Assignment mechanical behaviour of materials, prof. Laura vegani

Assignment of mechanical behaviour 2019/2020

Design of a pressure vessel with LEFM

Nicholas Agazzi, Linda Armanini, Tommaso Bachini, Giulio Benedini, Andreea Florina Bursuc

Data

We are considering a cylindrical cracked vessel with hemispheric ends containing a pressurized gas.

The data used are:

Data 5,80 mm 0,29 mm = 5% ⋅ 0 230 mm = − 2 218,4 mm 20 MPac 10 mmW 100 mmm 3,00 /−13C

With da/dN in mm/cycle and ΔK in MPa√mm 2,5 ⋅ 10 200 MPa√m

Static assessment

Request number one: following the approach of fracture mechanics, perform the static assessment of the vessel. Use a pressure P = 2Pw.

Point B is neglected because the most critical situation is point A and c value is kept constant (only radial propagation is considered).

In order to perform the assessment, the Mariotte equation is used since the following conditions are verified:

• Axisymmetric structure
• Axisymmetric radial load
• Small and constant thickness (t)
• No sharp variation in the diameter

In this case, Mariotte equation is applied to point A and only circumferential stress is taken into account and given by the formula: where and is equal to the internal diameter.

= = 2

2

As the vessel has complex geometry, it is useful to consider a specimen with a rectangular section. In this way, the formulas here reported are used to compute the corresponding stress intensity factor K.

I =

These formulas are obtained by simplifying the ones provided by the text, using , = 0 = /2 = , and .

0 = ⋅ ⋅ ( , , , )√

1.65 = 1 + 1.464 ⋅ ( )

2

4 = + ⋅ ( ) + ⋅ ( ) ⋅ ⋅ ⋅ [ ]

1 2 3 = 1,13 − 0,09 ⋅1

0,89 = −0,54 +2 0,2+ 241

= 0,5 − + 14 ⋅ (1 − )

3 0,65+ 12 = ( ⋅ )][sec √

2 = 1=1

Calculations

In this way we obtained the tabulated values.

753,1 MPa 1,004 1,1271 3,3462 5,9363 1,000 1,136