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At least 343 records · Page 19

Thermomechanical and isothermal fatigue behavior of a (90)sub 8 titanium matrix composite

An experimental investigation was conducted to analyze the fatigue damage mechanisms operative in a 35 fiber volume percent (90 deg) titanium matrix composite (TMC) under 427 C isothermal and thermomechanical loading conditions. The thermomechanical fatigue (TMF) tests were performed with a temperature cycle from 200 to 427 C under closely controlled conditions to define both the deformation and fatigue life behavior. Degradation of the TMC's isothermal elastic moduli and coefficient of thermal expansion were monitored throughout the TMF tests. The results indicated TMF life trends which contrasted those established in a comparable (0 deg) system, as TMF loading of the (90 deg) TMC was not found to be 'life-limiting' in comparison to maximum temperature isothermal conditions. In-phase lives were very similar to those established under 427 C isothermal conditions. High stress isothermal fatigue at 427 C produced increased strain ratchetting and stiffness degradation relative to TMF conditions. Out-of-phase loadings produced TMF lives approximately an order of magnitude greater than the lives determined under isothermal and in-phase conditions. Extensive fractography and metallography were also performed. Two key issues were identified and appeared to dominate the fatigue damage and life of the (90 deg) TMC, namely, the weak fiber/matrix interface and environmental attack of the fiber/matrix interface via the exposed (90 deg) fiber ends.

Castelli, Michael G.↗

Application of two creep fatigue life models for the prediction of elevated temperature crack initiation of a nickel base alloy

Cyclic Damage Accumulation (CDA) and Total Strain-Strain Range Partitioning (TS-SRP) models for predicting the creep-fatigue crack initiation life of high temperature alloys are presented. The models differ in their fundamental assumptions regarding the controlling parameters for fatigue crack initiation and in the amount of data required to determine model constants. The CDA model represents a ductility exhaustion approach and uses stress quantities to calculate the cyclic fatigue damage. The TS-SRP model is based on the use of total mechanical strain and earlier concepts of the Strain Range Partitioning Method. Both models were applied to a well controlled fatigue data set at a high temperature nickel base alloy, B1900 + Hf, tested at 1600 F and 1800 F. The tests were divided into a baseline data set required to determine model constants and a verification data set for evaluation of the predictive capability of the models. Both models correlated the baseline data set to within factors of two in life, and predicted the verification data set to within a factor of three or better. In addition, sample calculations to demonstrate the application of each model and discusions of the predictive capabilities and areas requiring further development are presented.

Moreno, V.↗

Highly stretchable organic electrochemical transistors with strain-resistant performance

Realizing fully stretchable electronic materials is central to advancing new types of mechanically agile and skin-integrable optoelectronic device technologies. Here we demonstrate a materials design concept combining an organic semiconductor film with a honeycomb porous structure with biaxially prestretched platform that enables high-performance organic electrochemical transistors with a charge transport stability over 30-140% tensional strain, limited only by metal contact fatigue. In this work, the prestretched honeycomb semiconductor channel of donor-acceptor polymer poly(2,5-bis(2-octyldodecyl)-3,6-di(thiophen-2-yl)-2,5-diketo-pyrrolopyrrole-alt-2,5-bis(3-triethyleneglycoloxy-thiophen-2-yl) exhibits high ion uptake and completely stable electrochemical and mechanical properties over 1,500 redox cycles with 10(4) stretching cycles under 30% strain. Invariant electrocardiogram recording cycles and synapse responses under varying strains, along with mechanical finite element analysis, underscore that the present stretchable organic electrochemical transistor design strategy is suitable for diverse applications requiring stable signal output under deformation with low power dissipation and mechanical robustness. Highly stretchable organic electrochemical transistors with stable charge transport under severe tensional strains are demonstrated using a honeycomb semiconducting polymer morphology, thereby enabling controllable signal output for diverse stretchable bioelectronic applications.

36 MATERIALS SCIENCE↗

Experimental Investigation of Vibratory Stresses in a Concentric-Ring Direct-Air-Cycle Nuclear Fuel Element

Preliminary tests made by the General Electric Company indicated that aerodynamic loads might cause large enough distortions in the thin sheet-metal rings of a nuclear fuel element to result in structural failure. The magnitude of the distortions in a test fuel element was determined from strains measured with airflow conditions simulating those expected during engine operation. The measured vibratory strains were low enough to indicate the improbability of failure by fatigue. A conservative estimate of the radial deflection that accompanied peak strains in the outer ring was +0.0006 inch.

