A New Rock Salt Model with Drag Stress and Back Stress Hardening.
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Abstract not provided.
According to Eshelby’s theory, inelastically inhomogeneous inclusions in a metallic matrix give rise to a distribution of internal stresses. In the case of particle strengthened materials, such as nickel base superalloys, the presence and evolution of this back-stress leads to various observable effects, such as primary creep, back-flow upon loading, and memory of prior deformation. This article presents the background of the concept of back-stress and how it applies to the scenario of creep. A derivation of an evolution equation for back-stress in the context of primary creep is also presented. The results from neutron diffraction with in-situ creep experiments on directionally solidified nickel superalloys are presented in order to demonstrate the validity of the proposed equation and the corollaries derived therefrom.
Here, in this work, an elasto-viscoplastic fast-Fourier-transform (EVP-FFT) model with a dislocation-density (DD) based hardening law is employed to study the growth of a {10$\bar{1}$2} tensile twin that is blocked by basal-precipitates in precipitate-hardened AZ91 magnesium alloy. It is frequently reported that twin growth is hindered in precipitate-hardened Mg alloys; however, thick twin domains are often observed experimentally in these material systems. Detailed numerical investigation of deformation twinning starting from an early propagation stage, before twin growth, reveals that the stress fields that result from two sequentially propagated twins co-impinging on a precipitate relaxes the twin back stress locally and promotes twin growth at the twin-precipitate junction. Based on these findings, a two-step growth mechanism is proposed for twins arrested by precipitates. In the first step, the interaction of a twin tip with a precipitate develops a stress concentration on the other side of the precipitate, prompting the formation of a second twin. Subsequently, the back stresses associated with the first twin are relaxed by the formation of the second twin, allowing the first twin to grow at the twin-precipitate junction and eventually engulf the precipitate. This mechanism suggests that twin growth can be achieved locally with minimal additional external forces, explaining how relatively large twin domains can develop even in the presence of arrays of precipitates.
A scientific injection campaign was conducted at the Utah Frontier Observatory for Research in Geothermal Energy (FORGE) site in 2017 and 2019. The testing included pump-in/shut-in, pump-in/flowback, and step rate tests. Various methods have been employed to interpret the in-situ stress from the test dataset. This study focuses on methods to interpret the minimum in-situ stress from step rate, pump-in/extended shut-in tests data obtained during the stimulation of two zones in Well 58-32. This well was drilled in low-permeability granitoid. A temperature of 199 °C was recorded at the well’s total depth of 2297 m relative to the rotary Kelly bushing (RKB). The lower zone (Zone 1) consisted of 46 m of the openhole at the toe of the well. Fractures in the upper zone (Zone 2) were stimulated between 2123–2126 m measured depths (MD) behind the casing. The closure stress gradient variation depended on the depth and the injection chronology. The closure stress was found to increase with the pumping rate/volume. This stress variation could indicate that poroelastic effects (“back stress”) and the presence of adjacent natural fractures may play an important role in the interpretation of fracture closure stress. Further, progressively increasing local total stresses may, consequently, have practical applications when moderate volumes of fluid are injected in a naturally fractured or high-temperature reservoir. The alternative techniques that use pump-in/flowback tests and temperature signatures provide a valuable perspective view of the in-situ stress measurements.
In this paper, we introduce a data-driven machine learning approach for modeling one-dimensional stress–strain behavior under cyclic loading, utilizing experimental data from the nickel-based Alloy 617. The study employs uniaxial creep–fatigue test data acquired under various loading histories and compares two distinct neural network-based ODE models. The first model, known as the black-box model, comprehensively describes the strain–stress relationship using a Neural ODE equation. To interpret this black-box model, we apply the Sparse Identification of Nonlinear Dynamical Systems (SINDy) technique, transforming the black-box model into an equation-based model using symbolic regression. The second model, the Neural flow rule model, incorporates Hooke’s Law for the linear elastic component, with the nonlinear part characterized by a Neural ODE. Both models are trained with experimental data to accurately reflect the observed stress–strain behavior. We conduct a detailed comparison with the standard Chaboche model, which includes three back stresses. Our results demonstrate that the neural network-based ODE models precisely capture the experimental creep–fatigue mechanical behavior, exceeding the standard Chaboche model’s accuracy. Furthermore, an interpretable model derived from the black-box neural ODE model through symbolic regression achieves accuracy comparable to the Chaboche model, enhancing its interpretability. The results highlight the potential of neural network-based ODE models to depict complex creep–fatigue behavior, eliminating the necessity for experts to define a specific, material-focused model form.
