Fracture Fatigue Entropy Research Articles

Numerical Simulation for Durability of a Viscoelastic Polymer Material Subjected to Variable Loadings Fatigue Based on Entropy Damage Criterion.

This study aims to explore the impact of load history on the premature failure of the viscoelastic polymer matrix in carbon-fiber-reinforced plastics (CFRPs) using a method based on the concept of fracture fatigue entropy (FFE). A user-defined subroutine (UMAT) developed by the authors in previous studies was incorporated to apply the FFE damage criterion using ABAQUS software. Several variable-amplitude load modes, including frequent load amplitude changes and intermittent interruptions, were designed based on the conventional linear damage accumulation method (Palmgren-Miner rule), and the fatigue life under these loadings was obtained via numerical simulations. The results show that both frequent amplitude changes and even brief pauses in loading can accelerate damage accumulation, leading to premature failure of the polymer matrix. In these scenarios, the fatigue life ranged from 33.6% to 91.9% of the predictions made using the Palmgren-Miner rule, which shows significant variation and highlights cases in which the predicted fatigue life falls far short of expectations. This study offers a more practical and reliable approach for predicting fatigue life under complex loading conditions. Since the accuracy of the FFE criterion has been comprehensively validated in previous studies, this research focuses on its application to predict failure under variable loading conditions.

Dislocation-based entropy as a criterion for fracture

Griffith’s 1920 fracture criteria is well known in the engineering community. Griffith produces a simple formula for the fracture stress of a material using the first law of thermodynamics by relating the decreased elastic energy of an applied load to the increased surface energy of a crack. However, evidence in fatigue research, most notably the concept of fracture fatigue entropy (FFE), suggests that the fracture mechanism is more intimately related to irreversibility and can be treated via the second law of thermodynamics. In this paper, Griffith’s model is approached from the perspective of the second law of thermodynamics, producing a new equation for fracture stress centered on entropy. Fracture tests are performed on 304 stainless steel (SS) and 110 copper specimens. Experimental crack lengths at fracture determined via digital image correlation (DIC) are compared to predicted crack lengths at fracture determined via the entropic fracture stress relation to assess accuracy. Predicted crack lengths at fracture are determined to be accurate to within 2.88% for 304 SS specimens and 7.62% for copper specimens, both of which are comparable to the corresponding accuracy of Griffith criteria predictions. Further, it is shown that the developed entropy model is capable of predicting the entropy-based debonding strength of a material, matching experimental debonding strength values evaluated via DIC to within 25%.

Investigating the relationship between fracture entropy and stress amplitude in CFRP laminates under low-cycle fatigue loading

Fracture fatigue entropy (FFE) is considered to be independent of the loading amplitude in fatigue experiments, and this conclusion has been applied to fatigue life prediction of composites and metals with satisfactory prediction accuracy. However, the existing research work mainly focuses on high-cycle fatigue, and it is not clear whether the FFE is independent of the loading amplitude in low-cycle fatigue, which requires more in-depth research. Fatigue experiments were conducted on three CFRP laminates with different ply orientations, and the FFE values corresponding to low-cycle fatigue were obtained by thermographic analysis. The results show that the FFE value is no longer independent of the loading amplitude under low-cycle fatigue conditions. On the contrary, it decreases with the increase of fatigue loading amplitude and also varies with different ply orientations. The relationship between low-cycle fracture fatigue entropy and loading amplitude of composites with different ply orientations was analyzed and modeled, and a novel low-cycle fatigue life prediction method based on FFE was developed.

Accelerated estimation of the very high cycle fatigue strength and life of polymer composites under ultrasonic cyclic three-point bending

Ultrasonic fatigue testing (UFT) offers a strong potential to accelerate the testing time of fatigue experiments of materials up to very high cycle (VHCF) and giga-cycle (GC) fatigue regimes. This can especially be useful during the materials selection processes when designing load-bearing structures. In this study, one increasing- and three constant-amplitude fatigue experiments were conducted using a UFT system on three different composites consisting of woven Carbon fibers with Poly-Ether-Ketone-Ketone (CF-PEKK), Polyphenylene Sulfide (CF-PPS), Epoxy (CF-Epoxy) as polymer matrix materials. The surface temperature data obtained from these experiments were used to evaluate the heat dissipation rate and fracture fatigue entropy (FFE) range of the three composite materials. The fatigue strength estimated using this FFE range for CF-PEKK (normal stress), CF-PPS (shear stress), and CF-Epoxy (shear stress) composites were 26.3 MPa, 4.7 MPa, and 15.1 MPa, respectively. The fatigue life comparison between the estimation model adopted in this study and the experimental results found in the literature was in reasonable agreement for all three composites. The FFE concept is adapted to the UFT method to rapidly estimate the VHCF properties of composite materials used in load-bearing structures within three weeks.

