Fatigue crack initiation and growth in solder alloys

In modern electronic packaging, especially surface mount technology (SMT), thermal strain is usually induced between components during processing, and in service, by a mismatch in the thermal expansion coefficients. Since solder has a low melting temperature and is softer than other components in electronic packaging, most of the cyclic stresses and strains take place in the solder. Fatigue crack initiation and fatigue crack propagation are likely to occur in the solder even when the cyclic stress is below the yield stress. It is an objective of this research to study the behaviour of fatigue crack initiation and propagation in both lead‐containing solder (63Sn‐37Pb), and lead‐free solders (Sn‐3.5Ag). The effect of alloying (Cu and Bi addition), frequency, tensile hold time and temperature on low cycle fatigue (LCF) behaviour of the solders is discussed. Mechanisms of LCF crack initiation and propagation are proposed and LCF life prediction, based on the various models, is carried out.     

The effect of microstructure on the mechanical properties of two-phase titanium alloys

This article presents the results of investigations of microstructure and mechanical properties of two-phase +β titanium alloys with different volume fraction of the β-phase. Microstructure of the specimens was examined using an optical microscope. Fracture surfaces were observed by SEM technique. The influence of the microstructure and phase composition on the mechanical properties of the alloys was studied. Static tensile tests, hardness tests and fatigue investigations were performed. It was noticed that the volume fraction and chemical composition of the β-phase has a significant effect on mechanical properties and cracking process during fatigue.     

Fatigue crack growth behaviour of gamma base titanium aluminides under different loading conditions

Static and cyclic fatigue crack growth behaviour of gamma base titanium aluminides with three different microstructures were investigated. Influence of cyclic test frequency on fatigue crack growth behaviour was also studied at room temperature under a controlled humidity condition. The crack growth behaviour both under static and cyclic loading was strongly influenced by the microstructure. The threshold stress intensity and crack growth behaviour under cyclic loading were much inferior than that under static loading indicating the ‘true-cyclic fatigue’ effect exhibited in gamma base titanium aluminides. No significant effect of test frequency on the crack growth behaviour was observed for the equiaxed and duplex microstructure materials.     

Fatigue crack initiation in Hastelloy X – the role of boundaries

In polycrystalline metals, microstructural features such as grain boundaries (GBs) influence fatigue crack initiation. Stress and strain heterogeneities, which arise in the vicinity of GBs, can promote the nucleation of fatigue cracks. Because of variations in grain size and GB types, and consequently variations in the local deformation response, scatter in fatigue life is expected. A deeper quantitative understanding of the early stages of fatigue crack nucleation and the scatter in life requires experimental and modelling work at appropriate length scales. In this work, experiments are conducted on Hastelloy X under fatigue conditions, and observations of fatigue damage are reported in conjunction with measurements of local strains using digital image correlation. We use a recent novel fatigue model based on persistent slip band–GB interaction to investigate the scatter in fatigue lives and shed light into the critical types of GBs that nucleate cracks. Experimental tools and methodologies, utilizing ex situ digital image correlation and electron backscatter diffraction, for high resolution deformation measurements at the grain level are also discussed in this paper and related to the simulations.     

Local texture and fatigue crack initiation in a Ti-6Al-4V titanium alloy

ABSTRACT Fatigue crack initiation was studied in a bimodal TA6V titanium alloy. A ghost structure inherited from the forging process, the scale of which is roughly 100 times the apparent grain size, was found to govern the initiation process. In these macrograins, that we have labelled macrozones, most of the primary alpha grains (α_p) are found to display the same crystallographic orientation. Fatigue cracks are initiated on the basal plane or, if basal slip is difficult, on the prismatic plane. Thus in macrozones, where basal or prismatic slip is easy, numerous neighbouring tiny cracks appear over the whole macrozone, which have the size of the primary α_p grains. In these macrozones the contribution of crack coalescence to crack growth is consequently very significant. On the contrary, if basal and prismatic slips are both difficult in the macrozone, no crack can be found in the corresponding macrozone. The crack initiation process is thus highly heterogeneous at the scale of the macrozone. Furthermore, this microstructure is found to induce a large scatter in the fatigue life of notched samples.     

On the mechanisms of fatigue facet nucleation in titanium alloys

A crystal plasticity model for near‐alpha hcp titanium alloys embodying a quasi‐cleavage failure mechanism is presented and employed to investigate the conditions necessary in order for facet nucleation to occur in cold‐dwell fatigue. A model polycrystal is used to investigate the effects of combinations of crystallographic orientations (and in particular, a rogue grain combination), the essential role of (cold) creep during hold periods in the loading cycle and the more damaging effect of a load hold rather than a strain hold in facet nucleation. Direct comparisons of model predictions are made with dwell fatigue test results. More generally, the crystal model for faceting is found to be consistent with a range of experimental observations.     

