Research on the Constitutive Relationship of the Coarse-Grained Heat-Affected Zone in Ship Thick-Plate Welded Joints of Ship Structures

Abstract

This study addresses the constitutive relationship of the welded coarse-grained heat-affected zone (CGHAZ) in 80-mm-thick DH36 marine steel plates. By integrating quasi-static tensile testing, digital image correlation (DIC) technology, and metallographic analysis, we systematically investigated the mechanical property differences and underlying mechanisms between the CGHAZ and base metal (BM). High-precision DIC technology enabled strain field characterization at the microscale in the CGHAZ, while the Ramberg-Osgood model was adopted to establish a dual-material constitutive equation. The results demonstrate that grain coarsening induced by welding thermal cycles significantly influenced the mechanical responses: the CGHAZ exhibited enhanced tensile strength but reduced plastic compatibility due to decreased grain boundary density. Notably, gradient differences in elastic modulus (CGHAZ: 184 GPa vs. BM: 213 GPa) and yield strength (CGHAZ: 363 MPa vs. BM: 373 MPa) between the BM and CGHAZ necessitate strict differentiation in engineering design. This work overcomes the limitations of oversimplified CGHAZ properties in conventional design approaches, providing a novel methodology for strength assessment and lightweight design of marine structures. The findings offer critical theoretical insights and practical guidelines for enhancing the reliability of offshore engineering equipment.

1. Introduction

The escalating demands of global trade and maritime transportation have driven the shipbuilding industry to progressively adopt large-scale vessel designs, necessitating the extensive use of thick steel plates (>40 mm thickness) to meet stringent structural integrity requirements [1]. This technological shift has concurrently led to the implementation of elevated heat input parameters during welding procedures, which inadvertently exacerbate the mechanical property gradients between the heat-affected zone (HAZ) and base metal (BM). Metallurgical analysis reveals that the HAZ microstructure typically differentiates into three distinct sub-zones: coarse-grained heat-affected zone (CGHAZ), fine-grained heat-affected zone (FGHAZ), and subcritical heat-affected zone (SCHAZ), as schematically illustrated in Figure 1 [2,3].

Beghini et al. [4] conducted quasi-static tensile tests on non-standard small specimens cut from characteristic regions of welded plates: BM, WM, and HAZ. The results showed that the properties of the HAZ differ significantly from those of the BM. Gan et al. [5] pointed out that the main reason for the fracture of welding joints in ship and marine engineering structures is brittle fracture, and the coarsening of grains and changes in the microstructure in the coarse-grained zone of the HAZ are the main causes of HAZ embrittlement, leading to a decline and deterioration in properties. These studies have shown a clear difference in mechanical properties between the CGHAZ and the BM, and the coarse-grained zone formed in the HAZ due to grain coarsening caused by welding has significant research implications. Therefore, in ship design and construction, the difference in mechanical properties between the BM and the HAZ, especially the CGHAZ, needs to be carefully considered. It is crucial to obtain the mechanical constitutive relationship between the BM and the CGHAZ.

At present, the positioning and measurement of the width of each part of the HAZ mainly rely on metallographic microscope observation, micro-hardness testing, and numerical simulation. Yang et al. [6] addressed the technical challenges posed by the submillimeter-scale width of the HAZ in welded joints, which renders conventional experimental methods inadequate for probing the microstructural mechanical properties of the CGHAZ. They developed a coupled thermo-mechanical-metallurgical finite element model for DP780 dual-phase steel welding to overcome this spatial resolution limitation. Xiong et al. [7] studied the width and properties of the HAZ of 4-mm-thick 16 Mn steel plate MAG welding joints under different welding line energy conditions through metallographic observation and micro-hardness testing of each zone of the welding joint. Georgios et al. [8] assessed the width of the HAZ of arc-welded ferritic ductile iron thin sheets by testing the micro-Vickers hardness of the welding joint and evaluating the hardness value changes. Liu et al. [9] studied the width and position of the HAZ of TIG welding joints of X70/316L bimetallic composite pipes with a wall thickness of 18.9 mm through macro-metallographic tests, hardness tests, transmission electron microscopy tests, and finite element simulation. Clearly, the CGHAZ is very narrow and requires metallographic microscopes and hardness measurements for measurement. These experiments often separate the mechanical measurement tests of the HAZ and the measurement of the position and spatial shape of the HAZ, making it difficult to combine the strain data and stress data generated in the HAZ during mechanical property measurement tests, and it is difficult to obtain its precise mechanical properties. Therefore, an urgent need exists for a measurement method to measure and evaluate its mechanical properties accurately.

