Function Of Fatigue Cycles Research Articles

Effect of matrix and fibre cracks on static and fatigue strength of composite laminates

The effect of matrix and fibre cracks on the static strength and stiffness of uni-directional plies and cross-ply laminates under tensile loads was examined with the goal of understanding the main damage mechanisms. The size of matrix cracks emanating from cracked fibres was determined and found to be in excellent agreement with test results. This was used to predict static tensile failure of uni-directional laminates and was shown to be in good to excellent agreement with test results for six different materials. The approach was extended to fatigue loading by determining the number of cycles for the plastic zone ahead of a matrix crack tip to fail. It was combined with an approach to quantify the effect of matrix cracks under any in-plane loading previously developed by the authors to predict changes in laminate stiffness as a function of cycles. Comparisons with test results showed good to excellent agreement between predicted and measured laminate stiffness as a function of fatigue cycles.

Highly Sensitive Nonlinear Identification to Track Early Fatigue Signs in Flexible Structures

Abstract This study describes a physics-based and data-driven nonlinear system identification (NSI) approach for detecting early fatigue damage due to vibratory loads. The approach also allows for tracking the evolution of damage in real-time. Nonlinear parameters such as geometric stiffness, cubic damping, and phase angle shift can be estimated as a function of fatigue cycles, which are demonstrated experimentally using flexible aluminum 7075-T6 structures exposed to vibration. NSI is utilized to create and update nonlinear frequency response functions, backbone curves and phase traces to visualize and estimate the structural health. Findings show that the dynamic phase is more sensitive to the evolution of early fatigue damage than nonlinear parameters such as the geometric stiffness and cubic damping parameters. A modified Carrella–Ewins method is introduced to calculate the backbone from nonlinear signal response, which is in good agreement with the numerical and harmonic balance results. The phase tracing method is presented, which appears to detect damage after approximately 40% of fatigue life, while the geometric stiffness and cubic damping parameters are capable of detecting fatigue damage after approximately 50% of the life-cycle.

Evaluation of Early Fatigue Signatures in Lightweight Aluminum Alloy 7075

The current work investigates early material changes that manifest in aluminum alloy 7075 subjected to fatigue loading. Tension-tension specimens linearly tapered in width were exposed to cyclic loading with compliance and eddy current measurements made in-situ, while nano-indentation, surface potential, x-ray diffraction, and ultrasonic response were made ex-situ. Early stage damage progression was evaluated at various size scales and used to estimate a remaining life in real time. Baseline, in-situ, and post failure measurements were compared and analyzed as a function of fatigue cycles. Eddy current and compliance measurements showed a strong correlation between signal strength and fatigue life with eddy current providing a more precise signal per specimen. Microscale electrical measurements showed a link between surface potential and regions of the specimen that experienced higher tensile stress. Results are discussed with an emphasis on multiscale damage detection and identification due to fatigue cycling, while highlighting the most promising techniques for improving structural durability and real-time state monitoring.

Structural state awareness through integration of global dynamic and local material behavior

Structural health monitoring and nondestructive inspection techniques typically assess the lifecycle and reliability of high-value aerospace, mechanical, and civil systems. Maintenance and inspection intervals are typically time-based and dependent on the structural health monitoring/nondestructive inspection technique to detect macroscale damage resulting from fatigue or environmental damage. The current work proposes an integrated materials-structures-dynamics approach for providing state awareness of structural health. The proposed approach shifts the conventional structural health monitoring/nondestructive inspection focus of searching for cracks to a health state awareness based on tracking changes in the energetics of the materials-structures-dynamics states. Energy variations are tracked in a cantilevered structure exposed to nonlinear harmonic oscillation, where the strain energy of the beam was derived and used to determine a health state index. Nanoindentation was used to probe the near-surface mechanical properties of the beam to characterize local material variations as a function of fatigue cycles. A nonlinear ultrasonic approach was considered in order to connect the local material behavior changes to the variations in the dynamic performance of the beam. The intent of the investigation was to connect the traditionally detached materials, structural, and dynamics approaches to structural health monitoring/nondestructive inspection, while providing a framework for enabling damage precursor detection.

