Reference Stress Intensity Factors Research Articles

Calculation of stress intensity factors for semielliptical cracks in a thick-wall cylinder

Weight functions for the surface and the deepest point of an internal semielliptical crack in a thick-wall cylinder were derived from a general weight function and two reference stress intensity factors. For several linear and nonlinear crack face stress fields, the weight functions were validated against finite element data. Stress intensity factors were also calculated for the Lamé through the thickness stress distribution induced by internal pressure. The weight functions appear to be particularly suitable for fatigue and fracture analysis of surface semielliptical cracks in complex stress fields. All stress intensity factor expressions given in the paper are valid for cylinders with an inner radius to wall thickness ratio, R i t = 4 .

Evaluation of stress intensity factors by multiple reference state weight function approach

The advantages of expressing stress intensity factors in terms of weight functions are widely appreciated. However, the main obstacle in the determination of weight functions has been the definition of the crack opening displacement (COD) field. There are several approaches currently used, the most common is assuming an expression to define COD in terms of the crack dimensions and stress state. A recent development in weight function application simplifies the tranditional stress intensity factor calculation. This development uses more than one reference stress intensity factor and associated stress field to eliminate the need to assume a COD field. This paper describes current application of COD for weight functions and explains the full advantage of adopting a multiple reference state (MRS) weight function approach.

Approximate weight function technique using single-layer potential for a cracked circular disc

An efficient weight function technique using the indirect boundary integral method was presented for cracked circular discs. The crack opening displacement field was presented by a single layer whose kernel was a modified form of the fundamental solution in elastostatics. The application of a single-layer potential to the weight function method leads to a unique closed-form SIF (stress intensity factor) solution. The solution can be applied to a cracked circular discs with or without an internal hole or opening. For these crack geometries over a wide range of crack ratios, the SIF solution can be applied without any modification.The calculation procedure of SIFs for the various cracked circular discs using only one analytical solution is very simple and straightforward. The information necessary in the analysis includes only two or three reference load cases. In most cases the SIF solution using two reference SIFs gives reasonably accurate results while the SIF solution with three reference load cases may be used to improve the solution accuracy of the crack configurations, with an internal opening or hole, compared with the solutions of the available literature.

Weight functions and stress intensity factors for mode I cracks in arbitrary 2D geometries under general crack surface loading

Stress intensity factors for Mode I cracks in arbitrary two-dimensional geometries under general crack surface loading are derived in closed form by boundary element calculations and approximate weight functions. The boundary element method was developed previously to deal with arbitrary two-dimensional crack problems involving uniform crack surface pressure. Reference stress intensity factors calculated by the boundary element method are used to derive stress intensity factors for the same crack under arbitrary crack surface loading with weight functions based on an improved Petroski-Achenbach crack surface displacement approximation. Various crack problems are studied and limitations of the method are discussed. The investigation shows that a self-consistency examination will effectively reveal the accuracy of the derived weight functions and the associated stress intensity factors.

A procedure for the determination of the weight function for semi-elliptical surface cracks by direct adjustment to reference solutions

A procedure is described that allows one to determine averaged weight functions by a direct adjustment to reference stress intensity factor solutions. In contrast to well known methods based on a nearly complete COD description, the proposed evaluation only requires the local stress intensity factors of reference loading cases to be known. A two-term weight function based on constant stress as the reference loading case and on the continuity of the weight function is compared with a three-term solution based on the bending load case as an additional reference solution.

Closure on discussion by D. Munz and T. Fett on “Determination of weight functions from reference stress intensity factors”

Closure on discussion by D. Munz and T. Fett on “Determination of weight functions from reference stress intensity factors”

Discussion: “Determination of weight functions from reference stress intensity factors”, by G. Shen and G. Glinka

Discussion: “Determination of weight functions from reference stress intensity factors”, by G. Shen and G. Glinka

Weight function method for mixed-mode loading and mixed boundary conditions

A simplified weight function technique for mixed-mode loading and mixed boundary value problems is proposed based on the concept of energy release rate. The Betti reciprocal theorem and superposition theorem are used in derivation of the weight function formula. The proposed new formula needs only the knowledge of crack line loading and the reference stress intensity factors, K 1 and k 2 . The method is easy to understand and to use.

