Fatigue crack growth behavior of Sn-Pb and Sn-based lead-free solders

Solder alloys of lead-rich composition have been commonly used as joining materials in electronic package. However, because of environmental concerns, lead-free solders will replace lead-rich solders more and more in the future. The fatigue characteristics of the solders used are most important in assessing the reliability of joints in electronic packaging. In the present study, the fatigue crack growth (FCG) behavior of a wide variety of solders of both lead-rich and lead-free types has been investigated under a range of mean stresses and frequencies. Both time dependent and time independent (cyclic dependent) behaviors were observed. In the cyclic dependent crack growth regime, the FCG rates could be expressed as a function of either ΔK_eff or ΔJ. Further, the lead-free solders were found to have a higher resistance to FCG than did the lead-rich solders. In the time dependent crack growth regime, the FCG rates were found to be a function of C∗. The point of transition between time dependent and time independent behavior was found to depend on the homologous temperature and strength of the alloys.     

Elastic correction of fatigue crack growth laws

Fatigue crack growth (FCG) is usually studied assuming that ΔK is the driving parameter. An effective ΔK is considered in the presence of crack closure. However, after crack opening, there is an elastic regime that does not contribute to FCG. The objective here is to quantify this elastic range of ΔK, ΔK_el, for different loading conditions and material properties. The yield stress was found to be the most important material parameter, followed by the hardening exponent. A linear decrease of ΔK_el with ΔK was found for the 7050‐T6, 6082‐T6, and 6016‐T4 aluminium alloys, while the 304L stainless steel presented a slight increase. On the other hand, the increase of K_max was found to increase the elastic fatigue range. Relatively high values of elastic range were obtained for the plane strain state, compared with the plane stress state.     

Effect of sudden load decrease on the fatigue crack growth in cold drawn prestressing steel

This paper analyzes the overload retardation effect (ORE) on the fatigue crack growth (FCG) of cold drawn prestressing steel when different loading sequences are used. The ORE is more intense for elevated load decrease or for low initial stress intensity factor (SIF) range ΔK₀. A transient stage can be observed in the Paris curve (da/dN–ΔK) when the K_maxΔK value suddenly decreases, associated with the ORE and with the evolution of the plastic zone and compressive residual stresses near the crack tip. In tests with K_max decrease, a small zone appears related to FCG initiation, with a fatigue fractography resembling the tearing topography surface (TTS) mode, and associated with a decrease of crack tip opening displacement (CTOD).     

Reflections on identifying the real ΔKeffective in the threshold region and beyond

The use of the crack tip stress intensity factor, K, has survived almost 50 years as the key parameter correlating fatigue crack growth. As time past the range of the stress intensity, ΔK, was recognized as causing alternating plasticity at the crack tip. The threshold level for ΔK was discovered. Further, the occurrence of crack closure was noted which affected the ΔK for different load ratios, R of cyclic loading. The ASTM method of counting the linear part of the load displacement for determining ΔK_open was found to understate the ΔK_effective, which correlates data for different load ratios. One approach to adjust for this problem is the “Partial Closure Model”, where the closure only occurs away from the crack tip. Here it will be discussed that such a model leads to a universal growth law. Moreover, this law shows application in estimating the order of magnitude of crack growth life (<10⁷ cycles) for example with very high cycle fatigue (>10⁹ cycles). Some advances in this application will also be cited.     

Fatigue crack growth of a metastable austenitic stainless steel

The fatigue crack growth behavior of an austenitic metastable stainless steel AISI 301LN in the Paris region is investigated in this work. The fatigue crack growth rate curves are evaluated in terms of different parameters such as the range of stress intensity factor ΔK, the effective stress intensity factor ΔK_eff, and the two driving force parameter proposed by Kujawski K¹.The finite element method is used to calculate the stress intensity factor of the specimens used in this investigation. The new stress intensity factor solution has been proved to be an alternative to explain contradictory results found in the literature.Fatigue crack propagation tests have been carried out on thin sheets with two different microstructural conditions and different load ratios. The influence of microstructural and mechanical variables has been analyzed using different mechanisms proposed in the literature. The influence of the compressive residual stress induced by the martensitic transformation is determined by using a model based on the proposal of McMeeking et al. The analyses demonstrate the necessity of including K_max as a true driving force for the fatigue crack growth. A combined parameter is proposed to explain the effects of different variables on the fatigue crack growth rate curves. It is found that along with residual stresses, the microcracks and microvoids are other factor affecting the fatigue crack growth rate in the steel studied.     