Effect of surface roughness and polishing orientation on fatigue life and fracture fatigue entropy

AbstractThe effect of surface roughness and polishing orientation on fatigue life is investigated. Fully reversed bending fatigue tests are conducted on ASTM A1008 specimens having surface roughness asperities ranging from mirror finish (Ra = 0.05 μm) to coarse (Ra = 1.5 μm). Two polishing directions (i.e., orientations) are examined. For the range of roughness values tested, the results suggest that polishing orientation has a strong influence on fatigue life. Specifically, within the range of surface roughness values tested, fatigue life was found to be relatively insensitive to surface roughness asperities when the roughness orientation was parallel to the direction of surface stress but sensitive to surface roughness asperities when the orientation crossed the direction of surface stress. Results are generalized using the concept of fracture fatigue entropy (FFE). It is shown that, unlike fatigue life, FFE is independent of polishing orientation, a noteworthy result. To explain the behavior of FFE in relation to surface roughness asperities, a fatigue thermodynamics theory is presented that hypothesizes that all specimens of the same material fail at equivalent entropy levels.

A two-scale thermodynamic entropy model for rapid high-cycle fatigue property evaluation of welded joints

This investigation attempts to propose a two-scale thermodynamic entropy model that can quantify the micro-scale fatigue behaviors from the macroscopic level. Both non-damaging anelastic and damaging inelastic microstructural motions that cause entropy generation at different stress amplitude blocks of specimens are considered. On this basis, a thermodynamically based correlation between the macro-stress amplitude and the microstructural motion is constructed following the framework of thermodynamics. Butt joints made of low carbon steel are used as the experimental materials in this work. The fatigue limit of welded joints is estimated in a short time using the developed approach in combination with the correlation coefficient optimization method. Finally, the fracture fatigue entropy (FFE) model, corresponding to the two-scale theory, is developed to achieve fast prediction of fatigue life by considering the threshold value associated with the irreversible inelastic entropy generation in high-cycle fatigue. The results show that the predicted data are in satisfactory agreement with the experimental data.

On the Characteristics of Fatigue Fracture with Rapid Frequency Change.

The effect of sudden variations in working modes and fatigue behavior of CS 1018 is studied. A general model based on the framework of the fracture fatigue entropy (FFE) concept is developed to capture such changes. Fully reversed bending tests are performed on flat dog bone specimens with a series of variable frequency tests without turning the machine off to simulate fluctuating working conditions. The results are then post-processed and analyzed to assess how fatigue life changes when a component is subjected to sudden changes in multiple frequencies. It is demonstrated that regardless of the frequency changes, FFE remains constant and stays within a narrow band range, similar to that of a constant frequency.

On the effect of environmental temperature on fracture fatigue entropy

Fracture behavior of carbon steel 1018 operating in low-temperature environments is investigated. Specifically, fully-reversed bending experimental tests are performed to examine the efficacy of applying the concept of Fracture Fatigue Entropy (FFE) for predicting fatigue life at different environmental temperatures. A large cooling chamber was constructed that houses the entire bending test rig and maintains the environmental temperature at the desired value down to −10 °C. It is shown that under conditions tested, fatigue life improves at lower operating temperatures. Results also reveal that FFE remains nearly constant and can be used for reliable prediction of fatigue life. Illustrative examples are provided to show the utility of the approach for prediction purposes.

Fatigue evaluation method based on fracture fatigue entropy and its application on spot welded joints

The present paper is devoted to the fatigue evaluation of material or structure based on thermodynamic entropy approach. The fracture occures once the cumulative entropy reaches a critical value, the fracture fatigue entropy(FFE). Therefore, in this paper, the relationship between entropy and F-N curves is studied, and an entropy-load-number of cycles(E-F-N) surface is developed. Meanwhile, the FFE-based F-N curve can be obtained at the critical entropy value. To verify the utility of proposed method, the E-F-N surface and FFE-based F-N curve are applied to the fatigue evaluation of spot welded joints during high-cycle fatigue. It is shown that the E-F-N surface can effectively represent the fatigue performance. And the accuracy of the FFE-based F-N curve is confirmed by comparing with the traditional traditional three-parameter power function F-N curve. The maximum relative error of the fatigue limits obtained by two different methods is 10.9 %.