Direct determination of weight functions from reference loading cases and geometrical conditions

A procedure is discussed that allows the determination of weight functions from a number of known reference stress intensity factors and two geometrical conditions, namely vanishing second and third derivatives of the weight function ( h'' = h''' = 0) at the crack mouth. The procedure is outlined in detail for an edge-cracked circular disc. A convergence consideration is included. Additionally, weight functions are determined for the central crack in a circular disc and the edge crack and central crack in a rectangular plate.

Determination of weight functions from reference stress intensity factors

A method of deriving weight functions for cracks subjected to mode I loading is discussed. The method requires two reference stress intensity factors to be known. The general weight function expression and its characteristic properties are used as the complementary information necessary for the determination of the unknown weight function parameters. Several weight functions derived by this method are compared to exact analytical weight functions available in the literature. Differences are less than 2%.

Weight function for the surface point of semi-elliptical surface crack in a finite thickness plate

The weight function for the surface point of a semi-elliptical crack in a plate of finite thickness has been derived and tested against numerical data available in the literature. Derivation was accomplished by using the universal weight function form and two reference stress intensity factors. It was found that a four term expression was sufficient to approximate weight functions for a variety of crack shapes and depths. Using this approach it was possible to calculate stress intensity factors for several nonlinear stress fields to an accuracy of better than 3% when compared with the finite element data.

Universal features of weight functions for cracks in mode I

An analysis of known analytical and numerical weight functions for cracks in mode I has revealed that they all have a similar singular term and that it is possible to approximate them with one universal expression with three unknown parameters. The unknown parameters can be determined directly from reference stress intensity factor expressions without using the crack opening displacement function. The universal weight function expression, with suitable reference stress intensity factors, was used to derive the weight functions for internal and external radial cracks in a thick cylinder. These weight functions were then further used to calculate the stress intensity factors for radial cracks in a cylinder subjected to several nonlinear stress fields and were compared to available numerical data.

Conditions for the determination of approximate COD fields

The procedure of determining approximate weight functions is based on the knowledge of approximate crack opening displacements for an arbitrarily chosen reference load case. The construction of the approximate crack opening displacement field is possible if the reference stress intensity factor is available and additional conditions are known. Numerous geometrical conditions as well as equilibrium conditions can be derived. In this investigation a selection of conditions is given. As an example, CODs and weight functions are determined for a plate of finite length.

Approximate weight function for 2D and 3D-problems

The weight function method is an important procedure to determine stress intensity factors for complex stress distributions. This approach is based on the knowledge of the crack opening displacement field for a reference load case. The approximate analytical determination of the crack opening field from the reference stress intensity factor is outlined in detail. In the absence of a reference solution the FE-method is used in some special applications. The general treatment is illustrated by a number of examples, which have been obtained by the authors in the last years.

Finite element investigation of creep crack growth from surface thumbnail cracks

The finite element method is used to predict creep crack growth from an initially semi-elliptical surface crack. Empirical correlations are used in conjunction with calculated fracture parameters and predictions are compared with results from a parallel experimental program. The material investigated is 316 stainless steel at 600°C. The reference stress and stress intensity factor produced poor results. The C ∗ contour integral gave a good prediction for crack growth, when a primary creep constitutive equation was used to model the behaviour. This model was the most appropriate for the nominal stresses and duration of the test.

On the “limitations of the Petroski-Achenbach crack opening displacement approximation for the calculation of weight function” — Do they really exist?

The limitations of the Petroski Achenbach crack opening displacement approximation discussed by F. Görner, C. Mattheck and P. Morawietz ( Engineering Fracture Mechanics, 22, 269 277 (1985)) have been re-analysed. It is shown that the Petroski-Achenbach crack opening displacement function can be determined from any reference stress intensity factor contrary to the conclusion drawn by Görner et al. Thus, the method does not need to be limited only to the cases where the reference stress intensity factors for the homogeneously distributed reference stresses are known.

Approximate WF Solution For Part-throughMode I Cracks

A generalised approximate weight function solution (WF) is presented for two-dimensional (2D) mode I part-elliptical crack subjected to arbitrary crack surface pressure. The WFs are derived from one or several reference stress intensity factors (SIFs) and the corresponding crack surface pressures. This procedure enables SIF computations for general crack surface pressures as function of both the crack size and the location along the crack front. The procedure has been shown to be rather effective and efficient in solving complex problems compared to various available numerical methods.