Coffin-Manson Relationship Research Articles

Bifurcation theory of plasticity, damage and failure

I developed a comprehensive theory of plasticity, damage and failure, which is independent of the micromechanical mechanism of plasticity. It includes all major components of the mechanical behavior of ductile materials, e.g. strain/work-hardening and Bauschinger effect, and covers all regimes of viscoplastic tensile/compressive loading/unloading. The theory is based on the concepts of free energy and damage parameter and has the attributes of both rate-dependent and rate-independent plasticity, kinematic and isotropic hardening. The ultimate failure of a specimen is defined as a point of critical value of the damage parameter. The theory provides justification for Drucker’s ad hoc condition of instability. The theory describes diverse phenomena of Lüders stress, creep, internal friction, and fatigue on the same self-consistent basis. In quasi-static low-cycle fatigue, I derive a Paris-type equation between the rate of degradation and cyclic plastic work and reveal a Coffin-Manson power-law relationship between the number of cycles to failure and plastic-strain amplitude. In dynamic fatigue, I find two regimes—low-cycle and high-cycle—whose loading amplitudes are separated by the yield point. The two regimes have significantly different dependencies on the frequency and viscosity. In this publication, I present the theory and computer simulations of a homogeneous viscoplastic body subjected to various conditions of isothermal strain-controlled uniaxial loading. In the follow-up publications, I will expand the theory on the cases of inhomogeneous three-dimensional bodies subjected to multiaxial loading at variable temperatures and compare the results to the experiments. Complete version of the theory can be used for the full-cycle cradle-to-grave design of new materials in service.

Improved prediction of low-cycle fatigue life for high-pressure die-cast aluminium alloy AlSi9Cu3 with significant porosity

The fatigue life of a high-pressure die-cast alloy, AlSi9Cu3, with significant porosity is investigated. Standard specimens were cyclically loaded (R = –1) until fatigue rupture occurred. The specimens were μ-CT scanned to obtain a 3D representation of the pores. Models were used to computationally predict the fatigue life using two different methods. First, the fatigue life was predicted using a notch-strain approach combined with a Coffin-Manson durability relationship for homogeneous material. Second, the fatigue life was predicted using an homogenised un-notched model that was combined with an adapted Coffin-Manson relationship which considered a fatigue life reduction due to different pore effects.

Coupled simulations for lifetime prediction of board level packages encapsulated by thermoset injection moulding based on the Coffin-Manson relation

A fibre orientation dependent material model of the thermoset is implemented to predict the lifetime of electronic components as a part of 2nd level encapsulated packages. Experimental data are used in combination with coupled simulations (process simulation – fibre orientation dependant material model – thermo-mechanical simulation) for defining this lifetime prediction model. An already existing lifetime prediction model based on the Coffin-Manson relation is used initially to evaluate the prediction accuracy. The prediction model is then adjusted and fitted for the current application.

A fatigue damage-cumulative model in peridynamics

While the present structural integrity evaluation method is based on the philosophy of assumed similitude, Fatigue and Damage Tolerance (F&DT) evaluations for next generation of air-vehicles require high-fidelity physical models within cyberspace. To serve the needs of F&DT evaluation in digital twin paradigm, a fatigue damage-cumulative model within peridynamic framework is proposed in this paper. Based on the concept of fatigue element block and damage accumulation law in form of Coffin-Manson relationship, the proposed model applies to both fatigue crack initiation and fatigue crack growth; fatigue crack growth rates under constant-amplitude and simple variable-amplitude block loading cases can be well predicted for three common structural materials without inputs of Paris law parameters. Additionally, the proposed model can also be easily extended to a probabilistic version; for verification, multiple-site-damage problems are simulated and the statistic nature of fatigue process in experiments can be well captured. In the end, main features of the proposed model are summarized, and distinctions from the other models are discussed. There may be a potential for the peridynamic damage-cumulative model proposed in this work to numerically predict fatigue problems in digital twin paradigm for future generations of aerospace vehicles.

