Fracture Mechanics

Тhe article offers an overview of different methods for evaluating the pile
group efficiency. An analysis of the known experimental results has been made and a
comparison between them has been proposed. An assessment of the applicability of the
various formulas is proposed.

The article offers an overview of various analytical methods for evaluating the pile group efficiency. An analysis of the known analytical expressions was also made and a comparison between the individual parameters involved in the calculation of the efficiency was proposed. Guidance is given for calculating the forces in the dimensioning of pile cap.

Mixed mode I/II fracture criterion based on strain energy density theory is presented for failure investigation of cracked composite materials. Crack is assumed to occur along the fibers in a highly orthotropic body. A new definition for fracture toughness of crack tip damage zone is proposed and employed to include the effects of dissipated energy due to formation of considerable fracture process zone. As crack propagation occurs between fibers in the isotropic matrix, reinforcement isotropic solid model is employed as a superior material model. Elastic and fracture properties of damage zone are characterized as a function of undamaged matrix properties and micro-crack density. Center notched disk tension (CNDT) specimen is introduced and employed for fracture tests. Comparison of the fracture limit curves with experimental data proves the capability of the new proposed mixed mode fracture criterion for fracture investigation of orthotropic materials.

Mixed mode I/II fracture criterion based on strain energy density theory is presented for failure investigation of cracked composite materials. Crack is assumed to occur along the fibers in a highly orthotropic body. A new definition for fracture toughness of crack tip damage zone is proposed and employed to include the effects of dissipated energy due to formation of considerable fracture process zone. As crack propagation occurs between fibers in the isotropic matrix, reinforcement isotropic solid model is employed as a superior material model. Elastic and fracture properties of damage zone are characterized as a function of undamaged matrix properties and micro-crack density. Center notched disk tension (CNDT) specimen is introduced and employed for fracture tests. Comparison of the fracture limit curves with experimental data proves the capability of the new proposed mixed mode fracture criterion for fracture investigation of orthotropic materials.

In selecting a disinfectant for dental prosthesis, compatibility between the disinfectant and the type of denture base material must be considered to avoid adverse effects in the acrylic resin. In this study a total of 75 specimens of heat cure acrylic of dimension (65x10x3) mm were prepared. 15 specimens were immersed in distilled water, used as control and 60 samples were treated. 30 were treated with 4.8% of sodium perborate (Fittydent ®) at 50 0 C for 8 hours and 24 hours. The third group were treated with 2.45% alkaline glutaraldehyde (Cidex®) at 37 0 C for 20 min and 1 hour. All the specimens were subjected to three point flexural load in universal testing machine. The findings were analyzed using one way Analysis of Variance (ANOVA). Acrylic resin selected for this study did not demonstrate any significant difference in flexural strength after immersion. As the flexural strength of the denture base resins remained unaffected, all immersion solutions evaluated in this study could be safely applied in everyday practice for the disinfection of dentures.

General and extended minimum strain energy density criterion for orthotropic materials with unidirectional fibers is employed to anticipate the onset of crack growth. It is postulated that the crack is embedded in the material in an arbitrary orientation with respect to fibers. As crack growth occurs in the isotropic matrix, isotropic stress state is used in the proposed criterion. Crack tip stress state of the isotropic matrix is related to composite one by definition of Reduced Stress (ReSt) coefficients. Since in the case of arbitrary crack-fiber angle, the effect of nonsingular term is significant on crack growth, T-stress term is considered in the calculations. Furthermore, a new concept of critical stress intensity factor is defined and formulated for arbitrary inclination cracks with respect to the fibers. Finally, a test procedure is presented to validate the proposed mixed mode I/II fracture criterion. Test results display excellent consistency with new criterion's fracture limit curve.

