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. An important founding pioneer in mechanics of materials was Stephen Timoshenko.
In the mechanics of materials, the strength of a material is its ability to withstand an applied load without failure or plastic deformation. The field of strength of materials deals with forces and deformations that result from their acting on a material. A load applied to a mechanical member will induce internal forces within the member called stresses when those forces are expressed on a unit basis. The stresses acting on the material cause deformation of the material in various manners including breaking them completely. Deformation of the material is called strain when those deformations too are placed on a unit basis.
The stresses and strains that develop within a mechanical member must be calculated in order to assess the load capacity of that member. This requires a complete description of the geometry of the member, its constraints, the loads applied to the member and the properties of the material of which the member is composed. The applied loads may be axial (tensile or compressive), or rotational (strength shear). 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. 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.
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 calculated deflection of the member may be compared to deflection criteria that are based on the member's use. The calculated buckling load of the member may be compared to the applied load. 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.
Material resistance can be expressed in several mechanical stress parameters. The term material strength is used when referring to mechanical stress parameters. These are physical quantities with dimension homogeneous to pressure and force per unit surface. The traditional measure unit for strength are therefore MPa in the International System of Units, and the psi between the United States customary units.Strength parameters include: yield strength, tensile strength, fatigue strength, crack resistance, and other parameters.[citation needed]
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 ultimate strength is the maximum stress that a material can withstand before it breaks or weakens.[12] For example, the ultimate tensile strength (UTS) of AISI 1018 Steel is 440 MPa. In Imperial units, the unit of stress is given as lbf/in or pounds-force per square inch. This unit is often abbreviated as psi. One thousand psi is abbreviated ksi.
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. Many machine parts fail when subjected to a non-steady and continuously varying loads even though the developed stresses are below the yield point. Such failures are called fatigue failure. The failure is by a fracture that appears to be brittle with little or no visible evidence of yielding. However, when the stress is kept below "fatigue stress" or "endurance limit stress", the part will endure indefinitely. A purely reversing or cyclic stress is one that alternates between equal positive and negative peak stresses during each cycle of operation. In a purely cyclic stress, the average stress is zero. 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. Generally, higher the range stress, the fewer the number of reversals needed for failure.
There are four failure theories: maximum shear stress theory, maximum normal stress theory, maximum strain energy theory, and maximum distortion energy theory. Out of these four theories of failure, the maximum normal stress theory is only applicable for brittle materials, and the remaining three theories are applicable for ductile materials.Of the latter three, the distortion energy theory provides most accurate results in a majority of the stress conditions. The strain energy theory needs the value of Poisson's ratio of the part material, which is often not readily available. The maximum shear stress theory is conservative. For simple unidirectional normal stresses all theories are equivalent, which means all theories will give the same result.
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 solution strengthening, precipitation hardening, and grain boundary strengthening and can be quantitatively and qualitatively explained. Strengthening mechanisms are accompanied by the caveat that some other 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 expressed in terms of the limiting values of the compressive stress, tensile stress, and shear stresses that would cause failure. The effects of dynamic loading are probably the most important practical consideration of the strength of materials, especially the problem of fatigue. Repeated loading often initiates brittle cracks, which grow until failure occurs. 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.
Strength of materials, also know as mechanics of materials, is focused on analyzing stresses and deflections in materials under load. Knowledge of stresses and deflections allows for the safe design of structures that are capable of supporting their intended loads.
Calculation of stress concentration is particularly important when the materials are very brittle, or when there is only a single load path. In ductile materials, local yielding will allow for stresses to be redistributed and will reduce the stress around the riser. For this reason, stress concentration factors are not typically applied to structural members made of ductile materials. Stress concentration factors are also not typically applied when there is a redundant load path, in which case yielding of one member will allow for redistribution of forces to the members on the other load paths. An example of this is a pattern of bolts. If one bolt starts to give, then the other bolts in the pattern will take more of the load.
Knowledge of stresses and deflections allows for the safe design of structures that are capable of supporting their intended loads. It is always desired for the stresses in a structure to remain within the limits of the structure's strength. The yield strength of the material is commonly chosen as the strength limit to which the calculated stresses are compared.
where σactual is the calculated stress in the structure, and σlimit is a maximum stress limit, typically a material strength such as the yield strength (Sty). The factor of safety indicates how far the actual stress is below the limiting stress. The FS value must be greater than or equal to 1 for the structure not to fail, but engineers will almost always design to some required factor of safety greater than 1. The required factor of safety will vary based on the criticality of the structure (i.e. the consequences if the structure were to fail) as well as the loading conditions (i.e. what types of loads are applied, how predictable are the loads, etc.). A high FS will result in a very safe structure, but if the value of FS is too high then the structure may become so large and heavy that it can no longer successfully perform its intended function. There are therefore many tradeoffs when selecting an appropriate factor of safety. Typical values of FS range from 1.15 to as high as 10.
983975eaba