Constant Stress Amplitude Research Articles

Cyclic fatigue of polymer nanocomposites

This paper presents an experimental study on cyclic fatigue of two polymer nanocomposites in two common failure modes: mechanical failure in epoxy nanocomposites and thermal softening in polyamide (PA, nylon) 6 nanocomposites. For epoxy nanocomposites, the effects of hard (silica) and soft (rubber) nano-particles on un-notched samples under constant cyclic stress amplitude fatigue were studied. Hard particles were shown to increase but soft particles decrease the fatigue life of nanocomposites compared to unmodified epoxy. At the same stress amplitude, the extent of fatigue crack growth prior to fast fracture was largest in rubber nanocomposites and least in pure epoxy, reflecting the differences in their fracture toughness values. Ternary nanocomposites with both hard and soft (silica and rubber) particles were also investigated and their fatigue performances were compared to the binary nanocomposites. Further, the stress ( σ a ) versus life ( N r ) test data of pure epoxy and its binary and ternary nanocomposites are well described by Basquin’s law. PA6 nanocomposites exhibited fatigue failure due to thermal softening when the maximum local temperature of the specimens subjected to cyclic loading reached the glass transition temperature, T g , of the material. Critical stress ( σ a ) versus frequency ( ω) envelopes for design against thermal failure were obtained for PA6/organoclay, PA6/POE-g-MA and PA6/pristine clay. Experimental results compared favorably with theoretical predictions.

Experimental study on multiaxial ratcheting behavior of vulcanized natural rubber

AbstractMultiaxial ratcheting characteristics of vulcanized natural rubber (NR) at room temperature were studied experimentally. The effects of axial stress, shear strain amplitude, shear strain rate, and their histories on ratcheting behavior were discussed. It is shown that the ratcheting strain depends on the axial stress and cyclic strain range. The ratcheting strain increases more rapidly as the constant axial stress or shear strain amplitude become larger. The ratcheting behaviors of the rubber exhibit nonsensitivity to the applied cyclic stress rate except initial axial strain. Furthermore, the loading histories also play an important role in progress of ratcheting. The prior cycles with higher axial stress, larger strain range or lower strain rate greatly restrains ratcheting strain of subsequent cycling with lower ones. Influence of creep on ratcheting behavior can not be neglected and its value reaches 87% of ratcheting strain. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers

Fatigue Damage Behavior of a Structural Component Made of P355NL1 Steel Under Block Loading

The common design practice of pressure vessels subjected to variable amplitude loading is based on the application of a linear damage summation rule, also known as the Palmgren–Miner’s rule. Even though damage induced by small stress cycles, below the fatigue limit, are often taken into account in design codes of practice by two-slope stress-life curves, the sequential effects of the load history have been neglected. Several studies have shown that linear damage summation rules can predict conservative as well as nonconservative lives depending on the loading sequence. This paper presents experimental results about the fatigue damage accumulation behavior of a structural component made of P355NL1 steel, which is a material usually applied for pressure vessel purposes. The structural component is a rectangular double notched plate, which was subjected to block loading. Each block is characterized by constant remote stress amplitude. Two-block sequences were applied for various combinations of remote stress ranges. Three stress ratios were considered, namely, R=0, R=0.15, and R=0.3. Also, constant amplitude fatigue data are generated for the investigated structural component. In general, the block loading illustrates that the fatigue damage evolves nonlinearly with the number of load cycles and is a function of the load sequence, stress levels, and stress ratios. In particular, a clear load sequence effect is verified for the two-block loading, with null stress ratio. For the other (higher) stress ratios, the load sequence effect is almost negligible; however the damage evolution still is nonlinear. This suggests an important effect of the stress ratio on fatigue damage accumulation.

Shear Mode Growth and Threshold of Small Fatigue Cracks in SUJ2 Bearing Steel

The shear mode propagation and threshold behaviors of small, semi-elliptical fatigue cracks were investigated in the JIS-SUJ2 bearing steel. Fully-reversed torsional loading was combined with a static axial compressive load to obtain crack growth in the longitudinal direction of cylindrical specimens. Non-propagating cracks smaller than ≅1mm in size were obtained (i) by decreasing the stress amplitude in tests using notched specimens, and (ii) by using smooth specimens in constant stress amplitude tests. The Mode II and Mode III threshold stress intensity factor ranges, ΔKIIth and ΔKIIIth, were estimated from the shapes and dimensions of non-propagating cracks. The threshold values decreased with a decrease in crack size, and there was no significant difference between ΔKIIth and ΔKIIIth. Wear on the crack faces was inferred by a powder and also by changes in microstructure in the wake of a crack. The ΔKIIth in the absence of interference of crack faces was estimated to be approximately 13MPa·m1/2 for a 1mm long crack.

