Cyclic Strain Energy Release Rate Research Articles

On the strain energy release rate and fatigue crack growth rate in metallic alloys

The field of fracture mechanics started with Griffith’s energy concept for brittle fracture in 1920. In 1963, Paris et al. used a fracture mechanics’ parameter to introduce an equation for the fatigue crack growth rate in ductile materials and this equation is now commonly known as the ‘Paris law’. However, the Paris law and the semi-empirical models that followed ever since do not fully account for the main intrinsic and extrinsic properties involved with fatigue crack growth in metallic alloys. In contrast, here a dimensionally correct fatigue crack growth rate equation is introduced that is based on the original crack driving force as introduced by Griffith and the presence of plasticity in a metal to withstand crack propagation. In particular it is shown that the fatigue crack growth rate shows a power law relationship with the cyclic strain energy release rate over the maximum stress intensity factor. The new description corrects for the ratio between the minimum and maximum stress in a cycle during constant amplitude loading and for crack growth retardation under variable amplitude loading. The method has been successfully applied to variable amplitude crack growth with spectra that are representative of different fatigue dominated aircraft locations. As such, it allows for accurate predictions of variable amplitude fatigue crack growth life in aerospace structures.

An energy principles based model for fatigue crack growth prediction

An energy principles based model is developed for fatigue crack growth (FCG) prediction. According to the equilibrium relationship between released strain energy and irrecoverable stored energy accumulated along the length of fracture process zone (FPZ), the FCG rate is calculated through dividing the accumulated stored energy by the elementary fracture released energy in each load cycle. The elementary fracture released energy is determined from the cyclic strain energy release rate. The accumulated stored energy is obtained by integrating the crack-tip stresses within the FPZ length. Comparison between model prediction and FCG test data is made and good agreement is observed.

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.

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.

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.

Effect of the Molding Conditions on Mode II Interlaminar Crack Propagation in Continuous Glass Fiber/Polypropylene Composites

The effect of molding conditions on the resistance to Mode II interlaminar crack propagation under monotonic and cyclic loading of unidirectional continuous glass-fiber composites with a polypropylene (PP) matrix was studied. The distribution of the fibers and of the crystalline and amorphous components of the matrix phase, the melting temperature and the amount of crystallinity are related to the molding conditions employed and to the resulting flexural strength and modulus, apparent interlaminar shear strength and Young’s modulus. Mode II crack propagation, either cyclic or monotonic, is strongly affected by the fiber-matrix interface and matrix morphology. The distribution of the soft amorphous PP phase in the semi-crystalline PP matrix appears to be the controlling parameter determining the fracture and fatigue resistance of the composite. The fractographic features clearly show the role that this phase plays during crack propagation. A relationship between the shear cusp size measured on the fatigue surfaces and the cyclic strain energy release rate is proposed.

Mixed-Mode Delamination Behavior of Carbon/Epoxy Composites

The mixed-mode bending (MMB) test was employed in an investigation of delamination fracture behavior in static and fatigue loading for carbon/epoxy composites 1300/M10 and HTA/6376. As specimens were loaded at different ratios of alL for different mixed-mode ratios, both investigated composites exhibited brittle unstable or brittle stable behavior of crack growth. Mixed-mode delamination fracture toughness was determined at a IL = 0.5. Fracture surfaces of MMB specimens were examined using scanning electron microscopy to distinguish fracture features. Stable crack growth was observed over the entire range of crack lengths investigated in the cyclic tests. A consistent relation of crack growth per cycle to the cyclic strain energy release rate was obtained. The trend of reduction in crack growth rate data with diminution in cyclic strain energy release rate suggests the presence of a threshold strain energy release rate.

Mode II delamination behavior of carbon/epoxy composites

The end-notched flexure (ENF) test was employed in an investigation of the interlaminar fracture behavior in mode II static and fatigue loading for carbon/epoxy composites T300/M10 and HTA/6376. The mode II interlaminar fracture toughness was determined by a compliance calibration method. The tests were performed in the range of the a/L ratio from 0.5 to 0.9. Both composites, T300/M10 and HTA/6376, exhibited brittle unstable and brittle stable behavior of crack growth. Stable mode II crack growth was observed during fatigue loading with R = 0.1 in a large range of cyclic strain energy release rate. A consistent relation of the crack growth rate to the cyclic strain energy release rate was obtained for both T300/M10 and HTA/6376 composites. Within the range of moderate crack growth rate, the data of mode II fatigue crack growth for the composites obeyed a power law. The trend of reduction in the crack growth rate data with degradation in the cyclic strain energy release rate suggests the presence of a thre...