Twinning is a key deformation mechanism in hexagonal close-packed (hcp) metals, which are typified by a lack of easily activated slip systems that can accommodate a general state of loading. Pragmatically, the nucleation and evolution of twin domains occurs concomitantly with slip, such that the eventual twin network is conditioned by both external and internal stresses resulting, among others, from the evolution of dislocations. However our understanding of the interplay between dislocations, and twin nucleation and stability remains limited. This work focuses on elucidating the influence of dislocation-mediated plasticity on the formation, growth, and stability of twin embryos. First, a new mesoscale spectral crystal plasticity-twinning framework is developed and used to quantify the change in the free energy landscape following the nucleation {$10\bar{1}2$} of twins in Mg. Representative twin morphologies are modeled under conditions of limited and profuse slip activity, which are emulative of small- and bulk-scale samples, respectively. Then, the driving traction profiles around twin embryos are investigated via a sharp interface approach to obtain insights into how concurrent slip-mediated plasticity can influence the growth/stabilization of nanometric twins. The driving traction profiles are further utilized to determine the stability of twin embryos post loading. The initial dislocation density in the samples, and within the different domains (i.e., twin vs. parent), is seen to have a significant effect on the twin nucleation stress. Namely, the activation of high levels of concomitant plasticity in the parent grain is seen to significantly drive the formation of nanometric twin nuclei at stresses as low as 250 MPa. Further, the sharp interface analysis reveals that profuse plasticity in the parent grain simultaneously alters the forward and back stresses, such that the magnitude/polarity of the driving tractions become increasingly favorable for nanometric twin growth when slip is active. Finally, prior plasticity in the parent grain is seen to result in favorable driving tractions for nanometric twin growth, even at applied stresses as low as ~ 100 MPa. In conclusion, these results are in stark contrast to a case without any dislocations, wherein applied stresses as high as ~ 500 MPa are necessary to grow the twin domains.
Crystal plasticity models evolve a polycrystalline yield surface using meso-scale descriptions of deformation mechanisms. The activation of deformation mechanisms is governed by crystallography and a set of model parameters, which are typically calibrated through the fitting of mechanical data such as stress–strain curves and elastic lattice strains. Microstructural data such as phase fractions and texture evolution are used for verifying crystal plasticity parameters. In this study, we use a multi-objective genetic algorithm to identify hardening parameters from flow stress curves with an option to incorporate texture into the optimization approach. Robust, generalized objective functions are developed and used to identify sets of parameters pertaining to dislocation density-based hardening laws in visco-plastic and elasto-plastic self-consistent (VPSC and EPSC) homogenization models. First, the parameters are identified for pure Nb directly from texture using an objective function based on generalized spherical harmonics. Since texture evolution is driven by the relative contribution of active slip systems, the parameters governing the evolution of slip resistance ratios can be recovered from fitting discrete textures at a series of strains. Next, a comprehensive set of load reversal data for dual phase (DP) 780 steel is used to fit a hardening law and a back-stress law in EPSC. Finally, parameters pertaining to a complex hardening law for the evolution of slip and twinning in pure α-Ti are identified. Remarkably, using texture as an objective in combination with stress–strain objectives constrains the model of Ti to fully reproduce not only stress–strain and texture evolution but also hierarchical twinning measurements as a function of initial grain size and texture. Furthermore, given an appropriate model fit to representative experimental texture evolution, underlying twin volume fractions contributing to texture evolution can be predicted.
High-entropy alloys (HEAs) with concentrated solid solutions are conceived to possess a rugged atomic and energy landscape in which dislocation motion necessarily proceeds to accommodate mechanical deformation. Fundamental questions remain as to how rough the energy landscape is and to what extent it can be influenced by the local ordering of their constituent elements. Here, we construct and report the potential energy landscape (PEL) governing screw dislocation motion in refractory HEAs that reveals a hierarchical and multilevel structure with a collection of small basins nested in large metabasin. This striking feature pertaining to HEAs exerts a trapping force and back stress on saddle point activations, retarding dislocation movement. Further, by introducing chemical short-range order, the energy landscape is smoothed but skewed to different degrees that shifts the rate-liming process from kink-glide to kink-pair nucleation. The chemical disorder-roughened PEL in HEAs, analogous to structural disorder induced in metallic glasses, signifies the role of various barrier-hopping processes underlying the extraordinary mechanical behaviors of the two distinct groups of materials.
