tailieunhanh - Introduction to Contact Mechanics Part 7

Tham khảo tài liệu 'introduction to contact mechanics part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Contact Between Elastic Solids 103 Table Equations for surface pressure distributions beneath the indenter for different types of indentations. Indenter type Equation for normal pressure distribution r a Sphere li 2 2 -311 - rr 1 Pm 2 a2 Cylinder 2-D 7 A12 2P i x2 ơz - l 1 2 1 na a Cylindrical Flat punch ư u V1 2 - ị 1 - rị 1 Pm 2 a2 Uniform pressure ơz - Pm Cone Ơ a - cosh-1 - Pm r Spherical indenter Consider the contact of a sphere of radius R with elastic modulus E and Poisson s ratio v with the surface of a specimen of radius RS whose elastic constants are E and v. With no load applied and with the indenter just touching the specimen the distance h between a point on the periphery of the indenter to the specimen surface as a function of radial distance r is given by .r2_ h 2R where R is the relative curvature of the indenter and the specimen 1 R R RS In Eqn. we set the radius of the indenter R to be positive always and RS to be positive if its centre of curvature is on the opposite side of the surface to that of R . 104 Elastic Contact c Fig. Schematic of contact between two elastic solids. a Nonrigid spherical indenter and nonrigid flat specimen b two identical nonrigid spheres c nonrigid spherical indenter and flat rigid specimen d rigid spherical indenter and flat nonrigid specimen with kind permission of Springer Science and Business Media Reference 4 . Now in Fig. load is applied to the indenter in contact with a flat surface RS in Eq. to such that the point at which load is applied moves a vertical distance s. This distance is often called the load-point displacement and when measured with respect to a distant point in the specimen may be considered the distance of mutual approach between the indenter and the specimen. In general both the indenter and specimen surface undergo deformation. These deformations are shown in the figure by u z and uz at some arbitrary point inside the contact circle for

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