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Low-cycle fatigue

Low-cycle fatigue (LCF) is a degradation process characterized by the and of cracks under cyclic loading conditions involving significant amplitudes, typically leading to failure after fewer than 10,000 cycles. This phenomenon occurs in components exposed to high-stress environments, such as or cycling, where stresses exceed the 's strength, resulting in irreversible deformation per cycle. Unlike high-cycle fatigue (HCF), which involves predominantly deformation and limits beyond 10^6 cycles under lower stress amplitudes, LCF is analyzed using -life approaches like the Coffin-Manson relation, emphasizing total range (elastic plus ) as the primary damage driver. In LCF, cyclic loading produces hysteresis loops in stress-strain curves, reflecting energy dissipation through plastic work, with crack initiation often occurring at persistent slip bands or microstructural defects like inclusions and grain boundaries. Failure mechanisms include transgranular propagation with striations, influenced by factors such as , , and hold times, which can accelerate via creep-fatigue interactions. For welded structures, LCF is particularly critical due to heterogeneous microstructures in the , where initial cyclic hardening gives way to softening, reducing and promoting early initiation. LCF is a key design consideration in high-performance applications, including turbine blades, engine components, and pressure vessels, where materials like nickel-based superalloys (e.g., Inconel 718) or must withstand extreme conditions. Testing protocols involve strain-controlled fatigue machines to generate strain-life curves or predict life using models that account for mean stress effects and environmental influences, ensuring reliability in , power generation, and automotive sectors. Advances in understanding LCF have led to improved life prediction models, incorporating multiaxial loading and microstructural evolution to mitigate failures in these demanding environments.

Fundamentals

Definition and Scope

Low-cycle fatigue (LCF) refers to a in subjected to cyclic loading where significant deformation occurs in each cycle, leading to and over a relatively small number of load cycles, typically fewer than 10^4 to 10^5 cycles to . This regime is characterized by high strain amplitudes that exceed the limit of the , resulting in irreversible deformation that accumulates progressively until . Unlike -dominated processes, LCF emphasizes the role of inelastic straining in driving the life. The scope of LCF encompasses engineering applications involving severe loading conditions that induce large strains, such as thermal cycling in engines and vessels, where gradients cause constrained and . It is also prevalent in structural components under seismic events, which impose sudden, high-amplitude displacements, and in machinery experiencing mechanical overloads like startup/shutdown cycles in . In these contexts, LCF results in a finite lifespan determined by the buildup of plastic , necessitating strategies focused on management rather than alone. Key parameters in LCF analysis include the total strain range (Δε_t), which combines and plastic components to quantify the overall deformation per cycle, and the plastic strain amplitude (Δε_p/2), which specifically measures the irreversible portion contributing to damage accumulation. These metrics distinguish LCF from infinite life regimes, where strains predominate and failure is avoided below an endurance limit, often in high-cycle scenarios exceeding 10^5 cycles.

Comparison with High-Cycle Fatigue

Low-cycle fatigue (LCF) is distinguished from high-cycle fatigue (HCF) primarily by the nature of deformation and the number of cycles to failure. In LCF, significant plastic strain occurs per cycle, leading to material failure typically in fewer than 10^4 to 10^5 cycles, whereas HCF involves predominantly elastic deformation with failure after more than 10^4 to 10^6 cycles. This plastic deformation in LCF serves as a hallmark, contrasting with the elastic response in HCF. Life prediction methods further highlight these differences: LCF employs strain-life curves, which account for both elastic and plastic strain components, while HCF uses stress-life (S-N) curves that focus on alternating stress amplitude versus cycles to failure. The transition regime between LCF and HCF lies approximately between 10^3 and 10^5 cycles, influenced by factors such as material and specific loading conditions. In terms of design implications, LCF requires strain-based for ductile materials under severe, high-strain loading scenarios to mitigate rapid and . Conversely, HCF design prioritizes identifying limits to ensure longevity in brittle materials or components subjected to repeated low-amplitude stresses over extended periods.

