Three-dimensional Fatigue Crack Propagation Research Articles

An X-FEM based framework for 3D fatigue crack growth using a B-spline crack geometry description

This paper presents an X-FEM based iterative framework for numerical simulation of three-dimensional fatigue crack propagation. To accurately describe the crack geometry, B-spline curves and surfaces are used for the crack front and faces respectively. A new crack front extension method based on the Möller–Trumbore algorithm is introduced to achieve fully automated crack growth for complex geometries. To validate the presented work, three different cases are discussed: (1) compact tension specimens with an asymmetrically located hole, (2) a beam with a slanted crack subjected to a three-point bending load and (3) a beam with a slanted crack subjected to a torsion load. Good agreement between the numerical and experimental results is observed.

Three-dimensional fatigue crack propagation by means of first order SIF approximation

In this paper we make use of a closed-form solution for mode I Stress Intensity Factors (SIF) in three-dimensional planar flaws based on homotopy transformations of a disc. The utilised equations are very accurate when the flaw is a small deviation from a circle. Under the hypothesis of an isolated crack, the SIF at each point of the crack border is calculated to assess the crack shape after propagation. The solution is proposed in terms of the Fourier series and the crack growth rate equation is taken according to Paris’ low. Many examples are proposed with the aim of predicting the final shape of different types of embedded planar flaws in butt welded joints under fatigue tensile loading.

Three-dimensional fatigue crack propagation analysis of welded steel beam based on global-local numerical model

The existing fatigue assessment approaches were mainly conducted on the component level. The interaction of local component damage and the global response cannot be well addressed. In this study, three-dimensional (3D) fatigue crack propagation analysis approach based on global-local numerical model was implemented, and examined to be accurate and effective through a series of systematic experimental data obtained by Fisher. Afterwards, the approach was introduced into a typical steel truss bridge for realizing more refined fatigue assessment from the global structural level. The fatigue performance of the longitudinal steel welded beam in the steel truss bridge was investigated based on global-local model and local model respectively. It was found that there is no difference in terms of the fatigue crack growth mechanism between the simulation between global-local model and local model due to that the stress level of the whole structure is relatively low. At last, the effect of heavy haul train operation on the fatigue performance of the steel truss bridge was analyzed. It was observed that the residual life of the longitudinal steel welded beam would have an obvious reduction when the axle load was increasing. The research work in this study presents a technical solution for the fatigue assessment of the global structure and can provide beneficial reference for relevant practical engineering projects.

Three-dimensional fatigue crack propagation simulation using extended finite element methods for steel grades S355 and S690 considering mean stress effects

The assessment of fatigue crack propagation of steel structures is essential and important especially to improve the application of high strength steel in construction. The load ratio R, reflecting mean stress effects, will be changed with crack extension in the steel structures with complicated geometry. In this paper, the Walker equation is employed to fit the fatigue crack propagation rate of steel grades S355 and S690 based on experimental data in the literature to incorporate the mean stress effects. The material fatigue crack propagation parameters with 95%, 97.7%, and 99% guarantee of Walker equation were obtained by a stochastic analysis using the Monte Carlo method. The fatigue life was firstly predicted by the analytical method and was used as a baseline for numerical fatigue crack propagation simulation. A user-defined fatigue crack propagation subroutine based on the Walker equation was developed using phantom nodes-based extended finite element method (PN-XFEM) and Virtual Crack Closure Technique (VCCT) to consider the mean stress effects. The proposed three-dimensional fatigue crack propagation simulation subroutine is successfully validated of both steel grades, S355 and S690.

Three-dimensional fatigue crack growth simulation of embedded cracks using s-version FEM

PurposeSince the most of structures and structural components suffers from cyclic loadings, the study on the fatigue failure due to the crack growth has a great importance. The purpose of this paper is to present a three-dimensional fatigue crack growth simulation of embedded cracks using s-version finite element method (SFEM). Using the numerical results, the validity of the fitness-for-service (FFS) code evaluation method is verified.Design/methodology/approachIn this paper, three-dimensional fatigue crack propagation analysis of embedded cracks is performed using the SFEM. SFEM is a numerical analysis method in which the shape of the structure is represented by a global mesh, and cracks are modeled by local meshes independently. The independent global and local meshes are superimposed to obtain the displacement solution of the problem simultaneously.FindingsThe fatigue crack growth of arbitrary shape of cracks is slow compared to that of the simplified circular crack and the crack approximated based on the FFS code of the Japan Society of Mechanical Engineers (JSME). The results tell us that the FFS code of JSME can provide a conservative evaluation of the fatigue crack growth and the residual life time.Originality/valueThis paper presents a three-dimensional fatigue crack growth simulation of embedded cracks using SFEM. Using this method, it is possible to apply mixed mode loads to complex shaped cracks that are closer to realistic conditions.

