Effect Of Crack Size Research Articles

Influence of Crack on the Instability of GFRP Composite Cylindrical Shells under Combined Loading

Buckling is a prominent condition of instability caused to a shell structure as a result of axial loadings. The process of buckling becomes more complex while analyzing thin walled structures like shells. Today such thin walled laminated composite shells are gaining more importance in many defense and industrial applications since they have greater structural efficiency and performance in relation to isotropic structures. Comprehensive understanding of the buckling response of shell structures is necessary to assure the integrity of these shells during their service life. The presence of defects, such as cracks, may severely compromise their buckling behavior and jeopardize the structural integrity. This work aims in conducting numerical analysis of cracked GFRP (Glass fibre-reinforced polymer) composite cylindrical shells under combined loading to study the effect of crack size on the buckling behavior of laminated composite cylindrical shells with different lay-up sequences. The numerical analyses were carried out using the finite element software, ABAQUS in order to predict the buckling behaviour of cracked laminated composite cylinders subject to different combinations of axial compression, torsion, internal pressure and external pressure from the interaction buckling curves.

Effects of crack inclination on shear failure of brittle geomaterials under compression

A micromechanics-based approach is proposed to predict the shear failure of brittle rocks under compression. Formulation of this approach is based on an improved wing microcrack model, the Mohr-Coulomb failure criterion, and a micro-macro damage model. The improved wing microcrack model considers the effects of crack inclination angle on mechanical behaviors of rocks. The micro-macro damage model describes the relation between crack growth and axial strain. Furthermore, comparing experimental and theoretical relations between crack initiation stress and confining pressure, model parameters (i.e., μ, a, β, and φ) hardly measured by test are solved. Effects of crack inclination angle, crack size, and friction coefficient on stress-strain relation, compressive strength, internal friction angle, cohesion, shear failure plane angle, and shear strength are discussed in details. A most disadvantaged crack angle is found, which is corresponding to the smallest compressive strength, cohesion, internal friction angle, and shear strength of rocks. Rationality of the theoretical results is verified by the published experimental results. This approach provides a theoretical prediction for effects of microcrack geometry on macroscopic shear properties in brittle rocks under compression.

A Permeability-Measuring Magnetic Flux Leakage Method for Inner Surface Crack in Thick-Walled Steel Pipe

It is difficult for traditional magnetic flux leakage (MFL) methods to detect inner surface cracks of thick-walled steel pipe or plate due to magnetic shielding of the wall and strong magnetic background noise, and for eddy current testing (ECT) as well due to its skin effect. On the basis of the nonlinear magnetic permeability of ferromagnetic materials, a new non-destructive testing method (NDT) permeability-measuring magnetic flux leakage (P-MFL) is proposed, in which the magnetization is perpendicular to the inner surface crack, and the surface layer permeability distortion caused by magnetic field distortion is measured by differential pick-up coils. Afterwards, its detection mechanism is presented and analyzed, and its feasibility is verified by simulations and experiments. Finally, some application cases for steel pipe are also realized effectively. Meanwhile, its testing characteristics for cracks are given and effects of crack size, specimen thickness, scanning paths to testing signal amplitude are briefly analyzed. Finally, the proposed P-MFL method compared to traditional MFL method is discussed in detail.

Characterising the early stages of crack development in environment-assisted cracking

ABSTRACTAn overview is given of recent NPL research to characterise the early stages of crack development in environment-assisted cracking, focusing on the nature of the crack precursors, the pit-to-crack transition, and the impact of solution chemistry on growth rate in the small and long crack growth rate regime. The impact on corrosion and cracking of surface grinding-induced changes in near-surface material and mechanical properties is highlighted, noting that awareness of this aspect in the corrosion community still remains limited. A major feature is the remarkable insight into the evolution of small surface cracks, from dealloyed layers and from corrosion pits, provided by advanced 3D imaging. Finally, further evidence for the concept of the solution conductivity-dependent crack-size effect in stress corrosion cracking and corrosion fatigue is put forward.

Modelling the electrochemical crack size effect on stress corrosion crack growth rate

A model has been developed to predict the crack-tip potential and local chemistry in a stress corrosion crack in a steam turbine blade steel as a function of crack size and bulk chloride-ion concentration. The model incorporates mass transport and chemical and electrochemical reactions in the crack, with the potential drop in the bulk solution outside the crack calculated from the solution to Laplace’s equation. The implications for crack-tip electrochemistry of full immersion vs a thin liquid layer are explored. The model predictions provide support for the concept of a solution conductivity dependent crack size effect on crack growth rates.