Chiarito, Patrick T.↗

Low Temperature Creep of Hot-Extruded Near-Stoichiometric NiTi Shape Memory Alloy: Effect of Thermal Cycling - Part 2

This paper is the first report on the effect prior low temperature creep on the thermal cycling behavior of NiTi. The isothermal low temperature creep behavior of near-stoichiometric NiTi between 300 and 473 K was discussed in Part I. The effect of temperature cycling on its creep behavior is reported in the present paper (Part II). Temperature cycling tests were conducted between either 300 or 373 K and 473 K under a constant applied stress of either 250 or 350 MPa with hold times lasting at each temperature varying between 300 and 700 h. Each specimen was pre-crept either at 300 or at 473 K for several months under an identical applied stress as that used in the subsequent thermal cycling tests. Irrespective of the initial pre-crept microstructures, the specimens exhibited a considerable increase in strain with each thermal cycle so that the total strain continued to build-up to 15 to 20 percent after only 5 cycles. Creep strains were immeasurably small during the hold periods. It is demonstrated that the strains in the austenite and martensite are linearly correlated. Interestingly, the differential irrecoverable strain, in the material measured in either phase decreases with increasing number of cycles, similar to the well-known Manson-Coffin relation in low cycle fatigue. Both phases are shown to undergo strain hardening due to the development of residual stresses. Plots of true creep rate against absolute temperature showed distinct peaks and valleys during the cool-down and heat-up portions of the thermal cycles, respectively. Transformation temperatures determined from the creep data revealed that the austenitic start and finish temperatures were more sensitive to the pre-crept martensitic phase than to the pre-crept austenitic phase. The results are discussed in terms of a phenomenological model, where it is suggested that thermal cycling between the austenitic and martensitic phase temperatures or vice versa results in the deformation of the austenite and a corresponding development of a back stress due to a significant increase in the dislocation density during thermal cycling.

Raj, S. V.↗

Development of Digital Twin Predictive Model for PWR Components: Updates on Multi Times Series Temperature Prediction Using Recurrent Neural Network, DMW Fatigue Tests, System Level Thermal-Mechanical-Stress Analysis

