Linear elastic fracture mechanics

2020 ◽  
pp. 485-505
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Stress Intensity ◽  
Fracture Mechanics ◽  
Critical Stress Intensity Factor ◽  
Linear Elastic Fracture Mechanics ◽  
Small Scale ◽  
Mode Iii ◽  
Linear Elastic ◽  
Elastic Crack ◽  
Scale Yielding ◽  
Elastic Fracture

This chapter introduces the basics of linear elastic fracture mechanics. It starts by recalling the asymptotic elastic crack tip solutions and the concept of stress intensity factors for Mode-I, Mode-II, and Mode-III loading. The concept of critical stress intensity factor is next introduced as a model for fracture under small scale yielding conditions. In this context the limits of linear elastic facture mechanics are discussed. Further, methods and requirements for fracture toughness testing are discussed.

Generalized Linear Elastic Fracture Mechanics: An Application to a Crack Touching the Bimaterial Interface

2010 ◽  
Vol 452-453 ◽  
pp. 445-448 ◽  
Author(s):  
Luboš Náhlík ◽  
Lucie Šestáková ◽  
Pavel Hutař ◽  
Zdeněk Knésl
Keyword(s):  
Fracture Mechanics ◽  
Composite Structures ◽  
Particulate Composite ◽  
Linear Elastic Fracture Mechanics ◽  
Bimaterial Interface ◽  
Small Scale ◽  
Layered Composites ◽  
Linear Elastic ◽  
Scale Yielding ◽  
Elastic Fracture

In the contribution the limits of the validity of classical linear elastic fracture mechanics are extended to problems connected with failure of composite structures. The work is focused mainly on the case of a crack touching the interface between two different materials, two different constituents. The approach suggested in the paper facilitates the answer to the question what is the influence of particle (in particulate composite) or layer (in laminates) on crack propagation through bimaterial interface. Different composite (bimaterial) structures are considered: layered composites and composites reinforced by particles. The presented approach follows the basic idea of linear elastic fracture mechanics, i.e. the validity of small scale yielding conditions is assumed, and has a phenomenological character.

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.

scholarly journals On the evaluation of the stress intensity factor in calving models using linear elastic fracture mechanics

2018 ◽  
Vol 64 (247) ◽  
pp. 759-770 ◽  
Author(s):  
STEPHEN JIMÉNEZ ◽  
RAVINDRA DUDDU
Keyword(s):  
Stress Intensity ◽  
Fracture Mechanics ◽  
Boundary Conditions ◽  
Edge Crack ◽  
Correlation Method ◽  
Linear Elastic Fracture Mechanics ◽  
Weight Functions ◽  
Ice Shelves ◽  
Linear Elastic ◽  
Elastic Fracture

ABSTRACTWe investigate the appropriateness of calving or crevasse models from the literature using linear elastic fracture mechanics (LEFM). To this end, we compare LEFM model-predicted stress intensity factors (SIFs) against numerically computed SIFs using the displacement correlation method in conjunction with the finite element method. We present several benchmark simulations wherein we calculate the SIF at the tips of water-filled surface and basal crevasses penetrating through rectangular ice slabs under different boundary conditions, including grounded and floating conditions. Our simulation results indicate that the basal boundary condition significantly influences the SIF at the crevasse tips. We find that the existing calving models using LEFM are not generally accurate for evaluating SIFs in grounded glaciers or floating ice shelves. We also illustrate that using the ‘single edge crack’ weight function in the LEFM formulations may be appropriate for predicting calving from floating ice shelves, owing to the low fracture toughness of ice; whereas, using the ‘double edge crack’ or ‘central through crack’ weight functions is more appropriate for predicting calving from grounded glaciers. To conclude, we recommend using the displacement correlation method for SIF evaluation in real glaciers and ice shelves with complex geometries and boundary conditions.

Fracture Mechanics Assessment of Hydrogen Storage Vessel

2021 ◽  
Author(s):  
Xiaoliang Jia ◽  
Zhiwei Chen ◽  
Fang Ji
Keyword(s):  
High Pressure ◽  
Fracture Mechanics ◽  
Hydrogen Storage ◽  
High Strength Steel ◽  
High Strength ◽  
Linear Elastic Fracture Mechanics ◽  
Storage Vessel ◽  
Linear Elastic ◽  
Elastic Fracture ◽  
Hydrogen Storage Vessel

Abstract High strength steel is usually used in fabrication of hydrogen storage vessel. The fracture toughness of high strength steel will be decreased and the crack sensitivity of the structures will be increased when high strength steels are applied in hydrogen environment with high pressure. Hence, the small cracks on the surface of pressure vessel may grow rapidly then lead to rupture. Therefore, this paper makes a series of research on how to evaluate the 4130X steel hydrogen storage vessel with fracture mechanics. This study is based on the assumption that there is a semi-elliptic crack on internal surface of hydrogen storage vessel. First of all, based on linear elastic fracture mechanics, the stress intensity factors and crack tolerance of 4130X steel hydrogen storage vessel have been calculated by means of finite element method based on interaction integral theory and polynomial-approximated approach from GB/T 34019 Ultra-high pressure vessels. Then, a comparative study has been made from the results of above methods to find out the difference between them. At last, the fatigue life of a 4130X steel hydrogen storage vessel has been predicted based on linear elastic fracture mechanics and Paris formula. The calculation methods and analysis conclusion can be used to direct the design and manufacture of hydrogen storage vessel.

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