scholarly journals A Phantom-Node Method with Edge-Based Strain Smoothing for Linear Elastic Fracture Mechanics

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
N. Vu-Bac ◽  
H. Nguyen-Xuan ◽  
L. Chen ◽  
C. K. Lee ◽  
G. Zi ◽  
...  
Keyword(s):  
Finite Element ◽  
Fracture Mechanics ◽  
Numerical Procedure ◽  
Linear Elastic Fracture Mechanics ◽  
Explicit Finite Element ◽  
Linear Elastic ◽  
Strain Smoothing ◽  
Elastic Fracture ◽  
Edge Based ◽  
Phantom Node Method

This paper presents a novel numerical procedure based on the combination of an edge-based smoothed finite element (ES-FEM) with a phantom-node method for 2D linear elastic fracture mechanics. In the standard phantom-node method, the cracks are formulated by adding phantom nodes, and the cracked element is replaced by two new superimposed elements. This approach is quite simple to implement into existing explicit finite element programs. The shape functions associated with discontinuous elements are similar to those of the standard finite elements, which leads to certain simplification with implementing in the existing codes. The phantom-node method allows modeling discontinuities at an arbitrary location in the mesh. The ES-FEM model owns a close-to-exact stiffness that is much softer than lower-order finite element methods (FEM). Taking advantage of both the ES-FEM and the phantom-node method, we introduce an edge-based strain smoothing technique for the phantom-node method. Numerical results show that the proposed method achieves high accuracy compared with the extended finite element method (XFEM) and other reference solutions.

Application of the Finite Element Method to Linear Elastic Fracture Mechanics

1991 ◽  
Vol 44 (10) ◽  
pp. 447-461 ◽  
Author(s):  
Leslie Banks-Sills
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
Fracture Mechanics ◽  
Displacement Field ◽  
Three Dimensional ◽  
Linear Elastic Fracture Mechanics ◽  
The Finite Element Method ◽  
Linear Elastic ◽  
Elastic Fracture

Use of the finite element method to treat two and three-dimensional linear elastic fracture mechanics problems is becoming common place. In general, the behavior of the displacement field in ordinary elements is at most quadratic or cubic, so that the stress field is at most linear or quadratic. On the other hand, the stresses in the neighborhood of a crack tip in a linear elastic material have been shown to be square root singular. Hence, the problem begins by properly modeling the stresses in the region adjacent to the crack tip with finite elements. To this end, quarter-point, singular, isoparametric elements may be employed; these will be discussed in detail. After that difficulty has been overcome, the stress intensity factor must be extracted from either the stress or displacement field or by an energy based method. Three methods are described here: displacement extrapolation, the stiffness derivative and the area and volume J-integrals. Special attention will be given to the virtual crack extension which is employed by the latter two methods. A methodology for calculating stress intensity factors in two and three-dimensional bodies will be recommended.

A Practical Approach to Implementing Linear Elastic Fracture Mechanics in Gas Turbine Rotor Disk Analyses

2015 ◽  
Author(s):  
Scott Keller
Keyword(s):  
Finite Element ◽  
Fracture Mechanics ◽  
Gas Turbine ◽  
Crack Growth ◽  
Turbine Rotor ◽  
Linear Elastic Fracture Mechanics ◽  
Linear Elastic ◽  
Rotor Disk ◽  
Elastic Fracture ◽  
Growth Analyses

The failure of vital components is not uncommon in the gas turbine industry. In the event excessive degradation occurs within a component, e.g. extensive cracking in a turbine blade or vane, solutions exist to either repair or replace defective parts. Such parts are readily accessible and mostly exchangeable in the field, limiting the amount of outage time and assessment required for defective parts. When more critical components exhibit extreme wear or cracking, e.g. a crack in a rotor disk, repairs typically necessitate a complete rotor destack and refurbishment or have the potential to require the replacement of individual disks. In extreme cases, defects found in rotor disks can be known to retire an entire compressor or turbine rotor. The OEM solution of replacing disks puts a substantial cost on the customer, thus providing an incentive for characterization and advanced analyses to determine the residual life in critical rotating components. Considered an advanced analysis, linear elastic fracture mechanics (LEFM) provides the theory and fundamental structure to conduct crack growth analyses in components that exhibit nominally elastic behavior. Successful implementation of LEFM requires extensive characterization of the material, engine operating boundary conditions, and high fidelity finite element models. Upon the detection of a flaw, whether an internal or external indication, the results from finite element analyses can be used to derive the crack tip stress field and subsequent crack tip driving parameters. These parameters are then utilized in a comprehensive crack propagation model, calibrated to temperature- and load-dependent material data, to determine the number of cycles to unstable propagation. As a result, the remaining life of a component with a given indication is readily obtained, enabling our engineering team to provide a thorough life assessment of critical rotating components. An overview of the linear elastic fracture mechanics crack growth analyses conducted is presented, with a special emphasis on compressor and turbine disks.

scholarly journals Discrete and Phase Field Methods for Linear Elastic Fracture Mechanics: A Comparative Study and State-of-the-Art Review

2019 ◽  
Vol 9 (12) ◽  
pp. 2436 ◽  
Author(s):  
Adrian Egger ◽  
Udit Pillai ◽  
Konstantinos Agathos ◽  
Emmanouil Kakouris ◽  
Eleni Chatzi ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Phase Field ◽  
Linear Elastic Fracture Mechanics ◽  
Field Methods ◽  
Linear Elastic ◽  
Elastic Fracture ◽  
Phase Field Methods ◽  
Element Method

Three alternative approaches, namely the extended/generalized finite element method (XFEM/GFEM), the scaled boundary finite element method (SBFEM) and phase field methods, are surveyed and compared in the context of linear elastic fracture mechanics (LEFM). The purpose of the study is to provide a critical literature review, emphasizing on the mathematical, conceptual and implementation particularities that lead to the specific advantages and disadvantages of each method, as well as to offer numerical examples that help illustrate these features.

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