Near-threshold Regime Research Articles

Subcycle fatigue crack growth and equivalent initial flaw size model for fatigue life assessment under arbitrary loadings for Al-7075

A novel fatigue-life prediction methodology combining a subcycle fatigue crack growth (FCG) analysis and equivalent initial flaw size (EIFS) concept is proposed in this paper. This research focuses on extending a previously developed time-based subcycle fatigue crack growth model to a near-threshold regime and under multiaxial loadings. First, the threshold FCG behavior using subcycle FCG is discussed, and a new temporal kernel function to include intensity factor corresponding to the near-threshold region is proposed. Following this formulation, the multiaxial load case scenario is considered for mixed-mode FCG using a critical plane approach. Next, the general multiaxial loading is converted to an equivalent uniaxial loading for life prediction. Next, model predictions under arbitrary loadings (e.g., uniaxial and multiaxial, constant and variable amplitude loading, and random spectrums) are compared with experimental data from open literature and internal testing. Multiple conclusions and potential future work have been suggested using the proposed model.

Controlling Metastable Infection Patterns in Multilayer Networks via Interlink Design

Recent research on epidemic spreading in networks has uncovered the phenomena of metastable infection patterns, where epidemics can be sustained in localized regions of activity, in contrast to the classical dichotomy between a quick extinction of infections and a network-wide global infection. Our objective in this work is to leverage this localized infection state to achieve <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">controlled</i> spreading in multilayer networks via intelligent design of the interlink structure between the network layers. Following the approach in recent works, the dynamic contact process is approximated by studying the dynamics in local regions around the hubs of the network. This allows us to approximately track the contact process in the near-threshold regime and estimate the mean metastable infection size over the lifetime of the infection. Furthermore, interlinking strategies are devised that can achieve a desired infection size under certain conditions. Theoretically optimal interlink structures can be derived under special cases, whereas greedy strategies are proposed for the general case. We compare the interlinking strategies developed in this work to some popular heuristics and demonstrate their superiority by extensive simulation experiments on both synthetic and real-world networks.

Microstructure evolution, fatigue crack growth, and ultrasonic fatigue in As-fabricated laser powder bed and conventionally cast Al–10Si-0.4Mg: A mechanistic understanding and integrated flaw-sensitive fatigue design methods

Additive manufacturing (AM) enables fabrication of lightweight components with high geometric complexity, and its broad adoption in high-integrity structural applications relies on a fundamental understanding of the processing-microstructure-fatigue performance relationships and development of fatigue design methods. In this study, microstructures, tensile properties, and long and small fatigue crack growth (FCG) behaviors of laser powder bed (LPB) manufactured Al–10Si-0.4Mg were systematically investigated in both orientations with respect to the build direction, and compared to those of an equivalent conventionally cast material. Tensile properties of the LPB material demonstrated orientation dependency, and exceeded on average those of the cast material, with higher yield (>170% increase) and tensile (>150% increase) strengths and enhanced elongation (88% increase in horizontal orientation). In contrast, long FCG properties at various stress ratios showed minor differences associated with orientation (attributed to residual stress), and were lower compared to the cast alloy, particularly in the near-threshold regime. Mechanisms of FCG were identified at all growth stages using fractography and electron backscatter diffraction, and further integrated with the loading conditions by creating dual-parameter load-microstructure-damage mechanisms design maps. Ultrasonic fatigue testing was complementary conducted on the LBP-fabricated materials to study the very-high cycle fatigue regime (for both orientations and different surface conditions), and the results were correlated with the FCG data using Kitagawa-Takahashi diagrams to unify the two fatigue testing methods, and together with the dual-parameter maps, provide a microstructure-sensitive design toolset for fatigue crack initiation and growth resistance.