In this study, a multi-length-scale strengthening approach was used to tailor the microstructure and the mechanical properties of a NiCoCr-based multi-principal element alloy (MPEA). Grain size refinement, severe lattice distortion, and stacking fault energy (SFE) reduction with Mo addition (up to 10 at.%) enhance yield strength by 85% with only 10% reduction in ductility in as-annealed MPEAs. A pronounced increase in the strain hardening rate was observed with the addition of Mo, which is ascribed to the promotion of complex stacking fault (SF) interaction and intersection, accompanied by Lomer-Cottrell (L-C) and Hirth locks inhibiting dislocation motion and substantial increase in the accumulation of back stress. To push the limit of the yield strength further, the Suzuki segregation phenomenon was manipulated by a careful control of SF density by pre-straining and a subsequent 500 °C heat treatment. The stress-strain responses of the pre-strained and heat treated MPEAs showed an obvious SF density and Mo concentration dependence. Furthermore, the yield strength of the pre-strained Mo-added MPEAs with subsequent heat treatment was increased up to true stress of 2.3 GPa with a corresponding fracture elongation of 12% true strain. SFs formed during pre-straining served as Cr segregation sites during subsequent heat treatment, which substantially varies the local SFE within the SF, presenting a roughened landscape and frustrating the dislocation dynamics.
The deformation behavior of commercially pure rolled titanium subjected to strain path changes is studied using experiments and a crystal plasticity model. Four different loading combinations are performed at room temperature to study the activation of slip, twinning, de-twinning and double-twinning in hexagonal closed packed titanium. The strain paths considered are: rolling direction compression (RDC) followed by normal direction compression (NDC), RDC followed by transverse direction compression (TDC), NDC followed by RDC, and NDC followed by TDC. An EBSD-based analysis of the distribution of boundary misorientation angles before and after reload was developed to analyze the evolution of {$10\bar{1}2$} tensile and {$11\bar{2}2$} compression twins. This analysis supports the model results concerning the treatment of twin reorientation. A de-twinning and double-twinning model accounting for back stress effects, an important feature of strain path changes, is implemented within the framework of the visco-plastic self-consistent (VPSC) model along with a dislocation density (DD) based hardening scheme. In the model, plasticity is accommodated by prismatic $\langle$a$\rangle$, basal $\langle$a$\rangle$ and pyramidal $\langle$c+a$\rangle$ slip modes, and {$10\bar{1}2$} tensile and {$11\bar{2}2$} compression twinning modes. The VPSC model predicts the evolution of twinning, de-twinning and double-twinning processes for both tensile and compression twinning modes under strain path change. The model predicts macroscopic stress-strain response, texture evolution, and twin volume fraction that are in agreement with experimental observations. The evolution of texture is investigated in detail by separately analyzing the twinned domains, rather than the evolution of the global texture.
Abstract Light-weight, high-strength, aluminum (Al) alloys have widespread industrial applications. However, most commercially available high-strength Al alloys, like AA 7075, are not suitable for additive manufacturing due to their high susceptibility to solidification cracking. In this work, a custom Al alloy Al 92 Ti 2 Fe 2 Co 2 Ni 2 is fabricated by selective laser melting. Heterogeneous nanoscale medium-entropy intermetallic lamella form in the as-printed Al alloy. Macroscale compression tests reveal a combination of high strength, over 700 MPa, and prominent plastic deformability. Micropillar compression tests display significant back stress in all regions, and certain regions have flow stresses exceeding 900 MPa. Post-deformation analyses reveal that, in addition to abundant dislocation activities in Al matrix, complex dislocation structures and stacking faults form in monoclinic Al 9 Co 2 type brittle intermetallics. This study shows that proper introduction of heterogeneous microstructures and nanoscale medium entropy intermetallics offer an alternative solution to the design of ultrastrong, deformable Al alloys via additive manufacturing.
DiscoFluxM is software for modeling the deformation behavior of crystalline materials within the third-party finite-element based software, MOOSE. The software enables full-field crystal plasticity finite element simulations of deformation processes of metals and other crystalline materials. DiscoFluxM is an implementation of the DiscoFlux theoretical and algorithmic framework for coupling single-crystal plasticity with dislocation transport. The continuum mesoscale modeling framework is founded upon a nonlocal dislocation-density based crystal plasticity theory. The nonlocal theory couples continuum dislocation transport with an otherwise spatially-local single-crystal model employing nonlinear thermoelasticity and crystallographic plasticity. Dislocation transport is modeled by enforcing dislocation conservation at a slip-system level through the solution of advection-diffusion equations. The configuration of geometrically necessary dislocation density gives rise to a back-stress that inhibits or accentuates the flow of dislocations.
