Coffin-Manson Equation Research Articles

Solder joint lifetime model using AI framework operating on FEA data

The thermo-mechanical reliability of electronic systems is often limited by the crack growth within the solder joints. Addressing this issue requires careful consideration of the design of the package and solder pads. Finite Element Analysis (FEA) is widely used to predict crack growth and to model their lifetime. Traditionally, FEA post-processing methods rely on human expertise to select appropriate regions for evaluating plastic and creep strain at critical locations and correlating these values with experimental data using the Coffin-Manson equation, which predicts fatigue lifetime based on cyclic plastic strain. This study introduces a novel method for FEA post-processing of surface-mounted devices (SMD) on printed circuit boards (PCB) using artificial intelligence. The method transforms the FEA data into a 2D grid map of creep strain values and employs a Convolutional Neural Network (CNN) for automatic feature extraction. Afterwards, a fully connected layer correlates the extracted features with the experimental measured solder joint lifetime, effectively capturing nonlinear relationships.The study focuses on the development of the concept of crack formation in the solder interconnects of ceramic based high-power LED packages used in the automotive industry for headlights. The validated FEA model is based on an extensive data set of 1800 LED packages including seven different ceramic-based LED packages and five different solders. The design of the ceramic LED package covers two-pad and three-pad footprint for soldering and thin film and thick film metallized ceramic carriers. Results show a strong agreement (R2 Score is 99.867 %) between simulations and experimental data for ceramic LED packages. This automatic feature extraction from FEA data sets a new benchmark for improving solder reliability predictions, and it has proved to be better than established methods for lifetime prediction of solder joints.

Analysis of fatigue damage of hot rolling work rolls coupled with wear effect

During the hot rolling process, the work roll experiences cyclic contact stress due to the deformation of the strip steel, as well as thermal stress from periodic heating and cooling. The surface failure of the work roll results from the combined effects of wear and fatigue damage. This study proposes a comprehensive approach to analyzing coupled wear and fatigue damage using a method based on the Manson-Coffin equation, modified slope formula, and the Miner criterion. Finite element models were developed to simulate simplified heat transfer and thermal coupling, taking into account the actual rolling parameters and high-temperature material properties of the work roll. The evolution of the physical field of the work roll during the rolling process was analyzed. The analysis of these models revealed that the maximum strain on the work roll occurred at the rolling exit and was predominantly influenced by temperature. The effects of rolling speed and temperature on work roll strain varied, with fatigue damage being significantly reduced when wear was considered compared to scenarios where wear was not accounted for, under the same number of cycles.

Weather ageing effects on the long-term thermal conductivity and biological colonisation of thermal insulating mortars with EPS, cork and aerogel

The use of thermal insulation materials in the opaque walls is one of the best strategies toward the improvement of the thermal performance of the building envelope, thereby contributing to increase the energy efficiency of the built environment. In this context, an increasing number of studies are focusing on the development of mortars with enhanced thermal performance, i.e., thermal insulating mortars. However, considering the innovative character of these materials, reliable data on their long-term performance is still lacking, particularly concerning the thermal performance and suitability to refurbishment works. The aim of this paper is to evaluate the long-term thermal conductivity and biological colonisation of industrially produced and experimentally designed thermal mortars with EPS, cork and silica aerogel aggregates. The long-term performance of the mortars was assessed prior, during and after exposure to three accelerated ageing tests including elevated temperature, freeze–thaw cycles and high humidity levels. For each test, an empirical model (i.e., Arrhenius law, Peck model, and Coffin-Manson equation) was used to compute the acceleration factor, thus allowing to correlate the accelerated and natural ageing results and to estimate the degradation levels that would be obtained after 10 years of exposure to natural weather conditions. The results of the thermal conductivity show that a maximum increase of 10 % and 30 % can be obtained after ageing for the industrially produced and experimentally designed mortars, respectively. Moreover, all mortars were susceptible to mould growth, with the greatest biological colonisation levels obtained after the high moisture content ageing for the experimentally designed mortars.