Low-Cycle Fatigue and Fracture Behavior of Aluminized Stainless Steel AISI 321 for Solar Thermal Power Generation Systems

The microstructure, low-cycle fatigue property, and fracture behavior of as-received and aluminized steel were investigated at room temperature, respectively. The results reveal that the aluminized layer is mainly composed of three layers: (I) the external Al2O3 layer, (II) the transition Fe-Al mesophase layer, and (III) the diffusion layer with AlFe and AlCrFe phase. The microhardness of as-received steel lower than that of aluminized steel until the distance from aluminized layer is greater than 150 μm. Compared to the original steel, the aluminized steel exhibits lower stress amplitude and fatigue life, which is correlated to the surface integrity. According to the Coffin-Manson relationship, the fatigue-ductility coefficients for as-received and aluminized steel is 4.347 and 3.528, respectively. Fractographic analysis reveals that the fatigue cracks tend to nucleate at the coating and propagate through the grain boundaries apace.

Investigation on fatigue crack resistance of Q370qE bridge steel at a low ambient temperature

The Q370qE steel has a wide application in the medium and long span railway steel bridges in China, due to its excellent material characteristics including high strength, high toughness and good weldability at room temperature. Nevertheless, the limited research work on the fatigue properties of the Q370qE steel challenges the safety of steel bridges in cold and severe cold regions under the cyclic actions. This study first conducts a series of strain-controlled fatigue tests of coupon specimens at room temperature and −60 °C to characterize the cyclic stress-strain curve, hysteresis loops, Masing behavior and fatigue crack initiation resistance by Coffin-Manson relationship. Thereafter, the fatigue crack propagation tests of the compact tension specimens under different stress ratios and different temperatures reveal the effect due to stress ratios and temperatures on the fatigue crack propagation resistance of the Q370qE steel through the Paris formula. Results demonstrate that the low temperatures enhance the resistance to the fatigue crack initiation and propagation of the Q370qE steel. Finally, to better quantify the performance of the Q370qE steel, this paper collects different bridge steels and compares the fatigue crack initiation resistance and fatigue crack propagation between the Q370qE steel and other bridge steels. The results quantify the excellent higher fatigue resistance of Q370qE steel in comparison with other bridge steels.

Maximum Entropy Models for Fatigue Damage in Metals with Application to Low-Cycle Fatigue of Aluminum 2024-T351

In the present work, we propose using the cumulative distribution functions derived from maximum entropy formalisms, utilizing thermodynamic entropy as a measure of damage to fit the low-cycle fatigue data of metals. The thermodynamic entropy is measured from hysteresis loops of cyclic tension–compression fatigue tests on aluminum 2024-T351. The plastic dissipation per cyclic reversal is estimated from Ramberg–Osgood constitutive model fits to the hysteresis loops and correlated to experimentally measured average damage per reversal. The developed damage models are shown to more accurately and consistently describe fatigue life than several alternative damage models, including the Weibull distribution function and the Coffin–Manson relation. The formalism is founded on treating the failure process as a consequence of the increase in the entropy of the material due to plastic deformation. This argument leads to using inelastic dissipation as the independent variable for predicting low-cycle fatigue damage, rather than the more commonly used plastic strain. The entropy of the microstructural state of the material is modeled by statistical cumulative distribution functions, following examples in recent literature. We demonstrate the utility of a broader class of maximum entropy statistical distributions, including the truncated exponential and the truncated normal distribution. Not only are these functions demonstrated to have the necessary qualitative features to model damage, but they are also shown to capture the random nature of damage processes with greater fidelity.

