IntermediateTopic 71 of 106Engineering Mechanics

Plasticity and yielding

Beyond yield, deformation is permanent and requires plastic analysis.

In depth

Beyond yield, deformation is permanent; stress and strain are no longer proportional. Plastic design uses plastic moment M_p=σy·Z, and collapse occurs when plastic hinges form a mechanism. Strain hardening raises strength with deformation.

Key points

  • Shape factor Z/S≈1.5 for rectangles
  • Bauschinger effect
  • Ductility allows redistribution
Example

A paperclip bent beyond yield stays bent.

Why it matters

Beyond yield, materials deform permanently, and plastic analysis gives the true load capacity of ductile structures and forming processes.

Where this is used

  • Computing the collapse load of a steel frame under overload.
  • Estimating the force needed to bend a steel plate in a press.
  • Designing a shackle that deforms safely before fracture.

Frequently asked questions

What is Plasticity and yielding?

Beyond yield, deformation is permanent and requires plastic analysis.

Why is it important to understand plasticity and yielding?

Beyond yield, materials deform permanently, and plastic analysis gives the true load capacity of ductile structures and forming processes.

What is the difference between elastic and plastic behaviour?

Elastic deformation is fully recovered when the load is removed. Plastic deformation is permanent and remains after unloading.

What is a plastic hinge?

A region of a beam where the moment has reached the plastic moment, and the section can rotate as a hinge, which is used to find collapse loads.

How is Plasticity and yielding used in practice?

Typical applications include computing the collapse load of a steel frame under overload, estimating the force needed to bend a steel plate in a press and designing a shackle that deforms safely before fracture.

What should I learn before Plasticity and yielding?

Study "Creep" first (topic 70 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.

What are the key points of Plasticity and yielding?

Shape factor Z/S≈1.5 for rectangles. Bauschinger effect. Ductility allows redistribution.

Can you give an example of Plasticity and yielding?

A paperclip bent beyond yield stays bent.

What comes after Plasticity and yielding?

The next topic is "Residual stress", which builds directly on this one.

How difficult is Plasticity and yielding?

It is classed as Intermediate in Engineering Mechanics (topic 71 of 106). It is an intermediate topic. Work through the beginner topics in Engineering Mechanics first.

Learning path

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