Fatigue life and experimental study of high-temperature bellows based on the improved Manson-Coffin equation

Based on the high-temperature fatigue failure mechanism, this study proposes the use of the maximum shear strain range of crystal slip systems as the fatigue damage parameter and improves the Manson-Coffin equation accordingly. An Inconel-625 bellows model is constructed using the ANSYS Workbench platform for thermo-mechanical coupled analysis (temperature of 650 °C, displacement load of 7 mm, internal pressure of 0.3 MPa). Stress tests, including circumferential and axial stress, are conducted on the bellows to verify the accuracy of the finite element model. The six strain components in the model are extracted, and the improved Manson-Coffin equation is applied to calculate the fatigue life of the high-temperature bellows, resulting in a value of 12,318 cycles. Additionally, high-temperature fatigue life tests are performed on the Inconel-625 bellows under the conditions of 650 °C, 7 mm displacement load, and 0.3 MPa internal pressure, yielding a measured fatigue life of 9163 cycles. By comparing the experimental results of this study with those from relevant literature and plotting error band charts, it is demonstrated that the results obtained using the improved Manson-Coffin equation fall within a two-fold error band, validating the applicability of the improved Manson-Coffin equation for calculating the high-temperature fatigue life of bellows with different temperatures and models.

Impact of Chaos on MOSFET Thermal Stress and Lifetime

The reliability of power electronic switching components is of great concern for many researchers. For their usage in many mission profiles, it is crucial for them to perform for the duration of their intended lifetime; however, they can fail because of thermal stress. Thus, it is essential to analyze their thermal performance. Non-linear switching action, bifurcation and chaotic events may occur in DC-DC power converters. Consequently, they show different behaviors when their parameters change. However, this is an opportunity to study these bifurcation phenomena and the existence of chaos, e.g., in boost converters, on their performance as the effects of load variations (mission profiles) on the system’s behavior. These variations generate many non-linear phenomena such as periodic behavior, repeated period-doubling bifurcations and chaos in the MOSFET drain-source current. Thus, we propose, for the first time, an analysis of the influence of chaos on the junction temperature. First of all, this paper provides a step-by-step procedure to establish an electrothermal model of a C2M0080120D MOSFET with integrated power loss. Then, the junction temperature is estimated by computing the power losses and a thermal impedance model of the switch. Additionally, this model is used to investigate the bifurcation and chaotic behavior of the MOSFET junction temperature. The paper contributes by providing a mathematical model to calculate several coefficients based on experimental data and thermal oscillations. Estimation of the number of cycles to failure is given by the Coffin–Manson equation, while temperature cycles are counted using the rainflow counting algorithm. Further, the accumulated damage results are calculated using the Miner’s model. Finally, a comparison is made between the damage accumulated during different mission profiles: significant degradation of the MOSFET’s lifetime is pointed out for chaotic currents compared to periodic ones.

Prediction of low-cycle fatigue properties of additive manufactured IN718 by crystal plasticity modelling incorporating effects from crystallographic orientations and defects

ABSTRACT In this work, wire arc additive manufactured IN718 materials with different textures and defect characteristics were obtained via two deposition strategies: parallel mode (P_mode) and oscillation mode (O_mode). The influences of these microstructure variables on the low-cycle fatigue (LCF) properties were systematically investigated by experimental and crystal plasticity finite element (CPFE) frameworks. Results revealed that the weak texture of the O_mode sample may be detrimental to LCF due to strain incompatibility between adjacent grains. However, large-sized pore defects in the P_mode samples significantly increased the dispersity of LCF life. The sensitivity of fatigue crack initiation to critical defect size and location was further accurately captured based on the stored energy density criterion, and the fatigue crack nucleation life was also quantified. Finally, the LCF limit was calculated based on the Coffin–Manson equation, and the life prediction intervals of WAAMed-IN718 alloys with different deposition strategies were unified.

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

Improving low-cycle fatigue life of ZK61 magnesium alloy via basal texture weakening by the compression-extrusion process

In response to the problem that intense basal texture seriously affects the low-cycle fatigue life of magnesium alloys, the compression-extrusion process for basal texture weakening was implemented in ZK61 magnesium alloys. The low-cycle fatigue life under uniaxial symmetrical tension-compression cyclic loading was dramatically improved by basal texture weakening, up to 1.5∼3 times that in an intense-textured state. Basal texture weakening promoted basal slip to dominate the cyclic deformation, thus significantly reducing the cyclic tension-compression asymmetry caused by the {10–12} twinning-detwinning. Further, the suppression of {10–12} twinning and the decrease of compressive plastic strain slowed down dislocation accumulation inhibiting the cyclic hardening and fatigue crack initiation. The Manson-Coffin equation was feasible to predict the fatigue life of the intense-textured and weak-textured ZK61 magnesium alloys. The promotion of basal slip arising from basal texture weakening led to the decrease of fatigue ductility coefficient and the increase of fatigue ductility exponent contributing to the higher fatigue life.

