Cyclic Strain Energy Research Articles

Insight on physical meaning of finite-width-correction factors in stress intensity factor (K) solutions of fracture mechanics

The physical meaning of the finite-width-correction factors (FWCF), which commonly appear in stress intensity factor solutions of fracture mechanics, is mysterious. The present work is an attempt to resolve this mystery. Specifically, it is shown that for the middle-crack-tension (M(T)) specimen and for the embedded-circular-crack in a specimen of round cross-section, the FWCF factor is related to the average net-section stress for a given crack size. An increase in K at the crack tip means an increase in the average net-section stress ahead of the crack, in addition to the increase in the level of normal stress in the near-tip (or singularity-dominated) zone of fracture mechanics. It is also shown that this increase in net-section stress can be determined, in a straightforward manner, using a simple approach based on strength of materials (SOM). The agreement between the net-section stress determined from the strength of materials approach and that from fracture mechanics is surprisingly good. This connection between the finite-width-correction factor and the net-section stress has not been demonstrated before, and, hence it provides a new point of view to analyze fracture mechanics problems. More importantly, the connection validates the correlation of fatigue crack growth on the basis of the change in the net-section cyclic strain energy, which has recently been demonstrated by the author elsewhere.

Porosity Effects on Interlaminar Fracture Behavior in Carbon Fiber-Reinforced Polymer Composites

Fiber-reinforced polymer composite materials have become materials of choice for manufacturing application due to their high specific stiffness, strength and fatigue life, low density and thermal expansion coefficient. However, there are some types of defects such as porosity that form during the manufacturing processes of composites and alter their mechanical behavior and material properties. In his study, hand lay-up was conducted to fabricate samples of carbon fiber-reinforced polymer composites with three different vacuum levels in order to vary porosity content. Nondestructive evaluation, destructive techniques and mechanical testing were conducted. Nondestructive evaluation results showed the trend in percentages of porosity through-thickness. Serial sectioning images revealed significant details about the composite’s internal structure such as the volume, morphology and distribution of porosity. Mechanical testing results showed that porosity led to a decrease in both Mode I static interlaminar fracture toughness and Mode I cyclic strain energy release rate fatigue life. The fractographic micrographs showed that porosity content increased as the vacuum decreased, and it drew a relationship between fracture mechanisms and mechanical properties of the composite under different modes of loading as a result of the porosity effects. Finally, in order to accurately quantify porosity percentages included in the samples of different vacuum levels, a comparison was made between the parameters and percentages resulted from the nondestructive evaluation and mechanical testing and the features resulted from fractography and serial sectioning.

A unified criterion for fatigue–creep life prediction of high temperature components

A unified ductility criterion for fatigue–creep life prediction is presented based on the static fracture toughness exhaustion and dissipated cyclic strain energy density of high temperature components. It provides a general failure criterion for both low and high cycle fatigue regimes. The effects of mean stress, creep and loading waveform on fatigue life are incorporated into this criterion. Applicability and prediction accuracy of the newly proposed criterion was validated through comparing model predictions to experimental results taken from the literature. The results show that the proposed criterion is robust for different loading conditions and more accurate than other existing strain energy/ductility-based methods.

Fatigue Life Prediction Based on Local Strain Energy for Healed Copper Film by Laser Irradiation

Changes of total cyclic strain energy at the notch for copper film specimen were analyzed before and after laser irradiation treatment. The results showed that laser irradiation can increase total cyclic strain energy and the effect of increase is more evident for the damaged copper specimen. Based on the damage-healing mechanism, an enhancement parameter and a healing parameter were defined by the local cyclic strain energy. A new model based on local strain energy was proposed to predict residual fatigue life for the damaged copper film specimen after laser irradiation. The predicted results by the proposed model agree well with the experimental lives.

How proper similitude can improve our understanding of crack closure and plasticity in fatigue

The appropriateness of some common similitude principles with respect to describing and predicting fatigue damage propagation is discussed. Linear elastic fracture mechanics have provided a basis to describe damage growth using stress intensity factors or strain energy release rates, both related to the work of Griffith and Irwin. The fatigue crack growth equations presented in the literature are discussed, and it is demonstrated that the principles of similarity in current methodologies have not yet been well established. As a consequence, corrections for the stress ratio effect are misunderstood. An alternative principle of similitude using cyclic work and strain energy release is proposed.