Historical Development

Origins in the Mid-20th Century

Low-cycle fatigue was first recognized in the mid-20th century through experimental observations during the testing of components and vessels, where materials subjected to high-strain cycles exhibited rapid after relatively few repetitions, often fewer than 10,000 cycles. These early insights emerged as engineers noted that traditional stress-based fatigue models, developed for high-cycle scenarios, inadequately predicted failures under severe deformation conditions prevalent in thermal cycling environments. A pivotal milestone occurred in 1953 when S.S. Manson published foundational work at the (NACA), analyzing material behavior under thermal stresses and emphasizing the role of plastic in fatigue life prediction for ductile metals. This was closely followed in 1954 by L.F. Coffin's strain-controlled experiments at the , which demonstrated a direct relationship between plastic strain range and cycles to in ductile materials, laying the groundwork for empirical relations in low-cycle regimes. Initial studies focused on ductile alloys such as steels and aluminum, common in these applications, revealing that fatigue life correlated strongly with total rather than alone. These developments were driven by post-World War II technological imperatives, particularly the rapid advancement of in aeronautical applications and , which introduced intense thermal fatigue from startup-shutdown cycles and high-temperature operations. In , components like experienced thermal strains per flight cycle, while faced similar challenges from fluctuating coolant temperatures, necessitating new understanding to ensure component durability and safety. This era's research thus established as a distinct failure mode, influencing subsequent broader investigations into material limits under cyclic loading.

Evolution of Research

Building on the foundational Coffin-Manson relation established in the 1950s, research in low-cycle fatigue (LCF) during the and increasingly incorporated finite element analysis (FEA) to simulate nonlinear stress-strain behaviors in components experiencing plastic deformation. This computational approach enabled more accurate modeling of local strain concentrations in complex geometries, particularly in high-stakes applications like turbine blades and pressure vessels. Concurrently, studies on temperature effects revealed that elevated temperatures accelerate fatigue damage by enhancing creep-fatigue interactions, with significant work conducted on alloys used in engines during the . In the energy and sectors, investigations into multiaxial loading conditions highlighted the need for strain-based criteria to account for non-proportional loading paths, leading to standardized testing protocols by the . From the 1990s to the 2010s, LCF research advanced through integration with principles to better predict crack and early under cyclic straining. This approach allowed for the assessment of microstructural influences on accumulation, improving life predictions for metallic components in cyclic environments. Limited but growing studies extended LCF analysis to non-metallic materials, such as fiber-reinforced composites, where matrix cracking and fiber debonding dominated failure modes, though applicability remained constrained compared to metals. Seismic events, including the 1994 Northridge and 1995 Kobe earthquakes, underscored LCF vulnerabilities in structures, prompting updates to structural design standards that incorporated strain-based fatigue limits for earthquake-resistant framing. Pre-2020 research addressed key gaps in predicting ultra-low cycle fatigue (fewer than 100 cycles), where traditional empirical models often underestimated ductile risks due to insufficient for void growth mechanisms. This led to a shift toward semi-mechanistic models, such as the cyclic void growth model (CVGM), which links macroscopic to microscopic evolution for more reliable ultra-low cycle predictions in seismic and impact loading scenarios.

Key Characteristics

Strain-Controlled Nature

Low-cycle fatigue (LCF) testing is inherently strain-controlled to accurately capture the material's response under conditions dominated by deformation, where levels fluctuate significantly during each due to changes in material stiffness and hardening effects. According to ASTM E606, the standard method for -controlled , specimens are subjected to fully reversed or mean-strain cyclic loading using extensometers clipped directly to the gage length to precisely measure and regulate the total , ensuring it remains constant throughout the test. This approach contrasts with load-controlled testing, which is unsuitable for LCF because the substantial cause continuous and variation, making it difficult to maintain consistent loading conditions. Typical strain rates in these tests range from 0.001 to 0.01 s⁻¹, allowing sufficient time for while minimizing rate-dependent effects in metallic materials. Under high initial strain amplitudes characteristic of LCF (typically 0.2% to 2%), materials often exhibit distinct behavioral traits that evolve over cycles. In symmetric loading (zero mean strain), the response may stabilize through shakedown, where initial plastic straining gives way to elastic-dominant cycling after a few cycles, preventing further net deformation accumulation. However, with nonzero mean strain, ratcheting can occur, leading to progressive, unidirectional plastic strain buildup that accelerates damage. Metals under such thermal or mechanical cyclic loads frequently display cyclic hardening, an increase in stress amplitude due to dislocation multiplication and tangle formation, or cyclic softening, a reduction in flow stress from dislocation annihilation or phase changes, influencing the overall fatigue endurance. These macroscopic behaviors stem from underlying deformation mechanisms involving dislocation interactions. The strain-controlled nature of LCF testing is particularly relevant for applications where imposed displacements are more predictable and controlled than stresses, mirroring conditions that induce large strains. For instance, in engines, repeated startups and shutdowns cause and contraction, generating strain amplitudes that lead to LCF in components like blades and disks. Similarly, in civil structures, shaking imposes cyclic displacements on foundations and braces, simulating the low-cycle, high-strain where strain control better represents the seismic loading path. This testing methodology thus provides critical data for designing against such transient overloads in , power generation, and seismic-resistant .

