Fracture Mechanics Studies Research Articles

Verification Study of Probabilistic Fracture Mechanics Analysis Code for Reactor Pressure Vessel During Pressurized Thermal Shock

This investigation is to present a verification study of probabilistic fracture mechanics (PFM) analysis code for a reactor pressure vessel (RPV) during pressurized thermal shock (PTS). The probabilistic fracture mechanics code FAVOR, developed by Oak Ridge National Laboratory, is used to calculate the conditional probabilities of crack initiation and penetration for welds that are located in the RPV beltline region. The procedure includes deterministic analyses of the temperature and stress distributions through the vessel wall at the PTS, and probabilistic analyses on the vessel failure probability as a result of PTS transients. The RPV geometries, material properties, and properties related to embrittlement are those in taken from previous studies. Two previously suggested hypothetical transients, which may seriously affect RPV integrity, are also taken into account. To verify the results of PFM round robin analysis of RPV during PTS events, several models and Monte Carlo methods for determining PFM performance are used and they agree on the accuracy of the failure assessment is obtained. The present work can be regarded as various important factors about performing PFM that affect in evaluating the structural safety and operational stability of RPVs. The comparisons of the paper also support the finding that the FAVOR code is very practically useful in assessing failure probability.

Contributions to the Study of Fracture Mechanics of Synthetic Fiber-Reinforced Soils Based on Flexural Tests and Imaging Techniques

Contributions to the Study of Fracture Mechanics of Synthetic Fiber-Reinforced Soils Based on Flexural Tests and Imaging Techniques

A Review Paper: Experimental Study of Fracture Mechanism and Crack Initiation Stresses in Rock to Analysed Rock Mass Failure

A Review Paper: Experimental Study of Fracture Mechanism and Crack Initiation Stresses in Rock to Analysed Rock Mass Failure

Crack Formation in the Tungsten Armour of Divertor Targets Under High Heat Flux Loads: A Computational Fracture Mechanics Study

Crack Formation in the Tungsten Armour of Divertor Targets Under High Heat Flux Loads: A Computational Fracture Mechanics Study

Numerical simulation study of fracture mechanics of the atherosclerotic plaque

Atherosclerotic plaque rupture is the main cause of many cardiovascular diseases, and biomechanical factors play an important role in the process of plaque rupture. In the study of plaque biomechanics, there are relatively few studies based on fatigue fracture failure theory, and most of them mainly focus on the whole fatigue propagation process from crack initiation to plaque rupture, while there are few studies on the influence of crack on plaque rupture at a certain time in the process of fatigue propagation. In this paper, a two-dimensional plaque model with crack was established. Based on the theory of fracture mechanics and combined with the finite element numerical simulation method, the stress intensity factor (SIF) and related influencing factors at the crack tip in the plaque were studied. The SIF was used to measure the influence of crack on plaque rupture. The results show that the existence of crack can lead to local stress concentration, which increases the risk of plaque rupture. The SIF at the crack tip in the plaque was positively correlated with blood pressure, but negatively correlated with fibrous cap thickness and lipid pool stiffness. The effect of the thickness and angle of lipid pool on the SIF at the crack tip in the plaque was less than 4%, which could be ignored. This study provides a theoretical basis for the risk assessment of plaque rupture with cracks.

Expected life-time of an optical silica fiber intended for open space applications: Probabilistic predictive model

