In materials science Materials science is an interdisciplinary field involving the properties of matter and its applications to various areas of science and engineering. This science investigates the relationship between the structure of materials at atomic or molecular scales and their macroscopic properties. It includes elements of applied physics and chemistry, the strength of a material is its ability to withstand an applied stress In continuum mechanics, stress is a measure of the average force per unit area of a surface within a deformable body on which internal forces act. In other words, it is a measure of the intensity of the internal forces acting between particles of a deformable body across imaginary internal surfaces . These internal forces are produced between the without failure. Yield strength refers to the point on the engineering stress-strain curve (as opposed to true stress-strain curve) beyond which the material begins deformation that cannot be reversed upon removal of the loading. Ultimate strength refers to the point on the engineering stress-strain curve corresponding to the maximum stress. The applied stress may be tensile Tensile strength is indicated by the maxima of a stress-strain curve and, in general, indicates when necking will occur. As it is an intensive property, its value does not depend on the size of the test specimen. It is, however, dependent on the preparation of the specimen and the temperature of the test environment and material, compressive Compressive strength is the capacity of a material to withstand axially directed pushing forces. When the limit of compressive strength is reached, materials are crushed. Concrete can be made to have high compressive strength, e.g. many concrete structures have compressive strengths in excess of 50 MPa, whereas a material such as soft sandstone, or shear Shear strength in engineering is a term used to describe the strength of a material or component against the type of yield or structural failure where the material or component fails in shear.

A material's strength is dependent on its microstructure. The engineering processes to which a material is subjected can alter this microstructure. The variety of strengthening mechanisms 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 that alter the strength of a material includes work hardening Work hardening, also known as strain hardening, is the strengthening of a material by, macroscopically speaking, plastic deformation . As the material becomes increasingly saturated with new dislocations, more dislocations are prevented from nucleating (a resistance to dislocation-formation develops). This resistance to dislocation-formation, solid solution strengthening Solid solution strengthening is a type of alloying that can be used to improve the strength of a pure metal. The technique works by adding atoms of one element to the crystalline lattice another element (the base metal). The alloying element diffuses into the matrix, forming a solid solution. In most binary systems, when alloyed above a certain, precipitation hardening Precipitation hardening, also called age hardening, is a heat treatment technique used to increase the yield strength of malleable materials, including most structural alloys of aluminium, magnesium, nickel and titanium, and some stainless steels. It relies on changes in solid solubility with temperature to produce fine particles of an impurity and grain boundary strengthening and can be quantified and qualitatively explained. However, strengthening mechanisms are accompanied by the caveat that some mechanical properties of the material may degenerate in an attempt to make the material stronger. For example, in grain boundary strengthening, although yield strength The yield strength or yield point of a material is defined in engineering and materials science as the stress at which a material begins to deform plastically. 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 is maximized with decreasing grain size, ultimately, very small grain sizes make the material brittle. In general, the yield strength of a material is an adequate indicator of the material's mechanical strength. Considered in tandem with the fact that the yield strength is the parameter that predicts plastic deformation Plastic deformation in solids is a term used in metallurgy, materials science and solid state physics, and refers to an irreversible change in the internal molecular structure of an object. This change may be due to either (or both) of the following factors: in the material, one can make informed decisions on how to increase the strength of a material depending its microstructural properties and the desired end effect. Strength is considered in terms of compressive strength Compressive strength is the capacity of a material to withstand axially directed pushing forces. When the limit of compressive strength is reached, materials are crushed. Concrete can be made to have high compressive strength, e.g. many concrete structures have compressive strengths in excess of 50 MPa, whereas a material such as soft sandstone, tensile strength Tensile strength is indicated by the maxima of a stress-strain curve and, in general, indicates when necking will occur. As it is an intensive property, its value does not depend on the size of the test specimen. It is, however, dependent on the preparation of the specimen and the temperature of the test environment and material, and shear strength Shear strength in engineering is a term used to describe the strength of a material or component against the type of yield or structural failure where the material or component fails in shear, namely the limit states of compressive stress Compressive stress is the stress that, when applied, acts towards the center of that material. When a material is subjected to compressive stress, then this material is under compression. Usually, compressive stress applied to bars, columns, etc. leads to shortening, tensile stress Tensile stress is the stress state leading to expansion; that is, the tensile stress may be increased until the reach of tensile strength, namely the limit state of stress and shear stress A shear stress, denoted , is defined as a stress which is applied parallel or tangential to a face of a material, as opposed to a normal stress which is applied perpendicularly, respectively. The effects of dynamic loading is probably the most important practical part of the strength of materials, especially the problem of fatigue In materials science, fatigue is the progressive and localized structural damage that occurs when a material is subjected to cyclic loading. The maximum stress values are less than the ultimate tensile stress limit, and may be below the yield stress limit of the material. Repeated loading often initiates brittle cracks, which grow slowly until failure occurs.

