strength assessment for rfd asme bpvc section viii div. 2 · asme bpvc section viii div. 2 giovanni...

Strength Assessment for RFD

ASME BPVC section VIII div. 2

Giovanni Casula

Summary

5/4/2018Giovanni Casula2

The strength assessment is composed by:

• Protection against Plastic Collapse

• Protection against Local Failure

• Protection against Collapse from Buckling

• Ratcheting Assessment

Protection Against Plastic Collapse

Limit Load Analysis Method


• Material model: elastic-perfectly plastic

• Since Niobium is not present in BPVC code a 0.8 factor has been applied to the yield strength according to Fermilab Technical Note.

Yield strength in the model = 52 MPa

• Small displacement theory → Large Deflection : OFF

• Loads multiplied by design factor = 1.5

• If convergence is achieved, the component is stable under the applied loads


Analysis Loads, Constraints and mesh



Results at P = 2.7 bar ; “ERESX, NO”


Equivalent Stress Eq. Total Strain

• Convergence achieved; cavity is stable under the considered Loads

• Some zones have a % stress error above 10%

% Stress Error


Eq. total strain vs mesh size; “ERESX, NO”


• Strains indicated by limit-load analysis are not reliable

• Convergence study on shown areas to check mesh independency

0.0023

0.0025

0.0027

0.0029

0.0031

3.85 mm 3 mm 2.5 mm

EQ

. T

OTA

L S

TR

AIN

ELEMENT SIZEΤ+ − 2% error

Protection Against Local Failure

Elastic Analysis – Triaxial Stress Limit


The algebraic sum of the three linearized primary principal stresses shall be used for checking :

( σ1 + σ2 + σ3 ) ≤ 4S

Where S = 0.8x43.3 = 34.64 Mpa

0.8 Fermilab multiplier applied to the allowable limit (⅔ Sy) recommended by the code

Protection Against Local Failure

Elastic Analysis – Triaxial Stress Limit – Results


Calculation done in the three zones with highest stress values

Region A has the highest sum of linearized principal stresses

( σ1 + σ2 + σ3 ) = 83.4 MPa ≤ 4S = 138.6 MPa → OK

Protection Against Collapse from Buckling

Elastic Stress Analysis without geometric nonlin.


RFD shape doesn’t belong to any of the 3 categories indicated in

the code ↓

the highest design factor (16.13) has

been considered for conservative reasons.

Protection Against Collapse from Buckling

Elastic Stress Analysis – Results


The first buckling mode multiplier is 1.53

↓cavity is considered safe

against collapse from buckling.

Ratcheting Assessment

Elastic-Plastic Stress Analysis


• Material model: elastic-perfectly plastic• Yield strength = 52 MPa as in Protection against plastic collapse

• Consider non-linear geometry→ Large Deflection : ON

• Minimum of three repetitions of the cycle → 5 loadings considered

Pressure [MPa] g acceleration [mm/s^2]




The plastic strains are not null everywhere

↓

Check on the overall dimensions




4 deformation probes defined to check the changes in the RFD dimensions:most displaced points for the 2 tuner areas and for the 2 poles

X displ.Y displ.


Elastic-Plastic Stress Analysis - Results


Values at the end of each loading phase are the sameDispl. after the 4th unload are less than 1e-4 mm

↓no change in dimensions

↓Ratcheting criteria are satisfied

-4.00E-01

-3.00E-01

-2.00E-01

-1.00E-01

0.00E+00

1.00E-01

2.00E-01

3.00E-01

4.00E-01

0.20.40.7 1 1.21.41.7 2 2.22.42.7 3 3.23.43.7 4 4.24.44.7 5 5.25.45.7 6 6.26.46.7 7 7.27.47.7 8 8.28.48.7 9

Displacements vs time

Y displ tuner 1 [mm] Y displ tuner 2 [mm] X displ pole 1 [mm] X displ pole 2 [mm]

strength assessment for rfd asme bpvc section viii div. 2 · asme bpvc section viii div. 2 giovanni...

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