The recently suggested probabilistic design-for-reliability (PDfR) concept in microelectronics and photonics reliability engineering enables quantifying the static fatigue (delayed fracture) lifetime and the corresponding (in effect, never-zero) probability of failure of optical silica fibers intended for open space (outside the spacecraft) applications. In the author's opinion, an adequate operational reliability of space photonics cannot be assured, if it is not quantified, and, because of numerous inevitable intervening uncertainties, such a quantification should be done on the probabilistic basis. Multi-parametric Boltzmann–Arrhenius–Zhurkov (BAZ) constitutive equation is used to design and interpret the results of a highly-cost-effective and highly focused failure-oriented accelerated testing (FOAT). Such testing is both the experimental basis of the PDfR and a physically meaningful proof-test for optical fibers. The combined action of a moderately low temperature, tensile loading, ionizing radiation and random vibrations is considered. Although random vibrations might not be an actual stressor in the application in question, it is nonetheless included in the analysis as a critical stimulus: fracture mechanics studies indicate that fatigue and brittle cracks propagate particularly rapidly, when the material under test is subjected to a low-temperature/vibration bias. The general concept is illustrated by a detailed numerical example. It should be pointed out, however, that the calculated data, although confirm the viability of the suggested methodology, use hypothetical input information and should be viewed just as a suitable illustration, not more. The developed approach is rather broad, and could be applied to any type of optical fibers, including laser fibers, and, perhaps, with some modifications, also to other types of optical, opto-electronic and even non-optical materials and vulnerable structural elements (such as, e.g., solder joint interconnections) intended for highly demanding space applications. The approach could be applied also, as has been indicated by one of the reviewers, in other astrophysics related conditions and locations, where optical fiber instrumentation is intended to be employed in low temperature conditions, such as, e.g., those that take place at the bottom of the Shackleton impact crater at the lunar south pole. The important restriction of our model has to do with the fact that the BAZ equation, which is based on classical thermodynamics, assumes that no failure could possibly occur at absolute zero. Because of that, the suggested model should be used at temperatures, sufficiently remote from the absolute zero. Future work should focus, first of all, on the experimental verification of the suggested approach and model.

Failure characteristics and meso-deterioration mechanism of pre-stressed coal subjected to different dynamic loads

The study of dynamic fracture mechanism of pre-stressed coal is of great importance to the coal bursts prevention and the coal pillar reinforcement subjected to the dynamic disturbance. In this paper, the effect of pre-static load and dynamic load on the initiation fracture evolution and destruction states of coal were studied using experimental and theoretical approaches. The results show that the coal usually splits into several blocks along the dominant fractures when subjected to the static load. The increase of pre-static load can make the post-peak dynamic stress–strain curve of the specimen gradually transform from type II to type I. The dynamic load plays the same role as that of pre-static load in terms of the effect on the dynamic stress–strain curve, but different in dynamic failure state of the coal. The enhancement of the former will make the dominant fracture expansion and leading the dynamic failure of coal gradually transform from the surface peeling to failure into several large pieces along the dominant fractures, while the increase of the latter will provid increasing kinetic energy to activate the internal fracture expansion of the specimen, and causing the failure state of the specimen transform from the surface peeling to the complete destruction into pieces. For the specimen with the surface peeling failure form, the peeling degree of the specimen depend on both the length of the fracture and the distance of the fracture to the free surface. Based on these results, the dynamic instability mechanism and protection focus of coal pillars under coupled static and dynamic loads were further discussed.

A framework for phase-field modeling of interfacial debonding and frictional slipping in heterogeneous composites

Modeling and simulating interfacial shear load transfer in fiber-reinforced composites is crucial for characterizing fiber pullout behaviors. Addressing this complicated topic, this work presents a novel phase-field framework to simulate interfacial failure behaviors in fiber-reinforced cementitious composites. Specifically, a comprehensive constitutive model is proposed to describe both interfacial debonding and frictional slipping, which accounts for snubbing and bonding effects in fiber-reinforced composites. The developed model has the following novel features: (1) The model can simultaneously characterize interfacial debonding and frictional slipping, and thus thoroughly describe the fiber-reinforcing mechanisms in quasi-brittle solids; (2) An interfacial slipping degradation theory is implemented in the model to describe interfacial slippage and stress degradation during slipping; and (3) The model effectively and precisely incorporates the friction law with interface normal vectors. The developed model is successfully validated against experimental and simulated results. Finally, a series of parameter studies are undertaken to provide strategic insights to improve the mechanical properties of the composites. The proposed method adds efficiency and robustness to the study of features and fracture mechanisms of fiber reinforcements in complex fiber–cement systems.

Confined Crack Propagation in MoS2 Monolayers by Creating Atomic Vacancies.

In two-dimensional crystals, fractures propagate easily, thus restricting their mechanical reliability. This work demonstrates that controlled defect creation constitutes an effective approach to avoid catastrophic failure in MoS2 monolayers. A systematic study of fracture mechanics in MoS2 monolayers as a function of the density of atomic vacancies, created by ion irradiation, is reported. Pristine and irradiated materials were studied by atomic force microscopy, high-resolution scanning transmission electron microscopy, and Raman spectroscopy. By inducing ruptures through nanoindentations, we determine the strength and length of the propagated cracks within MoS2 atom-thick membranes as a function of the density and type of the atomic vacancies. We find that a 0.15% atomic vacancy induces a decrease of 40% in strength with respect to that of pristine samples. In contrast, while tear holes in pristine 2D membranes span several microns, they are restricted to a few nanometers in the presence of atomic and nanometer-sized vacancies, thus increasing the material's fracture toughness.

