Modeling delamination growth in composites under fatigue loadings of varying amplitudes

A numerical model was developed to simulate the progressive delamination of a composite subjected to mode I fatigue loading regimes of varying amplitude. The model employs a cohesive zone approach, which combines damage mechanics and fracture mechanics, and requires only standard material data as input, namely the delamination toughness and the fatigue delamination growth curve. The proposed model was validated against delamination growth data obtained from a fatigue test conducted on a DCB specimen. The model predictions agree very well with the experimental results. This model is an initial step toward life prediction of composite structures subjected to complex fatigue regimes.     

复合材料疲劳分层的界面单元模型

提出一种三维黏聚力界面损伤模型,可以描述单调和交变载荷下层合复合材料混合型的分层损伤。损伤用界面所经历过的最大位移间断来定义,交变荷载下一个周期的加、卸载过程均考虑有损伤积累,模型还考虑了单调和疲劳损伤的门槛效应和交变载荷下裂纹的闭合效应。建立了包含该界面损伤模型的初始无厚度八节点等参界面单元,并引入加速损伤的算法,用一次计算循环代替若干次实际循环,提高计算效率。用该单元模型对某复合材料动部件疲劳分层裂纹的形成和扩展进行了模拟,得到了分层裂纹前沿界面局部损伤和结构疲劳分层的发展规律,模型预测的裂纹长度-荷载循环次数对数(a-log N)曲线和结构剩余刚度与试验数据吻合。     

A high-cycle fatigue apparatus at 20 kHz for low-cycle fatigue/high-cycle fatigue interaction testing

High-cycle fatigue (HCF) failures in aircraft engines are attributed to material damage states, created during processing or by in-service loading and environmental conditions, and then propagated to failure by HCF loading. The loading configuration experienced by aircraft engine turbine blades consists of an axial load caused by the centrifugal acceleration during rotation combined with the tensile and compressive loads caused by the natural vibrations of the blades themselves. To simulate these loading conditions a new testing apparatus was developed that is capable of providing interactive low-cycle fatigue/high-cycle fatigue (LCF/HCF) loading, in ratios (of magnitude and frequency) that give a realistic simulation of the actual flight loads experienced by engine components. This testing apparatus is based on a HCF cell operating at 20  kHz. The cell can also be integrated to a servo-hydraulic load frame, which provides a second fatigue cycle. The objective of this study was to demonstrate the capabilities of the new HCF apparatus via thermographic measurements and by performing LCF/HCF interaction tests.     

Transverse cracking and delamination in cross-ply gr/ep composites under dry, saturated and immersed fatigue

Motivated by experimental observations, the finite element method is employed to model the competition between the transverse cracking and delamination modes of failure that occur in cross-ply AS4/3501-6 gr/ep coupons subjected to fatigue. The results explain the extensive delaminations and reduced crack densities that arise under immersed fatigue, as compared with fatigue in air. This revised version was published online in August 2006 with corrections to the Cover Date.     

Multiaxial high-cycle fatigue constraints in structural optimization

The paper deals with parametric optimization of structures subjected to multiaxial high-cycle fatigue. A large number of load cycles corresponding to infinite fatigue life was taken into account in the analysis and optimization. The authors use simplified form of Dang Van’s criterion for fatigue damage estimation. For needs of optimization, a certain transformation pattern of the load time history was assumed, which allowed to considerably accelerate the fatigue analysis process. The proposed methodology has been illustrated by an example of optimization of a car suspension arm. As observed in the computational example, the proposed methodology of optimization allowed effectively to reduce the mass of the studied structure while maintaining its fatigue durability on an established level.     

Acoustic emission mechanisms during high-cycle fatigue

Acoustic emission was obtained during fatigue crack propagation in a D6 tool steel and a 1015 mild steel using two different load ratios, R. It was found that the slope of the acoustic emission count rate vs stress intensity factor was higher when R = 0.2 than when R = 0.4. These results are described in terms of several models of acoustic emission mechanisms available in the literature as well as by a proposed new model. It is concluded that the observed R dependence can be explained by the combination of the contribution of two different models. These two models are the new plastic yielding as well as the crack tip fracture processes.     

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, ΔG. 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 ΔG 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 ΔG relative to composites not containing CNTs.     

