Steel stress-strain diagram

Little error is introduced using the idealized stress—strain diagram (Eig. 4a) to estimate the stresses and strains in partiady plastic cylinders since many steels used in the constmction of pressure vessels have a flat top to their stress—strain curve in the region where the plastic strain is relatively smad. However, this is not tme for large deformations, particularly if the material work hardens, when the pressure can usuady be increased above that corresponding to the codapse pressure before the cylinder bursts. 

Response of a material under static or dynamic load is governed by the stress-strain relationship. A typical stress-strain diagram for concrete is shown in Figure 5.3. As the fibers of a material are deformed, stress in the material is changed in accordance with its stress-strain diagram. In the elastic region, stress increases linearly with increasing strain for most steels. This relation is quantified by the modulus of elasticity of the material. 

Figure 5.26 Stress-strain diagram for mild steel, illustrating different types of stress. From Z. Jastrzebski, The Nature and Properties of Engineering Materials, 2nd ed. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc.

The graphic results, or stress-strain diagram, of a typical tension test for structural steel is shown in Figure 3. The ratio of stress to strain, or the gradient of the stress-strain graph, is called the Modulus of Elasticity or Elastic Modulus. The slope of the portion of the curve where stress is proportional to strain (between Points 1 and 2) is referred to as Young s Modulus and Hooke s Law applies. 

Pig. 4.4 Stress-strain diagrams of a typical polymeric material (a) and, for comparison, for steel (6). The scheme of the experiment is shown in the inset in the lower figure one takes a sample of given dimensions and pulls on it with a measured force f. The stress a is defined as the ratio of force to the initial, undeformed cross-sectional area of the sample,... 

Fi ire t0.16 Stress-strain diagram for a mild steel sample (ksi = 1000 IbAn, elastic stress, (o-r), = upper-yield stress, (o-r)/ = loaer-yleld stress, a, = ultimate stress, and a, = fracture stress). 

Figure 10 Stress-strain diagram for steel showing springback.

Figure 10,11 Tensile stress-strain diagrams for continuous carbon and steel wire reinforced cements, after Aveston et al. (1974).

Figure 3-12. Tensile stress-strain diagrams. Top Hard and soft steels, polycarbonates. Bottom Polycarbonates, on an extended scale, with specific characteristics usable in a design analysis.

An approximate sketch of the stress-strain diagram for mild steel is shown in Fig. 2.8(a). The numbers given for proportional limit, upper and lower yield points and maximum stress are taken from the literature, but are only approximations. Notice that the stress is nearly hnear with strain until it reaches the upper yield point stress which is also known as the elastic-plastic tensile instability point. At this point the load (or stress) decreases as the deformation continues to increase. That is, less load is necessary to sustain continued deformation. The region between the lower yield point and the maximum stress is a region of strain hardening, a concept that is discussed in the next section. Note that if true stress and strain are used, the maximum or ultimate stress is at the rupture point. 

If the strain scale of Fig. 2.8(a) is expanded as illustrated in Fig. 2.8(b), the stress-strain diagram of mild steel is approximated by two straight lines one for the linear elastic portion and one which is horizontal at a... 

Ductile materials often have a stress-strain diagram similar to that of mild steel shown in Fig. 2.8 and can be approximated by a linear elastic-perfectly plastic material with a stress-strain diagram such as that given in Fig. 2.9(b). Failure for ductile materials is assumed to occur when stresses or strains exceed those at the yield point. Materials such as cast iron, glass, concrete and epoxy are very brittle and can often be approximated as perfectly linear elastic-perfectly brittle materials similar to that given in Fig, 2.9(a). Failure for brittle materials is assumed to occur when stresses or strains reach a value for which rupture (separation) will occur. 

Fig. 11.7. Idealized stress-strain diagram for mild steel.

Prestressing steel (see typical stress-strain diagram in Fig. 3) is used in external tendons (posttensioning) in the form of strands or wires or bundle of monostrands (inside corrugated metal or plastic ducts or inside smooth steel or plastic pipes) in concrete stmctures. 

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