Solder Joint Interconnections in Automotive Electronics: Design-for-Reliability and Accelerated Testing

Abstract Three practically important reliability-related questions for solder joint interconnections (SJIs) in automotive electronics, and particularly in its actuator and sensor electron devices, are addressed in this analysis:Could inelastic strains in the solder material be avoided by a rational physical design of the IC package, and, if not, could the sizes of the peripheral inelastic strain areas be predicted and minimized? It is clear that the low cycle fatigue lifetime is inversely proportional to the sizes of the inelastic zones and that the material's fatigue lifetime could be improved dramatically, if the induced strains remain within the elastic range. The Palmgren-Miner rule of linear accumulation of damages can be used, instead of Coffin-Manson relationships, in such a situation.Realizing that, because of the inevitable uncertainties, the difference between highly reliable and an insufficiently robust electronic products is “merely” in the levels of their never-zero probabilities of failure, could these probabilities be assessed, and could this be done at the design stage? A possibility of doing that is particularly critical for SJIs, the most vulnerable structural elements in the today's IC package designs. Reliability of an electronic material or a product cannot be assured, if it is not quantified, and, because of the inevitable and critical uncertainties, this should be done on the probabilistic basis.Should SJI accelerated testing based on costly, time- and labor-consuming and, because of temperature dependency of material properties, possibly even misleading temperature cycling, be replaced by a more physically meaningful, less expensive and more trustworthy accelerated test vehicle, and could low-temperature/random-vibrations bias be employed in this capacity? The rationale behind such a question has to do with the facts that the highest thermal stresses take place at the lowest temperature conditions, and that fatigue cracks, whether elastic or inelastic, propagate most rapidly, when the material experiences random vibrations. This technique has been already reduced to practice in an industrial lab two years ago. The objective of the analysis is to shed light, by using analytical (“mathematical”) modeling, rather than widely spread computer simulation, on the mechanical behavior and the underlying physics of failure in the SJI. Future work should focus primarily on experimentations to confirm theoretical findings and recommendations.

Strain controlled isothermal low cycle fatigue life, deformation and fracture characteristics of Superni 263 superalloy

The total axial strain controlled low-cycle fatigue (LCF) behaviour of a wrought nickel-base superalloy Superni 263 has been evaluated at 298 K, 673 K, and 923 K employing the strain amplitudes in the range ± 0.25% to ± 0.80%. All the tests were performed using a triangular wave form at a constant strain rate of 10−3 s−1. The Superni 263 alloy was subjected to a solutionizing treatment at 1373 K/1.5 h followed by water quenching. An ageing treatment of 1073 K/8 h was given to the solutionized samples. The microstructure of the alloy is composed of γʹ in the intragranular regions and discrete M23C6 precipitates on the grain boundaries. Few undissolved (Ti, Mo)C and TiN precipitates were also noticed in the matrix. The strain amplitude and temperature played a significant role in the evolution of macroscopic cyclic stress response and the development of deformation substructure. The alloy displayed serrated flow in the plastic portions of stress-strain hysteresis loops in the tests conducted at 673 K and 923 K, predominantly at strain amplitudes higher than ±0.40%. Several manifestations depicting the occurrence of dynamic strain ageing (DSA) were derived by analysing both the macroscopic and micro-mechanistic information generated. The comparative evaluation of monotonic and cyclic stress-strain curves was conducted and the factors responsible for rapid cyclic hardening during DSA were identified. The fatigue life decreased drastically with increasing temperature, particularly at low strain amplitudes. The strain-life data could be represented well by using Basquin and Coffin-Manson relationships. The slope in Coffin-Manson relationship revealed more negative values under the influence of DSA. The crack initiation and propagation modes at all the test conditions remained transgranular without the indications of interference from creep and oxidation effects. The deformation substructure at elevated temperatures was characterized by the occurrence of co-planar slip, stacking faults, micro twinning and high dislocation density in between the slip bands.

