Coffin-Manson Law Research Articles

Initiation and growth of fatigue cracks in sheets with U-shaped notches in the first and mixed modes of fracture

Initiation and growth of fatigue cracks in sheets with U-shaped notches in the first and mixed modes of fracture

Structural performance of H-type shear panel damper made of hot-rolled mild steel

In this study, cyclic loading experiments were performed to understand the mechanical characteristics of SPHC (hot-rolled mild steel) H-type shear panel dampers in a stud support-type installation. The specimens evaluated had panel width-to-thickness ratios of 48.9 and 52.5. Constant amplitude deformation loading was performed using shear deformation as a variable. A stable spindle-shaped hysteresis curve was exhibited with strength reduction caused by out-of-plane deformation. Maximum strength was achieved near the second cycle for all specimens and the specimens with the lower width-to-thickness ratio exhibited slightly higher strength increase ratios. Similarly, energy absorption capacity depended on load amplitude and width-to-thickness ratio of the panel part and specimens with a smaller width-to-thickness ratios corresponding to larger accumulative energy dissipation. Based on the Manson–Coffin law, the deformation capacity of the tested specimens was found to be lower throughout the fatigue curve when compared with the relative architectural guidelines.

Low Cycle Fatigue of G20Mn5 Cast Steel Relation between Microstructure and Fatigue Life.

Cast steel is commonly used to produce structural and safety parts. Foundry processes allow producing parts from scrap steel directly to the required dimensions without any forming operation. Cast components may, however, exhibit macro- and micro-shrinkage porosities. The combined effect of macro- and micro-shrinkages on the fatigue behavior of cast steel has been characterized in the literature. Macro-shrinkages may nowadays be eliminated by adequate positioning of risers. However, micro-shrinkages will always be present in cast steel components. Present work addresses the influence of micro-shrinkage porosity on a G20Mn5 cast steel. G20Mn5 (normalized) ingots have been cast under industrial conditions, but ensuring the absence of macro-porosities. Solidification leads to two very different microstructures prior to the normalization treatment: columnar dendrites beneath the surface (Skin) and equiaxed microstructures close to the center (Core). First, metallographic observations of the whole ingot revealed the same grain size in both areas. Fatigue samples were extracted, by differentiating two sampling volumes corresponding to columnar (S) and equiaxed solidification (C), respectively. The distribution of micro-porosities was determined on all samples by Micro-CT-scans. Core samples exhibit micro-porosities with volumes 1.7 larger than Skin samples. Low cycle fatigue tests (3 levels of fixed plastic strain) were run on both sample series (C, S). Results follow a Manson–Coffin law. Core specimens exhibit lower fatigue life than Skin specimens. The differences in fatigue life have been related successfully to the differences in micro-porosities sizes.

A non-unified viscoplastic constitutive model based on irreversible thermodynamics and creep-fatigue life prediction for Type 316 stainless

In this work, to describe the cycle behavior considering fatigue-creep interaction, a non-unified viscoplastic constitutive model for 316 stainless steel is derived within the irreversible thermodynamic framework. The internal variables considering kinematic and isotropic hardening properties are selected to construct the evolution equation of visco-plastic and creep terms. The proposed constitutive model was validated by the comparison with the existing literature. It was manifested that this constitutive model could successfully predict the hardening behavior and stress relaxation process under the cyclic loading. During the dwell period, the increment of the inelastic strain is decomposed into the viscoplastic and creep term. The viscoplastic deformation dominates first stage of the stress relaxation, while the stable stage is controlled by the creep term. Finally, the predicted values of mean stress are taken into the Manson-Coffin law, the low cycle fatigue life prediction are carried out based on the numerical model, which showed robust correlation with experimental results.

