Expressions For Stress Intensity Factors Research Articles

Determination of Stress Intensity Factors in Low Pressure Turbine Rotor Discs

An attention in this paper is focused on the stress analysis and the determination of fracture mechanics parameters in low pressure (LP) turbine rotor discs and on developing analytic expressions for stress intensity factors at the critical location of LP steam turbine disc. Critical locations such as keyway and dovetail area experienced stress concentration leading to crack initiation. Major concerns for the power industry are determining the critical locations with one side and fracture mechanics parameters with the other side. For determination of the critical locations in LP turbine rotor disc conventional finite elements are used here. For this initial crack length and during crack growth it is necessary to determine SIFs. In fatigue crack growth process it is necessary to have analytic formulas for the stress intensity factor. To determine analytic formula for stress intensity factor (SIF) of cracked turbine rotor disc special singular finite elements are used. Using discrete values of SIFs which correspond to various crack lengths analytic formula of SIF in polynomial forms is derived here. For determination of SIF in this paper, combinedJ-integral approach and singular finite elements are used. The interaction of mechanical and thermal effects was correlated in terms of the fracture toughness.

Determination of Stress Intensity Factor for Cracked Brazilian Disc Using Weight Function

To reduce stress concentration near the loading point, Brazilian test, normally used for the indirect determination of tensile strength for rock or concrete quasi-brittle materials, is usually subjected to uniformly distributed pressure over finite width (or arc) of the Brazilian disc. As an extension, the same geometry, in which a central notch is introduced in the symmetrical plane of applied forces, can be used to determine fracture toughness of the materials. For this purpose, accurate expression for stress intensity factor (SIF) for central cracked Brazilian disc should be provided first. To this end, weight function method is used in this paper where weight function for central cracked disc is available in general SIF handbooks. Meanwhile, the exact stress solution in the intact Brazilian disc subjected to uniformly distributed pressure is derived by use of numerical method. In the end, some finite element analysis is carried out using the program package ABAQUS on the Brazilian disc, and the comparison results regarding the SIF between the weight function method and numerical method prove the validity of the proposed method.

Anti-plane analysis on a finite crack in a one-dimensional hexagonal quasicrystal strip

The anti-plane fracture problem for a finite crack in a one-dimensional hexagonal quasicrystal strip is analyzed. By using Fourier transforms, the mixed boundary value problems are reduced to the dual integral equations. The solution of the dual integral equations is then expressed by the complete elliptic integrals of the first and the third kinds. The expressions for stress, strains, displacements and field intensity factors of the phonon and phason fields near the crack tip are obtained exactly. The path-independent integral derived by a conservation law equals the energy release rate, which can be used as a fracture criterion for a mode III fracture problem.

Analytical expressions for the notch stress intensity factors of periodic V-notches under tension by using the strain energy density approach

This article presents the notch stress intensity factors of a wide range of finite-width flat plates with periodic edge notches. A broad series of notch configurations, varying from shallow to very deep notches, complete range of notch spacing and wide range of notch opening angles, is considered. The significance of sharp notch approximation for the case of blunt notches with a very small notch radius is also demonstrated. Overall, more than 1200 models are carried out. Due to the desirability of analytical expressions for notch stress intensity factors evaluation, the numerical results, obtained from the strain energy density approach, are used to find some simple analytical expressions for the prediction of notch stress intensity factors of periodic sharp notches. The use of a coarse mesh in the finite element models and multiscaling are the promising advantages of such a method underlined in this study.

Analysis of Fatigue Life and Influence Factors of Tubing with Initial Crack

Three-dimensional stresses are analyzed in the tubing working based on the theory of thick-walled cylinder, and the stress intensity factor expression is derived on longitudinal and circumferential extending cracks in the tubing. Tubing fatigue life is calculated according to given condition through the preparation of the corresponding program. Influence of initial crack length, change of the pressure and the tubing wall thickness on the fatigue life are discussed.