This paper presents a mixed-mode I/II fracture criterion to investigate the crack initiation in orthotropic materials in which the crack is directed along fibers. The minimum strain energy density criterion is extended to investigate the cracked orthotropic materials. The reinforced isotropic solid model based on collinear crack propagation along fibers is proposed as an advantageous model to study the fracture behavior of composites. This model introduces fibers as reinforcements of the isotropic matrix in orthotropic materials in which their effects are qualified by defining reinforcement factors at tension and shear modes. The proposed criterion can predict the crack initiation phenomenon. Therefore, in this study a new concept of linear fracture toughness for orthotropic materials is proposed. Experimental data are used to validate the output of the proposed criterion. The coincidence of fracture limit curves and experimental data indicates the ability of the new criterion to predict crack initiation in orthotropic materials. K L IIc Mode I and mode II linear fracture toughness K NL Ic , K NL IIc Mode I and mode II nonlinear fracture toughness K Ic , K IIc Mode I and mode II fracture toughness K I , K II Mode I and mode II stress intensity factors ρ NL , ρ L Nonlinear and linear damage factor w m , w f , w The width of matrix, fiber, RVE l, δl RVE's Length and longitudinal displacement t The thickness of the RVE ε m , ε f , ε Strain of the matrix, fiber, RVE σ m , σ f , σ Normal stress of the matrix, fiber, RVE E m , E f , E x x , E yy Elastic module of matrix, fiber, RVE along fiber, RVE across fiber G m , G f , G xy , G yx Shear module of matrix, fiber, RVE in the x-y plane F m , F f , F or F c The force applied to matrix, fiber, RVE A m , A f , A The area in which the force is applied to matrix, fiber, RVE γ m , γ f , γ The shear angle of the matrix, fiber, RVE τ m , τ f , τ Shear stress of matrix, fiber, RVE m , f , The longitudinal displacements of matrix, fiber and RVE in pure shear loading V m , V f Matrix and fiber fraction in a composite E i j , G i j , ν i j

Fracture density is an important parameter of a fracture network. There are several definitions of fracture density and we are concerned here with the average fracture surface per unit volume. When fractures are not distributed equally among all directions, this parameter can be considered as a function of fracture pole. It can be evaluated from areal and/or linear surveys. This evaluation must account for the geometric bias due to the fact that fractures oblique to the scanline or surface are less easily observed than fractures orthogonal to it. A well-known technique to achieve this is the Terzaghi correction. We propose here an improved correction when survey outcrops and/or boreholes with different orientations are available.

A critical stress at a critical distance crack propagation criterion is a good way to model the fracture in cheese. This physical criterion states that the crack-tip node debonds when the stress at a specified distance ahead of the crack tip on the assumed crack path reaches a critical value. Although this criterion is already used in other research domains, no consistent information exists on how the critical stress and distance should be determined. A repeatable method for the determination of this criterion which combines experimental and numerical single edge notched bending tests was acquired. This criterion was validated with wire cutting experiments of cheese. The experimental and numerical results showed the same trend with a clear wire indentation and steady state cutting phase. The determination of a critical stress and distance criterion as proposed in this research is a good approach to model fracture and cutting of cheese.

This study presents a numerical prediction of the fatigue life of steel panels repaired by a composite patch. The effect of length cracks, the stress ratio R and properties of the patch is presented. The obtained results show that the bonded composite repair significantly reduces the stress intensity factors at the tip of repaired cracks. The results are in a good agreement with those in the literature. The Monte Carlo method is used to predict the distribution function governing crack propagation in fatigue analysis. In computing the failure probability of the structure, we consider the statistical uncertainty associated with key variables, along with the previously discussed model uncertainty. The results obtained highlight the considerable impact of variations in crack length and stress ratio on the distribution function. Notably, uncertainty in these parameters significantly amplifies the probability of structural failure in plates, thereby diminishing overall structural durability.

To understand the mechanisms behind chlorine-induced stress corrosion cracking (CISCC) in 304 stainless steel, synchrotron high energy x-rays were used to perform in-situ x-ray microtomography on a pre-cracked sample under load in a corrosive simulated marine environment. The tomography scans showed the crack morphology evolving into a branching crack around the surface of the sample. Finite element analysis and stress intensity analysis are conducted to explain the observed crack branching.

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Introduction: The accurate assessment of scaphoid bone morphometry is a prerequisite before internal fixation treatment for fractures. We intended to arrive at a method for exact quantification of the scaphoid length by measuring intact adjacent bones and the contralateral scaphoid in the normal population, which can then be translated into use for planning surgical repair in case of fracture or nonunion. Methodology: A prospective, descriptive study was conducted where three-dimensional reconstruction of the wrist with computed tomography scan was done to document lengths of the scaphoid (bilaterally), capitate, radius width, and lateral intra scaphoid angle and dorsal cortical angle of scaphoid were measured. Results: The mean scaphoid length, capitate length, and width of radius were significantly more in males as compared to females. The capitate length and contralateral scaphoid length were most significantly related to scaphoid length. The mean scaphoidcapitate ratio (SCR) was found to be 1.08. Conclusion: Using the liner regression model, scaphoid length can be predicted from variables such as capitate length and SCR with 99.99% accuracy, aiding surgeons in scaphoid fixation in cases of fractured scaphoid, malunion, and nonunion.