Comparisons of low cycle fatigue behavior of CP-Ti under stress and strain-controlled modes in transverse direction

Low cycle fatigue (LCF) behavior of CP-Ti along transverse direction under symmetrical strain and stress-controlled modes was compared systematically. For the strain-controlled tests, tension-compression asymmetry (TCA) has little effect on LCF behavior due to the negligible compressive mean stress. For the stress-controlled tests, TCA is detrimental to LCF resistance. The microstructure evolution during cycling deformation was characterized by EBSD and TEM to identify different deformation mechanisms. It was found that strain cycling deformation was dominated by dislocation slip and exhibited the transition from planar slip to wavy slip with the increase of strain amplitude. For the stress-controlled tests, tensile twinning together with dislocation slip accommodated the increased ratcheting deformation. The strain-life curve under stress-controlled tests is lower than that at strain-controlled tests due to the heterogeneous plastic deformation caused by ratcheting deformation. In order to obtain a unified fatigue life prediction model for different control modes, a novel effective strain range related model was proposed by introducing the TCA factor into the original Manson–Coffin relation. Furthermore, the application of this effective strain range related model was extended to the condition of asymmetrical stress cycling by correcting fatigue ductility coefficient and exponent.

The effect of ligament size on the thermal fatigue life of 9Cr 1Mo steel boiler header under cold, warm and hot starts

Abstract The finite element (FE) simulations for the evaluation of thermal fatigue life of 9Cr 1Mo steel boiler header is presented. Boiler headers experience load fluctuation during operation which leads to a significant magnitude of stress being experienced at the ligament region between two stubs in the header. The effect of load fluctuation during cold, warm and hot start on the peak stress has been computed for different ligament sizes. The stress magnitude is found to increase as the ligament size is decreased. When the thermal stress magnitude exceeds the yield strength of the material, it results in plastic deformation. From the cyclic variation of the stress and strain due to load fluctuations, the thermal fatigue life computed based on the Coffin-Manson relation. A reduction in the circumferential radial angle between stubs in the header is found to result in a reduction of thermal fatigue life.

Effects of work hardening models on low-cycle fatigue evaluations of coiled tubing with CT-100 steel

In the present study, low-cycle fatigue life of a coiled tubing (CT) with a CT-100 steel was evaluated by using various work hardening models. Tensile and low-cycle fatigue tests were performed, and experimental results were used to calibrate material model constants. A nonlinear finite element model was constructed in the ABAQUS program by using a CT fatigue test machine. During the test cycles, bending and straightening conditions were repeated and histories of strains were collected. The multiaxial low-cycle fatigue life was calculated by using Manson–Coffin relation and Tresca criterion. The kinematic and combined hardening models can be used to evaluate the fatigue life of CT, and their results are conservative compared with the fatigue test results. Results of the present study can be used as the basic data in establishing CT fatigue analysis.

Grain size based low cycle fatigue life prediction model for nickel-based superalloy

Abstract Nickel-based superalloys are easy to produce low cycle fatigue (LCF) damage when they are subjected to high temperature and mechanical stresses. Fatigue life prediction of nickel-based superalloys is of great importance for their reliable practical application. To investigate the effects of total strain and grain size on LCF behavior, the high temperature LCF tests were carried out for a nickel-based superalloy. The results show that the fatigue lives decreased with the increase of strain amplitude and grain size. A new LCF life prediction model was established considering the effect of grain size on fatigue life. Error analyses indicate that the prediction accuracy of the new LCF life model is higher than those of Manson-Coffin relationship and Ostergren energy method.