Influence of the matrix constituent on mode I and mode II delamination toughness in fiber-reinforced polymer composites under cyclic fatigue

Mode I and mode II fracture behaviour under static and dynamic loading was analyzed in two composites made up of the same reinforcement though embedded in two different matrices. Specifically, the delamination energy under static and dynamic loading was obtained for both materials and both fracture modes, i.e. the number of cycles necessary for the onset of fatigue delamination. Subsequently, the crack growth rate (delamination rate) was obtained for different percentages of the critical energy rate. The main goal of the study was to ascertain the influence of the matrix on the behaviour of the laminate under fatigue loading.From the experimental results for the onset of delamination, similar fatigue behaviour was observed at a low number of cycles for both matrices and both fracture modes, while in fatigue at a high number of cycles, a higher fatigue limit was obtained in the composite with the modified resin (higher toughness) for both fracture modes. From the point of view of crack growth rate, both materials behaved similarly for different levels of stress under fatigue and the two fracture modes for small crack lengths (initial growth zone < 5 mm), although the growth rate increased for large crack lengths. This behaviour was the same in both loading modes.     

Crystal plasticity modeling of damage accumulation in dissimilar Mg alloy bi-crystals under high-cycle fatigue

Damage accumulation in Mg AZ31–AZ80 alloy bi-crystals under fatigue loading at room temperature is studied using a modified version of the crystal plasticity finite element model of Abdolvand and Daymond. The model accounts for strain accommodation by both slip and tensile twinning, and is first shown to reasonably describe monotonic single crystal Mg experimental data from the literature. The high cycle fatigue behavior was then investigated in misoriented dissimilar alloy bi-crystals through stress-controlled simulations up to 1000 cycles. Nine different orientation combinations were simulated and the fatigue damage evolution, defined as the cumulative shear strain amplitude, were compared and analyzed. The bi-crystal geometry was used to simulate possible microstructure combinations occurring, for instance within an idealized friction stir weld. Findings suggest that when either of the alloy bi-crystal grains is oriented for basal slip, poor fatigue performance can occur by twinning or slip localization depending upon the neighboring orientation.     

On the anelasticity and fatigue fracture entropy in high-cycle metal fatigue

The concept of thermodynamic entropy generation in a degradation process is utilized to study the high-cycle fatigue of medium carbon steel 1018. Uniaxial tension–compression fatigue tests are carried out with tubular dogbone specimens at different stress levels and loading frequencies. It is shown that a phase lag between the stress and the strain caused by the internal friction includes a considerable amount of non-damaging anelastic energy in a hysteresis loop when the amplitude of cyclic load is substantially smaller than the yield strength of the material. A methodology is proposed to determine the anelastic energy associated with metal fatigue at a stress level lower than the yield strength of a material. Finite element simulations are carried out with a 3-D model of the specimen to determine the validity of the proposed methodology. The evolutions of the plastic strain energy and temperature are discussed and utilized to calculate the entropy accumulation. It is shown that the accumulation of entropy generation in the HCF of the material—beginning with a pristine specimen and ending at fatigue fracture—is nearly constant within the experimental and loading conditions considered. The concept of tallying entropy is useful for the prediction of the fatigue life evolution of a material undergoing cyclic loading.     

Development of a standardized procedure for the characterization of interlaminar delamination propagation in advanced composites under fatigue mode I loading conditions

A round robin exercise on opening mode I fatigue delamination propagation has been performed with the aim of developing a standardized test procedure. The material chosen for the test was one type of carbon–fiber reinforced polymer–matrix laminate (IM7 fiber, 977-2 epoxy). The Double Cantilever Beam specimen from the quasi-static mode I delamination resistance test (ISO 15024) has been used for the fatigue test. Test set-up, measurements and data acquisition have been defined with an emphasis on applicability in an industrial test environment. Selected test parameters have been varied in order to investigate their effect on the results. Three different approaches for delamination length determination have been compared. Visual determination of delamination length, a compliance-based approach and an effective delamination length calculation based on a separate measurement of the modulus of elasticity yield reasonable agreement. This agreement suggests that further development of the test procedure to incorporate automated data acquisition and analysis may be worthwhile.     

Propagation behaviour of microstructural short fatigue cracks in the high-cycle fatigue regime

In the high-cycle fatigue regime, it is assumed that crack initiation mechanisms and short fatigue crack propagation processes govern fatigue life of a component. Moreover, it is now becoming accepted that the conventional fatigue limit does not imply complete reversibility of plastic strain and is connected to crack initiation. However, interaction of the crack tip with microstructural barriers, such as, e.g. grain boundaries or second phases, leads to a decrease and eventually to a stop in the crack propagation. In the present contribution, examples for propagating and non-propagating conditions of short fatigue cracks in the microstructure of a duplex steel are given, quantified by means of automated EBSD. To classify the results within the scope of predicting the service life for HCF- and VHCF-loading conditions, a numerical model based on the boundary element method has been developed, describing crack propagation by means of partially irreversible dislocation glide on crystallographic slip planes in a polycrystalline model microstructure (Voronoi cells). This concept is capable to account for the strong scattering in fatigue life for very small strain amplitudes and to contribute to the concept of tailored microstructures for improved cyclic-loading behaviour.     