Fatigue yield

The paper starts with a brief review of fatigue damage progression under block loadings and then investigates in more details a fatigue yield model. The study identifies the fatigue yield as a cause–effect interaction of damage and endurance rather than as a physical process in the traditional fatigue engineering. The experimental data under variable and constant stress amplitude loadings reported up to date were used for the evaluation of the fatigue yield approach. Analytical, numerical and recursive procedures for fatigue yield assessments were carried out and illustrated by examples.

The Cyclic Deformation Behavior of Mg—Y2O3 Nanocomposites

Constant stress amplitude cyclic tests were conducted on monolithic Mg and Mg reinforced with 0.5, 1, and 2vol% of nano-size Y2O 3. The cyclic life of the monolithic Mg and its nanocomposites were found to be comparable at the three stress amplitudes tested. Hardening behavior is observed throughout the whole fatigue life of all the specimens tested. Forest dislocations observed in Mg and Mg nanocomposites are responsible for the cyclic hardening. Addition of nanoparticles provides additional strengthening sources that cause the Mg—Y2O3 nanocomposites to harden more intensely that monolithic Mg.

Equi-Biaxial Fatigue of Elastomers: The Effect of Oil Swelling on Fatigue Life

Abstract The effect of oil swelling on the fatigue life of ethylene propylene diene monomer rubber (EPDM) has been studied under conditions of equi-biaxial cycling using dynamic bubble inflation. Specimens were subjected to varying degrees of swelling in reference mineral oils and fatigued at constant engineering stress amplitudes. The reference oils used for swelling the EPDM had known aniline points, allowing the rubber-oil compatibility to be determined. The inflation fluid for fatigue testing was selected with a solubility parameter that would produce a desired level of incompatibility with the test specimens, thereby limiting the amount of additional swelling during cycling. Wöhler (S-N) plots were generated for dry and swollen specimens and the changes in complex elastic modulus E* and dynamic stored energy were analyzed. Specimen fractures were analyzed using scanning electron microscopy. The fractures in the swollen samples show that the failure surfaces flowed more readily over each other than did those of the dryer specimens.

Unnotched fatigue behavior of an austenitic Ni–Ti shape memory alloy

Constant stress amplitude fatigue life of an austenitic Ni (55.88 wt.%)–Ti shape memory alloy (SMA) within the stress amplitude range of 180–450 MPa was evaluated. The stress–strain hysteresis loops were monitored throughout the fatigue loading. They reveal that with the increasing number of fatigue cycles, the critical stress required for the stress-induced martensitic transformation, width of the hysteresis loop, recoverable and frictional energies of each cycle, all decrease while accumulated plastic strain increases. Post-mortem characterization of the fatigued specimens by employing differential scanning calorimetry (DSC), X-ray diffraction (XRD), and fractography were carried out, in order to understand the fatigue micromechanisms. Results indicate that the progressive accumulation of stress-induced martensite in the alloy is the source for the fatigue failure. Implications of these observations are discussed within the context of fatigue performance of SMAs and other materials that undergo stress-induced transformations.

Crack Size Dependency of Shear-Mode Fatigue Crack Threshold in Bearing Steel

Semi-elliptical shear-mode fatigue cracks were promoted in the axial direction of round specimens of SAE52100 bearing steel by fully-reversed cyclic torsion tests under a static axial compressive stress. Non-propagating cracks smaller than 1 mm were obtained in two ways; (i) stress amplitude decreasing tests of notched specimens, or (ii) constant stress amplitude tests of smooth specimens. The threshold stress intensity factor ranges, (KIIth and (KIIIth, showed a crack size dependency.

Composite GM (1, 1) Model for Treating Data of Constant Stress Amplitude Accelerated Life Tests

An accelerated life model is an important factor affecting the evaluation of test data. Avoiding the existent difficulties of treating mixed data and based on the grey theory with composite GM(1,1) model, approach is presented for treating fatigue data under constant stress amplitude accelerated life tests. Availability of the approach has indicated by an example.

Effect of rare earth on mechanical creep–fatigue property of SnAgCu solder joint

In this paper, the effects of rare earth (RE) element additions on the mechanical creep–fatigue property of the Sn3.8Ag0.7Cu solder joint have been investigated. The results show that adding a small amount of the RE elements can evidently increase the creep–fatigue rupture lifetime of the Sn3.8Ag0.7Cu solder joint. The increase in the creep–fatigue property can be attributed to the reduction of the creep–fatigue damages and the change of microcrack propagation site during the fracture process, which depends on the refining of intermetallic compounds due to the RE elements. In addition, it is also found that adding the RE elements decreases the strain amplitude of the solder joint under the constant stress amplitude.

