TECTONICS/Fractures (Including Joints) 355 inter-atomic bonds However, experiments revealed that the measured tensile strength of a material is usually several orders of magnitude lower than that calculated on the basis of their inter-atomic bond strength Griffith argued that this was because the materials contain small flaws or microfractures and that these resulted in a local stress magnification at the crack tips This is illustrated diagrammatically in Figure 6, which shows the stress configuration of a plate subjected to a horizontal extension In the first plate (Figure 6A), the stress is evenly distributed through the plate In the second plate, which contains a flaw represented by an elliptical crack (Figure 6B), the tensile stress is locally magnified at the fracture tips The amount of magnification depends primarily on the orientation and eccentricity of the crack The greater the eccentricity, the greater the magnification Griffith argued that by this means, a relatively low applied stress could be locally amplified at fracture tips within the material to the point where it reached the stress required to break the atomic bonds within the material causing the material to fail He developed the following failure criterion (the Griffith criterion of tensile failure) based on this model: t2 ỵ 4Ts 4T2 ẳ Figure (A) A uniform stress field represented by uniformly spaced stress trajectories in a stretched layer (B) The concen tration of tensile stress at crack tips in a uniformly extended layer ½7 where t is the shear stress, s the normal stress, and T the tensile strength of the material The graphical expression of this failure criterion is shown in Figure 7A It has the form of a parabola whose intersection with the normal stress axis gives the tensile strength and with the shear stress axis the cohesion The complete criteria for brittle failure, (the Griffith, Navier–Colomb criteria), is obtained by linking the two criterion (eqns [5] and [7]) at the point where their slopes are identical (Figure 7B) Any stress state can be represented on this graph as Figure (A) The graphical expression of the Griffith criterion of tensile failure (eqn [7]) It has the form of a parabola whose intersection with the normal stress axis gives the tensile strength of the material and with the shear stress axis the cohesion (B) The complete criteria for brittle failure, (the Griffith, Navier Colomb criteria), is obtained by linking the two criteria (eqns [5] and [7]) at the point where their slopes are identical