Tensile analysis and assessment of carbon and alloy steels using FE approach as an idealization of material fractures under collision and grounding

Abstract In this study, a numerical investigation tensile test using ANSYS on three different carbon and alloy sheets of steel: AISI 1030 medium carbon steel, AISI 1080 high carbon steel and high-strength low-alloy (HSLA) A606 steel, has been carried out. The influences of three different specimen geometries on the stress–strain curve were also investigated. Understanding the properties of these materials, such as stress–strain obtained from a tensile test, is important. Materials are subjected to forces or loads when in use, for example, steel in a ship’s hull experiences significant stresses and strains. In such situations, it is necessary to understand the characteristics of the material because grounding or collisions can occur, which deform the materials. The differences in stress and strain obtained from three specimens with different geometries and mesh sizes of 2.5, 5, 7.5, and 10 mm for all proposed steels, were observed. The results showed that the ultimate tensile strength was always lower in specimen 2 compared to the other specimens. Furthermore, the highest von Mises stress and strain contour was located in the midsection of specimens 1 and 3 in all of the proposed materials.


Introduction
Researchers and vehicle designers have gone to great efforts to explore the safety characteristics of several motor vehicles [1]. Often, two groups of methods are used to quantify the impacts of these characteristics on vehicle safety [2]. The first is based on testing the ability of a vehicle to avoid a crash at the pre-crash stage (crash avoidance) and the second is to protect its occupants at the postcrash stage (crashworthiness). In crashworthiness, the material used in the vehicle design can be damaged when a crash or collision occurs. The maritime transportation system is a critical component of transport worldwide and has an important contribution to the global economy which is covering more than 90% of international trade [3]. Approximately 11 billion tons of cargo was transported by sea in 2018 [4]. The efficiency and capacity of maritime transportation continues to develop with the growth of global trade activities and new technologies. Furthermore, shipping is one of the most important modes of transportation,.Over recent years, studies on maritime transportation, especially covering ship accidents, have been carried out [5][6][7][8][9]. However, the maritime transportation system (MTS) poses several risks as it consists of several elements related to humans, ships, the environment, and management. As a consequence, this system is vulnerable to several types of hazard, many of which can result in accidents such as collisions, groundings, contacts, sinking, and fires [10]. Moreover, maritime accidents create unavoidable risks for individuals and society in terms human and economic losses, and negative environmental consequences [11].
Recent computation power improvements have made it practical to carry out finite element modeling of large marine structures subjected to a collision. Since experimental tests in actual-scale marine structures demand heavy financial investment, heavy-duty equipment, and complicated logistics [12], reduced scale applications are particularly important in marine engineering. Experimental studies of the crashworthiness of marine structures most often deal with collision tests in simplified structures, and their aim is to represent sections of an actual marine structure. Tensile strength testing is one of the most important engineering tests used for metallic materials to obtain the material's characteristics. During a tensile test, a specimen is subjected to a controlled tension until failure, providing material characteristics such as yield strength, ultimate tensile strength, and strain at break.
In this paper, we assess the performance of three steel materials (i.e., AISI 1030 medium carbon steel, AISI 1080 high carbon steel and high-strength low-alloy (HSLA) A606) in tensile tests using a numerical approach with AN-SYS software. The different geometries of the specimen are also considered in the numerical approach. The influence of the mesh size on the values of the stress-strain curve in the steel materials are analyzed and we then summarize the results.

Tensile test
Materials are subjected to forces or loads when in service, for example, steel in a ship hull experiences significant stresses. In such situations, it is necessary to know the stress-strain characteristics of the material because grounding, impact, or collision can occur, deforming the materials. One of the most common mechanical stressstrain tests is performed using tension. The tension test can be used to ascertain several mechanical properties of materials that are important in design. In the tension test, a specimen is deformed with a tensile load that is applied uniaxially along the long axis of a specimen, usually until a fracture occurs. The output of a tensile test is recorded as a load or force versus elongation. The load and elongation are normalized to the respective parameters of engineering stress and engineering strain. Figure 1a shows the uniaxial tensile test sample and the tensile testing machine that is used to obtain a stress-strain curve. Figure 1b shows the changes in shape of the specimen during tensile testing.  Figure 1: (a) The uniaxial tensile test sample and tensile testing machine [13], and (b) the shape of the specimen changes during tensile testing [14] Engineering stress σ is defined by Equation 1.
where F is the instantaneous load applied perpendicular to the specimen cross-section and A 0 is the original cross-sectional area before any load is applied. Engineering strain ϵ is defined by Equation 2.
where l 0 is the original length before any load is applied and ∆l is the deformation elongation or change in length at some instant, as referenced to the original length [15].

Crashworthiness
Crashworthiness is the degree to which a transportation model or vehicle will protect its occupants from the effects of an accident. While in the ship, crashworthiness can be described as the ability of the structure to protect its cargo, Figure 2: Illustrations of (a) a single-hull design [21] and (b) the midship section of a double hull tanker [22] passengers, crew, or other important entities during an accident. There is great demand (both private and public) to reduce the risk of loss of human life and oil spillages at sea and to minimize the damage caused by groundings or collisions of the ship. Over the past decade, regulations covering ship designs have been strengthened in the United States (U.S.). One of the regulations-the use of the double hull structure-was enacted by the Oil Pollution Act in 1990, which requires that all new oil tankers operating in U.S. waters be designed with a double hull. Figure 2 shows illustrations of the single hull and double hull ship design. Furthermore, the increased demand for safety of marine transportation, especially in terms of ships and marine pollution, is closely related to environmental issues associated with disasters due to oil spillage. This has led to improvements in crashworthiness both in terms of hull structures and rescue operations. In ship-ship collisions or grounding events, the impact energy is mainly absorbed by large structural deformations in the ships' structure. An illustration of a ship-ship collision is shown in Figure 3. Over the last few decades, efforts have been made to develop reliable analysis tools and procedures for evaluating the response of hull structures during accidental load-  [23] ing [16]. Nevertheless, understanding the stress-strain of a material in which tensile load is applied uniaxially along the long axis of a specimen until a fracture occurs is still an important characteristic. Furthermore, various methods have been developed to analyze the structure of ship crashworthiness and internal mechanics during grounding and collision events.By knowing and controlling the structural behavior of ship hull structures during groundings and collisions, ship safety can be improved. It is very important to conduct research on the risk analysis of accidents and provide decision support for maritime safety management [17][18][19][20].

