塑封球栅阵列焊点热疲劳寿命预测有限元方法
佟 川, 曾声奎, 陈云霞
(北京航空航天大学可靠性工程研究所，北京 100083)
摘 要：选取典型的塑封球栅阵列封装器件，将其建模为由封装外壳、硅芯片和基板组成的三层结构，采用粘塑性材料模式描述锡铅钎料的力学本构关系，建立器件的三维有限元模型，通过有限元仿真得到焊点的应力应变分布云图、应力应变回线及关键焊点的应变范围，最后根据基于应变的Engelmaier疲劳模型预测塑封球栅阵列焊点的寿命。结果表明，在热循环条件下，塑封球栅阵列封装器件的关键焊点的位置位于器件芯片边缘的正下方，并不位于最边缘的焊点处，为改进塑封球栅阵列焊点的热疲劳可靠性提供了依据。
关键词：塑封球栅阵列；焊点；热疲劳；有限元
中图分类号:TG405 文献标识码:A 文章编号:0253-360X(2007)10-089-
04佟 川
0 序 言
现代电子信息产品组装密度越来越高，微电子器件中的焊点越来越小，而其所承载的力学、电学和热力学负荷则越来越重，焊点可靠性问题日益突出。从1989年在美国J P L’S Magenan宇宙飞船的地面试验时发现了表面组装器件焊点的失效以来，历届国际电子元件会议上都把S MT及其焊点可靠性问题作为重要内容进行专题讨论[1]，各种封装和材料焊点的可靠性研究得到普遍重视。
塑封球栅阵(plastic ball grid array，简称P BG A)以其性能和价格优势已经成为封装技术的主流。它采用将焊点隐藏在封装下表面的结构，能够满足电路小型化和高I/O引线数量的要求。但P BG A封装也存在着问题，如焊点检测困难。P BG A器件和印制电路板(printed circuit borad，简称PC B)材料的线膨胀系数(coefficient of thermal expansion，简称CTE)差别较大，容易使焊点内部产生热应力，并在应变不协调处产生应力集中，引起焊点的热疲劳失效。因此了解焊点内部的应力应变分布是提高焊点可靠性的关键。文中针对典型P BG A器件，将P BG A器件的封装划分为由塑封外壳、Si芯片和BT基板所组成的三层结构，使用成熟的商业有限元分析工具ANSY S建立其三维有限元模型，对焊点采用粘塑性本构关系，其它封装材料采用线弹性本构关系，计算P BG A焊点在温度循环应力下的应力应变分布，并得到关键焊点内部的最大等效应变范围，最后通过低周热疲劳寿命计算公式预测焊点的热疲劳寿命。
1 有限元模型建立
1.1 结构建模
P BG A的结构如图1所示，其中BT基板和PC B 材料的线膨胀系数差异不大，而BT基板和Si芯片的线膨胀系数差异较大。文献[2,3]将P BG A封装简化成单一外壳材料所构成的长方体进行建模，得到的结论是P BG A最外侧焊点所承受的应力最严重，与试验结果差距较大[4]。为了更准确地反映P BG A封
装材料的线膨胀系数差异对焊点热应力的影响，文中将P BG A封装划分为由塑封外壳、Si芯片和BT基板组成的三层结构进行建模
。
图1 PB G A结构示意图
Fig11 Sketch map of PB G A structure
有限元分析所选的对象是规格为9mm×9mm
第28卷第10期2007年10月
焊 接 学 报
TRANS ACTI ONS OF THE CHI NA WE LDI NG I NSTIT UTI ON
V ol.28 N o.10
October 2007
收稿日期:2006-12-18
×1.3mm，焊球直径为<0.5mm，间距为0.8mm的11×11阵列的P BG A封装器件，其芯片尺寸为2mm ×2mm×0.5mm，焊点高0.4mm。由于结构的对称性，为简化计算，取1/4建模，并在相应表面施加对称边界条件。
1.2 材料属性及网格划分
目前常用的钎料为63Sn37Pb共晶合金，这种钎料的熔点较低(约为183℃，即456K)，在室温下已达到熔点的0.65倍，在这样相对高的温度下,SnPb 钎料受力会有明显的蠕变和粘塑性特征。一般采用蠕变和塑性统一的Anand模型来描述钎料的力学本构行为。它包括一个流动方程和三个用来表示材料应变硬化和应变软化的演化方程。具体描述形式为流动方程
dεp d t =A
m
sin h
ξσ
S
exp
-Q
RT
,(1)
演化方程
d S d t =h0|B|a B
|B|
dε
d t
,(2)
B=1-
S
S3
,(3)
S3=S^
1
A
dεp
d t
exp
Q
