**1. Introduction**

High-quality carbon and low-alloyed steels are widely used to manufacture thin-walled metal products like tubes, vessels, beams, shells, panels, folds, membrane structures and other forms used in metalworking. However, application of these cheap steels has been limited due to inadequate mechanical strength, stiffness and low resistance to corrosion [1]. Reducing the weight of steel structures and the amount of metal required by improving the strength, hardness and stiffness of steel is a major task in the metalworking sector.

Thin-walled shell structures are lightweight constructions which are mostly designed to carry only tension loads, without taking into account compression or bending. However, such three-dimensional tensile structures can be subjected to unplanned bending loads and bending stresses due to concentrated transversal forces. These forces can be accidental impact, concentrated external or support/reaction forces, which may cause significant damage or failure of the whole construction [2].

Different design strategies are useful to avoid failure or the risk of collapse of the metal structure, and to increase the resistance to collapse or sensitivity of the structure to unplanned heavy loads. Heavily loaded thin-walled structural elements, such as the shell structures of buildings, rockets, chemical reactors, thin-walled pipes, vessels and other metal structures, are designed using special calculation methods that take plastic deformation into account. Then, calculations are carried out beyond the elasticity of the metals. The ultimate load method or limit-state design allows metal consumption to be reduced and gives access to additional reserves of structural strength in thin-walled steel structures. It also increases available workloads or ultimate bending moments in comparison with the results achieved by traditional working stress methods in the elastic stage [3,4].

Different heat-treatment or thermochemical treatment processes are very popular finishing techniques in metalworking, and can be useful to increase the yield, tensile strength and hardness of steel structures [5].

In practice, only steels with carbon content above 0.3% are reliably heat-treatable to improve their mechanical properties by formation of martensitic structures. Theoretically, steels with carbon content below 0.3% can be strengthened by refining grain size and using a sufficient cooling rate during traditional quenching. The critical cooling rate for low-carbon steels with 0.19 wt.% must be around 1925 ◦C/s [6], but the rate at which they must be cooled to produce martensite is so high that it cannot be attained by traditional quenching in water or induction hardening.

Furthermore, heat-treatment and thermomechanical treatment techniques are very expensive and complicated. The strengthening of the metal sheets by means of strengthening elements and reinforcing ribs, special steel profiles and sections of complex geometry or local thickenings of ribs, is a well-known engineering solution [2,3]. However, the application of geometric improvements increases the manufacturing costs and the weight of metal parts, and requires complex manufacturing methods, expensive metalworking equipment and tooling, special designs and very experienced engineering staff.

An alternative way to manufacture metal structures with better strength and stiffness can involve methods for fabricating rib-strengthened or grid-strengthened composite structures. All dual-phase steels have heterogeneous microstructures, similar to natural composite materials, the properties of which are determined by the properties of the individual phases, following the rule of mixtures [7]. The structure of steel in the necessary place can be modified by special local treatment, where creation of strengthening or a reinforcing phase due to local phase transformation and changes of microstructure become available. The creation of structural strengthening ribs can significantly affect the overall strength and elasticity of thin-walled steel parts which have insufficient or very low bending strength and stiffness. The bending stress increases linearly away from the neutral axis until the maximum values at the top and bottom of the bent plate. Therefore, the reinforcement of metal surface layers can be an effective method of strengthening thin-walled metal structures affected by bending loads.

Laser-assisted methods of surface treatment are one of the most popular and well-established methods of surface modification of metals. Laser treatment technologies allow local heating, high temperature gradients and cooling speeds of 105–106 ◦C/s due to the thermal conductivity of metal. Therefore, the hardening of low-carbon steels with less than 0.3 % carbon is also possible, whereas these steels cannot be hardened effectively by other heat treatment methods [8].

Transformation hardening, nitriding and carburizing by laser allows changes to the microstructure and properties such as strength, hardness, roughness, coefficient of friction, wear resistance, chemical resistance and corrosion resistance of the surface of various metals [9,10]. The typical thickness of the hardened layer after laser transformation hardening by CO<sup>2</sup> laser, without melting of the surface, usually does not exceed 0.3 mm, applying a laser pulse of 0.15 mm [11]. The efficiency of laser transformation hardening and the final strength of the laser-processed structure depends on the total laser-processed area and the depth of hardening.

