 | This article only references primary sources.(January 2023) |
Barsoum elements is a finite element analysis technique used in fracture analysis to determine the stress intensity factor of a crack. It was introduced by R. Barsoum in 1976. [1]
| This article only references primary sources.(January 2023) |
Barsoum elements is a finite element analysis technique used in fracture analysis to determine the stress intensity factor of a crack. It was introduced by R. Barsoum in 1976. [1]
In this method, the usual isoparametric 6 node triangular or 8 node isoparametric quadrilateral elements are employed. The mid side nodes on 2 adjacent sides are shifted towards the corner node to the quarter point location. For these locations of the mid nodes, the Jacobian becomes singular at the corner node thus making displacement derivatives infinite and stresses and strains become infinite as well. It can be shown that the variation of stresses along the 2 sides of the elements is according to 1/√r.
On the other hand, if all the three nodes on the side of an 8 node quadrilateral element are collapsed to one node (given the same node number) then the stress or strain varies as 1/√r along any radial line emanating from crack tip. All the mid side nodes adjacent to the crack tip are at quarter point locations. From the displacement field solution the stress intensity factor K1 in a mode 1 case can be calculated as per the following relation:
where VB and VC are the displacement in the y direction behind the crack tip.
It has been demonstrated that K1 found by this method is within 2% of theoretical solutions. Accuracy of finite element calculation can be improved if the neighboring elements are also modeled to have the terms depicting the stresses for a crack with its tip outside the element.
Structural analysis is a branch of solid mechanics which uses simplified models for solids like bars, beams and shells for engineering decision making. Its main objective is to determine the effect of loads on the physical structures and their components. In contrast to theory of elasticity, the models used in structure analysis are often differential equations in one spatial variable. Structures subject to this type of analysis include all that must withstand loads, such as buildings, bridges, aircraft and ships. Structural analysis uses ideas from applied mechanics, materials science and applied mathematics to compute a structure's deformations, internal forces, stresses, support reactions, velocity, accelerations, and stability. The results of the analysis are used to verify a structure's fitness for use, often precluding physical tests. Structural analysis is thus a key part of the engineering design of structures.
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Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture.
In fracture mechanics, the stress intensity factor is used to predict the stress state near the tip of a crack or notch caused by a remote load or residual stresses. It is a theoretical construct usually applied to a homogeneous, linear elastic material and is useful for providing a failure criterion for brittle materials, and is a critical technique in the discipline of damage tolerance. The concept can also be applied to materials that exhibit small-scale yielding at a crack tip.
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Crack tip opening displacement (CTOD) or is the distance between the opposite faces of a crack tip at the 90° intercept position. The position behind the crack tip at which the distance is measured is arbitrary but commonly used is the point where two 45° lines, starting at the crack tip, intersect the crack faces. The parameter is used in fracture mechanics to characterize the loading on a crack and can be related to other crack tip loading parameters such as the stress intensity factor and the elastic-plastic J-integral.
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A crack growth equation is used for calculating the size of a fatigue crack growing from cyclic loads. The growth of fatigue cracks can result in catastrophic failure, particularly in the case of aircraft. A crack growth equation can be used to ensure safety, both in the design phase and during operation, by predicting the size of cracks. In critical structure, loads can be recorded and used to predict the size of cracks to ensure maintenance or retirement occurs prior to any of the cracks failing.
