Residual Strength Model Research Articles

Electrical resistance based residual strength prediction method for SiC/SiC mini-composites after stress-free oxidation

A stress-free oxidation model considering the microstructural characteristics of SiC/SiC mini-composites was proposed based on the electrical resistance change before and after oxidation. The relationship between the electrical resistance and the thickness of the internal fiber oxide layer was established. The stress-free oxidation tests were carried out at different temperatures for different oxidation times. The results of the oxide layer thickness calculated by the model agree well with those of the SEM observation. Based on the microstructure of tensile fracture after oxidation, the residual strength model of SiC/SiC mini-composites was proposed. The residual strength of the specimens after stress-free oxidation was calculated based on the oxide layer thickness obtained from the model. The error between the calculated and experimental results is within 14.48 %.

Progressive fatigue modelling of composite pipes with a hole

Composite pipes are increasingly used in demanding applications thanks to their light weight and corrosion resistance. To manage their integrity, tools able to predict their fatigue life and residual properties under cyclic loads are required. A finite element progressive fatigue model was applied to filament-wound composite pipes with a hole submitted to tensile cyclic fatigue. The fatigue model combined continuum damage mechanics for intra-laminar failure mechanisms and cohesive zone modelling for inter-laminar and selected macroscopic cracks. A linear fatigue damage accumulation law was used along with an empirical sudden-death residual strength model, relying solely on the material S-N curve. The fatigue simulation was conducted by an external cycle-jump procedure. After calibration on one load level, the model was able to describe the fatigue life at other load levels within one standard deviation (0.63 decade) of the experiments and resulted in a S-N curve slope of −0.084 while the experimental one was −0.072.

A prediction model for residual shear strength of liquefiable soil based on lateral spreading cases

The residual shear strength of liquefiable soil plays an important role in evaluating the displacement magnitude of lateral spreading when applying the Newmark sliding block method. Currently, the empirical model is a mainstream alternative method for estimating the residual shear strength. In this study, a database of well-documented lateral spreading cases is used to establish an exponential function for residual shear strength evaluation correlated with the vertical effective stress and normalized standard penetration test blow counts for liquefied soil. A comparative analysis with two other empirical models is conducted, and the lateral spreading of the Wildlife Site during the Superstition Hills earthquake in 1987 is estimated using the Newmark sliding block method. The model exhibits good performance for soil residual shear strength estimation in cases of liquefaction-induced lateral spreading. The average estimated value of the residual shear strength may be appropriate for deterministic analyses in engineering practice.

An enhanced fatigue damage model based on Weibull strength distribution

AbstractConsidering the inherent characteristics of strength degradation, a residual strength model is improved reasonably through the incorporation of the two‐parameter Weibull distribution. Building upon this foundation, an enhanced nonlinear fatigue damage accumulation model that is closer to the actual situation is proposed in view of the randomness of fatigue damage. The model takes into account the effect of load action on fatigue damage. To ascertain the feasibility of the proposed model, the time‐varying reliability of the model is evaluated by applying the probability density evolution method. The model's precision in predicting residual life is corroborated through five experimental data sets under bilevel and multilevel loading conditions. The results demonstrate that the proposed model exhibits excellent applicability and remarkable precision, thereby confirming its potential value in practical applications.

A new progressive fatigue damage model for the three-dimensional braided composites subjected to locally-variable-amplitude loading

The fatigue-induced stress redistribution in three-dimensional (3D) braided composites, even when subjected to externally constant-amplitude fatigue loads, results in locally-variable-amplitude fatigue loading, significantly impacting their fatigue performance degradation. This paper is aimed to propose a novel fatigue damage analysis method to predict the fatigue behavior of 3D braided composites subjected to locally-variable-amplitude loading. To this end, the continuous damage method, residual strength, residual stiffness, and fatigue life models are combined to characterize the properties degradation of 3D braided composites with cycling. Once stress redistribution occurs, the fatigue properties degrade based on the new stress level, and the equivalent cycle number is recalculated accordingly. As the material undergoes different cycle blocks, damage accumulates, ultimately leading to failure when the overall stiffness of the material degrades to 80%. Traditional fatigue models are also employed to predict the fatigue behavior of representative volume elements for comparison. The results predicted by the present model shows good agreement with experiments. Furthermore, the influence of stress levels and architectures of 3D braided composites on fatigue performance is systematically discussed.

