Ductility is the ability of a material to sustain significant plastic deformation before fracture when undergoing tension, i.e. when the relevant elastic modulus is Young's; the equivalent for deforming under bulk compression, i.e. when using the bulk modulus, is malleability. Historically, materials were considered malleable if they were amenable to forming by hammering or rolling. Lead is an example of a material which is substantially more malleable than ductile.. Plastic deformation is the permanent distortion of a material under applied stress, as opposed to elastic deformation, which is reversible upon removing the stress. Ductility is a critical mechanical performance indicator, particularly in applications that require materials to bend, stretch, or deform in other ways without breaking. The extent of ductility can be quantitatively assessed using the percent elongation at break, given by the equation:
where is the length of the material after fracture and is the original length before testing. This formula helps in quantifying how much a material can stretch under tensile stress before failure, providing key insights into its ductile behavior. Ductility is an important consideration in engineering and manufacturing. It defines a material's suitability for certain manufacturing operations (such as cold working) and its capacity to absorb mechanical overload like in an engine.. Some metals that are generally described as ductile include gold and copper, while platinum is the most ductile of all metals in pure form. However, not all metals experience ductile failure, as some experience brittle failure instead, such as cast iron. Polymers can generally be viewed as ductile materials, as they typically allow for plastic deformation.Ductility and its effect on material failure. The Engineering Archive. (n.d.). https://theengineeringarchive.com/material-science/page-ductility-material-failure.html
Inorganic materials, including a wide variety of ceramics and semiconductors, are generally characterized by their brittleness. This brittleness primarily stems from their strong ionic or covalent bonds, which maintain the atoms in a rigid, densely packed arrangement. Such a rigid lattice structure restricts the movement of atoms or dislocations, essential for plastic deformation. The significant difference in ductility observed between metals and inorganic semiconductor or insulator can be traced back to each material's inherent characteristics, including the nature of their defects, such as dislocations, and their specific chemical bonding properties. Consequently, unlike ductile metals and some organic materials with ductility (%EL) from 1.2% to over 1200%, brittle inorganic semiconductors and ceramic insulators typically show much smaller ductility at room temperature.
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; this leads 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 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. Gold is the most malleable metal, while platinum is the most ductile of the pure metals.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 dislocations and crystal twins without noticeable hardening.
Quantification Basic definitions The quantities commonly used to define ductility in a tension test are relative elongation (in percent, sometimes denoted as ) and reduction of area (sometimes denoted as ) at fracture.Dieter, G. (1986) Mechanical Metallurgy, McGraw-Hill, Fracture strain is the engineering strain at which a test specimen fractures during a uniaxial tensile test. Percent elongation, or engineering strain at fracture, can be written as:
Percent reduction in area can be written as:
where the area of concern is the cross-sectional area of the gauge of the specimen.
According to Shigley's Mechanical Engineering Design, 'significant' denotes about 5.0 percent elongation.
Effect of sample dimensions An important point concerning the value of the ductility (nominal strain at failure) in a tensile test is that it commonly exhibits a dependence on sample dimensions. However, a universal parameter should exhibit no such dependence (and, indeed, there is no dependence for properties such as stiffness, yield stress and ultimate tensile strength). This occurs because the measured strain (displacement) at fracture commonly incorporates contributions from both the uniform deformation occurring up to the onset of necking and the subsequent deformation of the neck (during which there is little or no deformation in the rest of the sample). The significance of the contribution from neck development depends on the "aspect ratio" (length / diameter) of the gauge length, being greater when the ratio is low. This is a simple geometric effect, which has been clearly identified. There have been both experimental studies and theoretical explorations of the effect, mostly based on Finite Element Method (FEM) modelling. Nevertheless, it is not universally appreciated and, since the range of sample dimensions in common use is quite wide, it can lead to highly significant variations (by factors of up to 2 or 3) in ductility values obtained for the same material in different tests.
A more meaningful representation of ductility would be obtained by identifying the strain at the onset of necking, which should be independent of sample dimensions. This point can be difficult to identify on a (nominal) stress-strain curve, because the peak (representing the onset of necking) is often relatively flat. Moreover, some (brittle) materials fracture before the onset of necking, such that there is no peak. In practice, for many purposes it is preferable to carry out a different kind of test, designed to evaluate the toughness (energy absorbed during fracture), rather than use ductility values obtained in tensile tests.
In an absolute sense, "ductility" values are therefore virtually meaningless. The actual (true) strain in the neck at the point of fracture bears no direct relation to the raw number obtained from the nominal stress-strain curve; the true strain in the neck is often considerably higher. Also, the true stress at the point of fracture is usually higher than the apparent value according to the plot. The load often drops while the neck develops, but the sectional area in the neck is also dropping (more sharply), so the true stress there is rising. There is no simple way of estimating this value, since it depends on the geometry of the neck. While the true strain at fracture is a genuine indicator of "ductility", it cannot readily be obtained from a conventional tensile test.
The Reduction in Area (RA) is defined as the decrease in sectional area at the neck (usually obtained by measurement of the diameter at one or both of the fractured ends), divided by the original sectional area. It is sometimes stated that this is a more reliable indicator of the "ductility" than the elongation at failure (partly in recognition of the fact that the latter is dependent on the aspect ratio of the gauge length, although this dependence is far from being universally appreciated). There is something in this argument, but the RA is still some way from being a genuinely meaningful parameter. One objection is that it is not easy to measure accurately, particularly with samples that are not circular in section. Rather more fundamentally, it is affected by both the uniform plastic deformation that took place before necking and by the development of the neck. Furthermore, it is sensitive to exactly what happens in the latter stages of necking, when the true strain is often becoming very high and the behavior is of limited significance in terms of a meaningful definition of strength (or toughness). There has again been extensive study of this issue.
Poisson's Ratio Richard Christensen, a doctor in engineering mechanics, argues that ductility in an isotropic material can be quantified in terms of poisson's ratio. In particular, he manipulates the formula for converting a material's bulk modulus to shear modulus via poisson's ratio to determine a "ductility" quantity :
, the intermediate "ductility index", involves dropping the 3/2 term to normalize the ratio to normally be from 1.0 to 0.5 (as is usually between 0 and 0.5), taking the difference from 1 so that it scales up instead of down, and then squaring it to make easier to calculate in terms of it. Because this formula is partially based on the false assumption that is always positive, auxetics, such as defective graphene, will have positive , i.e. more ductility than a material with = 0; more "normal" values will have ductility values that directly correlate with poisson's ratio (so a higher value of one implies a higher value of the other, and vice versa). For the non-auxetics Christensen studied, this quantification of ductility appears to be reasonably close to other popular heuristics for quantifying it.
Ductile–brittle transition temperature