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MECH3020

Solid Mechanics II(Spring 2015)Professor Robin MA ( melwma@ust.hk )

Room 2552, Department of Mechanical and Aerospace EngineeringThe Hong Kong University of Science and Technology

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Plastic DeformationsElastic deformation while maximum stressis less than yield stressK

A AP avemax

Maximum stress is equal to the yield stressat the maximum elastic loading

K

AP Y Y

At loadings above the maximum elasticload, a region of plastic deformationsdevelop near the hole

As the loading increases, the plastic regionexpands until the section is at a uniformstress equal to the yield stress

Y

Y U

PK

AP

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Residual StressesWhen a single structural element is loaded uniformly beyondits yield stress and then unloaded, it is permanently

deformed but all stresses disappear. This is not the generalresult.

Residual stresses also result from the uneven heating orcooling of structures or structural elements

Residual stresses will remain in a structure after loading

and unloading if - only part of the structure undergoes plastic

deformation- different parts of the structure undergo different plastic deformations

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A cylindrical rod is placed inside a tubeof the same length. The ends of the rodand tube are attached to a rigid supporton one side and a rigid plate on theother. The load on the rod-tubeassembly is increased from zero to 25kN and decreased back to zero.

a) draw a load-deflection diagramfor the rod-tube assembly

b) determine the maximumelongation

c) determine the permanent setd) calculate the residual stresses in

the rod and tube.

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a) Draw a load-deflection diagram for the rod-tube

assembly

19.7

P (kN)

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b,c) determine the maximum elongation and permanent set

At a load of P = 25 kN, the rod has reached the plastic rangewhile the tube is still in the elastic range

The rod-tube assembly unloads along a line parallel to 0 Y r

19.7

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Calculate the residual stresses in the rod and tube.

Calculate the reverse stresses in the rod and tube caused by unloading and add them to the maximum stresses.

19.7

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