Applications on Three-Dimensional Mixed Mode Fatigue Crack Propagation Using Fracture and Crack Propagation Analysis System (FCPAS)

In this study, results from two applications on three-dimensional fatigue crack propagation using the in-house developed “Fracture and Crack Propagation Analysis System (FCPAS)” are presented. FCPAS uses finite element models to calculate three-dimensional mixed mode stress intensity factors and other sub-modules to predict shapes of the incrementally growing crack fronts and the resulting fatigue crack propagation lives. The evolving crack surfaces are generated by successively adding the incremental growth surfaces and re-meshing and re-solving the finite element model using the standalone program FRAC3D, a finite element-based standalone program employing three-dimensional enriched finite elements. The results show that the fracture surfaces evolve into a mode-I type three-dimensional crack as expected. Very good agreements are obtained between the results of the current studies and those of numerical applications in terms of both evolving crack surfaces and crack propagation lives. Therefore, it is concluded that the applied method is capable of accurately predicting linear elastic three-dimensional mixed mode fatigue crack propagation problems.

Simulation of three-dimensional fatigue crack propagation using enriched finite elements

A three-dimensional methodology for simulation of fatigue crack propagation is presented. The method is leveraged by the use of enriched crack tip elements to compute the mixed-mode stress intensity factors. The crack growth model used and the crack propagation life calculation are also described. As examples, fatigue crack propagation of a mode-I surface crack and crack advancements of mixed-mode surface cracks are simulated. The predicted results showed excellent agreement with experimental data from the literature. Thus, it is concluded that the crack propagation method developed allows efficient and accurate simulation of three-dimensional fatigue crack propagation problems.

Three-Dimensional Characterization of Fatigue Crack Propagation Behavior in an Aluminum Alloy Using High Resolution X-Ray Microtomography

Synchrotron X-ray microtomography was used to investigate the three-dimensional fatigue crack propagation behavior of an aluminum alloy. Local crack growth rates along specimen thickness were calculated. Crack observation revealed that crack propagation was retarded in three regions where there exist overlapping crack segments. Crack growth retardation was found to occur in these crack overlapping regions due to stress shielding. Observation of crack propagation process indicated that one of the overlapping crack segments initiated from the twisted crack. Crack tip opening displacement was measured and it was found that crack opening was larger in single planar crack region than that in crack overlapping region.

Comparison of Experimental and Numerically Simulated Fatigue Crack Propagation

The objective of this study is to present a methodology that can properly simulate three-dimensional fatigue crack propagation with consideration of the crack closure effect. To simulate fatigue crack growth in three-dimensional elastic structures, the superposition finite element method (S-FEM) is employed. A local model is used to represent the near crack area to overcome difficulties that appear in the process of re-meshing the FE model during crack propagation; therefore, many complex crack geometries that may be generated under mixed mode conditions can be easily modeled. Considering the plasticity-induced crack closure effect, elastic-plastic analysis was first conducted to study the behavior of the crack closure effect along the crack tip. Normalized crack opening level along the direction of thickness was obtained and applied to simulations. Experiments on single edge notch specimens under Mode I, Mode I+II or Mode I+II+III loading conditions were conducted to verify the method. Experimental results related to crack growth direction, crack shape and fatigue life were compared with simulation results. Better predictions on crack path were shown. Significant improvement of crack shape evolution in the simulation model was obtained considering the crack closure effect.

Predictions of Propagation Behavior of Slant Corner Fatigue Cracks in Residual Stress Fields Based on Simulations of the Partial Elastic Contact of Crack Surfaces

In residual stress fields, the so-called partial elastic contact of crack surfaces sometimes occurs, where a fatigue crack is closed at the crack mouth while it is open at crack tip. The partial elastic contact has significant effect on the lives of fatigue cracks. However there are few studies on the partial elastic contact of crack surfaces for three-dimensional cracks. In this paper, the propagation paths and lives of slant corner fatigue cracks are predicted by using three-dimensional fatigue crack propagation simulations considering the partial elastic contact of crack surfaces. The finite element method was employed for the simulations. The crack propagation rates obtained by simulations considering the partial elastic contact of crack surfaces differed from those without considering the contact, demonstrating the necessity of simulation considering the partial elastic contact of crack surfaces. However the propagation paths and crack shapes estimated considering the partial elastic contact hardly differed from those without the consideration.

き裂面部分弾性接触を考慮した有限要素伝ぱシミュレーションによる三次元斜めき裂の疲労寿命と伝ぱ経路の予測法(GS11 破壊・き裂進展・じん性評価)

In residual stress fields, sometimes the so-called partial elastic contact of crack surfaces occurs, where fatigue crack is closed at the crack mouth while it is open at crack tip. The partial elastic contact has significant effect on lives of fatigue cracks. However there are few studies on the partial elastic contact of crack surfaces for three-dimensional cracks. In this paper, the propagation paths and lives of fatigue cracks were predicted by using three-dimensional fatigue crack propagation simulations considering the partial elastic contact of crack surfaces. The finite element method was employed for these simulations. The results of simulations considering the partial elastic contact of crack surfaces differed from those neglecting the contact, demonstrating the necessity of simulation considering the partial elastic contact of crack surfaces.

