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Ductility test on towel. Image Credit: Shutterstock.com/liuhuaxuan

How To Calculate Ductility?

Learn more about how ductility is calculated and the common units of measurement for it.

Xomety X
By Team Xometry
April 21, 2023
 10 min read
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Ductility is defined as the ability of a material to inelastically stretch under tension without fracture or loss of integrity. In most cases, materials display some elastic behavior in tension. An applied load (stress) results in an elastic extension (strain) that recovers fully when the load is removed.

Ductility occurs when the applied load exceeds the elastic limit of the material and a plastic or permanent displacement/extension occurs in the line of the applied force. Many materials experience a very slow onset of such deformation with increasing load, with no clear, discernible alteration in strength. Others show a marked change in properties and experience a distinct and measurable “yield” point at which plastic deformation commences. As the load is removed, the plastic extension will remain, whereas the initial elastic extension will recover. This results in a hysteresis curve in the load/extension graph. Listed below are the methods on how to calculate ductility:

1. Elongation

One method for measuring the ductile behavior of a material sample uses a tensile test machine. This device can measure small longitudinal extensions and recoveries while applying well-controlled and stepped patterns of loading and unloading to a sample. This is a similar equipment/method used to measure Young's modulus. Ductility tests, however, are deliberately set to exceed the yield point of the material and cause plastic deformation. The simplest method for quantifying these test results lies in calculating the percentage elongation of the sample until the fracture point occurs. For more information, see our guide on Elongation.

2. Reduction of the Cross-Sectional Area

An alternative approach uses percentage change in cross-sectional area as the measure. This measures the area before and after the fracture loading—using the area at the fracture for the final measurement.

What Is Ductility?

Ductility is the ability of a material to distort plastically under tension. This is the result of non-fracturing intra-atomic, intracellular, or intra-molecular slippage. In a metal, the atomic structure consists of planes of metal atoms that are internally coupled by covalent bonds and intra-layer coupled by electrostatic or weak atomic forces. When the crystals are large, the interlayer coupling can act as “slip planes.” This allows crystals to step and reform the electrostatic bonds without fracture. This potential is strongest in metals with a face-centered cubic crystal structure.

In polymers, the mechanism is related. The structure is generally not crystalline but built from polymer chains that lie alongside and around each other. These are more weakly coupled than slip planes in metals, as their disordered nature prevents them from lying in such close proximity. Incidentally, this is why metals tend to be stronger and denser than polymers.

The slip mechanism in polymers (and also in some natural materials) is these polymer chains sliding against each other, generally without polymer chain failure. This can, in some polymers, allow long extensions and the onset of a form of crystallinity as chains are pulled into alignment. This property is exploited in biaxially oriented films such as those made by stretching PET and PP. For more information, see our guide on Ductility.

What Is the Importance of Ductility?

The importance of ductility is listed below:

  1. The ability to tolerate extension and displacement allows the forming of complex shapes in components. Where a bend is applied, ductility is exploited on the outside of the bend, as the material is extended and curved. On the inside of the bend, the sister property of malleability is exploited. This is a measure of the material’s ability to be squeezed and displaced by pressure (as opposed to tension).
  2. Critically useful feature in finished components and devices. Rigid and brittle materials that experience shock and vibrating overloads have a stronger tendency to crack/fail. A good example of this is the use of wrought iron in boilers in the early industrial revolution. Wrought iron is very strong but has nearly zero ductility, so boiler explosions were commonplace. The advent of more ductile steels rendered boilers more able to withstand the cyclic stresses of pressure and release without fracturing. Tiny plastic displacements made no functional difference to dimensions but rendered the boilers tougher and much more service capable.
  3. The primary mechanism in drawing down metals to form wires and drawn seamless tubes, both of which are valuable areas of engineering materials manufacture.

Why Calculating Ductility Is Necessary

Calculating ductility is necessary because it determines how much a material can be deformed before it fails. It is an essential factor in designing and selecting materials for safe and enduring use in a wide spectrum of applications. Industries such as construction, automotive, or aerospace, rely heavily on the ductility of materials, both for manufacture and use. So, it is a crucial factor in determining the manufacturing processes and the strength and reliability of components and structures.

Ductility is quantified in two ways: by measuring the elongation or reduction in the cross-sectional area of a sample at fracture loading. Comparing the results of these tests, helps engineers and scientists make informed decisions about the suitability of a particular material for a specific application. It also helps in making improvements in the material's properties to meet their desired requirements. It should be noted that comparisons of test results between the two methods are less reliable and interpretable. The relative ductility of materials should generally be compared to same-test results.

How Is Ductility Calculated Using the Tensile Test?

Ductility is expressed as a percentage reduction in cross-sectional area at the fracture. For more information, see our guide on Tensile Strength.