Effect of crack size on gas leakage characteristics in a confined space

We numerically investigated the influence of crack size on gas leakage characteristics in a confined space. The real scale model of underground Combined cycle power plant (CCPP) was taken for simulating gas leakage characteristics for different crack sizes such as 10 mm, 15 mm and 20 mm. The commercial code of Fluent (v.16.1) was used for three-dimensional simulation. In particular, a risk region showing such a probability of ignition was newly suggested with the concept of Lower flammable limit (LFL) of methane gas used in the present study to characterize the gas propagation and the damage area in space. From the results, the longitudinal and transverse leakage distances were estimated and analyzed for quantitative evaluation of risk area. The crack size was found to have a great impact on the longitudinal leakage distance, showing an increasing tendency with the crack size. In case of a crack size of 20 mm, the longitudinal leakage distance suddenly increased after 180 s, whereas it remained constant after 2 s in the other cases. This is because a confinement effect, which is caused by circulation flows in the whole space, increased the gas concentration near the gas flow released from the crack. The confinement effect is thus closely associated with the released mass flow rate changing with the crack size. This result would be useful in designing the gas detector system for preventing accidents in the confined space as like CCPP.

Lattice orientation and crack size effect on the mechanical properties of Graphene

The effect of lattice orientation and crack length on the mechanical properties of Graphene are studied based on molecular dynamics simulations. Bond breaking and crack initiation in an initial edge crack model with 13 different crack lengths, in 10 different lattice orientations of Graphene are examined. In all the lattice orientations, three recurrent fracture patterns are reported. The influence of the lattice orientation and crack length on yield stress and yield strain of Graphene is also investigated. The arm-chair fracture pattern is observed to possess the lowest yield properties. A sudden decrease in yield stress and yield strain can be noticed for crack sizes < 10 nm. However, for larger crack sizes, a linear decrease in yield stress is observed, whereas a constant yield strain of 0.05 is noticed. Therefore, the yield strain of 0.05 can be considered as a critical strain value below which Graphene does not show failure. This information can be utilized as a lower bound for the design of nano-devices for various strain sensor applications. Furthermore, the yield data will be useful while developing the Graphene coating on Silicon surface in order to enhance the mechanical and electrical characteristics of solar cells and to arrest the growth of micro-cracks in Silicon cells.

Fisheye failure analysis and life design approach for case-carburized gear steel based on statistical evaluation of defect size

The high cycle fatigue (HCF) and very high cycle fatigue (VHCF) properties of a case-carburized gear steel were investigated under tension and compression, and the distribution characteristics of defect size was analyzed using four statistical functions including Statistics of Extreme Values (SEV), Generalized Pareto distribution (GP), Generalized Extreme Values (GEV) and Exponential Generalized Pareto distribution (EXPGP). Results show that the interior inclusion-induced failure with the existence of fisheye becomes the predominant failure mode in HCF and VHCF regimes. With the increasing of applied stress amplitude, the effect of crack size within the fisheye on fatigue life is gradually reduced. Based on this, a fatigue strength prediction model associated with the variation of crack size was developed. At a given probability, the predicted fatigue strength is the highest by the estimated maximum inclusion size using the GEV distribution, then followed by using Gumbel distribution and by using GP distribution, and the lowest by using EXPGP distribution, which is inversely proportional to the evaluated maximum inclusion sizes. Based on the good agreement between the predicted and experimental results, the proposed approach based on statistical evaluation of defect size can be well used to predict the HCF and VHCF fatigue lives with interior fisheye failure.

Use of the Failure Assessment Diagram to Evaluate the Safety of the Reactor Pressure Vessel

Analysis of multiple failure modes is the key element of the integrity evaluation of the nuclear reactor pressure vessel (RPV). While the simple single-criterion failure code provides the guidance for structural integrity, the guidance ignores the interaction between fast fracture and plastic collapse. In this paper, the differences between the reserve factor (RF) in the R6 two-criteria failure procedure and the safety coefficient (SC) in the single-criterion failure code were compared. Based on 3D finite element (FE) analyses, the option 3 failure assessment diagram (FAD) of the beltline of the RPV was established according to the R6 basic route and alternative approaches, respectively. Also, the nonconservation of the secondary stress correction parameter ρ was reviewed. In this paper, it was shown that the effect of crack sizes on the FAD is considered to be limited, and the influence of the thermal stress on the FAD is obvious in the transition region of the failure assessment curve (FAC). The FAD only considering the mechanical load encloses the FAD considering the thermal–mechanical load for the Lr smaller than 1, but it is contrary when the Lr is bigger than 1. It is not enough to just satisfy the requirement in the IWB-3612 of the ASME code because the risk of plastic-collapse failure is ignored. And in this study, the maximum nonconservation of the fracture toughness RF is more than 7% due to the approximate value of ρ. Accordingly, the accurate method in the R6 procedure should be used in the integrity assessment of the RPV under the faulted transient.

