梯度应力场与电场下晶内微裂纹的演化

基于微结构演化的经典理论,建立力电作用下的有限单元法,数值再现梯度应力场与电场诱发表面扩散下内连导线中晶内微裂纹的演化过程。结果表明:在梯度应力场与电场共同作用下,晶内微裂纹形态演化存在临界应力梯度P_c、临界电场值X_c、临界形态比β_c,当PP_c、XX_c或ββ_c时,微裂纹在演化的过程中最终以稳定的形态沿着电场方向运动,不发生分节现象;当P≥P_c、X≥X_c或β≥β_c时,微裂纹在发生运动的同时分节成左、右两个裂腔,且应力梯度、电场值、形态比的增大能够加速微裂纹分节。     

应力诱发表面扩散下晶内微裂纹演化的有限元分析

基于物质表面扩散和蒸发-凝结的经典理论,对金属材料内部晶内微裂纹在应力诱发下不稳定外形演化进行了有限元模拟。结果表明,在拉压载荷下,椭圆形晶内微裂纹演化分叉存在临界形态比βc,当β＜βc 时,微裂纹逐渐圆柱化;当β≥βc 时,微裂纹分节为三个裂腔。微裂纹分节时间随形态比增大成近似线性减小,随着拉压应力的增大,微裂纹发生分节的临界形态比和分节时间都将减小。     

内压、外载下晶内微裂纹演化的有限元分析

为了研究和确定金属材料内部微裂纹的演化规律,本文基于物质表面扩散和蒸发-凝结机制的经典理论,建立了拉压外载和内压共同作用下的有限单元法,对金属材料内部晶内微裂纹在应力诱发表面扩散下的不稳定外形演化情况进行了有限元模拟,并系统地分析了外载、内压、形态比对微裂纹形态演化的影响。结果表明:内压q、外载0σ、形态比β是微裂纹演化的主要影响因素;当β和q固定时,存在临界外载荷cσ,若0 cσσ,裂纹不会发生分节,而0 cσ≥σ时微裂纹将分节成三个小裂腔,且分节时间随着0σ和β的增大而减小;当β和0σ为定值时,存在临界内压cq,若cq≤q时,裂纹将会发生分节,且内压阻碍裂腔分节;当0σ和q为定值时,存在临界形态比cβ,cβ≥β的裂纹将会发生分节。     

内压对多场诱发表面扩散下微裂纹演化的影响

根据表面扩散控制下物质迁移机制,建立力、电、热和内压共同作用下的有限单元法,详细讨论了多场诱发表面扩散下金属材料内部微裂纹的演化过程。结果表明：对于形态比为 的微裂纹,存在一临界电场值 。当 时,微裂纹逐渐圆柱化;当 时,微裂纹分节为上下或左右两个较小的微裂纹。随着内压的增大,微裂纹圆柱化时间增长,而分节时间显著减小,且内压有助于微裂纹分节。对于 的微裂纹,当 、 和 一定时存在一临界内压值 。当 时,随着电场和内压的增大会率先在裂纹的上下两端发生裂纹扩展。对于 的微裂纹,当 MPa时,内压对临界值 的影响较小。     

内压对电场下晶内微裂纹演化的影响

基于表面扩散的经典理论及其弱解描述,建立曲率、内压和电场共同作用下的有限单元法,分析了金属材料内部晶内微裂纹的演化过程。对于形态比为β的微裂纹,存在一临界电场值χc,当χ<χc时,微裂纹逐渐圆柱化;当χ>χc时,微裂纹分节为上下或左右两个较小的微裂纹。内压加速有助于微裂纹分节。对于β>1的微裂纹,当β和χ一定时存在一临界内压值qc,当q>qc时,随着电场和内压的增大会率先在裂纹的右端发生裂纹扩展。     

