A numerical method for a void–crack interaction under cyclic loads

This paper presents a numerical method to model a general system containing cracks and voids in an infinite elastic plate under remote cyclic loads. By extending Bueckner’s principle suited for a crack to a general system containing cracks and voids, the original problem is divided into a homogeneous problem (the one without cracks and voids) subjected to remote loads and a void-crack problem in an unloaded body with applied tractions on the surfaces of cracks and voids. Thus, the results in terms of the stress intensity factors can be calculated by considering the latter problem, which is analyzed easily by using the hybrid displacement discontinuity method (a boundary element method). Further, a fatigue growth technique of a mixed-mode crack is combined with the numerical approach to simulating a void–crack interaction problem under cyclic loads. Test examples are included to illustrate that the numerical method is very simple and effective for analyzing a void–crack interaction problem.     

Short and long-term cracking behaviour of GFRP reinforced concrete beams

A total of ten simply supported beams reinforced with different amounts of GFRP and steel bars were subjected to two consecutive test phases in order to evaluate their short and long-term cracking behaviour. The beams were initially tested up to service load and subjected to two additional load cycles. Subsequently, the specimens were subjected to two different levels of sustained load for 250 days. The effect of cyclic load during short-term tests resulted in an increase in crack width up to 25% more than the initial value. The sustained load led to an increase in crack width up to 2.9 times larger than that measured under the corresponding short-term load. A similar cracking behaviour was observed when reinforcing solutions with similar stiffness (GFRP or steel bars) were used.Existing models to estimate crack spacing and crack width for FRP and steel reinforced concrete elements, including ACI 440.1R-06, Eurocode 2 and Model Code 2010 are discussed and their performance is assessed against the experimental results. Model Code 2010 was found to yield more accurate predictions of the cracking behaviour of the test specimens under both short-term and long-term loading.     

Cyclic fatigue of ceramics

The fatigue behaviour of alumina, zirconia-toughened alumina (ZTA) and tetragonal zirconia (TZP) have been investigated using three different techniques. Direct push-pull testing has been used to generate both static and cyclic fatigue data. The results clearly show that all the materials studied are susceptible to both static and cyclic fatigue, and that the times to failure under cyclic loading are considerably shorter than under static loads. The fatigue failure origins have been identified and the influence of surface condition on fatigue life has been assessed. The slow propagation of cracks subject to cyclic tensile and compressive loads has been studied using compact tension specimens and tapered double cantilever beam specimens. These investigations have confirmed the existence of cyclic fatigue effects in coarse-grained alumina and have shown the crack increment per cycle (da/dN) to have a power-law dependence on the peak stress intensity factor. A technique, based on repeated indentation, has been used to investigate the propagation of sub-surface cracks subjected to cyclic loading in both fine-grained alumina and ZTA. The results of the investigation suggest that compressive or closure loads on the crack faces are factors which affect the cyclic fatigue crack growth in ceramics. Based on those observations, an explanation is proposed for the mechanical cyclic fatigue effects in the ceramics investigated.     

Delamination growth mechanisms in woven glass fiber reinforced polymer composites under Mode II fatigue loading at cryogenic temperatures

The purpose of this research is to characterize the cryogenic delamination growth behavior in woven glass fiber reinforced polymer (GFRP) composite laminates subjected to Mode II fatigue loading. Mode II fatigue delamination tests were performed at room temperature, liquid nitrogen temperature (77 K) and liquid helium temperature (4 K) using the four-point bend end-notched flexure (4ENF) test method, and the delamination growth rate data for the woven GFRP laminates were obtained. The energy release rate range was determined by the finite element method. Microscopic examinations of the specimen sections and fracture surfaces were also carried out. The present results are discussed to obtain an understanding of the fatigue delamination growth mechanisms in the woven GFRP laminates under Mode II loading at cryogenic temperatures.     

Numerical evaluation of the retrofit effectiveness for GFRP retrofitted concrete slab subjected to blast pressure

For retrofitting structures against blast loads, sufficient ductility and strength should be provided by using high-performance materials such as fiber reinforced polymer (FRP) composites. The effectiveness of retrofit materials needs to be precisely evaluated for the retrofitting design based on the dynamic material responses under blast loads. In this study, refined FEM analysis with high-strain rate dependent material model and debonding failure model is conducted for evaluating the FRP retrofitting effectiveness. The structural behavior of reinforced concrete (RC) slab retrofitted with glass fiber reinforced polymer (GFRP) under blast pressure is simulated and the analysis results are verified with the previous experimental results.     