Transient thermal cracking associated with non-classical heat conduction in cylindrical coordinate system

This paper studies the fracture behavior of a thermoelastic cylinder subjected to a sudden temperature change on its outer surface within the framework of non-classical heat conduction. The heat conduction equation is solved by separation of variable technique. Closed form solution for the temperature field and the associated thermal stress are established. The critical parameter governing the level of the transient thermal stress is identified. Exact expression for the transient stress intensity factor is obtained for a crack in the cylinder. The difference between the non-classical solutions and the classical solution are discussed. It is found that the traditional classical heat conduction considerably underestimates the transient thermal stress and thermal stress intensity factor.

Influence of cracks on dynamic characteristics and stress intensity factor of gears

Dynamic and three-dimensional finite element analytical models of cracked gears are established, and the dynamic characteristics (natural frequency and vibration shape) of the gear body are investigated when tooth cracks in the gear appear. Further, the influence of crack position and length on the dynamic characteristics of the gear structure are simulated and discussed. From this it was possible to determine that the crack position and crack length had an influence on the gear’s natural frequency and vibration shape. When the crack appears, the natural frequencies of the gear drop, and the vibration shapes also change. The influence of crack position on natural frequency and vibration shape are bigger than that of crack length. The natural frequencies’ decreases are bigger when the crack in the gear occurs at the tooth root rather than at the top of the tooth. Moreover, when the crack appears, the vibration shapes of the gear body are obviously different from without the crack, and the dynamic stresses of the gear body also change. On this basis, using the theory of fracture mechanics and the finite element method by ANSYS, the stress intensity factors were analyzed when the gear crack appeared. The variations in stress intensity factors are discussed related to changes in crack length, gear module, number of teeth, and load, when gear cracks occur at the pitch circle and tooth root. The pragmatic expressions of stress intensity factors are given by combining with the results obtained from the finite element method and the influence laws of multiple parameters on stress intensity factors are gained. These establish a good foundation for the fracture analysis and fault diagnosis of gears.

A semi-inverse method of a Griffith crack in one-dimensional hexagonal quasicrystals

A semi-inverse method of a Griffith crack in a one-dimensional hexagonal quasicrystal is proposed in this work. By introducing Westerggaard’s stress functions, the expressions for stress, strains, displacements and field intensity factors of the phonon and the phason fields in the vicinity of a crack tip are obtained in closed-form. The path-independent integral derived by a conservation law equals the energy release rate for a mode III fracture problem in a one-dimensional hexagonal quasicrystal. It is found that the energy release rate is dependent on the phonon fields as well as the phason fields, which can be used as a fracture criterion. In the absence of the phason fields, the obtainable results in this paper match with the classical ones.

Research of effects of bar geometric parameters on initial external force in precision cropping

In precise cropping of the metal bars with different geometrical parameters, it is very important to obtain the reasonable initial external forces required by the bars rapidly and accurately. Stress concentration factor and stress intensity factor are proposed to calculate the initial external force accurately in this paper according to geometrical sizes of metal bars. By means of numerical simulation and linear fitting method, the correctional expressions of stress concentration factor and stress intensity factor of V-shaped notch tip, which include the geometric parameters of the bar, are obtained respectively and the error analyses are also performed. The ratio of the depth of V-shaped notch to the diameter of the bar is presented to be a condition parameter. The numerical analytical results show that the method of stress concentration factor can be used to calculate the initial external force accurately when the ratio of the depth of V-shaped notch to the diameter of the bar is more than 0.05, and the method of the stress intensity factor can be used when the ratio is less than 0.05. The calculating formulas of reasonable initial external forces for the bars with different geometrical parameters are also given. The cropping experimental results have confirmed that it is feasible that the reasonable initial external forces required by the bars with different geometrical parameters are calculated effectively by using the stress concentration factor or the stress intensity factor in precision cropping.

Transient dislocation emission from a crack tip in an anisotropic elastic material

The emission of a dislocation with a general Burgers vector from the tip of a stationary semi-infinite crack in an anisotropic elastic material is examined. The dislocation is assumed to leave the crack tip along the crack extension plane at constant speed. Explicit expressions for the transient shielding stress intensity factors at the crack tip and the drag forces on the dislocations are derived. Numerical results for a class of cubic materials and two hexagonal crystals, zinc and cobalt, are given. Dislocation emission under plane stress wave loading is discussed.