Fused silica direct bonding is of particular interest for optical system manufacturing for spatial applications. However, in order to validate the European Space Agency standards, a better understanding of the assemblies mechanical behavior is required. Therefore, it is important to develop some predictive tools to determine numerically mechanical strength of complex assemblies. In this paper, a cohesive zone model is proposed to model the direct bonding interface behavior. In order to determine the mechanical strength of the interface, a propagation test, and an initiation test on a free edge the cleavage test have been performed on direct bonded fused silica samples. The FIT test (Flexible Initiation Test) is also used to identify the properties of the direct bonding joint. At the end, a comparative analyses is proposed between experimental results and finite elements models of the propagation and initiation tests.

The paper proposes and tests an approach to determine the stress intensity factors (SIF) of cracks subjected to mode III using full-field displacements as opposed to the crack opening displacement (COD) method, which uses only two data points. The proposed scheme fits displacement data into Williams' series for cracks, solving the equations using the over-deterministic Least Squares Method (LSM). The method is tested in tubes with through-cracks under axial and cyclic torque loading, and both proportional and non-proportional loading. The Digital Image Correlation (DIC) technique measured the displacement fields, and an approach is presented to address the curvature error in the tube samples. The experimentally determined SIF and SIF ranges with the proposed method are compared with respective values found using COD equations showing a pronounced nonlinear variation. It is concluded that for most, both methods agree, and for the LSM, the number of expansion terms in Williams' series seems to make no difference, exhibiting less noisy results than the COD method and effectively addresses nonlinear variations in SIF calculations across different loading conditions, ultimately enhancing the understanding of crack behavior under mode III loading.

An analytical algorithm for the estimation of the resistance forces exerted on the dipper of a cable shovel and the specific energy consumed in the cutting-loading process is presented. Forces due to payload and to cutting of geomaterials under given initial conditions, cutting trajectory of the bucket, bucket's design, and geomaterial properties are analytically computed. The excavation process has been modeled by means of a kinematical shovel model, as well as of dynamic payload and cutting resistance models. For the calculation of the cutting forces, a logsandwich passive failure mechanism of the geomaterial is considered, as has been found by considering that a slip surface propagates like a mixed mode crack. Subsequently, the Upper-Bound theorem of Limit Analysis Theory is applied for the approximate calculation of the maximum reacting forces exerted on the dipper of the cable shovel. This algorithm has been implemented into an Excel™ spreadsheet to facilitate user-friendly, "transparent" calculations and built-in data analysis techniques. Its use is demonstrated with a realistic application of a medium-sized shovel. It was found, among others, that the specific energy of cutting exhibits a size effect, such that it decreases as the (-1)-power of the cutting depth for the considered example application.

When reinforcing existing cracked asphalt pavements, the design and evaluation of the durability of the reinforced structure are quite different from those of a new pavement generally based on fatigue criteria deduced from stress and strain fields computed for the undamaged pavement. For the design of reinforcement solutions, the presence of cracks and their propagation must be considered explicitly. To move in this direction, the present article aims at improving the understanding of bottom-up crack propagation in asphalt pavements. Some investigations relying on the interpretation of an accelerated full-scale fatigue test are presented as well as the numerical analysis of this test through the theory of linear elastic fracture mechanics and the Paris law. The tested pavement section is composed of four layers. The two uppermost layers are made of asphalt concrete (AC) materials whose modulus and fatigue performances are different. The pavement is subjected to repeated loads applied by the Fatigue du Béton Armé Continu (FABAC) traffic simulator of the French Institute of Science and Technology for Transport, Development and Networks (IFSTTAR), and the development of cracking in the AC layers is monitored using embedded instrumentation and Falling Weight Deflectometer (FWD) test campaigns. To better control the crack pattern that develops during the fatigue test, an artificial flaw (metal angle) is purposely placed at the bottom of the AC layers (in the transverse direction to the moving loads) to localize the initiation of cracking. A bottom-up crack is supposed to grow vertically from this defect in the AC layers. This is effectively detected and followed by the experimental measurements, which are combined to model for the analysis of the test. Finally, the kinetics of crack growth deduced from the Accelerated Pavement Test (APT) results and those computed using the Paris law calibrated from fatigue tests performed in the laboratory are compared. Manuscript

