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A probabilistic fatigue life prediction framework for concrete bridges is proposed in this study that considers the stress history from the construction stage to the operation stage. The proposed fatigue analysis framework combines the fatigue crack growth-based material life prediction model and a nonlinear structural analysis method. A reliability analysis is proposed using the developed probabilistic model to consider various uncertainties associated with the fatigue damage. A Bayesian network is established to predict the fatigue life of a concrete bridge according to the proposed framework. The proposed methodology is demonstrated using an experimental example for fatigue life prediction of a concrete box-girder. Comparison with experimental data of fatigue life shows a satisfactory accuracy using the proposed methodology, and the ratio of the posterior predicted mean (updating time n = 8) to the test value decreases to 33%–1% in the current investigation.

A critical plane-based mixed-mode delamination growth model for composite materials under fatigue loadings is proposed in this study. A brief review for mixed-mode delamination is given and the special focus in the study is on a critical plane-based fracture criterion since it can automatically adapt for different local failure modes. An equivalent energy release rate range suitable for fatigue analysis is proposed for the delamination growth rate prediction under general proportional and non-proportional multiaxial loadings. The proposed methodology is validated with extensive experimental data available in the open literature. A general good agreement is observed between model predictions and experimental observations. Finally, some discussion and conclusions are drawn based on the proposed model.

Submersibles and submarines are subject to cyclic compressive sea loading during their service life, which is quite different from the ships and platforms under tensile and bending loading. It is important to study the fatigue crack propagation under cyclic compression in order to assess the fatigue life of the submersible and submarine. An extended McEvily model is proposed for the fatigue crack growth prediction under cyclic compression-compression loading. First, Finite Element Method (FEM) simulation and a simplified stress estimation method are proposed for efficient fatigue crack growth analysis. In the Finite Element Method simulation, the crack opening loads of different crack lengths are calculated individually instead of plastic wake calculation behind crack tip with node releasing technique, which will save a lot of calculating time. Afterwards the fatigue life under cyclic compression is predicted based on new fatigue crack growth rate curve model for cyclic compression. Meanwhile the analytical method is an engineering estimation for fatigue crack growth under constant amplitude compression. In this method, the crack opening load is estimated based on the symmetry of compression and tension. Then the fatigue life under cyclic compression is also predicted based on a new model for cyclic compression. Finally, fatigue life prediction of a double edged specimen under cyclic compressive loading is taken for example to illustrate the analysis procedure of two simplified methods. By comparing the predicted results with the test data, it is found that the a-N curve and final crack length by two methods are in good agreement with the test data, so the Finite Element Method and analytical method are reasonable and feasible for fatigue crack growth prediction of deepwater structure under cyclic compression.

A 3D finite element model (FEM) with realistic field measurements of temperature distributions is proposed to investigate the thermal stress variation in the steel–concrete composite bridge deck system. First, a brief literature review indicates that traditional thermal stress calculation in suspension bridges is based on the 2D plane structure with simplified temperature profiles on bridges. Thus, a 3D FEM is proposed for accurate stress analysis. The focus is on the incorporation of full field arbitrary temperature profile for the stress analysis. Following this, the effect of realistic temperature distribution on the structure is investigated in detail and an example using field measurements of Aizhai Bridge is integrated with the proposed 3D FEM model. Parametric studies are used to illustrate the effect of different parameters on the thermal stress distribution in the bridge structure. Next, the discussion and comparison of the proposed methodology and simplified calculation method in the standard is given. The calculation difference and their potential impact on the structure are shown in detail. Finally, some conclusions and recommendations for future bridge analysis and design are given based on the proposed study.

An experimental study is proposed to investigate the high-cycle fatigue behavior of prestressed concrete box-girders. Special focus is on the shear diagonal cracks in the webs of girders, which is rarely investigated in the open literature. Laboratory fatigue tests were designed and conducted to study the propagation of shear diagonal crack of PC box-girder specimens under cyclic loadings. The development of stirrup strain, propagation characteristics of diagonal crack and the related factors are discussed in detail. A finite element (FE) model for concrete damage of PC box girder under high-cycle fatigue loading is established to investigate the crack propagation behavior. Following this, a model for the calculation of diagonal crack widths of PC box-girder under fatigue loading is proposed based on the experimental observations. The calculation results are compared with experimental data for validation. It is observed that the maximum stirrup strain in crack zone increases 67.9% based on this investigation. The ratio of displacement during the last cycle and that during initial loading can research 40.3% in the current investigation. Finally, several conclusions are drawn based on the proposed study.

