Analysis of Elliptical Cracks in Static and in Fatigue by Hybridization of Green's Functions (original) (raw)

Computation of stress intensity factor in cracked plates under bending in static and fatigue by a hybrid method

International Journal of Fatigue, 2007

A hybrid weight-function technique is presented. It consists of dividing an elliptical crack into two zones, then using the appropriate weight function in the area where it is more efficient. The proportion between zones is determined by optimizing two crack parameters (axis ratio and curvature radius). Stress intensity factors for plates containing elliptical and semi-elliptical cracks are hence computed by a self developed computer code. Static and fatigue loadings of bending are considered. The results found by the present approach are in good correlation with the analytical solutions (when available) as well as with those of other researchers.

Fatigue growth of embedded elliptical cracks using Paris-type law in a hybrid weight function approach

Comptes Rendus Mécanique, 2008

A hybrid weight function method (HWFM), improving the calculation of the stress intensity factor (SIF) in mode I, has recently been proposed and validated in the static case [B.K. Hachi, S. Rechak, M. Haboussi, M. Taghite, Modélisation des fissures elliptiques internes par hybridation de fonctions de poids, C. R. Mecanique 334 (2006) 83-90]. In the present Note, the hybridization approach is presented for the fatigue crack growth prediction of embedded elliptical crack in infinite bodies. Hence, Paris's law of crack propagation is incorporated into the developed hybridization-based computer code, along with two degrees of freedom technique for managing the crack evolution and the cracked structure fatigue life. Simulations of the evolution of elliptical cracks (in infinite bodies) of different configurations (ellipse axes ratio, maximum crack advance) corresponding to fatigue and brittle fracture have been conducted. Comparisons with other numerical methods such as the classical weight function method (WFM) or the extended finite element methods (X-FEM) show the pertinence of the HWFM in the treatment of an aspect of fatigue cracking problems. To cite this article:

A new method for analysis of part-elliptical surface cracks in structures subjected to fatigue loading

Theoretical and Applied Fracture Mechanics, 2019

This paper presents a new analytical method for the analysis of fatigue growth of surface cracks in various structural components. The method is based on a governing equation describing the front evolution of surface cracks of elliptical and part-elliptical shapes. This method avoids the need for various numerical schemes for the calculation of the incremental crack front advance, which were used in all previous studies. Plasticity-induced crack closure models can also be incorporated into the method or these models can be deducted from a correlation of experimental data and the method predictions. When the plastic constraint conditions change significantly along the crack front, the implementation of the plasticity induced crack closure models can significantly improve the accuracy of fatigue life predictions. The method is validated against previous theoretical and experimental studies.

Fatigue growth prediction of elliptical cracks in welded joint structure: Hybrid and energy density approach

Theoretical and Applied Fracture Mechanics, 2010

A hybrid weight function approach (HWFM) is presented for the fatigue life prediction of infinite body and welded joint structure containing elliptical cracks. A self-containing computer code has been developed for this purpose. Numerical computations were first conducted on cracked infinite body showing a physical fact, that the elliptical shape of the crack becomes circular during its evolution. The prediction of the fatigue crack growth shows that the present results are in perfect concordance with those reported in the literature. Then, numerical tests were carried out on two types of specimens of welded joint structure. The present results were compared to the experimental and predicted ones of other authors, demonstrating that the hybridization method is a powerful numerical technique, and that the SEDF approach (using the Sih's law) is more valid for the critical cases of welded joints than the SIF approach (using the Paris law). A parametric study has been conducted on the stress ratio ''R" showing that the fatigue life to failure decreases with the increase of ''R".

Modelling of elliptical cracks in an infinite body and in a pressurized cylinder by a hybrid weight function approach

International Journal of Pressure Vessels and Piping, 2005

In this work, a hybridization technique is proposed. It consists of using two weight functions to model elliptical cracks for computation of the stress intensity factor 'SIF' in mode I. The idea of hybridization consists of dividing the ellipse into two zones, then to use each weight function in the area where it is more efficient. The proportion between the two zones is determined by optimization of the ellipse axis ratio. A computer code is developed for the computation of SIF. The treatment of the numerical procedures including singularities are presented in detail. The approach is tested on several applications (elliptical crack in infinite body, semi-elliptical cracks in thin and thick cylinders), to demonstrate its accuracy by minimization of the error of SIF and its correlation with respect to other researchers.

