# Ductility

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Ductility is a measure of a material's ability to undergo significant plastic deformation before rupture or breaking, which may be expressed as percent elongation or percent area reduction from a tensile test. According to Shigley's Mechanical Engineering Design [1] significant denotes about 5.0 percent elongation.

## Contents

Percent elongation, or engineering strain at fracture, can be written as: [2] [3] [4]

${\displaystyle \%EL={\frac {final\ gage\ length-initial\ gage\ length}{initial\ gage\ length}}={\frac {l_{f}-l_{0}}{l_{0}}}*100}$

Percent reduction in area can be written as: [2] [3] [4]

${\displaystyle \%RA={\frac {change\ in\ area}{original\ area}}={\frac {A_{0}-A_{f}}{A_{0}}}*100}$

, where the area of concern is the cross-sectional area of the gage of the specimen. Ductility is sometimes also characterized by a material's ability to be stretched into a wire.

Other definition require a ductile material to have a measurable yield strength, at which unrecoverable plastic deformation begins (see Yield (engineering)), and also must satisfy one of the following conditions: either have an elongation to failure of at least 5%, or area reduction to rupture at least 20%, or true strain to rupture at least 10%.

Malleability, a similar property, is a material's ability to deform under compressive stress; this is often characterized by the material's ability to form a thin sheet by hammering or rolling. Both of these mechanical properties are aspects of plasticity, the extent to which a solid material can be plastically deformed without fracture. Also, these material properties are dependent on temperature and pressure (investigated by Percy Williams Bridgman as part of his Nobel Prize-winning work on high pressures).

Ductility and malleability are not always coextensive – for instance, while gold has high ductility and malleability, lead has low ductility but high malleability; [5] one ounce (31.1 gr) of gold can be drawn into more than 80 km of thin gold wire. One ounce (31.1 gr) of gold can be beaten into a sheet covering 9 square meters and 0.8 μm thick. [6] The word ductility is sometimes used to encompass both types of plasticity. [7]

## Materials science

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

High degrees of ductility occur due to metallic bonds, which are found predominantly in metals, leading to the common perception that metals are ductile in general. In metallic bonds valence shell electrons 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.

Ductility can be quantified by the fracture strain ${\displaystyle \varepsilon _{f}}$, which is the engineering strain at which a test specimen fractures during a uniaxial tensile test. Another commonly used measure is the reduction of area at fracture ${\displaystyle q}$. [9] The ductility of steel varies depending on the alloying constituents. Increasing the levels of carbon decreases ductility. Many plastics and amorphous solids, such as Play-Doh, are also malleable. The most ductile metal is platinum and the most malleable metal is gold. [10] [11] When highly stretched, such metals distort via formation, reorientation and migration of dislocations and crystal twins without noticeable hardening. [12]

## Ductile–brittle transition temperature

The ductile–brittle transition temperature (DBTT), nil ductility temperature (NDT), or nil ductility transition temperature of a metal is the temperature at which the fracture energy passes below a predetermined value (for steels typically 40 J [13] for a standard Charpy impact test). 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. For example, zamak 3 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 amorphous materials.

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 dislocations 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 lattice defects 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.

For experiments conducted at higher temperatures, dislocation activity[ clarification needed ] increases. At a certain temperature, dislocations shield[ clarification needed ] 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 fracture, and the transition temperature is raised.[ citation needed ]

## Related Research Articles

Structural geology is the study of the three-dimensional distribution of rock units with respect to their deformational histories. The primary goal of structural geology is to use measurements of present-day rock geometries to uncover information about the history of deformation (strain) in the rocks, and ultimately, to understand the stress field that resulted in the observed strain and geometries. This understanding of the dynamics of the stress field can be linked to important events in the geologic past; a common goal is to understand the structural evolution of a particular area with respect to regionally widespread patterns of rock deformation due to plate tectonics.

Ultimate tensile strength (UTS), often shortened to tensile strength (TS), ultimate strength, or within equations, is the maximum stress that a material can withstand while being stretched or pulled before breaking. In brittle materials the ultimate tensile strength is close to the yield point, whereas in ductile materials the ultimate tensile strength can be higher.

In engineering, deformation refers to the change in size or shape of an object. Displacements are the absolute change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strain is the relative internal change in shape of an infinitesimally small cube of material and can be expressed as a non-dimensional change in length or angle of distortion of the cube. Strains are related to the forces acting on the cube, which are known as stress, by a stress-strain curve. The relationship between stress and strain is generally linear and reversible up until the yield point and the deformation is elastic. The linear relationship for a material is known as Young's modulus. Above the yield point, some degree of permanent distortion remains after unloading and is termed plastic deformation. The determination of the stress and strain throughout a solid object is given by the field of strength of materials and for a structure by structural analysis.

In physics and materials science, plasticity, also known as plastic deformation, is the ability of a solid material to undergo permanent deformation, a non-reversible change of shape in response to applied forces. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the material itself. In engineering, the transition from elastic behavior to plastic behavior is known as yielding.

A stress–strain curve for a material gives the relationship between stress and strain. It is obtained by gradually applying load to a test coupon and measuring the deformation, from which the stress and strain can be determined. These curves reveal many of the properties of a material such as the Young's modulus, the yield strength and the ultimate tensile strength.

