Keywords

1 Introduction

Welding as a common joining method for mechanical structures, residual stresses and certain thermal deformations exist in welded structural members in practical engineering, and the weld and heat affected zone (HAZ) will be destroyed and fail when large incidental loads are encountered. Gaudreault is one of the few who have presented a study dedicated to welded armor steel joints subjected to explosions [1]. His welded joints were modeled by shell units with HAZ material properties and did not take into account the weld geometry, so it was not possible to truly predict stress concentrations and plate fracture. Cerik investigated the dynamic plastic response and failure mechanisms of fusion-welded aluminum quadrilateral plates and orthogonally-reinforced plates subjected to blast loading, and performed a rigorous numerical parametric study in order to propose new empirical equations for welded aluminum plates subjected to blast loading, with a detailed investigation of effects of various geometrical aspects, heat affected zone location and impact strength on the overall deformation of the plate [2]. Xu et al. presented an experimental and numerical study of a near-field air blast loaded aluminum plate in order to evaluate its deformation pattern and failure mode [3]. Few papers dealt with the material behavior of armor steel with welded seams used to protect vehicles under high strain rates or the mechanical strength of welded substructures under impact loading. Based on the studies of many researchers mentioned above, this paper verifies the accuracy of the established model by establishing a finite element model of welded seam-connected armor steel under blast loading and using blast tests. Based on this, the structural strength of welded joints under single and repeated blast loading is further investigated, so the results of this paper can be used to evaluate the strength and safety of welded joints of armored steel under blast loading.

2 Explosive Impact Test of Armor Steel with Welded Joints

2.1 Test Setup and Results

In order to verify the structural strength of the welded joint armor steel under the explosion load, an explosion test rig was designed as shown in Fig. 1. The weld target plate is fixed in the front end of the steel bracket by M24 bolts all around, and the top and back side of the steel bracket have cement counterweights to make it fixed in the corresponding position. Three kinds of weld structures were adopted in this test: Sample 1 was butt-welded; Sample 2 was butt-welded with an additional 2 mm thick reinforcing beam; Sample 3 was overlap welded. The deformation of the target plate can be visualized by drawing an 80 × 80 mm grid on the backside for mesh visualization. The size of each target plate is 400 mm × 400 mm × 4 mm, of which the target plate material is bulletproof steel plate 6252, and the reinforcement beam is SAPH440. In Fig. 2, The distance between the explosive center and the center of the target plate is 560 mm, and the explosive equivalent is 2 kg, adopting the cylindrical charging mode, with the explosive diameter of 110 mm, height of 135 mm, and igniting from the 1/3 of the height.

Fig. 1
A schematic of an explosive test setup with three samples placed at equal distances from a central dynamite explosion.

Explosive test

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Fig. 2
A series of three photos featuring tools and materials, a person working, and measuring equipment on a circular object.

Schematic of explosives in the test

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The test results are shown in Fig. 3, the three target plates formed a bulge in the back convex, none of which showed cracks. The maximum deformation of the center of the backplane of the three samples was 29.7 mm, 25.9 mm and 27.8 mm, respectively, in which no fracture failure occurred in the weld portion of sample 1 and sample 3, while the deformation of the reinforcing beam of sample 2 was more intense, and some spalling occurred in the nearby spot weld edges.

Fig. 3
A series of three samples labeled Sample 1, Sample 2, and Sample 3, each showing different levels of wear or damage.

Explosive test results

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2.2 Finite Element Models

The corresponding finite element model was developed in LS-dyna simulation software based on the blast impact test. The structured ALE algorithm (S-ALE) is adopted, and the air flow field is simulated with structured grid, with a cell size of 20 mm, which is generated by the keywords ALE_STRUCTURED_MESH and ALE_STRUCTURED_MESH_CONTROL_POINTS [4]; and the keywords *CONSTRAINED_LAGRANGE_IN_SOLID are utilized to deal with the fluid–structure coupling problem [5]. The target plate is taken as a hexahedral body cell, with different cell sizes and mesh transitions for different regions, and is connected by a common node. The results are shown in Figs. 4, 5, and 6.

Fig. 4
A 3-dimensional illustration of the interaction between structural elements and air in the presence of T N T, with dimensions and boundaries marked.

Model schematic

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Fig. 5
An illustration of grid transition in welding, with labeled sections including WELD, H A Z, and BASE, different mesh sizes, and a fully clamped boundary.

Grid transition

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Fig. 6
A schematic of a target plate meshing featuring a long rectangular target plate with a square section, and an enlarged plan view detailing its 4-layer structure.

Target plate meshing

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The simplified model of the three groups of welded joints is shown in Fig. 7, according to the actual measurements of the test, the width of the butt weld is 4 mm, and the width of the heat-affected zone is taken as 6 mm according to the literature, so the total width of the welded area is 16 mm [6]. The elliptical cross-sectional region of the fillet weld is simplified to a regular polygon, and the simplified weld model must be close to the volume of the weld in the experimental study. Generally the strength of the heat affected region is about 60% to 80% of the base material, and in this paper the material parameter of the heat affected region is taken as 70% of the base material [7]. The Johnson–Cook material model is used to simulate the mechanical ontological relationship between the weld region and its base material, and the J–C dynamic parameters of some materials are shown in Table 1 [8].

