Three-dimensional Fracture Mechanics Analysis Research Articles

A super crack front element for three-dimensional fracture mechanics analysis

A super crack front element containing a part of a curved crack front is established to solve the stress intensity factors of three-dimensional curved cracks by using the numerical series eigen-solutions. The element can be directly incorporated into the existing three-dimensional linear brick elements without using transition elements. The intensity of singular stress fields is determined as the system unknowns appearing as nodal displacement values. Numerical studies are conducted to demonstrate the simplicity and effectiveness of the proposed technique in handling typical three-dimensional fracture problems of curved cracks. It is proved that the super crack front element can avoid mesh refinement near the crack front domain without loss of calculation accuracy and velocity of convergence, and can be used to deal with interfacial and anisotropic fracture problems directly.

A new numerical modelling for evaluating the stress intensity factors in 3-D fracture analysis

As an improvement on the isoparametric element method, the derivation presented in this paper is close to that done by Wang (1990) for the 2-D finite element. We extend this idea to solve 3-D crack problems in this paper. A new displacement modelling is constructed with local solutions of three-dimensional cracks and a quasi-compatible isoparametric element for three-dimensional fracture mechanics analysis is presented. The stress intensity factors can be solved directly by means of the present method without any post-processing. A new method for calculating the stress intensity factors of three-dimensional cracks with complex geometries and loads is obtained. Numerical examples are given to demonstrate the validity of the present method. The accuracy of the results obtained by the proposed element is demonstrated by solving several crack problems. The results illustrate that this method not only saves much calculating time but also increases the accuracy of solutions. Because this quasi-compatible finite element of 3-D cracks contains any singularities and easily meets the requirement of compatibility, it can be easily implemented and incorporated into existing finite element codes.

2710 回転自由度を有する四面体要素を用いた三次元破壊力学解析(OS27.一般セッション(1),ポスターセッションP-4)

2710 回転自由度を有する四面体要素を用いた三次元破壊力学解析(OS27.一般セッション(1),ポスターセッションP-4)

A singular element for three-dimensional fracture mechanics analysis

In this article, a singular boundary element for three-dimensional fracture mechanics analysis is presented. It is a nine-node quadratic element with plane geometry. These nodes are located at one quarter of the distance between two opposite sides of the element. Shape functions with a 11 √r singularity at the crack front are used to represent the tractions. The Stress Intensity Factors are computed as system unknowns appearing (except for a constant) as traction nodal values. Special attention is paid to the development of a simple and accurate integration approach for this singular element. The accuracy of the results obtained with the proposed element is demonstrated by solving several crack problems including edge and embedded cracks with different geometries. The element can be easily implemented and incorporated into existing quadratic boundary element codes. In a companion paper the element is formulated and used for fracture mechanics problems in transversely isotropic materials. Extension to other fields for which boundary element formulations exist, is quite simple.

Dual boundary element method for three-dimensional fracture mechanics analysis

In this paper, an effective numerical implementation of the three-dimensional dual boundary element method, for linear elastic crack problems, is presented. Displacement and traction integral equations which constitute the dual boundary formulation are used independently on crack surfaces to overcome the numerical difficulties associated with co-planar crack surfaces in boundary element analysis. The crack surfaces are modelled with discontinous quadrilateral quadratic elements. The use of discontinous elements allow for accurate integration of finite part integrals. The accuracy of the proposed method is demonstrated by solving a number of problems including edge and embedded cracks.

Surface integral and finite element hybrid method for two- and three-dimensional fracture mechanics analysis

This paper summarizes the development of the surface integral and finite element hybrid method for two and three dimensional fracture mechanics analysis. The fracture, which is a discontinuity in the displacement field, is modeled explicitly and efficiently by use of dislocations for two dimensional analysis and by dipoles of point forces for three dimensional applications. The boundary value problem of a fracture in a finite domain is solved by (incremental) superposition of a finite element model of the finite body without the crack and a surface integral model of an infinite body with the crack, ensuring proper traction and displacement matching at the boundaries. Finite elements are also used to model nonhomogeneity and plasticity, though isotropic kernels are used for the integral equation. A variety of two and three dimensional problems have been modeled and excellent agreement with analytical solutions has been obtained. Propagation problems in two dimensions have also been modeled and the predicted results agree very well with experimental observations.