Elsevier

Applied Ocean Research

Volume 114, September 2021, 102780
Applied Ocean Research

LARGE DEFORMATION BEHAVIOUR OF THIN MILD STEEL RECTANGULAR PLATES SUBJECTED TO UNDERWATER EXPLOSION LOADING UNDER AIR AND WATER BACKED CONDITIONS

https://doi.org/10.1016/j.apor.2021.102780Get rights and content

Abstract

Marine vehicles in their operation as military vehicle are susceptible for underwater explosion from mines, torpedo etc. The damage inflicted on such structures made of ductile materials can be large deformation, tearing, rupture etc. It is imperative to design such structures for withstanding explosive loads. The damages inflicted will be mostly localized between the frames and stiffener, which can be considered as plate clamped at the edges. Hence, an attempt has been made in this paper to study the localized deformation of thin mild steel plates subjected to underwater explosion through limited explosion bulge test using small explosives. The experiments exhibited Mode I: large deformation, Mode IIa: Partial tensile tearing, Mode IIc: central rupture and Counter Intuitive Behaviour (CIB). The problem is simulated numerically using LS DYNA nonlinear finite element code considering fluid – structure interaction and the results compared with experiments. Based on the confidence gained for the air backed conditions, the analysis is extended to water backed (fully filled, 75% filled, 50 % filled) conditions and results obtained for the large deformation behaviour for various conditions are presented. The results indicate that the large deformation behaviour considerably reduces the central permanent deformation under water backed conditions compared to air backed conditions due to the fact that part of shock wave gets transmitted to the water medium behind the plate in water backed conditions.

Introduction

The response of marine structures to shock loads generated due to underwater explosion is of greater importance in the design of marine vehicles such as ships and submarines. During underwater explosion, the marine vehicle is subjected to global whipping and localized plastic deformation in the welded plate between the frames and stringers. Because of the relatively high stiffness of frames and stringers and symmetry of construction of plates, the plate can be considered as clamped at the edges (Keil, 1961). Hence, in order to provide shock hardening to the hull material, considerable amount of research is being taken up to understand the hull panel under shock loading and Explosion Bulge Testing (EBT) is carried out extensively to establish the sequence of failures. In the explosion bulge test, the plate specimen to be tested is clamped at the ends by sandwiching between two surfaces using bolts with sufficient width of the clamped region to create the infinite plate conditions. With the advent of modern computers and coupled non-linear finite element codes, solving such problems numerically and assessing the shock damage inflicted is viable at design stage. However, the problem is quite complex involving material non-linearity, geometric non-linearity, strain rate effects, explosive-fluid interaction, shock wave-structure interaction etc.

The experimental investigations on the dynamic plastic behaviour of clamped rectangular and square plates subjected to air blast loads exploding small explosive charges were reported in literature by many researchers (Jones et al., 1970, Jones et al., 1971, Nurick et al., 1995, Nurick and Shave, 1996, Nurick and Martin, 1989, Olson et al., 1993, Zhu, 1996, Rudrapatna et al., 1999). The studies established different failure modes for the metallic plates subjected to impulse and shock loading, Mode I: large deformation (permanent deformation more than twice the thickness), Mode IIa: Partial tensile tearing (tearing of the plates at the edges near the support), Mode IIc: central rupture (tearing at the edges and rupture at the centre of the plate) and Mode III shear failure (Complete tearing of the plate near all the four edges). Zu et.al (Xu et al., 2019) presented the large deformation behaviour of thin aluminium plates subjected to blast loads. The elastic response of the air backed plate subjected to underwater explosion were studied experimentally and numerically by few authors (Hammond and Grzebieta, 2000, Hung et al., 2005). Inelastic failure modes similar to plates subjected to air blast loads were established for underwater explosion loading under air backed condition and reported in literature (Ramajeyathilagam and Vendhan, 2004, Ramajeyathilagam et al., 2000). Limited studies on coupled fluid-structure interaction based large deformation behaviour of thin rectangular plates subjected to air blast and underwater shock loadings were reported in literature (Suresh and Ramajeyathilagam, 2020, Suresh and Ramajeyathilagam, 2019). A new failure mode in which the final deformation is against the loading direction known as Counter Intuitive Behaviour (CIB) of plates subjected to shock loading due to underwater explosions was reported in few publications (Symonds and Yu, 1985, Galiev, 1996, Shams Alizadeh et al., 2018). Failure modes such as a) holing and petaling, b) complete or partial edge tearing due to shock only, c) complete or partial edge tearing due to shock and bubble collapse, and d) large deformation without rupture were reported on square and circular plates subjected to near contact explosion under air backed conditions (Riley et al., 2010, He et al., 2018).

