Toughness

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Toughness as defined by the area under the stress-strain curve Toughness area under curve.svg
Toughness as defined by the area under the stress–strain curve

In materials science and metallurgy, toughness is the ability of a material to absorb energy and plastically deform without fracturing. [1] Toughness is the strength with which the material opposes rupture. One definition of material toughness is the amount of energy per unit volume that a material can absorb before rupturing. This measure of toughness is different from that used for fracture toughness, which describes the capacity of materials to resist fracture. [2] Toughness requires a balance of strength and ductility. [1]

Contents

Toughness and strength

Toughness is related to the area under the stress–strain curve. In order to be tough, a material must be both strong and ductile. For example, brittle materials (like ceramics) that are strong but with limited ductility are not tough; conversely, very ductile materials with low strengths are also not tough. To be tough, a material should withstand both high stresses and high strains. Generally speaking, strength indicates how much force the material can support, while toughness indicates how much energy a material can absorb before rupturing.

Mathematical definition

Toughness can be determined by integrating the stress-strain curve. [1] It is the energy of mechanical deformation per unit volume prior to fracture. The explicit mathematical description is: [3]

where

If the upper limit of integration up to the yield point is restricted, the energy absorbed per unit volume is known as the modulus of resilience. Mathematically, the modulus of resilience can be expressed by the product of the square of the yield stress divided by two times the Young's modulus of elasticity. That is,

Modulus of resilience = Yield stress2/2 (Young's modulus)

Toughness tests

The toughness of a material can be measured using a small specimen of that material. A typical testing machine uses a pendulum to deform a notched specimen of defined cross-section. The height from which the pendulum fell, minus the height to which it rose after deforming the specimen, multiplied by the weight of the pendulum, is a measure of the energy absorbed by the specimen as it was deformed during the impact with the pendulum. The Charpy and Izod notched impact strength tests are typical ASTM tests used to determine toughness.

Unit of toughness

Tensile toughness (or deformation energy, UT) is measured in units of joule per cubic metre (J·m−3), or equivalently newton-metre per cubic metre (N·m·m−3), in the SI system and inch-pound-force per cubic inch (in·lbf·in−3) in US customary units:

In the SI system, the unit of tensile toughness can be easily calculated by using area underneath the stress–strain (σε) curve, which gives tensile toughness value, as given below: [4]

Toughest material

An alloy made of almost equal amounts of chromium, cobalt and nickel (CrCoNi) is the toughest material discovered thus far. It resists fracturing even at incredibly cold temperatures close to absolute zero. It is being considered as a material used in building spacecraft. [5]

See also

Related Research Articles

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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.

<span class="mw-page-title-main">Ductility</span> Degree to which a material under stress irreversibly deforms before failure

Ductility is a mechanical property commonly described as a material's amenability to drawing. 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. It defines a material's suitability for certain manufacturing operations and its capacity to absorb mechanical overload. 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 can be characterized with brittle failure like cast iron. Polymers generally can be viewed as ductile materials as they typically allow for plastic deformation.

<span class="mw-page-title-main">Composite material</span> Material made from a combination of two or more unlike substances

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<span class="mw-page-title-main">Young's modulus</span> Mechanical property that measures stiffness of a solid material

Young's modulus is a mechanical property of solid materials that measures the tensile or compressive stiffness when the force is applied lengthwise. It is the modulus of elasticity for tension or axial compression. Young's modulus is defined as the ratio of the stress applied to the object and the resulting axial strain in the linear elastic region of the material.

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 infinitesimal 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.

<span class="mw-page-title-main">Stress–strain curve</span> Curve representing a materials response to applied forces

In engineering and materials science, 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.

<span class="mw-page-title-main">Fracture</span> Split of materials or structures under stress

Fracture is the appearance of a crack or complete 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, it is called a normal tensile crack or simply a crack; if a displacement develops tangentially, it is called a shear crack, slip band, or dislocation.

In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal. This is in contrast to plasticity, in which the object fails to do so and instead remains in its deformed state.