Proposal of an Interlaminar Fatigue Life Evaluation Method for CFRP Based on Inelastic Two-Scale Analysis

In this paper, a prediction method for interlaminar fatigue life of carbon fiber-reinforced plastic (CFRP) is proposed based on an inelastic two-scale analysis method combined with the Coffin-Manson law. For this, the flatwise tension test of a CFRP is simulated using the two-scale analysis method, and the distributions of microscopic viscoplastic strain occurring at resin parts in micro-structures (unit cells) are examined. Then, the maximum value of microscopic viscoplastic strain is applied to the Coffin-Manson law for the resin to predict interlaminar fatigue life of the CFRP.

Thermomechanical fatigue damage modeling and material parameter calibration for thin film metallizations

Numerical fatigue damage models can help to save cost and time when studying fatigue damage in the copper metallization layers of power semiconductor devices. However, their predictive capabilities strongly depend on the parameters associated with these models. This paper presents a strategy for calibrating parameters of a numerical fatigue damage model using experimental results from thermomechanical fatigue experiments. Fatigue damage is predicted by the Fatemi–Socie critical plane method in combination with a Coffin–Manson law. Experimentally, test devices are utilized which can reproduce loading conditions that approximate those occurring in real semiconductor devices. Damage is measured in form of visible surface cracks by the means of surface imagery. Experimental results from devices with pronounced lateral thermal gradients are used for calibrating the fatigue parameters of the Coffin–Manson law. Eventually, the model with the calibrated fatigue parameters is used to predict fatigue damage for a second experiment with different loading conditions. For all investigated test devices the numerical predictions are in good agreement with experimental results. The simulations show that significantly more damage occurs in regions with higher temperatures and that the surface topology has a strong influence on local fatigue damage.

Cyclic deformation and fatigue behavior of 7075-T651 Al alloy with a gradient structure

Fully reversed stress-controlled tension–compression fatigue experiments (R = −1) were conducted to study the cyclic deformation and fatigue behavior of 7075-T651 aluminum alloys with and without a surface mechanical rolling treatment (SMRT). The strain amplitude, ratcheting effect, and asymmetric behavior of base metal (BM) and SMRT specimens were analyzed. SMRT specimens showed more remarkable ratcheting effects and tension–compression asymmetry under high stresses. Fatigue tests showed that the fatigue strengths of 7075 Al alloys were increased significantly by the SMRT. Both BM and SMRT specimens presented a failure-mode transition from the intrusions and extrusions failure modes to the Al18Ti2Mg3 constituent phase. The hysteresis loop was utilized to obtain the plastic-strain amplitude. Furthermore, according to the cyclic-deformation behavior combined with the Manson–Coffin law, strain–life evaluation of BM and SMRT specimens under the stress-control is given.

On the influence of ϰ-carbides on the low-cycle fatigue behavior of high-Mn light-weight steels

High-manganese light-weight steels offer a great potential for structural purposes in the mobility sector due to their reduced density combined with outstanding mechanical properties. As many of the envisaged applications of these materials will suffer from cyclic loading during their service life, the fundamentals of their fatigue behavior must be studied extensively. In the present work, the low-cycle fatigue (LCF) properties of an austenitic Fe-29.8Mn-7.65Al-1.11C light-weight steel were investigated. Two microstructurally different conditions are directly compared: a homogenized, fully austenitic condition and an aged, austenitic, ϰ-carbide-containing condition. Results elaborated by total strain-controlled fatigue tests are discussed considering microstructural insights revealed by scanning electron microscopy and synchrotron diffraction analysis. Although fatigue properties are improved upon aging due to ϰ-carbide formation for lower strain amplitudes as compared to homogenized counterparts, the cyclic deformation behavior is characterized by cyclic softening at increased strain levels. Shearing of the ϰ-carbides and their mechanical dissolution due to the onset of plastic deformation are found to be the underlying mechanisms. Determination of LCF parameters for both conditions was realized by evaluation of the fatigue life based on the Coffin-Manson law and Basquin equation, eventually providing explanations for the Masing and non-Masing behavior of the aged and homogenized condition, respectively, deduced from analysis of half-life hysteresis loops.

