李芮宇,孫宇新,周 玲,孫其然,趙亞運(yùn),馮江拓

(1.南京理工大學(xué)瞬態(tài)物理重點(diǎn)實(shí)驗(yàn)室,江蘇南京210094; 2.中國(guó)兵器科學(xué)研究院,北京100000)

計(jì)及熱傳導(dǎo)影響對(duì)長(zhǎng)桿彈侵徹陶瓷靶的數(shù)值分析*

李芮宇1,孫宇新1,周 玲2,孫其然1,趙亞運(yùn)1,馮江拓1

(1.南京理工大學(xué)瞬態(tài)物理重點(diǎn)實(shí)驗(yàn)室,江蘇南京210094; 2.中國(guó)兵器科學(xué)研究院,北京100000)

采用有限元方法離散瞬態(tài)熱傳導(dǎo)方程,編寫成侵徹過程熱傳導(dǎo)計(jì)算模塊,并將之嵌入已有的沖擊動(dòng)力學(xué)程序中,然后運(yùn)用于長(zhǎng)桿彈在900～1 800 m/s著速范圍內(nèi)侵徹AD95陶瓷靶的數(shù)值分析,得到了符合物理事實(shí)的計(jì)算圖像,所得的計(jì)算結(jié)果比采用傳統(tǒng)的絕熱模型得到的計(jì)算結(jié)果更符合實(shí)驗(yàn)結(jié)果。探討了計(jì)及熱傳導(dǎo)效應(yīng)對(duì)長(zhǎng)桿彈侵徹AD95陶瓷靶數(shù)值模擬的影響:著速在900～1 350 m/s范圍內(nèi)時(shí),計(jì)及熱傳導(dǎo)的數(shù)值計(jì)算所得侵深小于絕熱模型計(jì)算結(jié)果;著速在在1 350～1 450 m/s范圍內(nèi)時(shí),兩種模型計(jì)算侵深接近;著速在在1 450～1 800 m/s范圍內(nèi)時(shí),熱傳導(dǎo)模型計(jì)算侵深大于絕熱模型計(jì)算結(jié)果。

侵徹;熱傳導(dǎo);有限元;陶瓷

長(zhǎng)桿彈侵徹過程中,彈靶界面塑性變形嚴(yán)重,產(chǎn)生大量的熱,引起材料溫升,進(jìn)而導(dǎo)致材料的力學(xué)性能發(fā)生改變。所以,侵徹計(jì)算時(shí)必須考慮溫度因素。對(duì)此,李永池等[1]對(duì)鎢合金熱塑性互動(dòng)損傷和平頭彈丸沖塞進(jìn)行了計(jì)算,考慮了溫度對(duì)材料參數(shù)和損傷演化的影響;晏麓暉等[2]研究了絕熱軟化對(duì)空腔膨脹數(shù)值模擬的影響,發(fā)現(xiàn)不計(jì)入熱效應(yīng)會(huì)高估侵徹阻力;趙攀峰等[3]將溫度軟化考慮進(jìn)數(shù)值計(jì)算中,研究了桿彈高速貫穿金屬靶的有關(guān)規(guī)律。材料出現(xiàn)局部溫升必然存在熱傳導(dǎo)現(xiàn)象,影響材料的溫度分布和力學(xué)行為。然而,既往的數(shù)值計(jì)算[4-6]中普遍忽略了熱傳導(dǎo)因素,計(jì)算結(jié)果必然與真實(shí)狀況存在差異。

本文中,將熱傳導(dǎo)模塊嵌入沖擊動(dòng)力學(xué)源代碼,運(yùn)用于長(zhǎng)桿彈侵徹AD95陶瓷靶的數(shù)值分析,并將得到的計(jì)算結(jié)果與絕熱模型計(jì)算結(jié)果進(jìn)行比較。