A probabilistic approach for transverse crack evolution in a composite laminate under variable amplitude cyclic loading

This paper presents a theoretical approach for predicting transverse cracking behavior in a cross-ply laminate with a thick transverse ply under variable amplitude loads for which the cracks grow instantaneously, or very quickly, across the specimen width. The transverse crack density was derived on the basis of the slow crack growth (SCG) concept using the Paris law in conjunction with the Weibull distribution for a brittle material subjected to multi-stage cyclic loading. A fracture criterion obtained was related with the empirical rules by Miner and Broutman & Sahu. Next, the probabilistic SCG model was applied to transverse cracking in a cross-ply laminate under multi-stage cyclic loading. The two-stage fatigue tests with various loading sequences and amplitudes were conducted for carbon fibre reinforced plastic (CFRP) cross-ply laminates in addition to single-stage fatigue tests for various maximum stresses. The experiment results were compared with the predictions to verify the validity of the model.     

Damage performance of particles filled quasi-isotropic glass–fibre reinforced polyester resin composites

The purpose of this work was to determine the toughening mechanisms in interlayered quasi-isotropic glass–fibre reinforced polyester resin (GFRP) composites. Particles of polyethylene and aluminium tri-hydrate, Al(OH)3, were mixed with the polyester resin prior to laminating with woven E-glass-fibre cloth. Mode-I, mode-II, and impact tests were performed to determine critical strain energy-release rates (GIc and GIIc), absorbed energy and residual compressive strength for the laminates with and without particulate additions. Mode-I and mode-II delamination toughness were characterized using double cantilever beam (DCB) and end-notched flexure (ENF) specimens, respectively, and the delaminated surfaces of specimens were examined using scanning electron microscopy (SEM) to investigate the interlaminar morphology after fracture. The results indicate that the interlaminar toughness (GIc and GIIc), absorbed energy and residual compressive strength values of the GFRP composite increases with increase of particle content. The improved behaviour of particle containing GFRP is linked to stress-concentration induced plastic deformation and crack bridging. Polyethylene particles increase the toughness of the matrix material, which results in composites with higher values of mode-I, mode-II and impact than the composites with aluminium tri-hydrate particles. © 1998 Chapman & Hall     

The effect of residual stresses arising from laser shock peening on fatigue crack growth

Residual stresses have in the past been introduced to manipulate growth rates and shapes of cracks under cyclic loads. Previously, the effectiveness of shot peening in retarding the rate of fatigue crack growth was experimentally studied. It was shown that the compressive residual stresses arising from the shot peening process can affect the rate of crack growth. Laser shock peening can produce a deeper compressive stress field near the surface than shot peening. This advantage makes this technique desirable for the manipulation of crack growth rates. This paper describes an experimental program that was carried out to establish this effect in which steel specimens were partially laser peened and subsequently subjected to cyclic loading to grow fatigue cracks. The residual stress fields generated by the laser shock peening process were measured using the neutron diffraction technique. A state of compressive stress was found near the surface and tensile stresses were measured in the mid-thickness of the specimens. Growth rates of the cracks were observed to be more affected by the tensile core than by the compressive surface stresses.     

Mechanical behaviour of glass and carbon fibre reinforced composites at varying strain rates

The choice of composite materials as a substitute for metallic materials in technological applications is becoming more pronounced especially due to the great weight savings these materials offer. In many of these practical situations, the structures are prone to high impact loads. Material and structural response vary significantly under impact loading conditions as compared to quasi-static loading. The strain rate sensitivity of both carbon fibre reinforced polymer (CFRP) and glass fibre reinforced polymer (GFRP) are studied by testing a single laminate configuration, viz. cross-ply [0°/90°] polymer matrix composites (PMC) at strain rates of 10⁻³ and 450 s⁻¹. The compressive material properties are determined by testing both laminate systems, viz. CFRP and GFRP at low to high strain rates. The laminates were fabricated from 48 layers of cross-ply carbon fibre and glass fibre epoxy. Dynamic test results were compared with static compression test carried out on specimens with the same dimensions. Preliminary compressive stress–strain vs. strain rates data obtained show that the dynamic material strength for GFRP increases with increasing strain rates. The strain to failure for both CFRP and GFRP is seen to decrease with increasing strain rate.     