Deformation Mechanisms

In low-cycle fatigue (LCF), the primary microscopic deformation mechanisms involve localized plastic strain accumulation that leads to irreversible . In face-centered cubic (FCC) metals, such as and aluminum alloys, cyclic straining promotes the formation of persistent slip bands (PSBs), which are thin, ladder-like structures where dislocations organize into walls and channels, concentrating the majority of the plastic strain within a small volume fraction of the material. These PSBs emerge due to the reversible motion of dislocations during initial cycles, but repeated loading causes irreversible slip as dislocations interact and multiply, creating a heterogeneous strain distribution observable through strain-controlled testing. Dislocation pile-ups within PSBs generate high local stresses, often exceeding the theoretical strength of the , which initiate microcracks along the most favorably oriented slip planes. This process drives Stage I crack growth, characterized by -mode propagation parallel to the slip direction, with crack advances typically on the order of atomic distances per cycle until the crack reaches a critical length of about 10-100 μm. Damage accumulation in LCF proceeds through transgranular cracking, where cracks propagate within grains rather than along boundaries, facilitated by the intense localization in PSBs or at defects. Inclusions and other microstructural defects, such as non-metallic particles or pores, serve as nucleation sites by creating stress concentrations that accelerate dislocation interactions and void formation during cyclic loading. The strain ratio R = \frac{\epsilon_{\min}}{\epsilon_{\max}}, which quantifies the asymmetry of cyclic straining, influences damage by altering the mean strain; for instance, negative R values (compressive minima) can suppress crack opening and delay nucleation compared to R = 0. Material-specific effects highlight variations in these mechanisms. In steels, particularly low-carbon varieties, LCF damage often manifests as ductility exhaustion, where cumulative plastic deformation depletes the material's ability to accommodate , leading to rapid void coalescence and after a few dozen cycles. In aluminum alloys under ultra-low cycle fatigue (typically fewer than 100 cycles at strains exceeding 1-5%), void growth dominates, with cyclic triaxiality promoting the expansion of pre-existing microvoids at inclusions, resulting in ductile rupture rather than shear-dominated cracking.

Mechanics and Predictive Models

Coffin-Manson Relation

The Coffin-Manson relation provides a foundational empirical model for predicting the life in the low-cycle regime, where deformation dominates. It expresses the total strain amplitude as the sum of and strain components, each following a power-law relationship with the number of cycles to failure. This relation was developed through experimental studies on ductile metals under cyclic thermal and mechanical loading, establishing a baseline for strain-based analysis. The core equation is: \frac{\Delta \varepsilon_t}{2} = \varepsilon_f' (2N_f)^c + \frac{\sigma_f'}{E} (2N_f)^b Here, \Delta \varepsilon_t / 2 represents the total amplitude, \varepsilon_f' is the fatigue (often approximating the true ), c is the fatigue exponent (typically ranging from -0.5 to -0.7 for metals), \sigma_f' is the fatigue strength (approximating the true strength), b is the fatigue strength exponent (typically -0.05 to -0.12), E is the , and N_f is the number of cycles to failure. The factor of 2 accounts for the reversal in fully reversed loading. The derivation stems from separating the total strain into plastic and elastic contributions on a logarithmic scale. The plastic term originates from Coffin's observations of plastic strain accumulation in thermal cycling tests on aluminum alloys, yielding \Delta \varepsilon_p / 2 = \varepsilon_f' (2N_f)^c, while the elastic term draws from Basquin's high-cycle relation, \Delta \varepsilon_e / 2 = (\sigma_f' / E) (2N_f)^b. Manson extended this by integrating the components for broader applicability in thermal stress conditions, assuming stabilized hysteresis loops after initial hardening or softening. This logarithmic separation enables linear regression fitting to experimental data for parameter determination. The relation is valid primarily for fully reversed loading (stress ratio R = -1), where mean stress is zero, and applies to strain-controlled tests in the low-cycle domain (typically N_f < 10^4). Material-specific parameters must be calibrated through uniaxial low-cycle fatigue testing, as values vary with microstructure, composition, and processing. For non-zero mean stress, modifications such as the Morrow correction may be applied.