1 計(jì)算物理模型

IMPACT-2D是基于連續(xù)介質(zhì)力學(xué)的Lagrange型基本守恒方程所編寫的源代碼,主要用于高速撞擊現(xiàn)象的數(shù)值分析和數(shù)值模擬計(jì)算,是在借鑒其他有限元軟件的基礎(chǔ)上開發(fā)完成的。但是在軟件開發(fā)初期未考慮沖擊過程中的熱傳導(dǎo),無法分析熱傳導(dǎo)對(duì)沖擊問題模擬的影響,所以有必要引入熱傳導(dǎo)方程。軸對(duì)稱導(dǎo)熱微分方程為:

式中:T為物體的瞬態(tài)溫度,t為時(shí)間,k為材料的導(dǎo)熱系數(shù),ρ為材料密度,cp為材料的比熱,qv為材料的內(nèi)熱源強(qiáng)度。

由于有限元熱傳導(dǎo)計(jì)算是基于節(jié)點(diǎn)的,而有限元沖擊計(jì)算的溫度儲(chǔ)存在單元中,程序在計(jì)算單元應(yīng)力時(shí)采用的也是單元的溫度,只是在后處理時(shí)將單元的溫度轉(zhuǎn)換在節(jié)點(diǎn)上。但是無法通過該轉(zhuǎn)換方法將節(jié)點(diǎn)的溫度再轉(zhuǎn)換回單元,所以在進(jìn)行熱傳導(dǎo)計(jì)算時(shí)必須建立一個(gè)背景網(wǎng)格,方法是:以單元的中心節(jié)點(diǎn)為熱傳導(dǎo)計(jì)算的節(jié)點(diǎn),以此構(gòu)建背景網(wǎng)格。每一個(gè)循環(huán)結(jié)束后,以單元的溫度為初始條件作為背景網(wǎng)格節(jié)點(diǎn)的溫度,進(jìn)入熱傳導(dǎo)模塊進(jìn)行計(jì)算,這樣就實(shí)現(xiàn)了單元溫度的更新,并以更新后的單元溫度進(jìn)行下一步循環(huán)計(jì)算。如此一來,程序就實(shí)現(xiàn)了沖擊過程中的熱傳導(dǎo)計(jì)算。圖1為背景網(wǎng)格示意圖:i～l為原始三角形單元,1～6為原始三角形單元節(jié)點(diǎn),用于計(jì)算侵徹過程中材料的應(yīng)力應(yīng)變等;a～d為背景網(wǎng)格節(jié)點(diǎn),用于原始單元之間的熱傳導(dǎo)計(jì)算。

2 模型及參數(shù)

針對(duì)孫宇新等[7]的長(zhǎng)桿彈侵徹陶瓷復(fù)合靶的實(shí)驗(yàn)進(jìn)行數(shù)值模擬,彈丸材料為35Cr MnSi,口徑為7.62 mm,長(zhǎng)約70 mm。復(fù)合靶由蓋板/陶瓷靶/鑒證靶組成,靶板直徑為96 mm。蓋板的材質(zhì)為A3鋼,厚度為2 mm;陶瓷靶材質(zhì)為AD95陶瓷,直徑為80 mm,總厚度為30 mm;鑒證靶材質(zhì)也采用A3鋼。在陶瓷靶外緊圍一圈由45鋼制成的套筒以實(shí)現(xiàn)對(duì)陶瓷的徑向約束,壁厚8 mm。建立二維軸對(duì)稱離散模型,如圖2所示,三角形單元總數(shù)為36 000。

采用線性溫升軟化關(guān)系[8]計(jì)算溫度對(duì)彈性模量、泊松比等物理量的影響,采用Johnson-Cook本構(gòu)模型描述溫度對(duì)金屬材料屈服應(yīng)力的影響,并采用Grüneisen狀態(tài)方程。35Cr MnSi[9]、A3鋼[10]和45鋼[11]的材料參數(shù)如表1所示。對(duì)AD95陶瓷材料采用JH-2模型[12]描述,參數(shù)[13]分別為:ρ0= 3.625 g/cm3,A=0.88,N=0.64,C=0.007,σt=0.262 GPa,B=0.28,M=0.60,σHEL=5.3 GPa,σHEL,eff=3.75 GPa,pHEL=2.8 GPa,G=109.7 GPa,K1=228.6 GPa,K2=191.4 GPa,K3=111.5 GPa,

