of dislocation transport and reactions. Our investigations during the first four years were driven by the hypothesis that that dislocation patterning is triggered by spatiotemporal dislocation density and internal stress fluctuations, and that such fluctuations influence the collective dislocation dynamic through their effects on the short-range reaction rates and the collective dislocation mobility. This hypothesis was tested by modeling the influence of the dislocation reactions and dislocation correlations on collective dislocation dynamics. The main research components during the first four years were: 1) Reformulation of the CDD framework to integrate the dislocation correlations and dislocation reactions. 2) Simulation of the dislocation correlations and quantifying their contribution to the long-range stress of complex dislocation systems. 3) Computational implementation of the updated CDD model for FCC single crystals and development of an efficient CDD code. 4) Investigation of dislocation patterning in FCC crystals based on the updated CDD model. Some key findings from these investigations were: 1) The patterning of dislocations is initiated by cross slip and internal stress fluctuations, and the refinement of the pattern results from junction formation. 2) Patterning is more prominent under high stress. 3) The correlation stress was found to be a significant part of the mean field stress in continuum representations of dislocation dynamics. During the last year of the project, we have established a method for performing dislocation dynamics in inhomogeneous alloys and demonstrated the impact of composition inhomogeneity on the characteristics of initial yielding and dislocation character in BCC alloys. We also tested this method using an irradiated ferritic alloy in which the composition and dislocation loops effects are both present. In doing so, we have considered two aspects of the role of inhomogeneity, the creation of internal coherency stress due to the dependence of the lattice parameter on the local composition, and the dependence of the dislocation mobility on the local composition. These two aspects resulted in an unexpected behavior of the dislocation system, and, in turn, the yielding behavior of BCC alloys. Key findings include: 1) The composition inhomogeneity in BCC alloys alters the well-known role of screw dislocations by forcing a level of waviness on the average dislocation character, thus destroying the screw character dominance in the yielding observed in pure or homogeneous BCC metals. 2) In the case of irradiated alloys, while composition inhomogeneity by itself and dislocation loops by themselves result in some hardening, the superposition of the two mechanisms does not result in the sum of the two contributions via any known rule. The latter result contradicts the classical works related hardening via multiple mechanisms, which state that various hardening mechanisms can be added linearly or using some Pythagorean additive rule. We were able to rationalize this unexpected result by a closer loop at the origin of the hardening mechanisms themselves, which both involved long-range elastic interactions with dislocations. We reached the conclusion that the hardening resulting from the total stress associated with these two mechanisms (current work) differs from the sum of the effects of the individual stress fields (classical literature). We have also found a major flaw in the classical theory of spinodal hardening. The latter theory never considered the impact of composition undulation on the solute hardening. We have built a new general theory accounting for the effect of solute friction together with the composition undulations on the dislocation configuration at Critical Resolved Shear Stress (CRSS), which is yielding a new definition of the spinodal hardening and new different results. This work is the first to recognize the lack of the role of solute in spinodal hardening theory of alloys.
Experimental Observation of a New Attenuation Mechanism in hcp ‐Metals That May Operate in the Earth's Inner Core
Abstract Seismic observations show the Earth's inner core has significant and unexplained variation in seismic attenuation with position, depth and direction. Interpreting these observations is difficult without knowledge of the visco‐ or anelastic dissipation processes active in iron under inner core conditions. Here, a previously unconsidered attenuation mechanism is observed in zinc, a low pressure analog ofhcp‐iron, during small strain sinusoidal deformation experiments. The experiments were performed in a deformation‐DIA combined with X‐radiography, at seismic frequencies (∼0.003–0.1 Hz), high pressure and temperatures up to ∼80% of melting temperature. Significant dissipation (0.077 ≤ Q −1 (ω) ≤ 0.488) is observed along with frequency dependent softening of zinc's Young's modulus and an extremely small activation energy for creep (⩽7 kJ mol −1 ). In addition, during sinusoidal deformation the original microstructure is replaced by one with a reduced dislocation density and small, uniform, grain size. This combination of behavior collectively reflects a mode of deformation called “internal stress superplasticity”; this deformation mechanism is unique to anisotropic materials and activated by cyclic loading generating large internal stresses. Here we observe a new form of internal stress superplasticity, which we name as “elastic strain mismatch superplasticity.” In it the large stresses are caused by the compressional anisotropy. If this mechanism is also active inhcp‐iron and the Earth's inner‐core it will be a contributor to inner‐core observed seismic attenuation and constrain the maximum inner‐core grain‐size to ≲10 km.