Fracture Properties and Process Zone Length of High Strength Concrete Using Size Effect Method.(Dept.C)

This paper gives a report on a fracture mechanics study of legal strength concrete with compressive strength up 80 MPa.. 6 mixes were selected, designed to achieve a slump above 100 mm and strength up to 80 MPa.. The investigation used tiered levels of silica fume(0, 10%, 20% by weight of cement) and two coarse aggregate proportions of local aggregate (0.48, 0.65 by volume) In each case, compressive strength, splitting tensile strength, flexural strength fracture energy Gr and Fracture process zone Cr were determined. A test method for determining fracture energy Gr and process zone length Cr, defined by the size effect wide is generalized theory, has been proposed. It allows the use of specimenc of the different size and shape but with same notch length. This paper proposes test und data analysis procedures. The results obtained by the Size effect law (SEL) apparently follow the trend of fracture energy increasing as the compressive strength of the concrete increases. On the other hand, process zone length or decrease considerably with increase in strength. The Bazant's size effect taw gives a very good account of the size dependency of flexural strength for both normal and high strength concrete. As observed in the size effect curve, the fracture behavior of the HSC seems to be more brittle than that of the normal strength concrete. Linear classic fracture mechanics (LEFM) is applicable to HSC in the normal size range than nonlinear fracture mechanics.

Discrete configurational mechanics for the computational study of atomistic fracture mechanics

We formulate discrete configurational mechanics in an atomistic setting, discuss the corresponding computational details, and demonstrate its utility via computational analyses of atomistic fracture mechanics problems. To this end, we first propose a novel Configurational-Force-Criterion (CFC) to predict crack propagation into an atomic crystalline lattice. Thereby, specifically, the CFC relies on comparing discrete configurational forces with a corresponding Crack-Propagation-Threshold (CPT) in the quasi-static approximation of atomistic systems at zero Kelvin. Next, based on the CFC, we introduce a quasi-static computational atomistic crack propagation algorithm. Therein, whenever an atomic pair meets the CFC, we modify the lattice connectivity by deleting the corresponding interatomic bond, thus resulting in true irreversibility, i.e. dissipation upon crack extension. Finally, based on different choices for the magnitude of the CPT employed in the CFC, we demonstrate suitability and versatility of discrete configurational mechanics in analyzing atomistic fracture mechanics.

Multiple Pseudo-Plastic Appearance of the Dynamic Fracture in Quasi-Brittle Materials.

Understanding and simulating the dynamic response of quasi-brittle materials still remains as one of the most challenging issues in structural engineering. This paper presents the damage propagation material model (DAMP) developed in order to obtain reliable results for use in structural engineering practice. A brief overview focuses on the differences between fracture mechanics studies, and engineering material modelling is presented to highlight possible guideline improvements. An experimental dynamic test performed on ultra-high-performance concrete specimens was used to obtain evidence of the physical behaviour of brittle materials with respect to specimen size variations and, consequently, to verify the reliability of the material equations proposed. Two widely used material models (RHT and M72R3), as representatives of the classical brittle material models for structural purposes, and the proposed material model are compared. Here, we show how: (i) the multiple structural strength of brittle materials arises from the damage propagation process, (ii) there is no contradiction between fracture mechanics and the engineering approach once the velocity of damage propagation is chosen as fundamental material property and (iii) classical dynamic material models are intrinsically not objective with related loss of predictive capability. Finally, the original material model equation and the experimental strategy, dedicated to its extended verification, will be shown in order to increase the design predictiveness in the dynamic range considering structure and specimen size variations. The dynamic stress increasing factor (DIF), experimentally observed and widely recognised in literature as a fundamental concept for quasi-brittle material modelling, has been reviewed and decomposed in its geometrical and material dependencies. The new material model defines its DIF starting from the physical quantities of the damage propagation velocity applied to the test case boundary conditions. The resultant material model predictiveness results improved greatly, demonstrating its ability to model several dynamic events considering size and dynamic load variations with a unique material property set without showing contradictions between numerical and experimental approaches.