圖1 溫度背景網(wǎng)格示意圖Fig.1 Diagram of temperature background grid

圖2 模型及局部網(wǎng)格Fig.2 Model and local mesh

表1 3種金屬的材料參數(shù)Table 1 Parameters of three metals

3 計(jì)算結(jié)果及分析

3.1 結(jié)果驗(yàn)證

圖3給出了考慮熱傳導(dǎo)時(shí),著速為1 054 m/s的長(zhǎng)桿彈對(duì)陶瓷復(fù)合靶的侵徹過程。彈體的銷蝕、蓋板的鼓起、陶瓷靶正面的開坑、陶瓷靶內(nèi)部裂紋的擴(kuò)展等現(xiàn)象在圖3中均得到了清晰的描述,與圖4實(shí)驗(yàn)現(xiàn)象十分吻合,這也表明本文中所用程序及選取的材料模型及參數(shù)是可靠的。

圖3 典型長(zhǎng)桿彈侵徹陶瓷靶過程中的損傷云圖(1 054 m/s)Fig.3 Damage distribution of the ceramic target penetrated by a typical long-rod projectile of 1 054 m/s

圖4 典型長(zhǎng)桿彈侵徹后的AD95陶瓷靶(1 054 m/s)Fig.4 AD95 ceramic target penetrated by a typical long-rod projectile of 1 054 m/s

3.2 模擬結(jié)果分析

3.2.1 侵深與著速的關(guān)系

圖5給出了分別采用絕熱模型和熱傳導(dǎo)模型計(jì)算得到的長(zhǎng)桿彈侵深D隨著速v0的變化關(guān)系(圖5 (a))以及兩種模型計(jì)算侵深的差值百分比隨彈體著速的變化關(guān)系(圖5(b)),其中D1為熱傳導(dǎo)模型計(jì)算侵深,D2為絕熱模型計(jì)算侵深。由圖5(b)可以看出兩種模型計(jì)算侵深的差值百分比最大可達(dá)3%,因此熱傳導(dǎo)因素對(duì)長(zhǎng)桿彈侵深有較顯著的影響,當(dāng)彈體著速在900～1 350、1 350～1 450和1 450～1 800 m/s等3個(gè)范圍內(nèi)時(shí),熱傳導(dǎo)模型計(jì)算侵深分別小于、接近、大于絕熱模型計(jì)算結(jié)果。由圖5(a)可以看出熱傳導(dǎo)模型計(jì)算結(jié)果同實(shí)驗(yàn)結(jié)果最接近,這說明在侵徹計(jì)算中對(duì)彈體考慮熱傳導(dǎo)效應(yīng)很有必要。下面將從侵徹過程中長(zhǎng)桿彈的面密度變化、壓力變化等方面來解釋圖5呈現(xiàn)的現(xiàn)象。

圖5 兩種模型計(jì)算侵深的比較Fig.5 Comparison between the two models on penetration depth

3.2.2 彈體侵徹過程中的面密度和侵深

在此取2個(gè)典型著速(900和1 750 m/s)來說明問題,這2個(gè)著速分別代表圖5中的2種情況:熱傳導(dǎo)模型計(jì)算侵深低于和高于絕熱模型計(jì)算侵深。圖6(a)、(b)分別為900和1 750 m/s著速下的彈體面密度ρa(bǔ)和侵深時(shí)程曲線。由圖6可以發(fā)現(xiàn)對(duì)應(yīng)的2種侵徹過程:(1)彈體著速為900 m/s時(shí),在約40μs后熱傳導(dǎo)模型對(duì)應(yīng)的彈體面密度開始顯著小于絕熱模型對(duì)應(yīng)的彈體面密度,以致其侵徹過程所承受的平均過載較大,最終使得侵深低于后者;(2)彈體著速為1 750 m/s時(shí),總體上,熱傳導(dǎo)模型對(duì)應(yīng)的彈體面密度高于絕熱模型對(duì)應(yīng)的彈體面密度,其平均過載也就低于后者,侵深比絕熱模型計(jì)算結(jié)果大。

