Effect Of Cyclic Frequency Research Articles

Experiment study and numerical simulation on the dynamic rock-breaking process of rotary percussive drilling with different cyclic and stress-wave frequencies

The rotary percussive drilling tool was designed to improve rock-breaking efficiency, and the tool’s cyclic frequency and stress-wave frequency are the key influencing factors on the rate of penetration, but the correlative research reports are few. In view of this situation, the cyclic frequency of the rotary percussion drilling tool and the frequency of stress waves generated during impact were measured. A numerical model of polycrystalline diamond compact (PDC) cutter cutting hard rock was established, and the measured frequency parameters were imported into the numerical model. The effects of cyclic frequency and stress-wave frequency on the penetration depth, rock breaking volume, and rock debris size were studied. The finding demonstrated that the average penetration depth increased with the increase of cyclic frequency, and decreased with the rise in stress wave frequency. When the two parameters were simultaneously high, it was conducive to generating smaller rock cuttings and wellbore cleaning. When the cyclic frequency was high and the stress wave frequency was low, the effect on the drilling tooth penetration was the best. The research results can provide a practical reference for optimizing the structure of rotary impact drilling tools and improving the penetration rate.

Effect of cyclic frequency on uniaxial ratcheting behavior of a textured AZ31B magnesium alloy under stress control

The ratcheting behavior of magnesium alloy AZ31B was investigated under controlled cyclic stress at frequencies of 0.5 Hz, 1.0 Hz and 2.0 Hz. The result showed that cyclic loading accelerates strain accumulation as compared with static creep at room temperature, and the effect of cyclic frequency on strain rate dεr/dt, represented by strain in a unit time, is of multiplicity due to the diversification of deformation mechanisms. However, strain rate dεr/dN, represented by strain in one cycle, decreases evidently with increasing frequency at steady strain accumulative stage. High frequency promotes twinning-detwinning, and is favorable for prolonging the fatigue life in terms of cyclic number to failure. The fatigue life increases linearly with decrease of plastic strain energy density under all frequency conditions. This leads to conclude that frequency affects the fatigue life via changing plastic strain energy stored in the deformed microstructure.

Time- and cycle-dependent crack propagation in Haynes 282

Haynes 282 is a promising superalloy candidate for several high-temperature applications in both aero and land-based gas turbine engines. To study the crack growth behaviour under time-dependent conditions relevant to such applications, a test program was carried out at room temperature up to 700°C with conditions ranging from pure cyclic to sustained tensile loading. At 650°C and high stress intensity factors the crack growth was fully time-dependent for dwell-times of 90s and longer. At lower stress intensities, the behaviour was mainly controlled by the cyclic loading, even under dwell conditions. The behaviour under dwell-fatigue conditions was well described by a liner superposition model. The main crack growth occurred transgranularly at room temperature and there was a transition in cracking behaviour from cycle dependent transgranular growth to time-dependent intergranular propagation at ∼45MPam for the high temperature tests. No effect of cyclic frequency could be observed at room temperature, and at lower frequencies the crack growth rate increased with temperature.

Effect of cyclic frequency on fracture mode transitions during corrosion fatigue cracking of an Al-Zn-Mg-Cu alloy

Abstract There are complex issues remaining to be resolved before environment-assisted cracking models can be included in structural mechanics programs that are currently used to analyze mechanical fatigue crack growth. Considered here is the effect of cyclic frequency on fracture mode transitions that occur during corrosion fatigue of high-strength Al-Zn-Mg-Cu alloys. These alloys are used in civilian and military aircraft applications where they are exposed to detrimental aqueous saline environments. A previously developed “critical hydrogen at a critical distance” crack growth model is used to rationalize the observed transitions in crack-path fracture-modes, from intergranular (IG), to brittle transgranular (BTG), to ductile transgranular (DTG), as the alternating stress intensity factor and cyclic frequency increase beyond critical values. Corrosion fatigue crack growth rate data obtained on Al-Zn-Mg-Cu alloy 7017-T651 base metal and heat-affected “white zone” metal tested in aqueous NaCl solutions over a frequency range of 0.01–70 Hz are analyzed. For the white zone metal, dependence of the critical crack velocity on the critical frequency, at which the IG-BTG transition occurs, undergoes an abrupt reversal as the critical frequency increases above about 0.1 Hz. Mechanisms potentially responsible for this change in frequency dependency are discussed in the context of the critical hydrogen model. The transition from low to intermediate frequency behavior is speculated to be due to a change in the critical distance from microstructural control, for frequencies at or below 0.1 Hz, to control by the critical hydrogen criterion at higher frequencies. The low frequency behavior is discussed relative to the transition from static load stress corrosion cracking to low frequency corrosion fatigue, which occurs as cyclic frequency increases above zero.