Identification of crack progression in filled rubber by micro X-ray CT-scan

Micro X-ray computed tomography (micro X-ray CT) is a technology that uses computer-processed X-rays to produce tomographic images (virtual ‘slices’) of specific areas of the scanned object, allowing the user to get the inside information without cutting. In comparison with traditional methods, such as optical or scanning electron (SEM) microscopy, Micro X-ray CT-scan has advantages in the study of rubber filler aggregation and crack developments for its continuous and no-break scanning. In this research, two types of filled styrene-butadiene rubber (SBR) reinforced with carbon black or silica were prepared and subjected to cyclic fatigue loads. Micro X-ray CT-scan tests were performed on both pristine (no fatigue) and fatigued samples. Filler aggregation as well as crack development and progression were investigated as a function of fatigue cycles by using micro X-ray CT-scan. Cracks were observed in directions both parallel (mode I) and perpendicular (mode II) to the applied uniaxial tensile fatigue loads.

Fatigue study on the sensor performance of macro fiber composite (MFC): Theoretical and experimental approach

Due to its high flexibility and enhanced electro-mechanical coupling, macro fiber composite (MFC) is widely used in the area of sensing, vibration control and structural control. While in application, MFCs are subjected to continuous cyclic mechanical load which may lead to the deterioration of piezoelectric coupling coefficient, thereby affecting its sensing performance. In order to predict the life cycle of MFC (d31&d31 type) subjected to mechanical loading, an experimental setup has been devised and the tests are carried out for various loading conditions. For lowering the effort and cost involved in the experiments, a non-linear finite element model along with cumulative damage theory is introduced. The degradation in the piezoelectric coupling coefficient obtained using the current theoretical model are in good comparison with the experimental observations. The current non-linear FE model is also extended to predict the stiffnesses and strengths of the MFC as a function of fatigue cycles.

Fatigue analysis of notched laminates: A time-efficient macro-mechanical approach

A coupled, transversely isotropic, deformation and damage fatigue model has been implemented within the finite element method and utilized, along with a static progressive damage model, to predict the fatigue life, stiffness degradation as a function of number of cycles, and post-fatigue tension and compression response of notched, multidirectional laminates. The material parameters for the fatigue model were obtained utilizing ply-level classical lamination theory simulations and the provided [0], [90] and [±45] experimental composite laminate S–N data. Within the fatigue damage model, the transverse and shear stiffness properties of the plies were degraded with an isotropic scalar damage variable. The stiffness damage in the longitudinal (fiber) ply direction was suppressed, and instead the strength of the fiber was degraded as a function of fatigue cycles. A maximum strain criterion was used to capture the failure in each element, and once this criterion was satisfied, the longitudinal stiffness of the element was eliminated. The resulting, degraded properties were then used to calculate the new stress state. This procedure was repeated until final failure of the composite laminate was achieved or a specified number of cycles was reached. For post-fatigue tension and compression behavior, four internal state variables were used to control the damage and failure. The predictive capability of the above-mentioned approach was assessed by performing blind predictions of notched multidirectional IM7/977-3 composite laminate response under fatigue and post-fatigue tensile and compressive loading, followed by a recalibration phase. Tabulated data along with detailed results (i.e. stress–strain curves as well as damage evolution states at given number of cycles compared to experimental data) for all laminates are presented.

Damage quantification in polymer composites using a hybrid NDT approach

Damage is an inherently dynamic and multi-scale process. Of interest herein is the monitoring and quantification of progressive damage accumulation in a newly developed glass fiber reinforced polymer composite subjected to both tensile and fatigue loading conditions. To achieve this goal, the potential of data fusion in structural damage detection, identification and remaining-life estimation is investigated by integrating heterogeneous monitoring techniques and extracting damage-specific information. Damage monitoring is achieved by the use of a hybrid non-destructive testing system relying on the combination of acoustic emission, digital image correlation and infrared thermography. Full-field strain and temperature differential maps reveal appearance and development of damage “hot spots” at prescribed strain/load increments that also correlate well with distinct changes in the recorded acoustic activity. The use of non-destructive and mechanical testing data further allows the quantification of the observed hysteretic fatigue behavior by providing measurements of the: (i) stiffness degradation, (ii) energy dissipation, and (iii) average strain as a function of fatigue cycles. Furthermore, analysis of the real time recorded acoustic activity indicates the existence of three characteristic stages of fatigue life that can be used to construct a framework for reliable remaining life-predictions.