Investigating inhomogeneity effects on the crack driving force in two-phase electrode particles using a planar composite core-shell model

It is well known that phase separation occurs in many intercalation materials as a result of solute intercalation. In lithium storage materials, phase separation induced by electrochemical cycling is known to intensify mechanical stresses in the host, and results in the emergence of a variety of defects causing mechanical degradation of the electrode particles. Treating two-phase electrode particles as a homogeneous material, fracture mechanics models have been previously developed for studying fracture of two-phase electrode particles. Recent theoretical and experimental studies, however, reveal that the elastic properties of the coexisting phases in the material could significantly differ due to their markedly different solute contents. This work aims to present a fracture mechanics study of the two-phase electrode particles accounting for the different elastic moduli of the phases. To this end, a planar composite core-shell model is utilized to examine how different elastic moduli of the phases could impact the stress intensity factors and the energy release rates associated with the pre-existing cracks in the particle. Our results reveal that although softening of the material as a result of phase change could result in stress relief in the electrode particle, however, it could still raise the energy release rate for pre-existing cracks, since a softened material behaves like a weakened deformational constraint ahead of a pre-existing crack. The model presented is also applied to the material systems exhibiting modulus change as a result of phase separation, and implications of the modulus change on the energy release rate for crack growth are also discussed. It is shown that although significant changes in the toughness of the material could arise due to the phase transformation, however, changes in elastic moduli could still raise the energy release rate for a crack whose tip is embedded in the phase with the lower toughness.

Computational Fracture Mechanics: Evaluation of The Structural Integrity in a Penstock Applying the BS7910 Standard and Finite Element Analysis

The present work aims to determine the structural integrity of penstocks, applying the BS7910 standard and finite element analysis (FEA). For the study of fracture mechanics in thin-walled cylinders that have defects inside, the structural integrity of the element is determined through a failure assessment diagram (FAD) where the fracture failure index (Kr) is graphed versus plastic collapse index (Lr). Based on the locus of the initial point of failure, the safety factor is calculated, and it is defined if the element is fit for service or if corrective action must be taken to continue operating; later, crack growth is analyzed, where the critical point of rupture of the penstock and therefore its useful life is determined. To contrast results, a simulation of fracture mechanics is performed in ANSYS, where the stress intensity factor (KI) is determined using the fracture tool, and the useful life of the element is also calculated through a fatigue analysis. The use of tetrahedral elements is recommended for the overall meshing and a cobweb configuration for meshing at crack-tip. Finally, the results obtained are compared, where the mean average percentage error of 3.24% was obtained, denoting the usefulness of the two methods as well as the simplicity of the Paris’ law.

Study of Fracture Mechanics on Fibre Reinforced Concrete.

Study of Fracture Mechanics on Fibre Reinforced Concrete.

Fracture characterization of overmold composite adhesion

A general testing approach is presented via a fracture mechanics study on the interfacial delamination behavior in overmolded composite materials using a variant of the double cantilever beam (DCB) geometry. Overmolding, a common injection molding process, is used to fabricate asymmetric DCB test specimens with Lexan™ 3414 resin overmolded onto commercially available TenCate Cetex® FST woven glass fiber/polycarbonate laminates. An analytical beam theory model is employed to partition the planar fracture modes at the overmold interface into mode I and mode II components, which are functions of material properties and relative beam thicknesses. Specimen curvature measurements are integrated into the beam theory model to estimate the residual stress effects on fracture mode mixity. We use the overmold thickness as a tunable variable to control fracture mode mixity, and target near mode I fracture conditions, where we find mode I fracture energy ( GIc) values of approximately 1 kJ/m2. Fiber bridging across the failure interface is observed, which is not expected at the nominal polymer/polymer overmold interface. Complementary scanning electron microscopy images of the failure surfaces indicate crack initiation at the overmold interface, followed by a change in locus of failure to the nearby polymer/glass fiber interface in the top layer of the composite laminate. Fiber bridging is observed in all specimens tested over a modest range of mode mixity, including specimens modified to the single leg bending geometry, suggesting that the polymer/glass interface is more susceptible to crack propagation than the desired overmold interface, which likely derives its strength from molecular interdiffusion during the overmolding process.

