Fatigue Life Assessment of Ship Hatch Corner Based on Hot Spot Stress Method

Abstract

The hatch corner of ship is the most prone area for stress concentration, which makes the fatigue problem of hatch corner particularly serious, and becomes a position that is easily damaged. Firstly, the hot spot stress method based on surface extrapolation is introduced, and the hatch corner of a bulk carrier is selected as the research object, the scale model test is designed and carried out, the finite element model is established, and the parameters of the corner form and different transition radii are analyzed. The CCS calculation specification evaluates the fatigue strength of hatch corner, and compares the test results with the finite element calculation results. The results show that the hot spot stress method has good adaptability to the fatigue assessment of hatch corner, and the fatigue strength evaluation of hatch corner needs to select the corresponding S–N curve according to the position of the maximum hot spot stress. The form of corner and the increase of transition radius are of great significance for alleviating stress concentration effect and improving fatigue life of corner, which provides reference for fatigue resistance and optimal design of hatch corner structure.

1 Introduction

Because the cabin opening of a large-opening hull is usually large, its structural continuity is destroyed, which is not conducive to stress transmission. When deformed by the bending moment, stress concentration is easily formed at the hatch corners, which makes the fatigue problem of hatch corner particularly serious [1]. In view of the irreplaceable role of large ship in maritime transportation, the fatigue assessment of hatch corner of large-opening ship is a very meaningful research problem. Aiming at this problem, domestic and foreign scholars have carried out a series of related research. Yu et al. [2] used the semi-probability design wave method to calculate the fatigue cumulative damage of the hatch corner near the cargo hold of an 8530TEU large container ship, and at the same time predict the fatigue life. Yu et al. [3] used spectral analysis method combined with finite element method and crack propagation path to predict and evaluate the fatigue life of a large container ship hatch corner. Li et al. [4] used the global model method to evaluate the fatigue life of the circular hatch corner of bulk carriers, and analyzed the factors affecting the fatigue life. Cheng et al. [5] used finite element analysis and inertia release technology to evaluate the fatigue life and strength of hatch corner on container decks, and propose optimization measures.

The above studies on the fatigue performance of hatch corner are mostly designed to combine finite elements with different methods. The nominal stress method has some obvious shortcomings, and the fatigue performance evaluated at the same time has strong divergence. Therefore, Wang et al. [6] applied sub-model technology to evaluate the fatigue life of welded frames. Wang et al. [7] used hot spot stress to study the fatigue of FPSO welded structures.

In this paper, a typical joint of a large bulk carrier-hatch corner is selected as the research object, and scaled model tests of different forms and sizes of transition corner are carried out. The finite element model of the hatch corner structure is established, and its parameters are analyzed. The fatigue strength evaluation of hatch corner is carried out, and the test and finite element results are compared to provide reference for fatigue resistance of similar structures in hatch corner.

2 Hot Spot Stress Method

2.1 Hot Spot Stress Method Based on Surface Extrapolation

In a welded structure, the weld toe is the most prone to fatigue failure of the structure, and the hot spot stress usually refers to the structural stress at the weld toe. The nominal stress at the weld toe of the member and the corresponding structural stress concentration factor are used to obtain the hot spot stress of the welded joints [8]. For structures with complex forces in the field of ocean engineering, the nominal stress method is difficult to solve hatch corner. Therefore, this paper adopts the hot spot stress method based on surface extrapolation.

In welded structures, the surface linear extrapolation method usually uses the structural stress at a certain distance from the weld toe to perform linear or quadratic interpolation calculations to determine the hot spot stress of the weld toe. Its schematic diagram is shown in Fig. 1. The interpolation calculation formula of surface linear extrapolation method is shown in (1).

$$\updelta _{{{\text{h}}s}} = \frac{{\left[ {x_{2} x_{3} \left( {x_{3} - x_{2} } \right)\updelta _{1} + x_{1} x_{3} \left( {x_{1} - x_{3} } \right)\updelta _{2} + x_{1} x_{2} \left( {x_{2} - x_{1} } \right)\updelta _{3} } \right]}}{{\left[ {x_{2} x_{3} \left( {x_{3} - x_{2} } \right) + x_{1} x_{3} \left( {x_{1} - x_{3} } \right) + x_{1} x_{2} \left( {x_{2} - x_{1} } \right)} \right]}}$$

(1)

Fig. 1

Schematic diagram of hot spot stress method based on surface linear extrapolation

Fricke et al. [9] studied the hot spot stress of FPSO structural details, by comparing the hot spot stress solved by different extrapolation points, the results showed that the hot spot stress solved by applying the extrapolation points of 0.5t and 1.5t had strong convergence. (2) is the formula for solving hot spot stress with the extrapolation points being 0.5t and 1.5t respectively.

