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At least 73 records · Page 4

Molecular models for creep in oriented polyethylene fibers

Highly oriented and crystalline polyetheylene (PE) fibers have a large failure stress under rapid tensile loading but exhibit significant creep at much smaller stresses that limits applications. A possible mechanism is slip of chains due to stress-enhanced, thermally activated nucleation of dislocations at chain ends in crystalline regions. Molecular dynamics simulations are used to parameterize a Frenkel–Kontorova model that provides analytic expressions for the limiting stress and activation energy for dislocation nucleation as a function of stress. Results from four commonly used hydrocarbon potentials are compared to show that the qualitative behavior is robust and estimate quantitative uncertainties. In all cases, the results can be described by an Eyring model with values of the zero-stress activation energy Ea0≈1.5 eV and activation volume V* ≈ 45 Å3 that are consistent with the experimental results for increasingly crystalline materials. The limiting yield stress is ∼8 GPa. These results suggest that activated dislocation nucleation at chain ends is an important mechanism for creep in highly oriented PE fibers.

O’Connor, Thomas C. (ORCID:0000000293930295)↗

Subsurface mechanical damage of fused silica glass during grinding by various sub-aperture tools with and without ultrasonics

The subsurface mechanical damage (SSD) depth after grinding fused silica glass with a comprehensive set of sub-aperture fixed abrasive grinding tools [cup, wheel, belt, pad, and rotary face mill (with and without ultrasonics)] and process parameters has been statistically measured using the taper wedge technique and evaluated. Consistent with a previously reported grinding model [J. Non-Cryst. Solids 352, 5601–5617 (2006) Crossref , Materials Science and Technology of Optical Fabrication (Wiley & Sons, 2018)], based on the sliding indentation fracture by sliding particles or asperities where the normal load per particle determines the depth of the fracture (and ultimately the overall SSD depth), the dominant factor controlling SSD depth was found to be the abrasive size regardless of the tool type and process conditions. Compared to full aperture grinding methods, the overall SSD depth was higher using the sub-aperture tools, likely due to the higher effective pressure and higher load per particle distribution. Here, in addition to abrasive size, a significant reduction in SSD depth was achieved by: (1) reducing the load distribution on the abrasive particles via increase in contact area and/or decrease in mechanical loading; (2) using a more compliant host tool medium; and (3) in what we believe is a more novel way, using ultrasonics. Combining low abrasive size, larger contact area, and a compliant host, the 6 µm diamond in a resin matrix (Trizact) on a foam pad led to very low SSD depth (~ 4.6 µm), relatively fast grinding rate (186 mm 3 /h), and little or no figure degradation. This grinding tool/process is an attractive choice for final grind, resulting in significantly reduced polish out (i.e., “grey out”) times. With the rotary face mill tool, the use of ultrasonics consistently led to a SSD depth reduction (ranging from 17%–34%). A new fracture mechanics-based model, to the best of our knowledge, where the relevant normal load is parallel to the feed direction, has been developed to explain how ultrasonics leads to lower SSD depth. The key factors, supported by finite element stress analysis and load measurements, are (1) the initiation of fractures at higher z heights during the tool’s ultrasonic vertical oscillations, thus propagating less deep into workpiece; (2) reduction in load (and therefore reduction in fracture propagation distance) due to smaller tool-workpiece feed direction contact area (again caused by higher heights relative to depth of cut); (3) upward movement of the tool during oscillation leads to fracturing toward the surface instead into the depth; and finally (4) at tool’s lowest point of oscillation cycle, there may not be enough time for the fracture to propagate to its full length.

Optics and optical instruments↗

Variations of Stress Parameters in the Southern California Plate Boundary Around the South Central Transverse Ranges

