Coffin-Manson Relationship Research Articles

Low cycle fatigue behavior and life prediction of a directionally solidified alloy

Low cycle fatigue behavior and life prediction of a directionally solidified alloy

Ultrathin damage-tolerant flexible metal interconnects reinforced by in-situ graphene synthesis

Conductive patterned metal films bonded to compliant elastomeric substrates form meshes which enable flexible electronic interconnects for various applications. However, while bottom-up deposition of thin films by sputtering or growth is well-developed for rigid electronics, maintaining good electrical conductivity in sub-micron thin metal films upon large deformations or cyclic loading remains a significant challenge. Here, we propose a strategy to improve the electromechanical performance of nanometer-thin palladium films by in-situ synthesis of a conformal graphene coating using chemical vapor deposition (CVD). The uniform graphene coverage improves the thin film’s damage tolerance, electro-mechanical fatigue, and fracture toughness owing to the high stiffness of graphene and the conformal CVD-grown graphene-metal interface. Graphene-coated Pd thin film interconnects exhibit stable increase in electrical resistance even when strained beyond 60% and longer fatigue life up to a strain range of 20%. The effect of graphene is more significant for thinner films of < 300 nm, particularly at high strains. The experimental observations are well described by the thin film electro-fragmentation model and the Coffin-Manson relationship. These findings demonstrate the potential of CVD-grown graphene nanocomposite materials in improving the damage tolerance and electromechanical robustness of flexible electronics. The proposed approach offers opportunities for the development of reliable and high-performance ultra-conformable flexible electronic devices.

The effects of microstructure and temperature on the deformation heterogeneities and fatigue behaviour of a Ni-based superalloy

ABSTRACT This research investigates the coupling effect of microstructure and temperature on the fatigue performance of an equiaxed Ni-base superalloy, EA, at design-significant temperatures (750–930°C) for different strain amplitudes (Δϵ/2). It is observed that distinguishing damage features (specific to the temperature and Δϵ/2) remarkably affect the extent and distribution of strain localisation, leading to the divergence in associated fatigue behaviour. The strain is uniformly distributed at lower Δϵ/2 for all temperatures. Compared to the 850 and 930°C, the strain localisations at 750°C are more effectively alleviated, accounting for the highest fatigue life. Moreover, this alloy exhibited a bilinear Coffin-Manson (C–M) relationship. It is ascertained that the strain localisation resulting from the dislocation and precipitates (γ′, Cr6C23, and γ-γ′ eutectic) interactions are mainly responsible for the dual-slope C–M behaviour.

Low‐cycle fatigue life prediction of powder metallurgy superalloy considering characteristic parameters of inclusions

AbstractForeign non‐metallic inclusions can significantly reduce the low‐cycle fatigue (LCF) life of powder metallurgy (PM) superalloy and greatly affect the safety and reliability of aeroengines. In this paper, LCF experiments on PM FGH96 superalloy with and without inclusions were conducted. Effects of inclusions on the fatigue life and damage mechanism of FGH96 alloy are discussed by fractography analysis. Parameters related to inclusion characteristics such as strength–inclusion coefficient are proposed. By introducing characteristic parameters of inclusions, the LCF life prediction models are established based on the Manson–Coffin relationship, which significantly improved the prediction accuracy and reduced the scattering band by a factor of 2.

Seismic damage behaviors of structural steels under different constitutive and damage models

