Zone Law Research Articles

Numerical and experimental crack-tip cohesive zone laws with physics-informed neural networks

The cohesive zone law represents the constitutive traction versus separation response along the crack-tip process zone of a material, which bridges the microscopic fracture process to the macroscopic failure behavior. Elucidating the exact functional form of the cohesive zone law is a challenging inverse problem since it can only be inferred indirectly from the far-field in experiments. Here, we construct the full functional form of the cohesive traction and separation relationship along the fracture process zone from far-field stresses and displacements using a physics-informed neural network (PINN), which is constrained to satisfy the Maxwell-Betti's reciprocal theorem with a reciprocity gap to account for the plastically deforming background material. Our numerical studies simulating crack growth under small-scale yielding, mode I loading, show that the PINN is robust in inversely extracting the cohesive traction and separation distributions across a wide range of simulated cohesive zone shapes, even for those with sharp transitions in the traction-separation relationships. Using the far-field elastic strain and residual elastic strain measurements associated with a fatigue crack for a ZK60 magnesium alloy specimen from synchrotron X-ray diffraction experiments, we reconstruct the cohesive traction-separation relationship and observe distinct regimes corresponding to transitions in the micromechanical damage mechanisms.

Predictive modeling of regional carbon storage dynamics in response to land use/land cover changes: An InVEST-based analysis

Assessment of carbon stock (CS) in various land use/land cover (LULC) types is essential for environmental policies focused on reducing CO2 emissions and mitigating climate change. This study utilized the CA-Markov model to simulate future LULC scenarios and the InVEST model to evaluate CS changes in Pakistan from 2001 to 2030. The study employed two decades of yearly composite land cover data from MODIS, achieving high accuracy with a kappa value of 0.856. The results indicate that an increase of 38.1 × 103 km2 in cultivated land could lead to an increment of 13.5 Tg in Pakistan's total CS. In comparison, an increase in forest area can be the reason for raising above-ground carbon (AGC) by 16.8 Tg. These findings enhance the understanding of long-term LULC and CS changes in Pakistan. The study provides valuable insights for governments to refine land use strategies, adjust carbon emission reduction policies, and design better regulations based on the study's findings. Key recommendations include promoting vertical urban development to preserve carbon sequestration areas, implementing strict agricultural zoning laws, expanding afforestation initiatives like the Billion Tree Tsunami and Green Pakistan, and establishing a national LULC and CS monitoring program. Integrating data from various sources will create a comprehensive database to inform policy decisions and land management practices, contributing to global climate change mitigation efforts.

Recurrent neural network (RNN) and long short-term memory neural network (LSTM) based data-driven methods for identifying cohesive zone law parameters of nickel-modified carbon nanotube reinforced sintered nano-silver adhesives

In this paper, we presented three neural network models including deep neural network (DNN), recurrent neural network (RNN), and long short-term memory neural network (LSTM), which are proposed to predict the cohesive zone parameter of sintered silver DCB joint with different contents of nickel modified carbon nanotube, thus reducing the complexity of CZM parameter acquisition for nanoparticle reinforced adhesive. The bilinear CZM model is used as the prediction target model for sintered silver joints with different contents of nickel-modified carbon nanotube filler, and data sets suitable for different networks are established through experimental and numerical simulation results. Three kinds of networks are trained based on the optimized hyperparameters obtained from the Bayesian hyperparameters tuning process. The results show that DNN, RNN, and LSTM frameworks can all predict CZM parameters of nanoparticle-reinforced sintered silver adhesive through load-displacement curves. Based on loss analysis and statistical indicator comparison after K-fold cross-validation, the RNN and LSTM models have better prediction accuracy and performance than the DNN model, and the accuracy of the LSTM model is further improved compared with the DNN model. RNN and LSTM models have high prediction accuracy and stronger recognition ability for the time series data, they can be used as suitable alternative models for inverse recognition of CZM parameters of nanoparticle-reinforced adhesives, and have broad application prospects.