An invariant-based approach for high-cycle fatigue calculation

Fatigue failures of in-service components are frequently due to multiaxial loadings; therefore, damage quantification in such conditions is important to many industrial applications. In this work a multiaxial criterion suitable for high-cycle fatigue assessment is formalized. It makes use of hydrostatic stress component and deviatoric stress component to estimate fatigue damage. A new formulation for the equivalent amplitude of the deviatoric component is formalized and compared with definitions proposed by Deperrois and Li and De Freitas. Damage evaluation procedure is discussed for deterministic loads and explicit analytical formulation is presented for sinusoidal loadings. Fatigue criterion is applied to experimental data taken from literature, related to several materials subjected to either in-phase or out-of-phase loads. It is shown that the new approach gives good predictions for both smooth and notched specimens. A similar comparison between experimental and theoretical results is also presented for other common criteria. It appears that the quality of the fatigue assessments obtained with the present criterion is better or, at most, similar to that of the other criteria analysed.     

Cyclic fatigue delamination of carbon fiber-reinforced polymer-matrix composites: Data analysis and design considerations

Activities toward standardization of fracture mechanics tests on carbon fiber-reinforced polymer-matrix (CFRP) composites have recently focused on cyclic fatigue under mode I (tensile opening), mode II (in-plane shear) and mixed-mode I/II loading. Data from recent round robins performed by Technical Committee 4 (TC4) of the European Structural Integrity Society (ESIS) and from preliminary testing of additional CFRP epoxy laminates at the authors’ laboratories are analyzed with different approaches in attempts to reduce scatter and to identify parameters for CFRP structural design. Selected test data comparing load and displacement control for the cyclic fatigue tests are also discussed. Specifically, threshold values from Paris-law data fitting are compared with values from fitting with a modified Hartman–Schijve approach. Independent of the approach used for the analysis, mode I threshold values of selected CFRP seem to be in the range between about 30 and 100 J/m², i.e., roughly around the range of critical mode I energy release rate values (denoted by G_IC) obtained from fracture testing of neat commercial epoxy resins, but clearly below quasi-static initiation G_IC-values for unidirectional CFRP composites. Implications for CFRP structural design based on mode I fatigue fracture mechanics test data are briefly discussed.     

Transverse crack growth behavior considering free-edge effect in quasi-isotropic CFRP laminates under high-cycle fatigue loading

The high-cycle fatigue characteristics focused on the behavior of the transverse crack growth up to 10⁸ cycles were investigated using quasi-isotropic carbon fiber reinforced plastic (CFRP) laminates whose stacking sequence was [−45/0/45/90]_s. To assess the fatigue behavior in the high-cycle region, fatigue tests were conducted at a frequency of 100 Hz in addition to 5 Hz. In this study, to evaluate quantitative characteristics of the transverse crack growth in the high-cycle region, the energy release rate considering the free-edge effect was calculated. Transverse crack growth behavior was evaluated based on a modified Paris law approach. The results revealed that transverse crack growth was delayed under the test conditions of the applied stress level of σ_max/σ_b = 0.2.     

Influence of z-pin length on the delamination fracture toughness and fatigue resistance of pinned composites

The effect of z-pin length on the mode I and mode II delamination toughness and fatigue resistance of z-pinned carbon-epoxy composites is investigated. Experimental testing and mechanical modelling reveals that both the mode I fracture toughness and fatigue resistance increase with the z-pin length due to increased bridging traction loads generated by elastic stretching and pull-out of the pins. The opposite trend occurs for mode II toughness, which decreases with increasing z-pin length due to lower traction loads arising from restrictions on the shear-induced rotation and pull-out of the pins. The mode II fatigue resistance is increased by z-pinning, although it is not dependent on the z-pin length. Increasing the z-pin length beyond a critical size also changes the mode I and mode II delamination fracture and fatigue processes from single to multiple cracking. The effect of z-pin length on the delamination toughening and fatigue strengthening mechanisms is determined.