The advent of advanced Digital Image Correlation (DIC) techniques has revolutionized mechanical characterization capabilities, particularly for micrometer-scale strain analysis in challenging environments. Recent implementation in naval architecture research enables unprecedented quantification of mechanical heterogeneity within the CGHAZ of thick-plate ship welds. DIC measurement technology is an experimental technique based on optical principles, which obtains the displacement and strain information of the specimen surface by calculating the gray-level matrix of the digital speckle images before and after deformation of the specimen surface [10]. In recent years, DIC measurement technology has begun to be preliminarily applied to the measurement of the mechanical properties of metals [11,12,13]. Zhang and Peng et al. [14] assessed the fatigue crack expansion ability of rail tracks using DIC technology, and the DIC measurement technology was able to accurately and effectively obtain the tiny crack tip deformation behavior during the fatigue crack expansion process. It can be seen that DIC measurement technology can observe the tiny deformations of materials at the micro level.

In summary, within the HAZ, the coarse-grained region exhibits the most significant degradation in mechanical properties due to its large grain size, resulting in a substantial disparity compared to the mechanical properties of the BM. This area has thus become the focal point in the assessment of welding quality. However, in the current design calculations for ships, this difference is not taken into account, and the mechanical parameters of the BM are uniformly employed for design verification. To prevent potential casualties or property damage caused by the reduced mechanical properties of the coarse-grained region, it is imperative to elucidate the constitutive relationship of this area within the HAZ. Therefore, the present experiment aims to conduct quasi-static tensile tests using a universal testing machine, applying axial loading until specimen failure. During the loading process, strain data will be collected using DIC technology, while stress data will be obtained from the universal testing machine. After processing and calculating the collected data, the constitutive relationships of the CGHAZ and the BM will be determined based on the Ramberg-Osgood model.

2. Test Design

2.1. Specimen Preparation

An 80-mm-thick DH36 steel plate was selected with a single V-notch and welded using the SAW process to obtain the welded test plate, as shown in Figure 2. Five identical specimens were taken from the test plate. The total length of the specimen was 400 mm, with a test section length of 160 mm, a width of 25 mm, and a height of 5 mm. The specific dimensions of the specimen are shown in Figure 3.

2.2. Test Equipment

DIC measurement technology is a highly valuable non-contact optical measurement method with a wide range of applications in the field of mechanical property research. The system consists of an image acquisition system (including an industrial CCD camera and lighting equipment) and data processing software. The camera parameters determine the measurement accuracy and range, while the software is responsible for core algorithm calculations and data visualization. The DIC test equipment used was the XTDIC-CONST full-field strain measurement system from Xintuo Sanwei (Shenzhen, China), with two cameras model XTDIC-CONST-SD, with a pixel count of 5 million, a frame rate of 75 fps, a strain measurement accuracy of 0.5 με, and a strain measurement range of 0.005% to 2000%. The loading rate of the universal material testing machine was 3 mm/min. The positions of the instruments during the test are shown in Figure 4.

2.3. Metallographic Test of the HAZ of the Specimen

Through metallographic tests, the boundary line and microstructure of the HAZ of the specimen were observed to accurately select the stress-strain measurement points in the CGHAZ later. During the metallographic test, the specimen was first polished to remove surface oxides and impurities until the surface was clean and smooth. Then, the specimen was roughly and finely ground using a grinding machine and sandpaper of different grit sizes to make the surface smooth without obvious scratches. Next, the specimen was polished using polishing cloth and polishing liquid until a mirror-like effect was achieved. After polishing, the specimen was cleaned with alcohol to remove residual polishing liquid and then dried by heating. Subsequently, the specimen was etched with a 4% nitric acid alcohol solution to clearly show the boundary line of the HAZ (Figure 5), facilitating the accurate selection of the observation area under the electron microscope. Finally, the specimen was observed under the electron microscope at an appropriate magnification to obtain a clear microstructural characteristic metallographic image, as shown in Figure 6.

The metallographic image clearly reveals distinct characteristic regions and their boundaries, including: 1. The weld zone, 2. The coarse-grained heat-affected zone (CGHAZ), 3. The fine-grained heat-affected zone (FGHAZ), 4. The subcritical heat-affected zone (SCHAZ), and 5. The fusion line. The figure indicates that the CGHAZ was approximately 800 μm wide. The widths of the FGHAZ and the SCHAZ are 1100 μm and 600 μm, respectively.

2.4. DIC Test Speckle, Spraying, and Measurement Point Selection

We creatively adopted the semi-spraying speckle method, which selectively applies speckle patterns to the surface of the specimen, creating a 15 mm wide central speckled region while maintaining 5 mm wide unpatterned zones on both flanks. This configuration ensures sufficient characteristic points for DIC strain measurement while preserving visible fusion line contours etched during metallographic preparation. The unpatterned lateral regions serve as fiducial markers to precisely localize the CGHAZ within the HAZ, avoiding interference from speckle coverage over microstructural features. Using the distance data of the CGHAZ from the fusion line determined by the metallographic microscope, the position of the CGHAZ was marked, and the sampling points in the CGHAZ were obtained as shown in Figure 7.