303 三次元き裂のき裂面部分弾性接触を考慮に入れた疲労き裂伝ぱ挙動の予測(GS-4 疲労・クリープ)

303 三次元き裂のき裂面部分弾性接触を考慮に入れた疲労き裂伝ぱ挙動の予測(GS-4 疲労・クリープ)

Extended finite element method and fast marching method for three-dimensional fatigue crack propagation

A numerical technique for planar three-dimensional fatigue crack growth simulations is proposed. The new technique couples the extended finite element method (X-FEM) to the fast marching method (FMM). In the X-FEM, a discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity. This enables the domain to be modeled by finite elements with no explicit meshing of the crack surfaces. The initial crack geometry is represented by level set functions, and subsequently signed distance functions are used to compute the enrichment functions that appear in the displacement-based finite element approximation. The FMM in conjunction with the Paris crack growth law is used to advance the crack front. Stress intensity factors for planar three-dimensional cracks are computed, and fatigue crack growth simulations for planar cracks are presented. Good agreement between the numerical results and theory is realized.

Some Improvements of the Fast Marching Method

The fast marching method published by Sethian [Proc. Natl. Acad. Sci. USA, 93 (1996), pp. 1591--1595] is an optimally efficient algorithm for solving problems of front evolution where the front speed is monotonic. It has been used in a wide variety of applications such as robotic path planning [R. Kimmel and J. Sethian, Fast Marching Methods for Computing Distance Maps and Shortest Paths, Tech. Report 669, CPAM, University of California, Berkeley, 1996], crack propagation [M. Stolarska et al., Modelling crack growth by level sets in the extended finite element method, Comput. Methods Appl. Mech. Engrg., to appear; Internat. J. Numer. Methods Engrg., 51 (2001), pp. 943--960; N. Sukumar, D. L. Chopp, and B. Moran, Extended finite element method and fast marching method for three-dimensional fatigue crack propagation, J. Comput. Phys., submitted], seismology [J. Sethian and A. Popovici, Geophysics, 64 (1999), pp. 516--523], photolithography [J. Sethian, Fast marching level set methods for three-dimensional photolithography development, in Proceedings of the SPIE 1996 International Symposium on Microlithography, Santa Clara, CA, 1996], and medical imaging [R. Malladi and J. Sethian, Proc. Natl. Acad. Sci. USA, 93 (1996), pp. 9389--9392]. It has also been a valuable tool for the implementation of modern level set methods where it is used to efficiently compute the distance to the front and/or an extended velocity function. In this paper, we improve upon the second order fast marching method of Sethian [SIAM Rev., 41 (1999), pp. 199--235] by constructing a second order approximation of the interface generated from local data on the mesh. The data is interpolated on a single box of the mesh using a bicubic approximation. The distance to the front is then calculated by using a variant of Newton's method to solve both the level curve equation and the orthogonality condition for the nearest point to a given node. The result is a second order approximation of the distance to the interface which can then be used to produce second order accurate initial conditions for the fast marching method and a third order fast marching method.

Experimental observations and numerical predictions of three-dimensional fatigue crack propagation

Experimental observations of three-dimensional fatigue crack growth are compared to numerical predictions from three computer codes. For simple geometries contained in standard libraries of some codes, restricting numerically predicted crack shapes to elliptical quadrants does not adversely affect crack growth rate predictions. However, this approach is limited by the availability of pre-existing solutions. Furthermore, elliptical quadrants are not always representative of true crack shape. More general modeling capabilities allow accurate geometric representation of both the base specimen and the crack front shape for a wide range of configurations. This capability allows reasonable and/or conservative fatigue crack growth predictions for many cases not handled by geometric libraries. However, the more general modeling capability does not lead to improved fatigue life predictions for simple geometries. Further research is necessary to improve fatigue life prediction capabilities for complex geometries.

Three-dimensional fatigue crack propagation analysis using the boundary element method

The boundary element method and interactive computer graphics together make possible the analysis of general, three-dimensional linear elastic crack propagation. A program called the Fracture Editor has been developed for this purpose. The pre-processing, post-processing and fracture prediction capabilities of this program make up a general purpose fracture propagation processor. The function of the Fracture Editor is described in detail. These functions include file management, fracture propagation prediction, automatic crack front updating, interactive remeshing, attribute editing, mesh inspection, and post-processing of results. An example problem, fatigue crack propagation in a crane runway girder, is included. Predictions concerning crack front shape and size as a function of number of cycles of applied load are made with the Fracture Editor.