# Ductility

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Ductility is a measure of a material's ability to undergo significant plastic deformation before rupture, which may be expressed as percent elongation or percent area reduction from a tensile test. According to Shigley's Mechanical Engineering Design (10th Ed.) [2] significant denotes about 5.0 percent elongation (Section 5.3, p. 233). See also Eq. 2–12, p. 50 for definitions of percent elongation and percent area reduction. Ductility is often characterized by a material's ability to be stretched into a wire.

## Contents

From examination of data in Tables A20, A21, A22, A23, and A24 in Shigley's Mechanical Engineering Design, 10th Edition, [2] for both ductile and brittle materials, it is possible to postulate a broader quantifiable definition of ductility that does not rely on percent elongation alone. In general, a ductile material must 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%.

The yield point is the point on a stress–strain curve that indicates the limit of elastic behavior and the beginning plastic behavior. Yield strength or yield stress is the material property defined as the stress at which a material begins to deform plastically whereas yield point is the point where nonlinear deformation begins. Prior to the yield point the 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.

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).

In physics and materials science, plasticity describes the deformation of a (solid) material undergoing non-reversible changes 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 called yield.

A 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.

Percy Williams Bridgman was an American physicist who received the 1946 Nobel Prize in Physics for his work on the physics of high pressures. He also wrote extensively on the scientific method and on other aspects of the philosophy of science. The Bridgman effect and the Bridgman–Stockbarger technique are named after him.

Ductility and malleability are not always coextensive – for instance, while gold has high ductility and malleability, lead has low ductility but high malleability; [3] one ounce of gold can be drawn into more than 80 Km of thin gold wire. One ounce of gold can be beaten into a sheet covering 9 square meters and 0.000018 cm thick [4] . The word ductility is sometimes used to encompass both types of plasticity. [5]

Gold is a chemical element with the symbol Au and atomic number 79, making it one of the higher atomic number elements that occur naturally. In its purest form, it is a bright, slightly reddish yellow, dense, soft, malleable, and ductile metal. Chemically, gold is a transition metal and a group 11 element. It is one of the least reactive chemical elements and is solid under standard conditions. Gold often occurs in free elemental (native) form, as nuggets or grains, in rocks, in veins, and in alluvial deposits. It occurs in a solid solution series with the native element silver and also naturally alloyed with copper and palladium. Less commonly, it occurs in minerals as gold compounds, often with tellurium.

Lead is a chemical element with the symbol Pb and atomic number 82. It is a heavy metal that is denser than most common materials. Lead is soft and malleable, and also has a relatively low melting point. When freshly cut, lead is silvery with a hint of blue; it tarnishes to a dull gray color when exposed to air. Lead has the highest atomic number of any stable element and three of its isotopes are endpoints of major nuclear decay chains of heavier elements.

## 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.

Metalworking is the process of working with metals to create individual parts, assemblies, or large-scale structures. The term covers a wide range of work from large ships and bridges to precise engine parts and delicate jewelry. It therefore includes a correspondingly wide range of skills, processes, and tools.

A hammer is a tool consisting of a weighted "head" fixed to a long handle that is swung to deliver an impact to a small area of an object. This can be, for example, to drive nails into wood, to shape metal, or to crush rock. Hammers are used for a wide range of driving, shaping, and breaking applications.

In metalworking, rolling is a metal forming process in which metal stock is passed through one or more pairs of rolls to reduce the thickness and to make the thickness uniform. The concept is similar to the rolling of dough. Rolling is classified according to the temperature of the metal rolled. If the temperature of the metal is above its recrystallization temperature, then the process is known as hot rolling. If the temperature of the metal is below its recrystallization temperature, the process is known as cold rolling. In terms of usage, hot rolling processes more tonnage than any other manufacturing process, and cold rolling processes the most tonnage out of all cold working processes. Roll stands holding pairs of rolls are grouped together into rolling mills that can quickly process metal, typically steel, into products such as structural steel, bar stock, and rails. Most steel mills have rolling mill divisions that convert the semi-finished casting products into finished products.

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.

The electron is a subatomic particle, symbol
e
or
β
, whose electric charge is negative one elementary charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron has a mass that is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum (spin) of a half-integer value, expressed in units of the reduced Planck constant, ħ. Being fermions, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves: they can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer de Broglie wavelength for a given energy.

