engineering core courses

Solid Mechanics I
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Solid Mechanics I
 Course homepage
C8: Strain Transformation
8.1 Equations of Strain Transformation
- Theory - Example
8.2 Mohr’s Circle for Strain
- Theory - Example - Question 1
8.3 Generalised Hooke’s Law
- Theory - Example - Question 1 - Question 2
8.4 Theories of Failure
- Theory - Example - Question 1 - Question 2

C8.4 Theories of Failure

As engineers it is of utmost importance that we design structures against failure. But what constitutes failure? What criteria do we use?

In this subtopic, we look at the failure of ductile materials. (which will usually be tested on in exams!).

For ductile materials, failure is specified as the onset of yielding (before plastic deformation). That is, if we were to use ductile materials in our engineering structures, we design it such that the loadings do not cause yielding.

Here we present two failure theories for ductile materials. We’ll show you the formulas and how to use them; for the explanation of the theory please consult your textbooks.

C8.4 Theories of Failure

As engineers it is of utmost importance that we design structures against failure. But what constitutes failure? What criteria do we use?

In this subtopic, we look at the failure of ductile materials. (which will usually be tested on in exams!).

For ductile materials, failure is specified as the onset of yielding (before plastic deformation). That is, if we were to use ductile materials in our engineering structures, we design it such that the loadings do not cause yielding.

Here we present two failure theories for ductile materials. We’ll show you the formulas and how to use them; for the explanation of the theory please consult your textbooks.

Tresca failure criterion (maximum shear-stress theory)

The formula presented here applies for plane-stress conditions only (σ3 = 0).


Tresca failure criterion formula

In simple terms, the formula says that failure occurs when the principal stress reaches the yield stress.

von-Mises failure criterion (maximum distortion-energy theory)

Similar to the Tresca criterion, the formula presented here applies to plane-stress conditions only (σ3 = 0):


von-Mises failure criterion formula

When principal stresses increase enough to meet the condition above, failure occurs.

Let’s look at an example to see how we can apply these failure criteria.

Tresca failure criterion (maximum shear-stress theory)

The formula presented here applies for plane-stress conditions only (σ3 = 0).


Tresca failure criterion formula

In simple terms, the formula says that failure occurs when the principal stress reaches the yield stress.

von-Mises failure criterion (maximum distortion-energy theory)

Similar to the Tresca criterion, the formula presented here applies to plane-stress conditions only (σ3 = 0):


von-Mises failure criterion formula

When principal stresses increase enough to meet the condition above, failure occurs.

Let’s look at an example to see how we can apply these failure criteria.

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