A combined model for initiation and propagation of damage under fatigue loading for cohesive interface elements

A model for the simulation of damage initiation and subsequent propagation under cyclic loading is proposed. The basis for the formulation is a cohesive law that combines phenomenological SN-curves for damage initiation with a fracture and damage mechanics approach for crack propagation. The evolution of the damage variable is expressed as a function of fatigue cycles. The model is independently calibrated for mode I and mode II loading using SN-curves and Paris-law coefficients obtained from simple coupon tests. The model was applied to three initiation-driven cases: Bending of 90° laminates, the Short Beam Shear test and the Double Notched Shear test. The predictions for the first two cases showed an excellent correlation with experimental data. Some modifications to the model were required when applying it to the Double Notched Shear test.

The Effect of Mechanical Fatigue on the Lifetimes of Membrane Electrode Assemblies

Long-term durability of the membrane electrode assembly (MEA) in proton exchange membrane (PEM) fuel cells is one of the major technological barriers to the commercialization of fuel cell vehicles. The cracks in the electrode layers of the MEA, referred to as mud-cracks, are potential contributors to the failure in the PEM. To investigate how these mud-cracks affect the mechanical durability of the MEA, pressure-loaded blister tests are performed at 90°C to determine the biaxial fatigue strength of Gore-Primea® series 57 MEA. In these volume-controlled tests, leaking rate is determined as a function of fatigue cycles. The failure is defined to occur when the leaking rate exceeds a specified threshold. Postmortem characterization using bubble point testing and field emission scanning electron microscopy (FESEM) was conducted to provide visual documentation of leaking failure sites. The analysis of the experimental leaking data indicates that the MEA has much shorter lifetimes at the same nominal stress levels than membrane samples without the electrode layers. FESEM photomicrographs of leaking locations identified via the bubble point testing show cracks in the membrane that are concentrated within the mud-cracks of the electrode layer. These two pieces of information indicate that the mud-cracks within the electrode layers contribute to the leaking failures of the MEA assembly. For the fuel cell industry, this study suggests there is an opportunity to reduce the likelihood of membrane pinhole failures by reducing the size and occurrence of the mud-cracks formed during the MEA processing or by increasing the fatigue resistance (including the notch sensitivity) of the membrane material within the MEA.

Evolution of Slip Morphology and Fatigue Crack Initiation in Surface Grains of Ni200

The evolution of slipbands into fatigue cracks in surface grains of commercially pure Ni, Ni200 (99.35Ni-0.4Fe-0.25Cu, in wt pct), was studied at ambient temperature. Round-bar specimens with electropolished surfaces were fatigued under displacement-controlled, fully reversed conditions at four strain amplitudes under a nominal strain rate of 1 × 10−3 s−1. Low-cycle fatigue tests were periodically interrupted to characterize the slip morphology at various fatigue cycles using scanning electron microscopy. The results showed that the distribution of slip in Ni200 varied considerably in individual surface grains at a given strain amplitude. Some grains were deformed more severely and exhibited more intense slipbands than others, while some surface grains showed the absence of slip lines with no evidence of plastic deformation. The evolutions of slipband width and spacing in deformed surface grains were followed as a function of fatigue cycles in order to assess the slipband morphology at the onset of fatigue crack initiation.