Toughness Characterization of Fiber Reinforced Concrete Beam using Fracture Mechanics

The study of fracture mechanics was very much essential because it gives clear idea of arising and propagation of cracks, cause for failure, life of structure, etc. The main aim of this research was to study the fracture behavior of fiber reinforced concrete which was reinforced with polypropylene fiber. The fiber used in concrete with different volume fraction like 0.5%, 0.75% and 1% of total volume of cementitious material. The specimens were prepared with different grades of concrete with different dosage of fiber and then subjected to three point bending test. Using test results the fracture properties like fracture energy, flexural strength; stress intensity factor, fracture toughness and stiffness were found. The experimental results showed that effectiveness of polypropylene fiber for different grades of concrete that is normal, medium and high strength concrete increases with increase in fiber volume and also the fracture properties of fiber reinforced concrete increases with increase in fiber volume and effectiveness of fiber was found for dosage of about 0.75-1% volume.

Evaluation of ΔJ-integral for a shallow crack in steel for pressure vessels under large scale yielding (LSY) condition

Fracture mechanics studies on fatigue crack growth under elastic-plastic condition is usually characterized by J integral range, ΔJ determined by an approximation from area under load-displacement hysteresis loop developed by Dowling and Begley. Despite being supported by some experimental data which reported that fatigue crack growth rates under elastic-plastic conditions have good correlations with ΔJ, the applicability of ΔJ on crack growth in a material subjected to cyclic bending remains inconclusive. In this study, finite element analysis of a four point-bending rectangular plate model with an edge crack length a/W between 0.1 to 0.5 was carried out under displacement amplitude δa between 0.1 to 1.5 mm to represent small to large scale yielding conditions. The elastic component was found to be the driven force of fatigue crack growth parameter in small scale yielding (SSY) condition while in large scale yielding (LSY) condition, the plastic component must be considered. It was also found that the simple method of ΔJ-integral calculation using load-displacement approach is overestimated for shallow crack under LSY condition.

Study of Fracture Mechanism of Machinable Mica Glass-Ceramics under Quasi-Static Conditions

In order to study the deformation and fracture mechanism of machinable mica glass ceramics under different loading modes, quasi-static uniaxial tensile and compression experiments are designed and analyzed based on the obtained quasi-static stress-strain curves at different strain rates, the macroscopic and microscopic fracture morphology of the samples and the nano-indentation experiment. The results show that mica glass ceramics are basically elastic brittle bodies. A very short “softening” section before the compression fracture is observed. There is a significant SD (tensile and compressive strength difference) effect, and the ratio of compressive to tensile strength is 14. The fracture mechanism of mica glass ceramics is related to the loading mode. The fracture mechanism is normal tensile fracture perpendicular to the loading axis under tensile loading. Under compressive loading, there is a mixed mode of distensile splitting and local shear failure. The microcrack is preferentially nucleated and extends to the weak interface at the junction of two phases, and the critical nucleation load is about 20 mN. The energy consumption mechanism of crack initiation and propagation at the weak interface and cleavage steps are the reason for the softening of the compression end curve.

Dynamic fracture analysis of buried steel gas pipeline using cohesive model

Pipeline play an irreplaceable role in long-distance oil and gas transportation. However, the initiation and propagation of cracks associated with defects may lead to pipeline fracture or explosion. In this paper, the numerical model of dynamic fracture in full-size natural gas buried pipeline are established based on cohesive model. The dynamic crack propagation of X80 pipeline steel is simulated with and without backfill soil. These parameters, like the crack-tip-opening angle (CTOA), are investigated quantitatively in the simulation in this paper. The results show that a threshold value of the crack propagation rate and CTOA does exist. With considering the backfill soil, the crack propagation rate decreases dramatically, and the curve of crack propagation distance will appear many horizontal trend stage against time. The lower the internal pressure, the more obvious the horizontal trend stage will be. The soil layer stress caused by pipeline crack propagation is mainly near the pipeline. Comparing the buried pipeline with penetrating cracks and surface cracks, it is found that surface cracks are more dangerous. The study of the dynamic fracture mechanism of full-scale pipeline provides necessary supplement for experiment.