Evaluation of fatigue in unidirectional and cross-ply laminated composites using a coupled entropy-kinetic concept

A new approach is proposed to evaluate the fatigue life of laminated composites. It uses the concepts of kinetic strength of solid materials and fracture fatigue entropy. The kinetic strength formulation is based on Zhurkov’s model to consider the temperature and time dependence of the strength of solid materials in fatigue loading. The formulation is general and can be applied to any load ratios to predict the entropy accumulation during cyclic loading, stiffness damage, and fatigue life. Cyclic damage is considered as the expended capacity to generate entropy and the concept of fracture fatigue entropy is utilized as a failure criterion. Comparison between the predictions and experimental results on T300/EPL1012 carbon/epoxy composites shows that this model can reliably predict the fatigue life of laminated composites in a uniaxial stress state.

Investigation of metal fatigue using a coupled entropy-kinetic model

A new method is proposed to predict the fatigue life of metals based on the fracture fatigue entropy (FFE) criterion. This method enables a rapid prediction of the cyclic plastic strain energy and the temperature evolution using the concept of kinetic strength of solid materials. Theoretical predictions are compared with experiments results for Al 7075-T6, LCS 1018, API 5L X52, and MCS 1045. It is shown that this model can reliably predict the temperature evolution, plastic strain energy dissipation, and the fatigue life of metals.

Fatigue assessment of additively-manufactured C-18150 copper alloy at room and elevated temperatures via a microstructure-sensitive algorithm

The efficacy of a recently developed microstructure-sensitive fatigue framework is assessed for additively manufactured materials at different environmental temperatures. C-18150 copper alloy samples additively manufactured using the Laser Powder Bed Fusion process (L-PBF) are fatigue tested at the room, 204 °C, and 426 °C temperatures. Plastic strain energy as the damage representative is studied via the cyclic stress–strain hysteresis loop area measurements and analyzed via a microstructure-sensitive algorithm. A thermodynamics-based framework is used to calculate Fracture Fatigue Entropy (FFE) to assess the material’s fatigue performance. The results based on the hysteresis loop and the microstructure-sensitive method agree both in trend and magnitude.

Confidence level and reliability analysis of the fatigue life of CFRP laminates predicted based on fracture fatigue entropy

This study provides a novel methodology to evaluate fatigue life with the consideration of both confidence level and reliability for CFRP laminates by combining fracture fatigue entropy (FFE) theory and knowledge of statistics. After carrying out distribution analysis and statistical hypothesis testing, it is found that the FFEs obey well to log-normal distribution and the average values and deviations of logarithmic FFEs under different stress levels exhibit no obvious difference. The γ-p-S-N curves are predicted by single side allowance factor analysis and the prediction is found to be more conservative and have a larger scatter comparing to experimental results.

On the kinetic formulation of fracture fatigue entropy of metals

AbstractThe kinetic concept of the strength of solids is used to determine the fatigue life of stress‐controlled cyclic loading and evaluate the fracture fatigue entropy. Unlike the traditional stress or strain‐based models, this theory uses the applied stress amplitude and the specimen's surface temperature to determine the lifetime. The degradation fraction in each cycle is used to calculate the life cycle. Then the material parameters of the final life equation are obtained for two materials: low carbon steel 1018 and aluminum 7075‐T6. The number of cycles to fracture and the cyclic plastic strain energy ( ) are used to calculate the fracture fatigue entropy (FFE). It is shown that the life cycle prediction of the proposed model agrees well with the experimental results from the literature. Results provide further evidence for the constancy of FFE.

Experimentally validated thermodynamic theory of metal fatigue

Fracture due to cyclic actuation occurs when the accumulated entropy generation reaches a critical threshold known as the fracture fatigue entropy (FFE). The accumulated entropy generation is directly related to the intrinsic dissipations such as the supplied work, damage energy, cold work, and internal friction. In this paper, we examine the contribution of these mechanisms to fatigue damage via an irreversible thermodynamic framework and provide experimental evidence for the validity of the formulations. The formulations properly capture the evolution of temperature and reveal that experimentally observed abrupt temperature rise just before fracture is due to the rapid increase in damage and can be predicted.

