PSI - Issue 13

Konstantinos Kouzoumis et al. / Procedia Structural Integrity 13 (2018) 868–876 K. Kouzoumis et al. / Structural Integrity Procedia 00 (2018) 000–000

872

5

From the three surface correction factors provided in API / ASME for net section / global collapse Eq. 9C.18, that follows, is recommended for use in the assessments and will be used for the calculations.

1

M NS s

a B

1 M T , i ( λ a )

=

(11)

1 − a

B +

Eq. (11) uses a slightly modified shell factor ( λ a ) which is the same as Eq. (4) but with the thickness of the specimen ( B ) replaced by crack depth ( a ).

2.3. R6

Concerning axially oriented flaws in pressurized cylinders, the R6 fitness for service procedure provides limit load solutions, in terms of the variables a / B , B / r i and a / c , for internal (section IV.1.9.1) and external surface flaws (section IV.1.9.2). Through thickness flaws, are assessed with the use of internal / external solutions, where the flaw height has been set equal to the section thickness. The continuity between surface breaking and through thickness flaws provides an obvious advantage to the procedure and di ff erentiates the R6 procedure from the other two presented in this work. It should be noted that the R6 equations calculate limit loads instead of reference stresses. Solutions are given for local and global collapse conditions and can be chosen to satisfy either the Tresca or Mises yield criterion. In the forthcoming calculations the global solutions used both for external (IV.1.9.2-1) and internal flaws (IV.1.9.1-1) are based on the Tresca criterion, which gives lower limit loads. After analysing the three procedures, the di ff erences between them in assessing axial flaws in cylinders will be studied through example assessments. The comparison here concerns a range of di ff erent geometries, which will have the same thickness, membrane stress (arising from internal pressure) and structural width (i.e. length of the cylinder). The di ff erence in geometries is expressed in terms of internal radius-to-thickness ratio ( r i / B ), which will have either a very high ( r i / B = 60) value, which could be representative of large-diameter pipes such as hydroelectric penstocks or high-strength large-diameter onshore gas transmission pipelines, or a very low ratio ( r i / B = 1), representing thick walled, small-diameter tube, thus allowing a comparison at the extremes of procedures. The constant values of the geometries and loads for the example calculations are shown in Table 1. Internal, external and through-thickness flaws are all considered. Surface breaking flaws with two di ff erent ratios of crack depth-to-crack length, representing a shallow ( a / 2 c = 0 . 1) and a deep ( a / 2 c = 0 . 25) crack, are considered. In the following analysis, two solutions, relating to BS 7910, are presented for each assessment, i.e. the original BS 7910 equation and a modified equation that omits the factor of 1.2. The other procedures are implemented in the example calculations with the use of the equations described in Sections 2.2 and 2.3. 3. Comparison of Procedures

Table 1: Geometry & Loading used in example calculations

r i / B = 1

r i / B = 60

Diameter D (mm) Thickness B (mm)

50

1525 12.5

12.5 200 400 100

Membrane Stress P m (MPa) Yield Stress σ y (MPa) Internal Pressure p (MPa)

200 400

3.3

The results of the assessment are illustrated in Figs. 1a to 1d, in terms of plots of L r against crack depth-to thickness ratio ( a / B ) for surface flaws and L r against crack length-to-width ratio (2 c / W ) for through thickness flaws. Plots of the calculations for internal flaws are not provided, since the trends noted are identical to the ones relating to external flaws. Concerning the latter, it can be seen from Figs. 1a and 1b that the BS 7910 original solution lies above all the other solutions. In particular, it di ff ers in terms of L r by approximately 40% from the R6 local solution