Fatigue behaviour of joints bonded with either filled, or filled and toughened, adhesive

Mode I fatigue crack growth tests were conducted on double cantilever beam points bonded with two commercial adhesives (filled, and filled and toughened) at a load ratio of 0.2 and frequencies of 2 and 20 Hz. Using finite element analyses and incorporating the loading rate dependence of the adhesive modulus, the cyclic strain energy release rate range, Δ G, was calculated and correlated with fatigue crack growth rate, d a/d N. Fractography indicated that the fatigue crack growth mechanism in both joints involved the cracking of the filler particles and subsequent linkage of the resultant microcracks. Higher fatigue crack growth rates were found in the joints bonded with the filled and toughened adhesive, especially at the lower frequency. This was attributed mainly to the larger process zone ahead of the crack tip in this adhesive due to its lower strength. It was found that in the joints bonded with filled adhesive there exists a fatigue crack threshold ΔG th , near which there is a change in the mechanism of fatigue, whereby the crack grows predominantly through the matrix.

Interlaminar Fatigue Crack Propagation in Mode I of Carbon Fiber/PEEK Composites

A study of the mode I interlaminar fracture toughness of a unidirectional carbon fibre reinforced thermoplastic matrix composite has been made using Double Cantilever Beam, DCB, specimens. Delamination growth per fatigue cycle, da/dN, was related with the maximum applied cyclic strain energy release rate, GIMAX, using a power law.

Interlaminar Fracture Behavior and Fiber Bridging of Glass-Epoxy Composite Under Mode I Static and Cyclic Loadings

Interlaminar fracture behavior of composite materials under static and cyclic loadings has been studied using a width tapered double cantilever beam specimen. The fracture energy is evaluated by compliance, beam and area methods. The comparison results show that the initial fracture energy could be evaluated either by beam or area method while the crack growth resistance could be calculated by compliance method. Increases in the criti cal load and fracture energy due to fiber bridging are predicted by a power function of fracture area. The interlaminar fatigue crack growth behavior is studied through the con stant cyclic strain energy release rate range test. A modification of Paris' power law is made to interpret fatigue crack growth under the influence of fiber bridging. The predicted fatigue life by the modified power law is reasonably close to the experimental data. Frac tography study shows that the interlaminar failure mechanism of a composite beam in volves fiber breakage, matrix tearing and transverse microcracking as well as the delamination of the layers.

Mode II Cyclic Delamination Growth

The end notched flexure (ENF) specimen is employed in an investigation of the inter laminar fracture of unidirectional graphite/epoxy, graphite/polyimide, and graphite/PEEK composites subjected to Mode II fatigue loading. Fatigue crack growth rates are deter mined for the stable delamination growth observed under fully reversed cyclic loading. Within the crack driving force range studied, cyclic crack growth data obeyed a power law dependency on the cyclic strain energy release rate. The response of the various material systems is compared to crack growth under static loading. The importance of the data re duction scheme for the crack growth resistance is discussed. Friction is examined as a potential energy absorbing mechanism in the test by finite element analysis. Suggestions for appropriate experimental geometries minimizing frictional effects are presented. Finally, fatigue fracture surfaces are analyzed with scanning electron microscopy to identify crack growth mechanisms.

Interlaminar Fatigue Crack Growth in Random Short-Fiber SMC Composite

The interlaminar fatigue crack growth behavior in a random short-fiber SMC-R50 com posite is studied. Experiments were conducted on double-cantilever-beam (DCB) composite specimens under displacement-controlled cyclic loading. Owing to large defor mation experienced in the specimen, a geometrically nonlinear fracture mechanics analy sis is employed to evaluate the associated cyclic strain energy release rate during crack propagation. The effect of mean nominal stress on interlaminar fatigue crack growth is studied. The fatigue crack growth behavior in the composite with different thicknesses and orientations is also examined. For the SMC composite studied, the interlaminar fatigue crack growth rate is found to follow a power-law relationship with the cyclic strain energy release rate. The value of the exponent in the power-law expression is much higher than those obtained for in-plane fatigue crack growth in the same composite and for the homog eneous neat resin. The significant effect of mean nominal stress on the interlaminar fatigue crack growth rate is appreciable and can be accounted for by proper modification of the power-law crack-growth expression. The influence of composite thickness on the inter laminar fatigue crack growth rate is noted, but the specimen orientation effect is negligi ble.