Earthquake-induced damage updating for remaining-life assessment of steel frame substructure systems

This paper presents a framework combining theoretical, numerical, and experimental approaches for evaluating the remaining-life of high-rise steel buildings based on earthquake-induced fatigue damage propagation in local beam-to-column connections. A mesh-independent finite element model is developed and implemented using the concept of lumped damage mechanics to estimate the fatigue-induced life loss associated with the extent of crack propagation until complete rupture failure occurred in beam-to-column connection substructure of high-rises. In this framework, a damage state variable is introduced at each end of beam elements and can be linked to the extension of the fatigue fracture in real frame building joints. Then, the damage evolution law is developed by extending the conventional Manson–Coffin law and a new crack-driving parameter to quantify the extent of damage states and predict the remaining life of the associated components in high-rises buildings. The proposed model is validated by a damage index measured from the local wireless sensors in substructure tests of ductile steel beam-to-column connections subjected to ultra-low cycle fatigue loadings. The residual resistance can be quantified by updating the damage curve with the identified damaged conditions.

Fatigue behaviour and mechanical properties of PVD CrSiN coating using cyclic nanoindentation

ABSTRACT In this study, chromium nitride-based CrSiN coatings were deposited by PVD (physical vapour deposition) magnetron sputtering on XC100 steel substrate. Mechanical properties of CrSiN were investigated using monotonic nanoindentation test. It was found that CrSiN coatings had excellent mechanical properties, hardness of 30.52 ± 1.85 GPa and elastic modulus of 338.32 ± 13.5 GPa. Fatigue behaviour of CrSiN thin film was studied using multi-cycles nanoindentation test. Under cyclic nanoindentation, the unloading–reloading paths produced the hysteresis loops which reflect a fatigue effect. In addition, the increase in the number of indentation cycle induced the degradation of the film mechanical proprieties and the evolution of damage mechanism. The similarity between the indentation fatigue depth propagation and the conventional fatigue crack growth was exploited based on Manson–Coffin law to extract the fatigue properties of CrSiN coating. The obtained fatigue ductility coefficient was and the fatigue ductility exponent was c = −0.96.

Lifetime Prediction of a SiC Power Module by Micron/Submicron Ag Sinter Joining Based on Fatigue, Creep and Thermal Properties from Room Temperature to High Temperature

Ag sinter joining technology has gained increasing attention for its excellent thermal and mechanical properties, especially for high-temperature applications. This study focuses on the lifetime prediction of a SiC power module by Ag sinter joining based on mechanical properties including tensile, fatigue, and creep properties from room temperature to 200°C, as well as thermal properties including thermal conduction and the coefficient of thermal expansion. These mechanical properties and thermal properties of sintered Ag paste were evaluated in the study and the results show that mechanical properties of sintered Ag largely depend on the test temperature. The sintered Ag paste tends to soften at high temperature, and the fracture changed from nearly brittle to totally ductile with the testing temperature increase. From the S–N curve, the fatigue is close to the Morrow equation but not the Coffin–Manson law at room temperature. The finite element simulation of the lifetime based on Morrow’s equation for the sintered Ag layer shows that there has a crack occurrence with one fourth the side length after 10,000 cycles from − 40°C to 200°C but the crack extension area is less than one tenth of the sintered Ag layer. This study will add to the understanding of the high temperature properties and high temperature reliability as well as the lifetime of Ag sinter joining in high-temperature applications.

Low-cycle fatigue behavior of 7075-T6 aluminum alloy at different strain amplitudes

Low-cycle fatigue (LCF) life and failure mechanism of 7075-T6 high strength aluminum alloys were investigated under MTS 809. The cycling stress response and the cyclic stress—strain relationships under different strain amplitudes were investigated. Using Manson-Coffin law, the three parameter exponential function equation and the damage function model of tensile hysteresis energy (Ostergren equation), the regression analysis of LCF test data was carried out, it was found that the fatigue life prediction results of the three parameter exponential function equation were better than the other two life prediction methods in terms of statistical analysis methods of standard deviation and dispersion band. Analysis of microstructure and fatigue failure fracture revealed that fatigue crack initiated at the interface of precipitations and α-phase aluminium substrate in surface or near surface of the sample.