Previous studies have established a variety of cumulative damage models (CDMs) for either structural materials or members to perform an exquisite evaluation on plastic-induced deterioration of structural engineering under severe seismic actions. Nevertheless, the existing CDMs consider different influencing factors and hence tend to produce significantly different simulation performance. On the other hand, the influencing variables of CDMs are likely affected by the description on the cyclic stress-strain relation. Thus, the quantification of seismic damage is affected by the selection of both CDM and constitutive model. Existing relative studies mainly focus on the development and refinement of theoretical models. However, the understanding on simulation performance difference induced by the selection of models is still limited. This paper is aiming to clarify the influence of different constitutive models and CDMs on the cumulative damage behaviors simulated. Firstly, three types of cyclic constitutive models and nine CDMs are reviewed and their material parameters are summarized. The CDMs selected include the deformation-type models, the energy-type models and the combined-type models. Based upon different CDMs, the low-cycle fatigue (LCF) curves of mild structural steel are generated and compared to the corresponding Coffin-Manson relations. Subsequently, the damage evolutionary curves of different CDMs are simulated based upon several representative cyclic loading protocols. The influence of constitutive models and CDMs on the LCF curves and damage evolutionary curves are thoroughly studied. Besides, the sensitivity of CDMs on strain ratios and the influence of cyclic loading protocols on damage evolutionary curves are simultaneously clarified. The research findings can lay a solid foundation for the selection and combination of the relative analytical models with regards to different circumstances.

Effect of carbide precipitation on Coffin–Manson relationship of a polycrystalline nickel‐based superalloy

AbstractThis study explores the dual‐slope Coffin–Manson (C–M) behavior of a polycrystalline nickel‐based superalloy, EA, used in turbine engine applications with an emphasis on discerning the micro‐mechanisms responsible for it. The motivation for distinguishing the micro‐mechanisms responsible for bi‐linear C–M behavior stemmed from the earlier evolved comprehensions that state that the fatigue life estimation based on the extrapolation of any single line gives inaccurate results. Transmission electron microscopy (TEM) investigations of fatigue fractured specimens at low strain amplitudes, Δε/2, revealed that dislocations are homogeneously distributed in the γ‐channels and occasionally form networks at γ/γ′ interface. Whereas deformation is heterogeneous at high Δε/2 owing to the complex dislocation reactions. Cr23C6 carbides are precipitated during the high Δε/2 fatigue tests, which act as obstacles for dislocations. The deformation heterogeneity resulting from the dislocation–γ′ precipitate interactions and the dislocation–M23C6 carbide interactions accounts for the dual‐slope C–M behavior.

Numerical simulation of fatigue behavior of flexible metal films in multiphysics fields

AbstractThe operating ambient of flexible electronics interconnects is a complex environment that includes mechanical deformation, electric current, and temperature. It is a potential threat to the long‐term service reliability of flexible electronic devices. This paper aims to develop a multiphysics fatigue model for flexible metal films. The effect of multiphysics fields is considered in the Coffin–Manson relationship based on reasonable simplification. The fatigue behavior of copper films of various thicknesses on a flexible substrate was investigated when electrical current and mechanical displacement loads were applied simultaneously. The developed model is validated to compare with experimental results. The numerical results show that it can analyze the effect of multiphysics fields and predict the fatigue life of copper films. Therefore, it could be a means to assess the fatigue performance of metal films on flexible substrates in multiphysics fields.

Micromechanics-Based Low Cycle Fatigue Life Prediction Model of ECAPed Aluminum Alloy

Ultrafine-grained aluminum alloys (UFG AA) show great potential in the design of fatigue-resistant lightweight alloys, and the methodology to assess low-cycle fatigue (LCF) life remains to be studied. In this work, a micromechanics-based LCF life prediction model is presented by conducting crystal plasticity finite element simulation (CPFEM). The fatigue indicator parameter (FIP) of maximum accumulated equivalent plastic strain energy, modulated by triaxiality, is developed to assess the material damage in the microstructure. Particularly, a new multiaxial strain parameter is proposed by considering the combined influence of the mean strain and non-proportional cyclic additional hardening effect, and then directly embedding into the cyclic J-integral. Finally, the reformulated Manson-Coffin relationship is theoretically constructed by correlating the crack tip opening displacement to the crack propagation equation. The results show the scatter fatigue life of UFG AA6061 is not only related to the inhomogeneous evolution of plastic deformation but also to the local stress state. Since the proposed approach considers both the deformation mechanisms at the micro-scale and the corresponding macroscopic responses, it can predict the LCF life of UFG AA with reasonable accuracy.

