The recent implosion of the Titan submersible has brought up the discussion about material strength and how it is measured. As it turns out, the “strength” of a material is a complex topic, with many similar sounding properties, such as “tensile strength,” “yield strength,” “ultimate tensile strength,” “failure strength” and so on. Failing to understand the differences in these terms can lead to the wrong choice in materials — and often catastrophic results.

Stress versus strain

First, in common language, stress and strain get used interchangeably. However, in materials science and engineering, this is not the case. Stress is the amount of force applied over a cross-sectional area. Strain is the amount of elongation in a sample as it is stretched or squashed. Mathematically, stress is:

Equa1

Where σ is stress, F is the applied force and A is the cross-sectional area. Strain is:

Equa2

Where ε is the strain, δ is the elongation (the change in length), and L is the original length. With strain, there are a few subtleties, but for now, this definition will do.

Tension, compression and shear

Another common misunderstanding is how forces are applied to a material. Tension is when the material is stretched and compression is when the material is squashed. Shear is where the material is bent, twisted or otherwise loaded unevenly. The trick with shear stress is that shear stresses are applying both tension and compression. To visualize this, try gently bending or twisting a book. Part of the book will be loaded in compression (pushing together) while the opposite surface will be loaded in tension (pulling apart).

For most metals, their strength is similar whether they are stretched or compressed. However, not all materials share this property. Ceramics, such as glass or concrete are much stronger in compression than in tension. Reinforced concrete tries to load the steel rebar in tension and the concrete in compression for maximum strength of the overall structure. On the opposite end, certain types of wood are stronger in tension than in compression. This has to do with the nature of the cells that made up the tree. They can be stretched, say on the windward side of a tall tree, but if compressed, the sides of the cells rupture, which is why many trees break on the leeward side.

Different types of stress. Bending, torsion and fatigue (alternate forces for many cycles) are special cases of shear, which are their own special cases of tension and compression. Source: Almazi/CC BY-SA4.0

Elastic versus plastic

As soon as a material is placed under any load at all, it deforms. Visually, the deformation may not be noticeable, but right away, the material is deforming. There are two types of deformation: elastic and plastic. Elastic deformation is not permanent; as soon as the load is removed, the material springs back to its original shape. During the elastic deformation, energy is merely stored, ready to be released once the load has been removed. Plastic deformation is permanent, and alters the shape of the material forever. Energy is absorbed by the material, transferring it into breaking and reforming atomic bonds, heat, noise and other mechanisms.

Under normal circumstances, most designs are meant to be operated in the elastic region. All materials deform under any load, so the ability for the object to spring back to its original shape is desirable. Consider a valve spring that bends under load, but then returns to its original shape hundreds of times per minute for the life of the automobile engine.

A few items and a few operating conditions do take advantage of plastic deformation. While the material is being permanently deformed, it is absorbing energy. Crumple zones on vehicles are designed to bend, permanently, absorbing energy from a crash. Also, many pressure vessels are designed with “leak before break” criteria. This means that some components will begin to permanently deform and leak before over-pressurization.

The difference between elastic and plastic deformation is defined at the yield stress. Once the material has passed the yield stress (YS), the material begins permanent deformation.

Yield stress, ultimate tensile stress and failure stress

Yield stress is the point between elastic and plastic deformation. This is where the material begins to deform permanently and 99% of designs should use this stress (divided by a factor of safety) to define the maximum load the device can withstand.

Two other important stresses are the ultimate tensile stress (UTS) and the failure stress (FS). The UTS is the recognition that, even though the material is being permanently deformed, it is still able to sustain a heavier load. If the material is loaded to its UTS, it will never return to its original shape, but it can be useful in engineering calculations, as it shows the maximum, one-time stress a material can withstand. It can also give an indication of how much energy can be absorbed before failure, making it useful for designing crumple zones, rupture disks and other overload conditions.

At the UTS, the material begins to neck. If a piece of silly putty is stretched, there will be a point where the most stressed area begins to narrow rapidly. As the cross-sectional area increases, the stress at that point increases rapidly (remember, stress is force over cross-sectional area). Rapidly, the material approaches the fracture, or FS, where the material will break.

Necking begins to reduce the cross-sectional area. Source: Gisforgirard/CC BY-SA 4.0

There is an interesting dilemma with FS. When measured, the FS is less than the UTS. This is because for most materials, the stress throughout testing is calculated using the starting cross-sectional area. In reality, the material begins necking and the cross-sectional area decreases. This is difficult to measure in real time. The stress calculated with constant cross-sectional area is called “engineering stress” and the stress calculated with the actual cross-sectional area is called “true stress.” Often, the engineering stress is reported, because it is the one that is easily measured.

Final thoughts

A fatal mistake would be to simply look up a material’s “strength” or to use its UTS or FS in calculations where the YS is required. It is unlikely the engineers on the Titan submersible made this mistake, but many of the news outlets that have covered this story have been using these terms interchangeably.

The next article will cover tensile tests and how to interpret the data in terms of stresses, strains, strain rate and deformation.