Fatigue life prediction of corrosion-damaged high-strength steel using an equivalent stress riser (ESR) model. Part II: Model development and results

The fatigue life of metallic aircraft structural components can be significantly reduced by environmentally induced corrosion. However, there have historically been no analytical methods to quantify the specific fatigue life reduction of individual unfailed corroded components with any reasonable degree of confidence. As part of a NAVAIR high-strength steel corrosion–fatigue assessment program, methods were studied to predict the impact that corrosion-induced surface roughness has on the fatigue life of high-strength steel aircraft components. The steels of interest produce general corrosion in patches as well as localized material loss similar to pitting. In addition, this type of corrosion has characteristic features over a wide range of scales. Consequently, traditional finite element analysis approaches are not well suited to this problem, since the mesh required to accurately reflect the fine details distributed over the entire corrosion patch make computation unrealistic. Therefore, approximate methods were developed that allow localized regions of interest of high stress to be identified. Subsequently, a simple notch metric formula is employed to approximate the stress riser in these regions of interest. Finally, an extension of Peterson’s fatigue notch sensitivity theory is applied to these small “notches” that has the result of suppressing the effect of smaller notches compared to larger notches in the prediction of life. Each region of interest is assigned a probability of crack initiation as a function of fatigue cycles, based on a probabilistic strain–life analysis using the predicted notch factor. The net life (to crack initiation) for the component is then the product of the survivabilities of all of the individual regions of interest on the component surface. Tests on corroded fatigue specimens have been conducted to both calibrate the parameters in the Peterson model as well as to test the life prediction capability of the approach. Predictions from the resulting model have demonstrated that an empirical approach to corrosion surface damage can be utilized to generate probabilistic life predictions that have substantial engineering value in assessing the residual fatigue life of corroded AF1410 steel components, and that the modeling technique can capture the significant corrosion features that cause fatigue cracking in most cases, especially for more severely corroded surfaces.

Durability properties of piezoelectric stack actuators under combined electromechanical loading

This paper presents results on the electro-thermo-mechanical behavior of piezoelectric materials for use in actuator applications with an emphasis on durability performance. The objective of this study was to compare the performance of different commercially available actuator systems and to determine the properties necessary for the design of such actuator systems. Basic piezoelectric properties of five stack actuators were determined as a function of mechanical preload and temperature. Changes in these properties during ferroelectric fatigue up to 107cycles were determined from strain-field relations after a specified number of fatigue cycles. Experimental results indicate a strong dependence of piezoelectric properties and power requirements on mechanical loading conditions. Results indicate that the optimum operating conditions (i.e., mechanical preload) that will improve actuation capabilities of piezoelectric stack actuators can be determined. That is, strain output was found to increase by 60% for some actuators upon the application of certain compressive prestress. Results of fatigue tests indicate negligible degradation in strain output for some stack actuators even when operated under mechanical preload that causes large displacements through domain wall motion. Similar trends in strain output and current degradation curves (as a function of fatigue cycles) suggest that material degradation can be indirectly inferred from simply measuring the current being dissipated by the material and the fatigue predicted by measuring the strain output (quantity related to domain motion). Finally, temperature rise of lead zirconate titanate stacks due to self-heating should be taken into account when designing actuator systems, since temperature changes were found to significantly influence both strain output and power required to drive piezoelectric stack actuators. Physical mechanisms of ferroelectric fatigue are explored.

Fatigue Damage Accumulation in 3-Dimensional SiC/SiC Composites

The effect of fatigue loading on the mechanical performance of 3-D SiC/SiC composites was investigated. A non-destructive macromechanical approach was applied which permits for the evaluation of the material damage state by monitoring its dynamic response as function of fatigue cycles. The correlation of the results provided by this method to that of other non-destructive techniques such as Acoustic Emission (AE), leads to a detail micromechanical-macromechanical monitoring of the material fatigue behaviour. The damage modes identification and their successive appearance, together with the evaluation of the material performance at the different stages of fatigue loading, is among the inspection capabilities that provides the above mentioned combination of non-destructive techniques. The proposed methodology applied in the case of a 3-D SiC/SiC ceramic matrix composite material and the effect of fatigue loading on the material integrity was evaluated by measuring the degradation of the dynamic modulus of elasticity and the increase of the material damping. Conclusions, concerning design aspects using these materials, as well as fatigue life prediction were provided. Finally, the sensitivity of the proposed methodology for the definition, the characterisation of the development and the separation of the different damage modes during fatigue loading has been discussed.