应力诱发界面迁移下晶内孔洞的演化

随着微电子技术的迅猛发展,集成电路中内连导线的失效问题引起广泛关注.内连导线内部孔洞萌生、长大、漂移和失稳变形成狭长裂纹,从而导致电路的开路失效.这是内连导线失效的常见形式.而界面迁移是导致微结构形态演化的主要机制之一.本文基于界面迁移下微结构演化的经典理论和弱解描述,建立了应力诱发界面迁移下微结构演化的有限单元法,并验证了算法的可靠性.对铜内连导线中晶内孔洞的演化进行了数值模拟,详细分析了应力、线宽及形态比对晶内孔洞演化的影响.研究结果表明,椭圆形晶内孔洞存在生长和收缩两种演化分叉趋势.通过大量数值分析得到了晶内孔洞演化的临界应力?σ_c、临界线宽?h_c和临界形态比β_c.当?σ≥?σ_c,?h≤?h_c或β≥β_c时,晶内孔洞会沿长轴长大;反之,晶内孔洞会收缩甚至愈合.此外,应力?σ越大、线宽?h越小或形态比β越大,晶内孔洞越易发生长大,且孔洞面积增大速度越快;?σ越小、?h越大或β越小,晶内孔洞越易发生收缩,且孔洞面积减小速度越快.     

含层理页岩气藏水力压裂裂纹扩展规律解析分析

页岩气蕴藏在页岩层中,页岩层的层理性构造使其水力压裂裂纹扩展与常规均质储层不同.为研究页岩储层水力压裂的裂纹扩展规律,基于复变函数保角变换,得出裂纹尖端应力集中解,考虑页岩非均质、强度各向异性特点,通过比较裂纹沿各方向扩展所需的裂缝尖端水压力,推导出水力压裂裂纹垂直于最小地应力方向稳定扩展过程中在斜交层理后的扩展判据.分别定义了水力压裂裂纹在层理处起裂和沿层理扩展的弱层和岩石基体临界强度比,根据两个临界强度比确定水力压裂裂纹遇层理时在层理处起裂和沿层理扩展的层理弱面强度范围,以此表示水力压裂裂纹转向层理扩展的难易程度.通过对裂纹扩展判据的分析得出:层理起裂弱层和岩石基体临界强度比随层理走向线与第一主应力夹角和层理倾角的减小以及第三主应力和岩石基体强度的增大而增大;层理走向角小于35.26°时,层理起裂弱层和岩石基体临界强度比随第一主应力的减小以及第二主应力的增大而增大;反之,层理起裂弱层和岩石基体临界强度比随第一主应力的减小以及第二主应力的增大而减小;层理扩展弱层和岩石基体临界强度比随层理走向线与第一主应力夹角、层理倾角和地应力差的减小以及岩石基体抗拉强度的增大而增大.层理起裂条件与层理扩展条件同时满足时,水力压裂裂纹转向层理方向扩展.      

表面扩散控制下币型微裂纹的演化

根据表面扩散控制下物质迁移规律,建立轴对称有限单元法,分析了币型微裂纹的外形演化过程．在表面扩散控制下,形态比为β的币型裂纹演化的物理图像是:当β＜βⅠ＝18.0,币型裂纹直接球化; 当β≤β＜βⅡ＝34.6,演化为一环状裂腔;当βⅡ≤β＜βⅢ＝148.9时,演化为一环状裂腔和球形空洞;当βⅢ≤β＜βⅣ=240.0,演化为两环状裂腔．和分离出环状裂腔过程相比,球化过程是快过程;在逐层分离出环状裂腔过程中,后一级的分离相应前一级的分离是快过程．     

单晶与纳米多晶锡层裂的分子动力学研究

低熔点金属的层裂是目前延性金属动态断裂的基础科学问题之一。采用非平衡态分子动力学方法模拟了冲击压力在13.5～61.0 GPa下单晶和纳米多晶锡的经典层裂和微层裂过程。研究结果表明：在加载阶段,冲击速度不影响单晶模型中的波形演化规律,但影响纳米多晶模型中的波形演化规律,其中经典层裂中晶界滑移是影响应力波前沿宽度的重要因素;在单晶模型中,经典层裂和微层裂中孔洞成核位置位于高势能处;在纳米多晶模型中,经典层裂中的孔洞多在晶界（含三晶界交界处）处成核,并沿晶定向长大,产生沿晶断裂,而微层裂中孔洞在晶界和晶粒内部成核,导致沿晶断裂、晶内断裂和穿晶断裂;孔洞体积分数呈现指数增长,相同冲击速度下单晶和纳米多晶Sn孔洞体积分数变化规律一致;经典层裂中孔洞体积分数曲线的两个转折点分别表示孔洞成核与长大的过渡和材料从损伤到断裂的灾变性转变。     