3. Test Results

3.1. Extraction of Stress-Strain Data of the CGHAZ

Quasi-static tensile testing conducted via a universal testing machine yields force-time curves, which are subsequently converted into stress-time curves through post-processing. Strain data acquired from three measurement points using DIC equipment are synchronized with the temporal axis, enabling the derivation of individual stress-strain curves for each sampling location, as shown in Figure 8.

3.2. Extraction of Stress-Strain Data of the BM

Similar to the extraction method of the stress-strain data of the CGHAZ, three points were sampled in the BM, and the strain-time curves of the three points were extracted, respectively. After synchronizing the time axes with the stress-time curve measured by the testing machine, the stress-strain curves of the three points could be obtained, respectively, as shown in Figure 9.

An average method was used to process the stress-strain curves of the three points to ensure the rigor of the results. The average method for data is to average the strain values of three measurement points collected by DIC at the same tensile force level and then obtain the average stress-strain curves. The average stress-strain curves of the CGHAZ and the BM at the same stress level were drawn simultaneously on Figure 10.

4. Solution of the Constitutive Equations of the Specimen BM and CGHAZ

4.1. Solution of the CGHAZ Constitutive Equation

Common steel constitutive models include elastic models, plastic models, Ramberg-Osgood models, multi-linear models, Chaboche models, and Johnson-Cook models. The average stress-strain experimental data of the CGHAZ were substituted to solve the relevant coefficients and obtain the material constitutive equation. The Ramberg-Osgood steel constitutive model offers several advantages [15]. It features a simplified mathematical expression that enables easy description of the complex stress—strain behavior for engineering calculations and analyses. The model also has good fitting ability, particularly in representing the yield platform and plastic hardening stage of steel. Moreover, its parameters (e.g., yield stress, strain hardening index, and reference strain rate) can typically be acquired via simple tensile tests, which facilitates experimental determination.

The Ramberg-Osgood constitutive model is as follows [16]:

$$\epsilon ={\epsilon }_e+{\epsilon }_p={\displaystyle \frac{\sigma }{E}}+p{\left({\displaystyle \frac{\sigma }{{\sigma }_p}}\right)}^n$$

(1)

Among them, ${\epsilon }_e$ represents the elastic strain; ${\epsilon }_e$ represents the plastic strain; $p$ is the plastic strain corresponding to the conditional yield strength ${\sigma }_p$, which is usually taken as 0.2% (the corresponding conditional yield strength is ${\sigma }_{0.2}$); $n$ is the strain hardening index, which can be determined according to Equation (2):

$$n={\displaystyle \frac{\ln 20}{\ln \frac{{\sigma }_{0.2}}{{\sigma }_{0.01}}}}$$

(2)

Among them, ${\sigma }_{0.01}$ is the stress corresponding to a plastic strain of 0.01%. We need to fit the most appropriate curve to determine the value of $n$.

The fitting results of the elastic stage and the yield and strengthening stages are shown in Figure 11.

By substituting the calculations and linear fitting, the relevant coefficients were obtained as follows. According to the slope of the linear fitting in Figure 11 of the elastic stage, the elastic modulus E = 184 GPa, and the yield strength ${\sigma }_p$ = ${\sigma }_{0.2}$ = 363 MPa. According to the experimental data, ${\sigma }_{0.01}$ = 1.4 MPa, and the strain hardening index n = 0.539 was calculated using Equation (2). The constitutive Equation (3) is as follows:

$$\epsilon ={\epsilon }_e+{\epsilon }_p={\displaystyle \frac{\sigma }{1.84\times {10}^{11}}}+0.2{\left({\displaystyle \frac{\sigma }{3.63\times {10}^8}}\right)}^{0.539}$$

(3)

4.2. Solution of the BM Constitutive Equation

The solution method for the BM constitutive equation is the same as that for the CGHAZ. The fitting results of the elastic stage and the yield and strengthening stages are shown in Figure 12 (Readers should be aware of the limitations of the calculation results. We have checked the BM, but we are unable to perform the same inspection on the HAZ).

