Solder joint failures under thermo-mechanical loading conditions – A review

ABSTRACT Solder joints play a critical role in electronic devices by providing electrical, mechanical and thermal interconnections. These miniature joints are also the weakest links in an electronic device. Under severe thermal and mechanical loadings, solder joints could fail in ‘tensile fracture, fatigue failure and creep failure. This paper reviews the literature on solder joint failures under thermo-mechanical loading conditions, with a particular emphasis on fatigue and creep failures. Literature reviews mainly focused on commonly used lead-free Sn-Ag-Cu (SAC) solders. Based on the literature in experimental and simulation studies on solder joints, it was found that fatigue failures are widely induced by accelerated thermal cycling (ATC). During ATC, the mismatch in coefficients of thermal expansion (CTE) between different elements of electronics assembly contributes significantly to induce thermal stresses on solder joints. The fatigue life of solder joints is predicted based on phenomenological fatigue models that utilise materials properties as inputs. A comparative study of 14 different fatigue life prediction models is presented with their relative advantages, scope and limitations. A critical review of various creep models is presented. Finally, the paper outlined the combined effect of creep and fatigue on solder joint failure.


Introduction
In electronics packaging, solder joints provide the essential mechanical and electrical connections between package elements and substrate. These joints also serve as the weakest links in the overall package in the sense that if any of these joints fail then the whole system could eventually fail and stop functioning. From a structural point of view, solder joints are heterogeneous and dynamic systems, and it is essential to study various elements of the solder structure, to understand their thermo-mechanical behaviours. During operation, electronic products are exposed to a variety of application conditions such as vibration, which can cause impact and fatigue failures. Thermal ageing of solder joints, on the other hand, induces changes in solder microstructure and could trigger creep failure [1,2]. Knowledge and understanding of the failure of these systems are critical to averting accidents, which may result, in life or death and profit or loss associated costs [3].
The reliability of electronic devices has become very significant for the operational performance of electronics systems used in safety-critical applications such as automobile, aeroplane, oil & gas drilling applications, defence, power grids, medical devices and so forth. Because solder joints are small and employed at high temperatures, the reliability of solder joint is of ultimate concern to electronics manufacturing engineers. Solder joint reliability is defined as the capability of solder joints to remain in conformance with their electrical, visual, and mechanical specifications over a specified period, under a detailed set of operational conditions. Reliability of these joints is influenced by various factors such as creep resistance, thermal fatigue resistance, shear strength, drop shock, and vibration resistance. Due to the adoption of the Restriction of Hazardous Substances (RoHS) directives in July 2006, there have been new advancements and developments in lead-free solders as a substitute for the conventional lead-based solders, for use in the electronics manufacturing industries [4][5][6][7][8]. Amongst the lead-free solders investigated, Sn-Ag and Sn-Ag-Cu-based solders offer the most promising characteristics as replacement of lead-based solders [9,10]. Introduction of new lead-free solders added a new dimension to reliability issues in electronic devices.
The existence of intermetallic compounds (IMCs) in solder joints results in improved mechanical properties and can be enhanced by grain refinement and precipitate strengthening mechanisms [11,12]. However, the brittle nature of bulk IMC [13] and low creep resistance [14] are two significant drawbacks of these solders, while in service for highdensity devices. Thermo-mechanical fatigue occurs because most electronic packages consisted of a variety of materials with different coefficients of thermal expansion (CTE) and exposed to thermal fluctuations as a result of internal heating or ambient temperature changes. As a result of thermal and mechanical stresses, solder microstructure develops a weaker coarsened structure, and formation of brittle IMCs (through interfacial reactions) are accelerated. Both thermo-mechanical fatigue and thermal ageing pose a significant threat to the long-term reliability of solder interconnects. In order to understand how reliable these interconnects are, metallurgical changes that affect characteristics of solder interconnect, such as bond formation, creep and fatigue behaviour must be fully understood [15][16][17][18][19][20].