We examine the stress field in Southern California with a focus on the region near the South Central Transverse Ranges (SCTR), using a refined stress inversion methodology. We independently invert declustered and aftershocks focal mechanisms from the years 1981 to 2017. Comparisons between the stress field orientations and the stress ratios from these inversions provide information on local sources of the stress field. Regionally, the SHmax tends to be toward NNE and the stress ratios vary from transtensional stress regime near the Eastern California Shear Zone (ECSZ), to strike-slip faulting near the SCTR, and toward transpression near the Western Transverse Ranges. Detailed analysis of stress parameters near the SCTR indicates deviations from the regional strike-slip faulting including the following: (1) The San Bernardino Mountain area shows S Hmax direction toward NNW and transpressional stress components likely associated with the motions of the San Andreas Fault and ECSZ; (2) the Cajon Pass and San Gorgonio Pass show transpressional stress regime near the bottom of the seismogenic zone likely associated with the elevated topography; and (3) in Crafton Hills, rotation of the principal stress plunges and SHmax direction and transtensional stress regime below ~10 km, along with lower estimated apparent friction coefficient, suggest a weak fault possibly associated with deep creep. The performed multiscale analysis resolves effects of regional and local loadings. The average stress parameters in the analyzed 37 years do not show significant temporal variations of stress field near the SCTR region.

58 GEOSCIENCES↗

Multiobjective Dynamic Optimization for Optimal Load-Following of Natural Gas Combined Cycle Power Plants under Stress Constraints

With the increasing penetration of intermittent renewable energy sources into the electric grid, there is an associated need for conventional thermal power plants that are designed to operate at base-load conditions to cycle their load rapidly and frequently and operate under low-load conditions. Fast load-following operations lead to plant efficiency loss and the reduction of equipment life. A high-fidelity dynamic model of a natural gas combined cycle power plant, with rigorous equipment level submodels, is developed to capture the plant transient performance and the thermomechanical stress evolution at the high-pressure drum is computed to assess the drum life consumption. Stress evolution is modeled for the location of the edge at the drum/downcomer junction that experiences high circumferential stress amplitude during the fast load-following operation, leading to higher fatigue damage than locations considered under existing design standards. A dynamic optimization problem is solved for optimal load-following operation. Depending on the value of the stress constraint and the desired ramp rate, satisfying the desired stress constraint may be infeasible without relaxing the ramp rate. A multiobjective dynamic optimization problem is solved using a lexicographic approach that minimizes ramp rate relaxation and maximizes efficiency while satisfying stress constraints, avoiding spraying to saturation, and maintaining main steam and reheat steam temperature within bounds. It was observed that the optimal ramp rate can be highly nonlinear as opposed to the industry-standard linear ramp rate. Nonlinear optimal ramp-rate profiles not only help to avoid stress constraints that may be unavoidable by using the linear profile but also result in higher efficiency than the linear profile. Furthermore, the study shows that there is a strong tradeoff between the relaxation in the plant ramp rate and the time-average thermal efficiency.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A phase-field model for non-isothermal phase transformation and plasticity in polycrystalline yttria-stabilized tetragonal zirconia

Here we propose an elastoplastic phase-field (PF) model to investigate the mechanics of tetragonal-to-monoclinic phase transformation (TMPT) and elastoplastic deformation of polycrystalline yttria-stabilized tetragonal zirconia (YSTZ). A Landau polynomial with non-vanishing chemical energy at the equilibrium temperature is introduced to account for the actual formation energies of the phases. The effects of different grain orientations, latent heat, and temperature on TMPT and deformation mechanisms are considered. The suppressive transformation effects of the grain boundaries (GBs) is modeled using an inhomogeneous kinetic coefficient in the bulk and GBs. The simulation results for single crystals demonstrate the capability of the model to reproduce the orientation-dependent compressive deformation of YSTZ similar to atomistic simulations and micropillar experiments. The single crystal with [100] crystallographic orientation along the loading direction (SC[100]) displays both TMPT and plasticity, SC[101] experiences only phase transformation, while SC[001] undergoes only plastic yielding. The TMPT induced by compressive loading exhibits shape memory effect (SME) below the equilibrium transformation temperature and pseudoelasticity above it, while the critical transformation stress increases with increasing loading temperature. The irrecoverable plastic strain is found to trap a part of the monoclinic phase, which prevents a complete reverse transformation. The polycrystalline cases also display SME and PE at low and high temperatures, respectively. Due to the orientation differences between grains and the stress concentrations at geometric nonlinearities, plastic deformation occurs in polycrystalline YSTZ for an applied load less than the yield stress. The results suggest a possible limitation of plasticity and an improvement of the shape recovery of YSTZ if one can control the orientation of the grains and/or increase the density of stacking faults at the GBs during material processing.