The long-term operation (LTO) of nuclear power plant (NPP) beyond their original design life of 40 years, can lead to more material damage associated with cyclic fatigue under thermal-mechanical loading cycles and associated long-term exposure of reactor material to the deleterious reactor-coolant environments. However, under this LTO condition the reactor components can still safely operate but may require more frequent Nondestructive Evaluation (NDE) of reactor components. Frequent NDE requirement may lead to frequent shutdown of the NPP. This in turn can lead to power outage and additional NDE-inspection-cost related economic loss. The economic loss can be minimized by reducing uncertainty in life estimation of safety-critical pressure boundary components and by implementing more digital approach such as by using upcoming digital-twin (DT) technology for predicting the structural states (e.g., time and location dependent inside/outside thickness temperature, stress, strain, plastic deformation, etc.) and associated fatigue life of a component in real time. Towards this goal Argonne National Laboratory (ANL) with the sponsorship of DOE Light Water Reactor Sustainability (LWRS) program is working on the development of a DT framework that can be used for real time environmental fatigue prediction of reactor components. The DT framework is based on limited experiment-data, Artificial-intelligence (AI) – Machine-Learning (ML) - Deep-Learning (DL) based techniques and Multiphysics-computational-mechanics such as finite element (FE) based modeling tools. Towards this overall goal, following are some of the major contributions made during the FY21: 1) Multiple 82/182 dissimilar metal weld (DMW) specimens (both solid-weld and joint-weld representing the actual reactor multi-metal nozzles) were fatigue tested. The resulting fatigue lives were compared to the NUREG-6909 based best-fit and design fatigue curves. Additionally, the results of 52/152 DMW fatigue specimens (which were recently tested at Republic of Korea under the sponsorship of International Nuclear Energy Research Initiative - INERI program) were compared to the NUREG-6909 based best-fit and design fatigue curves. From the comparison of 82/182 and 52/152 DMW test data with NUREG-6909 best-fit curve, most of the reported test data fall way away from the NUREG-6909 suggested best-fit or mean curve. The NUREG-6909 suggested best-fit curve is the best-fit curve of austenitic stainless steel and due to lack of enough data on Nickel-based welds, this is currently being used for predicting the life of Nickel-alloy-based welded components. However, the above observation may require higher scaling factor (e.g., ASME suggested factor of 20 on cycles rather than the current NUREG-6909 suggested factor of 12 on cycles) for scaling the austenitic-stainless-steel best-fit-curve for estimating the design or safe-life of a welded component. Accordingly, for example, if a DMW component experience a strain amplitude of 0.6% the PWR-water life of the component would be 52 cycles instead of 85 cycles. However, more DMW tests are required to further ascertain the above-mentioned observations. 2) A system level CAD and finite element model were developed which consists of reactor pressure vessel (RPV), part of steam generator (SG), part of pressurizer (PRZ), hot leg (HL), and surge line (SL). This is with detailed nozzle geometry and thermal-mechanical material properties of different metals to simulate realistic thermal-mechanical stress under connected system global thermal-mechanical boundary conditions. 3) Different system level heat transfer analyses were performed with estimation of relevant heat transfer coefficients. The resulting data were used in subsequent system level thermal-mechanical stress analysis and for generating spatial-temporal training and validation data for a system level digital-twin based temperature predictor. Transient heat transfer analyses were performed considering thermal boundary condition under design-basis (DB) loading and EDF (Électricité de France) data-based grid-load-following (EDF-GLF) loading cycles. 4) System level thermal-mechanical stress analysis was performed for identifying damage-prone hotspots and for future extension of the model for cyclic state prediction. From the system-level model simulation under DB loading cycle it is found that HL and the SL nozzle that connect to the HL can experience significant stress and strain and could be one of the weakest links in the overall reactor coolant system (RCS). 5) An AI/ML based DT model was developed for multi-time-series temperature prediction at any inside/outside thickness locations of PWR pressure boundary components. This is by using Recurrent-neural-network (RNN) and keras machine learning libraries. The RNN model was validated against two laboratory test-based data sets with one obtained through ANL’s in-air fatigue test system and other through PWR-water test loop. The experimentally validated DT model further validated against FE model results to predict thermal scarification related spatialtemporal temperatures at random locations of a component. The well validated DT model was then used for demonstrating spatial-temporal temperature prediction under 100+ years of reactor operation subjected to combined DB, EDF-GLF and randomized grid-load-following (RANDOMGLF) loading Cycles. The expert-elicitation DT model framework was developed assuming field/input/process measurements can be available from a few existing plant sensors and can readily be used by the NPP operators. The above temperature prediction model will feed to the next-step stress analysis model based on which the life of a component can be predicted in realtime, which is one of our future works.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Proposed framework for thermomechanical life modeling of metal matrix composites

The framework of a mechanics of materials model is proposed for thermomechanical fatigue (TMF) life prediction of unidirectional, continuous-fiber metal matrix composites (MMC's). Axially loaded MMC test samples are analyzed as structural components whose fatigue lives are governed by local stress-strain conditions resulting from combined interactions of the matrix, interfacial layer, and fiber constituents. The metallic matrix is identified as the vehicle for tracking fatigue crack initiation and propagation. The proposed framework has three major elements. First, TMF flow and failure characteristics of in situ matrix material are approximated from tests of unreinforced matrix material, and matrix TMF life prediction equations are numerically calibrated. The macrocrack initiation fatigue life of the matrix material is divided into microcrack initiation and microcrack propagation phases. Second, the influencing factors created by the presence of fibers and interfaces are analyzed, characterized, and documented in equation form. Some of the influences act on the microcrack initiation portion of the matrix fatigue life, others on the microcrack propagation life, while some affect both. Influencing factors include coefficient of thermal expansion mismatch strains, residual (mean) stresses, multiaxial stress states, off-axis fibers, internal stress concentrations, multiple initiation sites, nonuniform fiber spacing, fiber debonding, interfacial layers and cracking, fractured fibers, fiber deflections of crack fronts, fiber bridging of matrix cracks, and internal oxidation along internal interfaces. Equations exist for some, but not all, of the currently identified influencing factors. The third element is the inclusion of overriding influences such as maximum tensile strain limits of brittle fibers that could cause local fractures and ensuing catastrophic failure of surrounding matrix material. Some experimental data exist for assessing the plausibility of the proposed framework.

