A tensile test-piece is shown in Figure 1.1. This is typical of a number of standard test-pieces having a parallel, reduced section for a length that is at least four times the width, w0. The initial thickness is t0 and the load on the specimen at any instant, P, is measured by a load cell in the testing machine. In the middle of the specimen, a gauge length l0 is monitored by an extensometer and at any instant the current gauge length is l and the extension is l = l − l0. In some tests, a transverse extensometer may also be used to measure the change in width, i.e. w= w − w0. During the test, load and extension will be recorded in a data acquisition system and a file created; this is then analysed and various material property diagrams can be created. Some of these are described below.
The load–extension diagram
Figure 1.2 shows a typical load–extension diagram for a test on a sample of drawing quality steel. The elastic extension is so small that it cannot be seen. The diagram does not represent basic material behaviour as it describes the response of the material to a particular process, namely the extension of a tensile strip of given width and thickness. Nevertheless it does give important information. One feature is the initial yielding load, Py, at which plastic deformation commences. Initial yielding is followed by a region in which the deformation in the strip is uniform and the load increases. The increase is due to strain-hardening, which is a phenomenon exhibited by most metals and alloys in the soft condition whereby the strength or hardness of the material increases with plastic deformation. During this part of the test, the cross-sectional area of the strip decreases while the length increases; a point is reached when the strain-hardening effect is just balanced by the rate of decrease in area and the load reaches a maximum Pmax .. Beyond this, deformation in the strip ceases to be uniform and a diffuse neck develops in the reduced section; non-uniform extension continues within the neck until the strip fails.
The extension at this instant is lmax ., and a tensile test property known as the total
elongation can be calculated; this is defined by
Etot. =[(lmax − l0)/l0].100%
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, A0 = w0t0, and the extension by l0, 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 1.3(a) shows the engineering stress strain curve calculated from the load, extension diagram in Figure 1.2.
Engineering stress is defined as ; σ = P/A0 (1.2)
and engineering strain as ; e = (l /l0). 100% (1.3)
In this diagram, the initial yield stress is; (σf)0 = Py/A0 (1.4)
The maximum engineering stress is called the ultimate tensile strength or the tensile
strength and is calculated as ; T S = Pmax/A0 (1.5)
As already indicated, this is not the true stress at maximum load as the cross-sectional area is no longer A0. The elongation at maximum load is called the maximum uniform elongation, Eu. If the strain scale near the origin is greatly increased, the elastic part of the curve would be seen, as shown in Figure 1.3(b). The strain at initial yield, ey, 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 = (σf)0 / ey (1.6)
If the strip is extended beyond the elastic limit, permanent plastic deformation takes place; pon unloading, the elastic strain will be recovered and the unloading line is parallel to the initial lastic loading line. There is a residual plastic strain when the load has been removed as shown in Figure 1.3(b).
In some materials, the transition from elastic to plastic deformation is not sharp and it is difficult to establish a precise yield stress. If this is the case, a proof stress may be quoted. This is the stress to produce a specified small plastic strain – often 0.2%, i.e. about twice the elastic straint yield. Proof stress is determined by drawing a line parallel to the elastic loading line which is offset by the specified amount, as shown in Figure 1.3(c). Certain teels are susceptible to strain ageing and will display the yield phenomena illustrated in Figure 1.4. This may be seen in some hot-dipped galvanized steels and in bake-hardenable steels used in autobody panels. Ageing has the effect of increasing the initial yielding stress to the upper yield stress σU; beyond this, yielding occurs in a discontinuous form. In the tensile test-piece, discrete bands of deformation called L¨uder’s lines will traverse the strip under a constant stress that is lower than the upper yield stress; this is known as the lower yield stress σL. At the end of this discontinuous flow, uniform deformation associated with strain-hardening takes place. The amount of discontinuous strain is called the yield point elongation (YPE). Steels that have significant yield point elongation, more than about 1%, are usually unsuitable for forming as they do not deform smoothly and visible markings, called stretcher strains can appear on the part.
***if some figures looking small, you can click on the pictures for magnify.
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