To assess fatigue damage accumulation for civil infrastructure, Miner’s rule or linear elastic fracture mechanics (LEFM) are usually used in many codes and specifications. However, large uncertainties are found when the short cracks are initiated. Currently, most physics-based models for crack initiation are built for constant amplitude loads (CA). Since the environmental or service load-induced stresses at local details for crack initiation are time-variant, these physics-based models could not be directly applied for real civil infrastructure. In this paper, a two-fold nonlinear grain-based fatigue damage model is proposed to process the variable amplitude loads (VA) induced fatigue damages by combining Persistent Slip Band (PSB)-based short fatigue crack model and grain-based Miner’s rule. In the sub-grain regime, linear damage accumulation is adopted. For the repeated stress blocks with variable amplitude, the stress block is rain-flow counted and the damage accumulation is modeled as short crack extension. Therefore, the crack associated damage will be accumulated grain by grain until it reaches characteristic length of a long crack. The damage accumulation from a stress block is added for each grain. Effect from subcritical loads is also considered in this damage accumulative model. Finally, a numerical demonstration is performed on statistical representative elements under variable stress histories from a long span bridge.

Traditionally, the fatigue damage assessment of steel bridges is conducted using cycle-based methods. Cycle-based methods require stress time history be transformed to cycle history first before fatigue analysis can be performed. However, well-defined cycle history does not exist for the traffic-induced stress time history of bridges as it contains numerous large and small cycles with random stress ranges embedded together. To address this inherent difficulty, a time-based fatigue crack growth (FCG) model is proposed for fatigue damage prognosis of steel bridges under traffic loading. The time-based FCG method describes the crack growth in the time domain through a crack growth kinetics function derived based on the physical mechanism of fatigue crack propagation. To demonstrate the proposed method, numerical simulations are first performed using full-scale coupled vehicle-bridge interaction framework to generate stress time histories of a typical steel bridge under traffic loading. Then, FCG analysis is performed using the time-based method and the effects of road surface roughness and vehicle weight on the FCG are studied. Finally, a case study on the I-10 Twin Span Bridge is presented to demonstrate the time-based FCG method for fatigue damage prognosis using in situ monitoring data. The results show that the proposed method can be used to directly predict the FCG of steel bridges in the time domain using stress time histories obtained either from stress analysis or in situ monitoring.

A time-based subcycle fatigue crack growth (FCG) formulation and validation are proposed to calculate the fatigue crack growth under general random variable amplitude loadings. The intrinsic difficulties of the classical cycle-based formulation for general random variable loadings are discussed first. Several typical spectrums that are not appropriate for cycle-based FCG are illustrated, such as the “Christmas tree” spectrums. A time-based subcycle formulation is then proposed to address this difficulty. The proposed model includes three major component: (1) a time-based crack growth kinetics function at the subcycle (time) scale; (2) an efficient crack tip opening displacement (CTOD) estimation method; (3) a crack tip plasticity zone tracking algorithms for crack opening level determination of a growing crack. Detailed derivation and calculation procedures are given. Following this, several numerical examples are illustrated for the proposed model under different loading spectrums for the crack growth and CTOD calculation. Randomly generated loading spectrums are used to illustrate the capability of the proposed method under arbitrary loadings. Next, in-house testing for “Christmas tree spectrum” and literature data on several representative variable loading spectrums are used for model validation. Finally, some conclusions and future work are drawn based on the proposed study.

An experimental testing procedure is proposed for generating creep-dominant creep-fatigue interaction in Alloy 617 at 950 °C. Most experimental studies on Alloy 617 at elevated temperatures employ a purely strain-controlled loading waveform with a tensile hold period. Strain-controlled loading can only generate interaction in the fatigue-dominant regime of the damage interaction diagram, due to the saturation effect of increasing hold time on cycle life. This saturation is caused by the rapid stress relaxation of Alloy 617 at high temperatures. Design codes for components undergoing creep-fatigue interaction at high temperatures require creep-fatigue testing data in the creep-dominant regime. This study investigates multiple creep-fatigue loading waveforms with the objective of producing creep-dominant interaction. The custom loading waveforms are implemented on a servo-hydraulic load frame with a furnace. A hybrid-control scheme with strain-controlled ramps and load-controlled hold periods is proposed due to its flexibility in generating varying proportions of creep and fatigue damage. Experimental data is presented and different loading schemes are compared. Special emphasis is on the creep and fatigue damage contributions by the newly proposed testing method. Several conclusions are discussed and an extension of this current work is suggested to improve the damage interaction diagram for design purposes.

A new critical plane-energy model is proposed in this paper for multiaxial fatigue life prediction of metals. A brief review of existing methods, especially on the critical plane-based and energy-based methods, is given first. Special focus is on the Liu–Mahadevan critical plane approach, which has been shown to work for both brittle and ductile metals. One potential drawback of the Liu–Mahadevan model is that it needs an empirical calibration parameter for non-proportional multiaxial loadings because only the strain terms are used and the out-of-phase hardening cannot be explicitly considered. An energy-based model using the Liu–Mahadevan concept is proposed with the help of the Mroz–Garud plasticity model. Thus, the empirical calibration for non-proportional loading is not needed because the out-of-phase hardening is naturally included in the stress calculation. The model predictions are compared with experimental data from open literature, and the proposed model is shown to work for both proportional and non-proportional multiaxial loadings without the empirical calibration.