The Dirichlet eta function, often referred to as the "alternating zeta function," is a crucial intersection of analytic number theory, fractal geometry, and modern physics. While it shares deep connections with the Riemann zeta function, its alternating series structure and unique analytic properties uncover hidden symmetries in prime distributions, recursive dynamics, and spacetime perturbations. This research investigates the interconnectedness of number theory, fractal geometry, and gravitational wave physics through the lens of the Dirichlet eta function. We introduce a novel prime product representation, highlighting the role of the even prime (2) as a path selector that governs scale-invariant dynamics across diverse scales.

Key Findings and Contributions:

Parity-Asymmetric Prime Distribution: We demonstrate a modulation that incorporates prime correlatives into exclusive corrections within the Dirichlet eta function's product formula, revealing an inherent asymmetry in prime distribution.

Fractal Clustering of Zeros: We observe fractal clustering in the zeros of the eta function, with spacing characterized by Fibonacci numbers (Tn+2 = Tn+1 + Tn, T1 = T2 = 1), indicating a structure mediated by metallic means, including the silver and plastic numbers.

Gravitational Wave Echo Spectra: We present new predictions for gravitational wave echo spectra from exotic compact objects (ECOs), derived from the eta function's structural properties. Employing Pöschl-Teller potential analogs, we show that scale intervals correspond to length-dependent signals, proportional to log(2)^n.

Metallic Mean Field Theory (MMFT) Extension: We extend the MMFT framework to explore phase transitions in ECOs, establishing a link between prime distribution and the structural properties of primes.

Dyadic Zeta Functions (DZF) Expansion: We expand the scope of the DZF through prime gap thermodynamics and AdS/CFT holography, providing new perspectives on the structure of primes and the universe.

Quantification of Chebyshev bias through log-periodic single-frequency oscillations. This work establishes the Dirichlet eta function as a fundamental geometric relation, connecting quantum arithmetic, fractal cosmology, and relativistic gravity.

The fracture surface is important evidence of the behavior of cement-based materials. Deflection, microcracking, and bridging are mechanisms that occur at the crack tip and absorb energy during the fracture process. Two optical microscopy techniques are used in this study to characterize surface geometry. The confocal laser microscope and a video density technique that uses video microscopy provide elevation data for the mesoscale of mortar and concrete. Recently, surface maps have been used to establish a link between surface roughness and fracture. In this paper, the tortuosity of the fracture surface is used in a micromechanical model to predict the increase in toughness due to aggregate. This analysis is performed for two sets of mortar specimens to investigate the influence of the aggregate size and gradation. The influence of crack deflection and aggregate fracture is compared to tested fracture parameters.

Welded structures place increasing demands on the level of increased resistance to fracture. A large number of fractures of welded structures, which occur during exploitation at a stress level below of the allowable, indicates the danger of brittle fracture. The assessment of brittle fracture susceptibility was analyzed by testing Sharpy specimens, and the total impact energy, components of total impact energy (crack energy initiation and crack energy propagation) were used as parameters in the analysis. Zavarene konstrukcije postavljaju sve veće zahtjeve u pogledu nivoa povećane otpornosti prema lomu. Veliki broj lomova zavarenih konstrukcija, do kojih dolazi u toku eksploatacije pri nivou napona nižem od dozvoljenog, ukazuje na opasnost od pojave krtog loma. Ocjena sklonosti ka krtom lomu je analizirana ispitivanjem Sharpy epruveta, a kao parametri u analizi su korišteni ukupna energija udara, komponente ukupne energije udara (energija stvaranja i energija širenja prsline).