RT
n
,(4)
式中:εp为粘性系数;t为时间;A为指数因子;m为
应变敏感指数;ξ为应力乘子;σ为应力;S为形变
阻抗;Q为粘塑性形变激活能;R为波尔兹曼常数,
其值为1.381×10
-23J/K;T为热力学温度;h
为硬
化/软化常数;B和S3为中间量;a为与硬化/软化
相关的应变率敏感指数;S^为系数;n为应变阻抗饱
和值的应变率灵敏度。此外，在求解方程时还需要
形变阻抗S的初始值S0。对于63Sn37Pb钎料，求解
Anand模型所需的参数如表1所示[5]。此外，在定
义Anand参数之前要首先定义钎料的线性参数，见
表2。其它封装材料均采用线弹性材料模式描述其
力学本构关系，材料参数[6]如表2所示。热循环过
程中焊点的应力应变采用ANSY S
有限元软件进行
分析,SnPb钎料的单元类型为粘塑性单元VIS
C O107，其它部分均采用S O LI D45单元，网格划分后
表1 Anand模型的粘塑性材料参数
Table1 Visco2pla stic parameter for Anand model
指数因子
A/s-1
粘塑性应变激活能
Q/J
应力乘子
ξ
应变敏感系数
m
系数
S^/MPa
应变率灵敏度
n
硬化常数
h0/MPa
应变率敏感指数
a
形变阻抗初值
S0/MPa 4×106 1.29×10-19 1.50.30313.790.071378.95 1.312.41
的模型如图2所示。
表2 线弹性材料参数
Table2 Liner ela stic material parameter
材料名称
弹性模量
E/MPa
线膨胀系数
α
l
/(10-6K-1)
泊松比
μ
塑封外壳1550015.00.25
S i芯片130000 2.60.278
BT基板1510013.00.195
63Sn37Pb3090024.50.35
FR-41110019.00.28
图2 PB G A三维模型图
Fig12 PB G A3D model
1.3 热循环载荷
热循环加载按照美国军用标准MI L—ST D—883
选取，温度范围为-55～125℃，升降温速率12℃/
min，高低温保持时间各15min，零应力参考温度取
室温20℃，如图3所示。已有研究表明，焊点的应
力应变在热循环过程中呈周期性变化，一般在第四
周期时趋于稳定[7]，因此在有限元分析时采用四个
热循环周期进行计算。根据以上循环条件，采用了
16个载荷步，每步又分6个载荷步进行计算。
图3 热循环剖面
Fig13 Profile of thermal cycling
90
焊 接 学 报第28卷
2 焊点热疲劳寿命预测模型
进行有限元模拟的最终目的就是进行寿命预
测，从而量化可靠性。当前，预测疲劳可靠性的模型主要分为：基于应力的疲劳模型、基于应变的疲劳模型、基于能量的疲劳模型和基于损伤的疲劳模型等。文中采用基于应变的Engelmaier 模型进行焊点热疲劳寿命预测，该模型的表达式为
N f =
百多12Δ
γ2εf
1
c
,(5)
式中:N f 为失效循环周次，即热疲劳寿命;εf 为材料
常数，对常用的63Sn37Pb 钎料，取εf =0.325;c 是由热循环剖面决定的参数，设T sj 为热循环平均温度,
t D 为高温保持时间，则有
c =-0.442-0.0006T sj +0.0174ln 1+
360
t D
。(6)
按图3所示的剖面计算,c =-0.42;Δ
γ是剪切应变范围，需要通过有限元模拟来确定其值。
3 计算结果及分析
结构的等效应力计算结果如图4所示。可以看出,P BG A 关键焊点(最危险焊点)的位置位于芯片边缘正下方的焊点处，并不在离中心最远的焊点处。这是因为塑封器件的BT 基板材料与PC B 板材料的线膨
胀系数差异很小，而Si 芯片与BT 基板的线膨胀系数差异较大，因而在其交界处产生了较大的局部热应力的缘故。在热循环的各个阶段，关键焊点的位置始终不变。
图5显示了关键焊点的总剪切应变随时间变化的曲线。仿真结果与文献[4]中的试验结果保持了较好的一致性。
图4 PB G A 等效应力分布
Fig 14 Equivalent stre ss distribution of
PB G A
选择关键焊点的最大应力单元进行分析，等效
应力和等效应变形成的迟滞环如图6所示，可以看
图5 应力最大焊点的总剪切应变随时间变化图
Fig 15 Figure of shear strain to time for max stress soldering spot