Investigation on fracture parameters of concrete through optical crack profile and size effect studies

In this paper, Digital Image Correlation (DIC) technique has been used to map the full field of displacement and strain for visualizing the fracture growth, fracture propagation and formation of Fracture Process Zone (FPZ) in notched concrete beams under bending. Further, for exact quantification of concrete fracture parameters such as crack opening displacement, characteristics of FPZ and fracture energy, a new scheme called Optical Crack Profile (OCP) originated through DIC experiments, is developed. In addition, a comprehensive analysis of fracture parameters estimated from Bazant size effect laws, Jenq–Shah model and OCP technique have been carried out.

Capturing material toughness by molecular simulation: accounting for large yielding effects and limits

The inherent computational cost of molecular simulations limits their use to the study of nano-metric systems with potentially strong size effects. In the case of fracture mechanics, size effects due to yielding at the crack tip can affect strongly the mechanical response of small systems. In this paper we consider two examples: a silica crystal for which yielding is limited to a few atoms at the crack tip, and a nanoporous polymer for which the process zone is about one order of magnitude larger. We perform molecular simulations of fracture of those materials and investigate in particular the system and crack size effects. The simulated systems are periodic with an initial crack. Quasi-static loading is achieved by increasing the system size in the direction orthogonal to the crack while maintaining a constant temperature. As expected, the behaviors of the two materials are significantly different. We show that the behavior of the silica crystal is reasonably well described by the classical framework of linear elastic fracture mechanics (LEFM). Therefore, one can easily L. Brochard (B upscale engineering fracture properties from molecular simulation results. In contrast, LEFM fails capturing the behavior of the polymer and we propose an alternative analysis based on cohesive crack zone models. We show that with a linear decreasing cohesive law, this alternative approach captures well the behavior of the polymer. Using this cohesive law, one can anticipate the mechanical behavior at larger scale and assess engineering fracture properties. Thus, despite the large yielding of the polymer at the scale of the molecular simulation, the cohesive zone analysis offers a proper upscaling methodology.

Novel concepts on the growth of corrosion fatigue small and short cracks

Corrosion fatigue small, short and long crack growth rates have been determined for a 12Cr steam turbine steel in aerated 300 ppb Cl‐ + 300 ppb SO42‐ solution and in air at 90 °C. The crack growth rate for short and long cracks was monitored by direct current potential drop (DCPD) and for the small cracks by combining high resolution optical microscopy and DCPD. Comparison of the fatigue growth rate demonstrated that in solution the short crack growth rate was remarkably enhanced in comparison to long cracks, when the crack size is smaller than 250 μm. This enhancement was attributed to the electrochemical crack size effect associated with greater anodic polarisation of the short crack in such low conductivity solution. However, such enhanced growth was not observed for small cracks, which was rationalised on the basis of additional contribution of current from the pit limiting crack‐tip polarisation.

Elastic-plastic analysis of the J integral for repaired cracks in plates

In this paper, three-dimensional finite element method is used to analyze the J integral for repaired cracks in plates with bonded composite patch and stiffeners. For elastic the effect of cracks, the thickness of the patch (er) and properties of the patch are presented for calculating the J integral. For elastic-plastic a several calculations have been realized to extract the plasticized elements around the crack tip of repaired and un-repaired crack. The obtained results show that the presence of the composite patch and stiffener reduces considerably the size of the plastic zone ahead of the crack. The effects of crack size and the inter-distance of repaired cracks were analysed.

Mechanism of crack healing at room temperature revealed by atomistic simulations

Three dimensional molecular dynamics (MD) simulations are systematically carried out to reveal the mechanism of the crack healing at room temperature, in terms of the dislocation shielding and the atomic diffusion to control the crack closure, in a copper (Cu) plate suffering from a shear loading. The results show that the process of the crack healing is actualized through the dislocation emission at a crack tip accompanied with intrinsic stacking faults ribbon forming in the crack tip wake, the dislocation slipping in the matrix and the dislocation annihilation in the free surface. Dislocation included stress compressing the crack tip is examined from the MD simulations and the analytical models, and then the crack closes rapidly due to the assistance of the atomic diffusion induced by the thermal activation when the crack opening displacement is less than a threshold value. This phenomenon is very different from the previous results for the crack propagation under the external load applied because of the crack healing (advancing) largely dependent on the crystallographic orientations of crack and the directions of external loading. Furthermore, based on the energy characteristic and considering the crack size effect, a theoretical model is established to predict the relationships between the crack size and the shear stress which qualitatively agree well with that obtained in the MD simulations.