Solder joint failures take place for many reasons, such as a) weak solder joint design; b) weak solder joint processing; c) solder material issues; d) excessive stresses applied to the solder joints and many more. In general, however, solder joint failures are merely ranked according to the characteristics of the stresses that applied to them, as well as the way the solder joints fail. The prominent failure concerns for solder joints are thermal cycling durability, creep deformation, mechanical cycling, vibration durability, solder joint ageing, stress overloading, fatigue, intermetallic growth, and electro and electrochemical migration. Understanding the physics of these failure mechanisms supports reliability improvement and evaluation [21]. Several solder joint failures occur under three significant categories: 1) fatigue failure as a result of the application of cyclical stresses; 2) creep failure due to the application of a long term, permanent load; and 3) tensile fracture due to stress overloading, which is short term. It should be known moreover that more than one of these stresses can act on a solder joint in any given circumstance. Degradation of solder joint by factors such as corrosion needs to be considered as well.
A detailed understanding of the thermo-mechanical behaviour of lead-free solder interconnect is vital in improving operational reliability. Numerous experimental studies were carried out to evaluate solder joint reliability, as evident from studies carried out by Chen & Chen [22] and Forde et al. [23]. A number of research studies [24][25][26][27][28][29] have also focused on the formation of IMC and its effect on the initiation and propagation behaviours of fatigue cracks and creep failures; and how those leads to the phenomenon of stress concentration, where cracks began to sprout and gradually extend. Relevant literature shows that the service life, reliability and performance of electronic products are greatly influenced by temperature which results in failures [30][31][32]. The emphasis of this paper is to examine the solder joint fatigue and creep failures under thermomechanical loading conditions.

Thermal fatigue failure models for solder joints
Thermal fatigue is a leading cause of failure of solder joints in surface-mount electronic components, and it is significant in high-reliability applications such as in telecommunication, military, and aeronautics. In electronic assemblies, solder joints usually experience thermal stresses because of combined effects of non-uniform temperature distributions in the package and a mismatch in CTE between the component and substrate material [33][34][35]. Thermo-mechanical fatigue arises when materials with different CTEs are joined and used in an environment that experiences cyclic temperature fluctuations resulting in imposed cycling strain. Figure 1 shows a solder joint with fatigue failure, mounted on a printed circuit board (PCB) [36]. Choi & Dasgupta [37] investigated the fatigue of solder interconnects in microelectronic assemblies under random vibration. They applied the well-known Coffin-Manson fatigue model and rainflow cycle counting to measure model constants and to compare fatigue damage accumulation rates under harmonic versus electro-dynamic (ED) random vibration excitation. They focused on solder durability and strain response under random and harmonic vibration loading, 1 Figure 1. Solder joint fatigue failure [36].
based on experiments and modelling. Multiscale finite element modelling (FEM) is required to address the vibration response of complex electronic assemblies. An analysis was conducted by the researchers in the time domain to manage the nonlinear material behaviour of solder. Their conclusions focus on solder strain response and durability under random and harmonic vibration loading, based on experiments and modelling.
Even small fluctuations of operating temperature can have a significant impact on solder integrity, due to CTE mismatch between connected components. Following a critical number of thermal excursions, such as the machine on/off cycles, solder joints encounter fatigue failure. The type and significance of strains in solder joints under conditions of thermo-mechanical fatigue are often quite complex. For surface-mount applications, the strain is nominally in shear. Nonetheless, tensile and mixed-mode strains can occur due to bending of the chip carrier or board. Figure 2(a) is showing the microstructure of a failed solder joint, adapted from Shen [33]. The heterogeneously coarsened colony boundaries are weaker than the rest of the joint and any additional deformation concentrates in the coarsened regions resulting in further coarsening. Failure finally happens because of cracks that form in the coarsened regions of the joint. Other solder alloys, such as the lead-free Sn-3.5Ag eutectic-based solders, experience thermal and mechanical fatigue damage and failure at tin grain boundaries, as presented in Figure 2(b) [33].
Thermal stresses can also be induced because of a mismatch in the CTE between different constituents of the assembly. Coyle et al. [38] investigated the thermal fatigue characteristics of Pb-free solder joints. A significant finding from their study is that positive impact of Ag on accelerated thermal cycling (ATC) reliability (measured by characteristic lifetime) reduces as the harshness of the ATC (expressed by higher ΔT, advanced peak temperature, and lengthier dwell time) increases. The outcomes also show that all the Pb-free solders are more dependable in accelerated thermal cycling than the SnPb alloy they have substituted [39,40]. Li et al. [28] reviewed typical thermal fatigue failure models for solder joints of electronic components. They examined several classifications of thermal fatigue failure models of the solder joint in electronics components as shown in the Figure 3.
