High Stress Regime Research Articles

High‐Temperature Micropillar Compression Creep Testing of Constituent Phases in Lead‐Free Solder

As the size of solder interconnects used in electronics packaging decreases, methods for characterizing the creep behavior of solder at ever smaller length scales need to be developed. Long duration micropillar compression experiments at constant loads and temperatures ranging from 60 to 160 °C were used to characterize the creep behavior in pure Sn dendrites and the Sn–Ag3Sn eutectic constituent in a lead‐free Sn–3.5Ag solder alloy. The stress exponent for the Sn dendtrites as well as the eutectic at low stresses was shown to be 1, suggesting a diffusion‐based mechanism, while at high stresses the eutectic stress exponent was 4, suggesting a dislocation‐based mechanism. Low activation energies indicative of a high diffusivity path (around 30 kJ mol−1) were seen in the dendrites at all temperatures and stresses as well as in the eutectic at low stresses. In the high stress regime of the eutectic, the activation energy transitions from 36 to 97 kJ mol−1 above 120 °C, indicating a transition to a lattice diffusion‐based mechanism.

Effect of Si on the creep properties of AZ61 cast magnesium alloy

In the present study, the effect of silicon on the impression creep properties of AZ61 alloy was studied under different normalized stress values between 0.02 and 0.0425 at temperatures ranging from 423 to 495 K. The results showed that the steady state creep rate is decreased with increasing silicon content. The improvement of creep resistance of the alloy was ascribed to the formation of Mg2Si intermetallic phase having two Chinese script and polygonal morphologies. It was found that the stress exponent, n, varies between 4 and 7 for low stress values and between 10 and 14 for high stress levels. Creep activation energy values of 102–123 kJ/mol and 167–190 kJ/mol obtained for the low and high stress regimes, respectively. The obtained stress exponent and creep activation energies reveal that climb controlled dislocation creep and PLB are the dominant mechanisms under low and high stress values, respectively and Si has no influence on the dominant creep mechanism.

Influence of Dislocation Density on Micromechanical Characteristics of Cu<sub>6</sub>Sn<sub>5</sub> and Cu<sub>3</sub>Sn

The influence of dislocation density on micromechanical characteristics of Cu6Sn5 and Cu3Sn was studied by nanoindentation. The dislocation density dependent hardness of Cu6Sn5 and Cu3Sn was quantitative analyzed. High dislocation density increased the critical shear stress corresponding to the first pop-in events and induced micro plastic deformation before the first pop-in events. For Cu6Sn5, dislocation creep and lattice diffusion dominate the high stress regime (HSR) and the low stress regime (LSR), respectively, regardless of the dislocation density. High dislocation density increases the stress exponent (n) of HSR, but decrease n of LSR. Dislocation motion is the dominate creep mechanism of unstrained Cu3Sn. After pre strain, the creep behavior of Cu3Sn was divided into HSR and LSR. But dislocation motion is still the dominate creep mechanism. Potential mechanism of the dislocation density dependent micromechanical characteristics was explained based on our experimental results.

A comparative study of indentation induced creep in pure magnesium and AZ61 alloy

Nanoindentation creep tests were performed on pure Mg and Mg–6wt% Al–1wt% Zn (AZ61) alloy at room temperature. Plastic flow and creep were more pronounced in Mg than in AZ61. Pure Mg was found to exhibit two distinct steady state stress regimes, with the values of stress exponent equal to 4.5 and 12. Twinning is most likely to dominate initially, in the high stress regime. Crystallographic re-orientation, caused by twinning renders the grains favorable for 〈c+a〉 slip in low stress regime. Grain boundary creep was also investigated, and appeared to be related to grain boundary sliding (n=2) in low stress regime. Creep response of AZ61 consisted of a single stress exponent regime (n~1) for both grain interior as well as grain boundary. A combination of extension and contraction twinning seems to be the dominant deformation mechanism. Chemical potential gradient induced diffusion is also likely to play an important role in creep deformation.

Overleveraging, Financial Fragility and the Banking-Macro Link: Theory and Empirical Evidence

We investigate consequences of overleveraging and financial sector stress on real economic activities. When banks become vulnerable, due to high leveraging, and there is a strong feedback between the real and the financial sector, a regime of high financial stress may arise. The vulnerability of the banking system in a high leverage and a high-stress regime can, through macro feedback effects, result in unstable dynamics. To assess this question empirically, we employ a nonlinear, multi regime vector autoregression approach (MRVAR), to explore the consequences of instabilities arising from regime dependent shocks. We analyze data on industrial production and the IMF Financial Stress Index. In order to assess how output is affected by the individual risk drivers making up the IMF index, we study eight economies, the U.S., Canada, Japan and the UK, and for the four largest euro zone economies, namely, Germany, France, Italy, and Spain, using Granger-causality and nonlinear impulse response analysis. Our results strongly suggest that financial sector stress, exerts a strong, nonlinear influence on economic activity, but that individual risk drivers affect economic activity rather differently across stress regimes and across countries.