Bond behavior and interface modeling of reinforced high-performance fiber-reinforced cementitious composites

High-performance fiber-reinforced cementitious-composites (HPFRCCs) reinforced with mild steel reinforcing bars have bond strengths that are higher than ordinary concrete under monotonic loading conditions. High bond strengths in HPFRCCs have been attributed to the material toughness of HPFRCCs, which effectively restrains splitting cracks under monotonic loads. Characterization of the interface between HPFRCCs and mild reinforcement under cyclic loads remains largely unknown. The bond-slip behavior of two HPFRCC mixtures are examined under monotonic and cyclic loads in beam-end flexural specimens. Bond strength is shown to deteriorate due to cyclic load reversals after the maximum bond stress is reached, resulting in lower bond-slip toughness. Three dimensional computational simulations are conducted to investigate observed crack patterns and internal deformations at the interface of the HPFRCC and steel reinforcement. Numerical simulation results predicted splitting crack patterns observed in physical experiments, and also suggest that interface crushing occurs at the intersection of the reinforcement lugs and HPFRCC material. Further, simulated performance shows that damage to the bond interface is altered by the deformation history applied to the interface.     

Fatigue analysis of concrete bridge deck slabs reinforced with E-glass/vinyl ester FRP reinforcing bars

FRP composites have been widely used as internal reinforcement for concrete bridge deck slabs. However, experimental researches on the behavior of such FRP-reinforced elements in general have been limited, especially those on fatigue performance. This research is designed to investigate the fatigue behavior of concrete bridge deck slabs reinforced with GFRP bars. A total of six full-size deck slabs were constructed and tested under concentrated cyclic loading conditions. Different reinforcement types, ratios, and configurations were used. Also, different schemes of cyclic loading were applied till failure. Finite element modeling was used to investigate the effect of different parameters on the ultimate static capacity. The results showed the superior fatigue performance and longer fatigue life of concrete bridge deck slabs reinforced with GFRP composite bars compared to the steel reinforced ones.     

基于失效评定图(FAD)研究含疲劳裂纹T型圆钢管节点的安全性

失效评定曲线(FAD)常用来评价焊接结构在出现裂纹后的安全性,为了验证这种曲线在评价焊接管结构在节点部位出现疲劳裂纹后安全性的适用性,采用实验测试和有限元分析的方法研究了3个含疲劳裂纹的T型管节点试件在静力作用下的极限承载能力及破坏过程。3个T型管节点试件首先进行疲劳实验在焊趾处产生表面裂纹,然后通过在支管端部施加轴向拉力作用检测节点的破坏过程。基于自行开发的含表面裂纹T型管节点的有限元网格自动产生程序以及ABAQUS分析软件,研究了在管节点破坏过程中表面裂纹最深点的应力强度因子大小,并通过实验的荷载-位移曲线确定了T节点试件的塑性极限承载力。在这些结果的基础上,验证了FAD在评价含疲劳裂纹的焊接管节点安全性方面的适用性。研究结果标明：FAD在评价含疲劳裂纹管节点的安全性方面是安全可靠的,但偏于保守。     

FATIGUE CRACK GROWTH IN DUCTILE MATERIALS UNDER CYCLIC COMPRESSIVE LOADING

Abstract— Mode I fatigue crack growth has been studied in notched specimens of 7017-T651 aluminium alloy subjected to fully compressive cyclic loads. The specimens were first subjected to a deliberate compressive preload which causes plastic deformation at the notch tip. On unloading, this region developed a residual tensile stress field and on subsequent compressive cyclic loading in laboratory air, a fatigue crack was nucleated at the notch and grew at a diminishing rate until it stopped. The final crack length increased with an increase in the value of the initial compressive preload and with an increase in the negative value of the applied cyclic mean load. To gain a better understanding of crack growth in residual stress fields, the magnitude and extent of residual stress induced from compressive preloads have been analysed. This was achieved when extending the notch by cutting while recording the change in the back face strain. From residual strain models it was found that the fatigue crack growth was confined to a region of tensile cyclic stress within the residual stress field. The effective stress intensity range was investigated at selected mean loads and amplitudes, for correlating purposes, using both the compliance technique and by invoking the crack growth rate behaviour of the alloy. Finally, a brief discussion of the fracture morphology of cracks subjected to cyclic compression is presented.     

Experimental study of FRP-strengthened RC bridge girders subjected to fatigue loading

The practical application of composite materials for retrofitting of reinforced concrete bridge T-sectional girders was investigated. Carbon and glass fibre-reinforced polymers (CFRP and GFRP) saturated in an epoxy resin matrix were used to enhance the service load-carrying capacity of the bridge. Three 5-m-long simply supported beams were tested under monotonic and cyclic loads for comparison to a beam subjected to more than 10⁶ cycles in the service load range. The results show that an FRP-strengthened T-beam subjected to fatigue loading demonstrated excellent behaviour that can be expected from well-detailed retrofit schemes incorporating carbon and glass fibre laminates.     

