strength of materials


  • [10] Stress–strain relations[edit] Main article: Stress–strain curve Basic static response of a specimen under tension • Elasticity is the ability of a material to return
    to its previous shape after stress is released.

  • 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 some materials, like aluminium alloys, the point of yielding is difficult to identify, thus it is usually defined as the stress required to cause 0.2% plastic strain.

  • • Fatigue strength is a more complex measure of the strength of a material that considers several loading episodes in the service period of an object,[6] and is usually more
    difficult to assess than the static strength measures.

  • When a part is subjected to a cyclic stress, also known as stress range (Sr), it has been observed that the failure of the part occurs after a number of stress reversals (N)
    even if the magnitude of the stress range is below the material’s yield strength.

  • • Compressive stress (or compression) is the stress state caused by an applied load that acts to reduce the length of the material (compression member) along the axis of the
    applied load, it is, in other words, a stress state that causes a squeezing of the material.

  • [5] • Compressive strength is a limit state of compressive stress that leads to failure in a material in the manner of ductile failure (infinite theoretical yield) or brittle
    failure (rupture as the result of crack propagation, or sliding along a weak plane – see shear strength).

  • The term material strength is used when referring to mechanical stress parameters.

  • • Tensile stress is the stress state caused by an applied load that tends to elongate the material along the axis of the applied load, in other words, the stress caused by
    pulling the material.

  • Definition In the mechanics of materials, the strength of a material is its ability to withstand an applied load without failure or plastic deformation.

  • • Shear stress is the stress state caused by the combined energy of a pair of opposing forces acting along parallel lines of action through the material, in other words, the
    stress caused by faces of the material sliding relative to one another.

  • Material strength refers to the point on the engineering stress–strain curve (yield stress) beyond which the material experiences deformations that will not be completely
    reversed upon removal of the loading and as a result, the member will have a permanent deflection.

  • Failure theories[edit] Main article: Material failure theory There are four failure theories: maximum shear stress theory, maximum normal stress theory, maximum strain energy
    theory, and maximum distortion energy theory.

  • The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials
    such as its yield strength, ultimate strength, Young’s modulus, and Poisson’s ratio.

  • • Impact strength is the capability of the material to withstand a suddenly applied load and is expressed in terms of energy.

  • The calculated stiffness and mass distribution of the member may be used to calculate the member’s dynamic response and then compared to the acoustic environment in which
    it will be used.

  • • Maximum Normal Stress Theory – This theory postulates that failure will occur if the maximum normal stress in the part exceeds the ultimate tensile stress of the material
    as determined from uniaxial testing.

  • The total elastic energy due to strain can be divided into two parts: one part causes change in volume, and the other part causes change in shape.

  • The theory began with the consideration of the behavior of one and two dimensional members of structures, whose states of stress can be approximated as two dimensional, and
    was then generalized to three dimensions to develop a more complete theory of the elastic and plastic behavior of materials.

  • In many materials, the relation between applied stress is directly proportional to the resulting strain (up to a certain limit), and a graph representing those two quantities
    is a straight line.

  • The field of strength of materials (also called mechanics of materials) typically refers to various methods of calculating the stresses and strains in structural members,
    such as beams, columns, and shafts.

  • , where FS: the factor of safety, R: The applied stress, and UTS: ultimate stress (psi or N/m2) Margin of Safety is also sometimes used to as design criteria.

  • The strain energy theory needs the value of Poisson’s ratio of the part material, which is often not readily available.

  • • Maximum Strain Energy Theory – This theory postulates that failure will occur when the strain energy per unit volume due to the applied stresses in a part equals the strain
    energy per unit volume at the yield point in uniaxial testing.

  • [8] • Strain or reduced deformation is a mathematical term that expresses the trend of the deformation change among the material field.

  • The ultimate strength of the material refers to the maximum value of stress reached.

  • Stress parameters for resistance[edit] Material resistance can be expressed in several mechanical stress parameters.

  • The calculated stresses may then be compared to some measure of the strength of the member such as its material yield or ultimate strength.

  • The stresses and strains that develop within a mechanical member must be calculated in order to assess the load capacity of that member.

  • In the case of cyclic loading it can be appropriately expressed as an amplitude usually at zero mean stress, along with the number of cycles to failure under that condition
    of stress.

  • The cracks always start at stress concentrations, especially changes in cross-section of the product, near holes and corners at nominal stress levels far lower than those
    quoted for the strength of the material.

  • [7] Strain parameters for resistance[edit] • Deformation of the material is the change in geometry created when stress is applied ( as a result of applied forces, gravitational
    fields, accelerations, thermal expansion, etc.).

  • Often measured with the Izod impact strength test or Charpy impact test, both of which measure the impact energy required to fracture a sample.

  • In order for a material or object to have a high impact strength, the stresses must be distributed evenly throughout the object.

  • Design terms Ultimate strength is an attribute related to a material, rather than just a specific specimen made of the material, and as such it is quoted as the force per
    unit of cross section area (N/m2).

  • The area can be the undeformed area or the deformed area, depending on whether engineering stress or true stress is of interest.

  • Once the state of stress and strain within the member is known, the strength (load carrying capacity) of that member, its deformations (stiffness qualities), and its stability
    (ability to maintain its original configuration) can be calculated.

  • Design stresses that have been determined from the ultimate or yield point values of the materials give safe and reliable results only for the case of static loading.