Petrone et al. [41] carried out a steady thermo-mechanical analysis for a surfacemount electronic device, as shown in Figure 4(a). Figure 4(b) presents the effective plastic strain distribution for SAC305. A copper frame essentially makes the device, a lead-free 2a 2b Figure 2. (a) Cracks propagate through the Sn-rich phase at Sn-Sn grain boundaries after thermomechanical fatigue (b) Optical micrograph of a failed Sn-3.5Ag solder joint after experiencing thermomechanical fatigue [33].
solder layer (solder die) and silicon die equipped with a front metal, which is connected to devise pins by several ribbons. Continuous equations were spatially discretised by a finite element approach based on the Galerkin technique on non-uniform and nonstructured computational grids made of tetrahedral Lagrange elements of order 2. Influence of spatial discretisation was preliminarily studied to guarantee meshindependent effects. Subsequently, a computational network composed of about 45,250 elements was preserved for calculations, generating 137,399 degrees of freedom. The thermal distribution results obtained from the study are presented in Figure 5(a, b). The thermo-mechanical analysis shows the von Mises stress distribution, triggered by the thermal cycling, shown in Figure 5(b). A snap view of the applied mesh is presented in Figure 6 and the thermal distribution developed from the results is further presented in Figure 7.  Thermal states computed was exploited for estimating the effective plastic strain distribution. The maximum value of plastic strain amplitude Δε p À Á was detected on the solder layer, joining the frame and the silicon die. In particular, the most critical and effective plastic strain was identified in the vicinity of the solder layer corners. Figure 7(a, b) shows the effective plastic strain distribution in the proximity to the solder layer corner, where the highest value of plastic strain ε p À Á was found in both thermal environmental conditions coldtemperature; T c andhottemperature; T h ð Þ . This result agrees with experimental result obtained by Scanning Acoustic Microscope (SAM) observations developed of surfacemount components. The number of cycles to failure for solder layer obtained for power cycle analysis is shown in Figure 7(b). The crack propagation is nearly concentric, originating almost directly under the silicon chip that is the hottest point [41].
The result of their investigations shows that the maximum von Mises stress calculated by the thermo-mechanical analysis is lower than the ultimate tensile strength (UTS) of  materials. The fatigue life prediction results in excellent agreement with both the experimental and reviewed literature findings, both quantitatively (number of cycles to failure) and qualitatively (device portion subjected by the highest plastic strain). A comparative study of 14 different fatigues life prediction models is presented in Table 1 with their scope.
Solder joints must maintain their mechanical and thermal integrity under various mechanical and thermal loads in service, including mechanical shock, thermal fatigue and creep. Mishandling of packages during manufacture, assembly, or by the user may cause solder joint failure. Because of the environmental concerns over the lead (Pb)containing solders, lead-free solders, such as Sn-Ag-Cu (SAC) and Sn-Ag alloys, have been extensively utilised in electronic packaging. Fei et al. [49] examined the fracture of Sn-Rich (Pb-Free) solder joints under mechanical shock conditions. The investigators used finite-element analysis (FEA) to analyse the fracture behaviour of single solder joints by coupling void-induced solder-based fracture and IMC-controlled brittle fracture. To capture the influence of defects in the IMC, they modelled the IMC as an inhomogeneous material where material properties varies with location. They employed a modified Gurson (GTN) model to simulate microvoid-induced ductile fracture. The GTN model proposes a yield surface given as: where f is void volume fraction and is defined as the volume of voids divided by the total volume of porous material (f = 0 describes an adequately dense material and, f ¼ 1 signifies a wholly voided material); σ y is the yield stress of the matrix material; q 1 is dependent on the strain-hardening behaviour of the metal, for example, q 1 ¼ 1:25 for n = 20 and q 1 ¼ 1:8 for n = 5, where n is the strain-hardening exponent. Recommendation Plastic strain + elastic strain High and low cycle fatigue b = fatigue strength exponent c = fatigue ductility exponent shows that q 2 ¼ 1:0 and q 3 ¼ q 2 1 . Figure 8 shows representative yield surfaces expressed as the relationship between normalised von Mises effective stress and hydrostatic stress for q 1 ¼ 1:8, q 2 ¼ 1:0 and q 3 ¼ 3:24. One can indisputably understand that the yield form differs on both the von Mises hydrostatic and effective stress and with increasing, void volume fraction, f, the material has the tendency to yield at diminutive von Mises and hydrostatic stress as shown in Figure 9(a, b) [50][51][52].