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<span class="mw-page-title-main">Compressive strength</span> Capacity of a material or structure to withstand loads tending to reduce size

In mechanics, compressive strength is the capacity of a material or structure to withstand loads tending to reduce size. In other words, compressive strength resists compression, whereas tensile strength resists tension. In the study of strength of materials, tensile strength, compressive strength, and shear strength can be analyzed independently.

<span class="mw-page-title-main">Fracture mechanics</span> Study of propagation of cracks in materials

Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture.

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In materials science, 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.

In engineering and materials science, necking is a mode of tensile deformation where relatively large amounts of strain localize disproportionately in a small region of the material. The resulting prominent decrease in local cross-sectional area provides the basis for the name "neck". Because the local strains in the neck are large, necking is often closely associated with yielding, a form of plastic deformation associated with ductile materials, often metals or polymers. Once necking has begun, the neck becomes the exclusive location of yielding in the material, as the reduced area gives the neck the largest local stress.

<span class="mw-page-title-main">Three-point flexural test</span> Standard procedure for measuring modulus of elasticity in bending

The three-point bending flexural test provides values for the modulus of elasticity in bending , flexural stress , flexural strain and the flexural stress–strain response of the material. This test is performed on a universal testing machine with a three-point or four-point bend fixture. The main advantage of a three-point flexural test is the ease of the specimen preparation and testing. However, this method has also some disadvantages: the results of the testing method are sensitive to specimen and loading geometry and strain rate.

The J-integral represents a way to calculate the strain energy release rate, or work (energy) per unit fracture surface area, in a material. The theoretical concept of J-integral was developed in 1967 by G. P. Cherepanov and independently in 1968 by James R. Rice, who showed that an energetic contour path integral was independent of the path around a crack.

Material failure theory is an interdisciplinary field of materials science and solid mechanics which attempts to predict 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.

<span class="mw-page-title-main">Fiber-reinforced composite</span>

A fiber-reinforced composite (FRC) is a composite building material that consists of three components:

  1. the fibers as the discontinuous or dispersed phase,
  2. the matrix as the continuous phase, and
  3. the fine interphase region, also known as the interface.
<span class="mw-page-title-main">Resilience (materials science)</span> Material ability to absorb energy when deformed elastically

In material science, resilience is the ability of a material to absorb energy when it is deformed elastically, and release that energy upon unloading. Proof resilience is defined as the maximum energy that can be absorbed up to the elastic limit, without creating a permanent distortion. The modulus of resilience is defined as the maximum energy that can be absorbed per unit volume without creating a permanent distortion. It can be calculated by integrating the stress–strain curve from zero to the elastic limit. In uniaxial tension, under the assumptions of linear elasticity,

The theoretical strength of a solid is the maximum possible stress a perfect solid can withstand. It is often much higher than what current real materials can achieve. The lowered fracture stress is due to defects, such as interior or surface cracks. One of the goals for the study of mechanical properties of materials is to design and fabricate materials exhibiting strength close to the theoretical limit.

References

  1. 1 2 3 "Toughness", NDT Education Resource Center, Brian Larson, editor, 2001–2011, The Collaboration for NDT Education, Iowa State University
  2. Askeland, Donald R. (January 2015). The science and engineering of materials. Wright, Wendelin J. (Seventh ed.). Boston, MA. p. 208. ISBN   978-1-305-07676-1. OCLC   903959750.{{cite book}}: CS1 maint: location missing publisher (link)
  3. Soboyejo, W. O. (2003). "12.3 Toughness and Fracture Process Zone". Mechanical properties of engineered materials. Marcel Dekker. ISBN   0-8247-8900-8. OCLC   300921090.
  4. Balkan, O.; Demirer, H. (2010). "Mechanical properties of glass bead- and wollastonite-filled isotactic-polypropylene composites modified with thermoplastic elastomers". Polymer Composites. 31 (7): 1285–1308. doi:10.1002/pc.20953. ISSN   1548-0569.
  5. Sparkes, Matthew (14 December 2022). "Toughest material ever is an alloy of chromium, cobalt and nickel". New Scientist. Retrieved 18 March 2023.