By substituting the calculations and linear fitting, the relevant coefficients were obtained as follows. According to the slope of the linear fitting in Figure 12 of the elastic stage, the elastic modulus E = 213 GPa, and the yield strength ${\sigma }_p$ = ${\sigma }_{0.2}$ = 373 MPa. According to the experimental data, σ_0.01 = 1.4 MPa, and the strain hardening index n = 0.536 was calculated using Equation (2). The constitutive Equation (4) is as follows:

$$\epsilon ={\epsilon }_e+{\epsilon }_p={\displaystyle \frac{\sigma }{2.13\times {10}^{11}}}+0.2{\left({\displaystyle \frac{\sigma }{3.73\times {10}^8}}\right)}^{0.536}$$

(4)

5. Comparison and Analysis of DIC Measurement Method and Traditional Force-Strain Method

In this test, to verify the accuracy of the test data, tensile specimens of the same material were prepared, and the elastic modulus was measured using the force-strain method according to the GB/T 22315-2008 [17]. The specimen size is shown in Figure 13 and Figure 14. Figure 14 shows the traditional elastic modulus testing method.

The specific linear fitting is shown in Figure 15. By linearly fitting the data obtained from the force-strain method, the slope and the elastic modulus of the specimen were 209 GPa. Compared with the 213 GPa measured above for the BM, the difference is 1.8%, indicating that the constitutive equation obtained based on DIC testing technology has high accuracy and feasibility.

6. Result Analysis

The comparison of material parameters and mechanical properties between the CGHAZ and the BM is shown in

Table 1. CGHAZ and BM’s material parameters and mechanical properties correlation table.

	CGHAZ	BM	Relative Differences (%)
The elasticity modulus (GPa)	184 ± 7	213 ± 5	13.62
Yield strength (MPa)	363 ± 9	373 ± 6	2.68

.

From Table 1, it can be seen that there are significant differences in elastic modulus and yield strength between the CGHAZ and the BM. The elastic modulus of the BM is greater than that of the CGHAZ, with a relative difference of 13.62%. The yield strength of the BM is slightly higher than that of the CGHAZ, with a relative difference of 2.68%. From the location of the specimen fracture, the fracture occurred in the BM region, indicating that the tensile strength of the CGHAZ is higher than that of the BM. In actual engineering calculations, the material properties of the CGHAZ cannot be equated with those of the BM, and the allowable stress and failure criteria need to be strictly distinguished.

After the quasi-static tensile test, the fracture morphology of the specimen is shown in Figure 16. The fractured specimen exhibited necking deformation, with a fibrous central zone and approximately 45° shear lips on both sides, indicative of ductile fracture characteristics [18,19]. Since the fracture occurred in the base metal (BM) region, the tensile strength of the coarse-grained heat-affected zone (CGHAZ) could not be directly determined. However, this observation strongly implies that the CGHAZ possesses higher tensile strength than the BM.

7. Conclusions

This study investigates the constitutive relationship of the welded CGHAZ using an 80-mm-thick DH36 marine steel plate as the research object. Through quasi-static tensile testing combined with advanced DIC measurement technology and an innovative semi-spraying speckle method, the precise localization of measurement points in the CGHAZ was achieved. Metallographic testing enabled the accurate identification of fusion line boundaries. Stress-strain curves for both the CGHAZ and BM were obtained. Based on the Ramberg-Osgood model, constitutive equations were formulated for the BM and welded CGHAZ; the following conclusions were drawn:

(1)

The experimental results revealed that the CGHAZ exhibited significantly higher tensile strength than the BM, with fracture strains of 11.86% for the BM and 9.7% for the CGHAZ, indicating distinct deformation compatibility between the two regions. This anomalous strengthening effect originates from the unique microstructural characteristics of the CGHAZ: the coarse-grained structure leads to a reduced grain boundary density per unit volume. Since grain boundaries, as defect-rich regions and stress concentration sites, are preferential locations for crack nucleation, the reduced number of grain boundaries effectively suppresses microcrack initiation and propagation, thereby enhancing macroscopic tensile strength. In nonlinear mechanical analyses, it is imperative to establish a dual-material constitutive model based on strain evolution to separately characterize the deformation behavior and failure mechanisms of the CGHAZ and BM. This approach is critical for accurately predicting the mechanical performance of welded structures.

(2)

This study innovatively employed DIC measurement technology to construct a precise constitutive model for the CGHAZ successfully. By utilizing a non-contact, full-field strain measurement method (spatial resolution: 5 μm), this technique overcomes the technical limitations of traditional extensometers in localizing microscale CGHAZ regions. In shipbuilding practices, leveraging these precise material parameters enables designers to optimize structural layouts more rationally, such as refining plate thickness near weld zones and strategically arranging stiffeners. Such optimizations ensure structural strength and stability under diverse operational conditions, effectively mitigating safety hazards caused by insufficient consideration of CGHAZ performance. This advancement significantly enhances the safety and reliability of marine structures, providing a robust framework for engineering applications in offshore industries. In the future, interested researchers may extend the proposed methodology to studies of other materials.