出,
在经过第三、第四周期后应变变化范围Δγ趋于稳定。
图6 应力最大焊球单元的应力应变回线
Fig 16 Loop of stress and strain for max stress soldering unit
以图6中第四周期的等效应变变化范围作为模
型(5)的输入，即Δγ=0.032。并将εf =0.325,c =-0.42代入Engelmaier 模型，可得P BG A 焊点在该
温度循环剖面下的疲劳寿命为:N f =651(周次)。
4 结 论
(1)进行有限元模拟时，合理地建模器件结构
能够反映内部结构对焊点应力的影响，使计算结果
更准确。
(2)在热循环条件下,P BG A 关键焊点的位置位于器件芯片边缘的正下方，并不位于最边缘的焊点处，为改进P BG A 焊点可靠性提供了依据。
参考文献:
[1] M ichael Pecht.E lectronic reliability engineering in the 21st century
[C ]∥M aryland :International Sym posium on E lectronic M aterials
第10期佟 川，等：塑封球栅阵列焊点热疲劳寿命预测有限元方法91
汽车出售and Packaging ,2001:231-238.
[2] 顾永莲.球栅阵列封装焊点的失效分析及热应力模拟[D ].成
冰箱排名都：电子科技大学,2005.
[3] 聂小龙.表面组装焊点热力行为研究[D].北京：北京工业大林黛玉怎么死的
学,2004.
[4] John H L ,Pao Y i 2Hsin.S older joint reliability of BG A ,CSP ,flip
chip and fine pitch S MT asmblies[M].Chicag o :M cG raw 2hill Press ,2001.
[5] W ang G uozhong ,Chen Zhaonian.Visco 2plastic and constitutive rela 2
tions of tin 2lead s older alloy[J ].Chine Journal of Applied M echan 2ics ,2000,17(2):133-139.
[6] Lioyd G Burrell.M odeling thermally induced visco 2plastic deformation
and low cycle fatigue of C BG A s older joints in a surface m ount package [C ]∥M aryland :Inter 2s ociety C on ference on Thermal Phenomena ,1996:158-165.
[7] Pan Tsung 2Y u.Thermal cycling induced plastic deformation in s older
joints :accumulated deformation in S MT s older joints[J ].IEEE T rans 2actions on C om ponents ,Hybrids and M anu facturing T echnology ,l999,14(4):224-232.
作者简介：佟 川，男,1981年出生，硕士。主要从事可靠性相关
领域研究。
Email :
spinstorm @
92
焊 接 学 报第28卷
expands along the finer grain boundary or subgrain boundary during the s olidification process.Furtherm ore,in690nickel2bad alloy sur facing metal,Mn weakens the negative in fluence of Nb on s olidi2 fication cracking resistance to s ome extent by restraining the grega2 tion effect of Nb,and then the cracking resistance is im proved.