Monotonic Tensile and Cyclic Deformation Behaviors of Carbide‐Free Bainitic Steel Subjected to Austempering and Tempering After Air Cooling

The monotonic tensile and tension–compression cyclic deformation behaviors of carbide‐free bainitic steel with two microstructures obtained by isothermal treatment (ISO) and air cooling followed by tempering (ACT) are investigated. Tensile results demonstrate that the ISO sample exhibits a lower yield strength but longer elongation due to more and bigger blocky retained austenite than that of the ACT sample, which can lead to a higher plastic deformation capacity for the former sample. Fatigue results indicate that the ACT sample shows a higher cyclic hardening capacity but lower cyclic softening capacity at lower strain amplitudes compared to the ISO sample, whereas an opposite phenomenon can be found at higher strain amplitudes. At given total strain amplitudes, the fatigue life of the ISO sample is shorter, which is mainly attributed to its lower yield strength and more brittle martensite. In comparison with the ACT sample, the ISO sample exhibits similar or slightly longer fatigue life at lower plastic strain amplitudes but shows shorter fatigue life at higher plastic strain amplitudes. Accordingly, a bilinear Coffin––Manson relationship is revealed for the ISO sample, which is closely associated with significantly more transformation at higher strain amplitudes compared to the lower strain amplitudes.

FEM simulation of thermo-mechanical stress and thermal fatigue life assessment of high-speed steel work rolls during hot strip rolling process

Work rolls used for hot strip rolling undergo the cyclic sequence of heating-cooling over the roll surface due to contact with the hot strip and the following cooling systems during every rolling revolution. Severe temperature gradient and thermal stress caused by cyclic heating-cooling loading are dominant factors for thermal fatigue failure of work rolls. Therefore, investigations on temperature and thermal stress-strain are essential for understanding the thermal fatigue of work roll. In this study, a thermo-mechanical analysis with elastic-plastic material parameters via a simplified finite element model is carried out to compute the stress-strain range experienced by the work roll during rolling and idling. Then, a model with the initial crack in the roll surface considering different depths and a model with the hot strip is conducted to better understand the thermal behaviors of the work roll during hot rolling respectively. Furthermore, the thermal fatigue life of work roll is assessed based on the modified Coffin-Manson relation, considering the effect of multi-axial stress state and temperature-dependent material properties caused by temperature fluctuations in work roll during hot rolling.

Low cycle fatigue behavior of Inconel 706 at 650 °C

Low cycle fatigue (LCF) behavior of 2- and 3-step-aged Inconel 706 (IN706) specimens that were prepared from the center and the periphery of forged disc was examined at 650 °C and an R ratio of −1. The resistance to LCF of IN706 alloy was greater in approximately half order at 650 °C than that of IN718 alloy for the same aging condition. Elevated temperature Coffin–Manson relationship between 2- and 3-step-aged IN706 specimens was similar with each other, despite a considerable difference in microstructure. The fractographic analysis suggested that cluster of carbides provided the sites for crack initiation for both 2- and 3-step-aged specimens. The mode of fatigue crack growth for each specimen was intergranular and transgranular, but with different magnitude for each mode. Depending on the location of specimen preparation form the forged block of IN706 alloy, no notable difference in LCF resistance was found. The role of grain boundaries, clusters of carbides and bands of acicular η platelets on the initiation and propagation mechanism of IN706 alloy was discussed based on detailed fractographic and micrographic analyses.

Dislocation Density Evolution in Low-Cycle Fatigue of Steels Using Dislocation-Based Crystal Plasticity

Dislocation accumulation caused by a crystallographic slip or plastic flow is one of the most critical factors for the growth of fatigue cracks. The dislocation density-based crystal plasticity method accounting for mobile and immobile dislocation densities has been widely used to evaluate crack behavior in polycrystals. However, the evolution of mobile and immobile dislocation densities in fatigue has not been carefully investigated, especially during the crack nucleation period. In the present study, a dislocation-based crystal plasticity model is employed and verified with experimental results. A representative domain with 39 grains is used to evaluate the dislocation density evolution in fatigue crack nucleation. The results indicate that mobile and immobile dislocation densities evolve at a decreasing rate in low plasticity and a constant rate in large plasticity for loading cases with constant strain amplitudes, whereas an increasing rate of dislocation density evolution is observed for loading cases with variable strain amplitudes. By analogy with cumulative plastic strain, a fatigue crack nucleation criterion is proposed, which is correlated well with the Coffin-Manson relationship. Based on a grain level analysis, a loading case with a low strain rate results in transgranular or mixed-mode (intergranular and transgranular) fatigue damage. In comparison, immobile dislocation density at a high strain rate mainly builds up at the grain boundary, indicating intergranular fatigue damage.