Self-heating forecasting for thick laminate specimens in fatigue

Thick laminate sections can be found from the tip to the root in most common wind turbine blade designs. Obtaining accurate and reliable design data for thick laminates is subject of investigations, which include experiments on thick laminate coupons. Due to the poor thermal conductivity properties of composites and the material self-heating that occurs during the fatigue loading, high temperature gradients may appear through the laminate thickness. In the case of thick laminates in high load regimes, the core temperature might influence the mechanical properties, leading to premature failures. In the present work a method to forecast the self-heating of thick laminates in fatigue loading is presented. The mechanical loading is related with the laminate self-heating, via the cyclic strain energy and the energy loss ratio. Based on this internal volumetric heat load a thermal model is built and solved to obtain the temperature distribution in the transient state. Based on experimental measurements of the energy loss factor for 10mm thick coupons, the method is described and the resulting predictions are compared with experimental surface temperature measurements on 10 and 30mm UD thick laminate specimens.

Short Creep-Fatigue Crack Growth in an Advanced 9 %Cr Steel

Abstract While the development of short cracks due to cyclic elastic loading has been relatively widely studied, in particular at room temperature, their consideration for cyclic inelastic loading at high temperatures and lower frequencies is not so common. Short creep-fatigue crack growth rates may be correlated in terms of cyclic strain range, cyclic J-integral or strain energy density factor, with appropriate allowance for associated creep damage accumulation. Candidate approaches are evaluated with reference to test results generated for an advanced 9 %Cr turbine rotor steel. This paper promotes the use of cyclic strain range and strain energy density factor relative to other candidate correlating parameters in relation to the results of a series of 30 min hold time creep-fatigue tests performed using fully instrumented uniaxial specimens with short crack starters. The focus of the testing campaign is an advanced 9 %Cr turbine rotor steel at temperatures of 600 and 625°C.

LCF Life Prediction Model of Coiled Tubing Based on Fatigue Damage Accumulation

This paper establishes a model to predict the fatigue behavior of coiled tubing subjected to variable total strain conditions. The approach based on nonlinear fatigue cumulative damage rule of effective hysteresis energy dissipation, but requires additional experimental results from fatigue tests that were performed under constant strain amplitude. Cyclic plastic strain energy is measured curve area of cyclic stress-strain curves. it is proved to be quite consistent between theoretical predictions and experimentl datas.

An energy‐based critical fatigue life prediction method for AL6061‐T6

ABSTRACTAn energy‐based critical fatigue life prediction method is developed and analysed. The original energy‐based fatigue life prediction theory states that the number of cycles to failure is estimated by dividing the total energy accumulated during a monotonic fracture by the strain energy per cycle. Because the accuracy of this concept is heavily dependent on the cyclic behaviour of the material, a precise understanding of the strain energy behaviour throughout each failure process is necessary. Examination of the stress and strain during fatigue tests shows that the cyclic strain energy behaviour is not perfectly stable as initially presumed. It was discovered that fatigue hysteresis energy always accumulates to the same amount of energy by the end of the stable energy region, which has led to a new ‘critical energy’ material property. Characterization of strain energy throughout the fatigue process has thus improved the understanding of an energy‐based fatigue life prediction method.

Analysis of Multiaxial Low Cycle Fatigue Life for Single Crystal Ni-Based Superalloy Based on Two-Phase Unit Cell Model

Based on micro structure of Ni-based single crystal superalloy, a γ/γ’ two-phase unit cell finite element model was established, and its cyclic stress-strain was simulated under tension/torsion cyclic loading. A low cycle fatigue (LCF) life prediction model of single crystal superalloy was proposed by using cyclic plasticity strain energy as a parameter based on energy dissipation theory. Calculation results of macro finite element model and γ/γ’ two-phase unit cell micro finite element model, and multiaxial LCF test data of CMSX-2 Ni-based single crystal superalloy along [001] orientation were applied to fit the LCF life model by multiple linear regression. The results show that the unit cell model not only reflects the microstructure characteristics of single crystal Ni-based superalloy, but also is better than the macro model in accuracy of analysis, and greatly improve the accuracy of fatigue life prediction. Almost test data fall into the factor of 2.0 scatter band.

Plastic Strain Energy in Low-Cycle Fatigue of A356 (Al-7Si-0.4Mg) Aluminum Alloys

In this paper, the problem of plastic strain energy density as a evaluation of low-cycle fatigue (LCF) properties for A356 alloys with various Ti content and Ti-addition methods is considered. The experimental results reveal that it is not the Ti-addition methods but the Ti content that has played an important role in influencing on the plastic strain energy density, thus on the LCF life. Whether for the electrolytic A356 alloys or for the melted A356 alloys, the alloys with 0.1% Ti content can consume higher cyclic plastic strain energy during the cyclic deformation compared with the alloys with 0.14% Ti content due to the better plasticity, giving rise to a better fatigue resistance and a longer LCF life. Because of the different macro or micro deformation mechanism, the fracture surface of electrolytic A356 alloy exhibits the diverse microstructural morphologies under the various strain amplitude.