Fracture is the separation of an object or material into two or more pieces under the action of stress. The fracture of a solid usually occurs due to the development of certain displacement discontinuity surfaces within the solid. If a displacement develops perpendicular to the surface of displacement, it is called a normal tensile crack or simply a crack; if a displacement develops tangentially to the surface of displacement, it is called a shear crack, slip band, or dislocation.

In materials science, creep is the tendency of a solid material to move slowly or deform permanently under the influence of persistent mechanical stresses. It can occur as a result of long-term exposure to high levels of stress that are still below the yield strength of the material. Creep is more severe in materials that are subjected to heat for long periods and generally increases as they near their melting point.

A material is brittle if, when subjected to stress, it breaks with little elastic deformation and without significant plastic deformation. Brittle materials absorb relatively little energy prior to fracture, even those of high strength. Breaking is often accompanied by a snapping sound. Brittle materials include most ceramics and glasses and some polymers, such as PMMA and polystyrene. Many steels become brittle at low temperatures, depending on their composition and processing.

Work hardening, also known as strain hardening, is the strengthening of a metal or polymer by plastic deformation. Work hardening may be desirable, undesirable, or inconsequential, depending on the context.

The Charpy impact test, also known as the Charpy V-notch test, is a standardized high strain-rate test which determines the amount of energy absorbed by a material during fracture. Absorbed energy is a measure of the material's notch toughness. It is widely used in industry, since it is easy to prepare and conduct and results can be obtained quickly and cheaply. A disadvantage is that some results are only comparative. The test was pivotal in understanding the fracture problems of ships during World War II.

In materials science and engineering, the yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Prior to the yield point, a material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible and is known as plastic deformation.

Hardness is a measure of the resistance to localized plastic deformation induced by either mechanical indentation or abrasion. Some materials are harder than others. Macroscopic hardness is generally characterized by strong intermolecular bonds, but the behavior of solid materials under force is complex; therefore, there are different measurements of hardness: scratch hardness, indentation hardness, and rebound hardness.

Critical resolved shear stress (CRSS) is the component of shear stress, resolved in the direction of slip, necessary to initiate slip in a grain. Resolved shear stress (RSS) is the shear component of an applied tensile or compressive stress resolved along a slip plane that is other than perpendicular or parallel to the stress axis. The RSS is related to the applied stress by a geometrical factor, m, typically the Schmid factor:

Constance Tipper was an English metallurgist and crystallographer. She investigated brittle fracture and the ductile-brittle transition of metals used in the construction of warships, and was the first female full-time faculty member at Cambridge University Department of Engineering.

Methods have been devised to modify the yield strength, ductility, and toughness of both crystalline and amorphous materials. These strengthening mechanisms give engineers the ability to tailor the mechanical properties of materials to suit a variety of different applications. For example, the favorable properties of steel result from interstitial incorporation of carbon into the iron lattice. Brass, a binary alloy of copper and zinc, has superior mechanical properties compared to its constituent metals due to solution strengthening. Work hardening has also been used for centuries by blacksmiths to introduce dislocations into materials, increasing their yield strengths.

Rubber toughening is a process in which rubber nanoparticles are interspersed within a polymer matrix to increase the mechanical robustness, or toughness, of the material. By "toughening" a polymer it is meant that the ability of the polymeric substance to absorb energy and plastically deform without fracture is increased. Considering the significant advantages in mechanical properties that rubber toughening offers, most major thermoplastics are available in rubber-toughened versions; for many engineering applications, material toughness is a deciding factor in final material selection.

Tensile testing, also known as tension testing, is a fundamental materials science and engineering test in which a sample is subjected to a controlled tension until failure. Properties that are directly measured via a tensile test are ultimate tensile strength, breaking strength, maximum elongation and reduction in area. From these measurements the following properties can also be determined: Young's modulus, Poisson's ratio, yield strength, and strain-hardening characteristics. Uniaxial tensile testing is the most commonly used for obtaining the mechanical characteristics of isotropic materials. Some materials use biaxial tensile testing. The main difference between these testing machines being how load is applied on the materials.

In Earth science, as opposed to Materials Science, Ductility refers to the capacity of a rock to deform to large strains without macroscopic fracturing. Such behavior may occur in unlithified or poorly lithified sediments, in weak materials such as halite or at greater depths in all rock types where higher temperatures promote crystal plasticity and higher confining pressures suppress brittle fracture. In addition, when a material is behaving ductilely, it exhibits a linear stress vs strain relationship past the elastic limit.

Polymer fracture is the study of the fracture surface of an already failed material to determine the method of crack formation and extension in polymers both fiber reinforced and otherwise. Failure in polymer components can occur at relatively low stress levels, far below the tensile strength because of four major reasons: long term stress or creep rupture, cyclic stresses or fatigue, the presence of structural flaws and stress-cracking agents. Formations of submicroscopic cracks in polymers under load have been studied by x ray scattering techniques and the main regularities of crack formation under different loading conditions have been analyzed. The low strength of polymers compared to theoretically predicted values are mainly due to the many microscopic imperfections found in the material. These defects namely dislocations, crystalline boundaries, amorphous interlayers and block structure can all lead to the non-uniform distribution of mechanical stress.

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