Boundary Conditions Effects on the Crack Growth Mechanism Under Cycling Bending

2019 ◽  
Author(s):  
Giovanni Pio Pucillo ◽  
Luca Esposito ◽  
Davide Leonetti
Keyword(s):  
Aspect Ratio ◽  
Boundary Conditions ◽  
Crack Propagation ◽  
Crack Front ◽  
Crack Depth ◽  
Internal Boundary ◽  
Design Stage ◽  
Crack Shape ◽  
Propagation Law ◽  
Bending Load

The recent increase of train speed and frequency determines a rise of the loads transmitted to the superstructure. Therefore, railway components might experience service loads that have not considered at the design stage. Moreover, wear and backlash modification between components of a mechanical system might be able to modify the internal boundary conditions of the assembly. According to damage tolerance philosophy, an initial flaw is assumed to exist in the fatigue critical location of a structural component, and the analysis of the crack propagation life for such component needs accurate Stress Intensity Factor (SIF) evaluations. In this study, the effects of the boundary conditions on the crack propagation life have been evaluated for a semi-elliptical surface crack having semi-axes a and c and growing from the root of a shoulder fillet notch in a round bar loaded in bending. Two cases have been analyzed: - the shoulder is free from external forces; - the shoulder is in contact with an adjacent generic body. At first, the SIF distribution has been calculated with the Virtual Crack Closure Technique, considering or not the nonlinear effect induced by the contact forces arising from the interaction between the shoulder and the neighboring component. Successively, in both the above cases a two-parameters propagation law has been utilized to predict the evolution of both crack shape and crack depth when a cyclic bending load is applied to the rod. For this purpose, different values of the Stress Concentration Factor at the root of the fillet, and of the initial aspect ratio of the crack front, were considered in the calculations. It is found that the aspect ratio evolves to a unique asymptote, taking or not into account the non-linearity introduced by the contact at the shoulder, and this value depends on the notch severity. The ratio between the dimensionless SIFs obtained with and without the unilateral constraint at the shoulder, βcs / βfs, does not depend on the relative crack depth and crack shape. Also, the effect of the notch severity on the dimensionless SIF appears to be evident only for the portion of the crack front in the vicinity of the free surface.

Stress Intensity Factor Equations for Internal Semi-Elliptical Cracks in Pressurized Cylinders

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
J. M. Alegre ◽  
I. I. Cuesta
Keyword(s):  
Fatigue Life ◽  
Stress Intensity ◽  
Aspect Ratio ◽  
Crack Propagation ◽  
Internal Pressure ◽  
Propagation Law ◽  
Continuous Crack ◽  
Section Viii ◽  
Accurate Procedure ◽  
Elliptical Cracks

In order to calculate the fatigue life of cylinders subjected to internal pressure using the fracture mechanics approach, the stress intensity factors (SIFs) for internal semi-elliptical cracks are needed. Nowadays, the most accurate procedure for fatigue life calculation consists in starting from a postulated internal semi-elliptical crack and updating the flaw aspect ratio during the crack propagation. In this sense, assuming a semi-elliptical shape during crack propagation, SIFs both at the deepest crack point and at the surface point must be calculated in order to update the crack aspect ratio through its fatigue propagation. This continuous crack shape updating cannot be done using the conventional tabulated solutions, as those provided in the main design codes and SIF handbooks. This paper presents a number of closed-form equations, which very accurately fit the tabulated results in ASME Boiler and Pressure Vessel Code, Section VIII, Division 3, to calculate the SIF for internal semi-elliptical cracks in cylinders subjected to internal pressure. These equations can be used to avoid the use of the tabulated solutions, and, as a consequence, an automatic numerical integration of the propagation law can be done.

Corrosion-Fatigue of High Strength Steel Bars: Evolution of Crack Aspect Ratio

2011 ◽  
Vol 488-489 ◽  
pp. 1-4
Author(s):  
Jesús Toribio ◽  
Juan Carlos Matos ◽  
Beatriz González ◽  
J. Escuadra
Keyword(s):  
Aspect Ratio ◽  
Corrosion Fatigue ◽  
Crack Front ◽  
Crack Depth ◽  
High Strength ◽  
Initial Crack ◽  
Crack Advance ◽  
Prestressing Steel ◽  
Steel Wires ◽  
Steel Bars

