G. Glinka

Universal features of weight functions for cracks in mode I

Abstract 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.

Critical parameters for fatigue damage

Abstract The fatigue damage analysis is examined from a historical perspective. The analysis indicates that some of the issues concerning the basic disparities between the experiment and model/interpretations. To help understand these issues, we have developed an approach with two driving force parameters to analyze the fatigue behavior. Such an approach helps in viewing the damage in terms of an intrinsic problem rather than an extrinsic one. In the final analysis one needs to unify the overall damage processes such that the description is complete from the crack initiation stage to short crack to long crack to final failure. In order to unify the damage process, three basic parameters are introduced for describing the overall fatigue process. These are Δ K , K max and internal stress contribution to K max . In addition, there are other effects from environment and temperature that can contribute to these parameters. In particular K max seems to play an important role in the overall damage process. We find that the internal stress is the missing link that can bridge the gap between the four main stages of damage that lies between the crack nucleation stage to final failure. Examples are sited in support of this view of explanation. Finally, it is suggested that systematic experimental data and analytical modeling to describe the internal stress gradients is required to help in forming a reliable life prediction methodology.

Calculation of stress intensity factors by efficient integration of weight functions

Abstract A numerical technique for simple and efficient integration of weight functions is presented. The method enables the stress intensity factors to be calculated with the aid of a hand calculator for any non-linear stress distribution normal to the crack surfaces. The proposed integration routine is validated against accurate numerical and analytical solutions.

Elastic-plastic stress-strain calculation in notched bodies subjected to non-proportional loading

An analytical method for calculating notch tip stresses and strains in elastic-plastic isotropic bodies subjected to non-proportional loading sequences is presented. The key elements of the two proposed models are generalized relationships between elastic and elastic-plastic strain energy densities, and the material constitutive relations. These two models form the lower and the upper limits of the actual energy densities at the notch tip. Each method consists of a set of seven linear algebraic relations that can easily be solved for elastic-plastic strain and stress increments, knowing the hypothetical notch tip elastic stress history and the material stress-strain curve. Results of the validation show that the proposed methods compare well with finite element data and each solution set forms the limits of a band within which actual notch tip strains fall.

Weight functions and stress intensity factors for internal surface semi-elliptical crack in thick-walled cylinder

Abstract Calculation of stress intensity factors for a crack subjected to a complex stress distribution can be highly facilitated by using the weight function method. The method separates influences of a stress field and the geometry of a cracked body on a stress intensity factor. In this paper, mode I weight functions were derived for the deepest and surface points of an internal, radial-longitudinal, surface, semi-elliptical crack in an open-ended, thick-walled cylinder with internal radius to wall thickness ratio R i / t = 2.0. Generalized weight function expressions for deepest and surface points of the crack were utilized. A method of two reference stress intensity factors was applied to determine coefficients of the weight functions. The weight functions were validated for several crack face stress fields against finite element data. Closed-form relations for calculation of stress intensity factors were obtained for a variety of one-dimensional stress distributions applied to crack faces. The paper complements a set of previously published weight function solutions for cracks in cylinders with other radius to thickness ratios.

Approximate weight functions for embedded elliptical cracks

Abstract An approximate weight function for embedded elliptical cracks was deduced from the properties of weight functions and available analytical weight functions for penny shape and half plane cracks. The weight function was then validated against available exact stress intensity factor solutions for embedded elliptical cracks for several linear and non-linear stress distributions. The proposed weight function is suitable for the calculation of stress intensity factors for embedded elliptical cracks under any stress distribution.

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

Abstract 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.

Weight functions for edge and surface semi-elliptical cracks in flat plates and plates with corners

Abstract A family of weight functions for edge and semi-elliptical surface cracks in flat plates and angular corners is presented in the paper. The weight functions were derived using the Bueckner-Rice definition of weight function and the Petroski-Achenbach crack opening displacement expression. A method of deriving the closed form weight functions is presented together with a discussion on the basic assumptions and limitations. The accuracy of all weight functions was examined with respect to available stress intensity factor data.

Stress intensity factors and weight functions for a corner crack in a finite thickness plate

Weight functions for the two surface points of a quarter-elliptical corner crack in a finite thickness plate of infinite width are derived from a general weight function and two reference stress intensity factors. The weight functions have been validated for several linear and non-linear crack face stress fields against finite element data. The weight functions appear to be particularly suitable for fatigue and fracture analysis of quarter-elliptical cracks in complex stress fields.

Weight functions and stress intensity factors for corner quarter-elliptical crack in finite thickness plate subjected to in-plane loading

Abstract Approximate weight functions for the profile and frontal plane crack front points of a corner quarter-elliptical crack in finite thickness plate, subjected to mode I, in-plane loading, were derived by using the method of universal weight functions by Shen and Glinka (Engineering Fracture Mechanics, 1991, 40, 1135–1146; Theoretical and Applied Fracture Mechanics, 1991, 15, 247–255.) Closed form expressions were obtained for the coefficients of the weight functions. The coefficients were derived from the reference stress intensity factor solutions obtained by Shiratori and Miyoshi (Stress Intensity Factors Handbook, Vol. 3, ed. Murakami et al. Pergamon, New York, 1992, pp. 591–597.) using the finite element method. A comparison of the stress intensity factors calculated using the weight functions with the finite element data for various applied stress distributions shows good accuracy of the present results.