In chemistry, delocalized electrons are electrons in a molecule, ion or solid metal that are not associated with a single atom or a covalent bond. The term delocalization is general and can have slightly different meanings in different fields. In organic chemistry, this refers to resonance in conjugated systems and aromatic compounds. In solid-state physics, this refers to free electrons that facilitate electrical conduction. In quantum chemistry, this refers to molecular orbital electrons that have extended over several adjacent atoms.

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 ${\displaystyle q}$. [7] 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. [8] [9] When highly stretched, such metals distort via formation, reorientation and migration of dislocations and crystal twins without noticeable hardening. [10]

## 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 [11] 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 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 fracture, and the transition temperature is raised.

## Related Research Articles

In materials science, deformation refers to any changes in the shape or size of an object due to

The relationship between the stress and strain that a particular material displays is known as that particular material's stress–strain curve. It is unique for each material and is found by recording the amount of deformation (strain) at distinct intervals of a variety of loadings (stress). These curves reveal many of the properties of a material.

Strength of materials, also called mechanics of materials, which deals with the behavior of solid objects subject to stresses and strains. The complete theory began with the consideration of the behavior of one and two dimensional members of structures, whose states of stress can be approximated as two dimensional, and was then generalized to three dimensions to develop a more complete theory of the elastic and plastic behavior of materials. An important founding pioneer in mechanics of materials was Stephen Timoshenko.

In materials science and metallurgy, toughness is the ability of a material to absorb energy and plastically deform without fracturing. One definition of material toughness is the amount of energy per unit volume that a material can absorb before rupturing. It is also defined as a material's resistance to fracture when stressed.

A material is brittle if, when subjected to stress, it breaks 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.

Hydrogen embrittlement (HE) also known as hydrogen assisted cracking (HAC) and hydrogen-induced cracking (HIC), describes the embrittling of metal after being exposed to hydrogen. It is a complex process that is not completely understood because of the variety of mechanisms that can lead to embrittlement. Mechanisms that have been proposed to explain embrittlement include the formation of brittle hydrides within certain metals, the creation of voids that can lead to bubbles and pressure build-up within a material and enhanced decohesion or localised plasticity that assist in the propagation of cracks.

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. This absorbed energy is a measure of a given material's notch toughness and acts as a tool to study temperature-dependent ductile-brittle transition. It is widely applied 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.

In materials science, fracture toughness is a property which describes the ability of a material to resist fracture, and is one of the most important properties of any material for many design applications. The linear-elastic fracture toughness of a material is determined from the stress intensity factor at which a thin crack in the material begins to grow. It is denoted KIc and has the units of or . Plastic-elastic fracture toughness is denoted by JIc, with the unit of J/cm2 or lbf-in/in2, and is a measurement of the energy required to grow a thin crack.

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.

Geodynamics is a subfield of geophysics dealing with dynamics of the Earth. It applies physics, chemistry and mathematics to the understanding of how mantle convection leads to plate tectonics and geologic phenomena such as seafloor spreading, mountain building, volcanoes, earthquakes, faulting and so on. It also attempts to probe the internal activity by measuring magnetic fields, gravity, and seismic waves, as well as the mineralogy of rocks and their isotopic composition. Methods of geodynamics are also applied to exploration of other planets.

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.

Environmental Stress Cracking (ESC) is one of the most common causes of unexpected brittle failure of thermoplastic polymers known at present. According to ASTM D883, stress cracking is defined as " an external or internal crack in a plastic caused by tensile stresses less than its short-term mechanical strength." This type of cracking typically involves brittle cracking, with little or no ductile drawing of the material from its adjacent failure surfaces. Environmental stress cracking may account for around 15-30% of all plastic component failures in service. This behavior is especially prevalent in glassy, amorphous thermoplastics. Amorphous polymers exhibit ESC because of their loose structure which makes it easier for the fluid to permeate into the polymer. Amorphous polymers are more prone to ESC at temperature higher than their glass transition temperature (Tg) due to the increased free volume. When Tg is approached, more fluid can permeate permeation into the polymer chains.

Failure theory is the science of predicting the conditions under which solid materials fail under the action of external loads. The failure of a material is usually classified into brittle failure (fracture) or ductile failure (yield). Depending on the conditions most materials can fail in a brittle or ductile manner or both. However, for most practical situations, a material may be classified as either brittle or ductile. Though failure theory has been in development for over 200 years, its level of acceptability is yet to reach that of continuum mechanics.

Polymer characterization is the analytical branch of polymer science.

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.

## References

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