Fatigue crack initiation and multiplication of unnotched titanium matrix composites

Fatigue crack initiation and multiplication of the unnotched SCS-6 silicon carbide fiber-reinforced titanium matrix composites with different matrix and interfacial properties have been investigated experimentally and analytically. Ti–15V–3Al, Ti–6Al–4V, and Ti–22Al–23Nb were chosen as matrix materials. The initiation and propagation of each individual matrix crack as a function of fatigue cycles and applied stress levels were carefully monitored. The statistical distribution of crack growth rates in each composite has been constructed and analyzed. The evolution of normalized matrix crack density and stiffness reduction of these composites under fatigue loading also has been characterized. A modified shear-lag model, coupled with the strain-life equation and a fiber bridging model were used to predict the fatigue crack initiation life, matrix crack growth rate, normalized matrix crack density, and residual stiffness of the composites. The predicted fatigue properties correlated well with experimental results.

Analysis of Fatigue Characteristics in Fe-doped Pb(Zr 0.52Ti 0.48)O 3 Thin Films by Switching Currents

The polarization fatigue for ferroelectric Pb(Zr0.52Ti0.48)O3 (PZT) thin films has a known relation with oxygen vacancies occurring in the films during fabrication processes. Fe-doped PZT thin films were intentionally deposited with consideration for the effects of oxygen vacancies regarding fatigue using rf-magnetron sputtering. The remanent polarization is suppressed to half its initial value after 109 bipolar switching cycles. From the observance of the switching currents with consideration to applied voltages, switching characteristics in the films were studied by fitting using the Kolmogorov-Avrami (K-A) theory. It was revealed from the switching currents as a function of fatigue cycles that the quantity of switched charges decreased with increasing switching cycles, but the dimensionality with respect to domain growth was unchanged as compared to its initial value. The velocities of domain wall motions before and after fatigue were also unchanged, indicating that the motion of the domain walls by applied pulse voltages was not an additional obstacle concerning fatigue processes. Therefore, in the case of polarization fatigue by subjecting to electric cycles, the domain states in these films may not be affected by the fatigue.

Effect of laminate stacking sequence on the high frequency fatigue behavior of SCS-6 fiber-reinforced Si3N4 matrix composites

In many potential applications, continuous fiber-reinforced ceramic matrix composites (CFCMCs) will encounter cyclic fatigue loadings at high frequencies (25 Hz or higher). While most of the work in the area of fatigue of CFCMCs has concentrated on low frequency behavior, high frequency behavior is equally important. In CFCMCs, stress-strain hysteresis occurs during fatigue and is associated with energy dissipation in the composite. In addition to this, the repeated friction and sliding between fiber and matrix are responsible for a substantial temperature rise at the fiber/matrix interface. In this study, [0/90] and [±45] SCS-6 (silicon carbide)/Si3N4 composites made by hot pressing were investigated under high frequency fatigue loadings. The angle-ply laminate showed the same extent of heating as cross-ply laminates, but at much lower stress levels. Frictional heating was caused by sliding at the fiber/matrix interface. Temperature rise due to heat generation in the specimens correlated very well with damage in modulus as a function of fatigue cycles in the composites. Matrix microcracking was more predominant in the angle ply than in the cross-ply composite, due to the much lower stiffness of the angle-ply composite in the longitudinal loading direction.

