Mixed-mode Stress Intensity Factors Research Articles

Long wavelength impact of izod fracture specimens: An experimental/numerical investigation

Elastic wave propagation fields for a stationary crack in an Izod fracture specimen have been investigated. Moire interferometry was used to obtain the asymptotic cracktip displacement fields under Hopkinson bar loading at sampling rates on the order of 100 kHz. Mixed-mode stress-intensity factors as a function of time were extracted from the displacement data using local asymptotic extrapolation. Two-dimensional continuum finite elements were employed and agreement was found between actual experiment and two-dimensional computation.

A study of the stress intensity factors for single or multiple cracks in thick-walled cylinders

The variation of stress intensity factors of a single semi-elliptical crack and multiple semi-elliptical cracks which are radial symmetric or unsymmetric array in an internal pressurized thick-walled cylinder is studied by use of the “frozen-stress” photo-elastic method. The method of determining mixed-mode stress intensity factors K I and K II is given. By means of experimental results and the relative results of other authors, the approximate expression for evaluating stress intensity factors of straight border, semi-circular, semi-elliptical internal surface cracks in thick-walled cylinders are presented.

Propagation of Semi-Elliptical Surface Cracks in Lubricated Rolling/Sliding Elliptical Contacts

In this paper the three-dimensional mixed mode stress intensity factors for semi-elliptical inclined cracks formed on elliptical Hertzian contact surfaces are calculated. This analysis accounts for both the frictional forces between the contact surfaces and between the crack faces, as well as including fluid pressure acting on the crack faces. Various factors affecting the crack growth are discussed and possible growth modes are investigated. In particular, the analytical results predict that the crack has a faster growth rate when the major axis of the contact ellipse is in the direction of motion of the load as compared to the minor axis being in the direction of motion of the load.

Mixed-mode stress intensity factors for three-point bending bars

Mixed-mode stress intensity factors for three-point bending bars

Interaction between parallel edge cracks

In this paper, experimental results for the interaction between two parallel edge cracks are presented. Two cases are considered. In the first, the cracks have equal lengths, while in the second, the two cracks have different lengths. The experimental method of reflected caustics is used. Mixed mode stress intensity factors are obtained and the results are compared to values obtained from using the numerical discontinuity method. The experimental and numerical results are in good agreement. Thin strips made of plexiglas containing two edge slits subjected to tension are studied. The extent of the three dimensional region of the crack tip stress field is investigated.

Stress Intensity Factors for Various Configurations of Axially Cracked Cylinders. (Proposal of an Approach Based on Matrix Method).

In this paper, a simple procedure based on the matrix method of structural analysis is proposed to estimate the stress intensity factors for various configurations of axially cracked cylinders. General formulation using matrix expression is presented at first. Then, this formulation is reformed by using the hoop stress in the uncracked configuration for the convenience of numerical ca1culations and analytical considerations. Proposed method enables us to estimate not only the mixed-mode stress intensity factors but also the J-integral for quite various configurations of axially cracked cylinders, and obtained results show good agreement with numerical data in the literature for a number of cracked configurations. In addition, explicit formulation in this study enables us to easily know the characteristic features of axially cracked cylinders ; the dependence of internal forces and K-values on mean radius, wall thickness, crack length, and the number of cracks.

Photoelastic investigation of mixed-mode fracture parameters with full-field selected line method

The mixed-mode SIF (stress intensity factor) and other fracture parameters, such as additional non-singular terms in the algorithm, for bending specimens with biased straight cracks and 60° inclined edge cracks have been measured using a full-field selected line method, which may simplify calculations and improve data analysis. The modified Westergaard expressions derived from only stress symmetry have been provided to increase the accuracy of measurements and amplify the data analysis region.

Higher-order forms of caustics in mixed-mode fracture

An improved method for evaluating the mixed-mode stress intensity factor (SIF) around a crack-tip is developed considering the first four terms of the Muskhelishvili complex potential. Since the present approach provides a better approximation of the caustics method engendered by large initial curves (LIC), it is suitable for problems of plasticity and elastic anisotropy.