Response Mechanism of the Residual Strength to the Mesostructure of the Shear Surface in the Gravelly Slip Zone of Ancient Landslides

AbstractAncient landslides tend to reactivate along pre‐existing slip zones that have reached a residual state. On the eastern margin of the Tibetan Plateau, previous research has indicated that the slip zone of ancient landslides is primarily composed of clayey soil with gravel, known as gravelly slip zone soil. However, the relationship between the macromechanical behavior of gravelly slip zones and the mesostructure of the shear surfaces affected by gravel is still unclear. Herein, ring shear tests and reversal direct shear tests were performed on gravelly slip zone soil, and the 3D morphology and shear surface roughness were quantitatively characterized by using 3D laser scanning technology and the power spectral density method. The results showed a significant correlation between the friction coefficient of the shear surface and its roughness. Gravel played a crucial role in influencing the macromechanical behavior of slip zones by altering the mesomorphology of the shear surfaces. By analyzing the mechanical properties of the contact unit on the shear surface, the residual strength of the gravelly slip zone was found to be jointly controlled by the basic strength of the fine‐grained soil and the undulations caused by the gravel. Finally, a residual strength model was developed for the gravelly slip zone considering both the strength of the fine‐grained soil and the shear surface roughness caused by the gravel.

Effects of steel fibers on the flexural fatigue performance of recycled aggregate concrete

To explore the flexural fatigue performance of steel fibers reinforced recycled aggregate concrete (SF-RAC), the flexural fatigue test and residual strength test with different stress levels were conducted. Besides, the fatigue cracks propagation under cyclic loading were observed and analyzed by digital image correlation (DIC) technology. The results show that the flexural fatigue life of SF-RAC increases when the content of steel fibers increases, and it is proved to be well in accordance with the three-parameter Weibull distribution. The flexural fatigue life equation with different stress level and reliability (S-N-P equation) is obtained based on it, which shows that when the fiber volume content is 1.5%, the fatigue strength of SF-RAC is about 37.2% higher than that of RAC without fibers. Then, a fatigue strain-based damage evolution model is established, and the derived residual strength model can well predict the damage degree and residual life of SF-RAC. Moreover, the steel fibers can improve the critical crack propagation length and loading cycles of RAC. The crack propagation rate can be decreased by 97.63% when the fiber volume content is 1.5%, and it is increased with the development of stress level. Finally, the influence mechanism of steel fibers on flexural fatigue performance of RAC were explained through microstructure tests.

The Fatigue Response’s Fingerprint of Composite Materials Subjected to Constant and Variable Amplitude Loadings

This paper discusses the theoretical and experimental correlations between fatigue and static strength statistical distributions. We use a two-parameter residual strength model that obeys the qualitative strength-life equal rank assumption (SLERA) for guidance. The modeling approach consists of recovering the model’s parameters by best fitting the constant amplitude (CA) fatigue data at a given stress ratio, R, and the experimental Weibull parameters of the static strength distribution function. An extensive set of fatigue life and residual strength data for AS4 carbon/epoxy 3k/E7K8 Plain Weave Fabric with [45/−45/90/45/−45/45/−45/0/45/−45]S layups, obtained at different stress ratios, R, have been analyzed. The modeling approach consists of recovering the model’s parameters from pure tension or compression fatigue data at R = 0.1 and R = 5, respectively. Once the parameters are fixed, the model’s capabilities, potential, and limits are discussed by comparing its predictions with residual strength and fatigue life data obtained at stress ratios with mixed tension/compression loadings, namely R = −0,2 and R = −1. Moreover, from a preliminary analysis, the theoretical extension of the model’s capabilities to variable amplitude loadings is conceptualized. The application of Miner’s rule is also discussed and compared with a new damage rule to analyze the fatigue responses under variable amplitude loadings.

