tailieunhanh - Introduction to Contact Mechanics Part 8

Tham khảo tài liệu 'introduction to contact mechanics part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Energy Balance Explanation of Auerbach s Law 123 For a high density of very small flaws in the size range Cf a the critical load Pc given by Eq. decreases as the flaw size increases since the stress level along the length of the flaw is fairly constant and is approximately equal to the surface stress as given by the Hertz equation. In this case the Griffith criterion for a uniform constant stress level may be employed. Smaller flaws are more likely to extend at a lower ro a since the surface stress level is higher closer to the contact radius. Auerbach s law would not hold in this case. For larger flaws in the size range Cf a the situation is qualitatively different. Equation and Fig. show that the critical load increases with increasing flaw size because the strain energy release rate given by ộ c a decreases with increasing flaw size. The reason for this surprising result is in the form of the integral in Eq. . The strain energy release rate depends on both the stress distribution along the flaw and the factor c2-b2 -1 2. Larger values of c cause the integral to evaluate to a lower value compared to smaller flaws at the same ro. From Eq. Pc a3 2 is proportional to ộ cf a -1 2. Figure shows that there is a range of cf a where the outer envelope ộ cf a and hence ỘỊcỵ a is fairly constant. This is the Auerbach range. In this range the critical load Pc which initiates fracture is virtually independent of the flaw size and is therefore proportional to a3 2. Assuming the existence of flaws of all sizes everywhere on the specimen surface then for a particular flaw size the starting radius is that which gives the maximum strain energy release rate. The Griffith criterion will be first met upon increasing load at the position where the maximum strain energy release rate occurs. For another flaw size the starting radius is different but the strain energy release rate and hence the critical load is not much different. For .

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