An experimental test is performed to investigate the flexural behavior of bonded post-tensioned concrete beams under strand corrosion. Eight beams are designed and subjected to accelerated method to different corrosion levels. The initial stiffness of beams is observed by cyclic loading-unloading test during the corrosion procedure. Corrosion effects on concrete cracking, post-cracking stiffness, ultimate strength, failure mode and ductility are then clarified by the flexural test. And, a coefficient is introduced to quantify the incompatible strain between corroded strand and concrete. Results show that the prestress force loss of strand has almost the linear relation with corrosion loss. Strand corrosion affects slightly the initial stiffness of beam before flexural cracking, but degrades significantly the post-cracking stiffness of beam as the corrosion loss exceeds 27.0%. Slight corrosion of strand has little effects on beams flexural behavior. The severe corrosion, however, decreases the number of crack, changes the failure mode form the concrete crushing to strand rupture, degrades the ductility and the ultimate strength of beams, and leads to the incompatible strain between strand and concrete. In the present test, the incompatible strain decreases about 20% of the flexural strength as the corrosion loss exceeds 27.0%.

An analysis model is proposed in the present study to predict the failure of corroded prestressed concrete (PC) beams under flexural load. The corrosion induced strand section loss, material deterioration and bond degradation are considered in the proposed model. The bond degradation is treated as a function of corrosion loss. The slip region caused by bond deterioration is determined by comparing the effective bond force and tension force of strand. And then, a strain-incompatibility analysis method is developed to calculate the flexural strength of beams. The proposed model is verified by experimental tests on corroded post-tensioned concrete beams. Results show that the bond degradation induced incompatible strain is important and should be considered into the flexural strength prediction. The proposed model provides an effective way to measure the incompatible strain and a reasonable prediction for flexural strength of beams. The incompatible strain depends on the corrosion loss and applied load levels. Corrosion loss

Strand corrosion within the insufficient grouted duct has become a serious problem affecting the durability of bridge structures. The residual flexural behavior of the locally ungrouted post-tensioned concrete beams after strand corrosion is investigated in the present study. Two experiments are performed: corroded strand test for the constitutive law development and beam test for the flexural behavior investigation. An analytical model is proposed to predict the ultimate strength, the deformation, and the strain response of corroded beams under external loadings. The proposed model considers the strain compatibility between strand and concrete, material mechanics deterioration of strand, and the asymmetric deflection due to local corrosion in ungrouted duct. The accuracy of the model is verified by the experimental observations. Results show that corrosion loss has less effect on the yield strength and elastic modulus than that on the ultimate strain of strand. It is also observed that light corrosion has little effect on the beam cracking and the load-deflection behavior before beam cracking. Severe corrosion degrades significantly the flexural capacity and the local post-cracking stiffness of beams, which leads to the asymmetric deformation and crack formation.

Alloy 617 is a primary candidate material to be used in the next generation of nuclear power plants. Structural materials for these plants are expected to undergo creep and fatigue at temperatures as high as 950 °C. This study uses a hybrid-control creep-fatigue loading profile, as opposed to the traditional strain-controlled loading, to generate creep dominated failure. Qualitative and quantitative image analysis through SEM, EDS, and EBSD, is used to show that hybrid control testing is capable of producing creep dominated failure and that time fraction approach is not a valid indicator of creep or fatigue dominated damage. The focus of image analysis is on surface fatigue cracks and internal creep voids. A creep-fatigue damage interaction diagram based on these micro-scale features is plotted. It is shown that the classical time fraction approach suggested by the ASME code does not agree with the experimental findings and has a poor correlation with observed microscale damage features. A new definition of creep damage fraction based on an effective hold time is found to correlate well with the micro-scale image analysis.

A new fatigue reliability assessment function which takes into account the vehicle and temperature loadings has been developed in this study. The vehicle and temperature loadings are important parameters as they can cause fatigue failure of the welds in a steel box girder. The temperature affects the traffic loading effect by changing the elastic modulus of asphalt pavement. The effect of the temperature difference has been considered based on the measured data and the finite element analysis. Linear regression equations between the equivalent stress and the temperature for different vehicle types have been developed. Using the thermal stress analysis and the rain-flow counting method, the temperature difference fatigue stress spectrum has been determined. Further, a limit equation for the fatigue reliability assessment, which takes into account both the vehicle and temperature loadings, has been developed. Finally, the effects of the temperature and the traffic growth rate on the fatigue reliability of two welding types of Nan-xi Yangtze River Suspension Bridge have been assessed.

A new energy-based fatigue life prediction model is proposed for arbitrary multiaxial constant loadings in this paper. First, a brief review for existing multiaxial fatigue models is given, especially focusing on energy-based models. It is observed that most multiaxial model formulation and validation are suitable for axial-torsional loadings, but may not be appropriate for biaxial tension-tension loading. One possible reason is the ignorance of hydrostatic stress-state difference under these two types of loadings. In view of this, a new model is proposed by including fatigue damage contributions of equivalent tensile energy, torsional energy, and hydrostatic energy. Next, a loading transformation is proposed to transfer a complicated three-dimensional loading to an effective loading for life prediction. Detailed discussion of different types of multiaxial loading and its relationship with the ratio of distortional energy and dilatational energy is given. The hysteresis energy can be calculated integrating the proposed model with the Garud cyclic plastic model, which is directly linked to the damage accumulation and fatigue life prediction. The proposed model is validated with extensive experimental data under both tension-torsion loadings and biaxial tension-tension loadings from open literature. Comparison with several widely used multiaxial model is also given to show the model performance with respect to different biaxial tension-tension loadings. Finally, concluding remarks and future work based on the investigated materials are discussed.