Assessment of Effect of Cyclic Frequency and Soil Modulus on Liquefaction Using Coupled FEA

The present paper describes briefly the establishment of an adequate mathematical framework to describe the liquefaction phenomenon which uses the Biot’s basic theory for dynamics of saturated porous media. The variational principle is applied to the field equations of fluid flow in a fully saturated porous elastic continuum, and the finite element method is used to numerically solve the resulting continuity equation and equilibrium equation. In-situ stresses are computed from static analysis prior to dynamic analysis. Pastor–Zienkiewicz Mark III constitutive model is used to describe the inelastic behavior of soils in the dynamic simulations. Kelvin elements are attached to transmitting boundary to absorb the wave energy and prevent back propagation of wave into the soil domain. The response of fluid-saturated porous media which are subjected to time dependent loads has been simulated numerically to predict the liquefaction of a loose sandy soil layer. It is noticed that liquefaction occurs throughout all the depth of sand layer at frequency 1 Hz of the cyclic loading. This model is compared with centrifuge experimental results and shows good predictive capacity. Effect of frequency is more significant. With increase in frequency, substantial increase in displacement and EPP is observed.

Effect of low cyclic frequency on fatigue crack growth behavior of a Mn–Ni–Cr steel in air and 3.5% NaCl solution

Corrosion fatigue phenomenon involves the time dependent corrosion and cycle dependent fatigue loading. The intention of this study is to develop a test method to evaluate the crack growth rate of a material in a corrosive environment at low frequencies. The effect of cyclic frequency on crack growth rate of a Mn–Ni–Cr steel in lab air and 3.5% NaCl solution is evaluated using frequency shedding method where the cyclic frequency is decreased exponentially as a function of crack length at a constant stress intensity factor range. A Zn sacrificial anode coupled to the specimen slows down the rate of crack growth.

Effect of silicon nitride coating thickness on fatigue of silicon microbeams

In this paper, two silicon nitride layers with thickness, 0.2 and 0.4μm, are coated onto single crystal silicon (SCS) in order to achieve Si3N4/Si cantilever microbeams. The effect of LPCVD silicon nitride surface coatings on fatigue properties of SCS cantilever microbeams is investigated. Fatigue testing is conducted at both 40Hz and 100Hz. Typical S–N (strain amplitude–fatigue cycle) curves of the beams are achieved and correlated fatigue failure modes are investigated. It is found that thinner Si3N4 coating of 0.2μm results in better fatigue lives of Si3N4/Si beams than thicker Si3N4 coating of 0.4μm. Both thinner and thicker coated beams have major fatigue crack planes along {111} planes; however, thicker coated beams possess specific failure mode of delamination, which is not found in thinner coated beams. Delamination reduces the reinforcing effect of thicker Si3N4 coating and leads to its shorter fatigue life. For thicker coated beams, fatigue life at 100Hz is longer than that at 40Hz. The mechanism for delamination and the effect of cyclic frequency is investigated, and factors for better fatigue life are proposed.