Crack precursor size for natural rubber inferred from relaxing and non-relaxing fatigue experiments

Fatigue life prediction for a dumbbell cylindrical natural rubber component under uniaxial tensile loading conditions was performed based on the Thomas fatigue crack growth model for relaxing (R=0) load cycles and the Mars–Fatemi model for non-relaxing (R>0) load cycles. By using a self-written program, we proposed a new approach to establish the relation between the power law exponent F and the R ratio in the Mars–Fatemi model. The approach is based on rubber fatigue life (S–N) data rather than crack growth rate and tearing energy (da/dN–T) data, avoiding certain difficulties often encountered using the crack growth method. The results indicate that the relation between F and R is a quadratic or cubic function over the range 0<R<0.3. Finally, the quantitative effect of initial crack size on fatigue life was studied. We found that the inferred mean size of crack precursors in the rubber component is around 30–40μm under both relaxing and non-relaxing loading conditions, and the fluctuation of fatigue life is due to the inhomogeneity of crack precursor size except the factors such as unavoidable variations in testing conditions and specimen variations. The good agreement of inferred crack precursor sizes from different R ratio loading conditions is a strong indication that the Mars–Fatemi model provides a proper accounting for the effects of strain crystallization, and it confirms yet again the understanding that nucleated cracks originate from similarly sized precursors in both relaxing and non-relaxing fatigue experiments.

Fracture toughness of Cu and Ni single crystals with a nanocrack

Abstract

Numerical study on the phase change heat transfer of LNG in glass wool based on the VOF method

In this study, the evaporation of a cryogenic gas in an insulating porous medium was investigated numerically and experimentally. The flow and heat transfer characteristics around the evaporating cryogenic gas in such a medium were analyzed based on the VOF (Volume of Fluid) method. The thermal leakage through the porous medium to the outer shell was then analyzed using heat transfer considerations. To support the numerical results, an experiment was then performed using LNG (Liquefied Natural Gas) as the fluid and glass wool as the porous medium. The numerical results for the outer shell temperature predict the experimental values well. Based on the validated numerical results, the transient behavior of temperature distribution in outer shell is analyzed. The effect of crack size on the reliability of insulation system is investigated. In addition, the behavior of the virtual evaporation velocity and the liquid film area was considered qualitatively. This work sheds light on technology related to cryogenic storage systems by suggesting a systematic method for predicting the temperature of the outer shell, the liquid film area, and virtual evaporation velocity.

Characterizing the Stress Intensity Factor of Graphene Sheet with Central Crack.

This paper aims to characterize the stress intensity factor (SIF) of atomistic graphene sheet with central crack subjected to uniaxial loading. The equilibrium configuration of the defective graphene sheet with missing covalent bonds was generated through molecular dynamics (MD) simulation. Subsequently, the local stress distribution near the crack tip of atomistic structure was evaluated using the Hardy stress formulation as well as the non-local elasticity theory. Based on the local stress distributions, the SIF of the atomistic graphene sheet was determined through the projection process. In comparison, the graphene sheet was also treated as a continuum solid, and the stress distribution near the crack tip as well as the SIF were evaluated from the finite element method (FEM). In an attempt to understand the crack size effect, the crack length was assumed to vary from 3 lattice distance to around 80 lattice distance. Results revealed that the SIF calculated based on the nonlocal elasticity theory in conjunction with the projection process is quite sensitive to the selection of the projection point. However, for the Hardy stress distribution, when the projection position is 1 lattice distance away from the crack tip, the SIF is quite consistent and the result is compatible to that obtained from the FEM analysis. Moreover, the agreement is better as the crack size is increasing. Therefore, the SIF calculated based on the Hardy stress formulation together with the projection approach could be a physical quantity correlating the defective atomistic graphene sheet with its continuum counterpart.

The topology optimization design for cracked structures

In this paper, the element free Galerkin method (EFG) is proposed for topology optimization of cracked structures using the bi-directional evolutionary structural optimization method (BESO). The mathematical formulation of the topology optimization is developed considering the nodal strain energy as the design variable and the minimization of compliance as the objective function. The element free Galerkin method is enriched by the crack-tip enrichment functions to increase the approximation accuracy near the crack-tip. The Lagrange multiplier method is employed to enforce the essential boundary conditions. Several numerical examples are presented to show the effectiveness of the proposed method. Many issues related to topology optimization of cracked structures such as the effects of crack size and location on the optimal topology are addressed in the examples. The common numerical instabilities do not exist in the results.

Small and short crack growth and the solution-conductivity dependent electrochemical crack size effect

Corrosion fatigue small crack growth rates have been determined for a 12Cr steam turbine steel in aerated 300ppb Cl− and 300ppb SO42− under simulated two-shifting conditions. The remarkably enhanced crack growth rate observed previously for a short crack (relative to that for a long crack) was not evident for small cracks initiated from pits. In contrast, the stress corrosion small crack growth rate determined in aerated 35ppm Cl− was markedly increased with respect to long crack growth. The concept of the solution-conductivity dependent electrochemical crack size effect is introduced to provide a fundamental framework to rationalise the disparate results. The engineering implications for two-shifting operation are discussed.