In the proposed study, the Linguo continuous rigid frame bridge was studied to determine the failure mechanisms combining both field investigation and a 3D finite element (FE) method. The characteristics of the failure on the bottom plate were analysed and three typical failure models are identified. The failure mechanism was investigated and verified using a proposed 3D nonlinear FE model. Retrofit methods are proposed and implemented for the damaged bridges. The measured stress response and calculated stress response from the proposed 3D finite element model are compared. Satisfactory results are observed between field measurements and numerical simulations. Parametric studies are performed using the developed model to investigate several important parameters for the bridge design and construction. Finally, conclusions and recommendations for future bridge analysis and design were provided on the basis of the proposed study.

A novel nonlocal discrete model is proposed in this paper to study the deformation and failure behaviors of cross-ply laminated composite plate under static or quasi-static mechanical loadings. Different from existing numerical approaches, the proposed model accounts for the material anisotropy at both constitutive and structural level. To achieve this purpose, the proposed model rotates the underlying topological structure, rather than transforming the material’s tangent stiffness matrix as in the continuum-based simulations. Thus, different failure behaviors can be modeled as the natural outcome of the breakage of connecting springs. The proposed model is verified and validated by comparing the simulation results with analytical solution and experimental observations from open literature.

A novel nonlocal lattice particle model for fracture simulation of anisotropic materials is proposed. The key idea is to handle material anisotropy by rotating topological lattice structure rather than transforming material stiffness matrix. One major advantage of this model is that the crack path preference of anisotropic materials is naturally incorporated by underlying lattice structure. First, analytical derivation and formulation of the proposed model are given. The equivalency of lattice structure rotation and stiffness transformation is discussed. Following this, numerical examples are used to demonstrate the modeling capability of proposed methodology. Discussions and future work are given based on the current investigation.

An experimental study is proposed to investigate the shear behavior of corroded reinforced concrete (RC) beams with stirrups and inclined bars. The proposed study aims to address the effects of corrosion in the two types of shear reinforcement on the shear capacity deterioration of RC beams with low shear span-to-effective depth ratio. The accelerated corrosion test is employed to obtain different corrosion levels in stirrups and inclined bars in fourteen RC beams. The corrosion-induced concrete cracking and section damage is discussed in detail. The shear behavior including load-deformation response, residual shear strength, diagonal cracking and failure mode is presented. The shear strength of beams is predicted by a modified ACI approach considering the corrosion loss of shear reinforcement and concrete section damage. It is observed that the slight corrosion loss less than 10% in stirrups and inclined bars has little effect on the degradation of shear behavior. The severe corrosion of stirrups and inclined bars, and the accompanied concrete section damage decreases the shear strength and stiffness significantly. Corrosion of stirrups and inclined bars does not change the shear compression failure mode of beams. Severe corrosion does reduce the number of cracks in beams and lead to early rupture of shear reinforcement.

In this paper, a real-time composite fatigue life prognosis framework is proposed. The proposed methodology combines Bayesian inference, piezoelectric sensor measurements, and a mechanical stiffness degradation model for in-situ fatigue life prediction. First, the composites stiffness degradation is introduced to account for the composites fatigue damage accumulation under cyclic loadings and a new growth rate-based stiffness degradation model is developed. Following this, the general Bayesian updating-based fatigue life prediction method is discussed. Several sources of uncertainties and the developed stiffness degradation model are included in the prognosis framework. Next, an in-situ composites fatigue testing with piezoelectric sensors is designed and performed to collected sensor signal and the global stiffness data. Signal processing techniques are implemented to extract damage diagnosis features. The detected stiffness degradation is integrated in the Bayesian inference framework for the remaining useful life (RUL) prediction. Prognosis performance on experimental data is validated using prognostics metric. Finally, some conclusions and future work are drawn based on the proposed study.

A multiaxial fatigue life prediction model under general multiaxial random loadings is proposed in this paper. First, a brief review for existing multiaxial fatigue models is given with a special focus is on the Liu- Mahadevan critical plane concept, which can be applied to both brittle and ductile materials. Next, the new model development based on the Liu-Mahadevan critical plane concept for random loading is presented. The key concept is to use two-steps to identify the critical plane: identify the maximum damage plane due to normal stress and calculate the critical plane orientation with respect to the maximum damage plane due to normal stress. Multiaxial rain-flow cycle counting method with mean stress correction is used to estimate the damage on the critical plane. Equivalent stress transformation is proposed to convert the multiaxial random load spectrum to an equivalent constant amplitude spectrum. The equivalent stress is then used for fatigue life predictions. The proposed model is validated with both literature and in-house testing data generated using an Al 7075-T6 alloy under various random uniaxial and multiaxial spectrums. Comparison between experimental and predicted fatigue life lives shows good agreements; thus, demonstrating efficacy of the proposed model. Finally, concluding remarks and future work based on the results obtained are discussed.