Evaluation of the Crystal Rotation Behavior at the Fatigue Crack Tip in Pure Titanium Films

Using a fatigue testing method by which fatigue cracks can be initiated and propagated in a film adhered to cover an elliptical through-hole in a base plate subjected to push-pull cyclic loads, annealed pure titanium films with the thickness of 90µm were fatigued under a constant stress amplitude with a stress ratio of -1. The crystal rotation behavior with the tensile/compressive loading at the fatigue crack tip was evaluated from the crystal orientation measured by EBSD (Electron Back-scatter Diffraction) method. The titanium films under the tensile /compressive stress condition were prepared as follows; the films were adhered to the base plates loaded by a servo hydraulic testing machine, then the base plates were detached from the testing machine. From the crystal rotation behavior at the fatigue crack tip, it was found that the crystal rotation angle was relatively small and the rotation axis tended to different directions between the upper side and lower side of the grain in front of the crack tip. The fatigue crack propagated along the borderline between two regions in the crystal grain where the crystal rotation axes with different directions were obtained before the fatigue crack propagation.

Effect of Grain Size on Fatigue Behavior of Pure Copper and Cu-Al Alloys

In order to clarify the grain size dependence on the fatigue behavior of polycrystalline metals including twins from the view point of dislocation theory, pure copper, Cu-3.5at%Al, Cu-6.8at%Al and Cu-14.8at%Al alloys having the average grain sizes ranging from 9 to 122μm were prepared by a strain-annealing method. Fatigue tests at room temperature for each specimen were performed under the constant stress amplitude over a life range of 104 to 107cycles. The fatigue properties at elevated temperatures for Cu-14.8at%Al alloys were confirmed up to 773K, and also the distribution of dislocations close to fatigue cracks was observed by using the etch pit technique. The grain size dependence on the fatigue strength for pure copper and Cu-3.5at%Al alloys disappears beyond 106cycles, whereas the fatigue lives of Cu-6.8at%Al and Cu-14.8at%Al alloys uniformly increase with grain refining over all ranges. Relationship between the fatigue strength at 107cycles and aluminum concentration for Cu-Al alloys of fcc solid solution can be approximately represented by a straight line as well as the shear stress. The fatigue strength of Cu-14.8at%Al alloys markedly decreases with increasing temperature and becomes almost half of that for room temperature at 773K. The results based on the etch pit observation indicate that the dislocations multiplied under cyclic loading pile up against the grain and twin boundaries, where large cracks along both boundaries form and propagate due to the stress concentration.

Effects of Crack Opening Behavior on Crack Growth Rate after Overload

It is well known that a single tensile overload applied during constant stress amplitude cycling at a positive stress ratio causes crack growth retardation. In the case of a negative stress ratio, however, the fatigue crack growth rate actually accelerated after a tensile overload. This crack growth behavior is related to the residual stress distribution and crack closure behavior. Therefore, the crack propagation rate before and after applying an overload can be evaluated by the effective stress intensity factor range. Where crack propagation was accelerated after applying an overload, blunted crack tips which occurred because of overload worked as sharp notch roots. The shape of the crack tip affected crack growth after overload in the case of negative stress ratio. In this study, it is found that acceleration of crack growth after overload is dependent on the crack opening behavior and loading conditions after overload.

Fatigue of a laterally constrained closed cell aluminum foam

An experimental investigation into the constant stress amplitude compression–compression fatigue behavior of closed-cell aluminum foam, both with and without lateral constraint, was conducted. Results show that while the early stages of strain accumulation due to fatigue loading are independent of constraint, the rapid strain accumulation stage behaviors are sensitive to the constraint. This was ascribed to the noticeable hardening with plastic deformation observed under constraint during quasi-static loading, which in turn reduces the effective maximum stress experienced by the foam specimen during fatigue loading. This was demonstrated through a simple empirical model that connects fatigue strain accumulation without constraint to that under constraint. Complementary X-ray tomography experiments suggest that the fatigue behavior of the foams is relatively less sensitive to morphological defects such as missing walls than the quasi-static mechanical properties such as plastic strength. Evaluation of the energy absorption behavior suggests that the damage that accumulates during fatigue does not affect the energy-absorbing ability of the foam adversely.

Ductility improvement and fatigue studies in Mg-CNT nanocomposites

The ductility improvement and fatigue behaviour of magnesium reinforced with 1.3 wt% of carbon nanotubes (CNTs) were investigated in this study. Dislocation studies were conducted to determine the deformation behaviour of the nanocomposite. A comparison was made between Mg-1.3CNT nanocomposite and monolithic Mg to identify the effect of CNTs on Mg. Ductility improvement was found to be the result of the high activity of the basal slip system and the initiation of prismatic 〈 a〉 slip. Constant stress amplitude cyclic tests revealed that the cycles to failure for the Mg-1.3CNT nanocomposite is lower than that of the monolithic Mg. Both monolithic Mg and Mg-1.3CNT nanocomposite were found to harden upon cycling. The formation of sessile forest dislocations was identified as one of the main hardening causes.