Mean Stress Corrections

In low-cycle fatigue (LCF) analysis, mean stress influences the fatigue life by altering the effective amplitude, particularly under non-zero conditions common in applications. The Morrow approximation provides a foundational correction to the baseline Coffin-Manson relation by modifying the elastic strain term to account for tensile stress, which reduces the driving force for crack initiation. This adjustment takes the form \frac{\sigma_f' - \sigma_m}{E} (2N_f)^b, where \sigma_f' is the fatigue strength coefficient, \sigma_m is the stress, E is the , N_f is the number of cycles to failure, and b is the fatigue strength exponent. The exponents in this model are tied to the material's cyclic n', with c = -\frac{1}{1+5n'} for the plastic strain term and b = -\frac{n'}{1+5n'}. This approach assumes that stress primarily affects the elastic component, becoming less influential at high plastic strains typical of LCF. Other established corrections extend this framework for broader applicability. The Walker model computes an equivalent zero-mean strain by incorporating a material-specific sensitivity parameter \gamma, expressed as \Delta \varepsilon_{eq} = \Delta \varepsilon (\sigma_m / \sigma_a)^{1-\gamma}, where \Delta \varepsilon is the total strain range and \sigma_a is the stress amplitude; this allows tailoring to different alloys and loading ratios. Complementing these, the Smith-Watson-Topper (SWT) parameter integrates maximum stress and total strain range to capture crack opening effects, defined as \sqrt{\sigma_{\max} \Delta \varepsilon_t E / 2}, where \sigma_{\max} is the maximum stress and \Delta \varepsilon_t is the total strain range; it is particularly suited for conditions where compressive mean stresses have minimal impact. These mean stress corrections are crucial for non-reversed loading in critical components like turbine blades, where thermal gradients and operational stresses introduce significant mean components that can accelerate failure if unaccounted for. Incorporating such models in LCF predictions for these applications enhances reliability by aligning simulations more closely with experimental outcomes, with validations demonstrating accuracy improvements of 20-30% over uncorrected baselines.

Advanced and Recent Models

Advanced models for low-cycle fatigue (LCF) prediction have evolved to address complex loading conditions and material-specific behaviors, building on foundational relations like the Coffin-Manson equation to incorporate multiaxial effects and computational enhancements. Established approaches include energy-based models that treat energy dissipation per cycle as a primary damage metric, capturing the work that drives crack initiation and propagation, particularly for materials exhibiting significant cyclic . These approaches aggregate loop areas from stress-strain to estimate cumulative damage, offering advantages over strain-only models by incorporating both and contributions. Multiaxial fatigue criteria focus on identifying critical planes where damage accumulates under combined loading paths, with the Fatemi-Socie model being a widely adopted approach that quantifies damage through the maximum strain amplitude on the critical , modified by the normal influence to account for mean and out-of-phase effects. This model improves predictions for non-proportional loading by integrating -dominated slip mechanisms with normal -induced crack closure, demonstrating superior accuracy in ductile metals under multiaxial control compared to uniaxial baselines. A comprehensive 2024 review classifies over a dozen such criteria, including extensions of Fatemi-Socie, emphasizing their application to components like blades and shafts subjected to complex cyclic . Advancements since 2020 have tailored LCF models to emerging materials and structures, including additively manufactured alloys where defect-induced variability is prominent. In seismic applications, strain-life models incorporate low-cycle damage accumulation for earthquake-resistant frames using structural aluminum alloys, informing performance modeling under cyclic loading. The cyclic void growth model (CVGM), used for ultra-low cycle fatigue in piers, employs micro-mechanical void coalescence criteria to forecast initiation under extreme cyclic s, with reviews confirming its efficacy in predicting damage during simulated seismic events. For bake-hardening steels, such as pre-strained HR420 variants, bake treatments at 170°C post-forming enhance LCF resistance at low amplitudes (0.2%) through dislocation pinning and strengthening, suppressing early crack nucleation as validated by simulations.

