Expansion Allowable Stress
Expansion Allowable Stress
(OP)
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
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





RE: Expansion Allowable Stress
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RE: Expansion Allowable Stress
RE: Expansion Allowable Stress
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 3ε 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 2ε), 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 4ε at the highest point and at unloading the residual strain will be 2ε, and so on.
Note that if the ΔT was producing a strain of only 2ε 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
RE: Expansion Allowable Stress
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.