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Introduction to Contact Mechanics Part 10

Tham khảo tài liệu 'introduction to contact mechanics part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 9.3 Meaning of Hardness 163 for the case of the spherical indenter and hence we need to consider the more general equation p 2 Y 3 1 lnl I E Y da c dc a R 4 1 - 2v 9.3.4.1i We require information concerning the product of da dc and c a. We may expect that since the elastic stress distribution within the specimen for a spherical indenter is directly proportional to a then if c a Ka where K is a constant then dc da 2Ka and hence p 2 Y3 1 lnff E Y 1 a 4 1 - 2V -.1-. vk 2 R J 6 1 - v 9.3.4.1j Equation 9.3.4.1j relates the core pressure p and the ratio a R for a spherical indenter based on the assumption that c a Ka. As noted previously in the case of a spherical indenter the transition between elastic and full plastic response occurs as a result of yielding of elastically constrained material some distance beneath the surface of the specimen at some finite value of contact radius a . Swain and Hagan17 suggested therefore that tanP in Eq. 9.3.4.1h should be replaced by a-a R but doing so not only ignores the condition of nongeometrical similarity associated with a spherical indenter but also violates the volumetric compatibility specified by Johnson25. If appropriate adjustments are made to Eq. 9.3.4.1h to account for both the geometry of the indentation and the finite value of the contact radius at the initiation of yield we obtain p 2 Y 3 rX 1 1 ln I EY 1 2 a af a 4 1 - 2v 1 R v J 6 1 -v J 9.3.4.1k where a a-a and is the effective radius of the core. The core pressure is directly related to the mean contact pressure beneath the indenter and according to Johnson32 is given by Pm p - Y 9.3.4.1l The size of the plastic zone c a can be found from Eq. 9.3.4.1g. We should note in passing that the expanding cavity model requires the distribution of pressure across the face if the indenter is uniform and equal to pm. 164 Hardness 9.3.4.2 The elastic constraint factor An alternative to the expanding cavity model is given by Shaw and DeSalvo26 27 who showed that the observed .