A simple analytical model for calculating the vibration frequencies of anchor span strands in suspension bridges is proposed in this study. The vibration frequencies of strands are importan...

A new crack growth-based corrosion fatigue life prediction method for aging reinforced concrete beam is proposed in this paper. The proposed method couples the corrosion growth kinetics and fatigue crack growth kinetics together. The relationship between corrosion damage morphology and corrosion loss is investigated by the experimental results. A phenomenological model is proposed to obtain the stress concentration factor model under different corrosion loss conditions. Following this, the developed model is integrated with an asymptotic method to calculate the stress intensity factor for the crack at corrosion pit roots. The fatigue life is predicted by the integration of the fatigue crack growth rate curve from the equivalent initial flaw size to the critical length. Probabilistic analysis methodology is proposed to consider various sources of uncertainties for the fatigue life prediction. Fatigue life prediction results are validated with experimental observations for various corroded steel bars and beams available in the literatures.

A general framework for probabilistic prognosis and uncertainty management under fatigue cyclic loading is proposed in this article. First, the general idea using the Bayesian updating in prognosis is introduced. Several sources of uncertainties are discussed and included in the Bayesian updating framework. An equivalent stress level model is discussed for the mechanism-based fatigue crack growth analysis, which serves as the deterministic model for the lap joint fatigue life prognosis. Next, an in situ lap joint fatigue test with pre-installed piezoelectric sensors is designed and performed to collect experimental data. Signal processing techniques are used to extract damage features for crack length estimation. Following this, the proposed methodology is demonstrated using the experimental data under both constant and variable amplitude loadings. Finally, detailed discussion on validation metrics of the proposed prognosis algorithm is given. Several conclusions and future work are drawn based on the proposed study.

An integrated experimental and numerical investigation of fatigue damage diagnosis in composite plates is presented in this study. First, the fatigue testing setup for carbon–carbon composite coupons is described with corresponding health monitoring approach through Lamb wave–based diagnostic data collection. In order to study the effects of degradation evolution, a finite element model is used to simulate the effect on Lamb wave propagation due to fatigue-induced delamination and matrix cracking. Simulation results are compared with the experimental testing to first validate the model and then develop several features as potential damage indicators. A parametric study is conducted on the effects of varying degrees of delamination and matrix cracking on these features. Results from the model simulations are presented along with the data analysis and discussions on the capability and limitations of the approach. Finally, some conclusions are drawn and future work is proposed based on the results obtained so far.

A novel Volume-Compensated Particle model (VCPM) is proposed for the modeling of deformation and fracture in solids. In this proposed method, two potentials are introduced to model the interactions between material particles, i.e., a local pair-wise potential and a non-local multi-body potential. The local pair-wise potential is utilized to account for the constitutive relationship within the connecting bonds between particles while the non-local multi-body potential is employed for considering the volumetric effects under general mechanical loadings. The potential coefficients are determined by matching the potential energy stored in a discrete unit cell to the strain energy at the classical continuum level. A volume conservation scheme is proposed to model the plastic deformation. The validity of the proposed model is tested against the classical elasticity and elasto-plasticity benchmarks before its application to fracture problems. Several conclusions are drawn based on the proposed study.

In this paper, the multi-resolution in situ experiment, optical microscopy experiment and SEM experiment are used to investigate the existence of crack closure and its sufficiency for crack growth prediction. In situ optical microscopy testing and the digital image correlation analysis are used to measure the plastic zone size in front of the crack tip. In situ scanning electron microscopy testing is used to measure the crack tip opening displacement and crack growth kinetics. Crack closure behavior under constant loading with a single overload is studied under SEM. The experimental methodology is applied to two different metallic materials (aluminum alloys and steels). Detailed imaging analysis and experimental results are presented and compared. It is found that the crack closure phenomena exist for aluminum alloys, but not for steels in the current investigation. If the crack closure happens, it will significantly alter the crack tip plasticity behavior. Under constant amplitude loading, the crack closure concept is able to uniquely correlate the crack growth kinetics. However, under single overload loading, the crack closure is not able to uniquely correlate with the crack growth kinetics and statistical crack growth experiment also shows the inefficiency of crack closure. Finally, a discussion about the necessarily and the insufficiency of crack closure for crack growth prediction is given.