Ratcheting-fatigue behavior and life prediction of Z2CN18.10 austenitic stainless steel elbow

The ratcheting fatigue behavior of Z2CN18.10 austenitic stainless steel elbow under internal pressure and cyclic loading was studied. The evolution of axial and hoop ratcheting strains at four different positions, respectively at intrados (0°), 45°, crown (90°) and extrados (180°) on the outer surface of the elbow was discussed. It is shown that the hoop ratcheting strain of the elbow is always greater than the axial ratcheting strain. Under cyclic test with force control, the order of ultimate hoop ratcheting strain is intrados (0°)>crown (90°)> 45°> extrados (180°). Under cyclic test with displacement control, the order of ultimate hoop ratcheting strain is 45°> intrados (0°)> crown (90°)> extrados (180°). Under cyclic tests with both force and displacement control, the crown (90°) of the elbow leaked first, which is the critical point to evaluate ratcheting fatigue life. Afterward, the ratcheting fatigue life is predicted based on ASME code, and it is found that the prediction results tend to be non-conservative. Then, a modified Manson-Coffin equation considering ratcheting strain is proposed to predict fatigue life of elbow well.

A damage coupled elasto-plastic constitutive model of marine high-strength steels under low cycle fatigue loadings

To investigate the low cycle fatigue (LCF) performance and damage behaviours of marine high strength steels (HSSs), experimental analysis and constitutive modelling are carried out in this study. Basic mechanical properties are obtained by the monotonic tensile tests. Cyclic loading tests with different loading protocols are conducted to examine the cyclic stress-strain response. Based on the experimental data, the evolutions of peak stress, yield surface radius, backstress and LCF damage are discussed. The Ramberg-Osgood model and Manson-Coffin equation are fitted to characterize the cyclic stress-strain relation and LCF damage behaviours, respectively. Based on the continuum damage mechanics, a damage coupled cyclic elasto-plastic constitutive model is proposed to describe the hysteresis behaviours of marine HSSs. The model parameters are calibrated, and the model accuracy for stress-strain response and fatigue damage prediction is then verified by experimental data.

Modified Coffin-Manson equation to predict the fatigue life of structural materials subjected to mechanical-thermal coupling non-coaxial loading

With regard to the structures subjected to severe mechanical-thermal coupling fatigue conditions, the consistency between service conditions and loading conditions was the prerequisite for the fatigue properties test and fatigue life prediction. A miniature piezoelectric-driven instrument integrating with a tripodal piezoelectric actuator and envelope-type heating function was developed to investigate the mechanical-thermal coupling fatigue properties and obtain the fatigue life of materials under approximate service conditions. A physical model was described to quantitatively calculate the alternating deformation under the mechanical-thermal coupling tensile-bending combined condition. Accordingly, a fatigue life prediction method based on the Coffin-Manson equation under tensile-bending combined loading was proposed to estimate the mechanical-thermal coupling fatigue life in terms of the total coupling deformation and plastic strain amplitude. The feasibility of the proposed instrument was verified through the analysis of displacement responses of high entropy alloy specimens under the thermal-mechanical coupling tensile-bending combined condition at temperatures ranging from RT to 600 °C. The comparison between fatigue lives directly measured through thermal-mechanical coupling experiments and theoretically predicted fatigue lives indicated the availability of the modified Coffin-Manson equation.

A comparative study on the mechanical behavior of S355J2 steel repair-welded joints

The mechanical behavior of repair-welded joints was particularly important for the service safety of steel structures. The microstructure and mechanical behavior of S355J2 steel base metal, welded and repair-welded joints were investigated in this paper. The low cycle fatigue tests on S355J2 steel base metal, welded, and repair-welded joints were conducted fully reversed with strain amplitudes varying from ±0.2% to ±1.1%. The results found that the microhardness of repair-welded joints decreased by about 20 HV with the growth in grain size of weld metal and heat-affected zone. Both elongations of welded and repair-welded joints were reduced by about 25.1% compared with the base metal. Considering the cyclic loading behavior, S355J2 steel base metal, welded, and repair-welded joints exhibited continuously softened, while the repair-welded joints exhibited a greater amount of softening than welded joints. Based on the Coffin-Manson equation, the decreased ratio of permissible total strain amplitude of repair-welded joints was significantly higher for medium and high cycle fatigue (> 104) compared to low cycle fatigue (< 104). The low cycle fatigue fracture surface shows that the defects in the repair-welded joints were the fatigue crack initiation position, but the S355J2 steel base metal and welded joints were initiated on the surface of the specimen.