Halford, Gary R.↗

Evaluation of hybrid composite materials in cylindrical specimen geometries

Static and fatigue properties of three composite materials and hybrids were examined. The materials investigated were graphite/epoxy, S-glass/epoxy, PRD-49 (Kevlar 49)/epoxy, and hybrids in angle-ply configurations. A new type of edgeless cylindrical specimen was developed. It is a flattened tube with two flat sides connected by curved sections and it is handled much like the standard flat coupon. Special specimen fabrication, tabbing, and tab region reinforcing techniques were developed. Axial modulus, Poisson's ratio, strength, and ultimate strain were obtained under static loading from flattened tube specimens of nine laminate configurations. In the case of graphite/epoxy the tubular specimens appeared to yield somewhat higher strength and ultimate strain values than flat specimens. Tensile fatigue tests were conducted with all nine types of specimens and S-N curves obtained. Specimens surviving 10 million cycles of tensile loading were subsequently tested statically to failure to determine residual properties.

Liber, T.↗

Full scale GLARE fuselage panel tests

A GLARE fuselage panel, representative of the crown section of the Fokker 100 fuselage in front of the wing, was tested. The panels were loaded by air pressure resulting in tangential stress in the panel by axial loading, representative of both the cabin pressure and the fuselage bending due to taxiing and gust loading. A fatigue test, simulating 180000 flights, followed by static tests were performed. The panel was loaded to failure at 1.32 ultimate load. The test set-up, the uniform strain distribution of the panel, and the fatigue loads applied at high test frequency are described. The use of GLARE leads to a substantial weight reduction without affecting the fatigue static strength.

Vercammen, Roland W. A.↗

Fatigue Behavior of Laser Powder Bed Fused HAYNES 214: Effects of Different Surface Treatments

In this study, under NASA’s Rapid and Analysis Manufacturing Propulsion Technology (RAMPT) project, effects of different surface post-treatments on surface texture and fatigue behavior of L-PBF Alloy 214 were investigated. Various subtractive SPTs including abrasive flow machining (AFM), machining (M), shot peening (SP), vapormatt (VM), dry electropolishing (DE), chemical milling (CM), chemical-mechanical polishing (CMP), electro chemical (ECP) were applied to study the variations of the surface texture, microstructure and uniaxial fatigue behavior under fully reversed strain-controlled condition at four different strain amplitudes of 0.005, 0.004, 0.003, and 0.0025 mm/mm. The insights gained regarding the relationship between structural and mechanical properties for different SPTs can help establish guidelines for selecting the most effective process to enhance the performance of Laser Powder Bed Fusion (L-PBF) Alloy 214, especially for critical aerospace applications.

Post-Processing↗

Hybrid AI-ML and FE-based Digital Twin Predictive Modeling Framework for a PWR Coolant System Components: Updates on Multi-Time-Series-3D-Location Dependent Usages Factor Prediction

The long-term operation (LTO) of nuclear power plants (NPP) beyond their original design life of 40 years can lead to more material damage associated with cyclic fatigue under thermal-mechanical loading cycles and associated long-term exposure of reactor material to the deleterious reactor-coolant environments. However, under this LTO condition, the reactor components can still safely operate but may require more frequent Nondestructive Evaluation (NDE) of reactor components. Requiring frequent NDE inspections may lead to frequent NPP shutdowns which can lead to power outages and additional NDE inspection cost-related economic loss. The economic loss can be minimized by reducing uncertainty in life estimation of safety-critical pressure boundary components and by implementing a more digital approach such as using upcoming digital-twin (DT) technology for predicting the structural states (e.g., time and location dependent inside/outside thickness temperature, stress, strain, plastic deformation, etc.) and associated fatigue life of a component in real time. The DT framework is based on limited experimental data, Artificial-intelligence (AI)-Machine-Learning (ML) and multiphysics-computationalmechanics such as finite element- (FE) based models. Given the real-time thermal-hydraulic process measurements from several existing plant sensors, the overall goal of the DT framework is to predict the cumulative usages factors or equivalent fatigue lives in real time and at any random 3D location of the components. This includes inaccessible locations such as inside the thickness or location of a component. This prediction can be at thousands to millions of 3D point clouds or locations like conventional FE-based models, but without running an FE model in real time.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Fatigue-environment interactions in a SiC/Ti-15-3 composite