Simulations of isothermal and thermomechanical fatigue of a polycrystal made out of austenitic stainless steels and relation to the Coffin-Manson law

Based on an experimental result of the literature showing that the crack remains in the grain of its initiation up to about 20% of the lifetime at low cycle fatigue of austenitic stainless steels, the lifetime of a polycrystal made out of these steels undergoing uniaxial isothermal or thermomechanical fatigue from 30 to 340 °C at constant total strain amplitude is calculated. The stresses and strains in the grains and polycrystal are determined in term of mean field with the Hill-Hutchinson model. Dipolar slip markings in the grains are predicted and assumed sites of initiation and propagation of the cracks calculated in terms of critical stress and of shear plastic strain, depth and grain boundary, respectively. There is agreement of the macroscopic stress and plastic strain, but at the residual stress, making the modelling not suitable for thermomechanical fatigue. For isothermal fatigue, the lifetime is in agreement. The lifetime - plastic strain power relationships are addressed to the Coffin-Manson law assumed to derive from the kinetic equation of the crack in a dimensional approach. The calculated constants of the power relationship of five austenitic steels of the literature are in qualitative agreement with those measured of the law. The relationships between the constants of the power relationship, law and kinetic equation are determined. The results and modelling are discussed.

A novel test method based on small specimens for obtaining low-cycle-fatigue properties of materials

In this study, a novel method for low-cycle-fatigue (LCF) tests on small funnel and Ring specimens to obtain the Manson–Coffin law of materials is proposed based on the median energy equivalence principle. It includes a method for solving the cyclic stress-strain relationship of the material according to the cycling stability curve of load amplitude–displacement amplitude, and another method for acquiring the conversion relationship between the measuring displacement amplitudes and local strain amplitudes of the specimen. LCF experiments under constant displacement amplitude loading were performed on small funnel and Ring specimens, as well as standard straight-round bar specimens of the two materials, G115 and 16Mn. The results indicated that the uniaxial cyclic stress–strain relationship and Manson–Coffin law results of the G115 and 16Mn materials obtained by the new method were highly consistent with those obtained by the traditional standard method.

Prediction of brittle fracture in notched specimens under cyclic loading

Brittle fractures in steel can have devastating effects during its use, such as the collapse of buildings during earthquakes. This paper describes the effects of cyclic loading on the occurrence of brittle fracture and presents a brittle fracture prediction method. Notched specimens of steels with low and high fracture toughness were tested under monotonic and cyclic loading. A cumulative ductility estimation method was developed to predict the occurrence of brittle fracture using the Coffin–Manson law and Miner's rule. This method is based on the empirical relationship between the ductility amplitude or Weibull stress and the number of cycles at brittle fracture. Cumulative damage theory was also used to consider different cyclic amplitudes. The proposed approach can be employed to predict cumulative ductility at brittle fracture and showed a relatively high correlation coefficient between the calculated and experimental results. In addition, this approach can be used to predict brittle fracture using data from samples with different toughness and notch shapes in a unified manner, unlike many previous methods.

Method for Predicting the Fatigue Life of Geometrically Discontinuous Structures Under Combined Bending and Torsion

The fatigue damage model based on theory of damage mechanics is capable of predicting the fatigue life under multiaxial loading. Meanwhile, the application of critical plane method in the prediction of multiaxial fatigue life has made certain progress. According to the law of thermodynamics, a new damage evolution equation is developed in the present study to predict the fatigue life of geometrically discontinuous structure under tension-torsion loading based on damage mechanics and the critical plane method. The essence of this approach is that the strain parameter of the uniaxial nonlinear fatigue damage model is replaced with the equivalent strain, which consists of the relevant parameters of the critical plane. However, it is difficult to calculate the stress–strain status and the critical plane position of geometrically discontinuous structure by theoretical methods because of the existence of stress concentration and the multiaxial nonproportional characteristics. Therefore, a new numerical simulation method is proposed to determine the critical plane of geometrically discontinuous structure under multiaxial loading by means of the finite element method and MATLAB software. The fatigue life of notched specimens subjected to combined bending and torsion is predicted using the proposed method, and the result is compared with those from the experiments and the Manson–Coffin law. The comparisons show that the proposed method is superior to the Manson–Coffin law and is capable of reproducing the experimental results reasonably when the geometry of the structure is complex. It completely meets the needs of engineering practice.