Notch Fatigue Life Prediction Model Considering Stress Gradient Influence Depth and Weight Function

Notch characteristics significantly affect the fatigue performance of engineered components, for which the stress gradient effect is worth careful consideration. The traditional stress gradient analysis method based on the Coffin–Manson equation does not take into account the stress gradient influence range regarding the definition of the stress gradient correction factor, nor the high-stress gradient region, which has a greater influence on fatigue life. To address the aforementioned problems, a new notch fatigue life model is proposed in this paper. First, the stress–strain field at the root of the notch is analyzed to define the depth of stress gradient influence, following which the influence of the low-stress gradient region is reduced by a weighting function in the calculation of the stress gradient correction factor. Finally, to validate the method, three sets of experimental data, including TC4, GH4169, and EN8B, were used and compared with three other models. The results demonstrate that the predicted lifetimes of the new model are all within a 2-fold dispersion band, and the prediction ability is better than that of the other three models.

Reliability modeling of the fatigue life of lead-free solder joints at different testing temperatures and load levels using the Arrhenius model

Reliability of the microelectronic interconnection materials for electronic packages has a significant impact on the fatigue properties of the electronic assemblies. This is due to the correlation between solder joints reliability and the most frequent failure modes seen in electronic devices. Due to their superior mechanical and fatigue properties, SAC alloys have supplanted Pb-solder alloys as one of the most commonly used solder materials used as interconnection joints on electronic packages. The main aim of this study is to develop a prediction model of the fatigue life of the solder joints as a function of the experimental conditions. Using a customized experimental setup, an accelerated fatigue shear test is applied to examine the fatigue life of the individual SAC305 solder joints at actual setting conditions. OSP surface finish and solder mask defined are used in the studied test vehicle. The fatigue test includes three levels of stress amplitude and four levels of testing temperature. A two-parameter Weibull distribution is used for the reliability analysis for the fatigue life of the solder joints. A stress–strain curve is plotted for each cycle to construct the hysteresis loop at each cyclic load and testing temperature. The acquired hysteresis loop is used to estimate the inelastic work per cycle and plastic strain. The Morrow energy and Coffin Manson models are employed to describe the effects of the fatigue properties on the fatigue life of the solder joints. The Arrhenius model is implemented to illustrate the evolutions in the stress life, Morrow, and Coffin Manson equations at various testing temperatures. The fatigue life of SAC305 solder joints is then predicted using a general reliability model as a function of the stress amplitude and testing temperature.

Microstructure, Tensile, and Fatigue Properties of Large-Scale Austenitic Lightweight Steel.

High-Mn lightweight steel, Fe-0.9C-29Mn-8Al, was manufactured using steelmaking, ingot-making, forging, and rolling processes. After the final rolling process, a typical austenite single phase was observed on all sides of the thick plate. The microstructural changes after annealing and aging heat-treatments were observed, using optical and transmission electron microscopy. The annealed coupon exhibited a typical austenite single phase, including annealing twins in several grains; the average grain size was 153 μm. After aging heat treatment, κ-carbide was observed within the grains and on the grain boundaries. Additionally, the effect of aging heat treatment on the mechanical properties was analyzed, using a tensile test. The fine κ-carbide that precipitated within the grains in the aged coupon improved the 0.2% offset yield and the tensile stresses, as compared to the as-annealed coupon. To estimate the applicability of high-Mn lightweight steel for low-pressure (LP) steam turbine blades, a low-cycle fatigue (LCF) test was carried out at room temperature. At a total strain amplitude of 0.5 to 1.2%, the LCF life of high-Mn lightweight steel was approximately three times that of 12% Cr steel, which is used in commercial LP steam turbine blades. The LCF behavior of high-Mn lightweight steel followed the Coffin-Manson equation. The LCF life enhancement in the high-Mn lightweight steel results from the planar dislocation gliding behavior.

High‐temperature creep‐fatigue‐oxidation behaviors of P92 steel: Evaluation of life prediction models

AbstractDamages caused by the effects of cyclic loading (fatigue) and high temperature (creep and oxidation) have been considered critical and need to be appropriately evaluated. A series of strain‐controlled fatigue and creep‐fatigue tests are performed on P92 at 873 K under oxygen‐containing environment. The creep‐fatigue life prediction results are summarized using models based on strain‐range partition, Manson–Coffin equation and linear damage summation (LDS) rule. Obviously, the models based on the LDS rule show relatively good performance with an error band of ±2.5. In view of the adverse effects of oxidation on creep‐fatigue endurance, this paper further develops a physically‐based oxidation damage equation, which is incorporated into LDS rule for the improvement of life assessment. The predicted and experimental results falling into ±1.5 error band proved the accuracy of the proposed oxidation damage equation in the LDS rule. Additionally, model selection criteria are recommended to evaluate the model prediction capabilities.