Calculation of fatigue growth of internal cracks

Nuclear Engineering and Design, 1977

A method for analysis of internal cracks using finite elements is presented. The analysis is based on the potential energy release rate which is determined as a function of the crack shape. For an elliptic crack subjected to a cyclical loading the crack-growth is found by integrating the energy release rates associated with incremental extensions of the half axes. As examples, internal elliptical cracks located centricaUy and eccentrically in a thick plate are analyzed. The plate is modelled by 20-node isopara.metric solid elements. A condensation of degrees of freedom is performed so that only the freedoms necessary for defining the geometry of the growing crack are retained. Elliptic shapes with only one axis of symmetry are allowed to develop. The potential energy is calculated for different crack shapes and a least square smoothing technique is used for finding the energy release rates associated with growth of the half axes of the ellipse. The results obtained for a centric crack are compared with analytical expressions for a through centercrack and for an elliptic crack in an infinite body under uniaxial tension. In general good agreement between the different methods is observed. The energy release rates are integrated according to Paris's crack growth formula, and the geometry of the growing crack is visualized by plots of the crack periphery for prescribed numbers of load cycles.

Analytical and experimental studies on fatigue crack path under complex multi-axial loading

Fatigue <html_ent glyph="@amp;" ascii="&amp;"/> Fracture of Engineering Materials and Structures, 2006

In real engineering components and structures, many accidental failures are due to unexpected or additional loadings, such as additional bending or torsion, etc. Fractographical analyses of the failure surface and the crack orientation are helpful for identifying the effects of the non-proportional multi-axial loading. There are many factors that influence fatigue crack paths. This paper studies the effects of multi-axial loading path on the crack path. Two kinds of materials were studied and compared in this paper: AISI 303 stainless steel and 42CrMo4 steel. Experiments were conducted in a biaxial testing machine INSTRON 8800. Six different biaxial loading paths were selected and applied in the tests to observe the effects of multi-axial loading paths on the additional hardening, fatigue life and the crack propagation orientation. Fractographic analyses of the plane orientations of crack initiation and propagation were carried out by optical microscope and SEM approaches. It was shown that the two materials studied had different crack orientations under the same loading path, due to their different cyclic plasticity behaviour and different sensitivity to non-proportional loading. Theoretical predictions of the damage plane were made using the critical plane approaches such as the Brown-Miller, the Findley, the Wang-Brown, the Fatemi-Socie, the Smith-Watson-Topper and the Liu's criteria. Comparisons of the predicted orientation of the damage plane with the experimental observations show that the critical plane models give satisfactory predictions for the orientations of early crack growth of the 42CrMo4 steel, but less accurate predictions were obtained for the AISI 303 stainless steel. This observation appears to show that the applicability of the fatigue models is dependent on the material type and multi-axial microstructure characteristics.

On the Modeling of Load Interaction Effects on Curved Fatigue Cracks

A hybrid global-local methodology to predict fatigue crack propagation in 2D structures is extended to model crack retardation effects induced by variable-amplitude (VA) loading histories. First, finite element (FE) models are used at each propagation step to calculate the generally curved fatigue crack path. However, the FE approach alone is not computationally efficient to predict crack growth rate, because it would require time-consuming remeshing of the entire structure after each event in VA loading. Therefore, the crack path and their mixed-mode stress intensity factors are FE calculated under constant-amplitude (CA) loading using fixed crack increments, requiring only relatively few remeshing steps. An analytical expression is then fitted to the calculated K I values, which is used in a local-approach fatigue design program to predict crack propagation lives under VA loading, considering load interaction effects such as crack retardation or arrest after overloads. This methodology is experimentally validated by fatigue crack growth tests on compact tension C(T) specimens, modified with holes positioned to attract or to deflect the fatigue cracks. Experiments under VA loading are also performed on C(T) specimens without holes. Several crack retardation models are calibrated based on straight-crack data. These models are then used to successfully predict the curved crack growth behavior under VA loading of the hole-modified specimens.