A new subcycle-based delamination growth model is proposed. The key idea is to model delamination growth at any time instant within a cyclic loading, rather than the cycle-averaged growth kinetics. First, some existing models are briefly reviewed for the fatigue delamination growth analysis of composite materials. Following this, two hypotheses are given for the derivation of the subcycle delamination growth model: (1) delamination growth does not happen during the unloading path and (2) delamination growth does not happen when the applied loading is below a reference level during the loading path. Mathematical expression is given for the calculation of delamination growth rate. Next, the extension of the proposed model is discussed to use both stress intensity factor and energy release rate as the driving force parameters, which are widely used in the open literature. Finally, the model predictions are compared with extensive experimental data under different stress ratios for model validation. One of the advantages of the proposed model is that the stress ratio dependent delamination growth can be predicted. Some conclusions and future work are drawn based on the proposed method.

An experimental study is proposed in this paper to investigate the effect of insufficient grouting and strand corrosion on flexural behavior of prestressed concrete (PC) beams. First, experimental design is discussed with different insufficient grouting conditions and the strand corrosion in ungrouted duct. Thirteen PC beams were designed and divided into two groups: five beams with different insufficient grouting conditions; eight beams subjected to accelerated corrosion to different strand corrosion levels. Next, experimental study was performed and the characteristic of strand corrosion in the PC beams with insufficient grouting is discussed using experimental observation. The influences of insufficient grouting including void and ungrouted length and position on flexural behavior are addressed. Following this, the flexural behavior deterioration induced by the combined effect of strand corrosion and insufficient grouting is analyzed. The experimental results show that the cracking behavior of beams is sensitive to the bond between strand and insufficient grout. The effect of no grouting on beam’s flexural behavior depends on its length and position. The strand corrosion in ungrouted duct can significantly decrease the ultimate strength of beam. The different levels of strand corrosion in ungrouted duct have different effects on the cracking behavior, the load–deflection curve, and the failure mode of beams.

In this paper, a multiaxial fatigue life prediction model is proposed under general multiaxial random loadings. First, a brief review for existing multiaxial fatigue models is given and special focus is on the LiuMahadevan critical plane concept, which can be applied to both brittle and ductile materials. Next, new model development based on the Liu-Mahadevan critical plane concept for random loading is presented. The key concept is to use two-steps to identify the critical plane: identify the maximum damage plane due to normal stress and calculate the critical plane orientation with respect to the maximum damage plane due to normal stress. Multiaxial rain-flow cycle counting method with mean stress correction is used to estimate the damage on the critical plane. Equivalent stress transformation is proposed to convert the multiaxial random load spectrum to an equivalent constant amplitude spectrum. The equivalent stress is used for fatigue life prediction. Following this, experimental design and testing is performed for Al 7075-T6 under various different random uniaxial and multiaxial spectrums. The developed model is validated with both literature and in-house testing data. Very good agreement is observed for the investigated material. Finally, conclusion and future work is given based on the proposed study.

A general methodology for probabilistic corrosion analysis of reinforcing bar in RC bridges is proposed in this paper. Uncertainties due to limited number of experimental data, incomplete inspection information, as well as the intrinsic randomness of random variables affect the prognostics of corrosion damage. The proposed study includes both fuzziness and randomness to consider different types of uncertainties. First, the chloride-induced corrosion initiation and propagation model are developed for reinforcement in RC bridge. The relationship between the area corrosion rate and the yield strength degradation is proposed on the basis of experimental investigation from accelerated corrosion testing. Following this, the randomness and fuzziness are included using fuzzy random variables to consider the uncertainties of the degradation under corrosive environments. The probabilistic modeling of the mean and the SD of reinforcement yield strength is discussed in detail. Finally, the proposed methodolog...

A probabilistic prediction framework of corrosion-induced strength degradation for flexural beams is proposed in this paper. The proposed framework considers both ductile and brittle failure modes of reinforcements. The area loss of steel bars is established considering the likelihood of corrosion types. Statistical data analysis is used to quantify the uncertainties of capacity variation of corroded reinforcing bars based on the experimental investigation of tensile tests of 452 corroded reinforcements from different members. Following this, the static tests on 48 beams are conducted, and the finite element method (FEM) is used to evaluate the effects of corrosion on carrying capacity. A probabilistic model to include the effect of inaccurate modeling of corrosion on the beam bearing capacity is developed. Area loss and strength degradation of corroded reinforcing bar, possible ductile and brittle failure of reinforcement and model uncertainty are incorporated into analysis of time-dependent strength degradation. Finally, a Bayesian updating methodology is proposed to update the prior belief of the uncertainties and the updated posterior distributions are used for probabilistic prediction using field inspection results. Three beams demolished from a 36-year old concrete bridge are used to demonstrate and to validate the overall procedure. The prediction combined with Bayesian updating provides a satisfactory result by comparing model predictions with realistic field inspection.

In this paper, an in situ scanning electron microscope (SEM) fatigue testing approach is proposed to investigate the crack closure phenomenon within one cyclic loading under plane stress conditions. One objective of this experimental study is to verify the existence and significance of crack closure by directly measuring the variation of crack tip opening displacement (CTOD) and evaluating the crack opening stress levels. During the testing, the loading cycle is divided into a certain number of levels. At each level, high resolution images are taken around the crack tip region by SEM. Following this, imaging analysis is used to process these images in order to quantify the crack tip behavior at any time instant. Four constant amplitude loading cases with different stress ratios are investigated. Crack closure phenomenon is directly observed and measured. A simple mechanical model (named virtual crack annealing model) is developed based on the in situ SEM testing observations. The calculated crack opening stress level is compared with experimental observations. A detailed discussion is given based on the current investigation to explain some well-known issues in the classical fatigue theory.

