QIAO Chi,ZHANG Shi-lian,WU Shao-bo,ZHENG Yi-kan

(State Key Laboratory of Ocean Engineering,Shanghai Jiao Tong University,Shanghai 200240,China)

New Impulsive Factor in Representing Cabin Damage under External Air Explosion

QIAO Chi,ZHANG Shi-lian,WU Shao-bo,ZHENG Yi-kan

(State Key Laboratory of Ocean Engineering,Shanghai Jiao Tong University,Shanghai 200240,China)

Based on blast energy blocked by structure,a new impulsive factor is proposed.In order to assess its applicability in external air explosion condition,dynamic structural response of a threecabin ship under blast loads with various detonation position and explosive mass were simulated by CONWEP algorithm,and residual ultimate strength of the damaged cabins was obtained by the quasistatic loading approach.The results indicated that new impulsive factor is more suitable in representing overall structural damage under external explosive loading than the traditional one.For far-field detonation,maximum displacement of strength deck,cabin plastic energy and residual ultimate strength showed high consistency in the measure of new impulsive factor.In near-field detonation cases,results showed divergence due to local effects.

external air explosion;impulsive factor;residual ultimate strength; CONWEP algorithm

0 Introduction

It is always a significant issue for navy to enhance vitality of damaged ships.Ships are subjected to attack of various kinds of anti-ship missiles in modern naval warfare.When detonation occurs above the ship,blast wave would cause large deformation and residue stress/ strain on strength deck,thus reducing its capacity in resisting longitudinal bending moment. Experiments are usually adopted to assess anti-explosion ability of ship during design stage. However,expense of ship experiment is so exorbitant that only a few detonation cases can be conducted.Model experiment,on the other hand,bears the shortage of conversion problem. Whether similarity relation from experiment results to practice holds is still under research.

With the development of numerical simulation technique,dynamic response of ships under blast loads can be obtained through transit nonlinear software,which greatly reduces research cost.Nonetheless,numerical results would be reliable only when several requirements are satisfied.For instance,fluid-structure coupling algorithm should be adopted to simulate the condition where interaction between complex structure and fluid exists,such as cabin inner explosion.Furthermore,mesh size of Euler elements should be diminished and more componentsshould be coupled in order to improve calculation accuracy.All these requirements inevitably increase CPU time.A typical inner cabin explosion simulation using fluid-structure coupling may cost weeks or even several months under present computer hardware condition.Therefore, it is still hard for researchers to get anti-explosion ability of structure under different detonation cases in a short time.If structural damage can be measured by certain impulsive factor, conversion would be possible from structural response under several typical detonation cases to any other detonation cases,thus reducing experiment cost as well as workload of numerical simulation.

Traditional impulsive factor is based on blast wave overpressure[1-2],and has been widely used in underwater explosion[3-6]as well as non-contact air explosion[7].Recently several new impulsive factors were proposed towards underwater explosion issue[8-10],which are more accurate in representing structural response under underwater blast load than traditional impulsive factor.

This paper proposed a new impulsive factor based on blast energy blocked by structure. Residual ultimate strength and cabin plastic energy of different detonation cases show high consistency under new impulsive factor.Therefore it is more suitable than traditional impulsive factor to represent structural damage under external air blast loads.

1 Impulsive factor

Traditional impulsive factor C1is defined as shown in Eq.(1):

where W is TNT equivalent mass in kilograms,R is the distance to the explosion’s origin in meters.

Previous research has demonstrated that blast wave overpressure can be expressed in terms of C1as single parameter function.For example,Brode proposed overpressure empirical formula of TNT explosive as follows:

Such empirical formula based on experiments shows high precision in a given point on structure.However,it cannot represent overall structural damage under blast loads.When detonation occurs with low explosive mass near the structure,traditional impulsive factor may equal to the condition where explosive mass is high meanwhile distance is far.The latter condition,nonetheless,generally causes more serious damage to the structure.Besides,given that detonation mass and height are fixed,damage is more severe when explosion occurs above the mid ship than occurs above the broadside,while the traditional impulsive factor is the same in these two conditions.

In order to better reflect overall damage of structure,a new impulsive factor C2is proposed,which is based on blast energy blocked by structure.Blast wave caused by spherical TNT explosives can be simplified as a spherical wave,with explosive energy distributed evenly on the surface.When structure is subjected to the blast,only part of the energy applied to the structure,determined by the projected area of the structure on sphere surface:

Total energy of explosive can be expressed as follows:

where ρeis the chemical energy per unit explosives mass(approximately 1 060 cal/g for TNT explosive),ηeis the conversion rate from chemical energy to blast wave energy.