However, the term strength of materials most often refers to various methods of calculating stresses in structural members, such as beams, columns and shafts. The methods that can be employed to predict the response of a structure under loading and its susceptibility to various failure modes may take into account various properties of the materials other than material (yield or ultimate) strength. For example failure in buckling is dependent on material stiffness (Young's Modulus).

Definitions

Stress terms

Uniaxial stress is expressed by

where F is the force [N] acting on an area A [m²]. The area can be the undeformed area or the deformed area, depending on whether engineering stress or true stress is used.

• Compressive stress Compressive stress is the stress that, when applied, acts towards the center of that material. When a material is subjected to compressive stress, then this material is under compression. Usually, compressive stress applied to bars, columns, etc. leads to shortening (or compression Physical compression is the result of the subjection of a material to compressive stress, resulting in reduction of volume. The opposite of compression is tension. In simpler words, Compression is a pushing force) is the stress state caused by an applied load that acts to reduce the length of the material (compression member For a compression member, such as a column, the principal stress comes mainly from axial forces, that is forces that fall along one line, usually the centerline) in the axis of the applied load, in other words the stress state caused by squeezing the material. A simple case of compression is the uniaxial compression induced by the action of opposite, pushing forces. Compressive strength for materials is generally higher than that of tensile stress. However, structures loaded in compression are subject to additional failure modes dependent on geometry, such as Euler buckling In engineering, buckling is a failure mode characterized by a sudden failure of a structural member subjected to high compressive stresses, where the actual compressive stress at the point of failure is less than the ultimate compressive stresses that the material is capable of withstanding. This mode of failure is also described as failure due to.

• Tensile stress Tensile stress is the stress state leading to expansion; that is, the tensile stress may be increased until the reach of tensile strength, namely the limit state of stress is the stress state caused by an applied load that tends to elongate the material in the axis of the applied load, in other words the stress caused by pulling the material. The strength of structures of equal cross sectional area loaded in tension is independent of cross section geometry. Materials loaded in tension are susceptible to stress concentrations such as material defects or abrupt changes in geometry. However, materials exhibiting ductile behavior(metals for example) can tolerate some defects while brittle materials (such as ceramics) can fail well below their ultimate stress.

• Shear stress A shear stress, denoted , is defined as a stress which is applied parallel or tangential to a face of a material, as opposed to a normal stress which is applied perpendicularly is the stress state caused by a pair of opposing forces acting along parallel lines of action through the material, in other words the stress caused by sliding faces of the material relative to one another. An example is cutting paper with scissors Scissors are hand-operated cutting instruments. They consist of a pair of metal blades connected in such a way that the sharpened edges slide against each other. Scissors are used for cutting various thin materials, such as paper, cardboard, metal foil, thin plastic, cloth, rope and wire. Scissors can also be used to cut hair and food.

Strength terms

• Yield strength The yield strength or yield point of a material is defined in engineering and materials science as the stress at which a material begins to deform plastically. 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 is the lowest stress that gives permanent deformation in a material. In some materials, like aluminium alloys Aluminium alloys are alloys in which aluminium is the predominant metal. Typical alloying elements are copper, zinc, manganese, silicon, and magnesium. There are two principal classifications, namely casting alloys and wrought alloys, both of which are further subdivided into the categories heat-treatable and non-heat-treatable. About 85% of, the point of yielding is hard to define, thus it is usually given as the stress required to cause 0.2% plastic strain. This is called a 0.2% proof stress.