Determination of fatigue crack propagation thresholds for steel in presence of environmental effects

The experimental determination of the resistance to fatigue crack propagation in steel, particularly in the so-called near-threshold regime, is a crucial issue for safety-relevant components which are designed to operate for a large number of loading cycles before undergoing periodic inspections. This work summarizes the most relevant results of extensive experimental campaigns conducted at BAM and IPM over the last years, which have been devoted to the determination of fatigue crack propagation characteristics on medium and high strength steels. The influence of environment, oxide-induced crack closure and test methodologies in the near-threshold regime are discussed.

Stretching Hookean ribbons part I: relative edge extension underlies transverse compression and buckling instability.

The wrinkle pattern exhibited upon stretching a rectangular sheet has attracted considerable interest in the "extreme mechanics" community. Nevertheless, key aspects of this notable phenomenon remain elusive. Specifically-what is the origin of the compressive stress underlying the instability of the planar state? what is the nature of the ensuing bifurcation? how does the shape evolve from a critical, near-threshold regime to a fully developed pattern of parallel wrinkles that permeate most of the sheet? In this paper we address some of these questions through numerical simulations and analytic study of the planar state in Hookean sheets. We show that transverse compression is a boundary effect, which originates from the relative extension of the clamped edges with respect to the transversely contracted, compression-free bulk of the sheet, and draw analogy between this edge-induced compression and Moffatt vortices in viscous, cavity-driven flow. Next, we address the instability of the planar state and show that it gives rise to a buckling pattern, localized near the clamped edges, which evolves-upon increasing the tensile load-to wrinkles that invade the uncompressed portion of the sheet. Crucially, we show that the key aspects of the process-from the formation of transversely compressed zones, to the consequent instability of the planar state and the emergence of a wrinkle pattern-can be understood within a Hookean framework, where the only origin of nonlinear response is geometric, rather than a non-Hookean stress-strain relation.

Fatigue crack propagation behaviors in Ti-5Al-3Mo-3V-2Zr-2Cr-1Nb-1Fe alloy with STA and BASCA heat treatments

Fatigue crack propagation behaviors of a novel high strength Ti-5Al-3Mo-3V-2Zr-2Cr-1Nb-1Fe alloy with equiaxed and lamellar microstructures were systematically investigated. Fatigue crack propagation tests at both increasing and decreasing stress intensity factor range values were carried out with a frequency of 15 HZ and stress radio R of 0.1 by using compact tension samples. The sample with lamellar microstructure displayed the faster fatigue crack propagation rates in near-threshold regime compared to the sample with equiaxed microstructure. The fatigue threshold (ΔKth) was 2.7 MPa·m1/2 for lamellar microstructure, and 3.2 MPa·m1/2 for equiaxed microstructure. The steady state crack growth rate in lamellar microstructure was slightly slower than that in equiaxed microstructure in the Paris regime, while much faster in the rapid growth regime. The interactions between crack path and microstructures as well as the microscopic fracture surface morphology in both microstructures were detected and analyzed by scanning electron microscope (SEM), revealing the different crack propagation behaviors in three regimes. The results showed that the crack propagation behaviors were a result of two contributing factors: interface obstacles and crack front profile. The increased fatigue crack propagation resistance of equiaxed microstructure in near-threshold regime can be attributed to the interface obstacles which dominated over the rougher crack front profile. While the higher fatigue crack growth resistance for lamellar microstructure in Paris regime was attributed to the more positive effect of rougher crack front profile. In the rapid growth regime, the crack in lamellar microstructure was found to be extended along the grain boundary α, which was regarded as a low energy crack path and led to the faster crack propagation rate.