Fatigue crack propagation behaviour of rotor and wheel materials used in steam turbines

The fatigue crack propagation characteristics of several rotor and wheel materials that are commonly used in rotating components of steam turbines were investigated. Particular emphasis was placed on the behaviour at near-threshold growth rates, ie below 10^?5 mm/cycle, approaching the fatigue-crack propagation threshold, $\text{ΔK}{}_{\mathrm{<mtext>th</mtext>}}$. The lifetimes of the cracks of interest lie mostly in this region, and it is also the region where few data are available.The effects of load ratio on the fatigue crack growth rates were examined, as well as the tensile, Charpy V-notch and fracture toughness properties of the rotor and wheel materials. The relationship between fatigue crack propagation behaviour and fractographic features was examined. Fatigue crack growth rate data, $\text{da/d}\text{N}$ vs stress intesity range $\text{ΔK}$, were fitted with a four parameter Weibull survivorship function. This curve fitting can be used for life estimation and establishment of $\text{ΔK}{}_{\mathrm{<mtext>th</mtext>}}$. The results show that load ratio and microstructure play a role in determining the fatigue crack threshold and fatigue crack growth behaviour.     

梯度钛合金裂纹扩展速率测试及梯度对扩展寿命影响

为明确梯度材料中裂纹扩展速率分布情况,对含裂纹TC11-TC4以及TA15-TA2两种组合梯度钛合金进行标准三点弯疲劳试验。试验结果表明:梯度结构中不同部位的相同组分扩展性能相同,给出了4种3D打印组分钛合金的Paris公式;梯度材料组分弹性模量的变化会改变裂纹尖端应力强度因子,对位于模量较低一侧的裂纹扩展有抑制作用;过渡层影响厚度范围内裂纹扩展速率介于两种组分之间且连续过渡,表明梯度材料可以消除异种材料连接的界面效应,提出基于组分材料体积分量的混合率描述梯度层中扩展性能的分布规律;恒定载荷试验中仅扩展方向不同情况下寿命有显著差别,验证了合理安排梯度参数可提高结构出现裂纹后的生存能力,其中扩展性能以及模量的变化分布对扩展寿命均有影响。     

Fatigue crack propagation behaviour of Al–Zn–Ce alloys

This paper presents the investigation on fatigue crack growth behaviour of Al–Zn and Al–Zn–Ce alloys. Fatigue tests were carried out on as‐cast and heat‐treated CT specimens according to ASTM E647 testing standard. The test results showed that the addition of rare earth element (cerium) and heat treatments (T6 and T5) had very strong influence on fatigue strength. This enhancement was due to metallurgical changes in the alloy system. Cerium eliminates the porosities and refines microstructures of the alloy, showing the improved fatigue crack growth behaviour. In addition, the fatigue fractured specimens were examined using a scanning electron microscope to clarify the fracture initiation points.     

Fatigue crack initiation in notched specimens of 17Mn4 steel

Fatigue crack initiation life is predicted for notched bend specimens with two different notch acuities and two stress ratios using the equivalent strain energy density method. The material used was 17Mn4 steel, widely applied in pressure vessel construction. The monotonic and cyclic mechanical properties and the strain-life constants were experimental determined in this work. A comparison was made between predicted and experimental lives obtained for two different optically measured crack lengths. Good agreement was obtained for stress ratios, R, of 0 and −1, and for two notch stress concentration factor values. The observed mean stress effect on crack initiation lives is well modelled in the prediction by the method used with calculation of both strain range and mean stress at the root of the notch.     

Fatigue crack initiation and growth in AlMg4.5Mn butt weldments

The fatigue life of full-penetration and partial-penetration 5 and 25  mm thickness AlMg4.5Mn (AA5083) aluminium alloy butt weldments was investigated under ( R = 0 and R = − 1) constant amplitude loading. The fatigue lives of the tested specimens were predicted using an analytical model which estimated both the crack initiation and crack growth portions of the total fatigue life. The fatigue life of partial-penetration weldments was found to be substantially less than that of full-penetration weldments because of the greater stress concentrations of the incomplete joint penetration and the consequent absence of a substantial crack-initiation life period. Tensile mean stresses ( R = 0 versus R = − 1-test conditions) markedly reduced the fatigue life of the weldments studied and greatly diminished the duration of the fatigue crack growth period. The extra material provided by the weld reinforcement noticeably increased the fatigue life of the partial-penetration weldments. Weld angular distortion-induced bending stresses greatly affected the smaller thickness (5  mm) full-penetration weldments offsetting the fatigue strength bonus anticipated for small-size weldments. Except for the predictions for R = − 1 full-penetration weldments at long life, which the analytical model underestimated, the agreement between experiment and analytical prediction was within a factor of 2, that is, as good as can be generally expected.     

Fatigue crack initiation detection by an infrared thermography method

In this paper, the study of the temperature variation during fatigue tests was carried out on different materials (steels and aluminium alloys). Tests were performed at ambient temperature using a piezoelectric fatigue system (20 kHz). The temperature field was measured on the surface of the specimen, by means of an infrared camera.
Just at the beginning of the test, it was observed that the temperature increased, followed by a stabilization which corresponds to the balance between dissipated energy associated with microplasticity and the energy lost by convection and radiation at the specimen surface and by conduction inside the specimen. At the crack initiation, the surface temperature suddenly increases (whatever the localization of the initiation), which allows the determination of the number of cycles at the crack initiation and the number of cycles devoted to the fatigue crack propagation. In the gigacycle fatigue domain, more than 92% of the total life is devoted to the initiation of the crack.
So, the study of the thermal dissipation during the test appears a promising method to improve the understanding of the damage and failure mechanism in fatigue and to determine the number of cycles at initiation.     