In this work we test field-relevant potential-induced degradation (PID) behavior by encapsulating laboratory Cu(In,Ga)Se 2 (CIGS) solar cells and applying +1000 V uniformly on the face of the front glass. In this configuration, we find that K-rich borosilicate glass reduces the extent of PID relative to Na-rich soda-lime glass. We also find that the standard testing protocol of stressing cells at short-circuit leads to faster PID than stressing cells at open-circuit. We characterize two types of CIGS PID: The first, front shunting PID, is driven by front-glass stress and occurs when alkali metal cations accumulate in the i-ZnO buffer, where they increase shunt conductance to reduce fill factor. The second, p-n junction PID, results from back-glass stress as alkali metal cations pile up near the CIGS surface/CdS buffer, where they reduce charge carrier concentration, open-circuit voltage, and fill factor to degrade efficiency ~160 times faster than front shunting PID.
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Back sheet failure has resulted in power loss and large-scale recall of photovoltaic modules, resulting in billions of dollars in lost revenue. The light exposure on the backside of a photovoltaic module comes primarily from reflected light which alters the distribution of natural sunlight. Because of this, modelling the backside exposure and duplicating the exposure is much more difficult than modeling the frontside exposure. This project aims to study how various back sheets and junction box materials degrade under different conditions and to develop Python code to help model and predict degradation. The stress factors for back-sheet degradation must be quantified to extrapolate accelerated stress tests to the field. Test samples were placed in the A3, A4, and A5 conditions, as defined in IEC 62788-7-2, to assess the temperature and humidity dependence of ultraviolet (UV) induced degradation. We are utilizing a custom chamber with exposure from 0.5 UV-suns to 5 UV-suns to understand the dependence of degradation on light intensity. A group of samples put in the A3 condition had glass filters with 50% UV cut-offs of 320 nm, 335 nm, and 360 nm to assess the wavelength dependence of UV degradation. All this data is necessary to assess the impact of non-standard UV light exposure. The material evaluation tests include gloss measurements, attenuated total internal reflectance Fourier transform infrared spectroscopy (ATR-FTIR), UV-visible reflectance/transmittance utilizing a Cary Ci7000 spectrophotometer, and a nano-indenter for surface hardness and modulus measurements. Alongside the experimental work, there is a computational effort using raytracing and Python open-source tools in PVDeg , PVLib, and Bifacial_Radiance. This code will create specific exposure scenarios and enable the evaluation of chamber degradation relative to field degradation. Equation 1 is a strawman equation used to model degradation on the backside of a PV module. We will create simplified code, based on the results of ray-tracing calculations, which uses a view factor approach to provide fast calculations for the most common exposure scenarios.
An integrated experimental characterization and molecular dynamics (MD) simulation approach was used to explore the dislocation-precipitate interactions in a dilute Magnesium–Neodymium (Mg–Nd) precipitation hardened alloy. In situ indentation in a transmission electron microscope (TEM) and postmortem TEM characterization of deformed samples and MD simulations revealed that basal < a > type dislocations interacted differently with β 1 (Mg 3 Nd) and β"(Mg 3-7 Nd) precipitates. For β" precipitates, the basal dislocations directly shear the precipitates. For β 1 precipitates, such shearing becomes much more difficult because it requires the creation of antiphase boundaries in the ordered lattice of β 1 precipitates. Screw dislocations were observed to cross-slip from basal to the prismatic plane, which could be parallel to the broad facet of β 1 precipitates. It is postulated that double cross-slip (basal to prismatic to basal) via the Hirsch mechanism may enable screw dislocations to overcome the β 1 precipitates. MD simulations also revealed that an edge dislocation is unable to bypass the precipitate via the generation of screw dislocation segments plus the double cross-slip mechanism. The edge dislocation can bow around the precipitate, and the segment that adopts a screw character can cross-slip to the prismatic plane but with increasing applied stress, cross-slips back to the original basal plane to continue glide via precipitate shearing. Finally, the implication of glide dislocation - β 1 -precipitate interaction mechanisms on the strength and ductility of β 1 precipitate dominant microstructures is discussed.
Abstract In the last decade and longer, photovoltaic module manufacturers have experienced a rapidly growing market along with a dramatic decrease in module prices. Such cost pressures have resulted in a drive to develop and implement new module designs, which either increase performance and/or lifetime of the modules or decrease the cost to produce them. In this paper, the main motivations and benefits but also challenges for material innovations will be discussed. Many of these innovations include the use of new and novel materials in place of more conventional materials or designs. As a result, modules are being produced and sold without a long-term understanding about the performance and reliability of these new materials. This has led to unexpected new failure mechanisms occurring few years after deployment, such as potential induced degradation or backsheet cracking. None of these failure modes have been detected after the back then common single stress tests. New accelerated test approaches are based on a combination or sequence of multiple stressors that better reflect outdoor conditions. That allows for identification of new degradation modes linked to new module materials or module designs.