### 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 “strength” in regards to materials is its ability to withstand stresses without failing. Unfortunately, it’s not a matter of “if”, but “when” and “how”. It’s a measure of a material’s strength in terms of tension, compression, and shear – the three forms of stress. A given material’s strength increases in proportion to its ability to resist these stresses.

a:compression b:tension c:shear

Stiffness and its Relationship with Young’s Modulus

Stiffness is an elastic material’s ability to resist deformation along a given degree of freedom. Although closely related to the elastic or Young’s modulus, stiffness is a measure of a solid body that is dependent on size and mass, an extensive property, whereas Young’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 Young’s modulus of a given board would depend only on its material makeup.

Young’s modulus is defined as “the ratio of the uniaxial stress over uniaxial strain in the range of stress where Hooke’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 – within its elastic limits (Hooke’s law).

One can think of stiffness as the overall measure of a given material’s ability to resist deformation, with its values increasing with any increase in its size and cross section, and Young’s modulus as a measure of that same material’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 δ 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 “constrained”, stiffness is equal to the Young’s modulus.

But this equation or definition won’t work with anything but this “special” case, as most objects have more than one degree of freedom. For example, the axial stiffness for a non- “special” member in tension or compression is defined by where A is the cross sectional area, E is the Young’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 material’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.