Phase-field framework with constraints and its applications to ductile fracture in polycrystals and fatigue

Modeling of ductile fracture in polycrystalline structures is challenging, since it requires integrated modeling of cracks, crystal plasticity, and grains. Here we extend the typical phase-field framework to the situations with constraints on the order parameters, and formulate two types of phase-field models on ductile fracture. The Type-I model incorporates three sets of order parameters, which describe the distributions of cracks, plastic strain, and grains, respectively. Crystal plasticity is employed within grain interiors accommodated by J2 plasticity at grain boundaries. The applications of the Type-I model to single crystals and bicrystals demonstrate the influences of grain orientations and grain boundaries on crack growth. In the Type-II model, J2 plasticity is assumed for the whole system and grain structures are neglected. Taking advantage of the efficiency of the fast Fourier transform, our Type-II model is employed to study low cycle fatigue. Crack closure and striation-like patterning of plastic strain are observed in the simulations. Crack growth rate is analyzed as a function of the J-integral, and the simulated fatigue life as a function of plastic strain agrees with the Coffin–Manson relation without a priori assumption.

Distinguishing process - impact of down milling and up milling in machining aluminium thin wall

The study aims to understand the deformation mechanics that occurs during down and up milling of aluminium thin wall fabrication. With cutting forces as inputs, material properties were defined by the Coffin-Manson relation and the Smith-Watson-Topper model. Hysteresis was found in the process of machining aluminium thin walls. Furthermore, the pattern of cutter loads differentiated the up and down milling through hysteresis. The finite element method was followed using ANSYS v14.5 software in the fatigue workbench to analyse the aspect. Down milling introduced both deflection and deformation. Conversely, up milling did not exhibit deflection. However, the Bauschinger effect and distinct fracture surfaces were diagnosed during up milling. By exploring the nature of hysteresis and fracture surfaces, the selection of down and up milling was made.

Design, analysis and experimental qualification of gripper bellows for FBTR control rod drive mechanism

The design of welded-disc bellows is not addressed in any design codes or standards. This paper discusses the design, analysis and experimental validation of the gripper bellows used in the control rod drive mechanisms of fast breeder test reactor. The material of construction of the bellows is 0.125 mm thick AM350-SCT1000. The design fatigue curve of the material at 803 K is not available in open literature. The fatigue curve of the material (Coffin-Manson's relation) was generated from the tensile testing data using four-point correlation method and universal slopes method. Elasto-plastic finite element analysis of the bellows was carried out and fatigue life of the bellows was estimated numerically. A factor of safety of 20 on number of cycles was used as suggested in codes such as ASME section-III and RCC-MR. Experimental qualification of the bellows as per ASME section-III, appendix-II was carried by testing of the bellows in sodium at 803 K.

Fatigue Analysis of NiTi Rotary Endodontic Files through Finite Element Simulation: Effect of Root Canal Geometry on Fatigue Life.

This article describes a numerical procedure for estimating the fatigue life of NiTi endodontic rotary files. An enhanced finite element model reproducing the interaction of the endodontic file rotating inside the root canal was developed, which includes important phenomena that allowed increasing the degree of realism of the simulation. A method based on the critical plane approach was proposed for extracting significant strain results from finite element analysis, which were used in combination with the Coffin–Manson relation to predict the fatigue life of the NiTi rotary files. The proposed procedure is illustrated with several numerical examples in which different combinations of endodontic rotary files and root canal geometries were investigated. By using these analyses, the effect of the radius of curvature and the angle of curvature of the root canal on the fatigue life of the rotary files was analysed. The results confirm the significant influence of the root canal geometry on the fatigue life of the NiTi rotary files and reveal the higher importance of the radius of curvature with respect to the angle of curvature of the root canal.

