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# Ductility  ( Continuum Mechanics )

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Ductility is a mechanical property commonly described as a material's amenability to drawing (e.g. into wire). In materials science, ductility is defined by the degree to which a material can sustain plastic deformation under tensile stress before failure.

Ductility is an important consideration in engineering and manufacturing, defining a material's suitability for certain manufacturing operations (such as ) and its capacity to absorb mechanical overload.
(2022). 9780073398204, McGraw Hill. .
.
Some metals that are generally described as ductile include and . /ref>

Malleability, a similar mechanical property, is characterized by a material's ability to deform plastically without failure under compressive stress. Historically, materials were considered malleable if they were amenable to forming by hammering or rolling. Lead is an example of a material which is relatively malleable but not ductile.

(1988). 9780486257426, Courier Dover Publications. .
.

Materials science
Ductility is especially important in , as materials that crack, break or shatter under stress cannot be manipulated using metal-forming processes such as , rolling, drawing or . Malleable materials can be formed cold using stamping or , whereas brittle materials may be or .

High degrees of ductility occur due to , which are found predominantly in metals; this leads to the common perception that metals are ductile in general. In metallic bonds are delocalized and shared between many atoms. The delocalized electrons allow metal atoms to slide past one another without being subjected to strong repulsive forces that would cause other materials to shatter.

The ductility of varies depending on the alloying constituents. Increasing the levels of decreases ductility. Many plastics and , such as , are also malleable. The most ductile metal is and the most malleable metal is .Vaccaro, John (2002) Materials handbook, Mc Graw-Hill handbooks, 15th ed.Schwartz, M. (2002) CRC encyclopedia of materials parts and finishes, 2nd ed. When highly stretched, such metals distort via formation, reorientation and migration of and without noticeable hardening.

Quantification of ductility
The quantities commonly used to define ductility in a tension test are percent elongation (sometimes denoted as $\varepsilon_f$) and reduction of area (sometimes denoted as $q$) at fracture.Dieter, G. (1986) Mechanical Metallurgy, McGraw-Hill, Fracture strain is the engineering strain at which a test specimen fractures during a . Percent elongation, or engineering strain at fracture, can be written as:
(2022). 9781305076761 .
(2022). 9780470419977 .

$\%EL = \frac\left\{\text\left\{final gage length - initial gage length\right\}\right\}\left\{\text\left\{initial gage length\right\}\right\} = \frac\left\{l_f - l_0\right\}\left\{l_0\right\} \cdot 100$

Percent reduction in area can be written as:

$\%RA = \frac\left\{\text\left\{change in area\right\}\right\}\left\{\text\left\{original area\right\}\right\} = \frac\left\{A_0 - A_f\right\}\left\{A_0\right\} \cdot 100$

where the area of concern is the cross-sectional area of the gage of the specimen.

According to Shigley's Mechanical Engineering Design significant denotes about 5.0 percent elongation.

Ductile–brittle transition temperature
[[File:Ductility.svg|thumb|right|Schematic appearance of round metal bars after tensile testing.
(a) Brittle fracture
(b) Ductile fracture
(c) Completely ductile fracture]]

The plastic deformation of ductile metals is important as it can be a sign of the potential failure of the metal. Yet, the point at which the material exhibits a ductile behavior versus a brittle behavior is not only dependent on the material itself but also on the temperature at which the stress is being applied to the material at. The temperature where the material changes from brittle to ductile or vice versa is crucial for the design of load-bearing metallic products. The minimum temperature at which the metal transitions from a brittle behavior to a ductile behavior, or from a ductile behavior to a brittle behavior, is known as the ductile-brittle transition temperature (DBTT). Below the DBTT, the material will not be able to plastically deform, and the crack propagation rate increases rapidly leading to the material undergoing brittle failure rapidly. Furthermore, DBTT is important since, once a material is cooled below the DBTT, it has a much greater tendency to shatter on impact instead of bending or deforming (low temperature embrittlement). Thus, the DBTT indicates the temperature at which, as temperature decreases, a material’s ability to deform in a ductile manner decreases and so the rate of crack propagation drastically increases. In other words, solids are very brittle at very low temperatures, and their toughness becomes much higher at elevated temperatures.