36 MATERIALS SCIENCE↗

Load Deflection Data (LDDATA)

The current data set is load deflection data (Stress vs strain for compression stress and stress vs elongation for tension stress) from a material test. The goal of the test was to characterize this rubber-like material by looking at different variables: sample creation process, anisotropy, temperature, etc. The data will be used with the Texas A&M Online Research Experience for Undergraduates (O-REU) program. This program is joint with LANL. The student is not an official LANL student so they will not be able to access data and documents on the yellow. The load deflection data set is unclassified and will be sent to the student for analysis. Analysis will include curve fitting, scalar value analysis (stiffness, toughness, etc.) and analysis of variance to determine what variables statistically affect the response while correcting for covariates (temperature soak time and humidity). Data will be stored as Matlab structs and as HDF5 files. Same data, different formats.

36 MATERIALS SCIENCE↗

The Impact of Carbonation Curing on the Fatigue Behavior of Polyvinyl Alcohol Engineered Cementitious Composites (PVA-ECC)

Use of Engineered Cementitious Composites (ECC) has been proven to enhance structural fatigue resistance and reduce the use-phase emissions for transportation infrastructure. Carbonation curing offers an opportunity to reduce the embodied carbon of ECC via direct CO 2 sequestration. In this study, the impact of carbonation curing on ECC’s fatigue resistance was examined. ECC’s CO 2 uptake, static flexural behavior, flexural fatigue performance, and single fiber pull-out behavior were studied experimentally. Midspan deflection up to 3 million cycles under fatigue load, fatigue stress-life relationship, and failure mechanism for carbonation-cured and air-cured ECC were investigated. Carbonation curing was found to significantly improved the fatigue life of ECC and lowered the midspan deflection under the same stress. Further, CO 2 -cured ECC can achieve >20% CO 2 uptake per cement mass after 24-hour carbonation curing. Carbonation curing increased ECC’s flexural strength by 32% and promoted crack width control capability, with maximum post-fatigue crack width reduced from 148 μm to 76 μm. As a result, the positive impact of carbonation curing on the fatigue behavior of ECC simultaneously lowers the embodied and operational carbon of ECC structural members subjected to fatigue loading during service.

36 MATERIALS SCIENCE↗

ReaxFF reactive force field model enables accurate prediction of physiochemical and mechanical properties of crystalline and amorphous shape‐memory polyurethane

Abstract We investigate reactive force field (ReaxFF) prediction of physiochemical and mechanical properties, and stimuli response behavior of a shape‐memory polyurethane (SMPU) rigid segment. We used SMPUs as a platform to link the rigid/hard segment domain crystallinity with properties that can also be experimentally measured. Specifically, we developed models for crystalline and amorphous forms of a common rigid segment of SMPUs, for example, 4,4′‐diphenylmethane diisocyanate (MDI) with n‐butanediol (BDO), denoted as MDI‐BDO. ReaxFF molecular dynamics simulations with equilibrium dynamics are performed by controlling mass, temperature, and pressure or volume to predict the structural and physiochemical properties of crystalline and amorphous rigid segments of SMPU systems, followed by simulating their XRD and FTIR patterns, respectively. Non‐equilibrium ReaxFF simulations are implemented by using uniaxial box deformation technique to study response‐behavior of crystalline SMPU under tensile loading and during stress‐relaxation. The model and simulation scheme presented in this study demonstrates a robust theoretical pathway toward application‐dictated, on‐demand design of high‐performance SMPUs in applications such as soft robotics.

Afroz, Mohammad M.↗

Virtual texture analysis to understand microstructure effects on deformation twinning and detwinning behavior in BCC metals

Understanding and predicting deformation twinning contributions to plastic deformation in BCC metals has been a long-standing challenge due to the interplay with dislocation slip and non-Schmid effects that render an asymmetry under tension and compression. This paper uses molecular dynamics simulations to understand the effect of unloading and grain orientation on deformation twinning in a nanocrystalline Fe (nc-Fe) system as a model BCC metal. The nc-Fe system is loaded under uniaxial stress tension and compression to understand the effect of grain orientation (Schmid effects) on deformation twinning behavior and the tension/compression asymmetry (non-Schmid effects). A new virtual texture analysis “VirTex” tool is used to understand the role of grain orientation on the nucleation of twins and their contributions to the observed stress–strain response. For certain grain orientations, the twinnability is observed to be different in tension and compression. In addition, the flow stress accommodation from twins in certain grains is observed to be different in tension and compression and different from that for the grains. Subsequent unloading leads to detwinning in the deformed microstructures, where the extent of detwinning depends on the strain from which the system is unloaded and on the morphology of the twin. Lastly, the simulations are carried out to analyze the role of the Schmid factor on the twinnability and asymmetry in tension and compression.