The outcome of their research demonstrates that the essential solder failure mechanism is dominated by fracture strength of solder and IMC growth. At reduced strain rates, the solder distorts plastically, and deformation in solder is constrained. At higher strain rates, the stress state is more triaxial. As the thickness of the IMC develops, defects in the IMC with pure fracture strength become more apparent, so that IMC-controlled fracture may happen. This outcome is furthermore usual at higher strain rates too. Consequently, the fracture of the solder joint depends on both IMC thickness and strain rate. In describing the qualitative mechanism of solder joint fracture, a '"mechanism chart"' of  solder joint fracture recommended is shown in Figure 10. The fracture strength of solder rises with strain rate (Figure 10a), while that of IMC reduces with IMC thickness (Figure 10b). The connection between the fracture strength of solder and IMC forms the crucial state for solder joint fracture (Figure 10c). The prognosis of the connection line is presented in the IMC thickness/strain rate space (Figure 10d). The line divides the IMC-controlled fracture (brittle) and solder-controlled fracture (ductile).
Tang et al. [53] investigated the FEA of SAC solder joint failure under impact test. They used a physical model of ball impact test (μm) shown in Figure 11(a) and the FEM half-symmetry is shown in Figure 11(b). In their research, they applied ANSYS LS-DYNA for the structural response of solder joints under high-speed impact test. Mathematical simulation outcomes show that three kinds of failure modes in ball impact test are simulated based on tiebreak connection established model design. They concluded that the fracture time grows with an increase of IMC strength. Failure time utilised was 30 μs for a brittle break, 40 μs~100 μs for a medial break and above 100 μs for a ductile break, respectively. The maximum shear force is between 1.3 and 13 N, which is significantly lower than the original impact force, owing to the neglect of the hardening mechanism of material constrained to high strain ratio loading.

Fatigue life prediction of solder joints
Fatigue damage is a serious concern in engineering applications involving cyclic or repetitive loading and can lead to fracture and catastrophic failure of materials and resources. Avoiding or somewhat delaying the failure of any electronic component exposed to cyclic loading is the ultimate goal of engineers or researchers who are involved in electronic system design and development. Packaging in electronics devices comprises of materials with very different mechanical and thermal properties. In service, discrepancies of CTE of various materials produces cycling shear stress on solder joints. The stresses build fatigue failure of solder joints, and fatigue life of solder joints typically determines the reliability of electronic packaging. Thus, the prediction of fatigue life is an important step in the design and development of electronic products [54,55].
The mathematical models that are used for predicting fatigue life are comprised of two groups. The first group is made up of models based on the prediction of crack nucleation, using a combination of damage evolution rule and criteria based on stress/strain of components. One of the essential characteristics of these models is the absence of dependence from loading and specimen geometry, being the fatigue life defined only by a stress/strain model [56,57]. The method of the second group is based alternatively on continuum damage mechanics (CDM), in which fatigue life is predicted by measuring a damage parameter, cycle by cycle. Ordinarily, the life prediction of elements subjected to fatigue is based on the 'safe-life' methodology [58,59], coupled with the rules of linear cumulative damage [60,61].
Paris & Erdogan formulated a power law which is commonly used to model stable fatigue crack growth [62]: Moreover, the fatigue life N obtainable from the following integrated equation: where the stress intensity factor range is represented by ΔK, and C and m are the material-related constants. The integration limits a f and a i represents the initial and final fatigue crack lengths; the crack propagation theory expressed as: where ΔJ is the J integral range corresponding to equation 16, while C 0 and m 0 are constants [61-64].