On the application of fracture fatigue entropy to multiaxial loading

An experimental and theoretical analysis of low carbon steel 1018 subjected to multiaxial loading is presented. Different loading conditions, including tension–compression, torsion, in-phase, and out-of-phase, are applied to investigate the effect of loading type on fatigue life. The fracture fatigue entropy (FFE) framework is then used to predict life using both hysteresis loops and thermography. The results show that the out-of-phase loading leads to the minimum fatigue life, while the torsion exhibit the maximum life at a similar equivalent strain. The FFE predictions using thermography successfully captured the specimens' fatigue life subjected to the multiaxial fatigue loading independent of the loading condition. Furthermore, the results show that the strain energy obtained from the hysteresis loop is a good measure of dissipation energy in the cases of tension–compression, torsion, and in-phase loading conditions. Accordingly, the predicted life using the hysteresis loop agrees well with the thermographic and experimental results. However, in the case of out-of-phase loadings, the plastic strain energy obtained from the hysteresis loop deviates from the dissipation energy because the stored energy originated from the internal state variable variation. Accordingly, the predicted life using the thermography is more accurate than the hysteresis loop, which agrees well with the experimental results.

Damage-entropy model for fatigue life evaluation of off-axis unidirectional composites

This research is devoted to studying the capability of the damage-entropy model for fatigue life prediction of the off-axis unidirectional composites. The damage process in composites was characterized by the micro-continuum damage mechanics (MCDM) and an available reformulated form of the Mori-Tanaka model was used. In the present study, the fracture fatigue entropy (FFE), which is the accumulated entropy generation up to final failure during the fatigue process, was considered as a fatigue failure criterion for the off-axis unidirectional composites. One of the outstanding characteristics of the damage-entropy model is considering the self-heating and temperature evolution during the fatigue life that is due to the damage evolution, irreversible work, and internal friction in composites. Moreover, the dissipated heat due to the viscoelastic intrinsic property of the polymeric matrix was considered. The proposed model was validated by investigating the fatigue behavior of unidirectional T800H/2500 and E-glass/epoxy composites under tension-tension cyclic loading. Results show that the fatigue life prediction of the damage-entropy model is in good agreement with the experimental data.

Fatigue reliability evaluation of Q460 welded joints using fracture fatigue entropy method

In this paper, the fracture fatigue entropy (FFE) was used to evaluate the fatigue reliability of Q460 welded joints during high-cycle fatigue. The Q460 butt welded joint fatigue tests were conducted under different loads. Meanwhile, the real-time temperature measurement, monitored by an infrared thermal scanner, was completed. The fatigue limit can be well estimated according to the cumulative damage entropy production rate in Phase II, and compared with the fatigue limit prediction value by the traditional staircase method, a good consistency is achieved. Furthermore, the P-S-N curves of 5%, 50%, and 95% survival probability rate are well predicted, which is consistent with the experimental data. Therefore, based on this, the accurate fatigue reliability evaluation based on the proposed method has been achieved.

On the intrinsic dissipation and fracture fatigue entropy of metals

Determination of the fracture fatigue entropy (FFE) in materials requires a proper assessment of the intrinsic dissipation terms in the entropy production equation. In this paper, physical terms that contribute to internal friction and their implications on measuring FFE in metals are discussed. We show that internal friction is one of the terms in the intrinsic dissipation equation that cannot be neglected even for low-cycle fatigue tests (LCF). Relevant to measuring internal friction, we also introduce a technique to identify the fatigue limit of metals by measuring their damping value at different stress levels. Fatigue tests are performed to examine the validity of the proposed technique for two types of steels (SS 304 and SS 1018). By comparing our results with the available data in the literature, we find that the discrepancy is less than 10%. The temperature dependence of internal friction for SS304 specimens is also investigated. The result demonstrates a linear relationship and the existence of a peak.

Rapid prediction of fatigue life based on thermodynamic entropy generation

The present paper is devoted to rapid prediction of fatigue performance of materials for medium- and high-cycle fatigue based on the thermography approach. During cyclic loading, the temperature of specimens or components increases due to both anelastic and plastic deformation, while only the plastic strain energy contributes to fatigue damage. Therefore, in this work, a model is proposed to estimate the damaging (plastic strain energy) and non-damaging (anelastic energy) parts of the dissipated heat during the cyclic loading. It is also shown that by taking advantage of the concept of fracture fatigue entropy (FFE), one can rapidly generate a stress-life diagram by conducting a stepwise test and only one fatigue experiment until failure. Further, it is shown mathematically that the dissipating energy is directly proportional to the steady-state temperature. Therefore, in situations where determining the dissipation energy is difficult, the fatigue performance can be readily predicted only by measuring the steady-state temperatures during stepwise testing. The predictions of the proposed models are verified by comparison to a series of experimental results for different materials.