Stress Intensity Factors for C-Shaped Specimens. Application of Statically Indeterminate Fracture Mechanics to Displacement-Controlled C-Shaped Specimens.

Stress intensity factors for load-controlled C-shaped specimens (LC-CSS) are discussed in some literatures, but those for displacement-controlled C-shaped specimens (DC-CSS), which are often used for environmental fracture toughness testing, are not. In this paper, an analytical procedure is shown by which to estimate mixed-mode stress intensity factors for DC-CSS with some internal and external axial cracks. The results obtained are summarized as follows : (1) Analytical results for LC-CSS show good agreement with the numerical data in the literature. (2) Mode II stress intensity factors are always negligible as compared to mode I stress intensity factors for commonly used thin-walled rings. (3) Explicit formulation of the stress intensity factors obtained in this paper is effective for both practical use and the discussion of influential parameters. (4) Several parameter studies for DC-CSS show that it is important for the analysis of such statically indeterminate structures to consider the variation of the system's compliance due to the presence of cracks.

Analysis of subsurface crack propagation and implications for wear of elastically deforming materials

Photoelastic methods are used to analyze the stress intensity factors and crack trajectories for subsurface cracks that are relevant to the process of wear particle generation. The specimen represents a half-plane with a shallow subsurface crack oriented parallel to the boundary. A concentrated load is applied to the boundary of the half-plane in close proximity to the crack tip. Three different series of experiments were conducted and results for the stress intensity factors for both the opening ( K I ) and shearing ( k II ) modes were determined. The mixed-mode stress intensity factors were combined to give the magnitude of an effective stress intensity factor which drives the subsurface crack. It was determined that the magnitude of K II was much smaller than K I . The relative signs of K i and K II , which depend on the location of crack tip with respect to the point of load application, were used to predict the crack trajectory.

Delamination Specimens for Orthotropic Materials

A semi-infinite crack in an infinite strip of orthotropic material is analyzed. Analytic expressions for mixed-mode stress intensity factors are derived with only parameter undetermined, which is then extracted from numerical solutions to integral equations. The results are relatively simple and complete, and provide the flexibility to simulate a wide range of practical problems, such as fracture specimens and edge delamination phenomena of woods and fiber-reinforced composites. As an illustration, specimens with transverse splitting from notches are analyzed based on the general solution. The validity of using solutions for an isotropic material to calibrate some testing geometries of orthotropic materials is discussed.

Determination of mixed-mode stress-intensity factors K I and K II for a subsurface crack near a concentrated force

Two-dimensional photoelastic experiments were conducted to obtain isochromatic fringe fields in the region between a crack tip and a concentrated load on the boundary of a half plane. An analysis method is developed to determine the mixed-mode stress-intensity factors due to two interacting stress singularities. The results obtained showed the dominance of the opening mode in extending a delamination crack by sliding surface loads.

Application of the [formula omitted] integral to mixed mode crack problems for anisotropic composite laminates

The J k integral method for determining mixed mode stress intensity factors separately in the cracked anisotropic plate is developed. Stress intensity factors are indirectly determined from the value of J 1 and J 2 . The J 2 integral can be evaluated efficiently from a finite element solution, neglecting the contribution from the portion of the integration contour along the crack faces, by selecting the integration contour in the vicinity of the crack tip. Using functions of a complex variable, the complete relations between J 1 , J 2 and K I , K II for anisotropic materials are derived conveniently by selecting narrow rectangular contours shrinking to the crack tip. Compared to the existing path independent integral methods, the present method does not involve calculating the auxiliary solution and hence numerical procedures become quite simple. Numerical results to various propblems are given and demonstrate the accuracy, stability and versatility of the method.

