» Axial Strain
An axial bar of length L, and cross-sectional area A, subjected to tensile force P, elongates by an amount, D. The change in length divided by the initial length is termed ENGINEERING STRAIN (or simply strain). The symbol used for engineering strain in most texts is e (epsilon). The strain in an axially loaded bar is defined as:

• Strain is positive in tension (D>0 means e<0) and negative in compression (D<0);
• Strain is a non-dimensional length - a fraction. Because strain is small, it is often given as a percentage by multiplying by 100%: e.g., e = 0.003 = 0.3%.

» Axial Stress
Consider the same bar as above. If a cut is taken perpendicular to the bar's axis, exposing an internal cross-section of area A, the force per unit area on the face of this cut is termed STRESS. The symbol used for normal or axial stress in most engineering texts is s (sigma). Stress in an axially loaded bar is:

• Stress is positive in tension (P>0) and negative in compression (P<0);
• English units: psi (pounds per square inch), or ksi (kilopounds per square inch);
• S.I. units: Pascal (Pa) (Newtons per square meter), or more commonly megapascal (MPa), (1 MPa = 1,000,000 Pa).

» Stiffness; Young's Modulus
Like a spring, all materials have a stiffness associated with them. In engineering, the stiffness of a material is defined through Hooke's Law:

Where E is the YOUNG'S MODULUS or stiffness of the material. Values of E for different materials are obtained experimentally from stress-strain curves. Young's Modulus is simply the slope of the linear region of the stress-strain curve. Values of Young's Modulus for various materials are given in Table 1 - Elastic Constants. Young's Modulus is generally large and usually expressed in either Msi (megapounds per square inch = thousands of ksi) or GPa (gigapascal).

» Stress-Strain Curve
The most common way of depicting the relation between stress and strain is through a STRESS-STRAIN CURVE. Stress-strain curves are obtained experimentally and provide useful material properties such as Young's Modulus, yield strength, ultimate tensile strength, etc.

   •Proportional Limit: the value of stress when the stress-strain curve no longer follows Hooke's Law.
   •Yield Strength: the practical value of the Proportional Limit; found using the 0.2% offset rule.
   •Ultimate Tensile Strength: the maximum value of stress that a material can support.

» Poisson's Ratio
As you stretch a rubber band, not only does it elongate, but it gets thinner. This holds true for structural components as well, although it is difficult to see with the naked eye. This is referred to as the Poisson Effect. Mathematically, POISSON'S RATIO is expressed as the negative ratio of the transverse strain (e_T) to the longitudinal strain (e), where the longitudinal strain is in the direction of the applied load:

Typical values of Poisson's Ratio for various materials are given in Table 1 - Elastic Constants.

» Elastic Strain Energy Density
The elastic strain energy density - the elastic strain energy per unit volume - stored in an axial member is:

The maximum value of the elastic strain energy is the RESILIENCE. It occurs when the stress in the axial member reaches the yield strength:

» Fatigue
The standard fatigue test (zero mean stress) has a strain-time history graph as shown at right. Tests are performed at different stress amplitudes s_a, and the number of cycles to failure is recorded, N_f. The points (NF, sa) are plotted and a line fitted. Variables S_f' and b are determined from the curve fit.

The fatigue strength of a material is the value of the stress amplitude for a given value of N_f can be calculated:

Typically, for steel, N_f = 10⁶ cycles and for aluminum N_f = 10⁷ cycles. Steels also have a fatigue limit...

Stress-time curve.

S-N Curve