Fatigue and Crack Growth under Constant- and Variable-Amplitude Loading in 9310 Steel Using “Rainflow-on-the-Fly” Methodology

Fatigue of materials, like alloys, is basically fatigue-crack growth in small cracks nucleating and growing from micro-structural features, such as inclusions and voids, or at micro-machining marks, and large cracks growing to failure. Thus, the traditional fatigue-crack nucleation stage (Ni) is basically the growth in microcracks (initial flaw sizes of 1 to 30 μm growing to about 250 μm) in metal alloys. Fatigue and crack-growth tests were conducted on a 9310 steel under laboratory air and room temperature conditions. Large-crack-growth-rate data were obtained from compact, C(T), specimens over a wide range in rates from threshold to fracture for load ratios (R) of 0.1 to 0.95. New test procedures based on compression pre-cracking were used in the near-threshold regime because the current ASTM test method (load shedding) has been shown to cause load-history effects with elevated thresholds and slower rates than steady-state behavior under constant-amplitude loading. High load-ratio (R) data were used to approximate small-crack-growth-rate behavior. A crack-closure model, FASTRAN, was used to develop the baseline crack-growth-rate curve. Fatigue tests were conducted on single-edge-notch-bend, SEN(B), specimens under both constant-amplitude and a Cold-Turbistan+ spectrum loading. Under spectrum loading, the model used a “Rainflow-on-the-Fly” subroutine to account for crack-growth damage. Test results were compared to fatigue-life calculations made under constant-amplitude loading to establish the initial microstructural flaw size and predictions made under spectrum loading from the FASTRAN code using the same micro-structural, semi-circular, surface-flaw size (6-μm). Thus, the model is a unified fatigue approach, from crack nucleation (small-crack growth) and large-crack growth to failure using fracture mechanics principles. The model was validated for both fatigue and crack-growth predictions. In general, predictions agreed well with the test data.

XFEL and HHG interaction with matter: Effects of ultrashort pulses and random spikes

The theory of photoionization describing the interaction of x-ray free-electron laser (XFEL) pulses and high-harmonic-generated (HHG) radiation is generalized to ultrashort laser pulses, where the concept of the standard ionization probability per unit time in Fermi’s golden rule and in Einstein’s theory breaks down. Numerical calculations carried out in terms of a generalized photoionization probability for the total duration of pulses in the near-threshold regime demonstrate essentially nonlinear behavior, while absolute values may change by orders of magnitude for typical XFEL and HHG pulses. XFEL self-amplified spontaneous emission pulses are analyzed to reveal general features of photoionization for random and regular spikes: the dependences of the nonlinear photoionization probability on carrier frequency and spike duration are very similar, allowing an analytical expectation value approach that is valid even when there is only limited knowledge of random and regular parameters. Numerical simulations carried out for typical parameters demonstrate excellent agreement.

Effect of Solution Annealing on Fatigue Crack Propagation in the AISI 304L TRIP Steel.

Fatigue crack propagation in near-threshold regime was studied in the 304L austenitic stainless steel in two microstructural states: as-received (AR) with finer microstructure and low susceptibility to the transformation-induced plasticity (TRIP) effect, and solution-annealed (SA) with coarser microstructure and higher susceptibility to TRIP. At the load ratio R = 0.1 the threshold was higher in the SA state than in the AR state due to coarser grains and possibly the TRIP effect. In order to clarify the role of crack closure, experiments at R = 0.7 were done. The threshold in the SA state was still higher by 1 MPa·m0.5. This effect was identified as crack tip shielding induced by phase transformation, an example of a non-closure shielding effect. Higher resistance to crack growth in the SA state was attributed to promoted martensitic transformation in non-favorable oriented grain families rather than thicker martensite layers in the crack path area. The conclusions were verified by experiments at R = 0.7 and temperature 150 °C > Ms which did not reveal any notable difference in thresholds. However, the threshold values were affected by the load-shedding gradient C = −dΔK/da, which had to be equalized in both experimental setups inside and outside the furnace.

Near-Threshold Fatigue Crack Growth Behavior of ECAPed Ultrafine-Grained Copper

Fatigue crack growth resistance of ultrafine grained Cu processed by equal channel angular pressing (ECAP) was investigated. Particular emphasis was devoted to the effects of microstructure evolution on fatigue crack growth in the near-threshold regime. The ultrafine grained Cu exhibits a lower fatigue threshold than coarse-grained Cu at stress ratios of 0.1 and 0.7. Fatigue induced coarsening of the UFG structure near the fatigue crack and intergranular fatigue crack growth are observed.

