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 that alter the strength of a material includes work hardening solid strengthening] precipitation hardening 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 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 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 tensile strength and shear strength namely the limit states of compressive stress tensile stress and shear stress respectively 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

Uniaxial stress is expressed by

- $$

*Compressive stress*(or compression) is the stress state caused by an applied load that acts to reduce the length of the material (compression member) 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

*Tensile 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*is the stress state caused by a 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

*Yield strength*is the lowest stress that gives permanent deformation in 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 02% plastic strain This is called a 02% proof stress

*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)

*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 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 ($Deltasigma=\; sigma\_mathrm\{max\}\; -\; sigma\_mathrm\{min\}$) 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

*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) 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)

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

*Elasticity*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

*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 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

Factor of safety 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 constraintIt 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 $R$ = 110×10

- Mechanics of Materials , EJ 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 MF
*Materials Selection in Design*Pergamon 1992 - Beer FP ER Johnston et al.
*Mechanics of Materials*3rd edition McGraw-Hill 2001 ISBN 0-07-248673-2 - Cottrell AH
*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 DC
*Introduction to Mechanics of Deformable Solids*McGraw-Hill 1967 - Gordon JE
*The New Science of Strong Materials*Princeton 1984 - Groover Mikell P.
*Fundamentals of Modern Manufacturing*2nd edition John Wiley & SonsInc 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 RC
*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 IH and FA 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 SP and DH Young
*Elements of Strength of Materials*5th edition (MKS System) - Davidge RW Mechanical Behavior of Ceramics Cambridge Solid State Science Series (1979)
- Lawn BR 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 DR Suresh S., Ward IM (1998)

- Dynamics
- Forensic engineering
- Fracture mechanics
- Heat transfer
- Materials science
- Statics
- Strength of glass
- Strengthening mechanisms of materials
- Stress-strain relations
- Microstructures of materials
- Elasticity of materials
- Plasticity of materials
- Plastic deformation in solids
- Creep of materials
- Fracture toughness
- Fatigue of materials
- Diffusion in materials
- Deformation-mechanism maps
- Material selection
- Specific strength

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