A holistic approach to Thermo-Mechanical Fatigue phase angle effects for an aerospace nickel superalloy

Thermo-Mechanical Fatigue (TMF) is one of the most complex mechanical phenomena that couples creep, fatigue and oxidation. So far, developing simple empirical relationships like those that exist in isothermal equivalents have proven elusive. This work presents a study on the TMF behaviour of the aerospace nickel based superalloy RR1000 using TMF fatigue crack growth rates, strain controlled TMF results, studies of the fracture morphologies and empirical lifing models. This paper takes a holistic approach to TMF lifing, specifically focusing on the impact of phase angle. As a result, this work develops an elastic modulus normalisation technique that when a Coffin-Manson type relationship is applied, predicts life of material under interim TMF phase angles.

Retained austenite-aided cyclic plasticity of the quenched 9Ni steel

This study focuses on the low cycle fatigue mechanism of the quenched 9Ni martensitic steel containing retained austenite films at martensite laths. HRTEM and EBSD suggested that extrusions developed along Low Angle Boundaries or along High Angle Boundaries at low and high strain respectively. Short cracks grew along LAB at low strain while they used any kind of boundary as well as crossed the martensite laths at high strain. Retained austenite allowed a flowing of matter along interfaces by acting as a lubricant. Consequently, the Coffin-Manson relation exhibited a bilinearity with a change in curve slope at Δεt = 1%.

Cumulative deformation capacity of structural steel subjected to extremely large amplitude strain histories

This study investigated deformation behavior of structural steel subjected to large strain. When structures experience powerful earthquakes, strain amplitudes at the fracture locations can be quite large, and the material fractures after few loading cycles. The Manson-Coffin relationship is commonly used to predict failure of metals subjected to cyclic loadings. However, the traditional Manson–Coffin relationship does not necessarily hold for some materials under extremely large strain amplitude. There are few relevant experiments, largely because it is difficult to reproduce structural steel behavior under large amplitude cyclic stains in the laboratory due to buckling. In this study, 71 steel plate specimens of structural steel were loaded until fracture under diverse cyclic axial strain loadings and monotonic tension. The relationship between cumulative strain and its skeleton portion was obtained based on the analysis of the hysteresis loops. Due to the limitation of test setup, the largest compression strain amplitude is 6%, which is still not sufficient to study the material behavior of structural steel under severe earthquakes. Therefore, numerical simulations of single steel elements subjected to cyclic strain were conducted to complement the material behavior under extremely large constant strain amplitudes. The cumulative deformation capacity of structural steel subjected to extremely large strain amplitudes was evaluated through a strain-life curve with the experimental and analytical results. In the final part of this study, experimental results from former research were introduced to validate the proposed strain-life curve.

Prediction of fatigue damage in ribbed steel bars under cyclic loading with a magneto-mechanical coupling model

As a ferromagnetic material, the magnetization of ribbed steel bars will change with the development of fatigue damage under cyclic loading, which can be used to evaluate the fatigue damage state of steel bars. However, the quantitative relationship between fatigue damage and the variation in magnetization is still unclear, and the existing magneto-mechanical model cannot be applied to ribbed steel bars directly. To accurately predict the magnetization and the fatigue damage state during fatigue, it is also necessary to consider the influence of stress concentration caused by ribs on stress and fatigue life. This paper proposes a magneto-mechanical model suitable for ribbed steel bars, which use the Neuber law and Coffin-Manson relationship to determine the stress range and fatigue life under stress concentration. Additionally, the magnetic induction intensity of the HRB400 ribbed steel bar in the tensile fatigue test was measured to verify the proposed model, and the mechanism of the magnetization change trend during fatigue was analyzed in detail. Through the fatigue damage formula based on the magnetic indicator, the simulation and experimental comparison results show that the proposed model can effectively describe the fatigue damage state of ribbed steel bars in the fatigue.