This paper intends to evaluate the influence of the intrinsic properties of the materials, namely plastic and cyclic plastic properties, on the overloading/underloading effect on crack propagation rate, at baseline negative stress ratios, under plane strain conditions. The importance of the negative loading part of the fatigue cycle on crack propagation rate has been shown by previous works of this same author. In those works has also been shown that under baseline negative stress ratios there exists negative open loads and crack propagation rate does not correlate properly with the crack closure concept. These features were shown to be strongly related to plastic properties and cyclic plastic properties of the materials. It has been concluded that the Bauschinger effect may be the explanation for the different sensitivity to negative loads. Thus, some materials may be very sensitive to negative loads and some others may not be so sensitive. Tensile overload and compression underload tests, at positive and negative baseline stress ratios were made in different materials, with different plastic properties, in order to predict their influence on crack propagation rate. The main emphasis in this paper is the importance of the compressive part of the loading cycle under negative baseline R ratios on overloads/underloads effect on crack propagation rate. Results will show that the effect of overloads and underloads on crack propagation rate, at baseline negative stress ratios, are not fully accounted for by crack propagation models and that the generalized accepted behaviour of OL/UL may not be the same at baseline negative stress ratios. It will be shown that Overloads may produce acceleration instead of the accepted retardation effect. A physical understanding on the effects of OL/UL is also provided in the paper.

With the aim of characterizing the different stress patterns in several egg types and evaluate the resistivity of the eggshell while impacting in free fall, experimental tests and computational simulations have been performed on eggs of the species Gallus gallus (domestic hen), Struthio camelus (ostrich), and Testudo sp. (tortoise). The different types of failure were determined for each taxa and stress distribution maps were recorded and correlated between experimental results and computational simulations using Finite Element Analysis (FEA). For domestic hens, the numerical results obtained in both tests have highly correlation with the results obtained in previous works; for ostrich (Struthio camelus) and tortoise (Testudo sp.) eggshells, the new data represent a very good tool to understand in further works the failure mechanisms of the eggshells. More interestingly, the present study provides the first empirical and mathematic results that allow establishing confident safety interval related to the laying process in the poultry industry.

The Wöhler curve approach to fatigue life assessment is here extended to include variable amplitude loads with mean value influence. This is done through the definition of an equivalent load amplitude, which depends both on the usual damage accumulation hypothesis and on some mean value correction model. The method is exemplified by using the Gerber model, the mean stress sensibility model and different parametrisations of the crack closure model. All models are applied to three different data sets, including aluminium, welded steel, and cast steel specimens subjected to different spectrum loads. The results are interpreted in relation to the complexity of the different models and the trade off between complexity, number of tests and random scatter is discussed in the context of prediction uncertainty.

day by day. This experience has shown me that through God, all things are possible. Next, I would like to thank the National Textile Center for providing the funds to do this research. I would also like to thank my advisor, Dr. Mary Lynn Realff for giving guidance and providing me with the opportunity to work on this project. I also appreciate the long and arduous work of Dr. Stephen Michielsen, who believed that this research could be accomplished, despite what was unsuccessful in the past. In addition, I would like to thank my co-chair, Dr. Richard Neu for helping me with technical related questions, even when he was busy, and for convincing me that this fracture mechanics research would work. I would also like to thank Dr. Jianmin Qu for agreeing to serve on my committee and providing technical expertise as well. In addition, I would also like to thank the love of my life, my wife Melody Averett, for supporting me throughout this arduous journey. More hard work and late nights are still to follow. But we will get through this! I would also like to thank my mom and dad, Jesse and Corene Averett for supporting me through all of my educational endeavors. You all have given me so much throughout my life, and I am sincerely grateful for that. Also, I want to thank Steve, Cheryl (Lynn), and Anthony (Tony) for being there when I needed them most. You guys have helped me a lot through the years. v

Fracture Mechanics of High Performance Nylon Fibers A Thesis Presented to The Academic Faculty By Rodney Dewayne Averett In Partial Fulfillment Of the Requirements for the Degree Master of Science in Mechanical Engineering Georgia Institute of Technology May 1, 2004 ...