It is calculated by the following equation:

Slide 1 of 1
ductility calculated using tensile test
ductility calculated using tensile test
ductility calculated using tensile test

Ductility calculated using tensile test.

How Is Ductility Measured Using the Elongation Test?

Ductility can be expressed as percentage extension at fracture using the equation below:

Slide 1 of 1
ductility measured with elongation test
ductility measured with elongation test
ductility measured with elongation test

Ductility measured with elongation test.

How Is Ductility Used in Engineering?

Engineers and designers use knowledge of the ductility of a material to determine its suitability for specific applications. Ductile materials such as steel and aluminum are generally selected in the construction and automotive sectors to absorb energy and prevent catastrophic failures. The ductility of a material can be used to design components that will be impact, vibration, and abuse-tolerant, without failure. Safety-critical components such as bridge cables, pipelines, and aircraft structures are always designed for ductility, even if distortions result in reduced function. Additionally, an understanding of ductility (and its limits) can be used to analyze the cause of material failures. Components that fail due to brittle fracture show that the material or designs did not possess enough survivability in the application. The ductility of a material can be improved through various techniques such as heat treatment and alloying. By optimizing these processes, engineers can increase the ductility of materials, making them suitable for specific applications.

What Is Ductility Index?

The ductility index is the proportion of total elongation at fracture that is ductile (i.e., plastic in nature). When a part is released before fracture, some component of the material’s extension will recover, elastically. When a tensile-loaded part fractures, a gap will immediately appear at the break, as the material on either side relaxes back the elastic extension that was included in the total extension. Highly elastic material with a short ductile phase will have a low ductility index. A low-elasticity material with a long ductile phase will have a high ductility index.

How Is Ductility Index Calculated?

Ductility index is calculated as:

Slide 1 of 1
ductility index calculation
ductility index calculation
ductility index calculation

Ductility index calculation.

What Are Some Common Units of Measurement Used for Ductility?

Ductility is a dimensionless number, as it is the result of a length divided by a length or an area divided by an area. In both cases, the measurement is expressed as a percentage.

What Factors Affect Ductility?

The ductility of materials is a factor that can be influenced by various treatments that should be selected according to the material class and condition. Listed below are some factors that affect it:

  1. Increasing Temperature, For Most Materials: At higher temperatures, the atoms in the material have more thermal energy and are more likely to move past each other, making it easier for the atoms to displace in the crystal structure.
  2. Rate at Which a Material is Loaded: Higher strain rates can cause the material to deform more quickly, making non-fracturing atomic displacements harder to achieve.
  3. Composition of Materials: For example, materials with a high concentration of impurities or defects may have lower ductility than purer materials. Where an alloying agent is of low ductility, it can significantly affect the behavior of the main constituent.
  4. Crystal Structure of the Material: Materials with a close-packed crystal structure, particularly metals with face-centered cubic structures, are generally more ductile than materials with a less-compact structure, such as body-centered cubic metals.
  5. Larger Molecular Structure: For example, polyethylene has significant ductility whereas nylon is more rigid, elastic, and brittle because of the polymer chain strength and entanglement.
  6. Presence of Other Phases (Inclusions or Second-phase Particles): These phases can act as stress concentrators, leading to localized plastic deformation and reducing the overall ductility of the material.
  7. Stress State of the Material: For example, materials under compression may have higher ductility than those under tension, as the compression can lead to the closure of pre-existing cracks and voids, reducing the likelihood of fracture.

Can I Calculate the Ductility of Iron?

Yes, the ductility of iron can be calculated. Iron exists in various forms, some of which are ductile and others brittle in response to tensile load. Pure iron (i.e., metallic, atomic iron) is highly ductile, and the ductility can be measured very accurately for a pure sample. Very different results can be expected from cast iron, nodular cast iron, wrought iron, etc.—but the ductility of all varieties is well recorded and understood.

Is Elongation at Break Used To Calculate Ductility?

Yes, elongation at fracture is measured. The percentage increase in length is the most common measure of ductility.

Are All Metals Ductile?

No, metals represent a full range of ductilities, from near zero to the most ductile of all materials. Often these degrees of ductility are characteristic of chemically near-identical materials in which some properties are altered subtly. For example, cast iron has no ductile phase, but goes straight from elasticity to fracture. However, when formulated as nodular cast iron, it becomes extremely ductile.

Is Gold Ductile Metal?

Yes, gold is a highly ductile material. Gold was long taken to be the most ductile material, with a gram of gold being commonly drawn to 1,000 meters in length. That “most-ductile” title is now held by platinum.

Summary

This article presented calculating ductility, explained what it is, and discussed the importance of calculating it and common units of measurement for it. To learn more about calculating ductility, contact a Xometry representative.

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Xomety X
Team Xometry
This article was written by various Xometry contributors. Xometry is a leading resource on manufacturing with CNC machining, sheet metal fabrication, 3D printing, injection molding, urethane casting, and more.