Stress Intensity Factor Solutions Research Articles

Point Load Weight Functions for Semi-Elliptical Cracks in Finite Thickness Plate

Abstract This paper presents the application of the weight function method for the calculation of stress intensity factors for surface semi-elliptical cracks in finite thickness plates subjected to arbitrary two-dimensional stress fields. A new general mathematical form of point load weight function has been formulated by taking advantage of the knowledge of a few specific weight functions for two-dimensional planar cracks available in the literature and certain properties of the weight function in general. The existence of the generalized form of the weight function simplifies the determination of a specific weight function for specific crack configurations. The determination of a specific weight function is reduced to the determination of the parameters of the generalized weight function expression. These unknown parameters can be determined from reference stress intensity factor solutions. This method is used to derive the weight functions for semi-elliptical surface cracks in finite thickness plates. The derived weight functions are then validated against stress intensity factor solutions for several linear and non-linear two-dimensional stress distributions. The derived weight functions are particularly useful for the fatigue crack growth analysis of planar surface cracks subjected to fluctuating nonlinear stress fields resulting from surface treatment (shot peening), stress concentration, or welding (residual stress)

On XFEM Applications to Crack Surface under External Force

The extended finite element method is applied to modeling growth of arbitrary crack with crack surface tractions. Firstly, the extended finite element method is investigated for the stress intensity factor solution of surface traction problems. Secondly, for different water pressure acting on the crack surfaces and different crack length, the variation of the stress intensity factors is investigated. Finally, the process of hydraulic fracturing is simulated with the method. Numerical simulations illustrate that the method can effectively model the fracture problems with surface tractions.

Dynamic fracture analysis of a smoothly inhomogeneous plane containing defects by BEM

In this work, the dynamic interaction between defects of different types such as cracks and cavities in a smoothly inhomogeneous, elastic anisotropic plane subjected to incident SH-waves is investigated.Solution of the ensuing boundary-value problem is numerically realized using the non-hypersingular, traction boundary element method (BEM). By employing a special functional transform, the wave equation for inhomogeneous media is reduced to one with constant coefficients and the relevant frequency-dependent fundamental solution for graded anisotropic continua is obtained by the Radon transform. All surface discretizations are then done by standard collocation procedure with a parabolic type of approximation of all field variables. Next, validation of the numerical method is carried out through comparisons with available solutions for crack stress intensity factors (SIFs) and for cavity stress concentration factors (SCF).A detailed parametric study is then undertaken for a circular cavity interacting with a stationary, mode III crack in the presence of a propagating SH-wave. In sum, the key parameters of the simulation study are the characteristics of the incident wave, the geometry and configuration of the defects, the material inhomogeneity, and the dynamic interaction between the defects. The influence of all these key parameters on the dynamic SIF and SCF for different defects is finally discussed.

OS0830 応力拡大係数解に求められる評価精度に関する検討

OS0830 応力拡大係数解に求められる評価精度に関する検討

Multiple Fatigue Crack Growth Prediction Using Stress Intensity Factor Solutions Modified by Empirical Interaction Factors

It is generally believed that multiple fatigue crack growth prediction is difficult with the use of conventional stress intensity factor (SIF) solution calculations because of issues such as SIF magnification and shielding effects. Therefore, almost all the existing Fitness for Service (FFS) rules such as the ASME Code Section XI and JSME Code adopt the procedure whereby multiple cracks grow independently after applying a certain alignment rule based on the initial crack configuration and are combined immediately into an enveloping crack when the crack tips touch. In some cases, the results of the procedures in the existing FFS rules are less accurate in predictions of the service life of cracked components. Therefore, there is still room for improvement, although the procedures are simple for utilities. This paper describes a new approach to predict fatigue crack growth life of multiple nonaligned cracks by the use of SIF solutions modified by empirical interaction factors. Several examples of two nonaligned cracks illustrate the accuracy and effectiveness of the procedure by comparison with numerical analysis by the body force method for two-dimensional problems and with the experimental results given in the literature for three-dimensional problems.