Prediction of fatigue crack growth under constant amplitude loading and a single overload based on elasto-plastic crack tip stresses and strains

It is generally accepted that the fatigue crack growth (FCG) depends mainly on the stress intensity factor range (ΔK) and the maximum stress intensity factor (K_max). The two parameters are usually combined into one expression called often as the driving force and many various driving forces have been proposed up to date. The driving force can be successful as long as the stress intensity factors are appropriately correlated with the actual elasto-plastic crack tip stress-strain field. However, the correlation between the stress intensity factors and the crack tip stress-strain field is often influenced by residual stresses induced in due course.A two-parameter (ΔK_tot, K_max,tot) driving force based on the elasto-plastic crack tip stress-strain history has been proposed. The applied stress intensity factors (ΔK_appl, K_max,appl) were modified to the total stress intensity factors (ΔK_tot, K_max,tot) in order to account for the effect of the local crack tip stresses and strains on fatigue crack growth. The FCG was predicted by simulating the stress-strain response in the material volume adjacent to the crack tip and estimating the accumulated fatigue damage. The fatigue crack growth was regarded as a process of successive crack re-initiations in the crack tip region. The model was developed to predict the effect of the mean and residual stresses induced by the cyclic loading. The effect of variable amplitude loadings on FCG can be also quantified on the basis of the proposed model. A two-parameter driving force in the form of: was derived based on the local stresses and strains at the crack tip and the Smith-Watson-Topper (SWT) fatigue damage parameter: D = σ_maxΔε/2. The effect of the internal (residual) stress induced by the reversed cyclic plasticity manifested itself in the change of the resultant (total) stress intensity factors controlling the fatigue crack growth.The model was verified using experimental fatigue crack growth data for aluminum alloy 7075-T6 obtained under constant amplitude loading and a single overload.     

Crack closure under high load-ratio conditions for Inconel-718 near threshold behavior

Fatigue-crack-growth (FCG) rate tests were conducted on compact specimens made of an Inconel-718 alloy to study the behavior over a wide range in load ratios (0.1 ? R ? 0.95) and a constant K_max test condition. Previous research had indicated that high R (>0.7) and constant K_max test conditions near threshold conditions were suspected to be crack-closure-free and that any differences were attributed to K_max effects. During a test at a load ratio of 0.7, strain gages were placed near and ahead of the crack tip to measure crack-opening loads from local load-strain records during crack growth. In addition, a back-face strain (BFS) gage was also used to monitor crack lengths and to measure crack-opening loads from remote load-strain records during the same test. The BFS gage indicated that the crack was fully open (no crack closure), but the local load-strain records indicated significant amounts of crack closure. The crack-opening loads were increasing as the crack approached threshold conditions at R = 0.7. Based on these measurements, crack-closure-free FCG data (ΔK_eff against rate) were calculated. The ΔK_eff-rate data fell at lower ΔK values and higher rates than the constant K_max test results. In addition, constant R tests at extremely high R (0.9 and 0.95) were also performed and compared with the constant K_max test results. The constant R test results at 0.95 agreed well with the ΔK_eff-rate data, while the R = 0.9 data agreed well with constant K_max test data in the low-rate regime. These results imply that the R = 0.7 test had a significant amount of crack closure as the threshold was approached, while the R = 0.9 and K_max test results may have had a small amount of crack closure, and may not be closure free, as originally suspected. Under the high load-ratio conditions (R ? 0.7), it is suspected that the crack surfaces are developing debris-induced crack closure from contacting surfaces, which corresponded to darkening of the fatigue surfaces in the near-threshold regime. Tests at low R also showed darkening of the fatigue surfaces only in the near-threshold regime. These results suggest that the ΔK_eff against rate relation may be nearly a unique function over a wide range of R in the threshold regime.     