Isothermal fatigue of solder joints
Wiese et al. investigated the fracture behaviour of flip chip solder joints. Their research examined Sn63Pb37 and Sn95.5Ag4.0Cu0.5 solder materials with a test temperature of 300 K. The strain wave amplitudes ranged from Δε = 0.3% . . . 4.0% and the strain wave frequencies ranged from f = 0.0004 Hz . . . 10 Hz. A flip chip specimen is shown in Figure 12 [65]. The crack propagation rate is calculated by: Figure 12. Flip chip specimen [65].
where n is the number of cracks that grow spherical and d is the diameter of the joint at the section where the crack propagates: The parameter ΔF corresponds to the force amplitude at the current cycle, while ΔF 0 represents the force amplitude at the initial cycle. Guo & Conrad [66] introduced a power law that correlated the crack growth rate da=dN with the plastic strain energy (ΔW pl ) as: For accumulated inelastic strain ε acc ð Þ: Zhang et al. [67] investigated the isothermal mechanical durability of three selected PBfree solders: Sn3.9Ag0.6Cu, Sn3.5Ag, and Sn0.7Cu. They used specimens comprising of two copper plates joined in a lap configuration by a thin layer of solder to characterise the isothermal mechanical durability of three lead-free solders (Sn-3.9Ag-0.6Cu, Sn-3.5Ag, and Sn-0.7Cu) and compared with those of the eutectic Sn-37Pb solder at the room temperature and at 135°C. The Sn-3.9Ag-0.6Cu and Sn-3.5Ag had much better durability than the Sn-37Pb, but the Sn-0.7Cu was worse. They used the Morrow energy model where D u is a thermal mismatch; Δe is the difference in CTE between the materials; L is the linear dimension of the component, and ΔT is the temperature changed. In reducing solder joint cracks, it is essential to reduce the thermal mismatch, which can be done by limiting the difference in CTE, minimising the temperature delta or reducing the size of the component. For high reliability, any mismatch of CTE must be supported by the solder joint [53,68,69]. Figure 13 shows solder joints subjected to shear loading due to CTE mismatch. Their result concluded that the CTE evolution of lead-free solder could be explained by the microstructural changes in the solder alloys during isothermal ageing. Thermal ageing induces the coarsening of different phases of the solder, resulting in a higher coefficient of thermal expansion. In contrast, the addition of microalloying elements into the solder alloys impedes the CTE developments with ageing. CTE evolution during isothermal ageing recommends potential reliability difficulties for lead-free solder joints subjected to long-term exposures to severe temperatures. The parts where cracks will become noticeable under thermal cycling environments are shown in Figure 14(a) by the numbers 1 to 7 and 14(b) shows cracked through-hole joint [70,71]. Coupled with the CTE mismatch connecting different elements of the device, cyclic thermal loading results in stress reversals and the possible growth of inelastic strain in the solder joint. This inelastic strain grows with repeated cycling and eventually produces solder joint cracking and interconnection failures [72,73], as follows:

For lead-free materials/devices
(1) At the interface connecting solder and metallisation under significant components such as lead-free chip carriers.

For through-hole materials/devices
(1) Annular cracks at the interface within solder fillet and wire. (2) In the majority of the fillet.

Creep failure of solder joints
The long-term reliability of solder joint is a fundamental necessity for electronics packaging. Solder joint failure, nonetheless, can comprise of compound mechanisms. One of the various simple failure processes in metals/alloys is the creep phenomenon. Creep is described as a time-dependent deformation when a material is subjected to stress for an extended period. This time-dependent deformation can hypothetically happen at any temperature over the absolute zero. Nevertheless, creep-dominant failure conventionally appears under elevated temperature close to the melting point of the material. Lead-free solders are low-temperature alloys with a melting point or liquidus/solidus temperature in the range of 210 -230°C. Subsequently, a detectable creep process under low level of mechanical load is expected even at ambient temperature. The research by Hwang & Vargas [71] provides initial data on the relative creep rate of twenty-two common solder alloys and endeavours to correlate the creep rate to the melting point, tensile strength, modulus, microstructure of alloys. The alloys under analysis comprises of Sn/Sb, Sn/Pb/Bi, Sn/Pb/Sb, Sn/Bi, Sn/In, Sn/Pb, Sn/Pb/Ag, Sn/Ag and Pb/in systems. They also examined the recommended mechanisms for solder creep phenomena.
