### Strength, Stiffness, and Stability of Materials

There are three properties used to analyze the overall strength of a material: strength, stiffness, and stability. In this article I will attempt to explain the meaning of these three physical properties, and outline their importance and roles in materials-selection. A proper balance between properties must be struck in the selection and production-phases, so that the end product has the required physical attributes.

Strength

The term â€œstrengthâ€ in regards to materials is its ability to withstand stresses without failing. Unfortunately, itâ€™s not a matter of â€œifâ€, but â€œwhenâ€ and â€œhowâ€. Itâ€™s a measure of a materialâ€™s strength in terms of tension, compression, and shear â€“ the three forms of stress. A given materialâ€™s strength increases in proportion to its ability to resist these stresses.

a:compression b:tension c:shear

Stiffness and its Relationship with Youngâ€™s Modulus

Stiffness is an elastic materialâ€™s ability to resist deformation along a given degree of freedom. Although closely related to the elastic or Youngâ€™s modulus, stiffness is a measure of a solid body that is dependent on size and mass, an extensive property, whereas Youngâ€™s modulus is an intensive property and has nothing to do with size, volume, area, length, etc.

For example, one could say that the stiffness of a given board depends not only on material makeup but also on its dimensions, while the Youngâ€™s modulus of a given board would depend only on its material makeup.

Youngâ€™s modulus is defined as “the ratio of the uniaxial stress over uniaxial strain in the range of stress where Hookeâ€™s law holds”, expressed in Pascals (SI unit of pressure). This just means that it is equal to the amount of force per square meter of cross-sectional area, that it takes to stretch a sample material to double its length â€“ within its elastic limits (Hookeâ€™s law).

One can think of stiffness as the overall measure of a given materialâ€™s ability to resist deformation, with its values increasing with any increase in its size and cross section, and Youngâ€™s modulus as a measure of that same materialâ€™s stiffness, expressed as a ratio and therefore an intensive property, having nothing to do with its size.

In a single degree of freedom, stiffness can be defined as for stiffness where k is the stiffness, F is the force applied to the body, and Î´ is the displacement, or change in length of the elastic body along a single degree of freedom. As you can see, when the applied force is only along a single degree of freedom, or â€œconstrainedâ€, stiffness is equal to the Youngâ€™s modulus.

But this equation or definition wonâ€™t work with anything but this â€œspecialâ€ case, as most objects have more than one degree of freedom. For example, the axial stiffness for a non- â€œspecialâ€ member in tension or compression is defined by where A is the cross sectional area, E is the Youngâ€™s modulus, and L is the length of the member. Stiffness is typically measured in newtons per meter or pound force (lbf) per inch.

Stability

Stability is simply a materialâ€™s ability to maintain its original configuration under various loads and stresses. For example, when a column is loaded axially to its buckling limit, it will experience what is called instability. Any further loading or even the slightest introduction of a lateral force such as wind, will cause it to fail by buckling. Resistance to time-dependent deformation such as creep can be thought of as a result of material stability.