An analytical model is proposed in this paper to evaluate the residual flexural strength for corroded RC beams. The steel slipping caused by bond degradation is included in the proposed model. Various failure modes of beams caused by different types of steel bar anchorage are also incorporated in the model. The bond degradation is considered as a function of the corrosion rate of steel. Bond degradation transfers prematurely the effective bond force, resulting in incompatible strain within the slipping region. A new method is developed to quantify the slipping region based on the transfer theory of effective bond force. Next, a new strain-incompatibility analysis method is proposed to determine the deteriorated flexural strength. The accuracy of the model is validated by experimental observations on the beams with different steel anchorage under corrosive environments. Results show that the proposed model can provide a reasonable prediction for the flexural strength and failure modes. The strain i...

Structural health monitoring has been studied by a number of researchers as well as various industries to keep up with the increasing demand for preventive maintenance routines. This work presents a novel method for reconstruct prompt, informed strain/stress responses at the hot spots of the structures based on strain measurements at remote locations. The structural responses measured from usage monitoring system at available locations are decomposed into modal responses using empirical mode decomposition. Transformation equations based on finite element modeling are derived to extrapolate the modal responses from the measured locations to critical locations where direct sensor measurements are not available. Then, two numerical examples (a two-span beam and a 19956-degree of freedom simplified airfoil) are used to demonstrate the overall reconstruction method. Finally, the present work investigates the effectiveness and accuracy of the method through a set of experiments conducted on an aluminium alloy cantilever beam commonly used in air vehicle and spacecraft. The experiments collect the vibration strain signals of the beam via optical fiber sensors. Reconstruction results are compared with theoretical solutions and a detailed error analysis is also provided.

A general probabilistic fatigue-crack growth prediction methodology for accurate and efficient damage prognosis is proposed in this paper. The methodology is based on an equivalent stress transformation and the inverse first-order reliability method (IFORM). The equivalent stress transformation aims to transform the random variable amplitude loading to an equivalent constant amplitude loading spectrum. The proposed transformation avoids the cycle-by-cycle calculation under general random variable amplitude loadings. An IFORM is used to evaluate the probabilistic fatigue-crack growth behavior and to further enhance the computational efficiency. The computational cost of the proposed study is significantly reduced compared with the direct Monte Carlo simulation. Thus, the proposed method is very suitable for real-time damage prognosis because of its high computational efficiency. Numerical examples are used to demonstrate the proposed method. Various experimental data under variable amplitude loadin...

In this paper, a novel methodology for delamination profile diagnosis is proposed. First, the general inverse heat conduction problem (IHCP) is formulated and the corresponding adjoint problem derivation is presented. Following this, the conjugate gradient method with bound constraints is discussed and an one-dimensional numerical example is given to show the general procedures. Next, the heat conduction for two delaminated composite coupons is simulated using the commercial software ABAQUS. The extracted temperature history on the top and bottom surfaces is given as the available measurements in the delamination damage diagnosis framework. The detected results are compared with the ground truth to validate the feasibility of the proposed method. Finally, some conclusions and future work are drawn based on the current study.

A novel in situ scanning electron microscope (SEM) fatigue testing is proposed in this paper to investigate the fatigue crack growth mechanisms within one cyclic loading under plane stress conditions. The objectives of the experimental study are to verify the hypotheses of a small time scale fatigue crack growth model and to develop a new experimental methodology for the detailed mechanism investigation of fatigue crack growth. During the testing, one loading cycle is uniformly divided into a certain number of steps. At each step, high resolution images are taken around the crack tip region. Imaging analysis is used to quantify the crack growth kinetics and crack tip deformation behavior at any time instant in a loading cycle. Crack closure phenomenon is directly observed during the crack growth process in the current investigation. It is also observed that crack growth is not uniformly distributed within a loading cycle and only happens during a small portion of the loading path. Multiple mechanisms exist within one cyclic loading, which is not able to be captured using the classical cycle-based approaches. A detailed discussion is given based on the current investigation to explain some well-known issues in the classical fatigue theory.

A comparative study is performed to demonstrate the difference and similarity between the two driving force approach and a small time scale model under both constant and variable amplitude loading. The small time scale model is different from most existing fatigue analysis methodologies and is based on the instantaneous crack growth kinetics within one cycle. The two driving force approach is cycle-based and uses two driving force parameters to describe crack growth rate per cycle under constant amplitude loadings. A simple modified two driving force approach is proposed based on the concept of forward and reverse plastic zone interaction and is used to calculate the fatigue crack growth under general variable amplitude loadings. Extensive experimental data for various metallic materials are used to validate the two driving force model and the small time scale model.