Fracture stability and residual strength assessment of reinforced concrete beams

In conventional analysis and design procedures of reinforced concrete structures, the ability of concrete to resist tension is neglected. Under cyclic loading, the tension-softening behavior of concrete influences its residual strength and subsequent crack propagation. The stability and the residual strength of a cracked reinforced concrete member under fatigue loading, depends on a number of factors such as, reinforcement ratio, specimen size, grade of concrete, fracture properties, and on the tension-softening behavior of concrete. In this work, a method is proposed to assess the residual strength of reinforced concrete beams subjected to cyclic loading. The crack extension resistance based approach is used for determining the condition for unstable crack propagation. The effect of reinforcement is modeled as a closing force counteracting the effect of crack opening produced by the external moment. The effect of percentage reinforcement and specimen size on the failure of reinforced beams is studied. Finally, the residual strength of the beams are computed by including the softening behavior of concrete.     

Some computational tools for the analysis of through cracks in stiffened fuselage shells

Reliable analytical methods that predict the structural integrity and residual strength of aircraft fuselage structures containing cracks are needed to help to understand the behavior of pressurized stiffened shells with damage, so that it becomes possible to determine the safe life of such a shell. Of special importance is the ability to determine under what conditions local failure, once initiated, will propagate. In this paper we shall present a reliable and efficient method for computing the energy release rate for cracks of varying length in a typical stiffened metallic fuselage under general loading conditions. The models used in the simulation are derived from an extensive analysis of a fuselage barrel section subjected to operational flight loads. Energy release rates are computed as a function of the length of the crack, its location, and the crack propagation mode.     

An investigation of brittle fracture of composite insulator rods in an acid environment with either static or cyclic loading

The effect of static and cyclic loading conditions on the stress corrosion cracking of unidirectional glass reinforced polymer (GRP) rods used in composite high voltage insulator has been investigated. A series of stress corrosion experiments have been performed on unidirectional E-glass/modified polyester composite rods. The rods have been subjected to mechanical tensile static and cyclic stresses in the presence of a nitric acid solution. The stress corrosion fracture process in the rods was monitored using acoustic emission techniques. The experimental loading conditions simulated possible in-service loadis for composite suspension insulators. The results obtained in this study showed that the brittle fracture process can be generated in the rods when subjected to relatively low tensile stresses in the presence of a nitric acid solution. The morphology of the experimentally generated brittle fracture cracks in the rods closely resemble those from in-service failed composite suspension. It has also been shown in this research that low frequency, low amplitude vibrations in tensile loads can significantly accelerate the fracture process. It appears that the brittle fracture cracks in the rods generated under cyclic loads are less planar in nature in comparison with the cracks formed under static conditions. It has also been found that the acoustic emission generated during the stress corrosion fracture process in the rods is sensitive to the placement of the transducers. However, reasonably good correlation between the stress corrosion crack growth rates and acoustic emission has been attained.     

Early-age restrained shrinkage cracking of GFRP-RC bridge deck slabs: Effect of environmental conditions

Most of codes and guidelines for glass fiber reinforced polymers (GFRP) - Reinforced Concrete (RC) are based on modifying corresponding formulas, originally developed for steel bars, taking into account the differences in properties and behavior between FRP and steel. The main objective of this research is to investigate the effect of cyclic environments on early-age cracking of GFRP-RC bridge deck slabs experimentally. Two full-scale (measuring 2500-mm long × 765-mm wide × 180-mm thick) cast-in-place slabs reinforced with similar amounts of reinforcement ratio of 0.7% with GFRP and steel bars, respectively, were tested in adiabatic laboratory conditions as control specimens. In comparison, two other GFRP-RC deck slabs were tested under freezing–thawing and wetting–drying conditions. The test results are presented in terms of materials degradation, cracking pattern, crack width, and spacing, and strains in reinforcement and concrete. Test results indicate that the minimum reinforcement ratio (0.7%) recommended by the Canadian Highway Bridge Design Code 2006 (CHBDC 2006) for bridge deck slabs reinforced with GFRP bars satisfied the serviceability requirements after being subjected to the simulated cyclic exposures.     

Predicting failure of composite structures containing cracks

The ability to predict failure loads in composite structures containing through-the-thickness cracks is a requirement in a variety of structural design circumstances. The objective of this study was to develop a practical computational technique that simulates progressive damage growth in the vicinity of the crack tip in a manner that allows the prediction of failure over a wide range of crack sizes. This was accomplished through the use of the discrete crack model with a general purpose finite element program. Calculations were performed for two different laminates with various crack sizes under tensile loading. An analysis was also performed on a section of a composite aircraft fuselage containing a crack and subjected to internal pressure loading. Reasonably good agreement was found between the calculations and the results from tests.