Research on multiaxial fatigue life of notched specimens based on Weibull distribution and Bayes estimation

In this study, based on the nominal stress method and the influence of stress gradient on fatigue life, a fatigue life prediction method combined with the Weibull distribution is proposed. Firstly, the strain energy density is defined as the damage parameter to determine the location of the critical plane. Then, the equivalent stress function is established by extracting the equivalent stress of the specific path on the critical plane, which is used to establish the modified nominal stress method by combining with the stress gradient factor. Secondly, the Weibull distribution is combined to establish a new fatigue life prediction model of the notched specimens under different failure probabilities. The accuracy of the model is verified with three materials, then the prediction life of the proposed model is compared with that of the SWT model, the FS model and the Manson-Coffin equation. The results show that the accuracy of the proposed model is higher than the other three models. Finally, the reliability of the proposed model is evaluated by the lower confidence limit (LCL) estimation and interval estimation to explore the feasibility of this method. In addition, the P-S-N curves under different failure probabilities are established to guide actual projects.

Investigation of low-cycle fatigue characteristics of nickel-based heat-resistant single-crystal alloy

Low-cycle fatigue under a hard loading cycle of a nickel-based heat-resistant single-crystal alloy with 001 crystallographic orientation at operating temperature is studied. The dependences of the change in the stress asymmetry coefficient on the number of cycles to failure are obtained. The fatigue curve and predictive curves obtained using shortterm strength characteristics are compared. Keywords: low-cycle fatigue, high-temperature alloy, single-crystal structure, nickel alloy, Basquin—Manson—Coffin equation, prediction of fatigue resistance characteristics. lab33@viam.ru

Multiaxial fatigue life prediction model considering stress gradient and size effect

Stress gradient effect (SGE) and notch size effect (NSE) have important influences on the fatigue performance of engineering components. In this paper, a new multiaxial fatigue life prediction model is developed by considering the effects of both. Firstly, with the help of the coordinate transformation principle (CTP), the location of the dangerous critical plane is found according to the energy-critical plane (ECP) method, and the equivalent stress gradient factor (SGF) within the fatigue damage zone is calculated by analyzing the equivalent stress distribution on the critical plane. Secondly, considering the size of the notch, the effect of stress concentration at the notch is analyzed. Meanwhile, a size influence factor is introduced to characterize the NSE and construct a new fatigue strength reduction factor. Further, combining with the Manson-Coffin equation (MC equation), a new fatigue life prediction model for multiaxial notched components is proposed by considering SGE and NSE on fatigue damage. Finally, the experimental data of fatigue specimens with different notch sizes processed by En8 and GH4169 materials are used for model validation and comparison with other three classical models, and the results show that the prediction life of the new model for proportional and non-proportional loads is within two-fold dispersion band and the prediction ability is better than the other three classical models.

Estimate of Coffin-Manson Curve Shift for the Porous Alloy AlSi9Cu3 Based on Numerical Simulations of a Porous Material Carried Out by Using the Taguchi Array.

In real engineering applications, machine parts are rarely completely homogeneous; in most cases, there are at least some minor notch effects or even more extensive inhomogeneities, which cause critical local stress concentrations from which fatigue fractures develop. In the present research, a shift of the Coffin–Manson εa–N material curve in a structure with random porosity subjected to dynamic LCF loads was studied. This allows the rest of the fatigue life prediction process to remain the same as if it were a homogeneous material. Apart from the cyclic σ–ε curve, which is relatively easy to obtain experimentally, the εa–N curve is the second most important curve to describe the correlation between the fatigue life N and the strain level εa. Therefore, the correct shift of the εa–N curve of the homogeneous material to a position corresponding to the porous state of the material is crucial. We have found that the curve shift can be efficiently performed on the basis of numerical simulations of a combination of five porosity-specific geometric influences and the associated regression analysis. To model the modified synthetic εa–N curve, five geometric influences of porosity by X-ray or μ-CT analysis are quantified, and then the porosity-adjusted coefficients of the Coffin–Manson equation are calculated. The proposed approach has been successfully applied to standard specimens with different porosity topography.