• Compressive strength Compressive strength is the capacity of a material to withstand axially directed pushing forces. When the limit of compressive strength is reached, materials are crushed. Concrete can be made to have high compressive strength, e.g. many concrete structures have compressive strengths in excess of 50 MPa, whereas a material such as soft sandstone is a limit state of compressive stress Compressive stress is the stress that, when applied, acts towards the center of that material. When a material is subjected to compressive stress, then this material is under compression. Usually, compressive stress applied to bars, columns, etc. leads to shortening that leads to compressive failure in the manner of ductile failure (infinite theoretical yield) or in the manner of brittle failure (rupture as the result of crack propagation, or sliding along a weak plane - see shear strength Shear strength in engineering is a term used to describe the strength of a material or component against the type of yield or structural failure where the material or component fails in shear).

• Tensile strength Tensile strength is indicated by the maxima of a stress-strain curve and, in general, indicates when necking will occur. As it is an intensive property, its value does not depend on the size of the test specimen. It is, however, dependent on the preparation of the specimen and the temperature of the test environment and material or ultimate tensile strength is a limit state of tensile stress Tensile stress is the stress state leading to expansion; that is, the tensile stress may be increased until the reach of tensile strength, namely the limit state of stress that leads to tensile failure in the manner of ductile failure (yield as the first stage of failure, some hardening in the second stage and break after a possible "neck" formation) or in the manner of brittle failure (sudden breaking in two or more pieces with a low stress state). Tensile strength can be given as either true stress or engineering stress.

• Fatigue strength In materials science, fatigue is the progressive and localized structural damage that occurs when a material is subjected to cyclic loading. The maximum stress values are less than the ultimate tensile stress limit, and may be below the yield stress limit of the material is a measure of the strength of a material or a component under cyclic loading, and is usually more difficult to assess than the static strength measures. Fatigue strength is given as stress amplitude or stress range (Δσ = σ_max − σ_min), usually at zero mean stress, along with the number of cycles to failure.

• Impact strength, it is the capability of the material in withstanding by the suddenly applied loads in terms of energy. Often measured with the Izod impact strength test The test is named after the English engineer Edwin Gilbert Izod , who described it in his 1903 address to the British Association, subsequently published in Engineering or Charpy impact test 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 toughness and acts as a tool to study temperature-dependent brittle-ductile transition. It is widely applied in, both of which measure the impact energy required to fracture a sample.

Strain (deformation) terms

• Deformation In materials science, deformation is a change in the shape or size of an object due to an applied force. This can be a result of tensile forces, compressive (pushing) forces, shear, bending or torsion (twisting). Deformation is often described as strain of the material is the change in geometry when stress is applied (in the form of force loading, gravitational field, acceleration, thermal expansion, etc.). Deformation is expressed by the displacement field of the material.
• Strain In continuum mechanics, deformation or strain is the change in the metric properties of a continuous body B in the displacement from an initial placement κ0 to a final placement κ(B). A change in the metric properties means that a curve drawn in the initial body placement changes its length when displaced to a curve in the final placement. If or reduced deformation is a mathematical term to express the trend of the deformation change among the material field. For uniaxial loading - displacements of a specimen (for example a bar element) it is expressed as the quotient of the displacement and the length of the specimen. For 3D displacement fields it is expressed as derivatives of displacement functions in terms of a second order tensor Tensors are geometric entities introduced into mathematics and physics to extend the notion of scalars, geometric vectors, and matrices to higher orders. Tensors were first conceived by Tullio Levi-Civita and Gregorio Ricci-Curbastro, who continued the earlier work of Bernhard Riemann and Elwin Bruno Christoffel and others, as part of the absolute (with 6 independent elements).
• Deflection In engineering mechanics, deflection is a term that is used to describe the degree to which a structural element is displaced under a load. The deflection of a member under a load is directly related to the slope of the deflected shape of the member under that load and can be calculated by integrating the function that mathematically describes the is a term to describe the magnitude to which a structural element bends under a load.

Stress-strain relations

• Elasticity Plastic deformation in solids is a term used in metallurgy, materials science and solid state physics, and refers to an irreversible change in the internal molecular structure of an object. This change may be due to either (or both) of the following factors: is the ability of a material to return to its previous shape after stress is released. In many materials, the relation between applied stress and the resulting strain is directly proportional (up to a certain limit), and a graph representing those two quantities is a straight line.

