Yield point lower

Expanded joints (Fig. 10-138) are confined to the smaller pipe sizes of ductile metals. A smooth finish is required on the outside of the pipe and on the faces of the ridges inside the bore. Pipe and bore must have the same coefficient of thermal expansion. Furthermore, it is essential that the pipe metal have a lower yield point than the metal... 

In a material exhibiting a distinct yield point, the stress corresponding to the yield point may be taken as the yield strength. When both upper and lower yield points occur, generally the stress corresponding to the lower yield point is taken to be the yield strength. 

Beyond point E, the material begins to plasticly deform, and at point Y the yield point is achieved. The stress at the yield point corresponds to the yield strength, Oy [see Eq. (5.20)]. Technically, point Y is called the upper yield point, and it corresponds to the stress necessary to free dislocations. The point at which the dislocations actually begin to move is point L, which is called the lower yield point. After point L, the material enters the ductile region, and in polycrystalline materials such as that of Eigure 5.26, strain hardening occurs. There is a corresponding increase in the stress... 

For some metals, notably steels, there is an abrupt break in the stress-strain plot at the upper yield point (Figure 10.18). This is followed by continued deformation at a lower yield stress, at the lower yield point, before the curve rises again. Between the upper and lower yield points, deformation occurs in localised regions that have the form of bands, rather than across the specimen in a uniform manner. The reason for this is that the dislocations, which would move during plastic deformation, are pinned in the steel, mainly by the interstitial carbon atoms present. At the upper yield stress, these become mobile and, once released, they can move and multiply at a lower stress value. This is analogous to sticking and slipping when a body over-... 

Figure 17.2 shows a a-8 curve for LiF that illustrates an abrupt elastic-plastic transition. Plastic deformation begins at the upper yield point and there is a decrease in stress. At the lower yield point deformation continues at lower stress levels. This type of behavior is similar to that of some low-carbon steels as well as aluminum oxide and magnesium oxide at high temperatures. 

Material Veh (mm/ min) Elastic limit (MPa) Upper yield point (MPa) Lower yield point (MPa) Strain at elastic limit (xl0 m/m) Strain at upper yield point (MPa) Elastic modulus (GPa)... 

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. 

The elastic-plastic tensile instability point in mild steel has received much attention and many explanations. Some polymers, such as polycarbonate, exhibit a similar phenomenon. Both steel and polycarbonate not only show an upper and lower yield point but visible striations of yielding, plastic flow or slip lines (Luder s bands) at an approximate angle of 54.7° to the load axis also occur in each for stresses equivalent to the upper yield point stress. (For a description and an example of Luder s band formation in polycarbonate, see Fig. 3.7(c)). It has been argued that this instability point (and the appearance of an upper and lower yield point) in metals is a result of the testing procedure and is related to the evolution of internal damage. That this is the case for polycarbonate will be shown in Chapter 3. For a discussion of these factors for metals, see Drucker (1962) and Kachanov (1986). 

Lower yield point, OLyp Proportional limit, OpL... 

About the strain hardening exponent of the material n it is necessary to know the cyclic curve of the material. To this purpose, the multiple specimens procedure described in Sect. 1.3.1 (see Fig. 1.24) has been adopted using short test pieces of 8 mm diameter and 2 cm length. The cyclic curve is shown in Fig. 6.35 together with the monotonic one for comparison. It is possible to see how the steel underwent a strain hardening process with the complete loss of the upper and lower yield point. The cyclic curve equation is... 

The first stress in a material, usually less than the maximum attainable stress, at which an increase in strain occurs without an increase in stress. Only certain metals - those that exhibit a localized, heterogeneous type of transition from elastic deformation to plastic deformation - produce a yield point. If there is a decrease in stress after yielding, a distinction may be made between upper and lower yield points. The load at which a sudden drop in the flow curve occurs is called the upper yield point. The constant load shown on the flow curve is the lower yield point. 

Some steels and other materials exhibit the tensile stress-strain behavior shown in Figure 6.10b. The elastic-plastic transition is very well defined and occurs abruptly in what is termed a yield point phenomenon. At the upper yield point, plastic deformation is initiated with an apparent decrease in engineering stress. Continued deformation fluctuates slightly about some constant stress value, termed the lower yield point, stress subsequently rises with increasing strain. For metals that display this effect, the yield strength is taken as the average stress that is associated with the lower yield point because it is well defined and relatively insensitive to the testing procedure. Thus, it is not necessary to employ the strain offset method for these materials. 

---