A new apparatus and method is proposed for the investigation of material behavior under high-strain-rate tensile loads. We refer this apparatus as a Split Flying Bar. The method is based on using the inertia of a working mass attached to a specimen. The specimen is placed between the working mass (front part of the bar) and backing part of the bar, which is captured in flight by special brake. When the back part of the flying split bar is stopped, the working mass continues the flight by inertia, creating specimen tension with strain rate depending on the length of specimen and velocity of flying bar. Properly choosing the working mass and the speed of the flying bar, one can tune maximal stress and strain rate over a wide range. The method is highly scalable and can be used for investigation of specimens from single filament up to reasonable macroscopic size. Contrary to tensile SHPB, the method provides a way to investigate materials with practically arbitrary strain to failure. For example, polyuria, whose strain to failure reaches hundreds of percent. Also, the method can be used for high-strain rate pull-out tests or to measure the quality of adhesion layers under high-stress rates, e.t.c. In this paper I introduce the basics of the method and interpretation of the data.

Variational approach to damage and fracture me-19 chanics; Variational formulation of damage and 20 fracture mechanics 21 Definitions 22 Damage is defined as the loss of material stiffness 23 under loading conditions. This process is in-24 trinsically irreversible and, therefore, dissipative. When the stiffness vanishes, fracture is achieved. In order to derive governing equations, variational methods have been employed. Standard variational methods for non-dissipative systems are here formulated in order to contemplate dissipative systems as the ones considered in continuum damage mechanics.

A series of high-martensite dual-phase (HMDP) steels exhibiting a 0.3 to 0.8 volume fraction of martensite (V m ), produced by intermediate quenching (IQ) of a vanadium and boron-containing microalloyed steel, have been studied for toughness and fatigue behavior to supplement the contents of a recent report by the present authors on the unusual tensile behavior of these steels. The studies included assessment of the quasi-static and dynamic fracture toughness and fatigue-crack growth (FCG) behavior of the developed steels. The experimental results show that the quasi-static fracturetoughness (K ICV ) increases with increasing V m in the range between V m ϭ 0.3 and 0.6 and then decreases, whereas the dynamic fracture-toughness parameters (K ID , K D , and J ID ) exhibit a significant increase in their magnitudes for steels containing 0.45 to 0.60 V m before achieving a saturation plateau. Both the quasi-static and dynamic fracture-toughness values exhibit the best range of toughnesses for specimens containing approximately equal amounts of precipitate-free ferrite and martensite in a refined microstructural state. The magnitudes of the fatigue threshold in HMDP steels, for V m between 0.55 and 0.60, appear to be superior to those of structural steels of a similar strength level. The Parislaw exponents (m) for the developed HMDP steels increase with increasing V m , with an attendant decrease in the pre-exponential factor (C ). ASIM BAG, Senior Materials Engineer, is with the Materials and Corrosion DP steels. McEvily and co-workers [24, have categorized

This work presents an exploratory experimental investigation of the ductile tearing properties for the girth weld of a typical CMn pipe internally clad with a nickel-chromium corrosion resistant alloy (CRA) using crack growth resistance curves (J − ∆a curves). Here, the material of the external pipe is an API 5L Grade X65 pipeline steel whereas the inner clad layer is made of ASTM UNS N06625 Alloy 625. Unloading compliance (UC) testing of the pipeline girth welds employed side-grooved, clamped SE(T) specimens with a weld centerline notch to determine the crack growth resistance curves. This exploratory experimental characterization provides additional toughness data which serve to evaluate the effectiveness of current procedures in determining experimentally measured R-curves for this class of material.

The aim of this contribution is the investigation of the influence of coating formulation on physical – mechanical properties; especially on the hardness of finished surfaces, the adhesion of the lacquers films to wooden substrates, the resistance of finished surfaces to impact, the resistance of finished surfaces to mechanical damage the impact tests. Tensile tests on free coating films of the same lacquers have also been measured. In this study we investigated transparent nitrocellulose, polyurethane and UV curing high solid acrylic lacquers. The results reached in this study have confirmed the relationship between elastic modulus and the stress at break of free lacquer films and the physical-mechanical properties of finished surfaces.

Prediction of hydrogen embrittlement requires a robust modelling approach and this will foster the safe adoption of hydrogen as a clean energy vector. A generalised computational model for hydrogen embrittlement is here presented, based on a phase field description of fracture. In combination with Part I of this work, which describes the process of hydrogen uptake and transport, this allows simulating a wide range of hydrogen transport and embrittlement phenomena. The material toughness is defined as a function of the hydrogen content and both elastic and elastic-plastic material behaviour are incorporated, enabling to capture both ductile and brittle fractures, and the transition from one to the other. The accumulation of hydrogen near a crack tip and subsequent embrittlement is numerically evaluated in a single-edge cracked plate, a boundary layer model and a 3D vessel case study, demonstrating the potential of the framework. Emphasis is placed on the numerical implementation, which is carried out in the finite element package COMSOL Multiphysics, and the models are made freely available.