The slope of this line is known as Young's Modulus In solid mechanics, Young's modulus, also known as the tensile modulus, is a measure of the stiffness of an isotropic elastic material. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds. This can be experimentally determined from the slope of a stress-strain curve created, or the "Modulus of Elasticity." The Modulus of Elasticity can be used to determine stress-strain relationships in the linear-elastic portion of the stress-strain curve. The linear-elastic region is either below the yield point, or if a yield point is not well defined for the material, taken to be between 0 and 0.2% strain, and is defined as the region of strain in which no yielding (permanent deformation) occurs.^[1]

• Plasticity In physics and materials science, plasticity describes the deformation of a material undergoing non-reversible changes of shape in response to applied forces. For example, a solid piece of metal or plastic being bent or pounded into a new shape displays plasticity as permanent changes occur within the material itself. In engineering, the or plastic deformation is the opposite of elastic deformation and is accepted as unrecoverable strain. Plastic deformation is retained even after the relaxation of the applied stress. Most materials in the linear-elastic category are usually capable of plastic deformation. Brittle materials, like ceramics, do not experience any plastic deformation and will fracture under relatively low stress. Materials such as metals usually experience a small amount of plastic deformation before failure while soft or ductile polymers will plasticly deform much more.

Consider the difference between a carrot and chewed bubble gum. The carrot will stretch very little before breaking, but nevertheless will still stretch. The chewed bubble gum, on the other hand, will plastically deform enormously before finally breaking.

Design terms

Ultimate strength is an attribute directly related to a material, rather than just specific specimen of the material, and as such is quoted force per unit of cross section area (N/m²). For example, the ultimate tensile strength (UTS) of AISI 1018 Steel is 440 MN The newton is the SI derived unit of force, named after Isaac Newton in recognition of his work on classical mechanics/m². In general, the SI unit of stress is the pascal The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength. It is a measure of force per unit area, defined as one newton per square metre. In everyday life, the pascal is perhaps best known from meteorological barometric pressure reports, where it occurs in the form of hectopascals (1 hPa ≡ 100, where 1 Pa = 1 N/m². In Imperial units, the unit of stress is given as lbf/in² or pounds-force per square inch The pound per square inch or, more accurately, pound-force per square inch is a unit of pressure or of stress based on avoirdupois units. It is the pressure resulting from a force of one pound-force applied to an area of one square inch:. This unit is often abbreviated as psi. One thousand psi is abbreviated ksi.

Factor of safety Factor of safety is a term describing the structural capacity of a system beyond the applied loads or actual loads. There are two distinct uses of the Factor of Safety: One as a calculated ratio of strength (structural capacity) to actual applied load. This is a measure of the reliability of a particular design. The other use of FoS is a constant is a design constraint that an engineered component or structure must achieve. FS = UTS / R, where FS: the Factor of Safety, R: The applied stress, and UTS: the Ultimate force (or stress).

Margin of Safety is also sometimes used to as design constraint. It is defined MS=Factor of safety - 1

For example to achieve a factor of safety of 4, the allowable stress in an AISI 1018 steel component can be worked out as R = UTS / FS = 440/4 = 110 MPa, or R = 110×10⁶ N/m².

See also

• Creep of materials
• Deformation-mechanism maps
• Diffusion in materials
• Dynamics In the field of physics, the study of the causes of motion and changes in motion is dynamics. In other words the study of forces and why objects are in motion. Dynamics includes the study of the effect of torques on motion. These are in contrast to Kinematics, the branch of classical mechanics that describes the motion of objects without
  • Thermodynamics In science, thermodynamics is the study of energy conversion between heat and mechanical work, and subsequently the macroscopic variables such as temperature, volume and pressure. The first to give a concise definition of the subject was Scottish physicist William Thomson who in 1854 stated that:
  • Fluid dynamics In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications,
• Elasticity of materials
• Fatigue of materials
• Forensic engineering Forensic engineering is the investigation of materials, products, structures or components that fail or do not operate or function as intended, causing personal injury or damage to property. The consequences of failure are dealt with by the law of product liability. The field also deals with retracing processes and procedures leading to accidents
• Fracture mechanics
• Fracture toughness
• Heat transfer
• Materials science
• Material selection
• Microstructures of materials
• Plastic deformation in solids
• Plasticity of materials
• Schmidt hammer
• Specific strength
• Statics
• Strength of glass
• Strengthening mechanisms of materials
• Stress-strain relations

References

1. ^ Beer & Johnston (2006). Mechanics of Materials (5th ed.). McGraw Hill. pp. 53-56. ISBN 978-0-07-352938-7.

