In addition to demonstrating protection against plastic collapse, the analyzed components must also qualify the local failure check per section 5.3 of ASME Sec VIII Div 2. The code gives two analysis methodologies to do this.The first method is to carry out an elastic analysis and check triaxial stress limit given as 4S by eq 5.5. The second method is to carry out an elastic plastic analysis using factored load from table 5.5 and check whether the strain limit given by eq 5.7 is met.
The same problem which was analyzed in the post – ASME PTB-3 Validation – Elastic Stress Analysis for protection against plastic collapse will be used to check protection against local failure.
The sum of principal stresses called as the triaxial stress can be found in ANSYS using the expression = S1 + S2 + S3 in a “user defined result”.
From plots its evident that Max(Triaxial Stress) = 72575 psi < 4S = 93200 psi. Hence the components satisfy elastic local failure check criteria and further stress linearization need not be performed. It shall be noted that local failure check is required only for linearized primary stresses for the load case – “Design Pressure + Static Head + Dead Loads” per sec 5.3.2.
ASME PTB-3 TRIAXIAL STRESS
The results compare very well with those provided in ASME PTB-3.
ELASTIC PLASTIC ANALYSIS
To check the above problem using elastic plastic methodology an analysis analogous to that performed in the post ASME PTB-3 Validation – Elastic Plastic Analysis is done but using a load factor of 1.7 instead of 2.4 used for checking protection against plastic collapse. Load factor is selected for local criteria from table 5.5.
Loads used in the model:
Internal Pressure = 1.7P = 714 psi
Pressure Thrust = 1.7 * Pressure Thrust in the Elastic Analysis = – 1669.9 psi
Computation of limiting triaxial strain was done using eq 5.6. The strain limit parameters were calculated from table 5.7 for both materials SA 105 and SA 516 Gr 70. Sample strain limit parameters for SA 516 Gr 70 are:
User Defined Results were used to plot the limiting triaxial strain using eq 5.6
NOTE: Strains above those at ultimate stress are shown in pink.
ASME PTB-3 Triaxial Strain Limit
Equivalent Plastic Strain
ASME PTB-3 Equivalent Plastic Strain
There was no forming strain in the components hence the equivalent plastic strain needs to be checked against the limiting triaxial strain. This can be done by computing and plotting strain ratio of the equivalent plastic strain and the limiting triaxial strain.
ASME PTB-3 Strain Ratio
Since the strain ratio < 1, protection against local failure check is satisfied. It shall be noted that though the strain ratio reported by ASME PTB-3 is 2% against 3% obtained from this analysis, we are still talking about very small values, hence the difference looks to be OK. Also the difference might have been due to a more accurate stress strain curve considered in this analysis (75 points) against a crude curve considered by ASME PTB-3 (20 points).
Find PTB-3 Validation for plastic collapse check using Elastic Stress Analysis here
Find PTB-3 Validation for plastic collapse check using Limit Load Analysis here
Find PTB-3 Validation for plastic collapse check using Elastic Plastic Analysis here