For more general applications, it is preferred to have a lower DBTT to ensure the material has a wider ductility range. This ensures that sudden cracks are inhibited so that failures in the metal body are prevented. It has been determined that the more slip systems a material has, the wider the range of temperatures ductile behavior is exhibited at. This is due to the slip systems allowing for more motion of dislocations when a stress is applied to the material. Thus, in materials with a lower amount of slip systems, dislocations are often pinned by obstacles leading to strain hardening, which increases the materials strength which makes the material more brittle. For this reason, FCC structures are ductile over a wide range of temperatures, BCC structures are ductile only at high temperatures, and HCP structures are often brittle over wide ranges of temperatures. This leads to each of these structures having different performances as they approach failure (fatigue, overload, and stress cracking) under various temperatures, and shows the importance of the DBTT in selecting the correct material for a specific application. For example, exhibits good ductility at room temperature but shatters when impacted at sub-zero temperatures. DBTT is a very important consideration in selecting materials that are subjected to mechanical stresses. A similar phenomenon, the glass transition temperature, occurs with glasses and polymers, although the mechanism is different in these . The DBTT is also dependent on the size of the grains within the metal, as typically smaller grain size leads to an increase in tensile strength, resulting in an increase in ductility and decrease in the DBTT. This increase in tensile strength is due to the smaller grain sizes resulting in grain boundary hardening occurring within the material, where the dislocations require a larger stress to bypass the grain boundaries and continue to propagate throughout the material. It has been shown that by continuing to refine ferrite grains to reduce their size, from 40 microns down to 1.3 microns, that it is possible to eliminate the DBTT entirely so that a brittle fracture never occurs in ferritic steel (as the DBTT required would be below absolute zero).

In some materials, the transition is sharper than others and typically requires a temperature-sensitive deformation mechanism. For example, in materials with a body-centered cubic (bcc) lattice the DBTT is readily apparent, as the motion of screw is very temperature sensitive because the rearrangement of the dislocation core prior to slip requires thermal activation. This can be problematic for steels with a high ferrite content. This famously resulted in serious hull cracking in Liberty ships in colder waters during World War II, causing many sinkings. DBTT can also be influenced by external factors such as neutron radiation, which leads to an increase in internal and a corresponding decrease in ductility and increase in DBTT.

The most accurate method of measuring the DBTT of a material is by fracture testing. Typically four point bend testing at a range of temperatures is performed on pre-cracked bars of polished material. Two fracture tests are typically utilized to determine the DBTT of specific metals: the Charpy V-Notch test and the Izod test. The Charpy V-notch test determines the impact energy absorption ability or toughness of the specimen by measuring the potential energy difference resulting from the collision between a mass on a free-falling pendulum and the machined V-shaped notch in the sample, resulting in the pendulum breaking through the sample. The DBTT is determined by repeating this test over a variety of temperatures and noting when the resulting fracture changes to a brittle behavior which occurs when the absorbed energy is dramatically decreased. The Izod test is essentially the same as the Charpy test, with the only differentiating factor being the placement of the sample; In the former the sample is placed vertically, while in the latter the sample is placed horizontally with respect to the bottom of the base.

For experiments conducted at higher temperatures, activity increases. At a certain temperature, dislocations shield the crack tip to such an extent that the applied deformation rate is not sufficient for the stress intensity at the crack-tip to reach the critical value for fracture (KiC). The temperature at which this occurs is the ductile–brittle transition temperature. If experiments are performed at a higher strain rate, more dislocation shielding is required to prevent brittle , and the transition temperature is raised.

• Deformation
• , which improves ductility in uniaxial tension by delaying the onset of instability
• Strength of materials

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