Fig. 7
A schematic of three samples of weld joints before and after simplification, with labeled parts including the base, weld, H A Z, and plate.

Simplification of weld and heat affected zone

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Table 1 Main J–C model material parameters
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2.3 Simulation Model Accuracy Verification

The displacement cloud and deformation results of each sample part obtained by simulation are shown in Fig. 8, the maximum deformation of sample part 1 is 29.74 mm, the maximum deformation of sample part 2 is 25.67 mm, and the maximum deformation of sample part 3 is 27.61 mm, and the weld seams of the three samples do not have rupture failure. The error of the test and simulation of each sample is within the allowable range, which verifies the accuracy of the finite element model.

Fig. 8
Three sets of visual data representing displacement maps and deformation results for different material samples.

Displacement maps and deformation results for each specimen

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3 Structural Strength Analysis of Welded Joints

3.1 Effect of a Single Blast Loading on the Strength of a Structure

This numerical analysis simulated 1, 1.5, 2, 2.5, 3, 3.5 kg a total of six explosion cases, as a comparison in the original model based on the addition of pure steel plate without welds. As shown in Figs. 9 and 10, sample 1 is the worst resistance to a single explosion, sample 2 is second, sample 3 is the best. The pure steel plate is more resistant to a single blast than any of the weld-connected plates, but the amount of deformation may be larger than that of the weld-connected plates. Figure 11 gives the failure form of each sample, in the structural optimization can be considered as far as possible to make the weld region away from the blast wave (sample 1), add a higher strength protective components (sample 2), there is an overlap in the region of the weld form can be changed to bolt connection (sample 3).

Fig. 9
A 3-dimensional bar graph titled Center Deformation plots the relationship between explosive yield, sample name, and center deformation for plain steel plates.

Center deformation

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Fig. 10
A scatterplot plots center deformation versus explosive yield. The plots have a diagonally rising pattern.

Center deformation vs. explosive equivalent

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Fig. 11
Three displacement maps for samples of materials, each undergoing different forms of failure under specific weights, 2.5, 3, and 3.5 kilograms.

Forms of failure for each sample

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3.2 Effect of Repeated Explosive Loading on the Strength of Structures

In order to simulate repeated explosive loading, this paper adopts the complete restart technique of LS-dyna [9], and sets four explosive equivalents of 0.65 kg, 0.85 kg, 1 kg and 1.15 kg, and the number of explosive loading times for each sample is 3 times. As shown in Fig. 12, the amount of center deformation brought about by using steel plates with different forms of weld connections varies considerably. The use of welded joints greatly reduces the structural strength, but has less effect on the amount of structural deformation within the range of non-failure. It can also be found that when the sum of the explosive equivalents of the repeated explosions is not much different from the explosive equivalents of the single explosion, the center deformation of all samples under the effect of repeated explosions is lower than under the effect of a single explosion.

Fig. 12
A set of four 3-dimensional bar graphs illustrating the deformation in the center of each sample due to repeated explosive loads at different weights (0.65 k g, 0.85 k g, 1.00 k g, and 1.15 k g).

Deformation in the center of each sample of repeated explosive loads

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As shown in Figs. 13 and 14, the center deformation of each part at the end of each blast load action increases linearly with increasing blast equivalent. With the increase in the number of explosions, in the range of non-failure (i.e., small equivalent stage) in the center of each piece of the deformation of the fitted line of the gradient is smaller than that of the pure steel plate, indicating that the use of welded seams can reduce the center of the repeated explosive load deformation, similar to the role of reinforcing bars. Define the difference between the center deformation between two consecutive repetitive explosive loads as the center asymptotic deformation, and power function curve fitting [10], it can be found that with the increase in the number of explosions is an exponential decrease, taking into account the residual stresses of the plate and the work-hardening phenomenon, so at the end of each explosion load will be further reduced, and the magnitude of the decrease will be smaller and smaller until the failure.

Fig. 13
Four-line graphs of the relationship between center deformation and the number of blasts at different explosive yields for various materials. The lines slope upwards from the left to the top right.

Plot of center deformation versus number of blasts at different explosive equivalents

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Fig. 14
A set of four-line graphs of center asymptotic deformation versus the number of blasts for different samples and a plain steel plate. The lines slope downwards from the top left to the bottom right.

Plot of center asymptotic deformation versus number of blasts

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4 Conclusion

This paper establishes a solid element finite element model of steel plate including weld region and heat-affected region, and adopts the material assignment method combined with J–C material intrinsic and structured ALE algorithm, and obtains the following conclusions in the experimental and numerical studies:

  1. (1)

    The blast resistance of different weld structures is compared by single explosion loading, and the linear relationship between the center deformation of steel plate and explosive equivalent under single explosion is fitted. Combined with the failure form and strength prediction of each sample, corresponding reinforcement measures are proposed.

  2. (2)

    through the repeated explosion loading of the steel plate center deformation and the number of explosions between the fitting relationship, can be used to predict the damage deformation of steel plate in a specific repeated explosion load; at the same time found that in the case of a small equivalent explosion of the welded structure can reduce the deformation of the plate, can play a certain reinforcing effect.