An investigation of fatigue behavior and residual strength model of steel-GFRP composite bar

Steel-fiber reinforced polymer (FRP) composite bar (SFCB) combines the advantages of corrosion resistance of FRP and good ductility of steel, and is a promising reinforcement material to improve the service life of marine structures. However, the fatigue behavior of SFCB is complex and has not been explored. Therefore, in this study, fatigue tests were conducted at different stress levels (0.32, 0.36, and 0.41 of quasi-static tensile strength with a fixed stress ratio of 0.1) and tensile tests were performed after fatigue pre-damage for a certain number of cycles (25%, 50%, and 75% of the fatigue life) to investigate the fatigue behavior of SFCB. The results show that fatigue failure is caused by steel core fracture, and the FRP layer can improve the fatigue life. Compared with the change of residual strength, the stiffness degradation of SFCB during fatigue loading was not significant. Finally, a residual strength prediction model containing known parameters of the S-N curve is also proposed, which can well predict the residual strength decay of SFCB after fatigue damage. In conclusion, these findings and the proposed residual strength prediction model contribute to the understanding and design of SFCBs.

Residual load-bearing capacity of corroded reinforced concrete columns with an annular cross-section

Reinforced concrete (RC) columns with an annular cross-section are commonly utilized as supporting structural members in ocean engineering structures, and their structural performance deterioration is mainly caused by the corrosion of rebar in aggressive marine environment. This paper proposes an effective method to investigate the effects of rebar corrosion on the structural performance of the annular RC columns under various loading conditions. Firstly, the material degradation and residual structural strength models are proposed based on the analysis of the corrosion-induced deterioration of RC structures. Then, the general method for determining the load-bearing capacity is developed using the equivalent steel ring assumption. To improve computational efficiency and practical applicability, an effective method for assessing the residual load-bearing capacity is proposed by simplifying the calculations of rebar load-bearing capacity coefficients using the regression fitting approach. Finally, the effectiveness of the proposed simplified method is demonstrated with the relevant experimental data available. The results show the capacity deterioration rate is strongly related to the corrosion level and loading condition with the most severe degradation typically at the corrosion level of 5–10%, and the smaller and larger eccentric columns drop the capacities by about 28% and 41% at 10% corrosion level, respectively.

Fatigue life prediction for composite materials based on the S-N-φ model

The strength degradation law of composite materials is very important to fatigue life prediction. However, establishing existing residual strength models requires various experimental data to confirm the parameters involved in the models. Sometimes, experimental data on the residual strength of composite materials are not available because of limitations on experimental cost and project progress. To solve these issues, a new fatigue life prediction model named the S-N-φ model is proposed. The S-N-φ model does not require the experimental data of residual strength, and the residual strength is only reflected in the theoretical deduction process. The S-N-φ model can clearly explain the probability characteristic of fatigue life because both initial strength and cyclic stress are considered. The S-N-φ model is verified by a set of experimental data of composite laminates. The results show that the S-N-φ model is more accurate than the widely used classical S-N curve model, and the probability characteristic of fatigue life predicted by using the S-N-φ model agrees well with the experimental data.

A semi-analytical model for failure analysis of delaminated composites under fatigue loading

Relative to static conditions, fatigue damage prediction of delaminated composites is widely recognized as a much more challenging problem, due to the gradually considerable reduction of mechanical characteristics and the delamination propagation, which further leads to catastrophic failure of laminates. To completely evaluate failure behaviors of delaminated composites under fatigue loadings, a semi-analytical model was established based on the residual stiffness theory and brittle damage mechanics. A stiffness degradation model was presented to describe the reduction of stiffness properties of composites, a residual strength model was found to predict the delamination propagation and strength degradation during cyclic loadings, and a failure evaluation criterion was proposed to judge the ultimate fatigue failure of laminates. Stiffness degradation tests and compressive fatigue tests were designed and conducted. Predicted results were highly consistent with experimental outcomes, which validated the effectiveness and accuracy of the semi-analytical model for the evaluation of fatigue failure behaviors of delaminated composites. Based on the proposed model, the strength degradation processes of delaminated composites in this work can be determined, and a safety load region can be additionally presented, which can provide significant guidance for the safety design of delaminated composites under fatigue loadings.