Abstract. This paper shows the evolution of the surface crack front in prestressing steel wires subjected to fatigue in air and to corrosion-fatigue in Ca(OH)2+NaCl. To this end, a numerical modelling was made on the basis of a discretization of the crack front (characterized with elliptical shape), considering that the crack advance at each point is perpendicular to such a front according to a Paris-Erdogan law, and using a three-parameter stress intensity factor (SIF). Each analyzed case (a particular initial crack geometry) was characterized by the evolution of the semielliptical crack aspect ratio (relation between the semiaxes of the ellipse) with the relative crack depth and by the variation of the maximum dimensionless SIF at the crack front

scholarly journals Actions, topological terms and boundaries in first-order gravity: A review

2016 ◽  
Vol 25 (04) ◽  
pp. 1630011 ◽  
Author(s):  
Alejandro Corichi ◽  
Irais Rubalcava-García ◽  
Tatjana Vukašinac
Keyword(s):  
Boundary Conditions ◽  
Symplectic Structure ◽  
Equations Of Motion ◽  
Hamiltonian Formalism ◽  
Action Principle ◽  
Internal Boundary ◽  
Four Dimensions ◽  
First Order ◽  
Conserved Charges ◽  
Boundary Terms

In this review, we consider first-order gravity in four dimensions. In particular, we focus our attention in formulations where the fundamental variables are a tetrad [Formula: see text] and a [Formula: see text] connection [Formula: see text]. We study the most general action principle compatible with diffeomorphism invariance. This implies, in particular, considering besides the standard Einstein–Hilbert–Palatini term, other terms that either do not change the equations of motion, or are topological in nature. Having a well defined action principle sometimes involves the need for additional boundary terms, whose detailed form may depend on the particular boundary conditions at hand. In this work, we consider spacetimes that include a boundary at infinity, satisfying asymptotically flat boundary conditions and/or an internal boundary satisfying isolated horizons boundary conditions. We focus on the covariant Hamiltonian formalism where the phase space [Formula: see text] is given by solutions to the equations of motion. For each of the possible terms contributing to the action, we consider the well-posedness of the action, its finiteness, the contribution to the symplectic structure, and the Hamiltonian and Noether charges. For the chosen boundary conditions, standard boundary terms warrant a well posed theory. Furthermore, the boundary and topological terms do not contribute to the symplectic structure, nor the Hamiltonian conserved charges. The Noether conserved charges, on the other hand, do depend on such additional terms. The aim of this manuscript is to present a comprehensive and self-contained treatment of the subject, so the style is somewhat pedagogical. Furthermore, along the way, we point out and clarify some issues that have not been clearly understood in the literature.

Shape and energies of a dynamically propagating crack under bending

2003 ◽  
Vol 18 (10) ◽  
pp. 2379-2386 ◽  
Author(s):  
Dov Sherman ◽  
Ilan Be'ery
Keyword(s):  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Crack Front ◽  
Three Dimensional ◽  
Strain Energy Release ◽  
Governing Parameter ◽  
Propagating Crack ◽  
Front Shape

We report on the exact shape of a propagating crack in a plate with a high width/thickness ratio and subjected to bending deformation. Fracture tests were carried out with brittle solids—single crystal, polycrystalline, and amorphous. The shape of the propagating crack was determined from direct temporal crack length measurements and from the surface perturbations generated during rapid crack propagation. The shape of the crack profile was shown to be quarter-elliptical with a straight, long tail; the governing parameter of the ellipse axes is the specimen's thickness at most length of crack propagation. Universality of the crack front shape is demonstrated. The continuum mechanics approach applicable to two-dimensional problems was used in this three-dimensional problem to calculate the quasistatic strain energy release rate of the propagating crack using the formulations of the dynamic energy release rate along the crack loci. Knowledge of the crack front shape in the current geometry and loading configuration is important for practical and scientific aspects.

Laminar Forced Convection in Annular Microchannels With Slip Flow Regime

2009 ◽  
Author(s):  
Arman Sadeghi ◽  
Abolhassan Asgarshamsi ◽  
Mohammad Hassan Saidi
Keyword(s):  
Nusselt Number ◽  
Fluid Flow ◽  
Aspect Ratio ◽  
Boundary Conditions ◽  
Knudsen Number ◽  
Gas Flow ◽  
Slip Flow ◽  
Outer Wall ◽  
Graphical Form ◽  
Uniform Temperature