THREE‐DIMENSIONAL CRACK‐SHAPE EFFECTS DURING THE GROWTH OF SMALL SURFACE FATIGUE CRACKS IN A TITANIUM‐BASE ALLOY

Abstract— A basic study was performed on the evolution of three‐dimensional shapes of small surface fatigue cracks during fatigue, and the effect of this evolution on small‐crack growth behavior of a titanium‐base alloy. Specifically, the nature and the magnitude of variations in crack aspect ratio, a/c (a is the crack depth and c is the half‐surface crack length), during cyclic crack growth and its impact on growth rates have been studied. Experiments were performed on naturally initiated micro‐cracks in a microstructure consisting of equiaxed primary‐α2 phase in a Widmanstätten (transformed β) matrix. Several cracks under stress ratio (R) levels of 0.1 and −1, were studied. A specialized experimental system, consisting of a laser interferometer (to measure precisely the small‐crack surface displacements), and a photo microscope (to automatically and continuously photograph the fatigue micro‐cracks) was employed in the study. Apparent aspect ratios of surface cracks were calculated from the compliance response and the surface crack length data as a function of fatigue cycles. These data enabled accurate calculations of growth rates at the surface crack tip as well as the tip at depth in the bulk over the entire crack growth period, thus giving an insight into the crack growth process. Measurements of closure levels of small cracks were also performed and were used to partly account for the differences in growth rates. In the comparisons of small‐crack growth data with the large‐crack data, surface growth rates correlated relatively well with the large‐crack data. Growth rates at depth exhibited large variations due to the irregularity of crack fronts at this location, and these rates deviated significantly from the large‐crack behavior. Additionally, these growth rates varied between different cracks. An attempt was made to rationalize these observations in terms of the effects of inhomogeneities present in the microstructure.

Understanding fatigue failure in structural materials

Fatigue failure is a common p h e n o m enon in s t ruc tura l components that are subjected to cyclic loading. To develop a l i f e p r e d i c t i o n methodology of cyclically loaded components, the fatigue characteristics of structural materia ls must be considered. In particular, methods must be found to detect the early stages of fatigue damage, which could occupy a significant portion of the fatigue life. Due to the rapid development of science and technology, advanced methods, such as scanning probe microscopy (SPM) (including atomic force microscopy [AFM] and scanning tunneling microscopy [STM]) can be used to detect early stages of crack initiation. Cracks with sizes as small as 100 ~ can be found using these advanced technologies. These methods provide opportunities to understand and model fatigue-crack-initiation behavior. After the detection of just-initiated cracks, the process of crack propagation behavior needs to be followed. Thus, the subjects of fatigue crack initiation and propagation have to be addressed to formulate an accurate life prediction technology. To explore the subject of fatigue failure, the TMS Mechanical Metal lurgy Committee of the Structural Materials Division has organized the following collection of five papers. In the first paper, the advanced technology of detecting fatigue crack initiation is described by Zhou and Chung. Specifically, the applications of SPM (including AFM and STM) in detecting early stages of fatigue deformation are described. SPM can be defined as a class of surface-analysis methods that operate by scanning a sharp probe across a specimen. The method offers high-resolution imaging of surfaces in vertical and horizontal directions with resolutions of -0.1 nm and 0.3 nm, respectively. This high resolution can be achieved in a liquid, air, or vacuum environment. The fatigue-crackinitiation behavior of titanium alloys, steels, and silver has been investigated using AFM. The dimensions (e.g., height and spacing) of slip bands can be quantitatively measured as a function of fatigue cycles. These detailed results can provide useful information for modeling fatigue-crack-initiation behavior. In the next paper, Holman and Liaw provide a brief review of the techniques typically employed to predict the fatigue life of structural components. The approaches include stress-life, localstrain, and fracture-mechanics methods. The life-prediction technology dealing with variable ampli tude cycling is rev i e w e d , with a specific emphasis placed on the l inear -damage-accumula t ion methodology. The stress-life, local-strain, and fracture-mechanics methods are then applied to variable amplitude loading conditions.

Fatigue damage evolution and property degradation of aSCS-6/Ti-22Al-23Nb“orthorhombic” titanium aluminide composite

The fatigue damage evolution and property degradation of aSCS-6/Ti-22Al-23Nb orthorhombic titanium aluminide composite under low cycle fatigue loading at room temperature was investigated. The fatigue test was conducted under a load-controlled mode with a load ratio (>R>) of 0.1, a frequency of 10 Hz, and a maximum applied stress ranging from 600 to 945 MPa. The stiffness reduction as well as the evolution of microstructural damage which includes matrix crack length, matrix crack density and interfacial debonding length as a function of fatigue cycles, and applied stresses were measured. An analytical model and a computer simulation were also developed to predict the residual stiffness and the post-fatigued tensile strength as a function of microstructural damage. Finally, a steady-state crack growth model proposed by Marshallet al., was used to predict the interfacial frictional stress and the critical crack length. Correlation between the theoretical predictions and experimental results were also discussed.