$$\updelta _{{{\text{h}}s}} = 1.5\updelta _{0.5t} - 0.5\updelta _{1.5t}$$

(2)

2.2 Hot Spot Stress S–N Curve

When performing fatigue life assessments on complex welded structures, using the nominal stress method to check the component fatigue is a relatively traditional method, but this method needs to select different values according to the different structural forms and complexity of the joints That is, multiple S–N curves. When calculating the fatigue life of components, (3) is a formula related to the S–N curve.

$$\lg N = \lg K - m\lg \left( {\Delta\upsigma } \right)$$

(3)

3 Static Load and Fatigue Test of Hatch Corner

3.1 Overview of the Test Piece

The research object of this test is a typical joint hatch corner of a large bulk carrier, and the test model range is selected from three rib lengths in the ship's length direction and three longitudinal frame spacing lengths in the ship's width direction. The geometric size of the test piece is scaled by 1:4. The thickness of the test piece except the arc is 4 mm, and the thickness of other plates is 6 mm. Figure 2 and Table 1 show the specific dimensions and specifications of the test pieces.

Fig. 2

Basic dimensions of specimen (unit: mm)

Table 1 Hatch corner model specification

The material of the model is AH36 steel, and the welding construction is carried out according to the requirements for welds in CCS “The rules and regulations for the construction and classification of sea-going steel ships”. Basic electrodes are used for the welding rods, and the welds are continuous welding. After the welding is completed, the corner of the hatch and other welds are to be polished to ensure that there are no visible defects. Material yield strength ${\delta }_{s}$ = 355 MPa, tensile strength ${\delta }_{b}$ = 490–630 MPa.

3.2 Static Load and Fatigue Test

Considering that the overall stress and local stress are mainly evaluated in the fatigue assessment process of the hull structure, the overall stress mainly presents a tendency to spread to both sides at the corner, and the simplified method of fixing one end and loading the other end is adopted to realize the hatch corner For loading, the specimen is fixed on the test bench by bolts, and the upper end of the specimen is connected to the MTS actuator chuck through bilateral double-hole chucks to realize the vertical loading of the entire model. The test loading device is shown in Fig. 3. The measuring points of the test are mainly distributed near A and B, that is, the connection between the arc and the free edge of the corner, to monitor the stress distribution near it. The measuring points are all unidirectional strain gauges, and the layout positions are shown in Fig. 4.

Fig. 3

Test loading device

Fig. 4

Location of measuring points

Before formal loading, it is necessary to preload the specimen several times to eliminate the influence of residual stress. According to the test results, the static load is determined to be 50 kN. After the static load test, the tension-tension fatigue test was carried out on the three groups of specimens in turn. The fatigue test was carried out on the QBS-350A fatigue testing machine. Table 2 is the fatigue test parameters.

Table 2 Fatigue test parameters

4 Numerical Simulation Verification of Hatch Corner Structure

The commercial finite element software ABAQUS is used to simulate and analyze the hatch corner model, and the steps are as follows:

• (1) Part module: Use solid element to build the hatch corner model.

• (2) Property module: Endow that corner model with correspond material properties.

• (3) Mesh module: Eight-node hexahedral linear reduced integral element (C3D8R) is selected for grid division. In order to accurately capture the stress and strain distribution near the corner, the grid of the area near the corner is refined, and the grid size is 4 mm, with a total of 128,644 elements.

• (4) Assembly module: Assemble different parts.

• (5) Step module: Adjust the analysis step and set the required field output.

• (6) Load module: A fixed constraint is added at one end of the model, and the tensile load is uniformly distributed at the other end in the form of nodes. See Fig. 5 for the constraint conditions.

  Fig. 5

  

  Constraints of hatch corner model

• (7) Job module: Submit the job for calculation and monitor the analysis results.

4.1 Comparative Analysis of Numerical Simulation and Test Results of Hatch Corner Structure

Static load test adopts step-by-step loading, and the loading load increases step by step according to 10, 30 and 50 kN. After the loading load stabilizes for a period of time, data will be collected. See Fig. 6 for the comparison between the axial stress test and the finite element method at R200 hatch corner.

Fig. 6

Experimental and finite element axial stress comparison diagram for R200 hatch corner model

From the analysis in Fig. 6, it can be obtained that: under all levels of load, the finite element numerical calculation and the experimental measurement results are basically consistent in trend and value, and the error is within 8%. Under this relatively small error, the accuracy and reliability of the finite element model are verified.

4.2 Hot Spot Stress Calculation

Wang et al. [10] compares the effects of different hot spot stress selection methods on fatigue damage, and should choose the maximum principal stress interpolation to calculate hot spot stress. Figure 7 is the cloud diagram of the first principal stress of each model of the hatch corner when the load is 50 kN.