Fluid flow and heat transfer at microscale have attracted an important research interest in recent years due to the rapid development of microelectromechanical systems (MEMS). Fluid flow in microdevices has some characteristics which one of them is rarefaction effect related with gas flow. In this research, hydrodynamically and thermally fully developed laminar rarefied gas flow in annular microducts is studied using slip flow boundary conditions. Two different cases of the thermal boundary conditions are considered, namely: uniform temperature at the outer wall and adiabatic inner wall (Case A) and uniform temperature at the inner wall and adiabatic outer wall (Case B). Using the previously obtained velocity distribution, energy conservation equation subjected to relevant boundary conditions is numerically solved using fourth order Runge-Kutta method. The Nusselt number values are presented in graphical form as well as tabular form. It is realized that for the case A increasing aspect ratio results in increasing the Nusselt number, while the opposite is true for the case B. The effect of aspect ratio on Nusselt number is more notable at smaller values of Knudsen number, while its effect becomes slighter at large Knudsen numbers. Also increasing Knudsen number leads to smaller values of Nusselt number for the both cases.

Probabilistic Crack Propagation Behavior of Railway B Grade Steel

2010 ◽  
Vol 97-101 ◽  
pp. 484-487
Author(s):  
Wei Li ◽  
Qiang Li ◽  
Ping Wang
Keyword(s):  
Crack Propagation ◽  
Reliability Assessment ◽  
Threshold Value ◽  
Threshold Region ◽  
Propagation Behavior ◽  
Propagation Law ◽  
Confidence Degree ◽  
State Region ◽  
Crack Propagation Behavior ◽  
Grade Steel

Fatigue crack growth rate (FCGR) test of B grade steel was performed to clarify the probabilistic behavior of crack propagation in near-threshold region and steady-state region. As a result, a crack propagation law considering influence of threshold value and average stress can be well proposed to estimate crack propagation behavior of B grade steel. The estimated value of threshold value ΔKth is 293.65MPamm1/2, approaching the experimental value of ΔKth, about 280.39MPamm1/2. Furthermore, the probabilistic FCGR curves of B grade steel are established from the viewpoint of survival probability and confidence degree, which reflects the influence of scatter regularity of data and sample size on reliability assessment.

NUMERICAL AND EXPERIMENTAL STUDY ON FREE VIBRATION OF DELAMINATED WOVEN FIBER GLASS/EPOXY COMPOSITE PLATES

2012 ◽  
Vol 12 (02) ◽  
pp. 377-394 ◽  
Author(s):  
J. MOHANTY ◽  
S. K. SAHU ◽  
P. K. PARHI
Keyword(s):  
Experimental Study ◽  
Aspect Ratio ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Numerical Study ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Fiber Glass ◽  
Number Of Layers

This paper presents a combined experimental and numerical study of free vibration of industry-driven woven fiber glass/epoxy (G/E) composite plates with delamination. Using the first-order shear deformation theory, an eight-noded two-dimensional quadratic isoparametric element was developed, which has five degrees of freedom per node. In the experimental study, the influence of various parameters such as the delamination size, boundary conditions, fiber orientations, number of layers, and aspect ratio on the natural frequencies of delaminated composite plates are investigated. Comparison of the numerical results with experimental ones shows good agreement. Fundamental natural frequencies are found to decrease with the increase in the delamination size and fiber orientation and increases with the increase in the number of layers and aspect ratio of delaminated composite plates. The natural frequency of the delaminated composite plate varies significantly for different boundary conditions.

Description of Small Fatigue Crack Propagation in ODS Steel

2014 ◽  
Vol 891-892 ◽  
pp. 911-916
Author(s):  
Pavel Hutař ◽  
Ivo Kuběna ◽  
Miroslav Šmíd ◽  
Martin Ševčík ◽  
Tomáš Kruml ◽  
...  
Keyword(s):  
Fatigue Crack ◽  
Crack Propagation ◽  
Fatigue Crack Propagation ◽  
Fatigue Testing ◽  
Low Cycle Fatigue ◽  
High Stress ◽  
Oxide Dispersion Strengthened ◽  
Ods Steel ◽  
Small Fatigue Crack ◽  
Propagation Law

The oxide dispersion strengthened (ODS) steels are widely studied as possible candidate material for fission and fusion technology. Due to application of the ODS materials, mainly low cycle fatigue is important. Therefore, small crack initiation and propagation for rather high stress amplitude are in focus. The main aim of the presented work is description of the small fatigue crack propagation for ODS-EUROFER steel. Due to limited quantity of ODS steel special miniaturized cylindrical specimens for fatigue testing were designed. Crack propagation law based on plastic part of J-integral is presented and applied for mentioned material. The resulting fatigue crack propagation rates for ODS-EUROFER steel and EUROFER 97 are compared and discussed.

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