Kannan, Aadhithyan [University of Connecticut, Sto↗

Complexity of segregation behavior at localized deformation sites formed while in service in a 316 stainless steel baffle-former bolt

Here, post-irradiation evaluation was performed on a 316 stainless steel baffle former bolt harvested after 40 years of service in a pressurized water reactor. Microstructure analysis revealed the presence of defect-free dislocation channels and strain-induced twins, indicative of loading at a stress level close to yield stress at least once while in service. Primary radiation-induced Ni/Si precipitates were destroyed during channel and twin formation, and secondary, significantly coarser Ni/Si precipitates formed along newly formed Σ3 boundaries during the continued irradiation. Additionally, an elevated phosphorus level was observed inside the strain-induced twin. Complex chemistry inside the strain-induced feature may overlap with dislocation pileups and impact localized corrosion, material long-term performance, and safety.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Comparison of Biotite Elastic Properties Recovered by Spherical Nanoindentations and Atomistic Simulations — Influence of Nano-Scale Defects in Phyllosilicates

Phyllosilicate minerals, due to their sheets structure and morphology, are known to cause anisotropy in bulk rock properties and make the bulk rock more compliant. Accurately characterizing the micromechanical behavior of phyllosilicate minerals from laboratory observations, which eventually translates to the bulk rock behavior, is still challenging due to their fine-grained nature. Recent advances in atomistic simulations open the possibility of theoretically investigating such mineral mechanical behavior. We compare the elastic properties of biotites recovered by spherical nanoindentation with those predicted from density functional theory (DFT) simulations to investigate to what extent theoretical predictions reproduce actual phyllosilicate properties. Spherical nanoindentation was conducted using schist rocks from Poorman Formation, South Dakota, USA, to recover continuous indentation stress-strain curves. Loading in the layer-normal orientation shows an average indentation modulus (M) of about 35 GPa, while loading in the layer-parallel orientation gives a higher average of about 95 GPa. To facilitate comparison, the elastic stiffness constants (cij) determined from DFT were converted to indentation modulus (M) using solutions proposed in this study. The majority of the nanoindentation modulus results are below the values inferred from the simulation results representing ideal defect-free minerals. We suggest that crystal defects present at the nano-scale, potentially ripplocations, are the dominant cause of the lower indentation modulus recovered from nanoindentation compared to those inferred from DFT simulations. Results highlight the importance of acknowledging the defects that exist down to the nano-scale as it modifies the mechanical properties of phyllosilicates compared to its pure defect-free form.

58 GEOSCIENCES↗

Thermohydraulic Design Analysis of the Target Assembly in the Material Plasma Exposure Experiment Facility

The Material Plasma Exposure eXperiment (MPEX) project seeks to design a steady-state linear plasma facility at Oak Ridge National Laboratory that will be used to study plasma-material interactions (PMIs) at fusion prototypic levels, supporting the evaluation and development of materials for the next generation of fusion devices. This study is focused on PMI exposure of small-size neutron-irradiated specimens, which are clamped onto an actively cooled component. A thermohydraulic evaluation of a new MPEX target assembly design to assess the appropriate operation during MPEX operation is presented. To further guide the design and assess the structural integrity of the components under expected loads, preliminary thermomechanical stress analyses were also conducted. To ensure good thermal contact between the components, thermal interface materials, such as silver flexible graphite, were used in the assembly. It was found that the maximum target temperatures of 1572, 1463, and 1315 K were obtained for Grafoil thicknesses of 0.61, 0.38, and 0.25 mm, respectively. The distribution of the axial deformation at high heat fluxes showed that there are no gaps between components, indicating good contact at material interfaces. Moreover, the contact pressure between the target and other components indicated that very good contact was established at these interfaces. Furthermore, the stress-strain conditions for the target will be further used to assess the appropriate operation during MPEX experiments and gain insight into materials science phenomena during PMI experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Transportation Analysis of the Fermilab High-Beta 650 MHz Cryomodule