Therefore, application of laser transformation hardening without melting for strengthening of low-carbon steel structures with less than 0.3% carbon is limited by the low thickness of the hardened layer, because a very large surface area must be processed. In contrast, laser processing with melting gives a thicker laser-processed layer.

The main objective of this research was to test and model the bending of laser-processed steel plates, evaluating the efficiency of the application of laser treatment with surface melting to strengthening thin sheet components from unalloyed and structural carbon steels containing less than 0.2% carbon.

The results of a study of the influence of laser treatment on the microstructure and mechanical properties of bent plates of low-carbon steel are presented. The results of modelling of elastoplastic deformations of differently laser-processed samples are compared with results obtained by bending tests on real samples. The research results show that local laser treatment with surface melting can be used to increase the bending strength of thin-walled structural elements from steel (1.0402) and to decrease its deflection under identical workloads.

#### **2. Object of the Study**

One of the most popular grades of structural high-quality-carbon steel (1.0402) containing less than 0.3% carbon was used (Tables 1 and 2). The microstructure and mechanical properties of this hypoeutectoid steel, according to standard EN 10250-2, can vary depending on the treatment applied [12]. Thin metal plates of size 20 mm × 150 mm × 2 mm were used for the bending test and structure analysis.


**Table 1.** Chemical composition of samples from steel (1.0402).

**Table 2.** Mechanical properties of samples from steel (1.0402).


First, before laser treatment, all the samples were subjected to tempering for internal stress relief. The microstructure of the steel (1.0402) samples after tempering demonstrated a typical hypoeutectoid ferrite-pearlite microstructure, with hardness 135 HV. The surface of the samples was subjected to additional blast cleaning to ensure uniform laser energy absorption. A "Power Plus Tools" (Shanghai, China) sandblaster and quartz sand, "Sakret" (Berlin, Germany) with a grain size of 0.1–0.5 mm were used for surface preparation until roughness Ra measured less than 5 µm.

#### **3. Research Methodology**

#### *3.1. Laser Surface Treatment*

The Nd:YAG 4-axis laser-welding machine BMM400 (Boaolaser, Beijing, China) was used for local laser treatment. The metal samples were tightly fixed to the work table of the laser machine. A shielding gas mixture Ar-CO<sup>2</sup> (20% CO2) with a shielding gas flow rate 20 L/min was used for Nd:YAG laser treatment. The depth of penetration should be the minimum necessary to provide sufficient hardening and avoid excessive embrittlement, cracking and deformation of the laser-processed, thin-walled steel plate [13,14]. Melting by laser or laser transformation hardening, without melting of most metal, proceeds at low energy density in the range of 103–10<sup>5</sup> W/cm<sup>2</sup> [15].

One of the criteria for the selection of the optimum processing mode was the required depth of laser penetration. A depth of penetration of about 0.35 mm, amounting to 20% of the total thickness of the metal plate, was used in the present experiments. The width of the track of the laser-processed metal was approximately 0.7 mm. The most appropriate laser processing parameters were calculated, using the methodology presented in reference literature [15], considering the physical properties of the steel (Table 3) and the technical characteristics of the 400 W laser equipment. The laser processing parameters, other than the number of processed sides, number of laser tracks and distance between them, remained constant throughout all experiments (Table 4).

The dimension of the laser-processed surface area in all cases was 40 mm × 20 mm. Four different laser-processing cases were adopted that differed in the number of laser tracks. In case I, no laser tracks were made at all, i.e., the metal plate was left unprocessed. In case II, 38 laser tracks were made, with the tracks overlapping in approximately 30% of their width. In case III, 17 laser tracks were made, with a distance between the tracks approximately equal to 50% of their widths. In case IV, 14 laser tracks were made, with a distance between the tracks equal to the track width.


**Table 3.** Physical properties of low-carbon steel (1.0402) [16].


All four cases were applied to both one-side-processed and two-side-processed plates. In case II, case III and case IV, the laser-processed tracks were oriented along the plate, in the direction in which the greatest stresses appear, by analogy with the principle of the strengthening of composite materials. A general view of the plate specimen and the laser-treated area is shown in Figure 1a. The plate cross-sections and the laser-processed layers are shown in Figure 1b,c. The laser processing cases, track width, depth and positions are depicted in Figure 1d.

**Figure 1.** The general view of the plate specimen (**a**); sketches of their cross-sections: of the one-side laser-processed plate (**b**), and of the two-side laser-processed plate (**c**); and cases of the laser tracks (**d**).