The effect of grain size on small fatigue crack growth in pure titanium

The growth behaviour of small fatigue cracks has been studied in both fine- and coarse-grained versions of a pure titanium under axial loading at stress ratio, R, of −1. The growth behaviour and its statistical properties in a coarse-grained version of a different pure titanium have also been investigated under rotating bending (R = −1), and the results obtained were compared with those of a fine-grained version of this titanium in a previous report. Under both loading conditions, small cracks grew faster than large cracks. As the growth data were plotted in terms of the effective stress intensity factor range ΔK_eff (after allowing for crack closure, the growth rates could be well correlated with large-crack data in a large-crack regime. In a small-crack regime, however, small cracks still grew faster than large cracks. Small cracks in coarse-grained material showed higher growth rates than those in fine-grained material owing to a much smaller effect of microstructure such as grain boundaries and crack deflection. Stage I facets were observed in all the specimens tested, and their depths were less than the maximum grain size estimated by the statistics of the extreme values, but the distribution of stage I facet depths approximately corresponded to the maximum value distributions of grain size of the materials. The growth rates of small cracks followed log-normal distributions independent of grain size. The coefficients of variation, η, of growth rate in coarse-grained material were smaller than those in fine-grained material. The η values were significantly large at a/d 3 (a = crack depth, D = grain size), indicating that the relative size of microstructurally small cracks was not dependent on grain size.     

Fatigue crack initiation and propagation under cyclic contact loading

A computational model for contact fatigue damage analysis of gear teeth flanks is presented in this paper. The model considers the conditions required for the surface fatigue crack initiation and then allows for proper simulation of the fatigue crack propagation that leads to the appearance of small pits on the contact surface. The fatigue process leading to pitting is divided into crack initiation and a crack propagation period.The model for prediction of identification of critical material areas and the number of loading cycles, required for the initial fatigue crack to appear, is based on Coffin-Manson relations between deformations and loading cycles, and comprises characteristic material fatigue parameters. The computational approach is based on continuum mechanics, where a homogenous and elastic material model is assumed and results of cyclic loading conditions are obtained using the finite element method analysis.The short crack theory together with the finite element method is then used for simulation of the fatigue crack growth. The virtual crack extension (VCE) method, implemented in the finite element method, is used for simulating the fatigue crack growth from the initial crack up to the formation of the surface pit. The relationship between the stress intensity factor K and crack length a, which is needed for determination of the required number of loading cycles N_p for a crack propagation from the initial to the critical length, is shown.     

Finite element modelling of fatigue crack initiation in SiC-fibre reinforced titanium alloys

In the present investigation, fatigue crack initiation in SiC fibre (SCS-6) reinforced titanium has been analysed on the basis of a finite element (FE) model. In this composite material after processing a complicated interfacial zone exists, consisting of the remains of the carbon coating and the reaction zone. This reaction zone usually causes the initiation of a fatigue crack as it fails at a low stress. The growth of a fatigue starting at a reaction layer crack is analysed for different thick reaction layers (from 0.5 to 3 μm). The conditions under which a fatigue crack can be arrested and the influence of additional fibre failure on fatigue crack growth have been analysed. The results show that the formation of the matrix crack largely depends on the applied stress and reaction layer thickness. Under an applied stress, σ_max<800MPa, a crack in 1-μm-thick reaction layer cannot extend into the matrix. For higher applied stress a matrix crack can grow form the cracked reaction layer but after an extension of several microns it can be arrested. A mechanism of ΔK-reduction is found to be responsible for the crack arrest. The thickness of the reaction layer up to 3 μm has no significant influence on fatigue crack growth rate for larger fatigue cracks (>10 μm).     

TA15钛合金的高周疲劳性能和断裂特征

研究了双态组织的TA15钛合金的高周疲劳性能和疲劳断裂特征,结果表明,β转变组织中次生α相的数量和形态对疲劳性能有显著影响,次生相α相的球化显著降低了合金抗裂纹扩展的能力,而大量的片状次生α相则通过造成疲劳裂纹的分枝有效地降低了疲劳裂纹的扩展速度,提高了疲劳极限.     

Fatigue analysis for crack initiation

For the prediction of life leading to fatigue crack initiation, a method for performing a cycle-by-cycle local stress analysis at the stress concentration area of a structural component was developed. Elastoplastic stress-strain values along the hysteresis loop are traced for each load reversal in making the life prediction calculations. In this manner, the load sequence effect and the residual stress due to local yielding are inherently included. Neuber's rule and a linear rule were used with this method and compared. The results of life prediction were compared with test results. The use of the linear rule provided more accurate predictions than using other alternatives, including Miner's rule.