Experimental Analysis of KI KII Mixed Mode Stress Intensity Factors by Combination of Slab Analogy and Moire Measurement

Experimental Analysis of K<SUB>I</SUB> K<SUB>II</SUB> Mixed Mode Stress Intensity Factors by Combination of Slab Analogy and Moire Measurement

Elementary real path-dependent integrals for the accurate evaluation of stress intensity factors at a class of straight crack tips

A class of real, very elementary, path-dependent integrals on circular contours around a crack tip are constructed in an extremely elementary way. These integrals are associated with the sum of principal stresses, which is a harmonic function, and can be efficiently and accurately used for the determination of mode I, mode II and mixed-mode stress intensity factors in straight crack problems where the MacGregor-Westergaard complex potentials are applicable. The case of one straight crack is used for the illustration of the method (together with the trapezoidal quadrature rule) and very accurate (practically exact) numerical results for the stress intensity factors are displayed.

Bueckner weight functions for cracks near a half-plane

A Bueckner singular displacement field is incorporated into the boundary element formulation of half-plane in order to calculate weight functions for mixed-mode stress intensity factors in a two-dimensional cracked body. Weight functions for mode I and II are evaluated for a crack near a half-plane. The weight functions are used to determine the opening and sliding mode stress intensity factors which are shown to be in closed agreement with existing results.

The use of the dynamic J integral (J′) in finite-element simulation of mode I and mixed-mode dynamic crack propagation

This paper summarizes recent theoretical and computational studies on the dynamic J integrals ( J′) and the moving-finite-element procedures for the simulation of dynamic crack propagation. The following topics are included: (i) invariance of the elastodynamic J integral ( J′), with respect to the shape of an infinitesimal process zone, (ii) a component-separation method for determining the mixed-mode stress-intensity factors using the path-independent integrals J′ k ( k = 1,2), (iii) the moving-finite-element method aided by computerized symbolic manipulation, and (iv) a concept of an element-controlling plane based on Lagrangian-element mapping, for the simulation of dynamic crack-curving. Pertinent numerical results in each topic are also included.

Photoelastic determination of mixed-mode stress intensity factors for inclined semi-circular cracks in thin tubes

Metal shims have been used to produce internal and external, semicircular, surface, crack-like flaws in cast, photoelastic models of thin tubes. The effects of crack depth, crack orientation, crack inclination, and crack position (i.e., internal or external) have been determined from the analysis of results from 69 slices taken from 24 ‘crack’ types.It has been shown that by taking eleven terms in the solutions for the crack-tip stress fields, rather than taking only the singular solution, more accurate stress-intensity factors are obtained.

Fatigue Crack Growth Analyses of Offshore Structural Tubular Joint

Fracture mechanics fatigue life estimation procedures have been developed for offshore structural tubular joints through analyzing a K-joint under the North Sea environment. The objective of this study was to establish reliable procedures for estimating the remaining fatigue life of a tubular joint with cracklike defects. The analysis approach was the utilization of fracture mechanics methods for fatigue crack growth and failure analyses. In this study, the fully mixed mode stress intensity factors of weld toe surface flaws of the K-joint, which were calculated through detailed three-dimensional finite element analyses, were used for fatigue crack growth simulation. For the failure analyses, the failure assessment diagram method was used to predict the conditions for brittle fracture during fatigue crack propagation. The loading conditions considered in the analyses are the brace axial force, in and out-of-plane bending, and torsion.

Determination of mixed mode stress intensity factors for a crack-stiffened panel

A method of analysis to determine stress intensity factors under mixed mode loading of a crack-stiffened panel is presented. In the analysis the stiffeners are considered to have both longitudinal and transverse stiffnesses. Case studies are presented to illustrate the effectiveness of the method. The variation of the shear stresses at the adhesive-stiffener interface are presented. The influence of these shear stresses on stress intensity factor is included. A parametric study involving the patch location, patch length, shear modulus of the stiffener, shear modulus of adhesive and thickness of adhesive is reported. The stress intensity factors depend on all these factors. The shear stress acting perpendicular to the stiffener is comparable to the shear stress acting parallel to the stiffener. There is a location of the stiffener which is the most advantageous. This is close to the crack-tip on the side opposite the ligaments.