Experiment and analysis profile
In this work, we validated our numerical simulation using ANSYS by comparing our results with a previous benchmark study by Jose and Anto [24]. The test was conducted by increasing the load to pull the specimen until a fracture occurred. The specimen created for this tensile test is shown in Figure 4 and the dimensions of the specimen are listed in Table 1. The material properties of the specimen in this study are described in Table 2. To obtain a variety of results, mesh sizes of 2.5, 5, 7.5, and 10 mm were chosen to be applied to the numerical models. The results of the nu-

Results
The results of the numerical calculation of the tensile test in the current study and the benchmark test from the previous study by Jose and Anto [24] are summarized and compared in Table 3. The results based on the simulations of the tensile test presented a good correlation with the previous study [24]. As listed in Table 3, the value of von Mises stress, stress, and strain of the specimen in the mesh size 7.5 and 10 mm produced the most similar to the previous study. Further, it was obtained that the mesh size 2.5 and 5 mm produced a higher value of von Mises stress and stress.
The overall results suggest that the present methodology in conducting the finite element simulation has successfully produced similarity result with the previous study by Jose and Anto [24]. The configuration and setting of the benchmark will be applied further in the tensile test study.

Geometry and material
Specimens with three different geometries were used in this study. The dimensions of the specimens are shown in Figure 5, and those shown in Figure 5a, 5b have both been used before in the numerical analysis of ship collision and   grounding [25,26]. Figure 5c shows a specimen that was used in a study of tensile tests conducted by Iannucci et al. [27]. We also used three types of steel in the tests, i.e., medium-carbon, high-carbon, and high-strength lowalloy (HSLA). The properties of these materials are presented in Table 4.

Scenario and boundary conditions
The tensile test was defined as the opposite axial load acting on both sides of the specimen gauge length until a fracture occurs. The meshing size was determined to be 2.5, 5, 7.5, and 10 mm for the specimens. We measured the stressstrain, von Mises contour and strain contour.  Figure 6b. The von Mises stress contours, which represent failure due to stress, are presented in Figure 7. The concentration of von Mises stress contours in specimen 1 were mainly found in the center of the reduced section of the specimen, and stress had started to expand and reached the grip section. A similar pattern was found for specimen 3 and a mesh size of 2.5 mm, in which the highest von Mises stress was located in the midsection. However, for specimen 2, the von Mises stress was found to be widely distributed across almost the entire specimen. An observation of the strain contour also indicated that there was a significant difference in terms of the contour obtained when specimen 2 had a mesh size of 10 mm, as shown in Figure 8. Even so, the biggest strain contour was mainly located in the midsection for all of the specimens.  Figure 9b. A similar pattern of von Mises stress contours was found in specimens 1 and 3 with material AISI 1080 and HSLA A606, as presented in Figures 10  and 11, respectively. It was found that the highest von Mises stress was located in the center of the reduced section of the specimens, and the stress started to expand and reached the grip section. A similar pattern was found for the strain contour, as shown in Figures 12 and 13. The most significant strain contour was mainly located in the midsection of the specimens. However, specimen 2 with a 10 mm mesh size showed a different pattern.

Overall discussion
For the tensile test process, specimens 1 and 3 showed almost the same result in terms of stress and strain values for the three proposed materials. Specimen 2 showed similar results to specimens 1 and 3 when the mesh size was 2.5 mm, but when the mesh size was 5, 7.5, and 10 mm, the stress-strain values were lower for all three proposed materials. In term of von Mises stress, it was found that in specimens 1 and 3 with the three proposed materials, the highest von Mises stress was located in the center of the reduced section of the specimen, and the stress started to expand and reached the grip section. However, for specimen 2, the von Mises stress was found widely distributed over almost the entire specimen in all of the proposed materials. An observation of the strain contour indicated that a significantly different contour was obtained for specimen 2 with a 10 mm mesh size. Besides that finding, the highest strain contour was located in the midsection of all of the specimens in all of the proposed materials.

Conclusions
This paper presents a study of the tensile test on different steel materials. A benchmark study was used to ensure that the numerical methodology used in this paper was able to provide reliable results. The geometry of specimens 1 and 3 always showed similar results in all proposed material configurations in terms of stress and strain. The geometry of specimen 2 only showed the same results as specimens 1 and 3 when the mesh size was 2.5 mm. A similar von Mises stress pattern was found in specimens 1 and 3 with all the proposed materials, that is, the highest von Mises stress was located in the center of the reduced section of the specimen, and the stress started to expand and reached the grip section. However, for specimen 2, von Mises stress was found widely distributed over almost the entire specimen in all of the materials. The strain contour results also indicated that there was a significant differ-ence in the contour obtained when specimen 2 had a 10 mm mesh size. Besides that finding, the biggest strain contour was located in the midsection of all of the specimens with all of the proposed materials.