The load–extension diagram

The extension at this instant is l max . , and a tensile test property known as the total elongation can be calculated; this is defined by E Tot. = l max . − l l × 100 1.1

1.1.2 The engineering stress–strain curve

Prior to the development of modern data processing systems, it was customary to scale the load–extension diagram by dividing load by the initial cross-sectional area, A = w t , and the extension by l , to obtain the engineering stress–strain curve. This had the advantage that a curve was obtained which was independent of the initial dimensions of the test-piece, but it was still not a true material property curve. During the test, the cross-sectional area will diminish so that the true stress on the material will be greater than the engineering stress. The engineering stress–strain curve is still widely used and a number of properties are derived from it. Figure 1.3a shows the engineering stress strain curve calculated from the load, extension diagram in Figure 1.2. Engineering stress is defined as σ eng. = P A 1.2 and engineering strain as e eng. = l l × 100 1.3 In this diagram, the initial yield stress is σ f = P y A 1.4 The maximum engineering stress is called the ultimate tensile strength or the tensile strength and is calculated as T S = P max. A 1.5 As already indicated, this is not the true stress at maximum load as the cross-sectional area is no longer A . The elongation at maximum load is called the maximum uniform elongation, E u . If the strain scale near the origin is greatly increased, the elastic part of the curve would be seen, as shown in Figure 1.3b. The strain at initial yield, e y , as mentioned, is very small, typically about 0.1. The slope of the elastic part of the curve is the elastic modulus, also called Youngs modulus: E = σ f e y 1.6 If the strip is extended beyond the elastic limit, permanent plastic deformation takes place; upon unloading, the elastic strain will be recovered and the unloading line is parallel to the initial elastic loading line. There is a residual plastic strain when the load has been removed as shown in Figure 1.3b. Material properties 3 50 100 150 200 250 300 5 10 15 20 25 30 35 40 45 50 Engineering strain, Engineering stress, MPa E Tot. E u s f TS a Engineering strain Engineering stress e y s f E e eng. s eng. b Engineering strain e eng. 0.2 s proof s eng. Engineering stress c Figure 1.3 a Engineering stress–strain curve for the test of drawing quality sheet steel shown in Figure 1.2. b Initial part of the above diagram with the strain scale magnified to show the elastic behaviour. c Construction used to determine the proof stress in a material with a gradual elastic, plastic transition. 4 Mechanics of Sheet Metal Forming