Study on fracture failure behaviour of sapphire transparent window under ultra-high hydrostatic pressure

ABSTRACT Accurately predicting the fracture damage behaviour of light transmission windows is crucial in the design of deep-sea optoelectronic devices. This study proposes a simulation model based on the exponential cohesive zone law to predict the fracture failure of sapphire transparent windows (STW) under multi-dimensional load conditions. By utilising finite element simulation technology, the model accurately determine the fracture damage morphology and failure location of STW in different assembly structure schemes under a hydrostatic pressure of 127 MPa. These simulation results are then effectively validated through full sea depth pressure test experiments. Furthermore, by analyzing the simulation data, this study uncovers the internal mechanism of the fracture damage process of STW and presents a method to predict the fracture damage of STW. This research enhances the understanding of fracture behaviour in light transmission windows and offers valuable insights for the design and development of deep-sea optoelectronic devices.

Effects of tougher school zone laws on road traffic safety in school zones for children in South Korea

IntroductionNew school zone laws in Korea were enforced in March 2020 to increase penalties for traffic violations and preferentially install road safety equipment including automated traffic enforcement devices in school zones. This study aimed to evaluate the effectiveness of tougher school zone laws on school-zone-related road traffic outcome (RTO) rates for children aged 0–12 years in Korea. MethodsMonthly child RTO rates in school zones were calculated per million vehicles and per million children using data on police-reported road traffic crashes, registered motor vehicles, and registered resident population between 2015 and 2021: the intervention series involved school-zone-related rates and the non-equivalent control series involved total and non-school-zone-related rates. The effectiveness of the laws on RTO rates in school zones was assessed using the Bayesian structural time-series models under the controlled interrupted time-series design. ResultsThe results found that considering the trends in the overall and non-school-zone-related RTO rates, enforcement of the laws did not significantly reduce any school-zone-related RTO rates for children aged 0–12 years, both per million vehicles and per million children: equivalent fatality, road traffic injury (RTI), severe RTI, minor RTI, and road traffic crash rates. ConclusionsThe ineffectiveness of Korea's new school zone laws on child RTO rates in school zones implies that other effective measures need to be accompanied to improve children's road traffic safety in school zones, rather than just focusing on raising the severity of punishment. Further research is needed to ensure the effectiveness of school zone laws and measures to mitigate child road traffic casualties in school zones.

Atomistic study of the properties and behavior under uniaxial tensile stress of some representative UO[formula omitted] grain boundaries

In irradiated polycrystalline uranium dioxide (UO2), the pressure generated at high temperature by the noble gases in the intergranular bubbles as well as the thermomechanical stresses due to temperature gradients cause the fracture of the grain boundaries. In this study, one analyzes through atomistic calculations of static and molecular dynamics type the properties of three UO2 grain boundaries and their behavior under uniaxial tensile loading up to fracture. In these atomistic simulations, the interactions between atoms are described using a many-body variable charge potential. Structural analysis, performed on the three grain boundary structures under uniaxial tensile stresses and over a wide temperature range, reveals no source of plasticity. This suggests a brittle behavior at fracture, in agreement with recent experimental studies carried out on micrometer size specimens containing grain boundaries. A method based on thermodynamic considerations is used to build normal cohesive zone laws for the UO2 grain boundaries using molecular dynamics simulation data. The cohesive zone laws will be employed in a future study in failure simulations at higher scales.

Investigation on Dynamic Impact Mechanism of Single Crystal Sapphire 3D Model Based on Cohesive Zone Law

AbstractBased on mesh reconstruction technology, a 3D solid model of single crystal sapphire (SCS) with global embedded cohesive element is established in this study. Using exponential cohesive zone law (CZL), the anisotropy of SCS can be effectively characterized by assigning the mechanical properties of matrix element and cohesive element. Taking the C‐plane SCS model as the research object, the whole process of dynamic evolution of cracks in the model under high‐speed surface impact and high concentrated stress impact is reproduced by finite element simulation technology. The simulation is compared with the experimental results from the aspects of crack initiation morphology, crack propagation path, sample fragmentation form, and mechanical response curve. The dynamic compressive strength reaches 1630.3 MPa with the impact velocity of 30 m s–1 in surface impact type. The initial maximum loading force reaches 320 N when the impact velocity is 8.35 m s–1 in the indentation impact type. In addition, by combining the simulation results, this study clarifies the mechanism of strain rate effect exhibited by SCS from the perspective of stress–strain data and crack evolution characteristics. Therefore, the model established in this study can effectively reflect the mechanical behavior of SCS under impact load.

