Strength of materials

In materials science, the strength of a material refers to the material's ability to resist an applied force. Materials Science or Materials Engineering is an interdisciplinary field involving the properties of matter and its applications to various areas of Science and A material's strength is a function of engineering processes, and scientists employ a variety of strengthening mechanisms to alter the strength of a material. Methods have been devised to modify the Yield strength, Ductility, and Toughness of both Crystalline and Amorphous materials These mechanisms include work hardening, solid solution strengthening, precipitation hardening and grain boundary strengthening and can be quantified and qualitatively explained. Work hardening, strain hardening, or cold work is the strengthening of a material by macroscopically speaking plastic deformation (which has the Solid solution strengthening is a type of Alloying that can be used to improve the strength of a pure metal Precipitation hardening, also called age hardening, is a Heat treatment technique used to strengthen Malleable materials including most structural Grain boundary strengthening (or Hall-Petch strengthening) is a method of strengthening materials by changing their average Crystallite (grain size However, strengthening mechanisms are accompanied by the caveat that mechanical properties of the material may degenerate in an attempt to make the material stronger. For example, in grain boundary strengthening, although yield strength is maximized with decreasing grain size, ultimately, very small grain sizes make the material brittle. The yield strength or yield point of a Material is defined in Engineering and Materials science as the stress at which a material 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 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. In Materials science, deformation is a change in the shape or size of an object due to an applied force. Strength is considered in terms of compressive strength, tensile strength, and shear strength, namely the limit states of compressive stress, tensile stress and shear stress, respectively. Compressive strength is the capacity of a Material to withstand axially directed pushing forces Tensile strength \sigma_{UTS} or S_U is the Stress at which a material breaks or permanently deforms 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 Compressive stress is the stress applied to materials resulting in their compaction (decrease of volume Stress is a measure of the average amount of Force exerted per unit Area. A shear stress, denoted \tau\ ( Tau) is defined as a stress which is applied Parallel or tangential to a face of a material The effects of dynamic loading is probably the most important practical part of the strength of materials, especially the problem of fatigue. 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, when the equations of equilibrium are not sufficient to solve the problem. In such problems, known as statically indeterminate problems, the elastic or plastic resistance of the material to deformation must be considered when calculating stresses. In this sense, the word ``strength" could well be replaced by ``stiffness", but the usage goes back to at least 1930 and is not likely to go away any time soon.

1 Definitions
2 Stress-strain relations
3 Design terms
4 Suggested reading
5 Other fundamental engineering topics
6 External links

Definitions

Stress terms

A material being loaded in a) compression, b) tension, c) shear.

Uniaxial stress is expressed by

$\sigma=\frac{F}{A},$

where F is the force (N) acting on an area A (m^2). The area can be the undeformed area or the deformed area, depending on whether engineering stress or true stress is used. Stress is a measure of the average amount of Force exerted per unit Area.

Compressive stress (or compression) is the stress state when the material (compression member) tends to compact. Compressive stress is the stress applied to materials resulting in their compaction (decrease of volume Physical compression is the result of the subjection of a material to Compressive stress, resulting in reduction of Volume. A compression member is a general class of structural elements of which a Column is the most common specific example 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, but geometry is very important in the analysis, as compressive stress can lead to buckling. In Engineering, buckling is a failure mode characterized by a sudden failure of a structural member subjected to high Compressive stresses where

Tensile stress is a loading that tends to produce stretching of a material by the application of axially directed pulling forces. Stress is a measure of the average amount of Force exerted per unit Area. Any material which falls into the "elastic" category can generally tolerate mild tensile stresses while materials such as ceramics and brittle alloys are very succeptable to failure under the same conditions. If a material is stressed beyond its limits, it will fail. The failure mode, either ductile or brittle, is based mostly on the microstructure of the material. Some Steel alloys are examples of materials with high tensile strength. Steel is an Alloy consisting mostly of Iron, with a Carbon content between 0