Influence of cyclic frequency on oxidation behavior of K38 superalloy with yttrium additions at 1 273 K

Cyclic oxidation test is a fundamental method to assess lifetime of materials in high temperature environment. Cycle length or cyclic frequency is one important variable in cyclic oxidation testing. In present work, cyclic oxidation tests were performed on cast K38 alloys with 0 wt.%, 0.1 wt.%, and 0.5 wt.% yttrium additions at 1 273 K respectively. Two cyclic frequencies were used to investigate the influence of cycle length (1 h vs. 20 h) on the high temperature oxidation behavior of superalloy. The results showed that the degradation of cast K38 alloy critically was dependent on the cyclic frequency. The yttrium addition was beneficial to reducing scale-growth rate, improving the scale adhesion and stress releasing, thereby increased the spallation resistance. It could be drawn that the effect of cyclic frequency was highly dependent on the scale adherence to the substrate.

Frequency Effects on Fatigue Behavior of a Silicon Carbide Fiber‐Reinforced Glass–Ceramic Composite (SiC/MAS)

The effects of cyclic frequency on the fatigue behavior of silicon carbide (Nicalon) fiber‐reinforced glass–ceramic matrix (SiC/magnesium aluminosilicate (MAS)) were investigated. Tension–tension fatigue tests were conducted at two frequencies, 10 and 900 Hz, to establish stress versus cycles to failure (S–N) relationships. Cycles to failure at a given stress level decreased with an increase of the applied frequency. Analysis of damage mechanisms suggests that there was an enhancement of fiber/matrix interfacial bonding at the higher frequency due to the formation of SiO2 from the reaction of oxygen species of the matrix with SiC of the fiber.

Accelerated bainitic transformation during cyclic austempering

Austempering is an important thermal processing operation, where strong and tough bainitic steel is produced in a single heat treatment [1, 2]. During the austempering process, the steel is first austenitized and then cooled rapidly just above the martensite start temperature until bainite nucleates and grows, usually until the transformation stops and then it is cooled to room temperature. Due to the sluggish solid-state transformation kinetics, industrial austempering necessitates isothermal holds of 2–24 h, depending on the size and composition of steel. In contrast to conventional isothermal processing, cyclic thermal processing has been shown to accelerate the kinetics of several phase transformations [3–5], with a significant beneficial impact on productivity and energy consumption of these energy intensive operations. This was attributed to the non-isothermal effects resulting from cyclic treatment. The non-isothermal effect on phase transformations has also been utilized to enhance the productivity of a modern batch annealing operation [6]. In the present work, the effect of cyclic processing on austempering kinetics has been compared with conventional isothermal processing for 1080 steel. Furthermore, the effect of cyclic frequency on the austempering kinetics has been studied. Austempering kinetics experiments were performed on 6 mm diameter cylindrical samples of a 1080 steel using a Gleeble 3500 thermo-mechanical simulator (DSI Poestenkill, NY). A diametrical dilatometer was mounted on the specimen to measure the diameter change during the thermal processing. The austempering experiments were performed in two cycles, where the first cycle provides the same initial microstructure prior to each experiment. After completing the first cycle, the cylindrical specimens were heated to the austenitizing temperature (850 C), held for 5 min and then cooled to different austempering temperatures, where the bainite transformation was monitored for the desired period of time, followed by cooling to room temperature. The cooling rate was sufficiently fast to avoid any transformation occurring before reaching the austempering temperature (Fig. 1). The isothermal experiments were carried out at austempering temperatures of 260 and 300 C, whereas the cyclic experiments were carried out between 260 C and 300 C at two different heating/ cooling rates of 1 and 5 C/min. The percentage of bainitic transformation as a function of time was computed from the dilation curve [2] in conjunction with the microstructural examination by optical microscopy and SEM. The normalized dilatation curves for isothermal austempering at 260, 300 C, and cyclic austempering between 260 C and 300 C for 1 C/min and 5 C/min are shown in Fig. 2. In this figure, only the portion of the curve corresponding to austempering is shown and the dilatation curve has been offset to start at zero. The plateau of the dilatation curve with respect to the time represents the end of the transformation to bainite. It must be noted that the end of the bainite transformation does not necessarily correspond to 100% volume fraction of bainite [1]. Previously, using the same type of Gleeble experiments, it was shown that the end of the transformation corresponds closely to the austenite carbon content corresponding to a T0 equal to the austempering temperature [2, 7]. Furthermore the transformation dilatation at the end of the V. Sista P. Nash (&) Thermal Processing Technology Center, IIT, 10 W 32nd St., Chicago, IL 60616, USA e-mail: philip.nash@iit.edu