Modelling the residual strength degradation in composite materials without using residual strength tests

Residual strength models are widely used to predict the fatigue life of composite laminates under highly variable loads. However, they often require considerable experimental effort to accurately determine model parameters. This paper introduces a new approach for predicting the residual strength of composite materials with less experimental data. The method is based on two common strength-based wearout models, the Sendeckyj model and Schaff and Davidson model. The Sendeckyj model consists of an equation with two model parameters, which describes the shape of the S-N curve by fitting fatigue test data. The Schaff and Davidson model is a single-parameter function which calculates the residual strength based on the number of fatigue cycles. Using a novel mathematical algorithm, the residual strength model parameter in the Schaff and Davidson model is estimated directly from the S–N curve without running any residual strength tests. Five data sets from the literature are used to validate the new methodology. The results show that the residual strength model parameter is dependent on both the stress level and the number of loading cycles experienced at this stress level, both of which are considered in the new strategy. In addition, if the fatigue data are well distributed, the residual strength model parameter estimated by the new strategy is close to the experimental data.

Fatigue life prediction of high‐speed train bearings based on the generalized linear cumulative damage theory

AbstractThe fatigue life prediction of the bearings is a crucial and challenging issue, especially under random cyclic loadings. Although numerous methods have been proposed, the remaining useful life of bearings is still unclear. In this study, the tensile and fatigue properties of high‐speed train bearings after various operating mileages were investigated. The experimental results reveal that the microhardness, tensile strength, elongation, and fatigue strength of the bearing steel present a downward trend with increasing the operating mileage. Based on Miner's law, we proposed the generalized linear cumulative damage theory, which illustrates that fatigue damage of components per unit mileage can be linearly superimposed. Accordingly, the residual strength model was established to evaluate the fatigue life of high‐speed train bearings. It would provide a new insight for the fatigue life prediction of bearings under random loadings.

Fatigue life prediction of 3D braided carbon/carbon composites with braided angle variation at elevated temperature

The braiding angle of 3D braided carbon/carbon composites (C/CCs) will change during high temperature fatigue loading, which will affect the fatigue properties of 3D braided C/CCs. In order to realize this dynamic simulation in the high temperature fatigue life prediction of 3D braided C/CCs and further improve the prediction accuracy of high temperature fatigue life of 3D braided C/CCs, a high temperature fatigue life prediction model of 3D braided C/CCs considering the change of braiding angle with fatigue cycle number was established. The establishment of the prediction model mainly includes: a meso-scale representative volume elements (RVEs) of 3D braided C/CCs considering yarn direction and fiber bundle cross-section shape is established at the meso-scale; the high temperature residual stiffness and residual strength models of fiber bundles considering high temperature and stress level are established. Based on the experimental data characteristics of high temperature fatigue residual stiffness of 3D braided C/CCs, a mathematical model of cycle number/braided angles (CN/BAs) is established. The fatigue life prediction model was used to predict the 3D braided C/CCs at 700°C and stress levels of 87% and 85%. The results showed that the prediction error of single flower node was less than 5%. The fatigue life prediction error is less than two times the tolerance.

Dynamic Lifetime Prediction of Fishing Nets Based on the Model of Wave Return Period and Residual Strength

The classical cumulative damage method based on the S-N curve or crack growth model is unrealistic for predicting the lifetime of fishing nets under actual service conditions. In this paper, a novel and practical method based on the wave return period model and residual strength model is presented to estimate the dynamic lifetime of fishing nets under different numbers of damaged netting bars. The tension distribution rules, dangerous breakage zones, damage-developing-paths, and breakage patterns of two types of tensioned nettings are calculated using the commercial software RIFLEX. The most dangerous breakage zones appear in the areas near the midpoint of the upper fixing boundary side for both square mesh and diamond mesh netting. The tension distribution of diamond mesh netting is more uniform than that of square mesh netting, which implies that diamond mesh is more durable than square mesh. The dynamic lifetime prediction shows that the netting will be damaged more and more quickly after its initial fracture. Relative dynamic lifetime curves provide a way to forecast the subsequent damage time according to the net’s initial fracture lifetime. Adjusting the installation angle of the polygon cage can reduce the maximum tension of a fishing net under the wave load, thus increasing the lifetime of the fishing net.