Further reading

• Mechanics of Materials , E.J. Hearn
• Alfirević, Ivo. Strength of Materials I. Tehnička knjiga, 1995. ISBN 953-172-010-X.
• Alfirević, Ivo. Strength of Materials II. Tehnička knjiga, 1999. ISBN 953-6168-85-5.
• Ashby, M.F. Materials Selection in Design. Pergamon, 1992.
• Beer, F.P., E.R. Johnston, et al. Mechanics of Materials, 3rd edition. McGraw-Hill, 2001. ISBN 0-07-248673-2
• Cottrell, A.H. Mechanical Properties of Matter. Wiley, New York, 1964.
• Den Hartog, Jacob P. Strength of Materials. Dover Publications, Inc., 1961, ISBN 0-486-60755-0.
• Drucker, D.C. Introduction to Mechanics of Deformable Solids. McGraw-Hill, 1967.
• Gordon, J.E. The New Science of Strong Materials. Princeton, 1984.
• Groover, Mikell P. Fundamentals of Modern Manufacturing, 2nd edition. John Wiley & Sons,Inc., 2002. ISBN 0-471-40051-3.
• Hashemi, Javad and William F. Smith. Foundations of Materials Science and Engineering, 4th edition. McGraw-Hill, 2006. ISBN 007-125690-3.
• Hibbeler, R.C. Statics and Mechanics of Materials, SI Edition. Prentice-Hall, 2004. ISBN 013-129-011-8.
• Lebedev, Leonid P. and Michael J. Cloud. Approximating Perfection: A Mathematician's Journey into the World of Mechanics. Princeton University Press, 2004. ISBN 0-691-11726-8.
• Mott, Robert L. Applied Strength of Materials, 4th edition. Prentice-Hall, 2002. ISBN 0-13-088578-9.
• Popov, Egor P. Engineering Mechanics of Solids. Prentice Hall, Englewood Cliffs, N. J., 1990. ISBN 0-13-279258-3.
• Ramamrutham, S. Strength of Materials.
• Shames, I.H. and F.A. Cozzarelli. Elastic and inelastic stress analysis. Prentice-Hall, 1991. ISBN 1-56032-686-7.
• Timoshenko S. Strength of Materials, 3rd edition. Krieger Publishing Company, 1976, ISBN 0-88275-420-3.
• Timoshenko, S.P. and D.H. Young. Elements of Strength of Materials, 5th edition. (MKS System)
• Davidge, R.W., Mechanical Behavior of Ceramics, Cambridge Solid State Science Series, (1979)
• Lawn, B.R., Fracture of Brittle Solids, Cambridge Solid State Science Series, 2nd Edn. (1993)
• Green, D., An Introduction to the Mechanical Properties of Ceramics, Cambridge Solid State Science Series, Eds. Clarke, D.R., Suresh, S., Ward, I.M. (1998)

External links

• Failure theories
• U. Wisconsin-Stout, Strength of Materials online lectures, problems, tests/solutions, links, software
• case studies in structural failure

Categories: Solid mechanics | Materials science | Building engineering | Deformation

See Also:

• Building Materials
• Category:Building Materials: Encyclopedia
• Business: Construction and Maintenance: Materials and Supplies: Wall, Floor and Decorative Finishes: Tile: Directory
• Regional: Europe: United Kingdom: Business and Economy: Construction and Maintenance: Materials and Supplies: Wall, Floor and Decorative Finishes: Tile: Directory

What Links Here:

Recently Viewed Pages:

• Home
• Midea, Greece: Blogs
• Decorate: Videos
• Decorate: Dictionary
• Cover: Dictionary
• Affixed: Shopping
• Affixed: Dictionary
• Clay: Dictionary
• Tiles: Auctions
• Tiles: Dictionary

Most Popular Pages:

• Brazil: Blogs
• Rubberized Asphalt: Blogs
• Bargeboard: Blogs
• Green Roof: Blogs
• Vitrified Tile
• Strength of Materials: Web Search
• Edward Giles Stone: Blogs
• Masonry: Blogs
• Tile: Answers
• Affixed: Blogs

Related 'Strength of Materials' Searches: