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Numerical study of ductile failure morphology in solder joints under fast loading conditions
Microelectronics Reliability 50 (2010) 2059–2070
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Numerical study of ductile failure morphology in solder joints under fast loading conditions Y.-L. Shen *, K. Aluru Department of Mechanical Engineering, University of New Mexico, Albuquerque, NM 87131, United States
a r t i c l e
i n f o
Article history: Received 15 February 2010 Received in revised form 5 May 2010 Available online 26 June 2010
a b s t r a c t A numerical study is undertaken to investigate solder joint failure under fast loading conditions. The finite element model assumes a lap-shear testing configuration, where the solder joint is bonded to two copper substrates. A progressive ductile damage model is incorporated into the rate-dependent elastic-viscoplastic response of the tin (Sn)–silver (Ag)–copper (Cu) solder alloy, resulting in the capability of simulating damage evolution leading to eventual failure through crack formation. Attention is devoted to deformation under relative high strain rates (1–100 s1), mimicking those frequently encountered in drop and impact loading of the solder points. The effects of applied strain rate and loading mode on the overall ductility and failure pattern are specifically investigated. It is found that, under shear loading, the solder joint can actually become more ductile as the applied strain rate increases, which is due to the alteration of the crack path. Failure of the solder is very sensitive to the deformation mode, with a superimposed tension or compression on shear easily changing the crack path and tending to reduce the solder joint ductility. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Mechanical failure of solder joints has been a serious reliability problem in microelectronic packages. Deformation of solder can be a result from the thermal expansion mismatch between the components (e.g., semiconductor chip, chip carrier, and/or printed circuit board) they connect, causing predominant shearing of the joint. In addition, when direct mechanical loading is imposed on the packaging structure, the solder joint can also experience shear as well as tensile and compressive deformations. Damage can be induced by the excessive monotonic or cyclic plastic deformation and/or creep inside the solder alloy, or by more brittle forms of failure along the thin intermetallic layer at the interfacial region of the joint. Failure of solder due to drop and impact of the components has emerged to be an important issue to the industry in recent years (see, e.g., [1–13]). This is different from the traditional thermomechanical fatigue problem, since the loading rate involved in drop and impact can be several orders of magnitude higher than that during thermal cycling. An additional concern is for the tin (Sn)-based lead (Pb)-free solders [14–20] being used and/or developed as environment-friendly replacements of the conventional Pb-bearing solder. Since the Pb-free solder alloys are generally more brittle compared to the conventional Sn–Pb eutectic, they may be more susceptible to failure caused by dynamic loading. * Corresponding author. E-mail address: [email protected] (Y.-L. Shen). 0026-2714/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.microrel.2010.06.001
During drop impact, the individual solder joints are not in general under direct mechanical shock. Rather, it is the flexural bending of the circuit board that forces the solder to undergo large deformation [7,10,12,13]. Thus, depending on the geometry and material of the test vehicle, detailed test condition or real-life drop scenario, and the location of the particular joint of interest, solder joints can experience shear, compression, tension and their combination during the dynamic loading history. The existence of fluctuating tension–compression experienced by the individual joint has been shown from experiments and package-level numerical modeling [4,6,12]. Finite element modeling has been a powerful tool in predicting and analyzing solder deformation. In the present work we report a systematic finite element analysis which concerns not only deformation but also damage and failure of solder joints. Attention is devoted to the morphology of ductile failure inside the solder under relatively fast loading rates. The model utilizes a simple lap-shear test setting, with nominally constant strain rates applied to the solder. This study includes the following salient features. The rate-dependent response of a tin-silver (Ag)–copper (Cu) solder is used in the model to specifically address the loading rate effect. A ductile damage model is incorporated, which, in conjunction with the element removal process in the explicit numerical scheme, is capable of simulating direct failure of the material. A parametric analysis is undertaken, which considers the superimposed tensile or compressive deformation on the shear
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D=0
Dσ σ0
H w
solder E
E
(1-D)E
vx
h
D=1
ε
pl 0
W
y
σ
σ
Copper
ε
ε
pl f
Fig. 2. Schematic showing the ductile damage response, in terms of the uniaxial stress–strain curve.
x
Copper
vy Fig. 1. Schematic of the solder joint model (plot not to scale) along with the boundary conditions. The applied velocities vx and vy give rise to the nominal shear and tensile (or compressive) deformations, respectively, of the solder. The dimensions used in the finite element analysis are: w = 1 mm, h = 0.5 mm, H = 2.5 mm and W = 0.5 mm.
deformation mode, so its effect on the cracking pattern can be examined. The primary objective of this work is to apply the damage modeling technique for gaining a baseline understanding on the evolution of ductile damage, without the possible interference of brittle
interfacial or intermetallic fracture. We aim to laying the foundation for developing comprehensive predictive modeling capabilities, to address the increasing concern of solder reliability under the high loading rate conditions. 2. Model description The computational model is schematically shown in Fig. 1, with the solder material bonded to two copper (Cu) blocks (termed ‘‘substrates” in this paper). The width (w) and thickness (h) of the solder joint are taken to be 1 mm and 0.5 mm, respectively. The substrate dimensions H and W are 2.5 mm and 0.5 mm, respectively. Note that W refers to the part of substrate outside the solder width. At each interface between the solder and the
Fig. 3. Contour plots of: (a) shear stress rxy and (b) equivalent plastic strain at the nominal shear strain of 0.05, for the case of 1 s1 shear strain rate.
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substrate, there is a 5 lm-thick intermetallic layer included in the model (not specifically shown in Fig. 1). Deformation of solder is induced by prescribing constant boundary velocities, vx and/or vy, at the far right edge and bottom, respectively, of the lower substrate. The velocity vx will give rise to a nominal shear deformation (i.e., the typical lap-shear test [9,21–31]). Depending on the direction of the prescribed vy, either nominal tension or compression can be superimposed on the solder. It is noted that, in actual high-rate loading situations such as drop and impact, the boundary velocities will not be constant. Nevertheless we adopt this simple modeling scheme to aid in a fundamental understanding. More realistic deformation histories may be incorporated into the analysis in a straightforward manner. During deformation the x-direction movement of the far left edge of the upper Cu is forbidden, but movement in the y-direction is allowed except that the upper-left corner of the upper substrate is totally fixed. The top boundary of the upper Cu is also fixed in the y-direction but its x-movement is allowed. The calculations were based on the plane strain condition, which effectively simulates the nominal simple shearing mode of the solder [32–34]. It is acknowledged, however, that the plane strain condition results in certain over-constraint under tensile or compressive loading. (In the plastic p regime the ffiffiffi flow stress is increased by a factor of approximately 2= 3, following the von Mises yield criterion.) In the model the Cu substrate is taken to be isotropic linear elastic, with Young’s modulus of 114 GPa, Poisson’s ratio of 0.31 and density of 8930 kg/m3. The Cu6Sn5 intermetallic layer is also assumed to be isotropic linear elastic, with Young’s modulus of 85.5 GPa, Poisson’s ratio of 0.28 and density of 8280 kg/m3. The
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solder, taken to be the Sn–1.0Ag–0.1Cu alloy [10], is treated as an isotropic elastic-viscoplastic solid, with Young’s modulus of 47 GPa, Poisson’s ratio of 0.36 and density of 5760 kg/m3. Its yielding and strain hardening response follows the experimental stress– strain curves for different strain rates [10]. At the strain rate of 0.005 s1 or below, the initial yield strength is 20 MPa; the flow strength increases to a peak value of 36 MPa at the plastic strain of 0.15, beyond which a perfectly plastic behavior is assumed. This slow-rate form is considered as the ‘‘static” response. The ratedependent plastic flow strength follows
re ¼ f ðep Þ R
p de ; dt
ð1Þ
where re is the von Mises effective stress, f (a function of equivalent plastic strain ep ) is the static plastic stress–strain response, and R (a p function of plastic strain rate ddte ) defines the ratio of flow strength at higher strain rates to the static flow strength where R equals unity. Compared to rate-independent plasticity, this formulation utilizes the scaling parameter R to quantify the ‘‘strain-rate hardening” effect. In this study the R values are 1.0, 1.9, 2.4, 2.8, 3.1, 3.4 and 3.5 at the plastic strain rates of, respectively, 0.005, 0.5, 6, 50, 100, 200 and 300 s1. It is noted that the stress–strain curves given in Ref. [10] are based on compressive tests. The present study assumes that the same rate-dependent behavior can be applied to tension, shear and multiaxial loading in general. A progressive ductile damage model is utilized to simulate failure of the solder alloy. Fig. 2 shows a schematic of the stress–strain curve which includes the damage response (solid curve) [35]. The damage process is quantified by a scalar damage parameter D, with
Fig. 4. Contour plots of: (a) shear stress rxy and (b) equivalent plastic strain at the nominal shear strain of 0.05, for the case of 10 s1 shear strain rate.
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r ¼ ð1 DÞr ;
ð2Þ
is the flow stress in the abwhere r is the current flow stress and r sence of damage. In addition to leading to softening of the plastic stress, damage is also manifested by the degradation of elastic modulus as shown by the dashed unloading/reloading line in Fig. 2. The pl equivalent plastic strains are epl 0 and ef at the onset of damage (D = 0) and failure (D = 1), respectively. A material element loses its capability to carry stress when its D attains unity, at which point the element will be removed from the mesh so a ‘‘void” thus develops. Cracking is then a consequence of linking multiple adjacent voids in the model. Note that removal of an element, an evolving process throughout the simulation history determined by the computational analysis, takes place when maximum degradation is reached at any one of its integration points [35]. rhyd In general epl 0 can be made a function of the stress triaxiality, re , where rhyd ¼ 13 ðrxx þ ryy þ rzz Þ is the hydrostatic stress and re is the von Mises effective stress. In the present study epl 0 is assumed to be independent of stress triaxiality due to the lack of systematic experimental data that may be used for defining the functional form. Upon damage initiation, strain softening and thus strain localization set in, which displays a strong mesh dependency. To alleviate the problem, a characteristic length L is used in the model, with
p ¼ Lep u p
ð3Þ
where u represents a plastic displacement quantity, and L is defined as the square root of the integration point area in each finite element. The softening phenomenon is now expressed as a stress– displacement relationship [36]. Prior to the initiation of damage, p ¼ 0; after damage initiation Eq. (3) starts to take effect. Failure u
p reaches the specified (and removal) of the element occurs when u pf . The evolution of the damage parameter is taken to failure value, u follow a linear form
D¼
p u : pf u
ð4Þ
The damage response is thus completely specified by the two p parameters epl 0 and uf . In the present study they are chosen to be 0.18 and 3 lm, respectively. It is noted that the chosen value of pf corresponds to a epl u f value of approximately 0.5. These parameters were based on some measured tensile stress–strain curves of bulk pure Sn or Sn-rich solder alloy [37–39]. It is understood that bulk materials and actual solder joints have significantly different physical sizes and microstructure and thus different constitutive responses. In addition, tensile loading tends to promote microvoid nucleation and coalescence, resulting in easier damage compared to other forms of loading. The present set of damage parameters should be viewed only as a lower-limit approximation. It is worth mentioning that, in our preliminary calculation, we have also used epl p 0 and uf values three times of those chosen above, and the fundamental failure features remained unchanged [40]. The finite element program Abaqus [35] was employed for the modeling, which features the explicit dynamics procedure well suited for analyzing the dynamic transient response of materials. The solder/intermetallic structure was discretized into 5000 fournoded linear elements, and each Cu substrate was discretized into 2400 elements. The mesh convergence was checked by another set of preliminary calculations using twice the number of elements in the model. In this study the nominal shear strain rate imposed on the solder joint is defined to be vhx (see Fig. 1) and the nominal
Fig. 5. Contour plots of: (a) shear stress rxy and (b) equivalent plastic strain at the nominal shear strain of 0.05, for the case of 100 s1 shear strain rate.
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v
tensile or compressive strain rates are defined as hy . We consider three different nominal shear strain rates: 1 s1, 10 s1 and 100 s1. These values are within the range of strain rate of interest in mobile device applications [10]. In Section 3.1, results of the shear loading are presented. Sections 3.2 and 3.3 are devoted to the effect of superimposed tension and compression, respectively. In particular, we use the ratio of nominal tensile (compressive) strain rate and nominal shear strain rate to quantify the different modes of loading. The tension (compression)/shear ratios of 1/1, 1/5, 1/10 and 1/20 are used for the presentation of results in Sections 3.2 and 3.3.
3. Results and discussion 3.1. Shear loading In this section the modeling results on the nominal shear loading of the solder joint are presented. We first examine the deformation fields prior to the initiation of fracture. Fig. 3a and b shows the contour plots of shear stress rxy and equivalent plastic strain, respectively, at a nominal shear strain of 0.05 for the case of 1 s1 shear strain rate. For clarity only a small portion of each copper substrate is included in the figure. The corresponding plots for the strain rates of 10 s1 and 100 s1 are shown in Figs. 4 and 5, respectively. It can be seen from Figs. 3a, 4a and 5a that the shear stress field in the solder is non-uniform, especially near the side surfaces and interfaces. The negative stress values are due to the choice of shear direction in this study. At the same nominal shear
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strain, the stress magnitude in solder increases as the applied strain rate increases owing to the viscoplastic effect. For example, in the center region of the joint the shear stress is about 30 MPa and 50 MPa under the applied shear strain rates of 1 s1 and 100 s1, respectively. Extensive plastic deformation has occurred in all cases. The equivalent plastic strain contours in Figs. 3b, 4b and 5b show very different patterns. Plastic deformation is localized near the interface region when the applied strain rate is small (Fig. 3b). In the other two cases, however, high plastic strains are seen around the four corners, and there is a tendency for the relatively high-strain regions to form a band parallel to the interface but inside the solder (Fig. 5b). This has implications for the damage evolution as will be shown below. Attention is now turned to the ductile failure pattern in solder under the different applied strain rates. Fig. 6a and b shows the contour plots of equivalent plastic strain along with the cracks (removed elements), during the cracking process and upon final failure, respectively, for the case of 1 s1 applied strain rate. Note that final failure occurs when a major crack traversing the entire span of the solider joint is formed. The corresponding contour plots for the cases of 10 s1 and 100 s1 strain rates are shown in Figs. 7 and 8, respectively. In all cases the initiation of cracks appears at the four corners of the solder joint. Crack propagation follows the path of greatest equivalent plastic strain, which in turn is evolving during the deformation and damage processes. In Fig. 6a local fracture at the top interface, away from the corners, can also be discerned. Final failure shows a cracking path along the interface between the solder and the intermetallic for the most part, but on the right hand side there is also a significant crack segment
Fig. 6. Contour plots of equivalent plastic strain and the evolution of failure, (a) during the cracking process (at nominal shear strain 0.094) and (b) upon final failure (nominal shear strain 0.104). The applied shear strain rate is 1 s1.
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close to, but not at, the interface (Fig. 6b). It is worth pointing out that the current numerical model does not include any true interface failure features; the simulated ‘‘interface” fracture is still due to the ductile damage model of solder adopted in the analysis. Nevertheless, it is also true that such mode of ductile fracture can indeed occur adjacent to the interface and thus leave an impression of ‘‘interface delamination” in actual solder joints. A different form of cracking pattern is observed when the applied shear strain rates are higher, as in Figs. 7 and 8. Cracks still initiate in the corner regions, and they first tend to grow inward along the near 45° direction. However, due to the dominant shear deformation mode, a band of strong plastic deformation in the horizontal direction gradually forms parallel to each interface. Damage therefore localized along the band where final linkage of cracks takes place. Note that in these two fast loading conditions, the ‘‘strain-rate hardening” effect is particularly strong and any concentration of plasticity adjacent to the interface is quickly ‘‘diffused” away, leading to a crack path farther from the interface. By comparing Figs. 6b, 7b and 8b, the greater distortion of the joint at final failure in the latter two cases is evident. The nominal shear strains at failure, defined to be the ‘‘ductility” of the solder joint, are 0.104, 0.295 and 0.290 under the applied shear strain rates of 1 s1, 10 s1 and 100 s1, respectively. This information is also listed in Table 1 (the row with the tension/shear ratio of zero). Conventional thinking stipulates that a metal tends to become more brittle under a higher strain rate, which is mainly associated with the intrinsic microstructural and defect mechanisms. The intermetallic and true interfacial characteristics also contribute to the failure behavior affected by the loading rate in real-life solder joints. However, the current theoretical study, which iso-
lates the effect of strain rate on the ductile damage evolution, suggests that the solder joint can actually display higher apparent ductility as the applied strain rate increases. This is due to the highly non-uniform deformation field and the associated alteration of failure path as seen above. As a consequence, this study brings about the possibility of improving solder joint ductility under drop and impact conditions, through proper design and choice of materials and geometry that may facilitate a more ductile type of cracking path. 3.2. Effects of superimposed tension on shear failure We now consider the superimposed tension on the shear failure of the solder. As described in Section 2, it is assumed that the normal stress is generated by a constant velocity in the y-direction, imposed on the bottom boundary of the lower copper substrate (simultaneously with the shear deformation). A given applied velocity in y results in a constant nominal tensile strain rate in the solder. Different tensile strain rates were chosen so as to give different ratios of tensile strain rate to shear strain rate. With a fixed time of deformation, the total tensile strain and shear strain also follow the same ratio. It should be noted that the present approach is an idealization of the loading condition, for the purpose of gaining a first-order insight into the phenomenon. In actual drop and impact scenarios, the strain rate experienced by the solder joint will not be constant and should be of pulsed vibrational form. A large number of simulations were carried out; to conserve space only salient results are included in the presentation. Before the effects of superimposed tension can be examined, failure patterns for the baseline case of pure tension are first
Fig. 7. Contour plots of equivalent plastic strain and the evolution of failure, (a) during the cracking process (at nominal shear strain 0.275) and (b) upon final failure (nominal shear strain 0.295). The applied shear strain rate is 10 s1.
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Fig. 8. Contour plots of equivalent plastic strain and the evolution of failure, (a) during the cracking process (at nominal shear strain 0.27) and (b) upon final failure (nominal shear strain 0.29). The applied shear strain rate is 100 s1.
presented. Fig. 9a–c shows the contour plots of equivalent plastic strain along with the cracking pattern upon final fracture, under pure tensile loading with the nominal tensile strain rates of 1, 10 and 100 s1, respectively. In the case of the lowest strain rate, cracks first form along the interface between the solder and the intermetallic layer. They then link up along the near 45° direction which is the highest shear path (Fig. 9a). A similar kind of damage mode is seen for the higher strain rates (Fig. 9b and c), with the exception that the interface part of the failure does not exist. This is again due to the strong strain-rate hardening effect when the applied tensile strain rate is high. With the tensile loading superimposed on shear, the failure pattern as well as the overall solder joint ductility are both affected. Table 1 lists the ductility of the solder joint, defined to be the nominal shear strain at failure, under the different nominal shear strain rates (1, 10 and 100 s1) and the tension/shear ratios of 0, 1/20, 1/ 10, 1/5 and 1/1. The ratio of zero corresponds to the case of shear
Table 1 Ductility of the solder joint (defined to be the nominal shear strain at failure) under the different nominal shear strain rates (1, 10 and 100 s1) and the tension/shear ratio. The ratio of zero means that only shear loading is imposed. Tension/shear ratio
1 s1
10 s1
100 s1
0 1/20 1/10 1/5 1/1
0.104 0.098 0.108 0.130 0.090
0.295 0.307 0.326 0.214 0.084
0.290 0.312 0.290 0.215 0.076
loading in Section 3.1. It can be seen that, for a small tension/shear ratio such as 1/20 and 1/10, the ductility follows the same trend as the case of no tension: about 0.1 for the strain rate of 1 s1 and about 0.3 for the strain rates of 10 and 100 s1. With a tension/ shear ratio of 1/5, the trend is still similar although the ductility under 1 s1 has increased and those for the higher rates have decreased somewhat. In the last row of Table 1 (tension/shear ratio of 1/1), the ductility values for all strain rates fall below 0.1, with a decreasing ductility as the strain rate increases. Therefore a high component of tension is seen to have a detrimental influence. Results on the fracture morphology due to superimposed tension are summarized in Table 2. Since pure tension and pure shear result in distinctly different failure appearances (near 45° in tension and mostly parallel to the interface in shear), the mixed-mode effect can be observed from the cracking configuration in a straightforward manner. Table 2 lists the apparent dominant failure mode (‘‘tension” or ‘‘shear”) for each combination of the shear strain rates and the tension/shear ratios. It can be seen that the superimposed tension can influence the failure model to a great extent. The influence becomes larger as the shear strain rate increases. For instance, at 100 s1, even a small tension/shear ratio (1/10) can force the cracking to follow the tensile mode. For smaller shear strain rates, a greater ratio is needed to change the mode. It is also observed that the failure mode itself does not have a clear one-to-one correlation with the ductility defined in Table 1. We chose two representative contour plots showing the failure morphology to present here, in Fig. 10, which pertain to the case of 100 s1 strain rate with the tension/shear ratios of 1/20 (part (a)) and 1/10 (part (b)) at the onset of final fracture. It is evident that
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Fig. 9. Contour plots of equivalent plastic strain and cracking pattern upon final fracture, in the case of pure tensile loading, under the nominal strain rates of: (a) 1 s1, (b) 10 s1 and (c) 100 s1.
the mode of failure indeed appears in a distinct manner, shear in Fig. 10a and tension in Fig. 10b corresponding to the information provided in Table 2. It is interesting to note in Fig. 10b that, near the upper-left and lower-right regions in the solder, there was actually a tendency to develop shear-like failure at the early stage of cracking. However, under the influence of tensile loading the two cracks linked up rather than propagated parallel to the interface, leading to an overall tensile failure model.
3.3. Effects of superimposed compression on shear failure Attention is now turned to superimposed compression. Results on pure compression is first presented in Fig. 11, where parts (a–c) shows the contour plots of equivalent plastic strain and cracking pattern under the nominal compressive strain rates of 1, 10 and 100 s1, respectively. It can be seen that the evolution of failure shows similar general features as in the case of pure tension. Initial
Y.-L. Shen, K. Aluru / Microelectronics Reliability 50 (2010) 2059–2070 Table 2 Dominant failure mode (‘‘tension” or ‘‘shear”) observed from the finite element simulation when tensile loading was superimposed on shear. Tension/shear ratio
1 s1
10 s1
100 s1
1/20 1/10 1/5 1/1
Shear Shear Shear Tension
Shear Shear Tension Tension
Shear Tension Tension Tension
cracking along the interface between the solder and the intermetallic occurs when the strain rate is low. Final fracture, however, takes the near 45° path in all cases. Note that the ‘‘overlapping” of solder and substrate after failure observed in Fig. 11a, due to the fact that there is no contact algorithm implemented in the simulation, is unphysical. Nevertheless, the fundamental features of ductile damage obtained from the simulation are still valid. Table 3 lists the ductility of the solder joint under the different nominal shear strain rates (1, 10 and 100 s1) and the compression/shear ratios of 0, 1/20, 1/10, 1/5 and 1/1. As before the ductility is defined to be the nominal shear strain at failure. The general trend is seen to be the same as in pure tension (Table 1). With a compression/shear ratio less than 1/5, the 1 s1 shear strain rate results in lower ductility values compared to the 10 and 100 s1 strain rates. However when the ratio is increased to 1/1, consistently low ductility is obtained regardless of the applied strain rate.
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The dominant failure modes for the various combinations of shear and compressive strain rates are listed in Table 4. Here the same strain rates and ratios as in the case of tension are included. In general, a similar type of behavior is seen. The only difference between the results in Tables 4 and 2 is that, at a shear strain rate of 100 s1 and the compression/shear ratio of 1/10, the failure mode is shear but in Table 2 the corresponding mode is tension. The effect of superimposed compression is thus only slightly smaller compared to superimposed tension. As in Section 3.2, out of the results summarized in Table 4 two contour plots were chosen for presentation here. Fig. 12a and b shows the plots corresponding to the compression/shear ratios of 1/10 and 1/5, respectively, under the nominal shear strain of 100 s1. As in the case of superimposed tension, the failure mode appears in a distinct manner, with either the compression model or the shear mode (although the loading has both the compression and shear components). On the basis of the presentation above, it is clear that ductile failure of the solder joint is very sensitive to the deformation mode. Under the constant strain rate conditions considered in this study, both the superimposed tension and compression can dramatically change the shear-induced failure morphology. Experimental studies correlating the shear strain rate and failure pattern in solder, under the constant high rate conditions with controlled superimposed tension or compression, are not available in a systematic way. For instance, high speed lap-shear tests of Sn–Pb solder joints
Fig. 10. Contour plots of equivalent plastic strain along with the cracking pattern upon final fracture, in the cases of combined tension/shear loading with the tension/shear ratios of: (a) 1/20 and (b) 1/10, under the nominal shear strain rates of 100 s1.
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Fig. 11. Contour plots of equivalent plastic strain and cracking pattern upon final fracture, in the case of pure compressive loading, under the nominal strain rates of: (a) 1 s1, (b) 10 s1 and (c) 100 s1.
Table 3 Ductility of the solder joint (defined to be the nominal shear strain at failure) under the different nominal shear strain rates (1, 10 and 100 s1) and the compression/shear ratio. The ratio of zero means that only shear loading is imposed. Compression/shear ratio
1 s1
10 s1
100 s1
0 1/20 1/10 1/5 1/1
0.104 0.110 0.120 0.150 0.084
0.295 0.286 0.288 0.226 0.082
0.290 0.299 0.290 0.220 0.072
Table 4 Dominant failure mode (‘‘compression” or ‘‘shear”) observed from the finite element simulation when compressive loading was superimposed on shear. Compression/shear ratio
1 s1
10 s1
100 s1
1/20 1/10 1/5 1/1
Shear Shear Shear Compression
Shear Shear Compression Compression
Shear Shear Compression Compression
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Fig. 12. Contour plots of equivalent plastic strain along with the cracking pattern upon final fracture, in the cases of combined compression/shear loading with the compression/shear ratios of: (a) 1/10 and (b) 1/5, under the nominal shear strain rates of 100 s1.
using the applied strain rates similar to the range considered in the present work, without the tension or compression components, have been reported [9]. However, the correlation between the shear failure pattern and the strain rate was not specifically addressed. As a consequence, a direct comparison between the modeling results with experiments is not possible. Future experimental investigations mimicking the present modeling approach, using controlled shear and normal strain rates (but not from direct drop test of circuit boards), are thus recommended. Nevertheless, the present study has demonstrated the feasibility of utilizing the ductile damage model in quantitatively predicting mechanical failure of solder joint. The modeling also offered mechanistic insight into the failure pattern affected by the combined shear and tension/ compression loading. Further analyses may be built upon the present model with complicated deformation histories, such as pulsed or cyclic strain rates and/or more randomly related shear and normal stress components, to predict solder joint reliability in more realistic settings. The incorporation of brittle failure in the intermetallic layer and along the interfaces is another important extension of the present work. 4. Conclusions Numerical finite element analyses were carried out to study ductile damage in solder joints under fast loading conditions. The effects of applied strain rate (in the range of 1–100 s1) and loading mode (shear with possible superimposed tension or compression)
on the shear ductility and failure pattern were investigated. It was found that under the shear loading mode, the ductility of solder increases as the applied strain rate increases. Final cracking is predominantly along the interface when the strain rate is relatively low (1 s1) but becomes away from the interface as the strain rate increases. The off-interface failure pattern leads to a higher ductility of the joint. The shear-induced failure pattern can be strongly affected by the superimposed tension and compression of the solder joint. With the tension or compression strain rate being only a small fraction of the shear strain rate, the failure pattern can change from the ‘‘shear mode” (near interface) to the ‘‘tension/ compression mode” (near 45° direction). Both the superimposed tension and compression can lead to a decrease in overall ductility, thus showing a negative impact on the solder joint reliability.
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[5] Lall P, Gupte S, Choudhary P, Suhling J. Solder joint reliability in electronics under shock and vibration using explicit finite-element submodeling. IEEE Trans Electron Packag Manuf 2007;30:74–83. [6] Syed A, Lin W, Sohn E-S, Cha S-W. Plastic deformation and life prediction of solder joints for mechanical shock and drop/impact loading conditions. In: Proc IEEE 2007 Electron Compon Technol Conf, p. 507–14. [7] Jang J-W, De Silva AP, Drye JE, Post SL, Owens NL, Lin J-K, et al. Failure morphology after drop impact test of ball grid array (BGA) package with leadfree Sn–3.8Ag–0.7Cu and eutectic SnPb solders. IEEE Trans Electron Packag Manuf 2007;30:49–53. [8] Chou CY, Hung TY, Yang SY, Yew MC, Yang WK, Chiang KN. Solder joint and trace line failure simulation and experimental validation of fan-out type wafer level packaging subjected to drop impact. Microelectron Reliab 2008;48:1149–54. [9] Jeon S-J, Hyun S, Lee H-J, Kim J-W, Ha S-S, Yoon J-W, et al. Mechanical reliability evaluation of Sn–37Pb solder joint using high speed lap-shear test. Microelectron Eng 2008;85:1967–70. [10] Wong E-H, Selvanayagam CS, Seah SKW, van Driel WD, Caers JFJM, Zhao XJ, et al. Stress–strain characteristics of tin-based solder alloys for drop-impact modeling. J Electron Mater 2008;37:829–36. [11] Lall P, Panchagade DR, Choudhary P, Gupte S, Suhling JC. Failure-envelope approach to modeling shock and vibration survivability of electronic and MEMS packaging. IEEE Trans Compon Packag Technol 2008;31:104–13. [12] Liu F, Meng G, Zhao M, Zhao JF. Experimental and numerical analysis of BGA lead-free solder joint reliability under board-level drop impact. Microelectron Reliab 2009;49:79–85. [13] Wong EH, Seah SKW, van Driel WD, Caers JFJM, Owens N, Lai Y-S. Advances in the drop-impact reliability of solder joints for mobile applications. Microelectron Reliab 2009;49:139–49. [14] Plumbridge WJ. Solders in electronics. J Mater Sci 1996;31:2501–14. [15] Abtew M, Selvaduray G. Lead-free solders in microelectronics. Mater Sci Eng R 2000;27:95–141. [16] Suganuma K. Advances in lead-free electronics soldering. Current Opin Solid State Mater Sci 2001;5:55–64. [17] Ladani LJ, Dasgupta A, Cardoso I, Monlevade E. Effect of selected process parameters on durability and defects in surface-mount assemblies for portable electronics. IEEE Trans Electron Packag Manuf 2008;31:51–60. [18] Subramanian KN, Lee JG. Physical metallurgy in lead-free electronic solder development. JOM 2003;55(5):26–32. [19] Tu KN, Gusak AM, Li M. Physics and materials challenges for lead-free solders. J Appl Phys 2003;93:1335–53. [20] Ma H, Suhling JC. A review of mechanical properties of lead-free solders. J Mater Sci 2009;44:1141–58. [21] Wright C. Effect of solid-state reactions upon solder lap shear strength. IEEE Trans Parts Hybrids Packag 1977;13:202–7.
[22] Frear D, Grivas D, Morris JW. Parameters affecting thermal fatigue behavior of 60Sn–40Pb solder joints. J Electron Mater 1989;18:671–80. [23] Tomlinson WJ, Fullylove A. Strength of tin-based soldered joints. J Mater Sci 1992;27:5777–82. [24] Raeder CH, Felton LE, Tanzi VA, Knorr DB. The effect of aging on microstructure, room-temperature deformation, and fracture of Sn–Bi/Cu solder joints. J Electron Mater 1994;23:611–7. [25] Frear DR. The mechanical behavior of interconnect materials for electronic packaging. JOM 1996;48:49–53. [26] Poon NM, Wu CML, Lai JKL, Chan YC. Residual shear strength of Sn–Ag and Sn– Bi lead-free SMT joints after thermal shock. IEEE Trans Adv Packag 2000;23:708–14. [27] Lee WW, Nguyen LT, Selvaduray GS. Solder joint fatigue models: review and applicability to chip scale packages. Microelectron Reliab 2000;40:231–44. [28] Pang JHL, Tan KH, Shi XQ, Wang ZP. Microstructure and intermetallic growth effects on shear and fatigue strength of solder joints subjected to thermal cycling aging. Mater Sci Eng A 2001;307:42–50. [29] Lee JG, Guo F, Choi S, Subramanian KN, Bieler TR, Lucas JP. Residual-mechanical behavior of thermomechanically fatigued Sn–Ag based solder joints. J Electron Mater 2002;31:946–52. [30] Chawla N, Shen Y-L, Deng X, Ege ES. An evaluation of the lap-shear test for Snrich solder/Cu couples: experiments and simulation. J Electron Mater 2004;33:1589–95. [31] Shen Y-L, Abell KCR, Garrett SE. Effects of grain boundary sliding on microstructural evolution and damage accumulation in tin-lead alloy. Int J Damage Mech 2004;13:225–40. [32] Shen Y-L, Chawla N, Ege ES, Deng X. Deformation analysis of lap-shear testing of solder joints. Acta Mater 2005;53:2633–42. [33] Moy WH, Shen Y-L. On the failure path in shear-tested solder joints. Microelectron Reliab 2007;47:1300–5. [34] Shen Y-L. Externally constrained plastic flow in miniaturized metallic structures: a continuum-based approach to thin films, lines, and joints. Prog Mater Sci 2008;53:838–91. [35] Abaqus 6.8, User’s Manual, Dassault Systèmes Simulia Corp., Providence, RI. [36] Hillerborg A, Modeer M, Petersson PE. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement Concr Res 1976;6:773–81. [37] Chanthery S. M.S. Thesis, University of New Mexico; 2004. [38] Adeva P, Caruana G, Ruano OA, Torralba M. Microstructure and high temperature mechanical properties of tin. Mater Sci Eng A 1995;194:17–23. [39] Ochoa F, Williams JJ, Chawla N. Effects of cooling rate on the microstructure and tensile behavior of a Sn–3.5 wt.%Ag solder. J Electron Mater 2003;32:1414–20. [40] Aluru K, M.S. Thesis, University of New Mexico; 2009.
Contents lists available at ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel
Numerical study of ductile failure morphology in solder joints under fast loading conditions Y.-L. Shen *, K. Aluru Department of Mechanical Engineering, University of New Mexico, Albuquerque, NM 87131, United States
a r t i c l e
i n f o
Article history: Received 15 February 2010 Received in revised form 5 May 2010 Available online 26 June 2010
a b s t r a c t A numerical study is undertaken to investigate solder joint failure under fast loading conditions. The finite element model assumes a lap-shear testing configuration, where the solder joint is bonded to two copper substrates. A progressive ductile damage model is incorporated into the rate-dependent elastic-viscoplastic response of the tin (Sn)–silver (Ag)–copper (Cu) solder alloy, resulting in the capability of simulating damage evolution leading to eventual failure through crack formation. Attention is devoted to deformation under relative high strain rates (1–100 s1), mimicking those frequently encountered in drop and impact loading of the solder points. The effects of applied strain rate and loading mode on the overall ductility and failure pattern are specifically investigated. It is found that, under shear loading, the solder joint can actually become more ductile as the applied strain rate increases, which is due to the alteration of the crack path. Failure of the solder is very sensitive to the deformation mode, with a superimposed tension or compression on shear easily changing the crack path and tending to reduce the solder joint ductility. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Mechanical failure of solder joints has been a serious reliability problem in microelectronic packages. Deformation of solder can be a result from the thermal expansion mismatch between the components (e.g., semiconductor chip, chip carrier, and/or printed circuit board) they connect, causing predominant shearing of the joint. In addition, when direct mechanical loading is imposed on the packaging structure, the solder joint can also experience shear as well as tensile and compressive deformations. Damage can be induced by the excessive monotonic or cyclic plastic deformation and/or creep inside the solder alloy, or by more brittle forms of failure along the thin intermetallic layer at the interfacial region of the joint. Failure of solder due to drop and impact of the components has emerged to be an important issue to the industry in recent years (see, e.g., [1–13]). This is different from the traditional thermomechanical fatigue problem, since the loading rate involved in drop and impact can be several orders of magnitude higher than that during thermal cycling. An additional concern is for the tin (Sn)-based lead (Pb)-free solders [14–20] being used and/or developed as environment-friendly replacements of the conventional Pb-bearing solder. Since the Pb-free solder alloys are generally more brittle compared to the conventional Sn–Pb eutectic, they may be more susceptible to failure caused by dynamic loading. * Corresponding author. E-mail address: [email protected] (Y.-L. Shen). 0026-2714/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.microrel.2010.06.001
During drop impact, the individual solder joints are not in general under direct mechanical shock. Rather, it is the flexural bending of the circuit board that forces the solder to undergo large deformation [7,10,12,13]. Thus, depending on the geometry and material of the test vehicle, detailed test condition or real-life drop scenario, and the location of the particular joint of interest, solder joints can experience shear, compression, tension and their combination during the dynamic loading history. The existence of fluctuating tension–compression experienced by the individual joint has been shown from experiments and package-level numerical modeling [4,6,12]. Finite element modeling has been a powerful tool in predicting and analyzing solder deformation. In the present work we report a systematic finite element analysis which concerns not only deformation but also damage and failure of solder joints. Attention is devoted to the morphology of ductile failure inside the solder under relatively fast loading rates. The model utilizes a simple lap-shear test setting, with nominally constant strain rates applied to the solder. This study includes the following salient features. The rate-dependent response of a tin-silver (Ag)–copper (Cu) solder is used in the model to specifically address the loading rate effect. A ductile damage model is incorporated, which, in conjunction with the element removal process in the explicit numerical scheme, is capable of simulating direct failure of the material. A parametric analysis is undertaken, which considers the superimposed tensile or compressive deformation on the shear
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D=0
Dσ σ0
H w
solder E
E
(1-D)E
vx
h
D=1
ε
pl 0
W
y
σ
σ
Copper
ε
ε
pl f
Fig. 2. Schematic showing the ductile damage response, in terms of the uniaxial stress–strain curve.
x
Copper
vy Fig. 1. Schematic of the solder joint model (plot not to scale) along with the boundary conditions. The applied velocities vx and vy give rise to the nominal shear and tensile (or compressive) deformations, respectively, of the solder. The dimensions used in the finite element analysis are: w = 1 mm, h = 0.5 mm, H = 2.5 mm and W = 0.5 mm.
deformation mode, so its effect on the cracking pattern can be examined. The primary objective of this work is to apply the damage modeling technique for gaining a baseline understanding on the evolution of ductile damage, without the possible interference of brittle
interfacial or intermetallic fracture. We aim to laying the foundation for developing comprehensive predictive modeling capabilities, to address the increasing concern of solder reliability under the high loading rate conditions. 2. Model description The computational model is schematically shown in Fig. 1, with the solder material bonded to two copper (Cu) blocks (termed ‘‘substrates” in this paper). The width (w) and thickness (h) of the solder joint are taken to be 1 mm and 0.5 mm, respectively. The substrate dimensions H and W are 2.5 mm and 0.5 mm, respectively. Note that W refers to the part of substrate outside the solder width. At each interface between the solder and the
Fig. 3. Contour plots of: (a) shear stress rxy and (b) equivalent plastic strain at the nominal shear strain of 0.05, for the case of 1 s1 shear strain rate.