Load-controlled isothermal and nonisothermal fatigue lives of a (0-deg)s SiC/Ti-15-3 were evaluated at temperatures between 150 and 550 C and a target strain range of about 0.45 percent. In nonisothermal fatigue tests, load was first cycled at minimum temperature and then temperature was cycled at zero load. For fatigue tests with peak temperatures at or above 300 C, fatigue life was dramatically reduced compared to that at 150 C. The shortest life was produced by the nonisothermal test with the greatest temperature range (Delta T = 400 C) and highest peak temperature (T(max) = 550 C). Vacuum testing showed that much of the life reduction under isothermal and nonisothermal conditions was related to environmental effects, although the nature of the fatigue-environment interaction was decidedly different for the isothermal and nonisothermal test cycles which were studied.

Gayda, J.↗

Additive Manufacturing Flaw Assessment Methodology

An evolution fatigue data and flaw tolerance of components produced using the Powder Bed Fusion (PBF) Additive Manufacturing (AM) process is documented in this report. Initial differences in fatigue data for AM components compared to smooth bar fatigue data indicated a need for a more detailed analysis of AM data available in technical literature. The investigation was initiated to support the development of a fatigue analysis methodology for AM components to support the of codification of AM technology for pressure equipment. The project was initiated to collect and analyze stainless steel 304L and 316L AM fatigue test data and corresponding process and quality information to develop S-N and E-N based fatigue data representation. Additional AM fatigue test data including Inconel Ti-6-4 and aluminum alloys were also considered for comparison purposes Metallic AM parts tend to contain various forms of defects distributed throughout the part. If an AM part is subjected to fatigue loading in service, a fatigue analysis needs to be performed during the design process to ensure an acceptable service life for the part. Post-process machining and polishing do not to improve fatigue resistance in any significant degree. The low cycle fatigue regime is of particular interest to this project in support of flaw acceptance criteria currently under development by ASME’s BPTCS/BNCS. Internal defects become exposed as external surface defects during machining for the machining of the AM part to final dimensions. This implies that as long as inherent AM defects are within a controlled limit in terms of both size and distribution characteristics, the corresponding fatigue test data in terms of either S-N (stress life) or E-N (strain life) can be investigated and characterized to establish fatigue properties of AM parts for design and fatigue evaluation purposes. The resulting S-N or E-N curves and their scatter bands can be used to derive fatigue design allowable stress values by capturing the effects of distributed discontinuities within an acceptable limit.

36 MATERIALS SCIENCE↗

Characterization of unnotched SCS-6/Ti-15-3 metal matrix composites at 650 C

Ti-15-3 reinforced with SCS-6 silicon carbide fibers, in five different layups, was tested at 650 C to determine monotonic and fatigue strengths, basic mechanical properties, and damage initiation and progression. The elevated temperature results were compared to those obtained at room temperature. Analytical predictions were made of the monotonic stress-strain response as well as cyclic stress-strain hysteresis. The fiber reinforcement was found to significantly increase the static and fatigue strengths of the laminates over that of the matrix material at elevated temperature while the increase was insignificant at room temperature. Initial damage, in either the fibers or the matrix, was partitioned as a function of the life and applied strain range in the constituents. High strains and short lives resulted in multiple fiber failure with no signs of matrix fatigue cracking. Low strains and long lives resulted in extensive matrix cracking and no fiber breaks away from the fracture surface. At 650 C the matrix was too weak to cause fiber-matrix interface failure prior to matrix yielding. Laminate fatigue lives were hypothesized to be a function of the 0 deg fiber stress. More scatter was found in the 0 deg fiber stress vs. high temperature fatigue life data than for the room temperature data. An initial unloading modulus that was greater than the initial loading modulus was observed in the elevated temperature fatigue tests.