Hydrogen threatens the structural integrity of metals and thus predicting hydrogen-material interactions is key to unlocking the role of hydrogen in the energy transition. Quantifying the interplay between material deformation and hydrogen diffusion ahead of cracks and other stress concentrators is key to the prediction and prevention of hydrogen-assisted failures. In this work, a generalised theoretical and computational framework is presented that for the first time encompasses: (i) stress-assisted diffusion, (ii) hydrogen trapping due to multiple trap types, rigorously accounting for the rate of creation of dislocation trap sites, (iii) hydrogen transport through dislocations, (iv) equilibrium (Oriani) and non-equilibrium (McNabb-Foster) trapping kinetics, (v) hydrogen-induced softening, and (vi) hydrogen uptake, considering the role of hydrostatic stresses and local electrochemistry. Particular emphasis is placed on the numerical implementation in COMSOL Multiphysics, releasing the relevant models and discussing stability, discretisation and solver details. Each of the elements of the framework is independently benchmarked against results from the literature and implications for the prediction of hydrogenassisted fractures are discussed. The second part of this work (Part II) shows how these crack tip predictions can be combined with crack growth simulations.

• A numerical model is developed for the simulation of fault and fracture mechanics. • The model is implemented in the framework of the Finite Element method and with the aid of Lagrange multipliers. • The proposed formulation introduces a new contribution due to the frictional work on the portion of activated fault. • The resulting algorithm is highly non-linear as the portion of activated fault is itself unknown. • The numerical solution is validated against analytical results and proves to be stable and accurate with quadratic convergence of the Newton-like scheme. • The model is experimented with in a realistic application simulating the generation of ground fissures due to aquifer over-exploitation in arid regions.

a.Air Force Wright Aeronautical Laboratories Air Force Systems Command _ Materials Laboratory m ^_^_^__^___^^^" 6c. ADDRESS (City, Slate and ZIP Code) P.O. Box 2691 West Palm Beach, FL 33402 7b. ADDRESS (City, State and ZIP Code) AFWAL/MLLN Wright-Patterson AFB, Ohio 45433 8a. NAME OF FUNDING/SPONSORING ORGANIZATION 8b. OFFICE SYMBOL (If applicable) 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER F33615-80-C-5160 8c. ADDRESS (City. State and ZIP Code) 10. SOURCE OF FUNDING NOS.

The rate-dependent failure response of multi-material adhesive joints for three deformation modes is investigated. A combination of carbon fibre reinforced polymers (CFRP) and titanium alloy Ti-6Al-4V is employed. The experiments provide important information about the failure sequence of a multi-material adhesive joints, which depends upon the loading rate regime. This is the first time that dynamic fracture mechanics experiments are performed in multi-material adhesive structures. The observed experimental results suggest a rate-dependent failure sequence for mode I dominated fracture. Simulations of the experiments are used to predict and rationalise the failure performance of the multi-material adhesive joint. The numerical analysis highlighted the importance of the individual knowledge of the rate-dependent mechanical performance of adhesive and composite to fully understand the fracture sequence of multi-material joints under impact.

The phenomenon of mechanoluminescence (ML) refers to the emission of light induced by mechanical stimulation applied to mechano-optical materials for example SrAl 2 O 3 :Eu,Dy (SAO). Numerous technologies on the basis of ML have been presented to visualize the stress or strain in various structures for the applications including structural health monitoring. As a result, extensive attention has been devoted to the design, synthesis, characteristics, optimizations, and applications of ML materials. However, challenges still remain in the standardization of ML measurement and evaluation, thereby commercially viable ML applications are currently unavailable. To overcome these difficulties, present study proposes ML measurement and evaluation techniques employing the ML fracture mechanics, finite element method, and dual deep learnings. For the effective normalization of visualized ML images under fixed initial ML intensity condition, continuous UV irradiation above the critical ML power density has been subjected to tensile and compact tension (CT) specimens. Therefore, Plastic Stress Intensity Factor (SIF) as well as crack tip stress field have been extracted successfully from normalized ML images based on ML fracture mechanics. To complement and verify the ML analysis, numerical FEM simulation and analytical ASTM calculation have been also provided. Finally, a double deep learning consists of Generative Adversarial Networks (GAN) and Convolutional Neural Networks (CNN) has been trained and tested for the standard evaluation of in-situ ML images.