The prototype High-Beta 650 MHz cryomodule for the PIP-II project will be the first of its kind to be transported internationally, and the round trip from FNAL to STFC UKRI will use a combination of road and air transit. Transportation of an assembled cryomodule poses a significant technical challenge, as excitation can generate high stresses and cyclic loading. To accurately assess the behavior of the cryomodule, Finite Element Analysis (FEA) was used to analyze all major components. First, all individual components were studied. For the critical/complex components, the analysis was in fine detail. Afterwards, all models were brought to a simplified state (necessary for computational expenses), verified to have the same behavior as their detailed counterparts, and combined to form larger sub-assemblies, with the ultimate analysis including the full cryomodule. We report the criteria for acceptance and methods of analysis, and results for selected components and sub-assemblies.

43 PARTICLE ACCELERATORS↗

Ammonia-Based Energy Storage Technology

The University of North Dakota Energy & Environmental Research Center (EERC), in partnership with the U.S. Department of Energy National Energy Technology Laboratory (NETL), Basin Electric Power Cooperative, Minnkota Power Cooperative, Otter Tail Power Company, and the North Dakota Industrial Commission (energy technology research and development sponsor), undertook a project to model, validate, and advance (from Technology Readiness Level [TRL] 2 to TRL 3) the ammonia-based energy storage technology (NH 3 -BEST) concept. The concept is designed to enable electricity-generating unit (EGU) accommodation of power demand fluctuations while steadily operating within an optimal-performance baseline power output range, ensuring maximum EGU operational efficiency and minimum degradation of materials, equipment, and performance because of load-cycling-driven stresses.

25 ENERGY STORAGE↗

Evaluation of 304L stainless steel deformation and failure under cyclic loading

The motivation for this work came from the simulation of components subjected to impact. In these problems, repeated loading can be generated by vibrational motion between internal parts of the component or by the occurrence of multiple impacts. Graphs of tensile equivalent plastic strain $(\overline{\varepsilon}_T^\rho)$ versus time from such cases had the character shown in Fig. 1. The equivalent plastic strain grew by alternating periods of accumulation and hold. The periods of hold indicate times when $d\overline{\varepsilon}_T^\rho$ did not accumulate. This can be due to the material unloading into the elastic range, or actually plastically reverse loading with hydrostatic stress σ h < 0 as was demonstrated for an impact simulation. Similar observations were made from the simulation of a 2-degree-of-freedom mass-elastic-plastic-spring system subjected to impact.