Lee et al. [74] investigated the mechanisms of creep deformation in pure Sn solder joints. The work reported by the investigators involves the creep of pure Sn solder joints with Cu metallization (Cu||Sn||Cu). The steady-state creep tests in shear along with electron backscatter diffraction (EBSD) were used to investigate the evolution of the microstructure during creep, and to define the deformation mechanism and the characteristics of the microstructural development. The creep behaviour of the joint changes significantly with temperature. The results imply that a 'segmented' constitutive equation of Dorn type is most suitable for the low-temperature behaviour, while a 'hyperbolic' constitutive equation preferably at high temperature. Related works undertaken by Lee et al. [74,75], Weertman [76] and Herring [77,78]. Weertman [76] and Wong et al. [79] examined the creep-fatigue models of solder joints. They reviewed creep-fatigue models in the aerospace and power electronics. Although the investigation by Choudhury et al. [80] identified a new SAC alloy with better thermal and mechanical reliability than Sn-Ag3-Cu0.5/Sn-Ag4-Cu0.5, research has not adequately studied the creep failure. Creep properties at high temperature give an excellent indication of the thermal cycling performance of the solder alloy. This is necessary throughout alloy advancement because thermal cycling testing demands time and needs resources such as the supply of power during experimentation.

Solder alloy creep model
As far as joining material concerned, solder alloys are widely used in all electronic packaging due to their lower melting temperature and excellent wetting properties. However, in most electronic packaging, solder alloys function at thermally activated condition even at room temperature, as a result of their low melting point. Numerous thermally activated developments, including grain boundary diffusion, dislocation-glide, dislocation climb, and lattice diffusion generate and accrue an enormous quantity of creep deformations [74,81]. These resulted in different kinds of failures in electronic packaging, particularly in soldered joints. Only a limited number of creep models are developed for viscoplastic behaviours of solder joints. Lee & Basaran [74], Gomez & Basaran [81] and Basaran et al. [82] have listed these references comprehensively on constitutive modelling of solder alloys. The analyses have shown that the creep behaviour of a solder alloy significantly depends on age, stress, temperature, and grain size. However, a full review and an evaluation of these models have never been published. Zhu et al. [83] suggested a new life prediction model under high strain rate with the experimental result compared with the predicted outcome and showed that the calculate life matches well with the test life under high strain rate. Ramachandran & Chiang [84] used unified viscoplastic Anand model to describe the rate-dependent behaviour of both eutectic and lead-free solder alloys at high homologous temperatures.
Kashyap & Murty [85] and Hacke et al. [86] has recommended the following mathematical model as the best universally used creep model, denoted here as Model 1: where _ γ is a creep strain rate; A is a material constant; G is the shear modulus; b is the burger's vector; k is the Boltzmann's constant; T is the absolute temperature; d is the grain size, τ is the applied shear stress; n is the stress coefficient; Q is the activation energy for creep process, and R is a universal constant. The Anand model which was proposed by Anand is shown in equation 11 [87,88].
where _ ε in is the inelastic strain rate, is a multiplier of stress, σ is the applied stress, s is a single scalar as an internal variable to represent the average isotropic resistance to plastic flow, and m is the strain rate sensitivity of stress. A steady-state creep equation is obtained by simplifying Anand Model. Model 2 is obtained as seen in equation 12: where n is 1 m , and β is the multiplier of hyperbolic-sine law obtainable from curve fitting to experimental data with the use of linear and non-linear least squares regression. Pan proposed the modification of the Anand model. Model 3 possesses additional grain size as well as some term original embedded into Model 2 as seen in equation 13 [89]: a creep function Model 4 was recommended by Darveaux& Banerji [74] as seen in equation 14. It is similar to Model 2: Another valuable creep model 'Model 5ʹ was recommended by Shi et al. [90], Model 5 is shown in equation 15. The model presumed that there are two systems of steady-state creep and that individual regime has a power-law dependence on stress and strain rate.
Shi et al. [90] also recommended another Model 6 in equation 16 founded on their experimental outcomes.