Influence of Numerical Modeling Approaches on Damped Behavior of Flexible Beams: Preprint
Composites structures are widely used in aerospace and wind energy applications for their excellent stiffness and strength-to-weight properties. In these structures, structural damping is critical to predict vibration amplitudes, performance, and reliability. Structural damping is of particular interest for slender wings, rotorcraft blades, and wind turbine blades that can exhibit complex vibration phenomena and are frequently modeled with geometrically exact beam theory (GEBT). Standard approaches of stiffness proportional or modal damping merely assign user defined values and cannot predict damping behavior. This work compares stiffness proportional damping to two more advanced damping approaches: modal strain energy and Prony series. The modal strain energy approach uses a sectional analysis tool to calculate the beam stiffness and postprocess internal stresses from GEBT simulations. The internal stresses are then used to calculate modal damping factors. The Prony series is implemented within GEBT to directly model viscoelastic behavior of the composites. These approaches are compared by modeling the evolution of the damping factors of a realistic flexible wind turbine blade with varying rotational speed. Discrepancies between the approaches suggest areas for future modeling development, but differences in nonlinear damping values are less than current uncertainties about the magnitude of structural damping.
A predictive strain-gradient model with no undetermined constants or length scales
A general meso–scale (GM) crystal plasticity (CP) model was developed that accounts for lower-order (strain hardening) and higher-order (internal stress) effects of geometrically necessary dislocations (GNDs). It is predictive: no arbitrary parameters or length scales were invoked and no ad hoc numerical techniques were employed. It uses general stress field equations for GND content and a novel harmonization technique to enforce consistency of elastic long-range singular defect fields with applied elastic-plastic fields. The model facilitates implementation in commercial finite element programs without requiring special elements, special boundary conditions, or access to element shape functions. GM simulations confirmed, with improved accuracy, previously published predictions of the Hall-Petch effect, Bauschinger effect, and anelasticity. Previously unpredicted phenomena were also predicted: anelasticity and hysteresis for single Ta crystals and strain-hardening stagnation. The internal stresses (higher-order effect) dominate at large length scales, while at small length scales, the GND density hardening (lower-order effect) dominates. As a result, GM predicts that strain heterogeneity and consequent GND internal stresses are important factors in anelasticity.
Effect of a micro-scale dislocation pileup on the atomic-scale multi-variant phase transformation and twinning
In this paper, we perform concurrent atomistic–continuum (CAC) simulations to assess the contribution of the internal stress induced by the microscale dislocation pileup at an atomically structured interface to the atomic-scale phase transformations (PTs), reverse PTs, and twinning. The main novelty of this work is to unify the atomistic description of the interface and the coarse-grained (CG) description of the lagging dislocations away from the interface within one single framework. Our major findings are: (a) the interface dynamically responds to a pileup by forming steps/ledges, the height of which is proportional to the number of dislocations arriving at the interface; (b) the pileup-induced internal stress concentration profile follows neither the classical Eshelby model nor the super-dislocation model alone, but a combination of them; (c) when the pre-sheared sample is compressed, a direct square-to-hexagonal PT occurs ahead of the pileup tip and eventually grows into a wedge shape. The two variants of the hexagonal phases form a twin with respect to each other; (d) upon a further increase of the loading, part of the newly formed hexagonal phase transforms back to the square phase. The square product phase resulting from this reverse PT forms a twin with respect to the initial square phase. All phase boundaries (PBs) and twin boundaries (TBs) are stationary and correspond to zero thermodynamic Eshelby driving forces; and (e) the microscale dislocation pileup-induced internal shear stress and the structural change at the atomic-scale interface reduces the stress required for initiating a PT by a factor of 5.5, comparing with that in the sample containing no dislocations. This work is the first characterization of the behavior of PTs/twinning resulting from the reaction between a microscale dislocation slip and an atomically structured interface. In conclusion, the gained knowledge will advance our understanding of how the multi-phase material behaves in many complex physical processes, such as the synthesis of multi-phase high-entropy alloys or superhard ceramics under high-pressure torsion, deep mantle earthquakes in geophysics, and so on, which all involve dislocation slip, PTs, twinning, and their interactions across from the atomistic to the microscale and beyond.