Material engineering properties

As mentioned in the introduction to this chapter, the most commonly used mechanical properties are derived from a standard tension test. This test is a displacement controlled test whereby a specimen is forced to gradually deform with a constant rate of displacement. The force required to impose this displacement is measured. By dividing with the loading area this force can be converted into a stress. The stress is calculated using the original cross-sectional area of the unstressed specimen. During a tension or compression tests necking and barrelling respectively occurs which influences the cross-sectional area of the test specimen. The stress calculated using the original cross-sectional area at the beginning of a test differs

therefore from the “true stress” in the specimen as the specimen deforms. It is however difficult to approximate this “true stress” as it would require sophisticated measurements of the change in cross-sectional area as the test progresses. For all practical purposes the original cross-sectional area is therefore used and the stress derived in this manner is called the “engineering stress”.

The strain can be derived from the incremental increase in length of the specimen as ratio per unit length. When the values of the stress versus the corresponding strain are plotted against each other a stress-strain diagram is obtained. A typical example of such a stress-strain diagram for a tension test is shown in Figure 32. Although steel is not a common road building material, it is used here because it is a good example to define the several limits and strengths that can be derived from a stress- strain diagram.

Figure 32: Typical tension stress-strain diagram of steel

A number of points of interest can be identified on the stress-strain curve. These are indicated with the Roman symbols in Figure 32. The stress and strain are proportional up to Point I, which is at the end of the first straight-line part of the curve. The stress corresponding with Point I is also called the proportional limit. In order to determine the elastic limit, a specimen would need to be subjected to a large number of loading cycles with small increments in the loading magnitude. After every unloading cycle it then needs to be checked whether all strain has been recovered until such time that a plastic strain (permanent) starts to develop. The elastic limit is defined as the lowest stress at which plastic strain starts to develop. For many materials the elastic limit is approximately equal to the proportional limit, with only the latter being determined for practical reasons.

After Point I the strain starts to increase more rapidly than the stress until at Point II the strain increases while there is no further increase in stress. This point is called the yield point. A yield point is defined as a stress, short of the ultimate stress, at which the material undergoes a marked increase in strain, without any significant increase in stress. Point III is therefore also a yield point. Points II and III are referred to as upper and lower yield point respectively. The position of the upper yield point

Stress Strain I II III IV V Ultimate strength Yield strength Proportional limit Fracture strength

depends on the speed of testing, the shape of the section and the form of the specimen. The lower yield strength is usually considered to be a true characteristic of the material and is referred to simply as the yield strength (Park and Paulay, 1975) When, as shown in Figure 32, a material is stressed beyond its yield point, strain- hardening takes place. Hereby the stress increases again with the strain until the ultimate strength is reached at Point IV. This is the highest stress that the material can withstand. In case of a tensile test the tensile strength is defined as the ultimate strength.

When deformation is continued beyond the ultimate strength, the stress at the corresponding strain will decrease until, in case of a tensile test, the specimen breaks. This is indicated by Point V. The fracture strength of a material subjected to tensile is defined as the stress at which fracture occurs (ordinate of Point V).

The stress-strain diagram shown in Figure 32 is a typical diagram of a tension test (e.g. steel). A similar stress-strain diagram can be derived from a compression test. Materials such a concrete are often subjected to compressive tests. A typical example of a stress-strain diagram of a compressive test on concrete is shown in Figure 33.

Figure 33: Typical compressive stress-strain diagram of concrete

The first linear part of the stress-strain curve is shorter and the proportional limit less clearly identifiable compared to the tensile stress-strain diagram. Furthermore, a yield point is not present. The maximum compressive strength is equal to the ultimate strength as defined by Point IV.

Road building materials such as asphalt concrete, stabilised materials and also compacted granular materials are often subjected to compressive testing and not to direct tension tests. In such cases similar behaviour as shown in Figure 33 can be expected.

Standard material characteristics of interest that can be derived from a stress-strain diagram include:

• Modulus of Elasticity or Young’s Modulus; • Yield and Ultimate Strength;

Stress

Strain I

IV

• Elastic vs. plastic behaviour; • Ductile vs. brittle behaviour.

The Modulus of Elasticity, also known as Young’s Modulus, is the ratio between stress and strain and is equal to the slope of the first straight line part of the stress- strain curve. It is therefore equal to the slope of the line from the origin of the stress- strain diagram through Point I. The Modulus of Elasticity is a measure of the stiffness of the material.

The Yield Strength has a significant meaning for engineering purposes. Yielding material may be deemed as failing because strains may increase significantly without any significant further increase in stress. The yield strength of a material is therefore often used for design purposes. However, this mostly applies to materials subjected to tensile stresses. A yield point does not occur in materials subjected to compression (see Figure 33). In this case the ultimate strength or maximum compressive stress is of most importance and used for design purposes.

The term “elasticity” as used in Modulus of Elasticity can be confusing. Elasticity refers to the ability of a material to deform when loaded and to return to its original shape when unloaded. Materials with a relatively low stiffness (low Modulus of Elasticity) can still exhibit a high degree of elasticity. Plasticity, on the other hand, is the ability of a material to deform when loaded and to retain this deformation when unloaded.

Elastic deformation takes place approximately up to the proportional limit. Thereafter plastic deformation occurs. The degree of elasticity or plasticity of a material can be judged from the shape of the stress-strain curve.

There is a difference between plastic and viscous deformation. In order for plastic deformation to occur, the proportional limit needs to be exceeded first. Deformation in viscous material occurs regardless of how small the load is. Viscous behaviour is time- and temperature-dependent. Plastic deformation is irreversible and so is pure viscous deformation. Delayed viscous deformation, however, is reversible and a certain relaxation time applies (visco-elastic material).

Ductility is the ability of a material to deform plastically prior to fracture under tensile stress. Malleability is the ability of a material to deform plastically prior to fracture under compressive stress. Materials that behave ductile under tensile stress often also behave malleable under compressive stress. Brittleness is the absence of ductility and malleability (Arges and Palmer, 1963).

There is no distinct boundary between ductile and brittle behaviour. The terms are relative and some degree of engineering judgement is required. Ductility or brittleness gives information on how failure is reached. Ductile behaviour implies that extensive plastic deformation takes place before failure occurs. The extent of the failure (or micro-fracture) increases progressively as the deformation or loading increases. Brittle behaviour, on the other hand shows relatively little plastic deformation before failure. When behaving brittle, failure (or cracking) propagates

rapidly without significant increase in deformation or loading. There is no “warning” that failure is imminent. Examples of ductile and brittle behaviour are given in Figure 34. It can be seen that the area under the stress-strain curve (dissipated energy) is much higher in the case of ductile curve compared to the brittle curve. The amount of dissipated energy is a measure for the toughness of the material.

Figure 34: Typical examples of ductile vs. brittle behaviour

3.3 Models for material properties and characteristic behaviour