Crack stress intensity factor

A combination of the two cases for cylinders is used to derive a relation for the case of a surface crack in a sphere. Solutions were sought which cover the entire range of the geometrical parameters such as cylinder thickness, crack aspect ratio and crack depth. Both the internal and external position of the cracks are considered for cylinders and spheres. The finite element method was employed to obtain the basic solutions.

Power-law form of loading was applied in the case of flat plates and axial cracks in cylinders and uniform tension and bending loads were applied in the case of circumferential thumb-nail cracks in cylinders. In the case of axial cracks, the results for tensile and bending loads were used as reference solutions in a weight function scheme so that the stress intensity factors could be computed for arbitrary stress gradients in the thickness direction. For circumferential cracks, since the crack front is not straight, the above technique could not be used.

Hence for this case, only the tension and bending solutions are available at this time. Document ID. Document Type. Mettu, Sambi R. Lockheed Engineering and Management Services Co. Houston, TX United States. Raju, Ivatury S. Analytical Services and Materials, Inc. Since the stresses and displacements are linearly proportional to the stress intensity factor, it follows that the superposition principle also applies to crack problems.

This provides a very important tool for applying fracture mechanics to practical problems with the aid of handbooks. The underlying principle is that stresses induced by various loads can be added together.

It should be pointed that the superposition method applies only to cases where a structure is subjected to various loads but of the same mode. For example, the crack tip stresses for a cracked component under combined tension and bending are,. In general, the stress intensity factor for a combination of load systems A , B , C can be obtained simply by superposition. Determine the stress intensity factor. By the principal of superposition and for a small crack length, we have.

Clearly for very short cracks the above approximation is very close to the numerical solution. We can now return to the Griffith's energy concept, with special reference to its relation to the stress intensity factor.

Proceeding as before, we may identify the mechanical energy release during the crack extension with the work done by hypothetically imposed surface tractions. As illustrated in Fig. The work done by this force is obviously equal to the amount of energy that needs to be consumed in order to make the crack grow by this distance. The thickness of the plate is denoted as B.

Similarly, for plane strain condition see Chapter 1. The total energy release rate in combined mode cracking can be obtained by summing up the energies for different modes:. However, it is important to note that the derivation of both the stress intensity factor and the strain energy release rate is independent of the actual fracture process hence critical condition of materials. In other words, these only represent the "driving" force for crack growth and bear no relations to the materials' "resistance".

This will be discussed in the next chapter. Obviously the "driving" force increases linearly with crack length for a constant applied load. The stress intensity factor can also be expressed in terms of the displacement, u ,. It should be observed that, under displacement control, the stress intensity factor decreases as the crack extends. Therefore the system is a stable one, in the sense that the crack would stop growing after a certain crack advance unless the displacement is further increased.

The thickness and height of the specimen are B and H , respectively. The stress intensity factor is given in Table 2. For comparison, two ratio between the two functions are shown in Fig. This is graphically shown below. Clearly the compliance of the specimen increases rapidly as the crack length increases.

These two examples demonstrate that the relationship between the energy release rate and stress intensity factor is not only useful in determining the stress intensity factor for a cracked component from compliance measurement or calculation, but also useful in assessing the compliance of a cracked component.

Engineering Library. Brittle Fracture DOE. Fracture Mechanics Calculator. PDH Classroom. View Courses. Relevant Textbooks. Other related chapters from "Introduction to Fracture Mechanics" can be seen to the right. Introduction to Fracture Mechanics. Looking for Fracture Calculators? Crack in an infinite body. Centre crack in a strip of finite width. Edge crack in a semi-infinite body. Centre crack in a finite width strip.