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substrate, there is a 5 lm-thick intermetallic layer included in the model (not specifically shown in Fig. 1). Deformation of solder is induced by prescribing constant boundary velocities, vx and/or vy, at the far right edge and bottom, respectively, of the lower substrate. The velocity vx will give rise to a nominal shear deformation (i.e., the typical lap-shear test [9,21–31]). Depending on the direction of the prescribed vy, either nominal tension or compression can be superimposed on the solder. It is noted that, in actual high-rate loading situations such as drop and impact, the boundary velocities will not be constant. Nevertheless we adopt this simple modeling scheme to aid in a fundamental understanding. More realistic deformation histories may be incorporated into the analysis in a straightforward manner. During deformation the x-direction movement of the far left edge of the upper Cu is forbidden, but movement in the y-direction is allowed except that the upper-left corner of the upper substrate is totally fixed. The top boundary of the upper Cu is also fixed in the y-direction but its x-movement is allowed. The calculations were based on the plane strain condition, which effectively simulates the nominal simple shearing mode of the solder [32–34]. It is acknowledged, however, that the plane strain condition results in certain over-constraint under tensile or compressive loading. (In the plastic p regime the ffiffiffi flow stress is increased by a factor of approximately 2= 3, following the von Mises yield criterion.) In the model the Cu substrate is taken to be isotropic linear elastic, with Young’s modulus of 114 GPa, Poisson’s ratio of 0.31 and density of 8930 kg/m3. The Cu6Sn5 intermetallic layer is also assumed to be isotropic linear elastic, with Young’s modulus of 85.5 GPa, Poisson’s ratio of 0.28 and density of 8280 kg/m3. The
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solder, taken to be the Sn–1.0Ag–0.1Cu alloy [10], is treated as an isotropic elastic-viscoplastic solid, with Young’s modulus of 47 GPa, Poisson’s ratio of 0.36 and density of 5760 kg/m3. Its yielding and strain hardening response follows the experimental stress– strain curves for different strain rates [10]. At the strain rate of 0.005 s1 or below, the initial yield strength is 20 MPa; the flow strength increases to a peak value of 36 MPa at the plastic strain of 0.15, beyond which a perfectly plastic behavior is assumed. This slow-rate form is considered as the ‘‘static” response. The ratedependent plastic flow strength follows
re ¼ f ðep Þ R
p de ; dt
ð1Þ
where re is the von Mises effective stress, f (a function of equivalent plastic strain ep ) is the static plastic stress–strain response, and R (a p function of plastic strain rate ddte ) defines the ratio of flow strength at higher strain rates to the static flow strength where R equals unity. Compared to rate-independent plasticity, this formulation utilizes the scaling parameter R to quantify the ‘‘strain-rate hardening” effect. In this study the R values are 1.0, 1.9, 2.4, 2.8, 3.1, 3.4 and 3.5 at the plastic strain rates of, respectively, 0.005, 0.5, 6, 50, 100, 200 and 300 s1. It is noted that the stress–strain curves given in Ref. [10] are based on compressive tests. The present study assumes that the same rate-dependent behavior can be applied to tension, shear and multiaxial loading in general. A progressive ductile damage model is utilized to simulate failure of the solder alloy. Fig. 2 shows a schematic of the stress–strain curve which includes the damage response (solid curve) [35]. The damage process is quantified by a scalar damage parameter D, with
Fig. 4. Contour plots of: (a) shear stress rxy and (b) equivalent plastic strain at the nominal shear strain of 0.05, for the case of 10 s1 shear strain rate.
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r ¼ ð1 DÞr ;
ð2Þ
is the flow stress in the abwhere r is the current flow stress and r sence of damage. In addition to leading to softening of the plastic stress, damage is also manifested by the degradation of elastic modulus as shown by the dashed unloading/reloading line in Fig. 2. The pl equivalent plastic strains are epl 0 and ef at the onset of damage (D = 0) and failure (D = 1), respectively. A material element loses its capability to carry stress when its D attains unity, at which point the element will be removed from the mesh so a ‘‘void” thus develops. Cracking is then a consequence of linking multiple adjacent voids in the model. Note that removal of an element, an evolving process throughout the simulation history determined by the computational analysis, takes place when maximum degradation is reached at any one of its integration points [35]. rhyd In general epl 0 can be made a function of the stress triaxiality, re , where rhyd ¼ 13 ðrxx þ ryy þ rzz Þ is the hydrostatic stress and re is the von Mises effective stress. In the present study epl 0 is assumed to be independent of stress triaxiality due to the lack of systematic experimental data that may be used for defining the functional form. Upon damage initiation, strain softening and thus strain localization set in, which displays a strong mesh dependency. To alleviate the problem, a characteristic length L is used in the model, with
p ¼ Lep u p
ð3Þ
where u represents a plastic displacement quantity, and L is defined as the square root of the integration point area in each finite element. The softening phenomenon is now expressed as a stress– displacement relationship [36]. Prior to the initiation of damage, p ¼ 0; after damage initiation Eq. (3) starts to take effect. Failure u
p reaches the specified (and removal) of the element occurs when u pf . The evolution of the damage parameter is taken to failure value, u follow a linear form
D¼
p u : pf u
ð4Þ
The damage response is thus completely specified by the two p parameters epl 0 and uf . In the present study they are chosen to be 0.18 and 3 lm, respectively. It is noted that the chosen value of pf corresponds to a epl u f value of approximately 0.5. These parameters were based on some measured tensile stress–strain curves of bulk pure Sn or Sn-rich solder alloy [37–39]. It is understood that bulk materials and actual solder joints have significantly different physical sizes and microstructure and thus different constitutive responses. In addition, tensile loading tends to promote microvoid nucleation and coalescence, resulting in easier damage compared to other forms of loading. The present set of damage parameters should be viewed only as a lower-limit approximation. It is worth mentioning that, in our preliminary calculation, we have also used epl p 0 and uf values three times of those chosen above, and the fundamental failure features remained unchanged [40]. The finite element program Abaqus [35] was employed for the modeling, which features the explicit dynamics procedure well suited for analyzing the dynamic transient response of materials. The solder/intermetallic structure was discretized into 5000 fournoded linear elements, and each Cu substrate was discretized into 2400 elements. The mesh convergence was checked by another set of preliminary calculations using twice the number of elements in the model. In this study the nominal shear strain rate imposed on the solder joint is defined to be vhx (see Fig. 1) and the nominal
Fig. 5. Contour plots of: (a) shear stress rxy and (b) equivalent plastic strain at the nominal shear strain of 0.05, for the case of 100 s1 shear strain rate.
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v
tensile or compressive strain rates are defined as hy . We consider three different nominal shear strain rates: 1 s1, 10 s1 and 100 s1. These values are within the range of strain rate of interest in mobile device applications [10]. In Section 3.1, results of the shear loading are presented. Sections 3.2 and 3.3 are devoted to the effect of superimposed tension and compression, respectively. In particular, we use the ratio of nominal tensile (compressive) strain rate and nominal shear strain rate to quantify the different modes of loading. The tension (compression)/shear ratios of 1/1, 1/5, 1/10 and 1/20 are used for the presentation of results in Sections 3.2 and 3.3.