Circuit design using Schmitt Trigger to reliability improvement

This paper presents a design strategy to reduce the impact of process variations and soft error susceptibility in FinFET circuits. The mitigation is provided by connecting a Schmitt Trigger at the logic gate output. The improvements in power and delay variability can reach up to 32.6% and 42.1%, respectively, with logic cells almost immune to soft error even at the near-threshold regime. When compared with other circuit-level methods such as sleep transistor, decoupling cells, and transistor reordering, on average, the Schmitt Trigger technique is at least 6%, 8%, and 10.5% more robust to process variability, respectively.

Room and elevated temperature fatigue crack propagation behavior of Inconel 718 alloy fabricated by laser powder bed fusion

The fatigue crack propagation (FCP) behavior of Inconel 718 alloy manufactured by laser powder bed fusion (L-PBF) was studied at 25 and 650 °C, and compared to those of conventionally processed counterpart. The FCP rates of L-PBF Inconel 718 alloy were found to be significantly higher than those of conventionally processed counterpart at 25 °C in low and intermediate ΔK regimes. The FCP rates decreased in near-threshold ΔK regime at 650 °C, while the reversal occurred above ΔK of 7 MPa√m, as compared to those at 25 °C. The FCP behavior of L-PBF Inconel 718 alloy was discussed based on micrographic and fractographic analyses.

Focal-shape effects on the efficiency of the tunnel-ionization probe for extreme laser intensities

We examine the effect of laser focusing on the effectiveness of a recently discussed scheme [M. F. Ciappina et al., Phys. Rev. A 99, 043405 (2019) and M. F. Ciappina and S. V. Popruzhenko, Laser Phys. Lett. 17, 025301 (2020)] for in situ determination of ultrahigh intensities of electromagnetic radiation delivered by multi-petawatt laser facilities. Using two model intensity distributions in the focus of a laser beam, we show how the resulting yields of highly charged ions generated in the process of multiple sequential tunneling of electrons from atoms depend on the shapes of these distributions. Our findings lead to the conclusion that an accurate extraction of the peak laser intensity can be made either in the near-threshold regime, when the production of the highest charge state happens only in a small part of the laser focus close to the point where the intensity is maximal or through the determination of the points where the ion yields of close charges become equal. We show that for realistic parameters of the gas target, the number of ions generated in the central part of the focus in the threshold regime should be sufficient for a reliable measurement with highly sensitive time-of-flight detectors. Although the positions of the intersection points generally depend on the focal shape, they can be used to localize the peak intensity value in certain intervals. Finally, the slope of the intensity-dependent ion yields is shown to be robust with respect to both the focal spot size and the spatial distribution of the laser intensity in the focus. When these slopes can be measured, they will provide the most accurate determination of the peak intensity value within the considered tunnel ionization scheme. In addition to this analysis, we discuss the method in comparison with other recently proposed approaches for direct measurement of extreme laser intensities.

Effects of crack orientation and heat treatment on fatigue-crack-growth behavior of AM 17-4 PH stainless steel

The effects of heat treatment and crack orientation on fatigue-crack-growth (FCG) behavior of 17-4 precipitation hardening (PH) stainless steel (SS) fabricated via a laser powder bed fusion (LPBF) additive manufacturing (AM) system were investigated. Accurate representation of FCG thresholds, the region defining crack growth as either very slow or nonexistent, is extremely important in adoption of AM for structural applications. In this study, new methods called compression pre-cracking constant-amplitude (CPCA) and load-reduction (CPLR) were used to generate FCG rate data in the near-threshold (low-rate) regime using non-standard or modified compact specimens. For comparison, the current ASTM load-reduction (LR) method was also used. Results indicate that FCG behavior of AM 17-4 PH SS in the Paris regime was comparable to that of wrought 17-4 PH SS in the peak-age condition. Although the post-manufacturing heat treatment was found to be necessary in order to improve tensile strength of this alloy, the results of this study indicate that this particular heat treatment process had no influence on FCG behavior of LPBF 17-4 PH SS. The effect of crack orientation with respect to the build direction however was evident. FCG rates were slightly lower for specimens with a crack parallel to the build direction (i.e. longitudinal crack) in the Paris regime as compared to that of specimens with a perpendicular crack (i.e. transverse crack). The near-threshold FCG behavior for specimens with a longitudinal crack did not show the usual stress ratio (R)-shift from low to high R. The low-R data was vastly different than the data generated using the specimens with a transverse crack. Our results also imply that both the current ASTM standard LR method and the new CPLR method induce remote closure, which prematurely slows down crack growth and produces an abnormally high threshold.