Shear stress is caused when a force is applied to produce a sliding failure of a material along a plane that is parallel to the direction of the applied force. A shear stress, denoted \tau\ ( Tau) is defined as a stress which is applied Parallel or tangential to a face of a material An example is cutting paper with scissors. Scissors are hand operated cutting instruments consisting of a pair of Metal Blades connected in such a way that the blades meet and cut materials placed

Strength terms

Yield strength is the lowest stress that gives permanent deformation in a material. The yield strength or yield point of a Material is defined in Engineering and Materials science as the stress at which a material In some materials, like aluminium alloys, the point of yielding is hard to define, thus it is usually given as the stress required to cause 0. Aluminium alloys are Alloys of Aluminium, often with copper zinc manganese silicon or magnesium 2% plastic strain.

Compressive strength is a limit state of compressive stress 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). Compressive strength is the capacity of a Material to withstand axially directed pushing forces Compressive stress is the stress applied to materials resulting in their compaction (decrease of volume 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

Tensile strength or ultimate tensile strength is a limit state of tensile 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 \sigma_{UTS} or S_U is the Stress at which a material breaks or permanently deforms Stress is a measure of the average amount of Force exerted per unit Area. Tensile strength can be given as either true stress or engineering stress.

Fatigue strength 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 or Charpy impact test, both of which measure the impact energy required to fracture a sample. Izod impact strength testing is an ASTM standard method of determining impact strength 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

Strain (deformation) terms

Deformation of the material is the change in geometry when stress is applied (in the form of force loading, gravitational field, acceleration, thermal expansion, etc. In Materials science, deformation is a change in the shape or size of an object due to an applied force. ). Deformation is expressed by the displacement field of the material.

Strain 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 (with 6 independent elements). History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually

Deflection is a term to describe the magnitude to which a structural element bends under a load.

Stress-strain relations

Elasticity is the ability of a material to return to its previous shape after stress is released. In Materials science, deformation is a change in the shape or size of an object due to an applied force. 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, or the "Modulus of Elasticity. In Solid mechanics, Young's modulus (E is a measure of the Stiffness of an isotropic elastic material " 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 taken to be between 0 and 0. 2% strain, and is defined as the region of strain in which no yielding (permanent deformation) occurs.

Plasticity 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 fresh 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 plasticly 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/m². The newton (symbol N) is the SI derived unit of Force, named after Isaac Newton in recognition of his work on Classical In general, the SI unit of stress is the pascal, 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 (symbol psi or lbf/in² or lbf/in²) is a unit of This unit is often abbreviated as psi. One thousand psi is abbreviated ksi.

Factor of safety is a design constraint that an engineered component or structure must achieve. Factor of safety ( FoS) can mean either the fraction of structural capability over that required or a Multiplier applied to the maximum expected load ( Force $F S = U T S / R$ , 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 $R = U T S / F S$ = 440/4 = 110 MPa, or $R$ = 110×10⁶ N/m².

External links

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

A network in the context of Electronics, is a collection of interconnected components In physics the term dynamics customarily refers to the time evolution of physical processes In Physics, thermodynamics (from the Greek θερμη therme meaning " Heat " and δυναμις dynamis meaning " Fluid dynamics is the sub-discipline of Fluid mechanics dealing with fluid flow: Fluids ( Liquids and Gases in motion Forensic Engineering is the investigation of materials, products, Structures or components that fail or do not operate/function as Engineering economics, previously known as engineering economy, is a subset of Economics for application to engineering projects In thermal physics, heat transfer is the passage of Thermal energy from a hot to a colder body Materials Science or Materials Engineering is an interdisciplinary field involving the properties of matter and its applications to various areas of Science and Statics is the branch of Mechanics concerned with the analysis of loads ( Force, torque/moment) on Physical systems in Static equilibrium Methods have been devised to modify the Yield strength, Ductility, and Toughness of both Crystalline and Amorphous materials

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