Applications, Failures, and Mitigation

Low-cycle fatigue (LCF) is a critical consideration in the of components subjected to high strains in applications such as turbine blades, power generation turbine disks, and parts. In these environments, materials like nickel-based superalloys endure thermal-mechanical cycling, where LCF limits and requires strain-life predictions to prevent at high-temperature hotspots.

Notable Failures

One of the most significant incidents involving low-cycle fatigue (LCF) occurred during the in , where magnitude 6.7 seismic shaking induced large strain amplitudes in welded beam-to-column connections of steel moment-resisting frames in mid-rise buildings, such as 10-story structures. These connections experienced extremely low-cycle fatigue (ELCF), leading to brittle fractures and partial collapses in over 100 buildings despite no total structural failures. The event resulted in over 9,000 injuries across the affected region, underscoring the vulnerability of pre-1994 welded designs to seismic distortions. In response, investigations prompted updates to building codes, including enhanced welding specifications in the 1994 Uniform Building Code to improve . Similarly, the 2010 Maule earthquake in , with a of 8.8, caused partial of the 21-story Torre O'Higgins office building in Concepción due to failures in its walls. The damage was exacerbated by torsional demands from a setback irregularity and insufficient confinement, resulting in shear cracks and rupture of longitudinal reinforcements. This incident highlighted critical vulnerabilities in high-rise designs, particularly those relying on slender walls under extreme ground motions. Following these events, post-2010 has seen heightened awareness of LCF risks in seismic design, with no major publicized catastrophes directly attributed to LCF in operational structures, though lab-simulated tests on additively manufactured metallic parts have revealed accelerated failures from defects like under low-cycle loading. These simulations demonstrate that microstructural anomalies in 3D-printed components can reduce life by up to 50% compared to wrought materials, emphasizing ongoing challenges in emerging for seismic applications.

Design and Prevention Strategies

In low-cycle fatigue (LCF) design, emphasizes alloys with high and to cyclic hardening to accommodate strains without premature initiation. Austenitic stainless steels, such as AISI 304 and 347, are preferred due to their excellent and ability to undergo significant deformation, which enhances LCF life by delaying fatigue growth. These materials exhibit low cyclic hardening rates, allowing them to maintain stable loops under repeated straining, as demonstrated in strain-controlled tests where life extension exceeds that of ferritic alternatives. Surface treatments like introduce compressive residual stresses that counteract tensile strains, significantly improving initiation ; for instance, severe on laser powder bed fusion parts has tripled the from 200 MPa to over 600 MPa in austenitic alloys. Design guidelines for LCF mitigation integrate strain-life analysis within finite element analysis (FEA) software to predict local plastic strains in components subjected to cyclic loading. Tools like nCode DesignLife employ the strain-life method to estimate cycles to failure based on Neuber's rule for elastic-plastic strain concentration, enabling proactive design adjustments in high-strain regions such as notches or welds. Safety factors of 2 to 3 times the predicted are typically applied, as specified in ASME Boiler and Pressure Vessel Code Section VIII Division 2, to account for uncertainties in material variability and loading spectra, particularly in thermal cycling applications like . For seismic and thermal environments, ASME Section III recommends incorporating environmental correction factors (e.g., Fen up to 12 for temperature and aqueous effects in components), while Eurocode 3 addresses environmental influences through protection and adjusted detail categories; cumulative rules like Miner's are used in both to ensure components withstand expected strain amplitudes without exceeding allowable lives. Post-2020 advancements in LCF prevention for (AM) focus on hybrid modeling approaches that combine physics-based simulations with to optimize microstructures and predict fatigue in as-built parts. These models integrate crystal plasticity finite element methods with data-driven corrections for defects like , achieving up to 50% more accurate life predictions for AM Ti-6Al-4V under LCF compared to traditional methods. In critical components such as disks, real-time monitoring using high-temperature gauges detects strain accumulation during operation, allowing early intervention; for example, gauges embedded in Ni-Co-base superalloys have validated LCF models by correlating measured with predicted damage at 650°C. This hybrid strategy, emphasized in recent reviews, addresses AM-specific challenges like anisotropic properties, promoting safer integration into applications.

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