Elliptic flaw, stress concentration

Flaw activity and the resultant stress concentration factors can also be expected to depend on the material s rheology. The sample loading history and path play a major role in determining the behavior of a given flaw as described elsewhere (6,11,12,13), and these ideas are currently being extended to account for recent developments in constitutive equation theory for solid polymers and the idea of a flaw spectrum. In this paper, time and path dependence are not considered further, and the calculations are based on elastic stress concentration factors associated with elliptic flaw geometries. 

Figure 3. Maximum algebraic stress concentrations (Q) developed by elliptic flaws, of various ellipticities R and for various orientations ft with re pect to the applied uniaxial tension, relative to the perpendicular orientation value (Q = 1 + 2/r).

Stress concentration factors associated with elliptic flaws in an anisotropic matrix are generally unavailable. In the absence of such information, the results presented in Figures 3-5 are a first approximation to the stress concentrations developed by the flaws in the drawn material. It follows that Equation 9 can be written as ... 

Ultimately, fracture can only occur if all atomic bonds in an area are pulled apart and break. The stress necessary to break a bond (the theoretical strength) is between E/S and E/20, where E is the elastic modulus of the material [51]. Typical tensile stresses applied to highly loaded components are in the order of /1000 or even smaller, and yet fracture of components still occurs. To explain this discrepancy, it is necessary that certain strong local stress concentrations exist these are termed Jlaivs. The action of flaws can be discussed by using the simple example of an elliptical hole in a uniaxial tensile-loaded plate. At the tip of its major semi-axis (which is perpendicularly oriented to the stress direction), the stress concentration is [52] ... 

The first understanding of why fracture starts from flaws is due to Griffith (1920, 1924) who used the study of Inglis (1913) on the concentration of stresses at an elliptical flaw (Figure 7.7). Let us assume that a flaw of semiaxes a and b a>b) is present in a beam submitted to uniform tensile stress a. The flaw concentrates stresses at the points of minimum curvature, and the maximum stress o is given by... 

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