36 MATERIALS SCIENCE↗

Enhancement of operational Flexibility of Power Plants Using IN740

Headers are crucial components within diverse industries, especially in the energy sector, as they enable the efficient transfer of fluids. The selection of materials for headers is determined by their specific applications; for example, Grade 91 and Grade 92 steels are commonly utilized. In our research, we recommend the adoption of INCONEL alloy 740 due to its exceptional robustness and heat-resistant characteristics. One critical parameter in header systems is the heat transfer coefficient, which directly influences the efficiency of heat exchange processes and can thereby impact the structural integrity of the headers. This coefficient is closely linked with factors such as the Nusselt number, which is influenced by fluid flow characteristics and thermal properties. The flow direction within headers, whether unidirectional or multidirectional—significantly affects the overall dynamics of heat transfer. This research focuses on exploring the behavior of headers, a specific pipeline system component, using ANSYS simulation software. The study aims to predict heat transfer and mechanical behavior within headers under various conditions through steady-state and transient simulations (parts 1 and 2 of the report). Key parameters such as heat transfer coefficient, velocity, and temperature are examined with the goal of optimizing header design. Part 3 of the report addresses the critical yet underexplored relationship between pressure drop and heat transfer coefficients in the transient flow regime within headers, specifically focusing on smooth horizontal circular tubes. Limited experimental work has been conducted in this area, prompting the need for comprehensive analysis. By leveraging machine learning techniques, this research aims to establish a correlation between pressure drop and heat transfer across various flow conditions, including laminar, transient, quasi-turbulent, and turbulent regimes. The data utilized for this analysis were meticulously gathered from existing literature, capturing simultaneous measurements of pressure drops and heat transfer. Part 4: In the context of power plants, header pipes are essential components that significantly influence system performance by facilitating the collection and distribution of steam. This report highlights the critical role of header pipes in enhancing reliability, efficiency, and overall power plant performance. A key aspect of this investigation is shape optimization, which aims to maximize performance while minimizing material usage. By focusing on shape optimization, this research contributes to improved efficiency and a reduced environmental footprint for power plant installations. The methodology developed in this study emphasizes optimizing header shapes to decrease reliance on expensive alloy materials and lower maintenance costs. Furthermore, a case study was conducted using a header from an operational power plant to validate the proposed optimization techniques. Finally, part 5 addresses the challenges associated with flexible operations in boiler systems, the study outlines several strategies for enhancing the durability and reliability of steam headers. Key approaches include material selection, which involves utilizing advanced materials with superior high-temperature properties and enhanced fatigue resistance to extend the lifespan of steam headers. Design modifications are also recommended, focusing on implementing changes that mitigate thermal stress and cyclic loading to reduce the likelihood of failures under varying operating conditions. Additionally, the study emphasizes the importance of regular inspection and monitoring by establishing rigorous protocols to detect early signs of damage, allowing for timely maintenance and minimizing the risks of catastrophic failures. Furthermore, operational guidelines are developed to minimize the frequency and severity of thermal transients, ensuring stable and efficient operations. Collectively, these strategies provide a robust framework for overcoming the unique challenges posed by flexible operation in boiler systems, ultimately contributing to improved reliability and performance in power plant operations. Through this comprehensive approach, the study not only enhances the understanding of pressure drop and heat transfer relationships but also promotes advancements in design and operation that will benefit the entire power generation industry.

01 COAL, LIGNITE, AND PEAT↗

Developing the Science Basis for Understanding Polymer Encapsulant Degradation Mechanisms: DuraMAT 2.0 Final Project Report

Polymeric encapsulants are essential materials in photovoltaic modules, protecting sensitive electronics from the environment while providing mechanical integrity to the multilayered assembly. However, these polymeric materials are susceptible to degradation processes driven by the ingress of environmental species, ultraviolet radiation, thermal stresses, and mechanical loading. In this study, we employ a combined atomistic simulation and accelerated aging experimental approach to study the molecular-scale mechanisms of encapsulant degradation. Classical molecular dynamics simulations quantify the diffusion of environmental and degradation species through the polymer matrix, producing composition-specific diffusion coefficients. Reactive simulations characterize activation energy barriers and reaction rate constants for key chemical pathways. In parallel, thermal-desorption analyses coupled with mass spectrometry monitor the emergence and concentration profiles of degradation products under controlled stressor conditions. By integrating simulation and experiment, we establish quantitative correlations between polymer composition, species diffusivity, and chemical reactivity. We anticipate that these relations and quantitative values could serve as high-fidelity inputs to reaction-diffusion models, enabling physics-informed lifetime predictions and guiding the design of more durable encapsulant materials for solar energy applications.

36 MATERIALS SCIENCE↗

Large Area Detection of Microstructural Defects with Multi-Mode Ultrasonic Signals

Cyclic loading or other stresses can lead to development of cracks and crack growth in mechanical structures, leading to eventual failure. While ultrasound imaging can be used for non-destructive testing of such structures, conventional ultrasound techniques are often limited by crack size, density, and areal coverage. An effective characterization of real-world, large-area structures is required at an early damage stage to prevent catastrophic failure and predict remaining life. In this study, a new nonlinear ultrasonic testing (NUT) method is proposed for large-area monitoring of practical structures with arbitrary complexity by using multiple-mode guided-wave ultrasonic signals. The proposed guided-wave NUT technique requires single-element transducers, simple electronics, and a mixed time-frequency domain signal processing. As a proof-of-concept demonstration, numerical simulations and experiments are performed on an A36 carbon steel beam assembly with previously formed microstructural defects that cause nonlinearities in ultrasonic response. The quadratic dependence of the nonlinear wave excitation on the input ultrasonic signal amplitude is shown by numerical simulations, and such a nonlinear ultrasonic response is experimentally observed in the zone with a high density of microstructural defects.

36 MATERIALS SCIENCE↗