The influence of stress-regime dependent creep model and ductility in the prediction of creep crack growth rate in Cr–Mo–V steel

In this paper, the stress-regime dependent creep model and ductility have been implemented in a ductility exhaustion based damage model, and their influence on creep crack growth (CCG) behavior of materials have been analyzed. By using the stress-regime dependent creep model and ductility, the CCG rate in a Cr–Mo–V steel over a wide range of C* has been predicted by finite element analyses. The predicted CCG rates agree with the available experimental data in the literature. The analysis results show that with increasing C*, the creep model and ductility for determining crack-tip creep damage accumulation change from the low-stress regime model and ductility through a combination of low- and high-stress regime model and ductility to high-stress regime model and ductility. These changes lead to the line segments of the da/dt−C* curves. In CCG life analyses and designs of high temperature components, the stress-regime dependent creep model and ductility need to be used.

Comparison of microstructural crack paths between hypo-eutectic Al–Si–Cu and Al–Si–Mg cast alloys in high plasticity regimes under rotating bending

Abstract It is nowadays widely recognized that good and profound knowledge of the deformation behavior and/or crack propagation behavior is a vital part of high performance simulation for advanced high stress fatigue life prediction. Concerning of those two different approaches, one must, however, be aware that additional and detailed information of fatigue induced crack nucleation, its further propagation path and the associated crack growth rate is important for the intrinsic understanding of the material damage process. This paper investigates how the fatigue process works in high stressed Al–Si–Mg and Al–Si–Cu fatigue samples starting from crack nucleation to sample rupture by rotating bending loads at room temperature. The samples themselves were taken directly from serial casted and heat treated cylinder head components and were processed to conventional hourglass specimens. Because no suitable test method which fulfils all the necessary test requirements was commercially available, a new rotating bending testing machine which directly operates in a confocal light microscope was developed. This test method allowed us to easily compare every change of the crack growth rate (especially for microstructural small cracks) with the microstructure and its crack path. At high stress regimes eutectic phases became very important for fatigue induced crack nucleation and early crack propagation. In the first third of the lifetime, both alloys cracked on multiple spots by interface cracking between hard phase particles (β-phase) and eutectic matrix. Depending on the crack length and stress intensity factor Δ K proceeding cracks were also able to move into the dentritic matrix (α-phase). At the end of the lifetime only a fraction of all nucleated cracks of each specimen became large enough to exert influence for fatigue failure. Furthermore, using this test method as an integral element of stress gradient fatigue investigation makes it possible to identify and define major microstructural crack relevant objects like particles during material fatigue. Hence, it not only increases the knowledge for high performance fatigue simulation but also provides a tool for material optimization by fatigue processes themselves.

Finite element and distinct element analysis of the stability of a large underground hydropower machine hall in the Himalayas

Numerical simulations have been performed to assess the stability of a large underground powerhouse in the Himalayas, using both finite element and distinct element approaches. Large convergences (around 250–300 mm) along the 45 m high wall of the Machine Hall have been measured by total station measurements during construction and up to 60 mm in the post construction and operational phase. Displacements are continuing at a reduced rate of about 3 to 6 mm per year. A large number of rock bolts have failed in the powerhouse and the shotcrete liner presents cracks and failure marks, thus questioning the long-term integrity and stability of the existing rock support system. The purpose of the numerical analysis was to back-calculate the prevailing rock mass conditions surrounding the machine hall, thereby gaining a better understanding of the mechanisms responsible for the instability in the cavern. The results from the analysis indicate that there was possibly an underestimation of the rock support requirements needed for the cavern, coupled with a not so good installation (incomplete grouting of the bolts). Both the length and the capacity of the rock bolts were underestimated presumably due to the existence of a high stress regime in the area, which may not have been taken into consideration in the design of rock support. The effect of a possible earthquake, frequent in this area, has also been studied and proves to induce a significant increase of the displacements and the support failure.