Geometric functions of stress intensity factor solutions for spot welds in cross-tension specimens

Stress intensity factor solutions for spot welds in cross-tension specimens are investigated by finite element analyses. Three-dimensional finite element models are developed to obtain accurate solutions. Various ratios of sheet thickness, half specimen width and half effective specimen length to nugget radius are considered. The computational results confirm the functional dependence on the nugget radius and sheet thickness of Zhang’s analytical solutions. The results also provide three geometric functions in terms of normalized half specimen width and normalized half effective specimen length to Zhang’s analytical solutions. Based on the analytical and computational results, the dimensions of cross-tension specimens and the corresponding approximate stress intensity factor solutions are suggested.

Fracture dynamics problems of mode I semi-infinite crack for anisotropic orthotropic body

By means of the theory of complex functions, fracture dynamics problems of mode I semi- infinite crack for anisotropic orthotropic body were researched. Analytical solutions of stress, displacement, and dynamic stress intensity factor under the action of moving increasing loads Px3/t3, Pt4/x3, respectively, are very easily obtained utilizing the approaches of self-similar functions. In the light of relevant material’s coefficients, the alterable rule of dynamic stress intensity factor was depicted very well. The correlative closed solutions are attained based on the Riemann–Hilbert problems. After those analytical solutions were applied by the superposition principle, the solutions of discretional complex problems could be attained.

Subcritical dyke propagation in a host rock with temperature-dependent viscoelastic properties

SUMMARY In this paper, we examine the effects of temperature-dependent viscoelastic properties of the host rock on the subcritical growth of a dyke from a magma chamber. A theoretical relationship between the velocity of subcritical dyke growth and dyke length is established using a perturbation solution of stress intensity factor at the dyke tip and a viscoelastic crack growth theory in which the temperature-dependent creep properties are taken into account. The temperature field around the dyke is calculated using an analytic solution. The numerical results for a dyke subcritically propagating from a magma chamber indicate that while the general dyke growth characteristics are similar to those with constant creep properties, the subcritical dyke growth velocity is increased by an order of magnitude by considering the temperature dependence of the creep properties. Hence, the subcritical growth duration before the dyke reaches the unstable growth state is significantly shortened.

A method for stress intensity factor calculation of infinite plate containing multiple hole-edge cracks

Multiple site damage is the occurrence of small fatigue cracks at several sites within aging aircraft structures. Focusing on this typical structure, an analytical method for calculating the stress intensity factor of an infinite plate containing multiple hole-edge cracks was introduced in this paper. The properties of complex variable functions are used to evaluate the stress function. The approximate superposition method is applied to solve stress intensity factor problems on multiple holes. The equivalent crack is introduced to modify the method. Some numerical examples of an infinite plate containing two hole-edge cracks are examined by the method. By comparing the analytical and finite element analysis results it was realized that the analytical results are accurate and reliable. This modified analytical method is easier to apply than some traditional analytical methods and can provide stress intensity factor solutions for an infinite plate containing a random distribution of multiple hole-edge cracks.

Solution of stress intensity factors of multiple cracks in plane elasticity with eigen COD formulation of boundary integral equation

The concept of eigen crack opening displacement (COD) can be defined as the COD of a crack in infinite plate under the tractions acting on the crack surface. By introducing this concept, the eigen COD formulation of boundary integral equation is proposed in this paper, together with the solution procedures for multiple crack problems in plane elasticity. With the proposed approach, the multiple crack problems can be solved with the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix as that in the numerical Green’s function (NGF) approach but without the trouble to determine the complementary solutions since the standard boundary element discretization on the crack surface is no longer required with the proposed approach. Some numerical examples computing the stress intensity factors are presented and compared with those in literature to show the accuracy and the effectiveness of the proposed approach.