A new methodology for concurrent dynamic analysis and structural fatigue prognosis is proposed in this paper. The proposed methodology is on the basis of a novel small time scale formulation of material fatigue crack growth that calculates the incremental crack growth at any arbitrary time within a loading cycle. It defines the fatigue crack kinetics on the basis of the geometric relationship between the crack tip opening displacement and the instantaneous crack growth rate. The proposed crack growth model can be expressed as a set of first-order differential equations. The structural dynamics analysis and fatigue crack growth model can be expressed as a coupled hierarchical state-space model. The dynamic response (structural level) and the fatigue crack growth (material level) can be solved simultaneously. Several numerical problems with single degree-of-freedom and multiple degree-of-freedom cases are used to show the proposed methodology. Model predictions are validated using coupon testing data from open literature. Following this, the methodology is demonstrated using a steel-girder bridge. The proposed methodology shows that the concurrent structural dynamics and material fatigue crack growth analysis can be achieved. The cycle-counting method in the conventional fatigue analysis can be avoided. Comparison with experimental data for structural steels and aluminum alloy shows a satisfactory accuracy using the proposed coupled state-space model.

A simple analytical approximation is proposed in this paper to calculate the crack tip opening displacement under general random variable amplitude loadings. This approximation is based on a modified Dugdale model for cyclic loadings. The discussion is first given under constant amplitude loading and is extended to several simple cases under variable amplitude loadings. Following this, a general algorithm is proposed under general random variable loadings. Numerical examples are verified with finite element simulations. Following this, hardening effect is included by including a hardening correction function. The proposed analytical approximation is very efficient compared to the direct finite element simulation. The solution can be used for detailed fatigue crack growth analysis under random variable amplitude loadings.

An experimental study is proposed to compare the corrosion-induced flexural behavior deterioration of beams with various bar types and bar diameters. The proposed study aims to distinguish the effects of the corrosion of different rebars on the flexural behavior of reinforced concrete (RC) beams. Twenty-two RC beams were designed and four variables were considered: the type and the diameter of reinforcement, corrosion loss, and concrete cover. Corrosion was induced in the laboratory using an accelerated corrosion technique. The corrosion-induced strength loss for two types of steel bars is discussed. Extensive statistical analysis is performed to compare the flexural performance of beams with different rebars. The experimental results show that (1) corrosion has a more significant effect on the flexural behavior deterioration in beams with smooth rebars than in beams with deformed rebars; (2) the corrosion-induced performance deterioration has a monotonic decreasing relationship with reinforcement...

An experimental study is proposed to investigate the effect of random loading sequence effect on the fatigue crack growth behavior of Al 7075-T6. The testing matrix includes different overload cycle percentage, overload ratios, and deterministic and random loading sequences in the current investigation. Multiple specimen tests and statistical data analysis are performed to show the effect of random loading sequence on the median and scatter behavior of fatigue crack growth. The proposed experimental study suggests that extreme value distribution is a good approximation of fatigue life distribution. It is observed that the effect of uncertain loading is different under different loading spectrums. For high overload cycle percentage spectrums, the random loading sequence has no major impact on the probabilistic crack growth behavior compared to the deterministic loading sequence with identical load cycle distributions. For low overload cycle percentage spectrums, the random loading sequence has huge impact on the probabilistic crack growth behavior compared to the deterministic loading sequence with identical load cycle distributions, for both the median and the scatter of the fatigue crack length curves. Finally, all experimental observations are reported in table format in Appendix A for future numerical model development and validation for interested readers.

A new methodology for concurrent dynamic analysis and structural fatigue prognosis is proposed in this paper. The proposed methodology is based on a novel small timescale formulation of material fatigue crack growth that calculates the incremental crack growth at any arbitrary time within a loading cycle. It defines the fatigue crack kinetics based on the geometric relationship between the crack-tip opening displacement and the instantaneous crack growth rate. The proposed crack growth model can be expressed as a set of first-order differential equations. The structural dynamics analysis and fatigue crack growth model can be expressed as a coupled hierarchical state-space model. The dynamic response (structural level) and the fatigue crack growth (material level) can be solved simultaneously. Several numerical problems with single-degree-of-freedom and multiple-degree-of-freedom cases are used to show the proposed methodology. Model predictions are validated by using coupon testing data from open literatu...

In this paper, a concurrent simulation framework for fatigue crack growth analysis is proposed using a novel small time scale model for fatigue mechanism analysis and the extended finite element method (X-FEM) for fatigue crack growth simulation. The proposed small time scale fatigue model does not require the cycle counting as those using the classical fatigue analysis methods and can be performed concurrently with structural/mechanical analysis. The X-FEM greatly facilitates crack growth simulation without remeshing requirements ahead of the crack tip as in the classical finite element method. The basic concept and theory of X-FEM was briefly introduced and numerical predictions of stress intensity factors are verified with reference solutions under both uniaxial and multiaxial loadings. The small time scale fatigue model is integrated into the numerical simulation algorithm for concurrent fatigue crack growth analysis. Model predictions are compared with available experimental observations for model validation.