Lee & Basaran [74] proposed a modified Anand model considering, shear modulus temperature dependency and grain size, as presented in Model 7 and 8: A hyperbolic-sine term was utilised instead of power-law used in the Dorn mathematical equation given in Model 1. When Model 7 was compared with Model 8, Lee & Basaran [74] suggested an observation of the effect of Gb=kT. Model 9 is presented in equation 19: The findings by Lee & Basaran [74] and Shi et al. [90] concluded that creep laws with the τ=G term in overall yield better results than those of stress term only represented by shear stress, τ and that grain size also plays an important role that cannot be ignored in creep model. Creep laws given in model 7, 8 and 9 were the most successful for experimental data. The differential form of the evolution equation for the internal variable s is assumed to be in the form: where h σ; s; T ð Þ is associated with the recovery process and progressive hardening. Parameter h o is the hardening constant, a is the strain rate sensitivity of the hardening process, and the term s Ã is expressed as: whereŝ is a coefficient and n is the strain rate sensitivity of the saturation value deformation resistance: For s < s Ã , equation 16 can be written as: Moreover, then integrated to yield where s 0 ð Þ ¼ s o represents the initial value of s at the time, t ¼ 0. Substituting equation 22 into equation 24 yields version of the evolution equation for the internal variable s: The calculation results in:  (27) or For the UTS, this can be obtained from the equation above. The UTS is given by the limit as ε p ! 1: When yield stress is given by the limit ε p ! 0 Using saturation stress, σ Ã ¼ UTS relation above, the post-yield stress-strain response (power-law) equation 30 above can be rewritten as:

Combined effect of creep and fatigue
The mechanisms associated when creep and fatigue act together are inadequately understood, but there is an indication that the summation of their properties is even more important than their distinctive influences. Since solders function at elevated homologous temperatures, if they have small stress acting on them, they are economically creeping all the time. Therefore, any methodology of stress or thermal cycling will present an unwanted occurrence of the combined effect of creep and fatigue. To make the circumstances worse, duty cycles could be: (1) Fluctuating stress levels at a constant high homologous temperature.
(3) Concurrent fluctuations in high homologous temperature and stress.
According to the research conducted by Huang et al. [92], it was acknowledged that SAC305 lead-free solder joint presents an excellent thermostable performance. Failures of the lead-free solder joint were studied under thermal cycling and thermal ageing conditions. The crack initiation point was found to have developed in the bulk solder and propagated along with the IMC. The location of fracture is primarily around the interface between the IMC layers and solder joint, and moreover, this may happen in the solder near the pad. After a specific time of observing the thermal cycling test, the spreading trend of the crack is shown and, the crack of the solder joint slowly changed from one crack to two or more cracks and the length become extended [93,94]. With the increased rate of the thermal cycling, the cracks continued along the IMC [95,96].

Finite element modelling
Generally, finite element method consists of three stages: (1) pre-processing, where the analyst generates the finite element mesh and applies specific parameters or boundaries to the model, (2) solver/solution, where the program runs the governing mathematical equation that was produced by the model and (3) [98] provide examples of mechanical failure analysis assessment that used finite element analysis software to verify findings regarding the failure incidents. Half 3D model was developed according to the original ball joint test samples as shown in Figure 11(a). After modelling, linear hexahedral solid elements are administered except the outer region of the solder joint where the anticipation of force concentration and large deformation illustrates. Alternatively, linear tetrahedral elements are applied for a further detailed simulation as presented in Fig. 15-17 [53]. Automatic nodes-to-surface contact is applied to the shear tool and solder ball, during tiebreak nodes-to surface contact between the solder and Cu pad. Tiebreak contact links adjacent meshes and limits the movements of nodes till the bond force is surpassed; the bond failure is characterised by: where the subscripts n and s denote normal, and shear, respectively, and f and S are the calculated nodal force and the given ultimate nodal force at which the bond breaks, respectively. The stress distribution in failure Models 1, 2 and 3 is shown in Fig. 15, 16 & 17. For Model 1, Figure 15, the interfacial fracture takes place within 45 μs, and the solder bump is sheared off by the shear tool. Model 2, Figure 16 shows much more IMC strength   (500MPa and above), solder surfers higher stress throughout the shear impact procedure. Fracture originates at 33 μs on the left edge of the interface till 60 μs while solder bulk starts to fail as a result of an overload of shear force and Model 3, Figure 17 indicates that the IMC strength is too high to break that failure only occurs in the solder. The interrelating period between the shear tool and solder is comparatively longer. Even after 132 μs, half of the ball is remaining on the pad [53,99,100]. When it comes to creep failures of solder joints, it was found that Dorn type segmented constitutive equation is used for the low-temperature creep behaviour and sine-hyperbolic constitutive equations are prefered for high-temperature creep. Among various sinehyperbolic models, the Anand's viscoplastic model is the most widely used creep model. As solders operate at high homologous temperatures, creep is the primary and dominant deformation mechanism in any solder joint failure. In that respect, while the paper summarises separately the mathematical models used to investigate solder fatigue and creep failures, it is critical to consider creep while considering solder fatigue failure.