Predicting fatigue life of Glare skin–stringer configurations in aerospace panels

The debonding of Glare skin–stringer configurations for aerospace applications has been studied. Fatigue life curves were produced experimentally for two types of skin–stringer configurations. Using the double cantilever beam specimen configuration and applying different loading conditions, material models for pure mode I and mixed mode I and mode II fatigue loading were generated for the adhesive used to bond the skin to the stringer. These material models describe the crack growth rate, da/dN, as a function of the maximum cyclic strain energy release rate, Gmax, and were used together with finite element analysis of the cracked skin–stringer configuration to derive predictions of the fatigue life. The predicted fatigue life was compared to the experimental results.

Hysteresis-loop representation for strain energy calculation and fatigue assessment

Improvements have been made to the cyclic strain energy density expression used in a fatigue life prediction method. The theory behind the prediction method is based on the understanding that the same amount of strain energy is dissipated during a monotonic fracture and a cyclic fatigue process. From this understanding, the failure cycle for a fatigue process can be determined by dividing monotonic strain energy by the average strain energy per cycle. Though this technique has been shown to be acceptable, it needs to be improved to account from the experimentally observed increase in the strain energy per cycle as the loading cycles approach fatigue. In order to improve the fatigue life prediction technique, experimental strain energy density per cycle is observed during the fatigue process of Aluminium 6061-T6 (Al 6061-T6) specimens. The results show exponential change in the strain energy density through the first 20 per cent and the last 30 per cent of the total failure cycles. The results lead to a new representation of strain energy density per cycle, which leads to an improved fatigue life prediction method. A comparison is made between the improved prediction method and experimental fatigue results. The comparison result validates the precision of the new hysteresis-loop representation.

Multi-objective evolutionary optimization of polynomial neural networks for fatigue life modelling and prediction of unidirectional carbon-fibre-reinforced plastics composites

In this article, evolutionary algorithms (EAs) are employed for multi-objective Pareto optimum design of group method data handling (GMDH)-type neural networks that have been used for fatigue life modelling and prediction of unidirectional (UD) carbon-fibre-reinforced plastics (CFRP) composites using input—output experimental data. The input parameters used for such modelling are stress ratio, cyclic strain energy, fibre orientation angle, maximum stress, and failure stress level in one cycle. In this way, EAs with a new encoding scheme are first presented for evolutionary design of the generalized GMDH-type neural networks, in which the connectivity configurations in such networks are not limited to adjacent layers. Second, multi-objective EAs with a new diversity preserving mechanism are used for Pareto optimization of such GMDH-type neural networks. The important conflicting objectives of GMDH-type neural networks that are considered in this work are training error (TE), prediction error (PE), and number of neurons ( N). Different pairs of these objective functions are selected for two-objective optimization processes. Therefore, optimal Pareto fronts of such models are obtained in each case, which exhibit the trade-offs between the corresponding pair of conflicting objectives and, thus, provide different non-dominated optimal choices of GMDH-type neural network model for fatigue life of UD CFRP composites. Moreover, all the three objectives are considered in a three-objective optimization process, which consequently leads to some more non-dominated choices of GMDH-type models representing the trade-offs among the TE, PE, and N (complexity of network), simultaneously. The comparison graphs of these Pareto fronts also show that the three-objective results include those of the two-objective results and, thus, provide more optimal choices for the multi-objective design of GMDH-type neural networks.

Contemporary fatigue damage aspects

The ways to treat Continuum Damage Mechanics in low cycle fatigue are following: (i) the fully coupled analysis and (ii) the post-processing analysis.With a view to treating the subject of the paper presented, the biaxial testing steel specimen was worked to exhibit stress concentrations, localized plasticity, and damage at notches, being chosen among examples of multiaxial and multilevel fatigue loadings.Concurrently, the failure conditions are determined after a single elastic reference computation by using the cyclic strain energy density method ensued by the time integration of the unified damage law. Characteristic effects of high cycle fatigue are predicted by the unified damage law within two-scale damage model; in an exemplary fashion, for a plate subject to a biaxial fatigue loading, the in-plane stresses σ1 and σ2 vary proportionally between (−σ1max and +σ1max) and (−σ2max and +σ2max).