Measuring stress in money markets: A dynamic factor approach

We extract an index of interest rate spreads from various money market segments to assess the level of funding stress in real time. We find that during the 2007–2009 financial crisis, money markets switched between low and high stress regimes except for brief periods of extreme stress. Transitions to lower stress regimes are typically associated with the non-standard policy measures by the Federal Reserve.

Creep behaviour of porous metal supports for solid oxide fuel cells

The creep behaviour of porous iron–chromium alloy used as solid oxide fuel cell support was investigated, and the creep parameters are compared with those of dense strips of similar composition under different testing conditions. The creep parameters were determined using a thermo-mechanical analyser with applied stresses in the range from 1 to 15 MPa and temperatures between 650 and 800 °C. The Gibson–Ashby and Mueller models developed for uniaxial creep of open-cell foams were used to analyse the results. The influence of scale formation on creep behaviour was assessed by comparing the creep data for the samples tested in reducing and oxidising atmospheres. The influence of pre-oxidation on creep behaviour was also investigated. In-situ oxidation during creep experiments increases the strain rate while pre-oxidation of samples reduces it. Debonding of scales at high stress regime plays a significant role affecting the creep behaviour of the metal supports, in particular the stress exponent. The variation of the elastic modulus as function of temperature and oxidation conditions was also determined by a high temperature impulse excitation technique. Additionally nano-indentation testing was performed in the metal oxide interface to elucidate the mechanical properties of the oxide scales and qualitative information about the oxide scale-metal interfacial bonding.

Geometrical Scale-Sensitive Fatigue Properties of Ti–6.5Al–3.5Mo–1.5Zr–0.3Si Alloys With α/β Lamellar Microstructures

Fatigue properties of the Ti–6.5Al–3.5Mo–1.5Zr–0.3Si alloy sheets containing different numbers of α/β Widmanstatten colonies in the thickness direction of the sheets were investigated by tension–tension fatigue testing. It is found that fatigue properties of the Ti alloy either in low- or high-stress amplitude regimes become more sensitive to the sheet thickness of the Ti alloy as the sheet thickness is comparable to the length scale of the Widmanstatten colonies. The basic mechanism of such length scale-sensitive fatigue properties in the Ti alloy was elucidated.

Indentation creep of a cast Mg–6Al–1Zn–0.7Si alloy

Creep behavior of an Mg–6Al–1Zn–0.7Si cast alloy was investigated by indentation creep in order to evaluate the correspondence of indentation creep results with those obtained by other creep test methods. All creep tests were carried out in the temperature range 423–523K and under constant loads of 5 and 20N. Based on the steady-state power-law creep relationship, the average stress exponents of about 5.8 and 11.3, and activation energies of 82.3 and 127.8kJ/mol were obtained in the low- and high-stress regimes, respectively. These results are in good agreement with those of the impression and conventional compressive creep tests reported in the literature. It is suggested that the operative creep mechanism is pipe-diffusion-controlled dislocation viscous glide in the low-stress regime, and dislocation climb with some sort of back stress, similar to those noted in dispersion strengthening alloys, in the high-stress regime.

The microstructure and creep characteristics of cast Mg–4Zn–0.5Ca and Mg–4Zn–0.5Ca–2RE alloys

The effect of 2wt% Ce-rich rare earth (RE) addition on the microstructure and creep behavior of the Mg–4Zn–0.5Ca (wt%) alloy was investigated by impression creep tests in the temperature range of 423–498K and under stresses in the range of 250–800MPa for dwell times up to 3600s. Addition of RE was shown to significantly improve the creep resistance of the base alloy. Formation of the thermally stable (MgZn)12RE and Mg17RE2 particles was responsible for such an improvement. The creep behavior can be divided into two stress regimes, with a change from the low-stress regime to the high-stress regime occurring, depending on the test temperature, around 0.024<(σ/G)<0.038 and 0.031<(σ/G)<0.045 for the base- and RE-containing alloys, respectively. In the low-stress regime, stress exponents were in the range 5.0–5.2 and 5.1–6.2, and activation energies were found to be 65±4 and 57±7kJmol−1 for the base and RE containing alloys, respectively. The activation energies were stress dependent and this implied that the stress assisted dislocation climb controlled by pipe diffusion is the rate-controlling mechanism. In the high-stress regime, stress exponents were in the range 10.8–11.7 and 12.1–14.0, and activation energies were 105±20 and 85±18kJmol−1 for the base and RE containing alloys, respectively. Power-law creep was invalid in this region and activation energies were stress dependent, suggesting that the stress-assisted dislocation climb controlled by lattice diffusion, accelerated due to high concentration of vacancies resulting from applying high stresses, is the rate-controlling mechanism.