Mechanisms for corrosion fatigue crack propagation

ABSTRACT The corrosion fatigue crack growth (FCG) behaviour, the effect of applied potential on corrosion FCG rates, and the fracture surfaces were studied for high‐strength low‐alloy steels, titanium alloys, and magnesium alloys. During investigation of the effect of applied potential on corrosion FCG rates, polarization was switched on for a time period in which it was possible to register the change in the crack growth rate corresponding to the open‐circuit potential and to measure the crack growth rate under polarization. Due to the higher resolution of the crack extension measurement technique, the time rarely exceeded 300 s. This approach made possible the observation of a non‐single mode effect of cathodic polarization on corrosion FCG rates. Cathodic polarization accelerated crack growth when the maximum stress intensity (K_max) exceeded a certain well‐defined critical value characteristic for a given material‐solution combination. When K_max was lower than the critical value, the same cathodic polarization, with all other conditions (specimen, solution, pH, loading frequency, stress ratio, temperature, etc.) being equal, retarded or had no influence on crack growth. The results and fractographic observations suggested that the acceleration in crack growth under cathodic polarization was due to hydrogen‐induced cracking (HIC). Therefore, critical values of K_max, as well as the stress intensity range (ΔK) were regarded as corresponding to the onset of corrosion FCG according to the HIC mechanism and designated as K_HIC and ΔK_HIC. HIC was the main mechanism of corrosion FCG at K_max > K_HIC (ΔK > ΔK_HIC). For most of the material‐solution combinations investigated, stress‐assisted dissolution played a dominant role in the corrosion fatigue crack propagation at K_max < K_HIC (ΔK < ΔK_HIC).     

Analysis of fatigue crack growth behavior of SS 316(N) welds using the unified approach

Fatigue crack growth (FCG) behavior of SS 316(N) weld has been evaluated at different R‐ratios at room temperature and compared with that of the base metal. The FCG resistance of weld is better than that of the base material and is due to the residual stresses developed during the welding. The data were analyzed using the unified approach that considers the two‐parametric (ΔK and K_max) nature of fatigue. The R‐ratio effects in both the base and weld metals are accounted for without invoking the extrinsic parameters, such as plasticity‐induced crack closure. Since the residual stresses are of the monotonic type, they affect the crack growth via the K_max‐parameter. The crack growth trajectory plots were developed, and they show how the two crack tip driving forces, ΔK and K_max, change to overcome the FCG resistance of the weld in relation to that of the base metal. The results also show that the effects from the compressive residual stresses are more dominant at low R‐values and occur via the K_max parameter.     

Effects of solidification structure on fatigue crack growth in rheocast and thixocast Al–Si–Mg alloys

Fatigue crack growth test was performed for rheocast and thixocast Al–Si–Mg aluminum alloys. At small stress intensity factor range (ΔK), fatigue crack growth (FCG) rate of sample with coarse acicular Si particles decreased slightly compared with specimen with small acicular Si particles. However, at large ΔK, fatigue crack growth rate of specimen with coarse acicular Si particles drastically increased. This is because large acicular Si particles induce high strain hardening at small ΔK, but such particles are easily cracked with the increase in ΔK. Morphology of the Si particles strongly affects striation formation.     

Effect of orientation and presence of hydride on the fatigue crack growth behavior of Zr–2.5 wt% Nb

Fatigue crack growth (fcg) behavior of cold-worked and stress relieved Zr–2.5 Nb was studied in the longitudinal (with and without hydrides) and transverse direction at ambient temperature and load ratio of 0.1 using compact tension samples. Fatigue loading in the transverse direction (distribution of both hard and soft grains) showed facet formation on the fracture surface and the highest ΔK_th whereas loading in the longitudinal direction (distribution of primarily soft grains) showed no facet formation and a lower ΔK_th. Hydrided Zr–2.5 Nb loaded in the transverse direction showed large facets with the lowest ΔK_th. Texture influenced fcg at low ΔK but not at higher ΔK.     