K ey w ords: 690nickel2bad alloy;s olidification cracking; mechanism
Ch aracterization on strength and toughness of w elded joint for ultra2low carbon b ainitic steel G UO Aimin1,2,LI U Jibin2, MI AO K ai2,DONG Hanxiong2,Z OU Dehui2,HE X inlai1(1.School of Materials Science and Engineering,Beijing University of Science and T echnology,Beijing100083,China;2.Rearch and Develop2 ment Institute,Wuhan Iron and S teel(G roup)C om pany,Wuhan 430080,China).p73-76
Abstract: The weldability was investigated on ultra low2car2 bon bainitic steel with therm omechanical control process by utilizing shielded metal arc welding,submerged arc welding and welding thermal simulation test.Results showed that hardness is a little dif2 ferent in the heat affected zone(H AZ).The maximum hardness in the heat affected zone was less than60H V.C om pared with the same class of low alloy high strength steels,the uniformity of strength in H AZ increas remarkably.The heat affected zone has high tough2 ness.The im pact abs orbing energy at-40℃reaches above60J in the simulated coar2grained zone when the heat input was56k J/ cm.The im pact abs orbing energy at-40℃reached above100J in shielded metal arc welding,and submerged arc welding.健康作息时间表
K ey w ords: ultra2low carbon bainitic steel;welding;heat affected zone;toughness
理想B razing process of high temperature brazing filler metal BCo45NiCrWB LI U Enze1,2,S UN Shuchen1,T U G an feng1, ZHE NG Zhi2,T ong Jian2,G uo Y i2(1.School of Materials and Met2 allurgy,N ortheastern University,Shenyang110004,China;2.Su2 peralloys Division,Institute of Metal Rearch Chine Academy of Sciences,Shenyang110016,China).p77-80
Abstract: Wettability and flow2ability experiments of a high tem perature brazing filler metal BC o45NiCrW B were studied.Dy2 namic analysis of brazing process was studied by a ST M D2300sur face tension test apparatus.M icrostructures of brazed joint with different brazing process were studied.M icrostructure of brazed joint was analyzed by optical microscope.The element distribution of brazed joint was analyzed by electron microprobe.Rupture life of brazed joint at the condition of980℃/132MPa was tested.The best braz2 ing process of BC o45NiCrW B alloy was established.The brazing pa2 rametens are1220℃/2h,+1080℃/4h+900℃/16h,all by arg on quench.Results show that the high tem perature brazing alloy BC o45NiCrW B has excellent process brazeability.At the condition of 980℃/132MPa the rupture life is m ore than60hours.
K ey w ords: brazing;wettability;flow2ability;rupture life
E ffect of therm al cycles of DSAW on microstructure in lowalloy high strength steel ZH ANG Huajun,
ZH ANG G uangjun, W ANGJunheng,W U Lin(S tate K ey Labortory of Advanced Weld2 ing Production T echnology,Harbin Institute of T echnology,Harbin 150001,China).p81-84
Abstract: According to the low alloy high2strength steel thick plate welding,a new high efficiency technique which does not need back chipping-double2sided double arc welding(DS AW)was pro2 vided.Backing run with double2sided double puld gas metal arc welding,and other pass with double2sided double gas metal arc welding.The tem perature fields of single TIG(tungsten inert2gas) welding and DS AW near the bond area were measured by the method of hiding thermal2couple in drilled hole.C om pared the thermal cy2 cles of tw o methods,the t8/5and t8/3of DS AW are higher.In DS AW,fore pass provides the rear pass with a preheat action and rear pass provides the fore pass with a postheat treatment.In single TIGwelding,microstructure of weld and coar grain zone is coar martensitic,but in DS AW weld contains a few of acicular ferrilite besides of martensitic.M oreover,microstructure of coar grain zone is smaller than that of single TIGwelding.M icrohardness distribution results indicated that hardness of DS AW was lower than that of single TIG welding.
