Aims Lecture 4

• Students will be able to:

– Calculate the permanent deformation of a piece loaded above the elastic limit.

– Describe creep and stress relaxation and sketch example curves – Determine Young’s modulus from stress strain diagrams – Determine the change in lateral dimensions of a piece given the Poisson’s ratio

Examples of loading and unloading for a material below the elastic limit (a) and for the same material above the elastic limit (b).

 

E

 In linear elastic region Use of offset strain to define Yield stress

Mechanical properties depend on the history of the piece.

After reloading of a piece the elastic and proportional limit can be increased.

Mechanical properties depend on time.

Creep

Creep is the increase in length of a piece under a steady load. After loading to an elongation of  0 at time t 0 the piece continues to increase in length with time.

Creep is very often more noticeable at elevated temperatures. It is particularly important for aircraft turbine blades.

Stress - relaxation

Stress-relaxation is the decrease in stress within a piece with fixed displacement. After loading to a stress of  0 at time t 0 the stress decreases over time.

This phenomenon results in the decrease in string tension of stringed instruments over time.

United Airlines flight 232 "UA232", "UAL232" (United 232 Heavy) was a scheduled flight operated by United Airlines . On July 19 , 1989 , its Douglas DC-10-10 (Registration N1819U) suffered a full hydraulic failure requiring an attempted landing under throttle control alone. It crashed on the runway at Sioux City, Iowa killing 110 of its 285 passengers and one of the 11 crew members.

Fatigue cracks caused failure of fan disk. Failed fan disk severs triply redundant hydraulics system leaving aircraft severely crippled.

Cycles to failure

Creep – continued extension under fixed load (often at elevated temperatures)

Poisson’s Ratio

Poisson’s ratio is a measure of the lateral change in dimensions of a material when a uniaxial load is applied.



long

   

L

  

L lat long



lat

 

r r

If volume is conserved Poisson’s ratio is 0.5 (maximum possible). Typically most materials are between 0.25 & 0.35. Lowest possible is 0

A steel pipe of length L=4.0 ft, outside diameter d 2 =6.0 in and inner diameter d 1 =4.5 in is compressed by an axial force P=140 kip. The material has modulus of elasticity E=30,000 ksi and Poisson’s ratio  =0.30.

Determine the following: i) The shortening of the pipe ii) The lateral strain iii) The increase in outer diameter iv) The increase in inner diameter v) The increase in the wall thickness