3. Results and discussion 3.1. Shear loading In this section the modeling results on the nominal shear loading of the solder joint are presented. We first examine the deformation fields prior to the initiation of fracture. Fig. 3a and b shows the contour plots of shear stress rxy and equivalent plastic strain, respectively, at a nominal shear strain of 0.05 for the case of 1 s1 shear strain rate. For clarity only a small portion of each copper substrate is included in the figure. The corresponding plots for the strain rates of 10 s1 and 100 s1 are shown in Figs. 4 and 5, respectively. It can be seen from Figs. 3a, 4a and 5a that the shear stress field in the solder is non-uniform, especially near the side surfaces and interfaces. The negative stress values are due to the choice of shear direction in this study. At the same nominal shear
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strain, the stress magnitude in solder increases as the applied strain rate increases owing to the viscoplastic effect. For example, in the center region of the joint the shear stress is about 30 MPa and 50 MPa under the applied shear strain rates of 1 s1 and 100 s1, respectively. Extensive plastic deformation has occurred in all cases. The equivalent plastic strain contours in Figs. 3b, 4b and 5b show very different patterns. Plastic deformation is localized near the interface region when the applied strain rate is small (Fig. 3b). In the other two cases, however, high plastic strains are seen around the four corners, and there is a tendency for the relatively high-strain regions to form a band parallel to the interface but inside the solder (Fig. 5b). This has implications for the damage evolution as will be shown below. Attention is now turned to the ductile failure pattern in solder under the different applied strain rates. Fig. 6a and b shows the contour plots of equivalent plastic strain along with the cracks (removed elements), during the cracking process and upon final failure, respectively, for the case of 1 s1 applied strain rate. Note that final failure occurs when a major crack traversing the entire span of the solider joint is formed. The corresponding contour plots for the cases of 10 s1 and 100 s1 strain rates are shown in Figs. 7 and 8, respectively. In all cases the initiation of cracks appears at the four corners of the solder joint. Crack propagation follows the path of greatest equivalent plastic strain, which in turn is evolving during the deformation and damage processes. In Fig. 6a local fracture at the top interface, away from the corners, can also be discerned. Final failure shows a cracking path along the interface between the solder and the intermetallic for the most part, but on the right hand side there is also a significant crack segment
Fig. 6. Contour plots of equivalent plastic strain and the evolution of failure, (a) during the cracking process (at nominal shear strain 0.094) and (b) upon final failure (nominal shear strain 0.104). The applied shear strain rate is 1 s1.
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close to, but not at, the interface (Fig. 6b). It is worth pointing out that the current numerical model does not include any true interface failure features; the simulated ‘‘interface” fracture is still due to the ductile damage model of solder adopted in the analysis. Nevertheless, it is also true that such mode of ductile fracture can indeed occur adjacent to the interface and thus leave an impression of ‘‘interface delamination” in actual solder joints. A different form of cracking pattern is observed when the applied shear strain rates are higher, as in Figs. 7 and 8. Cracks still initiate in the corner regions, and they first tend to grow inward along the near 45° direction. However, due to the dominant shear deformation mode, a band of strong plastic deformation in the horizontal direction gradually forms parallel to each interface. Damage therefore localized along the band where final linkage of cracks takes place. Note that in these two fast loading conditions, the ‘‘strain-rate hardening” effect is particularly strong and any concentration of plasticity adjacent to the interface is quickly ‘‘diffused” away, leading to a crack path farther from the interface. By comparing Figs. 6b, 7b and 8b, the greater distortion of the joint at final failure in the latter two cases is evident. The nominal shear strains at failure, defined to be the ‘‘ductility” of the solder joint, are 0.104, 0.295 and 0.290 under the applied shear strain rates of 1 s1, 10 s1 and 100 s1, respectively. This information is also listed in Table 1 (the row with the tension/shear ratio of zero). Conventional thinking stipulates that a metal tends to become more brittle under a higher strain rate, which is mainly associated with the intrinsic microstructural and defect mechanisms. The intermetallic and true interfacial characteristics also contribute to the failure behavior affected by the loading rate in real-life solder joints. However, the current theoretical study, which iso-
lates the effect of strain rate on the ductile damage evolution, suggests that the solder joint can actually display higher apparent ductility as the applied strain rate increases. This is due to the highly non-uniform deformation field and the associated alteration of failure path as seen above. As a consequence, this study brings about the possibility of improving solder joint ductility under drop and impact conditions, through proper design and choice of materials and geometry that may facilitate a more ductile type of cracking path. 3.2. Effects of superimposed tension on shear failure We now consider the superimposed tension on the shear failure of the solder. As described in Section 2, it is assumed that the normal stress is generated by a constant velocity in the y-direction, imposed on the bottom boundary of the lower copper substrate (simultaneously with the shear deformation). A given applied velocity in y results in a constant nominal tensile strain rate in the solder. Different tensile strain rates were chosen so as to give different ratios of tensile strain rate to shear strain rate. With a fixed time of deformation, the total tensile strain and shear strain also follow the same ratio. It should be noted that the present approach is an idealization of the loading condition, for the purpose of gaining a first-order insight into the phenomenon. In actual drop and impact scenarios, the strain rate experienced by the solder joint will not be constant and should be of pulsed vibrational form. A large number of simulations were carried out; to conserve space only salient results are included in the presentation. Before the effects of superimposed tension can be examined, failure patterns for the baseline case of pure tension are first
Fig. 7. Contour plots of equivalent plastic strain and the evolution of failure, (a) during the cracking process (at nominal shear strain 0.275) and (b) upon final failure (nominal shear strain 0.295). The applied shear strain rate is 10 s1.
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Fig. 8. Contour plots of equivalent plastic strain and the evolution of failure, (a) during the cracking process (at nominal shear strain 0.27) and (b) upon final failure (nominal shear strain 0.29). The applied shear strain rate is 100 s1.
presented. Fig. 9a–c shows the contour plots of equivalent plastic strain along with the cracking pattern upon final fracture, under pure tensile loading with the nominal tensile strain rates of 1, 10 and 100 s1, respectively. In the case of the lowest strain rate, cracks first form along the interface between the solder and the intermetallic layer. They then link up along the near 45° direction which is the highest shear path (Fig. 9a). A similar kind of damage mode is seen for the higher strain rates (Fig. 9b and c), with the exception that the interface part of the failure does not exist. This is again due to the strong strain-rate hardening effect when the applied tensile strain rate is high. With the tensile loading superimposed on shear, the failure pattern as well as the overall solder joint ductility are both affected. Table 1 lists the ductility of the solder joint, defined to be the nominal shear strain at failure, under the different nominal shear strain rates (1, 10 and 100 s1) and the tension/shear ratios of 0, 1/20, 1/ 10, 1/5 and 1/1. The ratio of zero corresponds to the case of shear
Table 1 Ductility of the solder joint (defined to be the nominal shear strain at failure) under the different nominal shear strain rates (1, 10 and 100 s1) and the tension/shear ratio. The ratio of zero means that only shear loading is imposed. Tension/shear ratio
1 s1
10 s1
100 s1
0 1/20 1/10 1/5 1/1
0.104 0.098 0.108 0.130 0.090
0.295 0.307 0.326 0.214 0.084
0.290 0.312 0.290 0.215 0.076
loading in Section 3.1. It can be seen that, for a small tension/shear ratio such as 1/20 and 1/10, the ductility follows the same trend as the case of no tension: about 0.1 for the strain rate of 1 s1 and about 0.3 for the strain rates of 10 and 100 s1. With a tension/ shear ratio of 1/5, the trend is still similar although the ductility under 1 s1 has increased and those for the higher rates have decreased somewhat. In the last row of Table 1 (tension/shear ratio of 1/1), the ductility values for all strain rates fall below 0.1, with a decreasing ductility as the strain rate increases. Therefore a high component of tension is seen to have a detrimental influence. Results on the fracture morphology due to superimposed tension are summarized in Table 2. Since pure tension and pure shear result in distinctly different failure appearances (near 45° in tension and mostly parallel to the interface in shear), the mixed-mode effect can be observed from the cracking configuration in a straightforward manner. Table 2 lists the apparent dominant failure mode (‘‘tension” or ‘‘shear”) for each combination of the shear strain rates and the tension/shear ratios. It can be seen that the superimposed tension can influence the failure model to a great extent. The influence becomes larger as the shear strain rate increases. For instance, at 100 s1, even a small tension/shear ratio (1/10) can force the cracking to follow the tensile mode. For smaller shear strain rates, a greater ratio is needed to change the mode. It is also observed that the failure mode itself does not have a clear one-to-one correlation with the ductility defined in Table 1. We chose two representative contour plots showing the failure morphology to present here, in Fig. 10, which pertain to the case of 100 s1 strain rate with the tension/shear ratios of 1/20 (part (a)) and 1/10 (part (b)) at the onset of final fracture. It is evident that
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Fig. 9. Contour plots of equivalent plastic strain and cracking pattern upon final fracture, in the case of pure tensile loading, under the nominal strain rates of: (a) 1 s1, (b) 10 s1 and (c) 100 s1.