Nonlocal modeling of crack-interface interaction in a composite system

The mechanical response and the fracture phenomena in a composite system not only depend on the elastic and fracture properties of individual constituents but also on additional parameters such as fiber alignment, fiber volume fraction, interface properties and laminate layup. Fiber alignment is one such parameter that governs the design of the composite according to the purpose required. In the present work, a nonlocal approach combined with a cohesive zone model is proposed and implemented in finite element framework. The proposed model can capture different failure phenomena in a matrix- fiber system. The influence of various properties of fiber, matrix, and the fiber-matrix interface on the mechanical response of the composite system is studied. An exponential coupled cohesive zone law is considered for modeling fiber-matrix interface. Smeared representation of crack and interface are considered in the analysis. The results are validated with numerical simulations present in the literature.

Phase-field regularised cohesive zone model for interface modelling

A discrete interface is represented as a smeared interface in the framework of phase field regularisation. Due to the numerical challenge when imposing boundary conditions we prescribe the phase field in the domain using analytical solutions. We obtain the displacement and the strain from the variational form of the energy functional, but also in the framework of the regularised extended finite element method. Indeed, both approaches result in identical forms, validating the rigour of the method. We have examined different forms of the phase field model and conclude that models with a compact support are more appropriate for modelling interfaces. The method combines advantages of discrete and smeared approaches. Compared to discrete interface models, the method holds similar properties as the extended finite element method (XFEM): no need to treat cracks as geometric discontinuities and avoiding mesh refinement around crack tips. Different from the XFEM, however, the method does not introduce enrichment functions to describe cracks. An advantage compared to the phase field method is that this method directly employs the cohesive zone law from the discrete model, which is physically relevant. The accuracy of the approach for cohesive interface modelling is demonstrated by several numerical examples, including a bar, an L-shaped specimen, and a fibre embedded in an epoxy matrix.

Cohesive Zone Interpretations of Phase-Field Fracture Models

Abstract Unlike micromechanics failure models that have a well-defined crack path, phase-field fracture models are capable of predicting the crack path in arbitrary geometries and dimensions by utilizing a diffuse representation of cracks. However, such models rely on the calibration of a fracture energy (Gc) and a regularization length-scale (lc) parameter, which do not have a strong micromechanical basis. Here, we construct the equivalent crack-tip cohesive zone laws representing a phase-field fracture model, to elucidate the effects of Gc and lc on the fracture resistance and crack growth mechanics under mode I K-field loading. Our results show that the cohesive zone law scales with increasing Gc while maintaining the same functional form. In contrast, increasing lc broadens the process zone and results in a flattened traction-separation profile with a decreased but sustained peak cohesive traction over longer separation distances. While Gc quantitatively captures the fracture initiation toughness, increasing Gc coupled with decreasing lc contributes to a rising fracture resistance curve and a higher steady-state toughness—both these effects cumulate in an evolving cohesive zone law with crack progression. We discuss the relationship between these phase-field parameters and process zone characteristics in the material.

