Manufacturing Processes Machinery's Handbook, 31st Edition
1401
SHEET METAL WORKING AND PRESSES Basic Theory of Metal Working
Metal working theory provides a background from which reasonable evaluations may be made of the deformations obtainable without instability and fracture. The fundamen- tal principles, rules, and laws of metal working theory are used to describe the plastic flow or deformation of solid materials when subjected to external loads. For this purpose, such materials are considered as homogeneous, continuous, isotropic media. Understanding the theory underlying metal working is important for both the design and production engineer. Solid materials may be subjected to forces that may be classified as either volume forces or surface forces. In this discussion, only surface forces acting on the surface as external forces are considered. In analyzing design situations for either dimensioning purposes or forming processes, it is most appropriate to use force per unit area as a measure of the load rather than the total force distributed over the area. The force per unit area is called the stress ( σ ) and is described as follows: (1) Common ways of loading solid bodies include compression, tension, shear, torsion, or a combination of these stresses, such as fatigue. Fig. 1 shows a tensile specimen loaded with force F . The stress on a cross section A perpendicular to the longitudinal axis is defined (2) where F = force (lb) and A = cross-sectional area (in 2 ). If a cross section is inclined at an angle to the longitudinal axis, the mean oblique stress may be defined by (3) where A θ = inclined cross-sectional area of specimen (in 2 ); and, θ = inclined angle cross- sectional area of specimen (º). The mean oblique stress lies in the direction of the longitudinal axis of the specimen. Force F can be divided into components F n , which is perpendicular to cross section A θ and F t , which is parallel to cross section A θ , so that the state of the stresses can be defined by area force σ = A F σ = sin A = = θ F A F m σ θ
A F F t = = θ = = θ A n
F
2
sin
θ σ
θ
A
(4)
2 A F
sin
τ
2θ
θ
where σ θ = normal stress—stress normal to cross section A θ (lb/in stress—stress parallel to cross section A θ (lb/in 2 ).
2 ); and τ
θ = shear
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