本文選題：電磁彈性柱　切入點：硬幣型裂紋　出處：《哈爾濱工業(yè)大學(xué)》2017年博士論文　論文類型：學(xué)位論文

【摘要】：電磁彈性材料作為一種新型智能材料,因其獨特的磁電耦合效應(yīng),在智能驅(qū)動器、換能器、傳感器、致動器等的制作領(lǐng)域具有廣泛的應(yīng)用前景。由于該類材料在制造和使用過程中常含有裂紋,故關(guān)于該類材料斷裂問題的研究已經(jīng)成為許多力學(xué)工作者的熱點研究方向。目前,雖然電磁彈性材料斷裂力學(xué)問題已經(jīng)取得了許多研究成果,但這些工作主要關(guān)注的是反平面和平面斷裂問題,對于更接近真實情況的三維斷裂問題,隨著材料參數(shù)和控制方程個數(shù)的增多,加大了數(shù)學(xué)求解上的困難,故研究成果相對較少。本文將考慮三維斷裂問題中的一種特殊情況—硬幣型裂紋問題,對含有硬幣型裂紋的電磁彈性柱的斷裂問題進行研究,揭示其斷裂規(guī)律,為設(shè)計和制造具有柱體形狀的電磁元器件提供理論參考。首先,研究了含電磁穿透硬幣型裂紋的徑向尺寸有限的電磁彈性柱在力-電-磁載荷作用下的斷裂問題�？紤]兩種電磁彈性柱側(cè)面邊界條件,利用勢函數(shù)理論和Hankel積分變換技術(shù),將混合邊值問題化為求解一對對偶積分方程,并進一步轉(zhuǎn)化為求解第二類Fredholm積分方程。利用高斯積分進行數(shù)值計算,獲得了裂紋尖端各種場強度因子的表達式。數(shù)值分析結(jié)果表明:結(jié)構(gòu)幾何尺寸、側(cè)面邊界條件對斷裂特性有顯著影響;考慮電磁穿透模型,電磁載荷是促進還是抑制裂紋擴展取決于遠場施加的機械載荷為應(yīng)力或應(yīng)變。其次,研究了含電磁半穿透硬幣型裂紋的電磁彈性柱在力-電-磁載荷作用下的斷裂問題。通過引入三個輔助函數(shù),最終將所研究的混合邊值問題轉(zhuǎn)化為求解三個耦合的非線性Fredholm積分方程組,獲得了各種場強度因子的表達式,給出了結(jié)構(gòu)幾何尺寸、電磁載荷、裂紋內(nèi)介質(zhì)的電容率和磁導(dǎo)率對裂紋張開位移強度因子的影響規(guī)律。數(shù)值分析結(jié)果表明:裂紋面電磁邊界條件對裂紋擴展有重要影響;電磁彈性材料的斷裂韌性與施加的電磁場的方向有關(guān);電磁穿透和電磁不穿透模型可看作是本問題的兩種特殊情況。再次,研究了含硬幣型裂紋的電磁彈性柱在熱沖擊載荷作用下的瞬態(tài)斷裂問題。采用電磁半穿透裂紋面邊界條件,假設(shè)電磁彈性柱的外表面為自由表面,首先給出無裂紋的電磁彈性柱在瞬時熱沖擊載荷作用下的溫度場,進而根據(jù)疊加原理,將溫度場在裂紋面處產(chǎn)生的熱應(yīng)力、電位移和磁感應(yīng)強度反向加在含硬幣型裂紋的電磁彈性柱的裂紋面上,從而形成了力-電-磁耦合的混合邊值問題。經(jīng)過復(fù)雜的數(shù)學(xué)推導(dǎo),最終給出了各種場強度因子的表達式,并討論了熱沖擊時間、結(jié)構(gòu)幾何尺寸、裂紋面電磁邊界條件對應(yīng)力強度因子的影響規(guī)律。數(shù)值分析結(jié)果表明:給定電磁彈性柱尺寸,裂紋半徑越大裂紋越容易擴展;在裂紋最不穩(wěn)定的時刻,考慮相同的裂紋半徑與電磁彈性柱半徑的比值,電磁穿透型裂紋最容易擴展;最后,研究了含Dugdale塑性區(qū)硬幣型裂紋的電磁彈性柱在力-電-磁載荷作用下的斷裂問題。采用電磁穿透的裂紋面邊界條件,問題最終轉(zhuǎn)化為求解一個分段的第二類Fredholm積分方程,借助于逐次逼近的數(shù)值計算方法,獲得了影響塑性區(qū)寬度的因素,同時給出了力-電-磁載荷、裂紋尺寸等對裂紋張開位移的影響。數(shù)值分析結(jié)果表明:遠場施加的力-電-磁載荷、結(jié)構(gòu)幾何尺寸對塑性區(qū)寬度有明顯影響;遠場施加相同的機械載荷,負的電磁載荷更易引起裂紋的擴展。
[Abstract]:The electromagnetic elastic material as a new type of smart materials because of its unique magnetoelectric coupling effect in intelligent driver, transducer, sensor, actuator field has broad application prospects and other production. Because of this kind of materials often contain cracks in the manufacture and use of the process, so the research on the material fracture problem has become a hot research topic the direction of many mechanical workers. At present, although the fracture mechanics problems in magnetoelectroelastic materials has made great achievements, but the work is mainly about the plane and anti plane fracture problems for 3D fracture problems, closer to the real situation, with the increase of the number of material parameters and control equations, increasing the difficulty in solving mathematics therefore, little research results. This paper will consider a penny shaped crack in a special case, 3D fracture problems, with a penny shaped crack Research on the fracture problem of electromagnetic elastic column, reveal the fracture rules and provide a theoretical reference for the design and manufacture of electromagnetic components have a column shape. First, studied with the electromagnetic penetration of a penny shaped crack in the radial dimension of the electromagnetic force in finite elastic cylinder electro magnetic load fracture problem under consideration two. Electromagnetic elastic column lateral boundary conditions, using the theory of potential function and Hankel integral transform technique, the mixed boundary value problem is solved on the dual integral equations, and further transformed into solving Fredholm integral equations of the second kind. The integral calculated by Gauss formula, a variety of crack tip field intensity factor was obtained. The numerical analysis the results show that the geometry of the structure, the side boundary conditions have significant influence on the fracture characteristics; consider the electromagnetic penetration model, electromagnetic load to facilitate or inhibit crack propagation depends on the far The mechanical load applied to the field of stress or strain. Secondly, study the electromagnetic elastic column containing electromagnetic semi penetrating penny shaped crack in force - electric - magnetic fracture loads. By introducing three auxiliary functions, will eventually be mixed on the boundary value problem into nonlinear Fredholm integral equations of the three groups a coupling, received a variety of field intensity factor expressions, the geometry of the structure, gives the electromagnetic load, influence of crack medium permittivity and magnetic permeability of the crack opening displacement intensity factor. The numerical results show that the crack surface electromagnetic boundary conditions have an important influence on the crack propagation; the fracture toughness of magnetoelectroelastic materials with the direction of the applied electromagnetic field; electromagnetic penetration and penetration of electromagnetic model can be regarded as two special cases of the problem. Thirdly, study with a penny shaped crack in electromagnetic elastic column 鐑啿鍑昏澆鑽蜂綔鐢ㄤ笅鐨勭灛鎬佹柇瑁傞棶棰，

本文編號：1595378