Benchmark experiments and characteristic cyclic plasticity deformation

Key issues in cyclic plasticity modeling are discussed based upon representative experimental observations on several commonly used engineering materials. Cyclic plasticity is characterized by the Bauschinger effect, cyclic hardening/softening, strain range effect, nonproporitonal hardening, and strain ratcheting. Additional hardening is identified to associate with ratcheting rate decay. Proper modeling requires a clear distinction among different types of cyclic plasticity behavior. Cyclic hardening/softening sustains dependent on the loading amplitude and loading history. Strain range effect is common for most engineering metallic materials. Often, nonproportional hardening is accompanied by cyclic hardening, as being observed on stainless steels and pure copper. A clarification of the two types of material behavior can be made through benchmark experiments and modeling technique. Ratcheting rate decay is a common observation on a number of materials and it often follows a power law relationship with the number of loading cycles under the constant amplitude stress controlled condition. Benchmark experiments can be used to explore the different cyclic plasticity properties of the materials. Discussions about proper modeling are based on the typical cyclic plasticity phenomena obtained from testing several engineering materials under various uniaxial and multiaxial cyclic loading conditions. Sufficient experimental evidence points to the unambiguous conclusion that none of the hardening phenomena (cyclic hardening/softening, strain range effect, nonproportional hardening, and strain hardening associated with ratcheting rate decay) is isotropic in nature. None of the hardening behavior can be properly modeled with a change in the yield stress.

Fretting Fatigue Behavior of Cu-Al-Coated Ti-6Al-4V

Fretting fatigue of a Cu-Al coating deposited on an alumina-gritted Ti-6Al-4V substrate was investigated. Two types of tests were conducted: one series involved fretting fatigue tests at different bulk stress amplitudes under a constant contact load and the second series was run at different contact loads under a constant bulk stress amplitude. The coefficient of friction (COF) was lower on the coated substrate than on the bare substrate before fretting. However, COFs of the coated and the bare (i.e., uncoated) substrates were identical after the exposure to fretting fatigue cycles since fretting fatigue caused wear of the coating. The coating thickness as a function of fretting fatigue cycles was monitored. The coating damage increased as the applied bulk stress amplitude increased. At lower bulk stress amplitudes, the coating damage was gradual and it survived over one million cycles. However, the coating delaminated from the gritted surface and/or caused premature specimen failure at higher stress amplitudes. At the lowest contact load used in the present study, the contact condition was gross slip and the life of the coating was the shortest due to fretting wear. On the other hand, the higher contact loads induced a partial slip contact condition that caused less coating damage, and the coating life increased with increasing contact load. *The views expressed in this article are those of the authors and do not reflect the official policy or position of the United State Air Force, Department of Defense, or the U.S. government

Crack Growth Characteristics of Pure Copper for Smart Stress Memory Patch

A new sensing method called “smart stress memory patch”, which could estimate the maximum stress, the stress amplitude and the fatigue cyclic number simultaneously using Kaiser effect of Acoustic Emission (AE) and crack length of this patch, was developed. In this study, the crack growth characteristics of this patch was evaluated. Pure copper was used for this patch because its good corrosion resistance, stable crack propagation and so on. Two kinds of samples which were rolled and electrodeposited copper were prepared to investigate the effect of microstructure on crack growth behavior. Fatigue test was performed under constant stress amplitude to evaluate the crack growth behavior using the relationship between stress intensity factor range and crack propagation rate. The scattering in fatigue crack growth was also investigated to obtain the relationship between crack length and the fatigue cyclic number including two-sided 95% confidence interval. The effect of thickness and grain size on the scattering was discussed. Finally, good crack growth behavior was obtained and the fatigue cyclic number could be estimated by this patch.

A Consistent Soil Fatigue Framework Based on the Number of Equivalent Cycles

Cyclic soil degradation and hardening affects soil stiffness and strength, and is linked to an increase or decrease in the mean effective confining stress due to void ratio or pore pressure changes. This change of state can be explicitly modeled by using effective stress methods, or implicitly modeled using total stress methods. In the latter, this is achieved by using empirical functions based on the number of loading cycles that are derived from constant-amplitude stress or strain laboratory tests. To suite generalized loading conditions, these functions must be extrapolated to variable-amplitude loading. This falls under the general class of a fatigue-based problem. The main focus of this paper is to present a generalized consistent soil fatigue formulation for soils under cyclic loading. The paper then goes on to discuss the implementation of various cyclic soil degradation and hardening models reported in the literature, and highlights their important underlying assumptions, capabilities and limitations.