Therefore,blast energy blocked by structure Escan be expressed as follows,by substituting Eq.(4)and Eq.(5)into Eq.(3):

For specific explosive genre,ρeand ηeare constants.Thus blast energy blocked by structure would be the same as long as ηW remains constant.

Define impulsive factor C2:

2 Finite element modeling

The subject of the research is a typical three-cabin structure with three decks and double bottom,as shown in Fig.1.The cabin is 40.5 m in length,17 m in breadth and 12 m in depth,separated by two transverse bulkheads equally.Nodes on the two sides of the cabin are combined with centroid of section through MPC.Simple supported boundary conditions were assumed throughout the research,with one of two independent points constrained as ux=uy=uz= rx=0,and the other independent point constrained as uy=uz=rx=0.Nonlinear program ABAQUS was adopted to simulate dynamic response of cabin structure under blast loads and calculate residual ultimate strength.

CONWEP algorithm was used in simulating external detonation impact of spherical TNT charge on strength deck.This algorithm had been proved to have enough precision in external blast conditions[11].Viscous pressure was applied 0.5 second after detonation time to absorb kinetic energy and stabilize structure.Shell element S4 was chosen for modeling.The S4 element is a fully integrated,finite-membrane-strain shell element,which is not sensitive to element distortion,and avoids hourglass effect under transit loading.Johnson-Cook model with yield stress σy=345 MPa,Young’s modulus E=210 GPa and Poisson’s ratio μ=0.3 was chosen to describe the rate dependent stress strain relationship under transit dynamic loadings[12]and fracture strain was set as 0.18.The model for the von Mises flow stress,σ,is expressed as

Deformation and residual stress/strain of the structure under blast wave were imported into the original model through restart file.Residual ultimate strength was then obtained by quasi-static loading approach.Shell element S4R was chosen to reduce CPU time.The S4R element is a 4-node,reduced integration shell element with hourglass control.The material was considered to behave in an elastic-perfectly plastic manner,with the same yield stress and fracture strain in the previous steps.

Fig.1 Three-cabin model and explosive location

3 Results and discussions

Blast wave energy would be partly absorbed by structure,converted into plastic energy of structure components and leading to large deformation on strength deck,thus reducing residual ultimate strength of the damaged ship.Hence,three parameters were selected to depict cabin damage,namely maximum displacement of stabled strength deck Umax,total plastic energy ofthe cabin EP,and reduction factor of residual ultimate strength Rf=M/M0(M0is the intact ultimate strength of the cabin).Values of those parameters in different detonation cases were compared under impulsive factors C1and C2.

3.1 Influence of explosive height Z

Structural response curves with explosive position Y=0 m and different detonation height were compared shown in Fig.2 and Fig.3.Response curves with explosive position other than Y=0 m showed similar characteristic.

Fig.2 Impulsive factor based on blast wave overpressure

Fig.3 Impulsive factor based on detonation energy

In Fig.2,plastic energy of cabin EP,reduction factor of residual ultimate strength Rf,and maximum displacement of strength deck Umaxshow low consistency in measure of traditional impulsive factor C1.With the increment of detonation height under the same C1,EPand Umaxincreases rapidly,while Rfdeclines drastically.Such inconsistency demonstrates limitation of C1in describing damage of structure under blast loads.For near-field detonation,overpressure value of mid-point of strength deck,which is right below explosive,is much higher than elsewhere.For far-field detonation,on the contrary,blast wave is more like a plane wave when it reaches strength deck,thus overpressure value is almost the same on the strength deck.Therefore,damage caused by far-field detonation would be severer than that of near-filed detonation under the same impulsive factor C1.

Impulsive factor C2shows better consistency(shown in Fig.3).In EPcurves for detonationheight Z≥4 m,the data coincide quite well.For Z=1 m and Z=2 m,plastic energy curve shows a little divergence.Besides,cube root of plastic energy showed a linear relation with impulsive factor C2.Similar pattern can be found in Rfcurve:when Z≥4 m,Rfdata showed good coincidence and linear relationship,while for Z＜4 m,Rfcurves diverge obviously,especially when impulsive factor C2is relatively low.Umaxcurves were not as coincide as EPcurves and Rfcurves,but still less divergent than that of impulsive factor C1as shown in Fig.2(c),especially for Z≥4 m and impulsive factor less than 8.