Mechanical Characterisation and Cohesive Law Calibration for a Nitrocellulose Based–Cyclotetramethylene Tetranitramine (HMX) Polymer Bonded Explosive

BackgroundMechanical characterisation of polymer bonded explosives (PBXs) is crucial for their safe handling during storage and transportation. At temperatures higher than the binder's glass transition temperature, fracture is caused predominantly by interface debonding between the binder and explosive crystals. Interfacial friction between debonded crystals can lead to accidental detonation of the PBX material, even under a very small external load. Cohesive zone laws can describe this interfacial debonding.ObjectiveThis study aims to experimentally calibrate the interfacial cohesive zone parameters of a nitrocellulose based–cyclotetramethylene tetranitramine (HMX) PBX, a particulate composite with an 88% volume fraction of crystals.MethodsCompact tension fracture tests, coupled with Digital Image Correlation (DIC) were used to capture the strain fields around the crack tip. The experimental data were used in conjunction with an extended Mori–Tanaka method considering the effect of interfacial debonding.ResultsThe cohesive zone parameters were successfully calibrated and were found to be crosshead rate independent. The values of the critical traction {sigma }_{int}^{max} and interfacial energy release rate, {gamma }_{if}, dropped significantly with increasing temperature. The experimental method followed in this study is generic, and it can be employed to extract the cohesive zone parameters characterising the interface behaviour between the filler and matrix in other particulate filled, polymer composite materials.ConclusionsCohesive zone properties can be experimentally determined to provide inputs in micromechanical simulations linking the microstructure of the PBX composite to its macroscopic response as well as enabling the estimation of hot spot formation at debonded crystal interfaces.

Mode II cohesive zone law of porous sintered silver joints with nickel coated multiwall carbon nanotube additive under ENF test

Various contents of nickel coated carbon nanotube added sintered silver joints are fabricated through mechanical alloying. An analytical method is presented to compute the fracture energy of ENF tests incorporating shearing effect and thickness effect, which shows better accuracy compared with traditional method, which are closer to the solutions of compliance based beam method. Mode II fracture energy, mode II fracture toughness and mode II cohesive zone model for different contents of nickel coated carbon nanotube added sintered silver joints are presented based on the data extraction of the ENF tests. With the increase of adhesive layer thickness, the fracture energy and the mode II fracture toughness improve. However, thickness effect is less significant but not negligible comparing with the strengthening effect on the improvement of fracture toughness, which is caused by adding nickel coated multiwall carbon nanotubes. The relation between mode II fracture toughness and porosity is also discussed. For most of the conditions, the mode II fracture toughness is higher than mode I fracture toughness regardless of additive content due to the crack deflection, crack bridging and pull-out mechanisms during the crack propagation except for those high content of additive whose fracture energy is reduced because of aggregation effect.

Quantitative Study on the Law of Surface Subsidence Zoning in Steeply Inclined Extra-Thick Coal Seam Mining

The damage of overlying strata and ground surface caused by the one-time mining space is relatively severe in steeply inclined extra-thick coal seams. The unique law of surface subsidence at these conditions is still missing. Taking Huating Dongxia Coal Mine as the research background, this paper reveals the law-governing effects on rock strata and surface movement and deformation caused by steeply inclined extra-thick coal seam mining with different coal seam dip angles and coal thicknesses by using the methods of surface measurement, theoretical analysis, and numerical simulation. Based on the characteristics of the surface inclination deformation, the surface is divided into four areas along the tendency section line—namely, an outcrop discontinuous deformation area, an overall subsidence area, a gradual subsidence area, and a slight subsidence area. The results show that the influence of the coal seam dip angle on surface subsidence zoning in steeply inclined and thick coal seams is mainly reflected in the affected area range and the form of damage. Coal thickness has a weak effect on the form of rock strata damage and surface movement. Utilizing the influence of the coal seam dip angle and coal seam thickness on the change in the surface subsidence zoning, the calculation formulas for each area range and zoning angle in relation to the coal seam dip angle, coal thickness, mining depth, and vertical stage height are established. The research results can provide a reference to evaluate the influence of mining, especially in steeply inclined extra-thick coal seams.