The propagation of a macro-scale crack was visualized in yittria-tettragonal zirconia polycrystal (Y-TZP) ceramics using a mechano-luminescence (ML) of SrAl2O4:Eu,Dy. The transformation zone around the crack was also clearly detected in both the crack front and side areas of the Y-TZP in a realistic time frame. The ML made it possible to precisely detect a relatively fast crack propagating in the speed range from 20 m/s to 140 m/s, thereby realizing so-called quasi-dynamic R-curve. Effective toughening then commenced and the applied stress intensity factor increased to 20 MPa . The ho values obtained from the ML observation deviated slightly from those predicted by the Evans-McMeeking model, and support Marshall's simple power law model of quasi-static crack propagation.

Shortly before the 2021 Fagradalsfjall eruption tomographic images indicated a large high V p /V s anomaly with a top at about 9 km depth directly below the ongoing seismic swarm. Using volcanotectonic principles we interpret this anomaly as part of the roof of a magma reservoir which, furthermore, ruptured on 24 February 2021. The roof rupture resulted in an injected dike-segment propagating vertically at an average rate of about 0.2 m s-1 until it became arrested beneath a stress barrier at ~2 km depth, from where the dike-segment propagated laterally. Further magma injections took place, following largely the path of the first dike-segment, resulting in part of the dike reaching outside the stress barrier and propagating vertically as a tiny 'finger' to form a 180-m-long disconnected fissure at the surface on 19 March 2021. The estimated maximum length of the arrested dike is about 9 km, its height 7 km, and its thickness 4 min excellent agreement with direct field measurements of basaltic dikes in Iceland. Seismicity also indicates that the same dike path was partly used during the 2022 and 2023 eruptions, in agreement with the location of the resulting volcanic fissures, resulting in the formation of a multiple feeder-dike.

This work is concerned with the calculation of fracture energy release rates in Peridynamics. The existing crack growth criterion and the related damage model in Peridynamics, e.g. the critical bond stretch in the prototype micro-elastic brittle (PMB) material model, are based on the energy release rate of an idealized infinite crack model. Therefore, applications of such damage model in Peridynamics to arbitrary fracture patterns, e.g. cracks with finite increment, kinked cracks, and penny-shaped cracks etc., are problematic, because that the idealized crack model assumes an infinitely large crack surface, and the crack growth direction is always assumed being along the direction of the old crack surface. In all engineering applications, we only encounter cracks of finite size. In this work, based on the celebrated Griffith theory that interprets the energy release rate as the surface energy density, we have systematically investigated the fracture energy release rate in Peridynamics for a number of finite crack models: two-dimensional (2D) plane strain finite size horizontal crack, 2D edge crack in a plate, 2D kinked crack, and three-dimensional (3D) penny-shaped crack. The highlights of this work are a set of elegant mathematical solutions: (1) We have proved that for 2D horizontal finite cracks, the energy release rate is exactly the same as that of 2D infinite large crack, i.e. Silling's original result; (2) We have derived the exact expressions of the energy release rates as well as the related critical bond stretch formulas for 2D finite edge cracks and kinked cracks, and (3) We have found an asymptotic solution of the energy release rate for 3D penny-shaped cracks of finite size in Peridynamics, showing that Silling's energy release formula for 3D crack model is only the zero-th order approximation of the exact solution. In addition, we have presented some numerical solutions of finite increment crack growths in Peridynamics, and discussed their implications, ramifications, and applications in nonlocal continuum fracture mechanics.

How effective was prehistoric bison hunting with ancient weaponry? Experimental archaeology offers some insights. Non-technical description of our experiments with atlatls (spearthrowers) and stone points on bison carcasses, penetration and point damage results, technology of early weaponry.

We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity between the SFEM and the virtual element method (VEM). Based on the VEM, we propose a new stabilization approach to the SFEM when applied to arbitrary polygons and polyhedrons. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity. Later, the SFEM is combined with the scaled boundary finite element method to problems involving singularity within the framework of the linear elastic fracture mechanics in 2D.