The shock response of marine ship structures to near field and far field non-contact underwater explosion has been reported by many researchers (Liang and Tai, 2006, Zong et al., 2013, He et al., 2020, Aman et al., 2011, Gong and Lam, 2006, Shin, 2004, Zhang et al., 2015). Yunlong Liu et al., (Liu et al., 2018) investigated the free field and buoyancy parameters on bubble dynamics with the multiphase interface captured by the Volume of Fluid (VOF) method. The bubble dynamics associated with underwater explosion in infinite medium based on Multi-Material Arbitrary Lagrange Euler (MMALE) formulation was reported by Barras et al. (Barras et al., 2012). Zhang et. al. (Zhang et al., 2008) presented the dynamics of an underwater explosion bubble near boundaries based on the potential flow theory in conjunction with the finite element method (FEM) and computed the interaction between a bubble and an elastic plastic structure. An et al. (An et al., 2018) studied experimentally and numerically the near-field shock wave generated by underwater explosion of different shaped charges. Guo-zhen Liu et al. (zhen Liu et al., 2017) reported the study on double plated structure filled with water between the plates subjected to underwater explosions by employing two different coupling for outer field with outer plates and internal fluid with inner plate in the analysis. Huang et. al. (Huang et al.) presented investigations on clamped circular aluminium plates subjected to underwater shock loads simulated using a projectile impact based non-contact underwater shock simulator under air backed and water backed conditions.

Schiffer and Tagarielli (Schiffer and Tagarielli, 2014) presented an analytical model to predict the shock response of wide range of plates considering flexural wave propagation in solids and fluid-structure interaction and the predicted structural response of plate compared with the numerical solutions obtained by using ABAQUS finite element code. Taylor's plate theory based analytical model for the transient response of sandwich panel subjected to blast load under three conditions namely; air blast/ air backed, waterblast/ air backed and waterblast/ water backed conditions and the comparison of the same using ABAQUS simulation was reported by Hoo Fatt and Srivolu (Hoo Fatt and Sirivolu, 2017). Sone Oo et. al (Sone Oo et al., 2020) studied the shock response of the composite panel using Taylor's plate theory based analytical approach and compared the same with three numerical schemes using LSDYNA/USA code and limited experiments.

It is noted that the coupled fluid – structure interaction based analysis on the EBT test plate subjected to underwater explosion loading is limited in literature. Also, in marine vehicles, the hull panels with fluid filled conditions available may also experience the shock damage due to underwater explosion. It is thought worth to investigate such problems numerically considering fluid-structure interaction. Hence, in this paper an attempt has been made to study the response of water backed EBT plate subjected to underwater explosion. As a prelude to the study, the experimental results presented in (Ramajeyathilagam and Vendhan, 2004) for air backed conditions are investigated considering the complete modelling of the EBT fixture, test plate, fluid domain, explosive and compared. Limited experimental studies on thin rectangular plates (1.2 mm thick) exhibiting large deformation, tearing, central rupture and Counter Intuitive Behaviour (CIB), tested using the EBT fixture (Ramajeyathilagam and Vendhan, 2004) is also presented. The experimental results of Ref. (Ramajeyathilagam and Vendhan, 2004) and present study compared well for the air backed conditions. Based on the confidence, numerical investigations on the partially water filled (50% and 75%) and fully water filled in the cavity of the EBT fixture with test plate is simulated using LSDYNA code and the failure modes are presented.

Section snippets

Problem description

The physical model considered for the numerical study using LS DYNA nonlinear finite element code is the rectangular mild steel plates tested under air backed conditions using EBT fixture and published in literature (Ramajeyathilagam and Vendhan, 2004). The test setup consists of a box model having a cavity (300 mm x 250 mm x 270 mm (depth)) with a top flange (550 mm x 450 mm x 25 mm) to simulate air backed conditions and a top cover plate of same dimensions as the flange. The test plates are

Theoretical Background

  • a

    Fluid modelling

The numerical study of submerged structure subjected to underwater explosion is a complicated phenomenon which involves complex fluid structure interaction problem including shock waves and structure interaction. In this paper, the Multi Material Arbitrary Lagrange Eulerian (MMALE) formulation is used to model and simulate the response of rectangular plates to underwater explosion. The MMALE formulation is a finite element method that will allow the mesh to move with the material

Finite element modelling

The finite element modelling of the EBT fixture along with test plate subjected to underwater explosion is performed using LS-DYNA nonlinear finite element code developed by Livermore Software Technology Corporation (LSTC). For the analysis, the EBT fixture, test plate, surrounding fluid and the explosive are modelled. The test plate is modelled using Belytschko-Tsay shell element, EBT fixture, bolt head, bolt shank and nut are modelled using Lagrangian solid element, water domain and explosive

Free field shock pressure

In order to gain the confidence on the numerical model, the incident pressure time history predicted for a charge weight of 30 g at a distance of 100 mm from the LS-DYNA is compared with the empirical relations of Cole (Cole, 1948) and Zamyshlyayev et. al. (Zamyshlyaev and Yakovlev, 1967) as shown in Fig. 4. The maximum pressure predicted from LS-DYNA code is 244.2 MPa, Cole's equation 187.81 MPa and Zamyshlyayev et. al. empirical relation for the near field is 241.54 MPa. The predicted

Conclusion

In this paper limited experimental studies carried out on 1.2 mm plate subjected to underwater explosion loading using small explosive charges exhibiting large deformation, tensile tearing, central rupture and counter intuitive behaviour are presented. Numerical simulation of the same problem is carried out using MMALE approach modelling explosive, fluid and structure, the simulated results for large deformation, tearing and central rupture compares reasonably well with the experimental results

Declaration of Competing Interest

None.

Acknowledgement

The authors are grateful to Naval Research Board (NRB), DRDO, India for the financial assistance given for the project work

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