圖6 彈體面密度和侵深時(shí)程曲線Fig.6 Areal density-and penetration depth-time curves of the long-rod projectile at different initial penetration velocities

3.2.3 侵徹過程中的彈頭壓力變化

圖7給出了2種典型著速下侵徹過程中彈頭的壓力時(shí)程曲線,在900和1 750 m/s的著速下,彈體侵徹過程所受的最大壓力分別為10和22 GPa,遠(yuǎn)高于彈體材料的靜態(tài)屈服強(qiáng)度Y0(1.64 GPa)。圖8為侵徹過程中彈頭平均壓力p隨彈體著速的變化關(guān)系,可見隨彈體著速v0的升高,彈頭在侵徹過程中所受平均壓力也隨之升高,可將本文中長(zhǎng)桿彈侵徹陶瓷復(fù)合靶的過程分為3個(gè)階段,見表2。

圖7 侵徹過程中彈頭的壓力時(shí)程曲線Fig.7 Pressure-time curves of the projectile head during penetration

圖8 侵徹過程中彈頭平均壓力隨著速的變化Fig.8 Average pressure of the projectile head varied with initial penetraion velocity during penetration

表2 長(zhǎng)桿彈侵徹陶瓷復(fù)合靶3個(gè)階段Table 2 Three phases of long-rod projectiles penetration into ceramic composite targets

3.2.4 原因分析

由3.2.1～3.2.3節(jié)的分析可知,熱傳導(dǎo)對(duì)長(zhǎng)桿彈侵徹計(jì)算有較顯著的影響,且存在如圖5和表2所示的規(guī)律。圖9為900和1 750 m/s的著速下長(zhǎng)桿彈侵徹過程中的剩余質(zhì)量變化,可見在著速為900 m/s時(shí)熱傳導(dǎo)模型對(duì)應(yīng)的剩余質(zhì)量一直小于絕熱模型對(duì)應(yīng)的剩余質(zhì)量;著速1 750 m/s時(shí),熱傳導(dǎo)模型對(duì)應(yīng)的剩余質(zhì)量一直大于絕熱模型對(duì)應(yīng)的剩余質(zhì)量,90μs后熱傳導(dǎo)模型對(duì)應(yīng)的剩余質(zhì)量開始向后者靠攏。由以上可以認(rèn)為:當(dāng)著速較低時(shí)(小于1 350 m/s),考慮熱傳導(dǎo)因素會(huì)使彈體在侵徹過程中銷蝕更快;當(dāng)著速較高時(shí)(大于1 450 m/s),考慮熱傳導(dǎo)因素會(huì)使彈體在侵徹過程中銷蝕變慢。