On the dominant role of crack closure on fatigue crack growth modeling

Crack closure is the most used mechanism to model thickness and load interaction effects on fatigue crack propagation. But assuming it is the only mechanism is equivalent to suppose that the rate of fatigue crack growth da/dN is primarily dependent on ΔK_eff=K_max−K_op, not on ΔK. But this assumption would imply that the normal practice of using da/dN×ΔK curves measured under plane-stress conditions (without considering crack closure) to predict the fatigue life of components working under plane-strain could lead to highly non-conservative errors, because the expected fatigue life of “thin” (plane-stress dominated) structures could be much higher than the life of “thick” (plane-strain dominated) ones, when both work under the same stress intensity range and load ratio. However, crack closure cannot be used to explain the overload-induced retardation effects found in this work under plane-strain, where both crack arrest and delays were associated to an increase in ΔK_eff. These results indicate that the dominant role of crack closure in the modeling of fatigue crack growth should be reviewed.     

Utilization of partial crack closure for fatigue crack growth modeling

Load ratio effects are of prime concern when modeling of fatigue crack growth (FCG) rate is required as a prerequisite for a reliable life prediction. The majority of research efforts regarding the load ratio effects are based on Elber's ΔK_eff approach. However, there are intrinsic difficulties encountered with its consistent application to FCG prediction. In this paper two popular crack-growth-life prediction codes FASTRAN and AFGROW are modified utilizing the enhanced partial crack closure model. The proposed utilization aggregates apparent closure mechanisms involved and demonstrates a better correlation and a significant scatter reduction of FCG data taken from literature, especially in the near-threshold region.     

Multiple mechanisms controlling fatigue crack growth

Recognizing that fatigue is a two‐parameter problem requiring two load parameters to define cyclic loads unambiguously, a unified approach has been developed to account for crack growth behaviour in terms of ΔK and K_max . Since both driving forces govern the crack growth rate, any analysis based on either ΔK or K_max will provide only partial information about the fatigue behavior of materials. It is shown that ΔK–K_max plots and the associated crack growth trajectory maps reflect the basic mechanisms that contribute to crack growth in a material. These plots also provide a convenient basis to recognize the changes in the micromechanisms that can occur as a function of load ratio or crack growth rate, or both. Taking examples from the literature, crack growth trajectory maps are provided showing such changes in the governing mechanisms of crack growth. It is shown that the ΔK–K_max approach is not an alternative to crack closure models, but it reflects the intrinsic material behaviour that must be understood before reliable crack prediction models can be developed.     

Limitations of elastic definitions in Al-Si-Mg cast alloys with enhanced plasticity: linear elastic fracture mechanics versus elastic-plastic fracture mechanics

Linear elastic fracture mechanics describes the fracture behavior of materials and components that respond elastically under loading. This approach is valuable and accurate for the continuum analysis of crack growth in brittle and high strength materials; however it introduces increasing inaccuracies for low-strength/high-ductility alloys (particularly low-carbon steels and light metal alloys). In the case of ductile alloys, different degrees of plastic deformation precede and accompany crack initiation and propagation, and a non-linear ductile fracture mechanics approach better characterizes the fatigue and fracture behavior under elastic-plastic conditions.To delineate plasticity effects in upper Region II and Region III of crack growth an analysis comparing linear elastic stress intensity factor ranges (ΔK_el) with crack tip plasticity adjusted linear elastic stress intensity factor ranges (ΔK_pl) is presented. To compute plasticity corrected stress intensity factor ranges (ΔK_pl), a new relationship for plastic zone size determination was developed taking into account effects of plane-strain and plane-stress conditions (“combo plastic zone”). In addition, for the upper part of the fatigue crack growth curve, elastic-plastic (cyclic J based) stress intensity factor ranges (ΔK_J) were computed from load-displacement records and compared to plasticity corrected stress intensity factor ranges (ΔK_pl). A new cyclic J analysis was designed to compute elastic-plastic stress intensity factor ranges (ΔK_J) by determining cumulative plastic damage from load-displacement records captured in load-control (K-control) fatigue crack growth tests. The cyclic J analysis provides the true fatigue crack growth behavior of the material. A methodology to evaluate the lower and upper bound fracture toughness of the material (J_IC and J_max) directly from fatigue crack growth test data (ΔK_FT(JIC) and ΔK_FT(Jmax)) was developed and validated using static fracture toughness test results. The value of ΔK_FT(JIC) (and implicitly J_IC) is determined by comparing the plasticity corrected elastic fatigue crack growth curve with the elastic-plastic fatigue crack growth curve. A most relevant finding is that plasticity adjusted linear elastic stress intensity factor ranges (ΔK_pl) are in remarkably good agreement with cyclic J analysis results (ΔK_J), and provide accurate plasticity corrections up to a ΔK corresponding to J_IC (i.e. ΔK_FT(JIC)). Towards the end of the fatigue crack growth test (above ΔK_FT(JIC)) when plasticity is accompanied by significant tearing, the cyclic J analysis provides a more accurate way to capture the true behavior of the material and determine ΔK_FT(Jmax). A procedure to decouple and partition plasticity and tearing effects on crack growth rates is given.Three cast Al-Si-Mg alloys with different levels of ductility, provided by different Si contents and heat treatments (T61 and T4) are evaluated, and the effects of crack tip plasticity on fatigue crack growth are assessed. Fatigue crack growth tests were conducted at a constant stress ratio, R = 0.1, using compact tension specimens.     