Research of fracture problem of composite plate with curved crack by conformal mapping

In this paper, the fracture problem of an anisotropic composite plate with a curved crack is solved by conformal mapping method. Using the conformal mapping method, the problem with boundary conditions is transformed into boundary value problem of partial differential equations, which can be solved analytically by complex function method. Based on the quoted conformal mapping function, the crack curve is mapped into a unit circle. The fracture analysis near the curve crack tip for both Mode I and Mode II of anisotropic composite materials in a state of plane stress is made. The stress functions are determined under the stress boundary conditions. Then the analytical expressions of stress intensity factors, stress fields and displacement fields near the curved crack tip for Mode I and Mode II in anisotropic composite materials are obtained.

Analysis of Mode I Periodic Parallel Cracks-Tip Stress Field in an Infinite Orthotropic Plate

The mechanical behavior near crack tip for periodic parallel cracks in an orthotropic composite plate subjected to the uniformly distributed load within the cracks surface is studied. The mechanical problem is turned into the boundary value problem of partial differential equation. By using the periodicity of the hyperbolic function in the complex domain and constructing proper Westergaard stress function, the periodicity of parallel cracks can be removed. Using the complex variable function method and the undetermined coefficients method, the boundary value problem of partial differential equation can be solved with the help of boundary conditions. The analytic expressions for stress intensity factor, stress, and displacement near the crack tip of periodical parallel cracks are obtained. When the vertical distance of cracks tends to infinity, the stress intensity factor degenerates into a single central crack situation. The stress intensity factor around the crack tip of periodic parallel cracks in an orthotropic composite plate depends on the shape factor. The interaction happens between the cracks. Finally, a numerical analysis of the stress and displacement changed with the polar angle is done.

Original Crack and Adhesion Development of Nano Diamond Coating

A theoretical original microvoid model which describes the micro structural aspects of tiny original crack was developed based on fracture mechanics to explain the interface strength between nano diamond coating (NDC) and its substrate. The expression of stress fields, displacement and stress intensity factor ( SIF ) K at interface crack tip were deduced. Based on the original microvoid model, the technique to improve the adhesion strength between the NDC and its substrate was obtained by improving the diamond nucleation density and adjusting the coating residue stress.

Dynamic characteristics of cracked gear and three-dimensional crack propagation analysis

The dynamic model and three-dimensional finite element analytical model of cracked gear structure are established respectively according to the cracked beam theory, and the dynamic characteristics (natural frequency, vibration shape) of cracked gear body are investigated. Further the influences of crack position and crack length on the dynamic characteristics of gear structure are simulated and discussed. On this basis, the fracture and damage of gear structure are investigated according to the theory of fracture mechanics. Using FRANC3D software, the three-dimensional (3D) propagation of crack at tooth root for involute gear is simulated, and stress intensity factor (SIF)s of semi-circular crack at tooth root including three types are analyzed, their variation laws are gained, then the expressions of SIFs are obtained by numerical fitting FEM results. Based on this, the 3D crack propagation path at tooth root is simulated and discussed, then, it is verified by comparing to experimental results, according to the mutation of the maximum SIF at crack tip, the fracture and damage of gear tooth are judged, and its work life also is predicted. These have very important value for damage monitoring and diagnosis of gear.

Theoretical Development of Lower Bound S - N Fatigue Curves

AbstractFatigue strength of welded structures is typically estimated through several approaches, including experimental S-N curves, the hot spot stress approach, and fracture mechanics. Recent work on the local stress field singularity of the weld toe has provided analytical expressions for the stress intensity factor of a crack emanating from the weld toe. Invoking the Paris law for fatigue crack growth together with the stress intensity factor expressions allows fatigue life to be evaluated in closed form. The fracture mechanics solution takes the same power-law form as the S-N curves and produces accurate lower bound estimates to the experimental fatigue data of stiffeners and attachments. The results show a strong relationship between the fracture mechanics, S-N curve, and hot spot approaches to fatigue that is based on two or more parameters from the local weld toe stress field. The two parameters may be tabulated as functions of weldment geometry and loading conditions for improved fatigue design an...