Stress Intensity Factor Solution for Cracks at an Offset Loaded Fastener Hole

Stress intensity factors were obtained for radial and diametrical cracks at an offset (noncentered) loaded fastener hole. The new closed-form solution was derived by superposing and compounding several stress intensity factor solutions, including a new key stress intensity factor solution developed for cracks in a finite plate with in-plane bending loads. The accuracy of the new closed-form solutions was verified for various configurations against results found in the literature as well as finite element analysis results. Nomenclature = half crack length from tip-to-tip = length of crack i from the edge of the hole to the tip = distance between the edge and the center of the crack = edge distance of the hole = bearing to bypass stress ratio (

노즐 이종금속용접부의 내면 보수용접부에서 수치해석법을 이용한 PWSCC 균열성장해석

In this paper, crack propagation analyses in the inner diameter (ID) repair weld of the dissimilar metal weldment of a nozzle were performed using a finite element alternating method (FEAM). To calculate the theoretical solution for the crack tip stress intensity factor, a weak type singular integral equation consisted of crack surface traction and dislocation density function was constructed and solved in conjunction with the FEAM. A two-dimensional axisymmetric finite element nozzle model was prepared and ID repair welding was simulated. An initial crack, 10% depth of weld thickness, was assumed and crack propagation trajectory from the initial crack to the 75% depth of thickness was calculated using the FEAM. Crack growth versus time curve was also calculated and compared with the curves obtained from ASME code method. With the method constructed in this paper, crack propagation trajectory and crack growth time were calculated automatically and effectively.

General analytical solution for stress intensity factor of a hypocycloid hole with many cusps in an infinite plate

In this article, the problem for the determination of the displacement functions and the stress intensity factors (SIFs) around a boundary of a hypocycloid hole with cusps in an infinite elastic plate subject to normal and shear stresses are presented. A hole with cusps (hypocycloid) is mapped onto a unit circle and the modified complex potential is used for solving the relevant boundary value problems. An analytical solution for the SIF of a hypocycloid hole is obtained. For a special case, our results agree with others.

Critical stress intensity factors in steel cracked wires

In the conceptual framework of fracture mechanics analyses, the study of cracked wires axially loaded has the highest interest since numerous structural elements (e.g. wires, cables, cordons or tendons) work under such a type of loading during their service lives. So, a method that allows the determination of stress states at the crack front should be welcome as a useful way for ensuring the structural integrity of those components for different environmental conditions (air, stress corrosion cracking, hydrogen embrittlement,…). To fill this gap, an engineering estimation of the critical stress intensity factor (SIF) is proposed in this paper for eutectoid steel cracked wires under axial loading. The critical SIF is calculated by considering, apart from the fatigue precrack, the subcritical crack propagation before final fracture. Such a subcritical crack propagation is the process zone (by micro-void coalescence MVC) in the case of fracture in air, the subcritical cracking by localized anodic dissolution (LAD) in stress corrosion cracking (SCC) and the tearing topography surface (TTS) in hydrogen assisted cracking (HAC). In addition, different SIF solutions are used in the analysis so as to have a more complete picture of the different phenomena leading to failure and to provide the designer with sound scientific tools. This method allows the engineer to design in the framework of structural integrity and damage tolerance.

Life prediction of titanium and aluminum alloys under fretting fatigue conditions using various crack propagation criteria. Part 2. Application of the technique to cylindrical specimens with semi-elliptical crack and account of the residual stresses

In order to simulate the operating fretting-fatigue conditions in cylindrical structural components, we have performed experimental studies on fretting fatigue of cylindrical specimens with clamped concave cylindrical pads of bridge type. Using the known solutions for stress intensity factors in the semi-elliptical cracks growing in cylindrical specimens, we predict the kinetics of propagation of fretting-fatigue cracks according to the two-parameter model described in Part 1. A close correlation of calculated and experimental fretting-fatigue life values is observed for AMg6N alloy for varied experimental fretting conditions (contact load, slip amplitude and friction coefficient). For alloy VT9 we have provided approbation of the technique, which takes into account distribution of the residual stresses in the material subsurface during calculation of stress-strain state and life under fretting-fatigue conditions.

