Yielding Flashcards
Lecture 6
What is the yield criteria tensile test?
Simple stress state
Used to measure yield stress
- may be referred to as (yield) strength
What do most real systems have?
complex stress state
How do we determine whether yielding will occur under complex loading?
express the complex stress state in terms of the principal stresses
combine the principal stresses in standard criterion
use the criterion to see if yielding will occur
What is the Rankine yield criterion?
A material yields if any of the principal stresses reaches the yield stress in simple tension, also known as the maximum principal stress theory. works well for materials that fracture at the elastic limit (e.g. some cast irons, glass, concrete and brittle polymers)
What is the von Mises yield criterion?
Maximum distortion energy, plastic flow occurs when the shear deformation energy in the complex state of stress = the shear deformation energy in uniaxial stress
What is the maximum shear stress?
Maximum in-plane shear stress is given by the radius of Mohr’s circle
What is the Tresca yield criterion?
A thin plate of material is used in such a way that it experiences a stress state described by (all values in MPa). Will the plate yield under these conditions if the material has a yield stress of σys = 170MPa? Use the von Mises yield criterion.
A component is made of a material with yield stresses of 120MPa. Which of the following plane stress states would cause it to yield by the Tresca criterion?
a) σ1 = 100MPa, σ2 = 30MPa
b) σ1 = 80MPa, σ2 = -30MPa
c) σ1 = 100MPa, σ2 = -30MPa
d) σ1 = 80MPa, σ2 = 30MPa
a) (|100 - 30| = 70, 100, 70) < 120
b) (|80 - (-30)| = 110, 80, 30) < 120
c) (|100 - (-30)| = 130, 80, 30) > 120
d) (|80 - 30| = 50, 80, 30) < 120
ANSWER: c
How do you determine whether yielding will occur?
Identify principal stresses
Use these in yielding criterion
What are the three yield criteria?
Rankline - failure based on maximum principal stress
von Mises - energy-based criterion
Tresca - shear based criterion