the mode of failure indeed appears in a distinct manner, shear in Fig. 10a and tension in Fig. 10b corresponding to the information provided in Table 2. It is interesting to note in Fig. 10b that, near the upper-left and lower-right regions in the solder, there was actually a tendency to develop shear-like failure at the early stage of cracking. However, under the influence of tensile loading the two cracks linked up rather than propagated parallel to the interface, leading to an overall tensile failure model.
3.3. Effects of superimposed compression on shear failure Attention is now turned to superimposed compression. Results on pure compression is first presented in Fig. 11, where parts (a–c) shows the contour plots of equivalent plastic strain and cracking pattern under the nominal compressive strain rates of 1, 10 and 100 s1, respectively. It can be seen that the evolution of failure shows similar general features as in the case of pure tension. Initial
Y.-L. Shen, K. Aluru / Microelectronics Reliability 50 (2010) 2059–2070 Table 2 Dominant failure mode (‘‘tension” or ‘‘shear”) observed from the finite element simulation when tensile loading was superimposed on shear. Tension/shear ratio
1 s1
10 s1
100 s1
1/20 1/10 1/5 1/1
Shear Shear Shear Tension
Shear Shear Tension Tension
Shear Tension Tension Tension
cracking along the interface between the solder and the intermetallic occurs when the strain rate is low. Final fracture, however, takes the near 45° path in all cases. Note that the ‘‘overlapping” of solder and substrate after failure observed in Fig. 11a, due to the fact that there is no contact algorithm implemented in the simulation, is unphysical. Nevertheless, the fundamental features of ductile damage obtained from the simulation are still valid. Table 3 lists the ductility of the solder joint under the different nominal shear strain rates (1, 10 and 100 s1) and the compression/shear ratios of 0, 1/20, 1/10, 1/5 and 1/1. As before the ductility is defined to be the nominal shear strain at failure. The general trend is seen to be the same as in pure tension (Table 1). With a compression/shear ratio less than 1/5, the 1 s1 shear strain rate results in lower ductility values compared to the 10 and 100 s1 strain rates. However when the ratio is increased to 1/1, consistently low ductility is obtained regardless of the applied strain rate.
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The dominant failure modes for the various combinations of shear and compressive strain rates are listed in Table 4. Here the same strain rates and ratios as in the case of tension are included. In general, a similar type of behavior is seen. The only difference between the results in Tables 4 and 2 is that, at a shear strain rate of 100 s1 and the compression/shear ratio of 1/10, the failure mode is shear but in Table 2 the corresponding mode is tension. The effect of superimposed compression is thus only slightly smaller compared to superimposed tension. As in Section 3.2, out of the results summarized in Table 4 two contour plots were chosen for presentation here. Fig. 12a and b shows the plots corresponding to the compression/shear ratios of 1/10 and 1/5, respectively, under the nominal shear strain of 100 s1. As in the case of superimposed tension, the failure mode appears in a distinct manner, with either the compression model or the shear mode (although the loading has both the compression and shear components). On the basis of the presentation above, it is clear that ductile failure of the solder joint is very sensitive to the deformation mode. Under the constant strain rate conditions considered in this study, both the superimposed tension and compression can dramatically change the shear-induced failure morphology. Experimental studies correlating the shear strain rate and failure pattern in solder, under the constant high rate conditions with controlled superimposed tension or compression, are not available in a systematic way. For instance, high speed lap-shear tests of Sn–Pb solder joints
Fig. 10. Contour plots of equivalent plastic strain along with the cracking pattern upon final fracture, in the cases of combined tension/shear loading with the tension/shear ratios of: (a) 1/20 and (b) 1/10, under the nominal shear strain rates of 100 s1.
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Fig. 11. Contour plots of equivalent plastic strain and cracking pattern upon final fracture, in the case of pure compressive loading, under the nominal strain rates of: (a) 1 s1, (b) 10 s1 and (c) 100 s1.
Table 3 Ductility of the solder joint (defined to be the nominal shear strain at failure) under the different nominal shear strain rates (1, 10 and 100 s1) and the compression/shear ratio. The ratio of zero means that only shear loading is imposed. Compression/shear ratio
1 s1
10 s1
100 s1
0 1/20 1/10 1/5 1/1
0.104 0.110 0.120 0.150 0.084
0.295 0.286 0.288 0.226 0.082
0.290 0.299 0.290 0.220 0.072
Table 4 Dominant failure mode (‘‘compression” or ‘‘shear”) observed from the finite element simulation when compressive loading was superimposed on shear. Compression/shear ratio
1 s1
10 s1
100 s1
1/20 1/10 1/5 1/1
Shear Shear Shear Compression
Shear Shear Compression Compression
Shear Shear Compression Compression
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Fig. 12. Contour plots of equivalent plastic strain along with the cracking pattern upon final fracture, in the cases of combined compression/shear loading with the compression/shear ratios of: (a) 1/10 and (b) 1/5, under the nominal shear strain rates of 100 s1.
using the applied strain rates similar to the range considered in the present work, without the tension or compression components, have been reported [9]. However, the correlation between the shear failure pattern and the strain rate was not specifically addressed. As a consequence, a direct comparison between the modeling results with experiments is not possible. Future experimental investigations mimicking the present modeling approach, using controlled shear and normal strain rates (but not from direct drop test of circuit boards), are thus recommended. Nevertheless, the present study has demonstrated the feasibility of utilizing the ductile damage model in quantitatively predicting mechanical failure of solder joint. The modeling also offered mechanistic insight into the failure pattern affected by the combined shear and tension/ compression loading. Further analyses may be built upon the present model with complicated deformation histories, such as pulsed or cyclic strain rates and/or more randomly related shear and normal stress components, to predict solder joint reliability in more realistic settings. The incorporation of brittle failure in the intermetallic layer and along the interfaces is another important extension of the present work. 4. Conclusions Numerical finite element analyses were carried out to study ductile damage in solder joints under fast loading conditions. The effects of applied strain rate (in the range of 1–100 s1) and loading mode (shear with possible superimposed tension or compression)
on the shear ductility and failure pattern were investigated. It was found that under the shear loading mode, the ductility of solder increases as the applied strain rate increases. Final cracking is predominantly along the interface when the strain rate is relatively low (1 s1) but becomes away from the interface as the strain rate increases. The off-interface failure pattern leads to a higher ductility of the joint. The shear-induced failure pattern can be strongly affected by the superimposed tension and compression of the solder joint. With the tension or compression strain rate being only a small fraction of the shear strain rate, the failure pattern can change from the ‘‘shear mode” (near interface) to the ‘‘tension/ compression mode” (near 45° direction). Both the superimposed tension and compression can lead to a decrease in overall ductility, thus showing a negative impact on the solder joint reliability.
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