Everything about Elastic Limit totally explained
The
yield strength or
yield point of a
material is defined in
engineering and
materials science as the
stress at which a material begins to
deform plastically. Prior to the yield point the material will deform
elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed some fraction of the deformation will be permanent and non-reversible.
In the three-dimensional space of the principal stresses (
), an infinite number of yield points form together a
yield surface.
Knowledge of the yield point is vital when designing a component since it generally represents an upper limit to the load that can be applied. It is also important for the control of many materials production techniques such as
forging,
rolling, or
pressing. In structural engineering, this is a soft failure mode which doesn't normally cause
catastrophic failure or
ultimate failure unless it accelerates
buckling.
Definition
It is often difficult to precisely define yielding due to the wide variety of
stress–strain curves exhibited by real materials. In addition, there are several possible ways to define yielding:
True elastic limit: The lowest stress at which dislocations move. This definition is rarely used, since dislocations move at very low stresses, and detecting such movement is very difficult.
; Proportionality limit : Up to this amount of stress, stress is proportional to strain (Hooke's Law), so the Stress Strain Graph is a straight line, and the gradient will be equal to the Young's modulus of the material.
Elastic limit : Beyond the elastic limit, permanent deformation will occur. The lowest stress at which permanent deformation can be measured. This requires a manual load-unload procedure, and the accuracy is critically dependent on equipment and operator skill. For elastomers, such as rubber, the elastic limit is much larger than the proportionality limit. Also, precise strain measurements have shown that plastic strain begins at low stresses.
; Offset yield point (yield strength or proof stress) : This is the most widely used strength measure of metals, and is found from the stress-strain curve as shown in the figure to the right. A plastic strain of 0.2% is usually used to define the offset yield stress, although other values may be used depending on the material and the application. The offset value is given as a subscript, for example Rp0.2=310 MPa. In some materials there's essentially no linear region and so a certain value of strain is defined instead. Although somewhat arbitrary, this method does allow for a consistent comparison of materials.
Upper yield point and lower yield point: Some metals, such as mild steel, reach an upper yield point before dropping rapidly to a lower yield point. The material response is linear up until the upper yield point, but the lower yield point is used in structural engineering as a conservative value.
Yield criterion
A yield criterion, often expressed as
yield surface, or yield locus, is an hypothesis concerning the limit of elasticity under any combination of stresses. There are two interpretations of yield criterion: one is purely mathematical in taking a statistical approach while other models attempt to provide a justification based on established physical principles. Since stress and strain are
tensor qualities they can be described on the basis of three principal directions, in the case of stress these are denoted by
,
and
.
The following represent the most common yield criterion as applied to an isotropic material (uniform properties in all directions). Other equations have been proposed or are used in specialist situations.
Isotropic yield criteria
Maximum Principal Stress Theory - Yield occurs when the largest principal stress exceeds the uniaxial tensile yield strength. Although this criterion allows for a quick and easy comparison with experimental data it's rarely suitable for design purposes.
»
Maximum Principal Strain Theory - Yield occurs when the maximum principal
strain reaches the strain corresponding to the yield point during a simple tensile test. In terms of the principal stresses this is determined by the equation:
»
Maximum Shear Stress Theory - Also known as the
Tresca yield criterion, after the French scientist
Henri Tresca. This assumes that yield occurs when the shear stress
exceeds the shear yield strength
:
»
where
» is the stress required to move dislocations,
k is a material constant, and
» d is the grain size.
Implications for structural engineering
Yielded structures have a lower stiffness, leading to increased deflections and decreased buckling strength. The structure will be permanently deformed when the load is removed, and may have residual stresses. Engineering metals display strain hardening, which implies that the yield stress is increased after unloading from a yield state. Highly optimized structures, such as airplane beams and components, rely on yielding as a fail-safe failure mode. No safety factor is therefore needed when comparing limit loads (the highest loads expected during normal operation) to yield criteria.
Typical yield strength
Note: many of the values depend on manufacturing process and purity/composition.
Further Information
Get more info on 'Elastic Limit'.
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