圖9 兩種模型長(zhǎng)桿彈剩余質(zhì)量時(shí)程曲線Fig.9 Residual mass-time curves by two models

圖10 觀測(cè)點(diǎn)溫度時(shí)程Fig.10 Temperature-time curves of observation points

有限元計(jì)算中,單元的銷蝕與塑性應(yīng)變相關(guān),塑性應(yīng)變達(dá)到閾值時(shí),會(huì)被刪除。考慮熱效應(yīng)時(shí),單元的應(yīng)變與溫度有很大的關(guān)系,單元溫度升高,材料的剪切模量和屈服應(yīng)力會(huì)下降,單元抵抗變形的能力也隨之降低,其應(yīng)變就會(huì)越早達(dá)到閾值,被刪除。圖10給出了彈體軸線距彈頭20 mm處單元的溫度時(shí)程曲線,可見:900 m/s時(shí)熱傳導(dǎo)模型觀測(cè)點(diǎn)溫度增長(zhǎng)速度快于絕熱模型,較早于后者達(dá)到銷蝕應(yīng)變,被刪除;1 750 m/s時(shí)結(jié)果與900 m/s時(shí)正好相反。這是因?yàn)榈退贂r(shí)彈頭壓力低(圖8),單元應(yīng)變率低,應(yīng)變達(dá)到銷蝕值所經(jīng)歷的時(shí)間長(zhǎng),彈頭由于塑性變形產(chǎn)生的高熱量有著較長(zhǎng)的時(shí)間向后擴(kuò)散,以致傳入后方單元的熱量多于后方單元傳出的熱量,使得該單元含有的熱量高于絕熱模型,高速情況下與之相反。

4 結(jié) 論

將熱傳導(dǎo)因素引入沖擊動(dòng)力學(xué)程序,對(duì)典型長(zhǎng)桿彈侵徹陶瓷靶的過程進(jìn)行數(shù)值計(jì)算,將計(jì)算結(jié)果與采用絕熱模型得到的計(jì)算結(jié)果進(jìn)行比較,發(fā)現(xiàn)長(zhǎng)桿彈著速由低到高變化時(shí),熱傳導(dǎo)對(duì)侵深的影響不同:長(zhǎng)桿彈著速為900～1 350 m/s時(shí),由于熱傳導(dǎo)模型彈銷蝕速度較快,其計(jì)算侵深小于絕熱模型計(jì)算結(jié)果;長(zhǎng)桿彈著速為1 350～1 450 m/s時(shí),兩種模型彈銷蝕速度接近,所以計(jì)算侵深接近;長(zhǎng)桿彈著速為1 450～1 800 m/s時(shí),熱傳導(dǎo)模型彈銷蝕速度慢于絕熱模型,其計(jì)算侵深大于后者計(jì)算侵深。由數(shù)據(jù)對(duì)比發(fā)現(xiàn)熱傳導(dǎo)模型計(jì)算侵深隨著速的變化規(guī)律與實(shí)驗(yàn)數(shù)據(jù)更接近,這說明侵徹過程中考慮熱傳導(dǎo)因素所得結(jié)果更合理可信。本研究改善了傳統(tǒng)侵徹計(jì)算中忽略熱傳導(dǎo)的狀況,可為相關(guān)研究提供參考。

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Influence of heat transfer on long-rod projectiles penetrating into ceramic targets

Li Ruiyu1,Sun Yuxin1,Zhou Ling2,Sun Qiran1, Zhao Yayun1,Feng Jiangtuo1
(1.National Key Laboratory of Transient Physics,Nanjing University of Science and Technology,Nanjing210094,Jiangsu,China; 2.China Academy of Ordnance Science,Beijing100000,China)

Based on the finite element method,the heat conduction equation was made discrete and written as the heat transfer computation code which was then embedded into the existing impact dynamics program.The new program was applied to the numerical analysis of the long-rod projectile penetrating into AD95 ceramic targets in the range of 900-1 800 m/s,and the influence of heat transfer on penetration capability was examined.Calculations show that the calculated penetration depth is less than that by the adiabatic model when the heat transfer is taken into account in the range of 900-1 350 m/s.However,it is opposite when the velocity of the projectile comes in the range of 1 450-1 800 m/s.The results by the heat transfer model and the adiabatic model are close to each other in the range of 1 350-1 450 m/s.

penetration;heat transfer;finite element;ceramic

O385國(guó)標(biāo)學(xué)科代碼:13035

:A

10.11883/1001-1455(2017)02-0332-07

(責(zé)任編輯 張凌云)

2015-09-25;

:2016-03-23

李芮宇(1991— ),男,博士研究生;

:孫宇新,yxsun01@163.com。