Divergence shown in EPcurves and Rfcurves under impulsive factor C2can be explained by Fig.4.It shows the deformation of cabin mid-section with explosive mass W=400 kg.Solid line corresponding to detonation height Z=4 m and dash line represents Z=2 m.Impulsive factor C2of these two detonation cases is close,respectively 11.79 and 12.96.Deformation of strength deck near broadsides is similar,while distinct local deformation exists in the middle of the strength deck for Z=2 m.This local deformation counts for the divergence shown in EPcurve when Z＜4 m.When detonation intensity is relatively low,such local deformation would lead to collapse of strength deck under longitudinal bending moment, corresponding to the obvious divergence in Rfcurve when Z＜4 m.

The divergence shown in Umaxcurves under C2indicates that this new impulsive factor is more suitable in representing overall structural damage.Although local deformation also exists in plastic energy and reduction factor of ultimate strength,the influence would be diminished by other unaffected area such as lower decks or double bottom.Umax,nevertheless,would be greatly influenced by local effect.

3.2 Influence of lateral distance Y

Structural response curves with detonation height Z=4 m and explosive position Y=0 m, 4 m,8 m were compared shown in Fig.5 and Fig.6.Response curves with detonation height other than Z=4 m had similar characteristic.

Fig.4 Deformation of cabin mid-section under explosive mass W= 400 kg and detonation height Z=4 m(solid line)and Z=2 m (dash line)

Fig.5 Impulsive factor based on blast wave overpressure

Fig.6 Impulsive factor based on detonation energy

Traditional impulsive factor C1remains constant for specific detonation height.The influenced area of blast wave,however,would be smaller when detonation occurs near the broadside.In Fig.5,the curve with Y=8 m demonstrates such difference,with plastic energy of the cabin on the lower side and Rfon the higher side.

Impulsive factor C2takes explosive position into consideration.When detonation occurs near the broadside,the shielding rate would decrease,so the impulsive factor would also decrease.In Fig.6,different explosive position shows good consistency.

4 Conclusions

A new impulsive factor is derived based on blast energy blocked by structure.Three parameters depicting structural damage were selected to be measured by traditional impulsive factor C1and new impulsive factor C2,and the following conclusions can be drawn:

(1)Traditional impulsive factor C1is based on blast wave overpressure.When used to measure structural damage,data show great divergence;

(2)New impulsive factor C2is based on input energy from blast wave on structure.It takes into consideration explosive mass,detonation location and area of structure subjected to blast;

(3)New impulsive factor C2performs better than traditional impulsive factor in representing structural damage.For far-field detonation cases,as long as impulsive factor C2equals, damage caused by blast loads would be similar.For near-field detonation,damage would be a little severer due to local effects.

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表征外部爆炸作用下艙段破壞的新型沖擊因子研究

喬遲，張世聯(lián)，武少波，鄭軼刊
（上海交通大學(xué)海洋工程國家重點(diǎn)實(shí)驗(yàn)室，上海200240）

基于結(jié)構(gòu)遮擋的沖擊波能量提出了一種新型沖擊因子。為驗(yàn)證該沖擊因子在外部爆炸問題中的適用性，使用CONWEP算法對典型三艙段模型在不同裝藥工況下的響應(yīng)進(jìn)行非線性有限元數(shù)值仿真，并采用準(zhǔn)靜態(tài)法計(jì)算受損艙段的剩余極限強(qiáng)度。計(jì)算結(jié)果表明新型沖擊因子相比傳統(tǒng)沖擊因子更適合用于表征外部爆炸作用下結(jié)構(gòu)的整體破壞。對于遠(yuǎn)場爆炸工況，強(qiáng)力甲板最大位移、艙段塑形應(yīng)變能和剩余極限強(qiáng)度在新型沖擊因子衡量下均顯示出較高的一致性。在近場爆炸工況中，由于結(jié)構(gòu)局部變形的影響，計(jì)算結(jié)果存在一定的離散。

外部爆炸；沖擊因子；剩余極限強(qiáng)度；CONWEP算法

O389U661.4

:A

喬遲（1990-），男，上海交通大學(xué)碩士研究生；

O389U661.4

:A

10.3969/j.issn.1007-7294.2017.06.010

1007-7294（2017）06-0761-08

張世聯(lián)（1952-），男，上海交通大學(xué)教授，博士生導(dǎo)師；

date：2016-07-24

Biography：QIAO Chi(1990-),male,master student of Shanghai Jiao Tong University,E-mail:joey@sjtu.edu.cn; ZHANG Shi-lian(1952-),male,professor/tutor,E-mail:slzhang@sjtu.edu.cn.

武少波（1985-），男，上海交通大學(xué)博士研究生；

鄭軼刊（1983-），男，上海交通大學(xué)博士研究生。