  • With a complete description of the loading and the geometry of the member, the state of stress and state of strain at any point within the member can be calculated.


Works Cited

[“1. Beer & Johnston (2006). Mechanics of Materials (5th ed.). McGraw Hill. p. 210. ISBN 978-0-07-352938-7.
2. ^ Beer & Johnston (2006). Mechanics of Materials (5th ed.). McGraw Hill. p. 7. ISBN 978-0-07-352938-7.
3. ^ Beer & Johnston (2006). Mechanics
of Materials (5th ed.). McGraw Hill. p. 5. ISBN 978-0-07-352938-7.
4. ^ Beer & Johnston (2006). Mechanics of Materials (5th ed.). McGraw Hill. pp. 9–10. ISBN 978-0-07-352938-7.
5. ^ Beer, Ferdinand Pierre; Johnston, Elwood Russell; Dewolf, John
T (2009). Mechanics of Materials (5th ed.). p. 52. ISBN 978-0-07-352938-7.
6. ^ Beer & Johnston (2006). Mechanics of Materials (5th ed.). McGraw Hill. p. 60. ISBN 978-0-07-352938-7.
7. ^ Beer & Johnston (2006). Mechanics of Materials (5th ed.).
McGraw Hill. pp. 693–696. ISBN 978-0-07-352938-7.
8. ^ Beer & Johnston (2006). Mechanics of Materials (5th ed.). McGraw Hill. p. 47. ISBN 978-0-07-352938-7.
9. ^ Beer & Johnston (2006). Mechanics of Materials (5th ed.). McGraw Hill. p. 49. ISBN
10. ^ R. C. Hibbeler (2009). Structural Analysis (7 ed.). Pearson Prentice Hall. p. 305. ISBN 978-0-13-602060-8.
11. ^ Beer & Johnston (2006). Mechanics of Materials (5th ed.). McGraw Hill. pp. 53–56. ISBN 978-0-07-352938-7.
12. ^
Beer & Johnston (2006). Mechanics of Materials (5thv ed.). McGraw Hill. pp. 27–28. ISBN 978-0-07-352938-7.
13. ^ Beer & Johnston (2006). Mechanics of Materials (5th ed.). McGraw Hill. p. 28. ISBN 978-0-07-352938-7.
2. Fa-Hwa Cheng, Initials. (1997).
Strength of material. Ohio: McGraw-Hill
3. Mechanics of Materials, E.J. Hearn
4. Alfirević, Ivo. Strength of Materials I. Tehnička knjiga, 1995. ISBN 953-172-010-X.
5. Alfirević, Ivo. Strength of Materials II. Tehnička knjiga, 1999. ISBN 953-6168-85-5.
6. Ashby,
M.F. Materials Selection in Design. Pergamon, 1992.
7. Beer, F.P., E.R. Johnston, et al. Mechanics of Materials, 3rd edition. McGraw-Hill, 2001. ISBN 0-07-248673-2
8. Cottrell, A.H. Mechanical Properties of Matter. Wiley, New York, 1964.
9. Den
Hartog, Jacob P. Strength of Materials. Dover Publications, Inc., 1961, ISBN 0-486-60755-0.
10. Drucker, D.C. Introduction to Mechanics of Deformable Solids. McGraw-Hill, 1967.
11. Gordon, J.E. The New Science of Strong Materials. Princeton, 1984.
12. Groover,
Mikell P. Fundamentals of Modern Manufacturing, 2nd edition. John Wiley & Sons, Inc., 2002. ISBN 0-471-40051-3.
13. Hashemi, Javad and William F. Smith. Foundations of Materials Science and Engineering, 4th edition. McGraw-Hill, 2006. ISBN 0-07-125690-3.
14. Hibbeler,
R.C. Statics and Mechanics of Materials, SI Edition. Prentice-Hall, 2004. ISBN 0-13-129011-8.
15. 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.
16. Chapter 10 – Strength of Elastomers, A.N. Gent, W.V. Mars, In: James E. Mark, Burak Erman and Mike Roland, Editor(s), The Science and Technology of Rubber (Fourth Edition), Academic Press, Boston, 2013, Pages 473–516,
ISBN 9780123945846, 10.1016/B978-0-12-394584-6.00010-8
17. Mott, Robert L. Applied Strength of Materials, 4th edition. Prentice-Hall, 2002. ISBN 0-13-088578-9.
18. Popov, Egor P. Engineering Mechanics of Solids. Prentice Hall, Englewood Cliffs,
N. J., 1990. ISBN 0-13-279258-3.
19. Ramamrutham, S. Strength of Materials.
20. Shames, I.H. and F.A. Cozzarelli. Elastic and inelastic stress analysis. Prentice-Hall, 1991. ISBN 1-56032-686-7.
21. Timoshenko S. Strength of Materials, 3rd edition.
Krieger Publishing Company, 1976, ISBN 0-88275-420-3.
22. Timoshenko, S.P. and D.H. Young. Elements of Strength of Materials, 5th edition. (MKS System)
23. Davidge, R.W., Mechanical Behavior of Ceramics, Cambridge Solid State Science Series, (1979)
24. Lawn,
B.R., Fracture of Brittle Solids, Cambridge Solid State Science Series, 2nd Edn. (1993)
25. Green, D., An Introduction to the Mechanical Properties of Ceramics, Cambridge Solid State Science Series, Eds. Clarke, D.R., Suresh, S., Ward, I.M.Babu
Tom.K (1998)
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