Indentation size effect and micromechanics characterization of intermetallic compounds in the Au–Sn system

The indentation size effect and the micromechanics characterization of intermetallic compounds in the Au–Sn system have been investigated by nanoindentation, using continuous multi-cycle loading mode and load-control mode, respectively. An analytic model based on the enlarged plastic zone and the maximum allowable density of geometrically necessary dislocation was established to describe the relationship between the indentation hardness and depth. Our new model gives better predictions of the indentation hardness of Au5Sn, AuSn and AuSn2 for small indentation depths compared to the Nix–Gao model. Pop-in events in the load–displacement curves corresponding to the peaks in the normalized velocity–load curves represent the elastic–plastic or harden-yield transition during indentation. A viscoplastic creep equation was employed to evaluate the creep behavior of the Au–Sn intermetallics. The stress exponents (n) can be well defined into two stress regimes: the high stress regime (HSR) and the low stress regime (LSR). In the HSR, dislocation motion is the dominant creep mechanism with n>5, while in the LSR, grain boundary sliding dominates the creep of Au5Sn and AuSn2 with n≈2, and dislocation viscous glide dominates the creep of AuSn and AuSn4 with n around 3.

Comparing potentials for gas outburst in a Chinese anthracite and an Australian bituminous coal mine

Gas outbursts in underground mining occur under conditions of high gas desorption rate and gas content, combined with high stress regime, low coal strength and high Young’s modulus. This combination of gas and stress factors occurs more often in deep mining. Hence, as the depth of mining increases, the potential for outburst increases. This study proposes a conceptual model to evaluate outburst potential in terms of an outburst indicator. The model was used to evaluate the potential for gas outburst in two mines, by comparing numerical simulations of gas flow behavior under typical stress regimes in an Australian gassy mine extracting a medium-volatile bituminous coal, and a Chinese gassy coal mine in Qinshui Basin (Shanxi province) extracting anthracite coal. We coupled the stress simulation program (FLAC3D) with the gas simulation program (SIMED II) to compute the stress and gas pressure and gas content distribution following development of a roadway into the targeted coal seams. The data from gas content and stress distribution were then used to quantify the intensity of energy release in the event of an outburst.

Reservoir stimulation and induced seismicity: Roles of fluid pressure and thermal transients on reactivated fractured networks

We utilize a continuum model of reservoir behavior subject to coupled THMC (thermal, hydraulic, mechanical and chemical) processes to explore the evolution of stimulation-induced seismicity and related permeability in EGS reservoirs. Our continuum model is capable of accommodating changes in effective stresses that result due to the evolving spatial variations in fluid pressure as well as thermal stress and chemical effects. Discrete penny-shaped fractures (∼10–1200m) are seeded within the reservoir volume at both prescribed (large faults) and random (small fractures) orientations and with a Gaussian distribution of lengths and location. Failure is calculated from a continuum model using a Coulomb criterion for friction. Energy release magnitude is utilized to obtain the magnitude-moment relation for induced seismicity by location and with time. This model is applied to a single injector (stimulation) to the proposed Newberry EGS field (USA). Reservoir stimulation is assumed to be completed in four zones at depths of 2000, 2500, 2750 and 3000m. The same network of large fractures (density of 0.003m−1 and spacing 300m) is applied in all zones and supplemented by more closely spaced fractures with densities from 0.26m−1 (deepest zone) through 0.5m−1 (shallow zone) to 0.9m−1 (intermediate depth zone). We show that permeability enhancement is modulated by hydraulic, thermal, and chemical (THMC) processes and that permeability increases by an order of magnitude during stimulation at each depth. For the low density fracture networks, the increase in permeability reaches a smaller radius from the injection point and permeability evolution is slower with time compared to the behavior of the higher density fracture network. For seismic events that develop with the stimulation, event magnitude (Ms) varies from −2 to +1.9 and the largest event size (∼1.9) corresponds to the largest fractures (∼1200m) within the reservoir. We illustrate that the model with the highest fracture density generates both the most and the largest seismic events (Ms=1.9) within the 21 day stimulation. Rate of hydraulic and thermal transport has a considerable influence on the frequency, location and time of failure and ultimately event rate. Thus the event rate is highest when the fracture network has the largest density (0.9m−1) and is located at depth where the initial stresses are also highest. Also apparent from these data is that the closely spaced fracture network with the higher stress regime (at the deeper level) has the largest b-value ∼0.74.

