Expansion Allowable Stress

[carletes]

Dear all,

As far as I know, allowable expansion stresses of B31 codes has got the aim of avoiding incremental cyclic plastic strains in pipes (ratchetting)that could lead to collapse.

But, is it possibble that strains of a pipe under thermal cycles could get bigger and bigger up to pipe collapse? I thought that thermal stress were self limiting and the strain could never be bigger than the strain of the first cycle.

Thanks in advance

 

[prex]

Your last sentence is only true with a single thermal cycle. With more cycles the pipe could have a residual plastic deformation when coming back to low temperature, so that the next cycle will go beyond the first one, and so on.

prex

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[carletes]

Sorry, but I don't see the reason why the deformation could increase afeter each cycle. If the thermal expansion provokes a deformation of 40 mm in certain pipe (suppose that this deformation provokes a cycle with plastic deformation in cold and plastic deformation in hot condition) I thought that the deformation in every cycle would range from 0 mm in cold condition up to 40 mm in hot condition, but it would never grow til pipe collapse altough it was a plastic deformation cycle. What is my mistake?

 

[prex]

Take the simplest example of a heated bar with fixed ends and apply a [Δ]T producing a strain of 3 times the elastic strain [ε].
During the first heat up the strain will go elastically up to [ε], the stress going down to (compressive) -Y, then the plastic deformation will accumulate, ending with a total strain of 3[ε] and still a stress of -Y.
Now if the temperature goes down, the stress starts immediately decreasing its absolute value, going down first to 0 (the strain being at 2[ε]), then it changes its sign to tensile and continues growing up to Y, with the strain at [ε]. Here the deformation stops because the stress Y equilibrates the strain [ε]: hence a residual strain of [ε] is accumulated in the first cycle.
Now the second cycle will reach a total strain of 4[ε] at the highest point and at unloading the residual strain will be 2[ε], and so on.
Note that if the [Δ]T was producing a strain of only 2[ε] the plastic deformation would occur in the first cycle only, with no strain build up in the subsequentt cycles. That's why the limit on expansion stresses (all other stresses included) is placed somewhere close to 2Y (stresses calculated with elastic analysis of course).

prex

http://www.xcalcs.com

Online tools for structural design

 

[bvi]

The allowable thermal expansion stress in the B31 piping (not pipeline) codes such as B31.1 and B31.3 is aimed to 1) result in shake down to elastic cycling after the first thermal expansion cycles, 2) prevent fatigue failure, and 3) prevent ratchet.

Ratchet is generally not caused by thermal expansion induced stresses alone, it is caused by an interaction of sustained stresses such as those due to weight and pressure, and thermal expansion stresses. Note that in computing the allowable thermal expansion stress, the sustained stresses are subtracted (in some cases, the rules are simplified, and the allowable thermal expansion stresses are simply reduced by the allowable sustained stress). If ratchet didn't need to be considered, the allowable thermal expansion stress would not be reduced by the value of the sustained stress.

For information on ratchet mechansims, refer to the early papers by Bree, Miller, etc.