Short crack threshold estimates to predict notch sensitivity factors in fatigue

The notch sensitivity factor q can be associated with the presence of non-propagating fatigue cracks at the notch root. Such cracks are present when the nominal stress range Δσ_n is between Δσ₀/K_t and Δσ₀/K_f, where Δσ₀ is the fatigue limit, K_t is the geometric and K_f is the fatigue stress concentration factors of the notch. Therefore, in principle it is possible to obtain expressions for q if the propagation behavior of small cracks emanating from notches is known. Several expressions have been proposed to model the dependency between the threshold value ΔK_th of the stress intensity range and the crack size a for very small cracks. Most of these expressions are based on length parameters, estimated from ΔK_th and Δσ₀, resulting in a modified stress intensity range able to reproduce most of the behavior shown in the Kitagawa–Takahashi plot. Peterson or Topper-like expressions are then calibrated to q based on these crack propagation estimates. However, such q calibration is found to be extremely sensitive to the choice of ΔK_th(a) estimate. In this work, a generalization version of El Haddad–Topper–Smith’s equation is used to evaluate the behavior of cracks emanating from circular holes and semi-elliptical notches. For several combinations of notch dimensions, the smallest stress range necessary to both initiate and propagate a crack is calculated, resulting in expressions for K_f and therefore for q. It is found that the q estimates obtained from this generalization, besides providing a sound physical basis for the notch sensitivity concept, better correlate with experimental data from the literature.     

Load history effects in ductile cast iron for wind turbine components

Fracture-mechanics experiments were carried out on samples of ductile cast iron to investigate the fracture behaviour under cyclic and random loading. Under cyclic loading, the crack growth rate was described well by the ESACRACK model. Fatigue crack growth behaviour depends on the graphite particle size. Increasing particle size leads to higher threshold-values ΔK_th, lower da/dN values and higher transition to static fracture K_fc. The investigation of load history effects with low–high and high–low transitions shows that crack growth acceleration is independent of the transition type. The computation of the a–N curves based on different load history models yields non-conservative results.     

Fatigue strength of the Cu/Si interface in nano-components

The fracture behavior of the Cu/Si interface in a nano-cantilever specimen with a 200 nm-thick Cu film (Specimen-200), which possesses a nanometer-scale strain-concentrated region, is examined under a cyclic bending load. The fatigue strength is around GPa level owing to the high yield stress of the Cu nano-film and the deformation constraint associated with the neighboring hard materials. The S-N curve shows clear dependence of fatigue life on the applied stress in the high-stress range, Δσ. Specimens with a 20 nm-thick Cu film (Specimen-20) are also investigated for comparison. The stress range in the fatigue fracture of Specimen-20 is higher than that of Specimen-200 for the same fatigue life. However, there is good coincidence in the Δσ/σ_s (σ_s: strength in monotonic load) vs. N_f (number of cycles to fracture) at high Δσ. The S-N curves suggest the existence of a fatigue threshold (Δσ_w) at low Δσ. The ratio of fatigue limit to the fracture stress in a monotonic loading, Δσ_w/σ_s, is large compared with the magnitude of bulk metal, which suggests the brittle behavior of the interface. Moreover, the fatigue limits have good coincidence with their yield stresses.