－Technical Note－ MODELING OF SOLDER FAILURE DUE TO DUCTILE DAMAGE

K. Aluru * Department of Mechanical Engineering University of New Mexico Albuquerque, NM 87131, U.S.A.

F.-L. Wen **

Department of Mechanical and Computer-Aided Engineering Downloaded from https://academic.oup.com/jom/article/26/4/N23/5943627 by guest on 27 September 2021 St. John’s University Taipei, Taiwan 25135, R.O.C.

Y.-L. Shen *** Department of Mechanical Engineering University of New Mexico Albuquerque, NM 87131, U.S.A.

ABSTRACT A numerical study is undertaken to simulate failure of solder joint caused by cyclic shear deformation. A progressive ductile damage model is incorporated into the rate-dependent elastic-viscoplastic finite element analysis, resulting in the capability of simulating damage evolution and eventual failure through crack formation. It is demonstrated that quantitative information of fatigue life, as well as the temporal and spatial evolution of fatigue cracks, can be explicitly obtained.

Keywords : Solder joint, Fatigue, Ductile damage, Plastic deformation, Finite element analysis.

1. INTRODUCTION metals, the present study thus aims at incorporating failure into the finite element analysis and simulating Fatigue failure of solder joints in microelectronic fatigue performance of a model joint structure. We packages has long been a reliability concern [1-3]. attempt to test the feasibility of applying this direct ap- Aside from the traditional slow-rate thermo-mechanical proach to address the solder fatigue problem. fatigue [4,5], solder joints may also experience severe The model utilizes a simple lap-shear test scheme. cyclic loading, such as vibrational fatigue, in many A damage model is built into the analysis, which, in military and civilian applications. Damage can be conjunction with the element removal process, is capa- generated by the excessive plastic deformation and/or ble of simulating direct failure of the solder material. inside the solder . For analysis and design Attention is devoted only to the evolution of ductile purposes, it is of interest to develop numerical simula- damage, without the possible interference of interfacial tion capabilities which can quantitatively predict failure or intermetallic during deformation of the sol- in solder. der joint. Numerical prediction of solder fatigue typically in- volves the calculation of or plastic strain ranges, which can then be substituted to the empirical Basquine 2. NUMERICAL APPROACH [6] or Coffin-Manson [7,8] types of fatigue criteria to obtain the number of cycles to failure [2,9-14]. This approach, while indirect, is largely necessitated by the Figure 1 shows the computational model. The sol- impracticality of simulating direct material failure in a der material is bonded to two copper substrates. The realistic setting. However, since numerical method- width (w) and thickness (h) of the solder joint are taken ologies exist for modeling damage and failure in ductile to be 1mm and 0.5mm, respectively. The substrate

* Graduate Student ** Professor *** Professor, corresponding author

Journal of Mechanics, Vol. 26, No. 4, December 2010 N23 p p d  e fR()    , (1) Copper dt  H w solder where e is the von Mises effective stress, f (a function of equivalent plastic strain  p ) is the static plastic y stress–strain response, and R (a function of plastic strain h v x rate ddt p / ) defines the ratio of flow strength at x higher strain rates to the static flow strength where R W equals unity. Compared to rate-independent , this formulation utilizes the scaling parameter R to Copper quantify the “strain rate hardening” effect. The R val- ues of the solder alloy are 1.0, 1.9, 2.4, 2.8, 3.1, 3.4 and