考虑应变能密度的铜互连导线电迁移应力分析

铜互连导线导电后会产生由热扩散主导的电迁移现象,而根据广泛使用的一维电迁移引起的回流模型和原子通量散度的概念,可得到传统的线性应力演化方程.通过在表面晶体材料的表面自由能中计入应变能密度的影响,推导出适合铜导线的非线性应力演化方程.数值求解有界和半无界边界条件下铜导线中的瞬时应力分布.结果表明当考虑应变能密度影响后,导线中的拉应力演变较线性应力演化方程的解更缓趋于稳态,拉应力数值较线性方程应力解更小,而压应力则恰恰相反.同时还讨论了铜条的临界长度效应.计入应变能的影响后,导线内部的应力呈非对称分布,而这种趋势在导线长度减小时更加明显.文中的研究结果将为集成电路设计和铜互连材料的制备提供技术参考.     

Finite element analysis on evolution process for damage microcrack healing

Based on the thermal kinetic and mass conservation, a series of controlling equations for the finite element are derived and related programs are developed to simulate the damage microcrack healing process controlled by surface diffusion. Two kinds of typical models for microcrack splitting are proposed, i.e., the grain boundary energy existing on the crack surface and residual stresses applying on the crack surface. And the conditions of microcrack splitting in the two models are given as a function of the microcrack aspect ratio. The microcrack with traction-free surfaces will directly evolve into a spheroid. The project supported by the National Natural Science Foundation of China (19972053 and 59889101), and the National Outstanding Young Scientist Fund of China (59925104)     

Evolution of penny-shaped microcracks by interface migration

An axisymmetric finite element method is developed and employed to simulate healing evolution of intragranular penny-shaped microcracks under interface migration driven by total free energy change consisted of surface tension and chemical potential difference between phases. The validity of the method is confirmed by an agreement of the shrinkage and growth behavior, simulated numerically, of an isolated spherical grain with those predicted theoretically. The results showed that the surface tension alone serves to evolve the initial penny shape to a spherical one and, coupled with the chemical potential difference, dominates volume shrinkage of the microcracks. As the initial aspect ratio of a microcrack increases, both spheroidization and volume shrinkage times increase continuously. And the volume shrinkage process of the microcracks can be greatly promoted with an increase in the chemical potential difference.     

纳米晶体铝在单轴拉伸下的位错堆积对微裂纹扩展的影响

摘要：针对纳米晶体材料,研究了单轴拉伸载荷作用下纳米晶体铝中的裂纹与裂纹尖端发射的位错所形成的滑移面之间的相互作用。通过分布位错法,将裂纹和滑移面等效为均匀分布的连续位错,获得了裂纹面上应力场。并引入裂纹尖端的无位错区,研究了裂纹尖端无位错区对微裂纹的萌生和主裂扩展之间的影响。结果表明,不考虑裂纹尖端无位错区时,裂纹长度较短,会先在晶界处形成微裂纹,主裂纹较长时,主裂纹会直接穿晶扩展。滑移面与裂纹尖端夹角较大时,会增加裂纹尖端发射的位错个数,从而抑制主裂纹的扩展。考虑裂纹尖端无位错区时,无位错区先于晶界处出现微裂纹,通过主裂纹与微裂纹之间位错的相互发射,导致裂纹与尖端处微裂纹汇合,有效加速了主裂纹的扩展。     