A Fully Static True-Single-Phase-Clocked Dual-Edge-Triggered Flip-Flop for Near-Threshold Voltage Operation in IoT Applications

A Dual-Edge-Triggered (DET) flip-flop (FF) that can reliably operate at low voltage is proposed in this paper. Unlike the conventional Single-Edge-Triggered (SET) flip-flops, DET-FFs can improve energy efficiency by latching input data at both clock edges. When combined with aggressive voltage scaling, significant efficiency improvement is expected. However, prior DET-FF designs were susceptible to Process, Voltage and Temperature (PVT) variations, limiting their operation at low voltage regimes. A fully static true-single-phase-clocked DET-FF is proposed to achieve reliable operation at voltages as low as a near-threshold regime. Instead of the two-phase or pulsed clocking scheme in conventional DET-FFs, a True-Single-Phase-Clocking (TSPC) scheme is adopted to overcome clock overlap issues and enable low-power operation. Fully static implementation also enables robust operation in a low voltage regime. The proposed DET-FF is designed in 28nm CMOS technology, and a comprehensive analysis including post-layout Monte Carlo simulation for wide PVT ranges is performed to validate the design approaches. Extensive analysis and comparison with prior-art DET-FFs confirmed that the proposed DET-FF can operate at the lowest voltage of 0.28 V for a temperature range of −40 °C to 120 °C while maintaining nearly-best energy efficiency and power-delay-product.

VASTA: A Wide Voltage Statistical Timing Analysis Tool Based on Variation-Aware Cell Delay Models

In the advanced technology nodes, process parameter variations are increasingly resulting in unpredictable device behavior. The issue is even aggravated by low power requirements which stretches the transistor operation into near-threshold regime. Despite device simulation gives precise results, it is time-consuming for static timing analysis and dynamic timing analysis. In this paper, we propose VASTA, a statistical timing analysis tool based on the variation-aware standard cell library. The tool efficiently supports statistical static timing analysis (SSTA) and statistical dynamic timing analysis (SDTA). The standard cell library models delay under operating environment effects by using quadratic regressions and multivariate adaptive regression splines. VASTA works on industry formats (.v and.sdc) and is designed to run in parallel during both SSTA and SDTA. The statistical cell library is built and verified using SMIC 40 nm and 28 nm PDK. The mean and standard deviation errors of cell delay models are 2.77% and 1.68% compared with SPICE simulation results under 10k Monte Carlo samples. The SSTA and SDTA are tested with ISCAS85, ISCAS89, and EPFL benchmark suites. The average mean and standard deviation errors of SSTA are 4.01% and 2.03%, which are similar to SDTA. Meanwhile, our SDTA is 17.7 times faster than traditional corner-based dynamic timing analysis which relies on generating .vcd cell activity files.