Fatigue behavior of calcium carbonate filled polypropylene under high frequency loading

Fatigue behavior of polyproylenes filled with three different percentages of CaCO 3 (0%, 20%, and 40%) was investigated in this study. Specimens were produced by injection molding. Tensile properties were also evaluated. Tensile–tensile cyclic loading was applied using MTS 810 test apparatus at different frequencies of 23 and 50 Hz. Effects of cyclic frequency and filler content were examined to their fatigue behavior. S–N diagrams were obtained also with normalization of stress amplitudes with respect to their tensile strengths. Besides that temperature rise curves were presented. It is reported that filler content influences the fatigue performance. Increasing the filler content reduces the fatigue performance of PP from pure to PP40, respectively, if normalization effects are not included. The situation differs if normalization effects are included. Results show that fatigue failure mode occurs with thermal fatigue failure mechanism at both frequencies with necking of specimens and it is excessive at higher frequencies and amplitudes.

Effects of Humidity and Water Environment on Fatigue Crack Propagation in Magnesium Alloys

This paper presents the effects of environment on fatigue crack propagation (FCP) in two magnesium alloys, rolled AZ31 and extruded AZ61. FCP tests have been performed using electro-hydraulic fatigue testing machine operating at a frequency of 1Hz at a stress ratio, R, of 0.05 in distilled water and in dry air. The dew point of dry air was −60°C. The obtained results were compared with those already established in laboratory air, and the effects of humidity and water environment were discussed on the basis of fractographic analysis of fracture surfaces. The effect of cyclic frequency was also studied. Both alloys exhibited basically the same FCP behaviour regardless of environment. FCP rates were nearly the same in laboratory air and in distilled water, while approximately an order of magnitude slower in dry air than in those environments. After allowing for crack closure, the effect of environment still existed, where FCP rates were the fastest in laboratory air, then in distilled water, in dry air in decreasing order. Fractographic analysis revealed that fracture surfaces were extensively brittle in laboratory air, while entirely covered with corrosion products in distilled water. It was believed, therefore, that different FCP mechanisms operated in laboratory air and in distilled water, possibly hydrogen embrittlement and anodic dissolution, respectively. The frequency dependence of FCP rate was not recognized in dry air and less remarkable in laboratory air over a wide range of frequencies of 0.01Hz to 10Hz, while FCP rates became faster with decreasing frequency in distilled water.

Fatigue performance of an injection‐molded short E‐glass fiber‐reinforced polyamide 6,6. I. Effects of orientation, holes, and weld line

AbstractThis article presents the experimental results of stress‐controlled fatigue tests of an injection‐molded 33 wt% short E‐glass fiber‐reinforced polyamide 6,6. The effects of specimen orientation with respect to the flow direction, hole stress concentration, and weld line on the fatigue life have been considered. In addition, the effect of cyclic frequency has been examined. In addition to the modulus and tensile strength, the fatigue strength of the material was significantly higher in the flow direction than normal to the flow direction, indicating inherent anisotropy of the material caused by flow‐induced orientation of fibers. The presence of weld line reduced the modulus, tensile strength, failure strain, and fatigue strength. The fatigue strength of specimens with a hole was lower than that of un‐notched specimens, but was insensitive to the hole diameter. At cyclic frequencies ≤ 2 Hz, failure was due to fatigue, and fatigue life increased with frequency. However, at cyclic frequencies > 2 Hz, the failure mode was a mixture of fatigue and thermal failures, and fatigue life decreased with increasing frequency. POLYM. COMPOS., 27:230–237, 2006. © 2006 Society of Plastics Engineers.

