KR Webzine Vol.163

Membrane-type hull and cargo holds have been designed and built for large ships and now there is a growing interest in applying the same technology to small and medium-sized liquefied natural gas (LNG) carriers, to meet the recent increase in demand for LNG as an ecofriendly fuel and to expand LNG bunkering infrastructure. 

The advantage of the HMD type-B tank lies in the possibility of a separated design for the hull and the cargo tank, ensuring appropriate structural stability inside the tank to manage the impact load caused by the motion of the liquid cargo. It also offers design flexibility as a fuel tank.

Figure 1. Design procedure for Type B tank system

The LNG cargo tank has been developed through high-level engineering, for example, crack propagation analysis has been used to install a partial drip tray in the lower part of the LNG cargo tank. This is then used to calculate the amount of leaked gas in the structure which is supporting the cargo tank.

The spherical structure of a type B tank, which is well-known as the Moss type, has excellent structural stability. However, due to the characteristics of the shape, it is disadvantageous in terms of cargo loading capacity and visibility. Although these problems have been overcome as the LNG cargo tank enters the hull, complicated processes such as crack propagation analysis and uncertain processes such as leaked LNG cargo calculation are essential.

The fatigue crack propagation analysis and leaked cargo calculation procedure for the partial second barrier design follows a relatively simple deterministic analysis method based on the traditional fracture mechanics and the international code (IGC Code). BS-7910, the British Standard for Crack Propagation Evaluation of Metal Structures, contains methods for evaluating crack propagation analysis based on fracture mechanics. 

If the residual stress is calculated without considering the actual welding conditions, accurate crack propagation analysis cannot be performed, and there is uncertainty about the capacity and design of the partial second barrier for the leakage of liquefied LNG – a high-risk cargo group. In order to overcome the limitations of this deterministic basis, detailed research is being carried out for technological advancement as shown in Figure 2.

Figure 2. Research objective and contents

The welding process of a metal structure consists of repeated heating and cooling of the bead. In this repeated heating and cooling process, local deformation and stress are formed by thermal expansion, and residual stress is formed by the balance remaining inside after cooling. This is called weld residual stress, and if a more accurate residual stress distribution in the weld zone is applied to the crack propagation analysis, the reliability of the analysis can be increased. A weld analysis should be performed taking into consideration the shape, welding conditions, and boundary conditions of welded part.  Stress components such as residual stress, membrane stress, and bending stress should be analyzed in the crack tip.

                           Figure 3. Welding analysis for residual stress calculation

The more complex the structure, the  more difficult to calculate the Stress Intensity Factor (SIF) using the Finite Element Method. In order to overcome this disadvantage, research on  XFEM (eXtended Finite Element Method), which can realize a discontinuous surface by inserting a crack shape into the entire shape, is being conducted. The XFEM is based on GFEM (Generalized Finite Element Method) and PUM (Partition of Unity Method). The existing FEM shows calculation results that depend on the shape of the element, but the XFEM does not go through a re-mesh process regardless of the shape of the element.

The XFEM was proposed to provide a solution to a problem that could not be solved by the existing finite element method, and it is a method to solve the element displacement discontinuity at the crack tip by adding the concept of extended degrees of freedom to the finite element method. In addition, this method can also define discontinuities at the interface surface due to the occurrence of cracks. The displacement field of the crack assumes the form shown in the following equation, including the expansion displacement in the element where the discontinuous jump occurs and the expansion displacement in the element including the crack tip.

In the above equation, N_i is a general finite element shape function, and H(X) is a Heaviside step function. The first term includes the continuous displacement field of a general finite element, the second term includes the displacement field of the element field in which the jump occurs, and the last term includes the displacement field of the crack tip (theoretical solution of fracture mechanics,

Figure 4 is an example of crack propagation by fatigue load using the XFEM. It shows that the crack length increases as the number of repetitions increases, and the stress intensity factor can also be checked in a text file, so it can be compared with a numerical solution. The XFEM can also simulate multiple cracks, and it is expected that meaningful results can be derived through many trials in the future.

Figure 4. XFEM (eXtended Finite Element Method)

By assessing the residual stress through welding analysis and the stress intensity factor of the crack tip using the XFEM, an accurate solution in a complex crack shape can be obtained, and more accurate cargo leakage during the diversion period after crack detection can be calculated. This can be expected to compensate for the uncertainty in determining the size of the partial double barrier and it can be more efficiently deployed accordingly. This study will become a base technology that can lead new markets, such as small and medium-sized LNG carriers.