NUMERICAL STUDY OF THE BEHAVIOR OF A BUBBLE ATTACHED TO A TIP IN A NONUNIFORM ELECTRIC FIELD

In order to investigate the effects of a nonuniform electric field on the behavior of a bubble, a numerical study on the shape of a bubble attached to a conducting tip on a supporting wall is performed. The equilibrium bubble shape is determined by solving the free boundary problem that consists of the governing equation for electric field and the normal stress condition at the bubble surface. A numerically generated composite orthogonal coordinate system is employed to solve the free boundary problem. A bubble on a tip is found to be extended in the direction parallel to the applied electric field. The elongation increases steeply with an increase of the electric field strength and the height of the tip. It is also observed that a highly elongated bubble has a shape with slender waist. The bubble shape obtained from numerical studies are qualitatively similar to the shapes observed in experiments. If the contact radius is maintained during bubble deformation, the contact angle and the aspect ratio increase with the increase of the electric field strength and the tip height. On the other hand, if the contact angle is fixed during bubble deformation, the contact radius decreases as the electric field strength increases. In order to estimate the effect of electric field on the bubble departure volume, the surface tension force and the downward electric force exerted on a bubble are also computed for a bubble of fixed volume under the fixed contact angle condition. The sum of the two forces is found to decrease with increasing strength of nonuniform electric field. This fact suggests that the bubble departure volume decreases in a nonuniform electric field.     

On collinear microcrack–inclusion arrays interaction and related problems

Investigated is a crack problem for an array of collinear microcracks in composite matrix. Inclusions are situated in between the neighbouring microcracks tips and exhibit different elastic properties than matrix. The problem is solved using the technique of distributed dislocations. A developed approximate fundamental solution for a single dislocation lying in a general point between inclusions is employed in the distribution of continuously distributed dislocation to cracks modelling. Stress intensity factor is calculated for various cracks/inclusions geometries and elastic moduli mismatches. Stability and/or instability of the straight microcrack paths is investigated for slowly growing microcracks with inclusions located in between the neighbouring microcracks tips. Applications to periodic microcrack tunnelling and microcracks weakening ahead of the main crack are discussed.     

随机分布共线微裂纹的强相互作用

微裂纹串接为宏观灾难性裂纹的过程取决于相邻微裂纹的强相互作用。微裂纹的分布规律影响材料的强度和韧性。本文研究简单的共线微裂纹构型，确定由于微裂纹长度和韧度尺寸的统计分布所产生的影响。研究结果预计了脆性材料的尺度效应，即对于相同密度的微裂纹分布，大尺寸构件的强度比小尺寸构件要低。计算还表明脆性体的强度随微裂纹分布函数标准方差的增加而减小。     

超重力作用下软材料薄膜失稳的有限元分析

软材料在自然界和工业应用中无处不在,其显著特点是对外界刺激极其敏感,相对于传统材料其弹性模量更小,容易发生表面形态的失稳现象．现有研究主要把光、声、电等作为诱导材料失稳的因素进行研究,而重力往往作为常量考虑．本文通过有限元模拟,建立超重力作用下环向受限的圆柱状软材料薄膜失稳模型,探究了薄膜材料的密度、厚度、半径、剪切模量等材料和几何参数对失稳临界超重力和临界失稳模态的影响．结果表明,触发薄膜失稳的超重力随薄膜厚度和密度增大而减小,随剪切模量增大而增大,随着薄膜半径增大快速减小并迅速趋于常数．另外,当径厚比R/H较小时,无量纲临界超重力随着径厚比增大而单调减小,但当径厚比R/H大于3 时,此量为一个常数．超重力作用下软材料的临界失稳模态与密度、剪切模量等参数无关,随径厚比R/H增大,临界失稳模态波数增大、波长减小．     

A theoretical analysis of the electromigration-induced void morphological evolution under high current density

In this work,analysis of electromigration-induced void morphological evolution in solder interconnects is per-formed based on mass diffusion theory. The analysis is conducted for three typical experimentally observed void shapes: circular, ellipse, and cardioid. Void morphological evolution is governed by the competition between the electric field and surface capillary force.In the developed model,both the electric field and capillary force on the void's surface are solved analytically.Based on the mass conversation princi-ple,the normal velocity on the void surface during diffusion is obtained. The void morphological evolution behavior is investigated, and a physical model is developed to predict void collapse to a crack or to split into sub-voids under elec-tric current.It is noted that when the electric current is being applied from the horizontal direction, a circular void may either move stably along the electric current direction or col-lapse to a finger shape,depending on the relative magnitude of the electric current and surface capillary force.However, the elliptical-shaped void will elongate along the electric cur-rent direction and finally collapse to the finger shape.On the other hand,the cardioid-shaped void could bifurcate into two sub-voids when the electric current reaches a critical value. The theoretical predictions agree well with the experimental observations.