Pollock, W. D.↗

Characterization of unnotched SCS-6/Ti-15-3 metal matrix composites at 650 C

Ti-15-3 reinforced with SCS-6 silicon carbide fibers, in five different layups, was tested at 650 C to determine monotonic and fatigue strengths, basic mechanical properties, and damage initiation and progression. The elevated temperature results were compared to those obtained at room temperature. Analytical predictions were made of the monotonic stress-strain response as well as cyclic stress-strain hysteresis. The fiber reinforcement was found to significantly increase the static and fatigue strengths of the laminates over that of the matrix material at elevated temperature while the increase was insignificant at room temperature. Initial damage, in either the fibers or the matrix, was partitioned as a function of the life and applied strain range in the constituents. High strains and short lives resulted in multiple fiber failure with no signs of matrix fatigue cracking. Low strains and long lives resulted in extensive matrix cracking and no fiber breaks away from the fracture surface. At 650 C the matrix was too weak to cause fiber-matrix interface failure prior to matrix yielding. Laminate fatigue lives were hypothesized to be a function of the 0 deg fiber stress. More scatter was found in the 0 deg fiber stress vs. high temperature fatigue life data than for the room temperature data. An initial unloading modulus that was greater than the initial loading modulus was observed in the elevated temperature fatigue tests.

Pollock, William D.↗

Phase-Field Model Incorporating Large Inelastic Strain with Application to the Oxidation of High-Temperature Coating Systems

Structural metallic and ceramic materials at high temperatures often suffer from creep, fatigue and oxidation, which typically involves local large inelastic strain. The large strain is usually approached by Lagrangian-description-based finite deformation theory. Here we develop an efficient, Eulerian-description-based, Incremental Realization of Inelastic Deformation (IRID) algorithm to deal with large inelastic strain with small elastic strain. We apply this algorithm to simulate high temperature oxidation with severe volume expansion using a phase-field approach. The oxidation and deformation of bond coat can lead to spallation and failure of the thermal barrier coatings (TBC) and environmental barrier coatings (EBC), which is a critical concern in design of these coatings. We simulate the growth of thermally grown oxide (TGO) in these coating systems, with phase transformations and microstructure evolution incorporated. The simulation results are compared with relevant experimental reports in the literature.

Cheng, Tianle↗

High energy X-ray diffraction and small-angle scattering measurements of hydrogen fatigue damage in AISI 4130 steel

Accurate lifetime predictions are critical for repurposing existing pipelines for hydrogen transmission as well as for developing novel steels which are minimally susceptible to lifetime degradation by hydrogen. Ultimately, lifetime prediction models assess the amount of damage a material undergoes during a typical service cycle and the cumulative damage a material can withstand prior to failure. However, not all damage processes are equal, and neither is the manner in which mechanical loading translates to damage the same when materials are in inert environments compared to in hydrogen environments. For example, in the three leading proposed mechanisms of hydrogen embrittlement (Hydrogen-Enhanced Decohesion (HEDE), the Hydrogen-Enhanced Localized Plasticity (HELP), and the Nano-Void Coalescence (NVC)), hydrogen is proposed to enhance the manifestation of grain separation, dislocation generation/movement, and void coalescence, respectively. A full understanding of the damage modes requires a measurement capable of probing all three mechanisms at once. Here we present simultaneous High Energy X-ray Diffraction (HEXRD) and Small-Angle X-ray Scattering (SAXS) during fatiguing of steel in hydrogen. HEXRD measurements probe strain and dislocation density; SAXS measurements probe nano-pore generation and coalescence. We will discuss the differences in damage modes between steels fatigued in air and in hydrogen and the role these difference play in lifetime predictions.

36 MATERIALS SCIENCE↗

Crack tip field and fatigue crack growth in general yielding and low cycle fatigue

Fatigue life consists of crack nucleation and crack propagation periods. Fatigue crack nucleation period is shorter relative to the propagation period at higher stresses. Crack nucleation period of low cycle fatigue might even be shortened by material and fabrication defects and by environmental attack. In these cases, fatigue life is largely crack propagation period. The characteristic crack tip field was studied by the finite element method, and the crack tip field is related to the far field parameters: the deformation work density, and the product of applied stress and applied strain. The cyclic carck growth rates in specimens in general yielding as measured by Solomon are analyzed in terms of J-integral. A generalized crack behavior in terms of delta is developed. The relations between J and the far field parameters and the relation for the general cyclic crack growth behavior are used to analyze fatigue lives of specimens under general-yielding cyclic-load. Fatigue life is related to the applied stress and strain ranges, the deformation work density, crack nucleus size, fracture toughness, fatigue crack growth threshold, Young's modulus, and the cyclic yield stress and strain. The fatigue lives of two aluminum alloys correlate well with the deformation work density as depicted by the derived theory. The general relation is reduced to Coffin-Manson low cycle fatigue law in the high strain region.

Minzhong, Z.↗