Fatigue Cycling of Electrical Interconnects Dispensed on Flexible Substrate

Abstract In the presented work, electrical traces were directly printed on 2 mil thick polyimide flexible substrate by a dispenser system using two different silver pastes, SW 1400 paste from Asahi Co. and 125-13 HV paste from Creative Materials Co. The dispenser printing parameters were optimized to achieve the finest possible line width and the printing quality of both materials was investigated. The electrical behavior of the dispensed traces was investigated by monitoring the change in the electrical resistance of the test samples during fatigue cycling at different strains, strain percentage of 1.50%, 2.0%, and 2.5% for different number of cycles up to 1000 cycles. The life time of the dispensed traces versus the applied strain was modeled using Coffin-Manson relation setting 20% change in the initial resistance as the failure criteria. Based on the change in the trace resistance during testing, we concluded that the dispensed SW 1400 silver paste traces were less robust than the dispensed 125-13 HV traces. The finer microstructure, smaller particle size, and shorter inter particles distances of the 125-13 HV silver paste enhanced its durability when subject to fatigue cycling. Moreover, 125-13 HV paste presented better and more uniform printed traces.

Low-cycle fatigue behavior and property of TA15 titanium alloy with tri-modal microstructure

Low-cycle fatigue (LCF) behavior and property characteristics of titanium alloy with a tri-modal microstructure, consisted of equiaxed α (αp), lamellar α (αl) and β transformed matrix (βt), were explored in this work. The results show that, at different strain amplitude (εta) levels, the cyclic hardening/softening is determined by the competition (εta < 0.9%) or superposition (εta ≥ 0.9%) effect of the variations of back stress and friction stress. As well, the fractography shows remarkably different features at different εta levels. When εta < 0.9%, there exists only one fatigue crack initiation site activated by the dislocation pile-ups at αp/βt and αl/βt interfaces. Besides, narrow fatigue striation space in fatigue crack propagation region implies a relatively slower crack propagation. When εta ≥ 0.9%, the additionally high-stress-induced crossed slip bands and coarse slip bands in αp cause the multiple fatigue crack initiations. Moreover, wider fatigue striation space in propagation region indicates a faster crack propagation. The above divisional LCF behavior and fracture features determine a two-part linear Coffin-Manson relationship. On the other hand, increasing αp content could delay the fatigue crack nucleation and propagation due to its positive effect for improving deformation compatibility. This will effectively increase the LCF life. However, increasing αl content would produce αl colonies, which promote the dislocation slip and reduce the slip reversibility. So, the crack nucleation and propagation will be facilitated and then the LCF life is decreased.

Shear fatigue behavior of AW2099-T83 aluminum-lithium alloy

Monotonic shear and strain-controlled shear fatigue behavior of AW2099-T83/SHP Aluminum-Lithium alloy were investigated. Torsion fatigue testing was performed at strain amplitudes ranging from 0.5% to 1.5%. The material strain hardened under monotonic shear loading but cyclically softened after few fatigue cycles for all the ranges of applied strain amplitudes. Under torsion fatigue, macroscopic plastic deformation was observed only for strain amplitudes higher than 0.7%. Cyclic plastic strain was found to increase with the number of cycles and the mean stress remained very small during most of the specimen life. Coffin-Manson relation was used to determine the shear fatigue constants of the material. The developed properties were used to arrive at a good correlation between estimated and experimental fatigue life under shear strain loading. The shear fatigue properties were compared to values reported for traditional Al alloys 2xxx, 6xxx and 7xxx series in axial fatigue after the conversion of the shear fatigue parameters to axial equivalent. The surface crack paths were observed to be mostly in the longitudinal direction with a 90° bifurcation at low strain amplitudes. Resulting crack morphologies were analyzed by SEM.

Effect of Overaging on the Cyclic Deformation Behavior of an AA6061 Aluminum Alloy