Fracture characterisation of bone-cement bonded joints under mode I loading

Over the years, many techniques have been developed for the stabilisation of bone fractures. The study of the adhesion of bone-to-bone cement is an important step towards the development of new immobilization systems. Although bone cement has been used for more than fifty years, very few studies have been performed regarding the evaluation of fracture properties. In this work, numerical and experimental investigations were conducted to evaluate the strain energy release rate under mode I loading in a bone-cement bonded joint, using the Double Cantilever Beam (DCB) test. Cohesive zone laws were also measured combining the finite element method with non-linear elastic fracture mechanics. This has been made in a cortical bone bonded joint with polymethylmethacrylate (PMMA). Consistent results have been obtained regarding fracture toughness in a widely used bone-to-bone cement joint in many biomedical applications.

Learning by Regulating: The Evolution of Wind Energy Zoning Laws

Learning by Regulating: The Evolution of Wind Energy Zoning Laws

An inverse method to reconstruct crack-tip cohesive zone laws for fatigue by numerical field projection

Cohesive zone failure models are widely used to simulate fatigue crack propagation under cyclic loadings, but the functional form of such phenomenological models does not have a strong micromechanical basis. While numerical techniques have been developed to extract the crack-tip cohesive zone law for monotonic fracture from experimental strain information, elucidating the unloading-reloading hysteresis representing accumulated and irreversible damage under fatigue cycling is still challenging. Here, we introduce a novel field projection method (FPM) to reconstruct the cohesive zone laws for steady-state fatigue crack growth from elastic strain field information at various loading and unloading stages within a single steady-state fatigue cycle. The method is based on the Maxwell-Betti’s reciprocal theorem, which considers the material response to be linear elastic during loading and unloading, albeit with a reciprocity gap to account for the inhomogeneous residual elastic strain accumulated at the end of each fatigue cycle. Through numerical experiments, we demonstrate that this FPM is capable of accurately extracting the crack-tip cohesive tractions and separations, along with the elusive unloading-reloading hysteresis, which constitute the cohesive zone law for fatigue crack growth. We discuss the errors and uncertainties associated with this inverse approach.

КОМПЛЕКСНАЯ ГЕОГРАФИЯ КАК НАПРАВЛЕНИЕ ТЕОРЕТИЧЕСКИХ ИССЛЕДОВАНИЙ И МОДЕЛИРОВАНИЯ

The paper formulates basic terms and axioms of the concept of complex geography, defines its subject, methods and models, traces the differences between this approach and other directions in the development of the theory of geographical science, presents quantitative models of geocomplexes constructed based on remote sensing data. By complexes we mean metrized, inductive, commutative, transitive, linearly ordered, discrete-continuous, limited, and changing homotopy systems of information exchange that consist of functionally related heterogeneous elements. This distinguishes the complex approach from the geosystem-dynamic one and from other models of reality. The paper considers the terms of the theory of complex systems: bundle, compositions, combinations, configurations, congruences, tangent transformations, analogy, homology and homotopy, categories and toposes. In modeling, we use the Jacobi determinant as a measure of connectivity and rank distributions for ordinalistic evaluation. The models are illustrated by examples from traditional geographical science (the comparative-geographical method, factor-dynamic series, the law of geographical zoning, etc.). Based on the developed models, we carried out a comparative analysis of the landscapes of the Baikal region using remote sensing data. The elevation and the potential insolation according to the digital elevation model were considered as independent variables (influencing factors). As the dependent variables, the average duration of occurrence of stable snow cover and the earth's surface temperature according to MODIS data were used. The research revealed a congruence of different parts of the territory, which justifies the complexity of the climatic characteristics of the Baikal region according to the selected indicators.

Morphological Structure Of Mountain Soils

This article discusses morphological structure of mountain soils. The mountainous regions of the Republic of Uzbekistan are located mainly in Tashkent, Surkhandarya, Samarkand, Jizzakh, Syrdarya, Fergana Valley and Navoi regions, and differ from each other in their greenery, charm and structure. Mountain soils are distributed sequentially according to the law of vertical zoning, depending on the altitude above sea level. The soil cover in these regions is characterized by their development (evolution), genesis, agrochemical, agrophysical properties and, most importantly, morphological structure. Each region has its own natural factors, which directly affect the development and morphological structure of the soil cover.