Fig. 7

The first principal stress cloud diagram of hatch corner models

It can be seen from Fig. 7 that the hot spot area of the R200 and (200 × 120) hatch corner model is located near A, while the hot spot area of the R120 hatch corner model is located near C. The stress values ${\sigma }_{0.5t}$ and ${\sigma }_{1.5t},$ substituting the hot spot stress results obtained in (2), and counting them in Table 3.

Table 3 Hot spot stress results

5 Parametric Analysis

The size and shape of the transition corner may have a great influence on the stress state in the corner area. Based on the test results, this paper explores the influence of corner transition radius and main shape parameters on stress distribution in the hot spot area and the fatigue life of corner. The applied load is 50 kN.

5.1 Stress Analysis in Hot Spots

In order to accurately capture the stress distribution state at the corner of the model, the regional grid at the corner is refined, and that relationship between the principal stress of each specimen and the weld toe distance is drawn in the Fig. 8.

Fig. 8

Relationship diagram between principal stress and toe distance of each specimen

Compared with the stress value at hot spot A of the R120 hatch corner model, the stress value of the R200 hatch corner model at hot spot A is reduced by 10.4%; (200 mm × 120 mm) hatch corner model is reduced to 19.5%, indicating that the transition corner Radius size and shape play an important role in alleviating stress concentrations caused by structural discontinuities between cabins. Therefore, (200 mm × 120 mm) hatch corner is the best for alleviating the stress concentration effect of the corner. At the same time, for the arc hatch corner, the stress concentration effect at the corner is alleviated with the increase of the transition corner radius.

To sum up, R120 hatch corner has no maximum stress at the welding toe. Due to the influence of weld defects, fatigue damage will first occur at the weld toe. Therefore, the fatigue strength analysis and evaluation of hatch corner will be carried out next.

5.2 Fatigue Strength Analysis

Reference [11] stipulates that for welded joints, the fatigue strength evaluation adopts the D curve; for the free edge of base metal, the fatigue strength evaluation adopts the C curve. See Table 4 for the relevant parameters of the S–N curve referring to CCS. Use (3) to calculate the fatigue evaluation results of C and D curve, $\Delta\upsigma$ is the hot spot stress value in Table 3, $m$ and $K$ are the values in Table 4 respectively. The fatigue evaluation results of hatch corner specimens are shown in Table 5, and the test results are plotted in Fig. 9.

Table 4 S–N curve related parameters

Table 5 Fatigue life evaluation results

Fig. 9

Hot spot stress data points in hatch corner

From the results in Table 5 and Fig. 9, The fatigue test data points of each specimen are above the D curve. Among them, data point of the R120 hatch corner is above the C curve, and the R200 hatch angle Compared with (200 mm × 120 mm) hatch corner, the fatigue life of R200 hatch corner and R120 hatch corner are reduced by 20.4% and 33.2% respectively, and (200 mm × 120 mm) hatch corner has the best fatigue performance.

6 Conclusions

This paper first introduces the hot spot stress method, designs and carries out hatch corner scale model tests, establishes its finite element model, conducts parameter analysis on the hatch corner form and transition radius, the fatigue strength of corner structure is evaluated by using CCS calculation specification, and the test results are compared with the finite element calculation results, and the following conclusions are obtained:

• (1) The fatigue strength assessment of ship hatch corner needs to select the corresponding S–N curve according to the position of its maximum hot spot stress. For the maximum stress at the junction of corner and the free edge of corner; the D curve should be selected; the maximum stress in the arc transition area should be the C curve.

• (2) The fatigue life of the hatch corner is closely related to the transition radius at the corner, and the increase of the transition radius at the corner is beneficial to alleviate the stress concentration effect of the corner and improve its fatigue life.

• (3) For the corner forms of arc and ellipse, it is concluded that the corner arm lengths are equal, that is, when both are 120 mm, (120 mm × 200 mm) elliptical hatch corner has the best fatigue resistance performance, and it is suggested that the elliptical hatch corner should be considered in the design form.

Appendices

Appendices

$\updelta _{{{\text{h}}s}}$:

Extrapolation of weld toe hot spot stress values

$\updelta _{1}, \updelta _{2}, \updelta _{3}$:

Structural stress values at extrapolated points 1, 2 and 3

$x_{1}, x_{2}, x_{3}$:

The length of the extrapolated point from the position of the weld toe

$\updelta _{0.5t}, \updelta _{1.5t}$:

Stress values at 0.5 and 1.5 plate thickness lengths from the weld toe position

$N$:

Number of fatigue cycles

$\lg K$:

Intercept of the curve under the log–log axis

$m$:

Material S–N Curve Index

$\Delta\upsigma$:

Stress range