Fig. 1 Schematic of the solder joint model along with 3.5 at the plastic strain rates of, respectively, 0.005, 0.5, Downloaded from https://academic.oup.com/jom/article/26/4/N23/5943627 by guest on 27 September 2021 the boundary conditions (plot not to scale). 6, 50, 100, 200 and 300 s1. The applied velocity vx gives rise to the nomi- A progressive ductile damage model is utilized to nal shear deformation of the solder. The di- simulate failure of the solder alloy. Figure 2 shows a mensions used in the finite element analysis schematic of the stress–strain curve which includes the are: w  1mm, h  0.5mm, H  2.5mm and W  damage response (solid curve) [19]. The damage 0.5mm process is quantified by a scalar damage parameter D, with dimensions H and W are 2.5mm and 0.5mm, respec- tively. Note that W represents the part of substrate  (1D )  , (2) outside the solder width. At each interface between the solder and substrate, there is a 5m-thick intermet- where  is the current flow stress and  is the flow allic layer included in the model (not specifically shown stress in the absence of damage. In addition to leading in Fig. 1). Deformation of solder is induced by pre- to softening of the plastic stress, damage is also mani- scribing a constant boundary velocity, v , at the far right x fested by the degradation of elastic modulus as shown edge of the lower substrate. This gives rise to a nomi- nal shear deformation. For reversed loading back to by the dashed unloading/reloading line in Fig. 2. The the zero nominal shear strain, the boundary velocity is equivalent plastic strains at the onset of damage (D  0) pl pl then vx. During deformation the x-direction move- and failure (D  1) are 0 and  f , respectively. A ment of the far left edge of the upper Cu is forbidden, material element loses its capability to carry stress when but movement in the y-direction is allowed. The top its D attains unity, at which point the element will be boundary of the upper Cu is fixed in the y-direction but removed from the mesh so a “void” thus develops. their x-movement is allowed. The bottom boundary of Cracking is then a consequence of linking multiple ad- the lower Cu is constrained to remain horizontal but its jacent voids in the model. nodal displacements in x and y are otherwise free. The pl calculations are based on the plane strain condition, In general 0 can be made a function of the stress which effectively simulates the nominal simple shearing triaxiality, hyd / e, where hyd = 1/3(xx + yy + zz) is mode of the solder [15-17]. the hydrostatic stress and e is the von Mises effective pl In the model the copper substrate is taken to be iso- stress. In the present study 0 is assumed to be in- tropic linear elastic, with Young’s modulus 114GPa, dependent of stress triaxiality due to the lack of experi- 3 Poisson’s ratio 0.31 and density 8930kg/m . The mental data that may be used for defining the functional Cu6Sn5 intermetallic layer is also assumed to be iso- form. Upon damage initiation, strain softening and tropic linear elastic, with Young’s modulus 85.5GPa, thus strain localization set in, which displays a strong Poisson’s ratio 0.28 and density 8280kg/m3. The sol- der material, taken to be the Sn-1.0Ag-0.1Cu alloy [18], mesh dependency. To alleviate the problem, a charac- is treated as an isotropic elastic-viscoplastic solid, with teristic length L is used in the model, with Young’s modulus 47GPa, Poisson’s ratio 0.36 and den- sity 5760kg/m3. Its yielding and strain hardening re- uLp   p (3) sponse follows the experimental stress–strain curves for 1 different strain rates [18]. At the strain rate of 0.005s where u p represents a plastic displacement quantity, or below, the initial strength is 20MPa; the flow and L is defined as the square root of the integration strength increases to a peak value of 36MPa at the plas- point area in each finite element. The softening phe- tic strain of 0.15, beyond which a perfectly plastic be- havior is assumed. This slow-rate form is considered nomenon is now expressed as a stress–displacement as the “static” response. The rate-dependent plastic relationship [20]. Prior to the initiation of damage, flow strength follows u p  0 ; after damage initiation Eq. (3) starts to take

N24 Journal of Mechanics, Vol. 26, No. 4, December 2010 enced by solder joints. The nominal shear strain range D  0 used in the simulation was arbitrarily chosen to be be-  (undamaged response) tween 0 and 0.01, and the simulations were conducted  until the entire joint was severed.