Cyclic Hysteresis Evolution as a Damage Parameter for Notched Composite Laminates

In cyclically loaded polymer matrix composites, structural health monitoring is useful for detecting and tracking progressive damage. Existing approaches use stiffness degradation, crack propagation/strain energy change, or dynamic parameters such as frequency response. These approaches, however, depend on prior assumptions of the dominant damage mechanisms. In this study, a new hysteresis-based damage parameter, D′, that is a measure of damage progression and failure is shown to be more sensitive than stiffness degradation and can be determined during cycling without the use of additional instrumentation. D′ was measured for cyclically loaded notched glass fiber laminates and was found to be useful as a measure of damage progression. Cyclic hysteresis strain energy dissipated at each cycle was monitored continuously without interruption. A conventional servo-hydraulic fatigue testing system was modified with the incorporation of new custom code for performing command and data acquisition on a cycle-by-cycle basis. In this fashion, progressive damage at each cycle was determined quantitatively in real time during each test. Hysteresis data were obtained from fatigue tests conducted on notched [0/90] E-glass/epoxy laminates in real time on a cycle-by-cycle basis and used to estimate failure. The damage parameter D′ exhibited an approximately linear increase with cycling followed by an exponential increase just before failure. Modeling this behavior allowed for the prediction of damage progression and residual life as a function of load cycles. Hysteresis-based damage parameters for other material configurations were also calculated and found to give good estimates for the cyclic life.

Enhancement of delamination fatigue resistance in carbon nanotube reinforced glass fiber/polymer composites

We show that the addition of small volume fractions of multi-walled carbon nanotubes (CNTs) to the matrix of glass–fiber composites reduces cyclic delamination crack propagation rates significantly. In addition, both critical and sub-critical inter-laminar fracture toughness values are increased. These results corroborate recent experimental evidence that the incorporation of CNTs improve fatigue life by a factor of two to three in in-plane cyclic loading. We show that in both the critical and sub-critical cases, the degree of delamination suppression is most pronounced at lower levels of applied cyclic strain energy release rate, Δ G. High-resolution scanning electron microscopy of the fracture surfaces suggests that the presence of the CNTs at the delamination crack front slows the propagation of the crack due to crack bridging, nanotube fracture, and nanotube pull-out. Further examination of the sub-critical fracture surfaces shows that the relative proportion of CNT pull-out to CNT fracture is dependent on the applied cyclic strain energy, with pull-out dominating as Δ G is reduced. The conditions for crack propagation via matrix cracking and nanotube pull-out and fracture are studied analytically using fracture mechanics theory and the results compared with data from the experiments. It is believed that the shift in the fracture behavior of the CNTs is responsible for the associated increase in the inter-laminar fracture resistance that is observed at lower levels of Δ G relative to composites not containing CNTs.

An experimental approach to low-cycle fatigue damage based on thermodynamic entropy

This paper presents an experimental approach to fatigue damage in metals based on thermodynamic theory of irreversible process. Fatigue damage is an irreversible progression of cyclic plastic strain energy that reaches its critical value at the onset of fracture. In this work, irreversible cyclic plastic energy in terms of entropy generation is utilized to experimentally determine the degradation of different specimens subjected to low cyclic bending, tension-compression, and torsional fatigue. Experimental results show that the cyclic energy dissipation in the form of thermodynamic entropy can be effectively utilized to determine the fatigue damage evolution. An experimental relation between entropy generation and damage variable is developed.

An Experimental Approach to Evaluate the Critical Damage

An experimental study has been carried out to determine the critical damage parameter based on the concept of entropy flow. The fatigue damage is either a cumulative process that progresses toward a maximum tolerable damage, or is an irreversible progression of cyclic plastic strain energy that reaches its critical value at the onset of fracture. In the present study, irreversible heat dissipation in terms of entropy is utilized to experimentally determine the degradation of different specimens subjected to low cyclic bending fatigue. An experimental correlation between entropy and damage is proposed. It is shown that the cyclic energy dissipation in the form of thermodynamic entropy can be effectively utilized to determine the critical damage value.

Effect of cyclic straining at elevated-temperature on static mechanical properties, microstructures and fracture behavior of nickel-based superalloy GH4145/SQ

A series of experiments, including constant amplitude low-cycle fatigue tests, uniaxial tension failure tests, TEM observations and SEM examinations, were carried out to investigate the effect of cyclic straining at a temperature of 538 °C on the static mechanical properties, the deformation microstructures and the fracture behavior of nickel-base superalloy GH4145/SQ. The change characteristics of the various basic static mechanical property parameters, such as the yield strength ( σ 0.2), the ultimate strength ( σ b), the modulus of elasticity ( E), the reduction of area ( φ f), the elongation ( δ) and the strain-hardening exponent ( n), during elevated-temperature low-cycle fatigue of the alloy were obtained experimentally and their micromechanisms were further discussed through analyzing both deformation microstructures and fracture features of the cyclically deformed specimens. A composite static mechanical property parameter called static toughness ( U t) was proposed to characterize comprehensively the variation of the various basic static mechanical property parameters ( σ 0.2, σ b, φ f and n), and an approximate formulation describing the exhaustion of the static toughness during high-temperature fatigue failure process was constructed. A quantitative correlation between the exhaustion of the static toughness and the dissipation of the cyclic plastic strain energy during the course of high-temperature fatigue failure of the current alloy was developed in theory and further verified in experiment.