The uneven shrinking city: neighborhood demographic change and creative class planning in Birmingham, Alabama

ABSTRACT This research examines the uneven spatial-demographic distribution of population loss in one US “shrinking” city, Birmingham, Alabama, and analyzes the city’s planning role in and response to population loss. It examines the connections between Birmingham’s historic racial zoning law and urban renewal practices and the resulting patterns of depopulation and demographic change, and its present-day use of creative class planning – an approach critiqued for perpetuating inequalities – to revitalize neighborhoods and reverse depopulation. Using a novel methodological approach, this research describes the characteristics of Birmingham’s population loss from 1970 to 2010 and examines the city’s planning response to this population loss. Findings demonstrate that the variables associated with depopulation change over time and space. By linking these spatialized demographic trends to the city’s current planning approach, we problematize creative class and residential attractiveness-based planning logics, while highlighting the importance of addressing inequality in the planning of shrinking cities.

Evaluation of water resources changes of the Mountain Dniester in 20th century following the RCP8.5 scenario and based on the “climate-runoff” model

The relevance of the research consists in the need for evaluating the water resources changes of the Dniester due to global warming. The mountain part of the Dniester Basin is a zone of the river's runoff formation that determines its water content. The subject of research includes a process of climate changes and their impact on the water resources of the Mountain Dniester’s catchments. The research focuses on determining the water resources changes under current and possible future climatic conditions represented by climatic scenarios.
 The research aims at evaluating the water resources changes of the mountain part of the Dniester’s catchment area at the present and in the future by the mid-21 st century (2021-2050) based on the “climate-runoff” model using meteorological observations data (up to 2018 inclusive) and scenario data (averaged data based on 14 mathematical models of the CORDEX project, RCP8.5 scenario).
 During the research the resources of humidification, heat (heat equivalent) and water content for modern (1989-2018) and scenario (RCP8.5, 2021-2050) climatic conditions based on application of the "climate-runoff" model were evaluated. The theoretical basis for estimating the natural (undisturbed by water management) annual runoff in this model is represented by the water-heat balance equation. The meteorological characteristics (average monthly air temperatures and precipitation) serve as input data. The runoff calculated using the water-heat balance equation is called a climatic runoff. One of the peculiarities of the research consists in the use of the vertical zoning law with respect to distribution of runoff and climatic factors of its formation. During the comparative analysis the dependence of annual runoff norms on height of the Mountain Dniester’s terrain specified in modern regulatory documents served as a basic dependence. Such dependence reflects an altitude-dependant distribution of runoff for the climatic conditions that preceded the significant impact of global warming on air temperature (until 1989).
 The analysis of the dependences of average long-term values of the annual runoff depending on the terrain altitude showed that the runoff changes for two studied periods (before and after 1989) are within ±12,3%. The analysis of the graphs of chronological course of annual water flow of the mountain tributaries of the Dniester made it possible to confirm the absence of statistically significant trends in their fluctuations.
 According to the RCP8.5 climate scenario over the period of 2021-2050 and following the results of calculations based on the “climate-runoff” model, the dependences of the average long-term altitude-related values of climatic factors and climatic runoff were retrieved. It was found that the effects of global warming decrease with increasing altitude. In the foothills (up to 200 m) the annual precipitation decreases (up to 11%), the maximum possible evaporation increases (up to 17%) and water resources decrease (up to 46%). Heat resources cease to increase and water resources cease to reduce at the altitudes over 800 m. The average deviation of the scenario and baseline values for precipitation over the estimated period will amount to 2.41% for precipitation, 5.79% for maximum possible evaporation and 8.87% for water resources. Thus, reduction of water resources in the mountainous part of the Dniester by the mid-21 st century will be insignificant. When evaluating the current state of water resources of the Mountain Dniester no significant changes were discovered, thereby not contradicting the other authors’ data.