The tensile test

6.1.2 The tensile test

In a tensile test the ends of a test piece are fixed into grips, one of which is attached to the load- measuring device on the tensile machine and the other to the straining device. The strain is usually applied by means of a motor-driven crosshead and the elongation of the specimen is indicated by its relative movement. The load necessary to cause this elongation may be obtained from the elastic deflection of either a beam or proving ring, which may be measured by using hydraulic, optical or electromechanical methods. The last method (where there is a change in the resistance of strain gauges attached to the beam) is, of course, easily adapted into a system for autographically recording the load–elongation curve.

The load–elongation curves for both polycrystalline mild steel and copper are shown in Figure 6.1a and b. The corresponding stress (load per unit area, P/A) versus strain (change in length per unit length, dl/l) curves may be obtained knowing the dimensions of the test piece. At low stresses the deformation is elastic, reversible and obeys Hooke’s law with stress linearly proportional to strain.

The proportionality constant connecting stress and strain is known as the elastic modulus and may

be either (a) the elastic or Young’s modulus, E, (b) the rigidity or shear modulus μ, or (c) the bulk modulus K , depending on whether the strain is tensile, shear or hydrostatic compressive, respectively. Young’s modulus, bulk modulus, shear modulus and Poisson’s ratio ν, the ratio of lateral contractions

to longitudinal extension in uniaxial tension, are related according to

In general, the elastic limit is an ill-defined stress, but for impure iron and low-carbon steels the onset of plastic deformation is denoted by a sudden drop in load, indicating both an upper and lower

290 Physical Metallurgy and Advanced Materials

Upper

yield point Unirradiated 2 )

40 Irradiated (MN m

Lower yield point

(1.9⫻10 30 19 neutrons 100

Luders strain

1 per cm 2 )

0 Energy of fracture (J)

load

⫺ 80 ⫺ 40 0 40 80 orig. area

(a)

Temperature (°C)

Nominal tensile stress

Uniform elongation

Total elongation 0 10 20 30 40 50 60

Elongation

(b) Figure 6.1 Stress–elongation curves for: (a) impure iron, (b) copper, (c) ductile–brittle

transition in mild steel (after Churchman, Mogford and Cottrell, 1957).

yield point. 1 This yielding behavior is characteristic of many metals, particularly those with bcc struc- ture containing small amounts of solute element (see Section 6.4.6). For materials not showing a sharp yield point, a conventional definition of the beginning of plastic flow is the 0.1% proof stress, in which

a line is drawn parallel to the elastic portion of the stress–strain curve from the point of 0.1% strain. For control purposes the tensile test gives valuable information on the tensile strength (TS =

maximum load/original area) and ductility (percentage reduction in area or percentage elongation) of the material. When it is used as a research technique, however, the exact shape and fine details of the curve, in addition to the way in which the yield stress and fracture stress vary with temperature, alloying additions and grain size, are probably of greater significance.

The increase in stress from the initial yield up to the TS indicates that the specimen hardens during deformation (i.e. work hardens). On straining beyond the TS the metal still continues to work-harden, but at a rate too small to compensate for the reduction in cross-sectional area of the test piece. The deformation then becomes unstable, such that as a localized region of the gauge length strains more than the rest, it cannot harden sufficiently to raise the stress for further deformation in this region above that to cause further strain elsewhere. A neck then forms in the gauge length, and further deformation is confined to this region until fracture. Under these conditions, the reduction in area

1 Load relaxations are obtained only on ‘hard’ beam Polanyi-type machines, where the beam deflection is small over the working load range. With ‘soft’ machines, those in which the load-measuring device is a soft spring, rapid load variations

are not recorded because the extensions required are too large, while in dead-loading machines no load relaxations are possible. In these latter machines sudden yielding will show as merely an extension under constant load.

Mechanical properties I 291

True stress

Instability strain

⫺ 1 0 Nominal strain ε n

Figure 6.2 Considère’s construction. (A 0 –A 1 )/A 0 , where A 0 and A 1 are the initial and final areas of the neck, gives a measure of the

localized strain, and is a better indication than the strain to fracture measured along the gauge length. True stress–true strain curves are often plotted to show the work hardening and strain behavior at large strains. The true stress σ is the load P divided by the area A of the specimen at that par- ticular stage of strain, and the total true strain in deforming from initial length l 0 to length l 1 is ε

l 0 (dl/l) = ln(l 1 / l 0 ). The true stress–strain curves often fit the Ludwig relation σ = kε , where n is a work-hardening coefficient ≈0.1–0.5 and k the strength coefficient. Plastic instability, or necking,

occurs when an increase in strain produces no increase in load supported by the specimen, i.e. dP = 0, and hence since P = σA, then

dP = Adσ + σdA = 0 defines the instability condition. During deformation, the specimen volume is essentially constant

(i.e. dV = 0) and from dV = d(lA) = Adl + ldA = 0, we obtain

dσ dA dl (6.2) σ =− A = l = dε.

Thus, necking occurs at a strain at which the slope of the true stress–true strain curve equals the true stress at that strain, i.e. dσ/dε

= σ. Alternatively, since kε n = σ = dσ/dε = nkε −1 , then ε = n and necking occurs when the true strain equals the strain-hardening exponent. The instability condition

may also be expressed in terms of the conventional (nominal strain), dσ

dσ dε n

dσ dl/l 0 dσ l

dε = dε dε = n dε

dl/l n = dε n l 0

which allows the instability point to be located using Considère’s construction (see Figure 6.2), by plotting the true stress against nominal strain and drawing the tangent to the curve from ε n = −1 on the strain axis. The point of contact is the instability stress and the tensile strength is σ/(1 +ε n ).

Tensile specimens can also give information on the type of fracture exhibited. Usually in poly- crystalline metals transgranular fractures occur (i.e. the fracture surface cuts through the grains) and the ‘cup-and-cone’ type of fracture is extremely common in really ductile metals such as copper. In this, the fracture starts at the center of the necked portion of the test piece and at first grows roughly perpendicular to the tensile axis, so forming the ‘cup’, but then, as it nears the outer surface, it turns into a ‘cone’ by fracturing along a surface at about 45 ◦ to the tensile axis. In detail the ‘cup’ itself consists of many irregular surfaces at about 45 ◦ to the tensile axis, which gives the fracture a fibrous appearance. Cleavage is also a fairly common type of transgranular fracture, particularly in materials

292 Physical Metallurgy and Advanced Materials of bcc structure when tested at low temperatures. The fracture surface follows certain crystal planes

(e.g. {1 0 0} planes), as is shown by the grains revealing large bright facets, but the surface also appears granular, with ‘river lines’ running across the facets where cleavage planes have been torn apart. Intercrystalline fractures sometimes occur, often without appreciable deformation. This type of fracture is usually caused by a brittle second phase precipitating out around the grain boundaries, as shown by copper containing bismuth or antimony.