The prediction models for fatigue crack propagation rates of mixed-mode I-II cracks

The Manson–Coffin law for the low-cycle fatigue of a representative volume element and the fatigue crack propagation rate of a cracked component are crucial for characterizing the fatigue resistance of a material. Using the average plastic-strain-energy density and the average linear damage accumulation in the plastic zone at the crack tip, two fatigue crack growth models for mixed-mode I-II cracks, without artificial parameters, are proposed, based on the low-cycle fatigue properties of a representative volume element under cyclic plastic strain. For 30Cr2Ni4MoV rotor steel, the proposed models are used for theoretically predicting the mixed-mode I–II fatigue crack propagation rates of compact tension shear specimens subjected to loadings at four different loading angles; and the theoretical prediction results are found to be consistent with the experimental ones.

Design and Performance Evaluation of Al2O3-SiC Composite for Direct-Bonded Copper Substrate

A computational material design approach is applied to propose a novel ceramic material for direct-bonded copper (DBC) substrate with enhanced thermal and structural performance. The material design inherently consists of many competing requirements that require careful decisions regarding key trade-offs in terms of material composition, inclusion size, shape, and distribution to achieve the target properties. The alumina-silicon (Al2O3-SiC) composite, as compared to commercial alumina, used in DBC is found to be the most suitable design among other candidates with improved thermal and structural properties. In order to study the performance characteristics and the effects of the new ceramic composite with improved properties in terms of structural behavior and fatigue life of the DBC substrate, the normal working and extreme thermal cycling conditions were simulated and analyzed using finite element method. The temperature, strain, and localized stress distribution within the substrate at a steady-state condition were analyzed, and the improved Coffin–Manson law was used to calculate the fatigue life of the substrate under extreme thermal cycling conditions. The proposed Al2O3-SiC composite is found to be more robust than the commercial alumina as DBC substrates considering the thermal–mechanical performance. The fatigue life cycle of the DBC substrate with the proposed material is predicted to be about two times longer than the commercial alumina DBC ceramic under transient thermal cycling test.

Analytical theory for fatigue crack propagation rates of mixed-mode I–II cracks and its application

The Manson–Coffin law for the low-cycle fatigue (LCF) of a representative volume element (RVE) and fatigue crack propagation (FCP) rate of cracked components can characterize material fatigue resistance. This paper proposes an LCF–FCP model for predicting the FCP rate of plane-stress mixed-mode I–II cracks. A semi-analytical model is also proposed for the Je integral of mixed-mode I–II compact tension shear (CTS) specimens based on energy equivalence method. The combination of these two models predicted the FCP rates of CTS specimens made from 30Cr2Ni4MoV rotor steel with mixed-mode I–II cracks and subjected to four different loading angles. The theoretical results were consistent with the experimental results.

A two-phase approach to estimate fatigue crack initiation and propagation lives of notched structural components

Total fatigue lives of notched structural components are considered as a summation of crack initiation and propagation phases and a two-phase approach to fatigue life prediction is presented. The local strain approach and fracture mechanics-based approach are used to predict the lives spent in the two phases. A strain-life curve corresponding to the transition crack size where the two phases are divided is formulated based on the equivalence between the Coffin-Manson law and a simple Elastic-Plastic Fracture Mechanics crack growth law in the low cycle fatigue regime. A crack growth model that includes the short crack behaviour is used to predict the crack propagation life. The transition crack size, related to the average grain size of the material, is chosen in such a way that the proposed approach can be appropriately adopted in both phases, considering the stress gradient and microstructure effects. The proposed approach is applied to predict fatigue lives of various notched specimens. The three-dimensional effect is considered in the assessment. The predictions are in good agreement with the experimental results.