23.6:
Yield Criteria for Ductile Materials under Plane Stress
Structural elements and machine parts made from ductile materials are designed to resist yielding under an expected load.
The yield point is identified through a tensile test on a similar material under uniaxial stress. However, predicting failure is not straightforward when the stress state changes to the plane stress, resulting in biaxial stress.
This condition is different from uniaxial stress and requires the establishment of a failure criterion to compare the effects of these two stress states.
The Maximum Shearing Stress Criterion, based on shearing stresses causing yield in ductile materials, proposes that a component is safe if its maximum shearing stress is smaller than that in the yielding of a tensile test specimen.
Graphically represented by Tresca's hexagon, it helps predict material failure under different stress conditions.
The Maximum Distortion Energy Criterion, also known as the Von Mises criterion, determines the safety of a structure based on distortion energy per unit volume.
The component is safe if the distortion energy is less than that, which causes yielding in a tensile test specimen.
23.6:
Yield Criteria for Ductile Materials under Plane Stress
In designing structural elements and machine parts using ductile materials, it is crucial to ensure that these components withstand applied stresses without yielding. Yielding is initially determined through a tensile test, which evaluates the material's response to uniaxial stress. However, tensile stress is insufficient when components face biaxial or plane stress conditions This condition requires advanced criteria to predict failure.
The Maximum Shearing Stress Criterion, also known as the Tresca Criterion, assesses component safety under various stress states by comparing the maximum shearing stress within the material to that at the yield point in a uniaxial tensile test. Shearing stress, which is significant in the yielding of ductile materials, is visualized through Tresca's hexagon in stress space. This graphical representation forms a boundary condition: stresses within the hexagon indicate safety, while those outside suggest potential yielding.
Alternatively, the Maximum Distortion Energy Criterion, known as the Von Mises criterion, is based on the distortion energy theory. This criterion states that yielding occurs from the energy stored due to distortion. A component is considered safe if the distortion energy per unit volume from applied stresses is less than that at the yield point. The Von Mises stress, derived from principal stresses, quantifies this energy, aiding in evaluating material behavior under complex stress states.