P Pallav, PhD

Ductile vs. Brittle Materials

Ductile and brittle are opposite notions in materials science; ‘more brittle’ means exactly the same as ‘less ductile’.

A large part between the proportional limit and the point of fracture in a stress-strain diagram characterizes a ductile material. Reducing this to tangible stress levels, clay is a ductile material and crispies are (or should be) brittle.

Returning to engineering stresses, metals are like extremely hard and tough clay, and ceramics are like very hard and strong crispies. When overstretched, iron (ductile) bends and glass (brittle) breaks.

With pure, i.e. unalloyed metals, the stress-strain diagrams in tension or in compression are nearly the same, but opposite. This also tends to be true for very ductile materials. With brittle materials the tensile strength is several times smaller than the compressive strength. Composites are generally about five times as strong in compression, many ceramics are often ten times stronger in compression than in tension.

Ductile Materials

Many ductile materials are metals. On an atomic scale, these consist of positively charged metal ions, which are held together by a negatively charged electron fluid. Because of this metals are strong, tough, deformable, impermeable, and good conductors of heat and electricity. The atoms are nearly always arranged in cubic or hexagon crystalline lattices. Hexagons (e.g. martensites) are often plastically more deformable and have lower elastic limits. By shearing along so-called slide planes, these can adapt to very much plastic deformation.

Work Hardening

When a tensile test has developed to an arbitrary point in the plastic region, the straight line may be produced by slowly unloading the sample (left). 

This line is exactly parallel to the first elastic (=straight) part of the curve. 

When at zero load, the load is increased again, this new test will look like the right figure. The first straight part is a copy of the unloading line of the previous test, which is shifted to the left because it is a new test.

It may be concluded that by loading the material into the plastic range, the elastic limit has increased to meet the applied load. This phenomenon is called work hardening. 
At the same time the proportional limit and the point of fracture are now closer together, which implies that the material has become more brittle.

Brittle

Brittleness influences the way materials fail (see: Fracture Mechanics), because it increases the sensitivity to tensile opening of pre-existing flaws. Less ductile materials and alloys (more flaws) are generally much weaker in tension.

With plaster, ceramics, composites, or glasses the proportional limits even coincide with the ultimate strengths. Composites are about five times as strong in compression. With concrete or plaster this is more, and with many ceramics this may exceed a factor of ten.

Super Elastic and Memory Materials

Although these effects were known from certain (visco-elastic) plastics, certain metal alloys, especially of nickel and titanium exhibit super elasticity and a shape memory effect in a very clear and distinct way.

Super Elasticity

With these rather special properties it is important to understand the distinction between the proportional limit(s) and the elastic limit, i.e. elasticity refers to the reversibility of the deformation, and proportionality to its linear relationship with the stress, the straight part in the stress – strain diagram.

Two temperature transitions or thresholds govern the behavior of these materials. When the metal is colder than the lowest temperature, only the deformable hexagon lattice can exist and the material behaves as a memory metal. It can handle substantial plastic deformation and springs back only very little. As such this resembles the deformability of soft metals like lead or copper. The memory effect, return to the original shape, occurs only when the metal is warmed up to the lower threshold and enters the super elastic region.

These figures show this translated in stress-strain diagrams at different temperatures.

The super elasticity and the memory effect are caused by so-called stress induced trans-crystallization between the hexagon and the cubic lattice. In both cases the cubic stores the original shape and the hexagon is deformable.

Trans-crystallization

The cubic austenite lattice, which works as the shape memory is a so-called bcc arrangement. Bcc means Body Centered Cube, the atoms are lined-up to form (square and equilateral) cubes like the white balls in the picture, which represents a bcc unit cell.

'Body centered' refers to the yellow extra atom, exactly at the center of the cube. In solid metals this structure is repeated nearly infinitely.

Although the picture seems to suggest more, one bcc unit cell is made up of two atoms. This is because each of the eight white corner atoms is shared by eight identical cubes and therefore is counted as only one eighth, so each cell contains eight eighth makes one white and one yellow, which is a total of two atoms.

Individual crystals, which are made of very many atoms, have an equal number of 'corner' and 'center' atoms. The 'quotes' illustrate the swap-ability of these notions, which we try to explain with the following figures.

This figure shows that the bcc comes down to a double cubic lattice, i.e. a cubic arrangement merged into another, yet identical cubic arrangement. All atoms may be called both 'corner' and 'center' atoms.

The colors of the balls do not refer to Ni or Ti. These are only used to show the difference in the arrangements. In super elastic alloys the Ni and Ti atoms are distributed randomly.  

Above the lower threshold temperature, depending on the stress, both the cubic and hexagon lattice can exist. Without stress it will spring back to the cubic lattice, which works as the shape memory.

When the lattice changes from cubic to hexagon or vice versa with temperature without stress (left top and bottom in the figure below), actually only one of the cubic arrangements changes. The yellow atoms at the bottom-left are still in the same cubic arrangement.

Warm Cold

Typical to the hexagon lattice is that certain planes can flip as is shown with the lower right sketch. In the right pictures the cubic arrangement of the center atoms (yellow) changes to hexagon at the shear plane (dotted line) and effectively blocks further shearing along this plane. With ordinary alloys this cannot be distinguished from plastic deformation and therefore hexagon alloys tend to have relatively low proportional limits.

It is interesting to see that by flipping only one of the three possible layers, a spectacular shear strain of 0.16 is obtained, whereas with ordinary metals a maximum elastic strain of 0.002 is normal.

 This figure shows the clinical significance of the parts of the stress – strain diagram, as well as the effect of a hot beverage. 

Manufacturers warn against warming up to the upper threshold, as this may result in significant changes in properties. At the best, only the cubic lattice can exist and any strain will become permanent, because shearing in this case is irreversible.

Visco Elastic Materials

These materials have properties that are normally associated with viscosity fluids, which means that their load response is time dependent. The figure shows the concept of retardation (constant stress) and relaxation (constant strain). Relaxation causes the force delivered by elastics to decrease with time.

Relaxation	Retardation
Applied strain Resulting stress	Applied stress Resulting strain

Generally a division is made between thermo-set materials, which are usually cross-linked, and thermo-plastic materials.

Thermo-plastics are generally less strong and stable than thermo-sets, therefore these are easier to melt or to solve, discolored, penetrated by water and other environmental compounds, and deteriorate more with time and applied stress.

This figure shows the influence of the temperature on the stress – strain diagram, however; with thermo-plastics there is some interchangeability between temperature and loading rate and the effect would have been about the same if the load had been applied (very) much slower.

Certain resin materials such as PMMA, are pseudo-crystalline below their glass-transition temperature. An electron microscopic cross-section shows regions where the polymer chains are arranged in a perfectly parallel order, which resembles the structure of poly-crystalline materials. The elastic module of the poly-crystalline material is considerably greater than in the amorphous state.