The present work encompasses the effect of overaging on the strain-controlled low-cycle fatigue (LCF) behavior of an extruded AA6061 aluminum alloy at varying strain amplitudes. During the T7 aging treatment, the size of precipitates increased from 60 nm under T6 conditions to 220 nm after aging for 48 h at 200 °C, leading to a decrease in the monotonic tensile strength. During the LCF tests, nearly symmetrical hysteresis loops can be observed in the mid-life cycle under all test conditions, whereas the first-cycle hysteresis loops were moderately inflected under long-aging conditions. With increasing aging time, the cyclic peak stresses decreased and the plastic strain increased. Nearly ideal Masing behavior was exhibited under T6 conditions, while it was lost under T7 overaging conditions. The cyclic stress responses were similar under all tested conditions, involving stabilization at low strain amplitudes and softening at high strain amplitudes, with initial hardening for the first few cycles. Compared to the T6 condition, the fatigue life increased with increasing T7 aging time. Various LCF parameters were estimated based on the Coffin-Manson and Basquin relationships and on the LCF experimental results. The relationship between the fatigue life, strength, and microstructure of the investigated AA6061 aluminum alloy under various aging conditions was discussed.

A novel evaluation strategy for fatigue reliability of flexible nanoscale films

In order to evaluate fatigue reliability of nanoscale metal films on flexible substrates, here we proposed an effective evaluation way to obtain critical fatigue cracking strain based on the direct observation of fatigue damage sites through conventional dynamic bending testing technique. By this method, fatigue properties and damage behaviors of 930 nm-thick Au films and 600 nm-thick Mo-W multilayers with individual layer thickness 100 nm on flexible polyimide substrates were investigated. Coffin-Manson relationship between the fatigue life and the applied strain range was obtained for the Au films and Mo-W multilayers. The characterization of fatigue damage behaviors verifies the feasibility of this method, which seems easier and more effective comparing with the other testing methods.

Low cycle fatigue property and fracture behavior of low yield point steels

For seismic control and isolation techniques, low yield point steels are among the most reliable and ideal energy-dissipating materials. Structures under earthquake conditions are usually subjected to cyclic loads with large strain amplitudes, where excellent low cycle fatigue and fracture performance under repeated loading is an essential requirement. In the study presented in this paper, comprehensive and systematic investigation was conducted on the low cycle fatigue properties and fracture behaviors of low yield point steels (LY100, LY160, and LY225). Axial steel coupons were tested under different constant strain amplitudes ranging from 0.5% to 6% with increments of 0.5%. Following introduction of the experimental details, observations and fatigue life are reported. Then, based on the experimental data, the cyclic hardening behavior and the cyclic stress-strain response are thoroughly analyzed. Finally, with the aim of predicting the low cycle fatigue life, the material parameters of the Coffin-Manson relationship and Kuroda model are determined and comparative analyses are performed. This paper may provide a valuable reference for engineering applications and further research into the low cycle fatigue performance of low yield point steels.

Long-term thermal conductivity of aerogel-enhanced insulating materials under different laboratory aging conditions

Aerogel-enhanced materials are known to have significantly lower thermal conductivity than traditional insulating materials. However, given the lack of long-term experiences with aerogel-enhanced products, the consistency of their superior thermal performance under the effect of the various climatic aging processes is still unknown. This study describes the effects of accelerated aging processes in laboratory conditions over the thermal performance of aerogel-enhanced insulating materials. Several products including aerogel-enhanced plasters, blankets, and boards, were exposed to different climatic accelerated stresses, which exceeded typical use conditions. The tests included freeze-thaw cycles, elevated temperature, high humidity levels, and the exposure to cycles of high UV levels alternated to high temperature and moisture levels. The thermal properties of the products before, during, and after the accelerated aging periods were measured. The Peck model, Arrhenius equation, and Coffin-Manson relation were hence employed to correlate the accelerated aging results with the corresponding real service conditions. The paper discusses the acceleration factors of the aging tests and their calculation methods. The long-term performance of the products is quantified through the changes of their thermal conductivity measured over wide temperature ranges. The results show that for the different investigated materials, the increase in the thermal conductivity over the pristine conditions is typically below 10% for aging exposure corresponding to 20 years in typical conditions. Finally, this study suggests that despite some aging-driven degradation, the thermal conductivity of aerogel-enhanced materials after aging remains significantly lower than that of non-aged traditional insulating materials.