Error estimation for the finite element evaluation of and in mixed-mode linear elastic fracture mechanics

2005 ◽  
Vol 41 (11-12) ◽  
pp. 1079-1104 ◽  
Author(s):  
E. Giner ◽  
F.J. Fuenmayor ◽  
L. Baeza ◽  
J.E. Tarancón
1991 ◽  
Vol 44 (10) ◽  
pp. 447-461 ◽  
Author(s):  
Leslie Banks-Sills

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.


1987 ◽  
Vol 109 (3) ◽  
pp. 282-289 ◽  
Author(s):  
D. K. Shetty

Increasing use of ceramics in structural applications has led to the development of a probabilistic design methodology that combines three elements: linear elastic fracture mechanics theory that relates strengths of ceramics to size, shape, and orientation of critical flaws, a characteristic flaw size distribution function that accounts for the size effect on strength via the weakest-link concept, and a time-dependent strength caused by subcritical crack growth or other mechanisms. This paper reviews recent research that has been focused on the first of the above three elements, the investigation of fracture criteria for arbitrarily oriented flaws in ceramics, i.e., the mixed-mode fracture problem in linear elastic fracture mechanics theory. Experimental results obtained with two-dimensional through cracks and three-dimensional surface (indentation) cracks are summarized and compared to mixed-mode fracture criteria. The effects of material microstructure and the stress state on mixed-mode fractures are discussed. The application of mixed-mode fracture criteria in reliability analysis is illustrated for several simple stress states in the absence of time-dependent strength degradation.


Author(s):  
Scott Keller

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.


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