tailieunhanh - Introduction to Contact Mechanics Part 2

Tham khảo tài liệu 'introduction to contact mechanics part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Elasticity 3 77 _ 77 i nx F Fmi x sinl I 2L where L is the distance from the equilibrium position to the position at Fmax. Now since sin0 0 for small values of 0 the force required for small displacements x is 77 _ 77 nx F F max 2L _ Fmaxn 2L x Now L and Fmax may be considered constant for any one particular material. Thus Eq. takes the form F kx which is more familiarly known as Hooke s law. The result can be easily extended to a force distributed over a unit area so that Ơ Fìaỵn 2L where ơmax is the tensile strength of the material and has the units of pressure. If Lo is the equilibrium distance then the strain e for a given displacement x is defined as x e Lo Thus Ơ e Lonơ max 2L E All the terms in the square brackets may be considered constant for any one particular material for small displacements around the equilibrium position and can thus be represented by a single property E the elastic modulus or Young s modulus of the material. Equation is a familiar form of Hooke s law which in words states that stress is proportional to strain. In practice no material is as strong as its theoretical tensile strength. Usually weaknesses occur due to slippage across crystallographic planes impurities and mechanical defects. When stress is applied fracture usually initiates at these points of weakness and failure occurs well below the theoretical tensile strength. Values for actual tensile strength in engineering handbooks are obtained from experimental results on standard specimens and so provide a basis for engineering structural design. As will be seen additional knowledge regarding the geometrical shape and condition of the material is required to determine 4 Mechanical Properties of Materials whether or not fracture will occur in a particular specimen for a given applied stress. Strain energy In one dimension the application of a force F resulting in a small deflection dx of an atom from its equilibrium .

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