Corrosion fatigue crack growth behaviour of naval steels

Fatigue crack growth behaviour of two varieties of HSLA steels used in naval structural applications have been evaluated in air and 3.5% NaCl solution. In air both the HSLA steels showed similar resistance to fatigue crack growth. However, in 3.5% NaCl, the fatigue crack growth resistance of HSLA-80 steel was superior to that of HSLA-100. The apparent inferiority of HSLA-100 to corrosion fatigue crack growth resistance is attributed to rapid film formation and rupture, and occurrence of planar modes of failure. Effect of R-ratio on air fatigue and corrosion fatigue crack growth behaviour is rationalised by the concept of crack closure. Effect of cyclic frequency on corrosion fatigue behaviour is examined. It is noted that the mechanism of corrosion fatigue crack growth for the two HSLA steels changes with attendant change in the Paris slope. This leads to increase or decrease of crack growth rates, depending up on the Δ K range of interest.

An investigation on fatigue and dwell-fatigue crack growth in Ti–6Al–2Sn–4Zr–2Mo–0.1Si

This paper presents the results of a combined experimental and analytical study of fatigue crack growth and dwell-fatigue crack growth in forged Ti–6Al–2Sn–4Zr–2Mo–0.2%Si (Ti-6242). Following an initial characterization of microstructures and basic mechanical properties, the micromechanisms of long fatigue crack growth are presented for three microstructures. These include: a duplex α/ β structure, an elongated α/ β structure, and a colony α/ β microstructure. The colony microstructure is shown to have the best resistance to fatigue crack growth. The elongated α structure has intermediate resistance, while the equiaxed α structure exhibits the fastest fatigue crack growth rates. The fatigue crack growth rates in the near-threshold, Paris and high Δ K regimes are then characterized with empirical crack growth laws that relate the crack growth rates to the stress intensity factor range and key parameters on the fatigue crack growth curve. Finally, the results of dwell-fatigue crack growth experiments are presented for the three microstructures. The dwell-fatigue crack growth rates are shown to be almost identical to the fatigue crack growth rates in the intermediate Δ K regime. However, the fatigue crack growth rates are faster at higher stress intensity factor ranges. The underlying mechanisms of dwell crack growth are compared with the mechanisms of fatigue crack growth before discussing the implications of the work for the prediction of dwell or fatigue crack growth in Ti-6242. The effects of cyclic frequency on fatigue crack growth are also explored.

Effects of cyclic frequency and contact pressure on fretting fatigue under two‐level block loading

Fretting fatigue tests involving the contact of flat and cylindrical titanium alloy Ti–6Al–4V surfaces, and constant‐ and two‐level block remote bulk stresses are described. The constant‐amplitude tests have been performed at cyclic frequencies of 1 and 200 Hz. The two‐level block spectra involve the superposition of a 1‐Hz, low‐cycle fatigue (LCF) constant‐amplitude component and a 200‐Hz, high‐cycle fatigue (HCF) component. Two values of contact pressure are considered. The cyclic frequency of 200 Hz is found to curtail the constant‐amplitude fretting fatigue life regardless of the contact pressure applied. Increasing the contact pressure reduces life at 1 Hz but does not have any effect at 200 Hz. Under two‐level block loading, the fretting fatigue life is determined primarily by the stress amplitude and high‐cyclic frequency of the HCF component of the load spectrum. The LCF component is found to play a secondary role in the determination of the two‐level block fretting fatigue life. Fracture topographies for the different test conditions are documented.

EFFECTS OF TEMPERATURE, CYCLIC FREQUENCY AND ENVIRONMENT ON FIBRE DEGRADATION AND FATIGUE CRACK GROWTH RESISTANCE IN A FIBRE‐REINFORCED TITANIUM METAL‐MATRIX COMPOSITE UNDER DISPLACEMENT‐RANGE LOADING

