29-11-2012, 06:21 PM
Working Stress and Failure Theories A Simplified Approach
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We are interested in learning how static mechanical stress can cause failure in machine parts.
Static stress means that the stress has been applied slowly and is maintained at a steady level.
Failure from cyclic (or dynamic) stress and impact stress will be treated later. Here, we
should also keep in mind that, there are many other factors such as, surface wear damage from
friction, overheating, chemical corrosion, metallurgical fault or a combination of these and other
factors may also cause failure.
Molecular Concept of Mechanical Failure
Engineering materials have a crystalline molecular structure , which means the atoms (or
molecules) of the material are arranged in a fairly ordered fashion and the atoms are held in fixed
position with respect to each other by strong inter-atomic bond. An external mechanical force
tends to displace these atoms from their original positions in the direction of the force, which is
resisted by the inter-atomic forces. Up to a certain limiting level of the external force, the atoms
are displaced to some extent, but are pulled back to their original position when the external
force is removed. This phenomenon gives rise to the elastic behavior of material (elastic
deformation), that is up to a certain stress level generally the displacement is proportional to
force. Hook’s law essentially is the same that is stress is proportional to strain.
If a force is applied parallel to an atomic plane (shear force) and the force is high enough, a
plane of atoms may slide over the adjacent plane of atoms overcoming the inter-atomic forces of
the immediately neighboring atoms. When this sliding occurs, atoms in the sliding plane will slip
under the influence of new set of atoms. Conceptual model of this slip deformation is shown in
the diagram below. After the slip has occurred, the positions of the atoms have changed
permanently, resulting in a permanent change in shape or size of the part. This type of permanent
deformation is called plastic deformation. Plastic deformation is not acceptable in most
mechanical design situations, because the permanently deformed part may no longer serve its
intended purpose, and from the mechanical design stand point we may say that the part has
failed. For example, a landing gear of an aircraft deforms elastically during landing from the
ground reaction forces, but we certainly don’t want it to be permanently (or plastically)
deformed, because then the actuators or other mechanisms may not work properly during the
next landing.
Tensile test
A tensile test, also known as uniaxial stress test, is probably the most fundamental type of
mechanical test that can be performed on material to determine its mechanical properties. Tensile
tests are simple, relatively inexpensive, and fully standardized. As the material is being pulled
apart, its strength, along with how much it will elongate can be easily determined. During this
test, instead of plotting the force versus elongation, it is customary to plot the stress versus strain,
where stress is force per unit area (P/A), and strain is elongation per unit length (dl/L)
Engineering stress and problem of predicting failure
In a mechanical part, we have seen that due to various types of external loading, a complex
three-dimensional state of stress can develop at a point. The most generalized state of stress will
have three normal (sx, sy, sz) and three shear stresses (txy, tyz, tzx) at a point in three mutually
perpendicular directions. The value of each of these six stress components can be negative, zero
or positive. Because a specific state of stress can affect the material quite differently than the
stress applied in tens ion test described in section 2 above, the limiting stress levels (Syp or Su)
determined from tension test may not be directly applicable when a complex state of stress
exists.
A conceptual model based on the atomic structure can explain this effect for complex
stress in influencing the limiting failure stress. For example in if a compressive stress is applied
in addition to a shear stress, as shown below, it may take more shear stress to slide an atomic
plane over the neighboring atomic plane, as compared to the shear stress in absence of the
compressive stress. This is so, because the compressive stress is adding up with the inter-atomic
bond forces and thus increases the resistance to slip. Alternatively, if a tensile stress is applied
with shear stress, the slip may occur at a lower shear stress.