Fatigue behaviour of notched ADI castings

This work aims at studying the capability of mechanical stress analysis software (ANSYS 12·0) as a non-destructive tool to characterise and quantify the fatigue strength of notched austempered ductile iron (ADI) castings with different radii (from 1 to 3 mm). Castings were made of ductile iron with a chemical composition of 3·55C–2·18Si–0·35Mn–0·022P–0·008S–0·045Mg. The samples were heat treated by austenitising at 900°C for 1 h and then rapidly quenched into two different salt baths at 350 and 400°C for 1 h each. Because the properties of the samples austempered at 350°C were matched with the ASTM standard for ADI alloy grade 2 (1050-700-07), the fatigue strength of the samples austempered at 350°C was first predicted using a mechanical stress analysis software (ANSYS 12·0). To verify these theoretical results obtained by ANSYS 12·0, experimental fatigue tests using rotating bending fatigue machine at high stress regime were performed on the samples austempered at 350°C. The fatigue samples were machined with different radii of 1, 1·5 and 2 mm. The results showed that the predicted fatigue strength by ANSYS 12·0 is very close to the experimental one. In addition, both austempering temperatures of 350 and 400°C showed relatively similar notch sensitivity factor q, and its value decreased with increasing notch radius.

Carry Funding and Safe Haven Currencies: A Threshold Regression Approach

In this paper, we analyze which currencies can be regarded as safe haven currencies. Our empirical approach allows us to distinguish between a low and high stress regime, and to control for the impact of carry trade reversals and other fundamental determinants. We therefore address the question of whether a supposed safe haven currency only appreciates in times of crises because carry trades are unwound, in which the corresponding currency has served as funding currency, or whether it possesses “true” safe haven qualities; i.e. it provides a hedge against global stock market losses in stressful times even after controlling for the impact of carry trade reversals. The latter issue has largely been brushed aside in the extant literature but has important policy implications for the justification of central bank FX interventions in times of crises. According to the estimation results, two currencies, the Swiss franc and (to a lesser extent) the US dollar qualify as safe haven currencies, and the euro serves as a hedge currency. Results for the yen support its role as a carry funding vehicle, but not necessarily that of a safe haven currency. While the focus is on effective exchange rates, the paper also contains a separate analysis of bilateral euro-based exchange rates, given the euro’s prominent role during the euro area sovereign debt crisis.

High Temperature Plasticity of Bimetallic Magnesium and Aluminum Friction Stir Welded Joints

The high temperature deformation of a bimetallic AZ31/AA6061 Friction Stir Welded joint was investigated in the present study by constant load creep experiments carried out at 473 K (200 °C). The microstructural analysis revealed the strongly inhomogeneous nature of the weld, which was characterized by an extremely fine grain size in the magnesium-rich zones and by the extensive presence of intermetallic phases. In the high stress regime, the creep strain was concentrated in the refined and particle-rich microstructure of the weld zone, while the AA6061 base metal remained undeformed. In the low stress regime, deformation became more homogeneously distributed between the AZ31 base metal and the weld zone. The creep behavior of the weld was found to obey the constitutive equation describing the minimum creep rate dependence on applied stress for the base AZ31, slightly modified to take into account the finer microstructure and the role of secondary phase particles, i.e., the retardation of grain growth and the obstruction of grain boundary sliding.

In situ monitored in-pile creep testing of zirconium alloys

The experiments described herein were designed to investigate the detailed irradiation creep behavior of zirconium based alloys in the HALDEN Reactor spectrum. The HALDEN Test Reactor has the unique capability to control both applied stress and temperature independently and externally for each specimen while the specimen is in-reactor and under fast neutron flux. The ability to monitor in situ the creep rates following a stress and temperature change made possible the characterization of creep behavior over a wide stress–strain-rate–temperature design space for two model experimental heats, Zircaloy-2 and Zircaloy-2+1wt%Nb, with only 12 test specimens in a 100-day in-pile creep test program. Zircaloy-2 specimens with and without 1wt% Nb additions were tested at irradiation temperatures of 561K and 616K and stresses ranging from 69MPa to 455MPa. Various steady state creep models were evaluated against the experimental results. The irradiation creep model proposed by Nichols that separates creep behavior into low, intermediate, and high stress regimes was the best model for predicting steady-state creep rates. Dislocation-based primary creep, rather than diffusion-based transient irradiation creep, was identified as the mechanism controlling deformation during the transitional period of evolving creep rate following a step change to different test conditions.