The fatigue crack growth resistance of a [0/90°]2s cross‐ply SCS6 fibre‐reinforced Ti–6Al–4V alloy metal‐matrix composite has been assessed under displacement range control (i.e. under load shedding conditions with crack extension) to investigate potential fibre degradation and the process of crack extension at room temperature, and at 450°C, in air and in vacuum. Attention is focused on initial conditions that will promote crack arrest at room temperature. Under the test conditions employed here, regions of crack growth can occur where the applied nominal stress intensity factor range (ΔK) is relatively constant. This ‘constant’ΔK range is the result of a fortuitous balance between the particular test‐piece geometry, loading conditions utilized, matrix crack growth and the rate of fibre fracture. It allows the influence of environment, cyclic frequency and temperature on fatigue crack growth resistance to be analysed more easily than for tests carried out under load control.The crack growth rate remained almost constant but with some steep local retardations in growth rate in the constant ΔK region at a temperature of 450°C, while crack arrest occurred at room temperature for the same initial ΔK. The average crack propagation rate in this ‘constant ΔK region’ at a temperature of 450°C in air was much greater than that at a temperature of 450°C in vacuum. This indicates that environment plays an important role in the process of fibre degradation. The effect of cyclic frequency is saturated at a frequency of less than 1 Hz. The process of crack growth at various frequencies is also discussed.

Cyclic behavior of unidirectional and cross-ply titanium matrix composites

Abstract Relatively simple and efficient micromechanical models are used to obtain the uniaxial response of SCS-6/Timetal 21S with [0] 4 and [0/90] s laminates when subjected to isothermal and thermomechanical fatigue (TMF) loadings. Features of the modeling that are required to obtain the accurate deformation behavior for this class of materials under these loadings are highlighted. To this end, a comparison is made between the concentric cylinder model and the uniaxial stress model for representing the [0] laminate. The axial stresses from the two models are very similar under mechanical loading. The greatest differences appear under thermal loading alone. The differences on the composite response between a time-independent elastic-plastic and a viscoplastic matrix constitutive model are also examined. The latter is based on the Bodner-Partom unified constitutive model. The [0/90] laminate is treated by adding a parallel element with smeared [90] ply properties to the [0] model and invoking axial strain compatibility as well as stress equilibrium. The proposed constitutive law for the [90] ply includes both matrix viscoplasticity and fiber/matrix separation damage and is based on damage mechanics concepts. The effect of cyclic frequency on TMF behavior is examined. The in-phase TMF life is shown to be very sensitive to frequency due to the relaxation of matrix stress and the attendant increase in fiber stress.

FATIGUE CRACK GROWTH IN NICKEL‐BASED SUPERALLOYS AT 500‐700°C. I: WASPALOY

Abstract— The effects of cyclic frequency, hold time, and stress‐intensity‐factor range (δK) on rates of fatigue crack growth in air at 500‐700°C have been studied for Waspaloy—a nickel‐based superalloy used for gas‐turbine engine discs. The main effects observed were: (i) higher rates of crack growth for lower cyclic frequencies at high δK at 600 and 700°C. and (ii) lower rates of crack growth at low δK (and higher δK thresholds) for longer hold times at 700°C, compared with those at a baseline frequency of 2 Hz. Metallographic and fractographic observations suggested that the effects of cyclic frequency and hold time could be rationalised in terms of the competing effects of enhancement of cracking due to creep and inhibition of cracking caused by oxide‐induced crack closure, fracture‐surface‐roughness induced crack closure, and crack‐branching/deflection. Possible mechanisms for promoting intergranular and transgranular cracking at low cyclic frequencies or long hold times are discussed.

Sub-critical crack growth in a Ti 3Al-based aluminide at elevated temperatures

Fatigue crack growth has been studied at ambient temperature and at 700 °C (in air and in vacuum) for “super α 2”, heat treated to give a microstructure consisting of approximately 20% volume fraction of primary α 2 precipitates in a transformed β matrix. At ambient temperature, α 2 precipitates fail by transgranular cleavage under cyclic loading and a steeper dependence of crack increment per cycle on the applied alternating stress intensity is observed. At temperatures of 600 °C and above, the material suffers from sustained load cracking in air, particularly at test temperatures of 650 and 700 °C. Static-cyclic interactions during fatigue loading are therefore possible. These have been modelled and effects of cyclic frequency have been predicted accurately at 700 °C. This mechanism alone cannot account for the higher fatigue crack growth rates observed in air compared with those observed in vacuum at 700 °C.