Effect of Different Environmental Conditions on Durabilities of Polyester- and Vinylester-Based Glass-Fiber-Reinforced Polymer Pultruded Profiles

This paper presents the results of experimental investigations on the durability of glass-fiber-reinforced polymer (GFRP) pultruded profiles made of unsaturated polyester (UP) and vinylester (VE) resins commonly used in civil engineering. The water absorption, tensile properties, and microstructures of GFRP profiles exposed to several typical accelerated aging environments (e.g., deionized water, salt water, salt fog, and combined hygrothermal cycles) for 12 months were investigated. Moreover, a sustained loading factor was included in the test to reflect the behavior of the GFRP profiles in real structures. A normalization approach based on the controlled specimens was used to assess the effectiveness and relevance of the accelerated exposure. The results indicated that the maximum moisture absorption of both UP and VE GFRP profiles was immersed in deionized water, where the masses increased by 1.03 and 0.53%, respectively, leading to the maximum degradation of tensile strength (24.03%) of UP GFRP profile immersion in deionized water after 360 days of aging. However, the tensile modulus was more sensitive to high temperatures and has the maximum degradation (47.03%) after hygrothermal cycles. Moreover, VE GFRP profiles show superior humidity and temperature endurance. Furthermore, the sustained loading exacerbated the degradation of tensile properties slightly under the same conditions. Finally, by incorporating the cumulative damage caused by the sustained loading and a time-dependent factor into a residual strength model, a revised model was proposed to describe the tensile strength loss of pultruded UP GFRP profiles.

Strength and stiffness degradation modeling and fatigue life prediction of composite materials based on a unified fatigue damage model

The performance degradation of composite materials under fatigue loading is so complex that the present knowledge is far from complete. This study aims to present a pair of residual strength and residual stiffness models based on a unified fatigue damage formula, and predict fatigue life under variable amplitude cyclic loading. Firstly, a unified fatigue damage model for composite materials is proposed, which is capable of characterizing fatigue damage development caused by strength degradation and stiffness degradation, respectively. Subsequently, a pair of residual strength and residual stiffness models is presented to estimate the performance degradation of composite materials. Finally, the corresponding life prediction methods are developed from the viewpoints of strength degradation and stiffness degradation, respectively. A set of experimental data for composite laminates are utilized to validate the proposed models and methods. The results show that the proposed residual strength and stiffness models are flexible enough to fit strength and stiffness degradation data with good agreement. Moreover, the developed life prediction methods are capable of calculating fatigue life of composite laminates with high accuracy.

A stiffness-based phenomenological model to predict the fatigue life of unidirectional CFRP laminates under tensile fatigue loadings

Fibre-reinforced composite materials can withstand large number of loading cycles compared to traditional materials. However, predicting the damage progress and strength loss in a composite structure due to fatigue is difficult because of the complex interaction of different failure mechanisms. This work investigates the decrease in the stiffness and strength in a high-performance undirectional CFRP laminate subjected to on-axis fatigue loads. A stiffness-based phenomenological model is proposed in order to evalute the damage growth due to fatigue through the longitudinal stiffness degradation. Assuming that the laminate ultimate strain is independent of the distributed damage caused by fatigue, the residual strength model can be deduced, or its integral form, the S-N curve. Thanks to this assumption, the residual stiffness model is related to the residual strength model, and thus it has reduced the experimental characterization of phenomenlogical-based approaches. The accuracy of the model is verified by comparing the experimental data against the derived S-N curves.

An appraisal of the models for the prediction of compressive strength of thermally damaged self-compacting concrete

Self-compacting concrete (SCC) mixtures were prepared using 5% and 10% micro silica (MS). Fresh properties are measured using slump flow with T500 time, L-box ratio and V-funnel time. SCC with lower MS content yielded better workability properties. Hardened SCC samples were heated up to 200 °C, 400 °C and 600 °C in an electric furnace and allowed to cool naturally. The compressive strength of unheated and heated samples after cooling was determined. It was observed that up to 400 °C, SCC with 10% MS suffered higher strength loss than SCC with 5% MS. For 600 °C, strength loss for both the SCC mixtures was approximately equal. Furthermore, residual compressive strength of one hundred seven SCC specimens (including eighteen of this study) was predicted using the residual compressive strength models available in the literature. Though the available models were proposed for normal vibrated concrete (NVC), statistical analysis showed that they could also be used for SCC.