D

0 3. RESULTS AND DISCUSSION E E (1D)E D  1 We first present a representative result of fatigue cracking configuration. Figures 3(a) and 3(b) show the  pl  pl 0 f contour plots of equivalent plastic strain along with the  cracks, after 11.5 and 16.5 cycles, respectively, of de- 1 Fig. 2 Schematic showing the ductile damage re- formation under the 100s shear strain rate. For clar- Downloaded from https://academic.oup.com/jom/article/26/4/N23/5943627 by guest on 27 September 2021 sponse, in terms of the uniaxial stress–strain ity only a small portion of each copper substrate is in- curve cluded in the figures. It can be seen that extensive plastic deformation has occurred. The initiation of cracks appears in the corner region of the solder joint. effect. Failure (removal of the element) occurs when Crack propagation follows the path of greatest equiva- p p u reaches the specified failure value, u f . The lent plastic strain, which in turn is evolving during the evolution of the damage parameter is taken to follow a deformation and damage processes. linear form, Figure 3(b) corresponds to the final failure state where a major crack traversing the entire span of the solder joint u p has just formed. Here two major cracks can be seen: D  . (4) p The upper one has traversed the entire joint and the lower u f one also has propagated over a significant distance. The damage response is thus completely specified by Therefore, although only one crack is responsible for the the two parameters  pl and u p . They are chosen to final failure, the damage process itself is not associated 0 f with only one dominant crack. We attribute this to the be 0.18 and 3m, respectively [21]. It is noted that the p pl steadily progressive accumulation of plastic strain during chosen value of u f corresponds to a  f value of the cyclic deformation, which leads to significant strain approximately 0.5. These parameters were largely rate hardening so the two main cracks had to “take turns” based on measured tensile stress–strain curves of bulk to continue with the propagation process. It is worth pure Sn or Sn-rich solder alloy. It is understood that pointing out that, for the most part, the cracking path is bulk materials and actual solder joints have significantly near and parallel to, but not at, the interface between the different physical sizes and microstructure and thus dif- solder alloy and the intermetallic layer. This is in con- sistence with experimental observations of ductile failure ferent constitutive responses. In addition, formation in fatigued solder joints, as discussed in ref. [16]. and coalescence of microvoids tend to occur more read- In the present work two other applied shear strain ily under tensile loading. The present set of damage rates, namely 1 and 10s1, were also simulated. Simi- parameters should be viewed only as a lower-limit ap- lar cracking morphologies were obtained. Figure 4 proximation. Nevertheless, for the present work em- shows the number of cycles required for the initiation of phasizing qualitative comparison, the choice of damage fatigue cracks and final failure, as a function of the ap- parameters has a benefit of reducing the number of fa- plied shear strain rate. It can be seen that crack tigue cycles, thus computing time, needed to cause fail- propagation generally involves more cycles than those ure. needed to initiate the first crack. Crack initiation is not The finite element program ABAQUS [19] was em- a strong function of applied strain rate. However, in ployed for the modeling. The solder/intermetallic the case of 100s1 strain rate, the crack spends a much structure was discretized into 5000 four-noded linear shorter time (number of cycles) in traversing the entire elements, and each Cu substrate was discretized into solder joint than the cases of slower rates. This ob- 2400 elements. The mesh convergence was checked servation suggests the detrimental effect on the life of by another set of preliminary calculations using twice solder joint caused by high frequency cyclic loading. the number of elements in the model. In this study the The numerical results presented above have demon- nominal shear strain rate imposed on the solder joint is strated the feasibility of incorporating damage models defined to be vx / h (see Fig. 1). We consider three for direct simulation of fatigue failure in solder joints. different nominal shear strain rates: 1s1, 10s1 and It should be noted that the material damage parameters 100s1. It is noted that these strain rates are pertinent chosen for the current work were based on an idealized to the range typical of vibrational fatigue, rather than condition, that of a simple tensile stress-strain response the much slower thermo-mechanical fatigue, experi- without consideration of the effect of stress triaxiality

Journal of Mechanics, Vol. 26, No. 4, December 2010 N25 etc. Therefore the numerically predicted fatigue life should only be considered as a lower-limit estimate. For future investigations, it is suggested that the damage parameters of solder alloys, needed as input for the simulation, be experimentally characterized in detail. The brittle fracture features, such as decohesion along the interface between the solder and intermetallic layer, can also be incorporated into the modeling framework. A more comprehensive modeling capacity can thus be facilitated for the quantitative prediction of solder fail- ure.

(a) 4. CONCLUSIONS Downloaded from https://academic.oup.com/jom/article/26/4/N23/5943627 by guest on 27 September 2021 Numerical finite element modeling of solder joint fa- tigue was carried out. The analysis incorporated a ductile damage model capable of simulating material failure through the element removal process. It was illustrated that the technique can be employed to di- rectly model fatigue failure of solder joint induced by cyclic shear. Fatigue cracks were seen to propagate primarily near the interface but inside the solder. The number of cycles to failure can be influenced by the applied strain rate.

ACKNOWLEDGMENTS (b) This work was supported in part by the National Fig. 3 Contour plots showing the equivalent plastic Science Council of Taiwan, under contract # NSC 98- strain and crack profile for the case of 100s1 2221-E-129-005 and contract # NSC 99-2811-E-129- strain rate at (a) 11.5 cycles and (b) 16.5 cycles 001.

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