Dependence of stress intensity factors on elastic constants for cracks in an orthotropic bimaterial with a thin film

An interface crack and a subinterface crack in an orthotropic bimaterial structure consisting of a thin film and a half plane substrate are analyzed. The orthotropic bimaterial structure is subjected to compressive load and bending moment per unit thickness. Complete expressions of stress intensity factors for the two cracks are obtained based on the path independence of the J integral, apart from one dimensionless parameter undetermined each. The dependence of the dimensionless parameters on material constants is examined. A reduction of the number of necessary material parameters for the parameters is made based upon the modified Stroh formalism. The explicit dependence of the dimensionless parameters on one orthotropic parameter for the film is determined by using the orthotropy rescaling technique. Variations of the dimensionless parameters with the other material parameters are also obtained through numerical computations.

Simple New Expressions for the Notch Stress Intensity Factors in an Array of Narrow V–Notches Under Tension

Taking advantage of some recent closed form expressions for the strain energy density in a control volume embracing the notch tip, some simple expressions are derived for the Notch Stress Intensity Factors of an infinite array of double symmetric lateral notches and edge notches under tension loading. The new expressions are applicable to narrow notches when the ratio between the notch depth and the plate width, a/W, is lower than 0.025 providing very accurate results.

Interaction between a Screw Dislocation Located in Strained Reinforcement Layer and a Lip-Shaped Crack

The paper is aim to investigate the interaction of a screw dislocation in strained reinforcement with a lip-shaped crack under remote longitudinal shear load using complex variable method of Elasticity. The exact solution of complex function of the matrix and the renforcement layer are obtain in series form; then, the expressions of stress field, image force and stress intensity factor of crack tip can be derived; finally, numerical disccusions are pesented and the results shows that the lip-shaped crack in reinforcement layer has interference effect on the interaction of dislocation and reinforcement layer, and the eigenstrain in x-direction has little effect on image force; however, the eigenstrain in y-direction has great influence on image force.

Research of stress intensity factor of V-shaped notch tip in precision cropping

For carrying out the precise cropping of metal bar with different geometrical sizes, it is very important to obtain the reasonable stress intensity factor of V-shaped notch tip rapidly and accurately. At first, a new precise cropping method, which is the high-speed peripheral low-stress bending fracture cropping is presented in the paper, and its working mechanism is also given in detail. The stress field near V-shaped notch tip is analyzed, and the stress extrapolation method is presented to compute the stress intensity factor of V-shaped notch tip. Based on it, the correctional expression of theoretical stress intensity factor in a handbook of stress intensity factor is also given. The contrasts between stress intensity factor results obtained by means of the stress extrapolation method and the corresponding theoretical results in the handbook of stress intensity factor are also carried out in detail. The results show that the two errors are not more than 5 % and are within a reasonable engineering range. The cropping experimental results for initial loading force and crack propagation life have also confirmed that the correctional expression of theoretical stress intensity factor is feasible.

Stress concentration factor expression for tension strip with eccentric elliptical hole

Two explicit expressions of the stress concentration factor for a tension finite-width strip with a central elliptical hole and an eccentric elliptical hole, respectively, are formulated by using a semi-analytical and semi-empirical method. Accuracy of the results obtained from these expressions is better, and application scope is wider, than the results of Durelli’s photo-elastic experiment and Isida’s formula. When eccentricity of the elliptical hole is within a certain range, the error is less than 8%. Based on the relation between the stress concentration factor and the stress intensity factor, a stress intensity factor expression for tension strips with a center or an eccentric crack is derived with the obtained stress concentration factor expressions. Compared with the existing formulae and the finite element analysis, this stress intensity factor expression also has sufficient accuracy.