Variation-Aware Prediction of Circuit Performance in Near-Threshold Regime Using Supply-Independent Transition Threshold Points

Due to the highly variation-prone nature of the near-threshold voltage (NTV) circuits, it is critical to have design and performance models that consider process, voltage, and temperature (PVT) variations. However, in the NTV regime, the existing timing models are based on arbitrarily chosen ${V}_{\text {DD}}$ -dependent threshold points for effective current calculation that results in unreliability. In this article, an effective current delay model for an inverter operating in NTV regime is presented using supply-independent threshold points. The model is developed considering the input–output coupling capacitance and by relating the input and output currents of an inverter stage. This approach is physics-/topology-based and is valid for different technologies. This has been verified against HSPICE simulations and Synopsys Sentaurus 3-D technology computer-aided design (TCAD) simulations for STM 65-nm MOSFETs and 16-nm fin-shaped field-effect transistors (FinFETs), respectively, at different supply voltages, considering variation in threshold voltage and at different operating temperatures. The model predicts the transition delay values with an average (maximum) error of 3% (6%) and 4% (6%) for MOSFET and FinFET, respectively. Furthermore, the model is employed for digital buffer chain and single-ended ring oscillators (SEROs) for a wide range of supply voltages. Finally, we show an application of the model to calculate the change in the oscillation frequency of SERO with PVT variations and compare the same with the time-consuming Monte Carlo simulations.

Quantitative relationship between weld defect characteristic and fatigue crack initiation life for high-cycle fatigue property

In this paper, the effect of interior defects on high cycle fatigue (HCF) life of welded joint made by narrow-gap arc welding was investigated. The HCF tests were conducted with a stress ratio (R) of −1 at room temperature, including two specimens pre-tested with R=0.1. Interior defect fatigue crack origins (IDFCO) like inclusion and pore were studied by fracture surface observation. The crack initiation life (Ni), non-ignorable for short-life specimens, was obtained by excluding the long crack propagation life within the fish-eye area. The traditional threshold value of stress intensity factor at R=0 (ΔKth,0) can be regarded as a suitable parameter for fatigue life partition by considering the incremental life in the near-threshold regime. The fatigue initiation life is mainly affected by the applied stress level and projection area of defect. The defect shape plays an important role in the stress distribution at the defect-matrix interface, which is also indirectly affected by defect size due to elastic anisotropy and inhomogeneous microstructure. The combined effect of defect shape and size may induce multi-cracks formation at the defect-matrix interface. A new numerical model considering the multi-cracks formation effect was proposed to predict the fatigue initiation life, which agrees with the experimental results.

Quantitative dependence of oxide-induced crack closure on air humidity for railway axle steel

The paper analyses fatigue crack closure in the near-threshold regime of the EA4T railway axle steel. The dependence of fatigue crack growth threshold on air humidity was experimentally obtained. Varying air humidity led to changes of fatigue threshold values Kmax,th in the range from 4 to 7 MPa m0.5, which was explained by the effect of oxide-induced crack closure (OICC). Such a wide range of threshold values results in significant changes of residual fatigue lifetime of railway axles (by one or two orders of magnitude) operated under various humidity conditions. The Newman's model of plasticity-induced crack closure is not sufficient to explain high portions of crack closure near threshold and their variation, since roughness-induced crack closure (RICC) and OICC has also be taken into account. Detailed explanations and interpretations of the parameters quantifying crack closure are presented. A quantitative model for separation of the crack closure components was applied to threshold data from literature for dry and humid atmosphere as well as for new experimental data of the EA4T steel tested at various levels of humidity. The levels of OICC determined from threshold values were compared to those calculated from thicknesses of oxide debris measured on fracture surfaces. The oxide layers were measured after the experiments in scanning electron microscope using focused-ion-beam cuts. The results were plotted as dependences on absolute air humidity and were in a good agreement. Very low threshold values measured in dry air can occur in operation when the temperature is around 0 °C which is not exceptional in many countries.

Modeling R-dependence of near-threshold fatigue crack growth by combining crack closure and exponential mean stress model

A previously proposed equivalent driving force model was modified to account for crack closure for modeling stress ratio, R, dependence of fatigue crack growth in near-threshold regime. A new fatigue crack growth driving force model was established in the form of ΔK⋅f(R), where the f(R) includes both crack closure and mean stress contributions, and well informs the shift from dominance of stress intensity factor range ΔK to maximum stress intensity factor Kmax with increasing R. The model was validated widely with sound agreement between modeling results and experimental data.