Shake-down occurs if the material accumulates plastic strain on the first few cycles and behaves plastic for each subsequent cycles – no accumulating plastic strain. This means that there is a plastic strain amplitude in each cycle but the level of plastic strains does not increase.

The next case is when the material accumulates plastic strain on the first few cycles and this continues for each subsequent cycle. In this case shake-down does not occur. However, Based on ASME section III the accumulated plastic strain in the entire component life is limited to maximum of 5 %.

- Fracture mechanics analysis (LEFM & EPFM):

We perform crack propagation analysis on pressure vessels, piping systems and supporting structures by stress intensification factor, VCC, J-integral and C*-integral methods to study the behavior of existing cracks, utilizing advanced finite element analysis.

- Creep crack growth analysis:

We perform nonlinear finite element analysis to study the crack propagation of the existing cracks in the components operating under the elevated temperature to estimate the remaining life of the cracked components.

- Stability analysis:

We perform stability analysis on pressure vessels, piping systems and supporting structures, utilizing finite element analysis.

Slug Flow Analysis:
slug flow analysis using dynamic methods.

For dynamic analysis Caesar II software provides a very nice module, dynamic module where we have to simply provide the input parameters to get the output result. Before you start the dynamic analysis you have to perform conventional static analysis of the system (without using any slug force) and qualify the system from all criteria. To open the dynamic module in Caesar II click on dynamic analysis button as shown in Fig.1.

Fig. 1: Opening the Dynamic Module in Caesar II

When you click on the dynamic analysis button following window (Fig.2) will open. Select Slug Flow (Spectrum) from drop down menu. The window will be filled with some pre-existing data. For clarity simply select all those and delete. Now we have to provide inputs for analysis.

Fig. 2: Selecting Slug Flow Module in Caesar II

During dynamic analysis our first input will be the generation of spectrum profile. Slug load is one type of impulse load. So the magnitude of load varies from zero to some maximum value, remains constant for a time and then reduces to zero again. The force profile can be represented by a curve as shown in Fig. 3.

Fig. 3: Graphical Representation of Slug Force Profile

So from the above profile it is clear that in addition to slug force (Refer Static method of Slug Flow using Caesar II for calculation of slug force), we need to calculate two additional parameters,
a) Slug Duration and
b) Slug Periodicity.

Slug Duration:
Slug duration is defined as the time required for the slug to cross the elbow. Mathematically it can be denoted as, Slug Duration=Length of Liquid Slug/Velocity of Flow.

Slug Periodicity:
Slug Periodicity can be defined as the time interval for two consecutive slugs hitting the same elbow. So mathematically it can be denoted as, Slug Periodicity = (Length of Liquid Slug + Length of Gas Slug)/Velocity of Flow.

Let’s assume that the calculated slug duration is 8 milliseconds and periodicity is 400 milliseconds as shown in Fig. 3. We will use these data for generation of spectrum profile.