Metal Fatigue Part 2

Tham khảo tài liệu 'metal fatigue part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 14 Chapter 2 K 1 2 ị t J p Figure Approximation of the stress concentration at a notch by the equivalent ellipse concept. I t t Figure Stress concentration at a spherical cavity. Stress Concentration Figure Stress concentration at a spherical inclusion. Notches having a geometrically similar shape have the same value of stress concentration factor regardless of the difference in size. Most fatigue cracks initiate at the sites of stress concentrations. However it is known that the maximum stress at a stress concentration is not the only factor controlling the crack initiation condition. This phenomenon has been studied by many researchers as the problem of the fatigue notch effect Chapter 3 . Stress Concentration at a Crack Unlike holes and notches a crack has a sharp tip whose root radius p is zero. The definition of a crack in elastic analysis is the limiting shape of an extremely slender ellipse. As an extremely slender elliptical hole is reduced towards the limiting shape then the stress concentration ahead of the elliptical hole that is at the tip of the crack becomes unbounded regardless of the length of the crack. Therefore it is not appropriate to compare the maximum stresses at the tips of various cracks as a measure of their stress concentration. The idea needed to solve the difficulty of treating unbounded stresses at crack tips was proposed by . Irwin at the end of the 1950s 8 9 . From the theory of his idea the stresses in the vicinity of a crack tip have a singularity of r_ 2 where r is the distance from the crack tip 10 . The stress intensity factor is defined as the parameter describing the intensity of the singular stress field in the vicinity of a crack tip 8 9 . As shown in Fig. when we have a crack of length 2a in the x-direction in a wide plate which is under a uniaxial tensile stress ƠQ in the y-direction the stress intensity 16 Chapter 2 Figure Two dimensional crack length 2a. factor which describes the singular .

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