Stress intensity factor solutions for estimation of fatigue lives of laser welds in lap-shear specimens

Fatigue behavior of laser welds in lap-shear specimens of high strength low alloy (HSLA) steel is investigated based on experimental observations and two fatigue life estimation models. Fatigue experiments of laser welded lap-shear specimens are first reviewed. Analytical stress intensity factor solutions for laser welded lap-shear specimens based on the beam bending theory are derived and compared with the analytical solutions for two semi-infinite solids with connection. Finite element analyses of laser welded lap-shear specimens with different weld widths were also conducted to obtain the stress intensity factor solutions. Approximate closed-form stress intensity factor solutions based on the results of the finite element analyses in combination with the analytical solutions based on the beam bending theory and Westergaard stress function for a full range of the normalized weld widths are developed for future engineering applications. Next, finite element analyses for laser welded lap-shear specimens with three weld widths were conducted to obtain the local stress intensity factor solutions for kinked cracks as functions of the kink length. The computational results indicate that the kinked cracks are under dominant mode I loading conditions and the normalized local stress intensity factor solutions can be used in combination with the global stress intensity factor solutions to estimate fatigue lives of laser welds with the weld width as small as the sheet thickness. The global stress intensity factor solutions and the local stress intensity factor solutions for vanishing and finite kinked cracks are then adopted in a fatigue crack growth model to estimate the fatigue lives of the laser welds. Also, a structural stress model based on the beam bending theory is adopted to estimate the fatigue lives of the welds. The fatigue life estimations based on the kinked fatigue crack growth model agree well with the experimental results whereas the fatigue life estimations based on the structural stress model agree with the experimental results under larger load ranges but are higher than the experimental results under smaller load ranges.

Investigation on Mixed Mode Stress Intensity Factors for Inclined Surface Crack in Finite-Thickness Plates and Parameters Influence

In this paper, mixed mode stress intensity factor (SIF) solutions are computed for inclined surface cracks in finite-thickness plates. The S-version finite element method (S-FEM), which is an adaptive method and multi-scale computing method, are employed in the analyses. When S-FEM is applied to solve the fracture problem, local mesh model including cracks can be built independently from the global mesh model for modeling overall structure. The local model is superposed on the g- lobal one. Therefore, it is easy to introduce cracks in an existing mesh model. The influences of inc- lination angles, crack shape and plate thickness on the mixed mode fracture solution were investiga- ted. The solutions presented can be used to assess fail/safe conditions and fatigue crack growth for the three-dimensional cracks studied.

Developments in the Treatment of Residual Stresses in Welded Components

A long-term UK research programme on environmentally assisted cracking (EAC), residual stresses [1, 2] and fracture mechanics [3, 4] was launched in 2004. It involves Rolls-Royce plc and Serco Technical Services, supported by UK industry and academia. The residual stress programme is aimed at progressing the understanding of residual stresses and on the basis of this understanding manage how residual stresses affect the structural integrity of plant components. Improved guidance being developed for the treatment of residual stresses in fracture assessments includes the use of stress intensity factor solutions for displacement controlled loading as opposed to the more commonly used load controlled solutions. Potential reductions in crack driving force are also being investigated in relation to (i) utilizing a residual stress field that has “shaken-down” due to operational loads, (ii) introducing a crack progressively as opposed to instantaneously, and (iii) allowing for the fact that a crack may have been initiated during the life of a component as opposed to being present from the start-of-life. This paper describes some of these latest developments in relation to residual stress effects

The mode III cracks emanating from an elliptical hole in the piezo-electro-magneto-elastic materials

The mode III crack problem in a medium possessing coupled electro-magneto-elastic is considered. Two asymmetrical edge cracks emanate from an elliptical hole. Combined stress, electric and magnetic loads are considered. The elliptical hole and cracks are assumed to be either magneto-electrically impermeable or permeable. The closed-form solution for stress, electric and magnetic intensity factors are derived explicitly. Also the solution for energy release rate is given in closed form. The solution is based on the complex variable method combined with the method of conformal mapping. Numerical computations are given to illustrate the effect of variable geometrical and material parameters on stress, electric and magnetic intensity factors and energy release rate.

Dynamic Propagation of Mode Ⅲ Interfacial Crack Subjected to Variable Moving Concentrated Loads

Dynamic propagation of mode Ⅲ crack under variable moving loads on the crack surface is investigated using the theory of complex functions. Using the approaches of self-similar functions, the problems are readily transformed into Riemann-Hilbert problems. The paper presents a new mechanical model for dynamic crack propagation, in which the crack is under the conditions that the variable concentrated loads Pt3/x2 and Px/t move along x-axial with velocity β. At last, analytical solutions of stress, displacement and stress intensity factor are attained, respectively.