In a much-ignored paper in 1920, A. A. Griffith developed the modern conception of what happens when a material cracks under stress. Energy is required to crack a material. This can be obtained as strain energy is released from the material around the crack. Because the strain energy released is directly proportional to the square of the crack length, it is only when the crack is relatively short that its energy requirement for propagation exceeds the strain energy available to it. Beyond the critical Griffith crack length, the crack becomes dangerous.
Even if the local stress at the tip of a crack is much higher than the "official" tensile strength of the material, the structure may be safe as long as no crack exceeds the critical length.
© Paul Taylor 2001