K ey w ords: double2sided double arc welding;tem perature field;T joint;low alloy high strength steel
世界青年节
E ffects of heat treatment on microstructure and properties of electron beam w elded TC4titanium alloy G U Baolan,DI NG Dawei,W ANG Li,X U Xuedong(Institute of M icrostructure and Properties of Advanced Material,Beijing University of T echnology, Beijing100022,China).p85-88
Abstract: F or electron beam welding(E BW)of T C4titanium alloy with different preheat treatments and post2weld heat treatment, microstructure and pha com position characteristics of the welds of T C4were studied by means of optical microscope and X2ray diffrac2 tion.T ension and im pact test were carried out at room tem perature. The results indicated that the microstructure of tw o kinds of ba metals is the mixture ofαphas andβpha,but their state and distribution are different.The post2weld s olution and aged operation carried out in the ca of annealed welds leads to a coarning and hom ogenous of the acicularα,the microstructures is typically reticu2 lar structure.The welds in s olid s olution state were given a relief an2 nealed after welding,who microstructure at FZ is tem pered martensiteαin side priorβgrains and at grain boundaryα.I t induced that the ultimate tensile strength(UTS)of annealed state welds is less than that of s olution treated welds,but the im pact toughness of the former is greater than that of the latter.H owever,the UTS and im pact toughness of the tw o kinds of welds are greater that that of ba metal.
K ey w ords: T C4titanium alloy;electron beam welding;mi2 crostructure;mechanical properties
Finite element analysis simulations of life prediction for PBG A soldered joints under therm al cycling T ONG Chuan,ZE NG Shengkui,CHE N Y unxia(Reliability Rearch Institute,Beihang University,Beijing100083,China).p89-92
Abstract: A typical plastic ball grid array(P BG A)com po2 nent was lected and the plastic ball grid array packaging was m od2 eled as a tri2layer structure com pod of encapsulation,die and sub2 strate.Visco2plastic m odel was ud to describe the behavior of SnPb
2007,V ol.28,N o.10 TRANS ACTI ONS OF THE CHI NA WE LDI NG I NSTIT UTI ON Ⅴ
s older.ANSY S finite element analysis tool was ud to im plement the simulation.In the end,the stress and strain distribution were obtained.The strain range was achieved from the hysteresis loop. The fatigue life of P BG A was predicted using Engelmaier m odel.The simulation result of the m odel shows that the position of the critical s oldered position of a plastic ball grid array com ponent is right below the edge of its die,but not the outboard s olders.This result is help2 ful to im prove the thermal fatigue reliability of plastic ball grid array com ponents.
K ey w ords: plastic ball grid array;s olded joint;thermal fa2 tigue;finite element method
E ffect of cladding m aterial on LY12CZ aluminium alloy by Lar Cladding S UN Fujuan,H U Fangy ou,H UANG Xuren, T ANG Y uanheng(Qingdao Branch,Naval Aeronautical Engineering Academy,Qingdao266041,China).p93-96
Abstract: Through controlling process parameters of im pul lar,current,pul width,frequency,spot diameter and scanning velocity,lar cladding LY12and Al2Ywas ud to repair corrosion damage of aluminum alloys.A fter cladding,fatigue test,fracture and microstructure of the specimens were studied.The result indicat2 ed that the life of the specimen cladded by Al2Y was402%of that by LY12.There was no large pore and crack in the Al2Ylayer which joined with the substrate firmly.There was much im purity in the cladding layer of LY12.
K ey w ords: aluminum alloys;lar cladding;fatigue life; fatigue fracture;microstrcture
Comp arison of stress relief by PWHT and VSR in large2dimen2 sion straight w elded pipe ZH ANG Chao,LU Qinghua,X U Ji2 jin,CHE N Lig ong(School of Materials Science and Engineering, Shanghai Jiaotong University,Shanghai200030,China).p97-100 Abstract: P ost2weld heat treatment(PWHT)and vibratory stress relieving(VSR)were ud to control the residual stress in large2dimension welded pipes.The results show that both PWHT and VSR are able to relieve the res
idual stress effectively in large2dimen2 sion straight welded pipe and make the distribution of residual stress m ore uniform.Their effect in weld zone is m ore obvious than the in ba metal.The results of stress relieving of VSR of as2cast mi2 crostracture are qualified but not acceptable in cold plastic deforma2 tion zone.The effect of PWHT on the stress relieving and stress uni2 form ability is better than that of VSR.H owever,considered of e2 conomy factor and technique convenience,VSR is con firmed as stress relieving technique to control the residual stress in large2di2 mension straight welded pipe.
K ey w ords: vibratory stress relieving;post2weld heat treat2 ment;residual stress
Progress in friction stir w elding of high melting point m aterials LI U Huijie,ZH OU Li(S tate K ey Laboratory of Advanced Welding Production T echnology,Harbin Institute of T echnology, Harbin150001,China).p101-104
Abstract: The rearch status of friction stir welding(FSW) of high melting point materials was introduced from the aspects of FSW tool design,microstructural characteristics and mechanical properties of the joints,welding tem perature distribution and residual stress and FSW assisted by hybrid heating s ources.I t indicates that the W2Re alloy and polycrystalline cubic boron nitride are s
uitable FSW tool materials.The FSW joints with high strength and fine mi2 crostructure can be produced when the proper tool geometry and welding parameters were ud.F or simulation of tem perature distri2 bution and residual stress in the FSW joints,physical m odels should be im proved according to the real FSW process.The utilization of hybrid heating s ource is benefit to weld formation and tool life.
K ey w ords: high melting point materials;friction stir weld2 ing;tool design;microstructural characteristics;residual stress;hy2 brid heating s ource
R eview of X100pipeline steel and its field w eld ability Y AN Chunyan1,LI Wushen1,FE NGLingzhi1,X UE Zhenkui2,BAI Shi2 wu2,LI U Fangming2(1.School of Materials Science and Engineer2 ing,T ianjin University,T ianjin300072,China;2.Petroleum2G as Pipeline Rearch Institute of China,Lang fang065000,Hebei,Chi2 na).p105-108
Abstract: In view of the ever2increasing pipeline length and operating pressure,development of high2strength linepipes has be2 come increasingly attractive and needed.The current knowledge of X100pipeline steel about rearch and development status,metallur2 gical principles,mechanical properties,field weldability,and s o on were prented.Production of grade X100steel requires combi
nation of super2clean refining,therm o2mechanical controlled process,prop2 er metallurgical design and s ome other advanced techniques.Excel2 lent mechanical properties and satis fying weldability are possd for grade X100steel.Y ield strength of X100grade steel generally ex2 ceeds690MPa.High strength2toughness welded joint can be ob2 tained through proper welding procedures.Further w ork is required to im prove the production of X100pipeline steel and to establish ap2 propriate material standards.
偶然徐志摩K ey w ords: X100pipeline steel;microstructure;ductile fracture arrest;girth welding;weldability
G eneral rules of w riting scientific and technical p apers W ANG Y a(Harbin Welding Institute,China Academy of Machinery Science and T echnology,Harbin150080,China).p109-112 Abstract: In order to help scientific and technical w orkers to know the basic requirements of writing academic papers,master its general methods and im prove their rules,comm on problems in the submitted original manuscripts were analyzed and the methods to re2 s olve the problems were given,bad on the features of academic papers and combined with the experiences of the author on editing a2 cademic papers for many years.The basic structures of academic pa2 pers,requirements on writing and s ome problems needing in atten2 tion were als o stated.According to s ome national and professional standards,standardized us of professional terms and phas,sym2 bols of physical q
uantity and measurement units,the requirements on figures and tables and regulations of references literature in papers were briefly explained.
K ey w ords: scientific and technical papers;writing;stan2 dardization
Ⅵ MAI N T OPICS,ABSTRACTS&KEY W ORDS 2007,V ol.28,N o.10
