Residual Stiffness Model Research Articles

Fatigue life prediction of CFRP flat-fold-flat adhesive joints

Taking the flat-fold-flat (FJF) adhesive joints of carbon fiber reinforced bismaleimide resin-based composite materials as the object, the regularized fatigue life model and residual stiffness model of the one-way plate and the cohesive model parameters of the adhesive layer were fitted experimentally, and based on this, the fatigue life of the adhesive joint was predicted by ABAQUS software. The results show that under specific maximum load conditions, the predicted cracking life of the adhesive layer at the end of the lap joint and the final fatigue life are not greater than the error values of the test results 3% , which has a relatively good calculation accuracy. The cracking life of the adhesive layer at the end of the lap joint is approximately equal to the final fatigue life of the adhesive joint, indicating that the cracking of the adhesive layer at the end of the lap joint accounts for the main part of the total life of the adhesive joint, and the crack propagation life of the adhesive layer can be ignored.

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.

A quantitative residual stiffness model for carbon fiber reinforced polymer tendons

AbstractIn this study, tension‐tension fatigue tests were conducted to investigate the residual stiffness degradation of carbon fiber‐reinforced polymer (CFRP) tendons. Different stress levels were used in the tests, and measurements of residual stiffness and the number of loading cycles were taken. Based on experimental data for CFRP tendons, a quantitative residual stiffness model was developed by modifying Yao's model. This model is applicable to various stress levels. To assess its accuracy and applicability, the predicted results of this model were compared with those of cited models from other researchers. The findings revealed a three‐stage degradation of residual stiffness in CFRP tendons under different stress levels. Furthermore, it was observed that the proportion of fatigue life accounted for by Stage III decreased with smaller stress ranges, while the proportion accounted for by Stage II increased. The proposed quantitative residual stiffness model was verified using both experimental and cited data.

Numerical and experimental investigation on tensile fatigue performance of reinforced thermoplastic pipes

With the rapid development of offshore drilling for harvesting oil and gas from the deep sea, the fatigue performance of offshore risers is increasingly demanding. This study investigated the tensile fatigue performance of reinforced thermoplastic pipes (RTPs). The theory of three-dimensional (3D) anisotropic elastic mechanics was combined with a strain potential-energy density function to construct the 3D constitutive relation of RTPs. The stiffness degradation law of RTPs was predicted by introducing a modified 3D Hashin failure criterion and the residual stiffness model. A user-defined material (UMAT) subroutine was developed to evaluate the progressive fatigue failure process of RTPs. A uniaxial tensile fatigue experiment of RTPs was designed to validate the numerical model's correctness. The analysis examined the damage failure modes of RTPs under cyclic loading conditions and revealed the stiffness degradation mechanism. Results suggested that the matrix fatigue damage of the reinforced layer of RTPs is the primary cause of the rapid stiffness degradation, which was observed to be faster with increasing cyclic load stress levels.

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.

Coupling effect between highly nonlinear solitary waves and composite plate with matrix cracking

As a good information carrier, solitary waves have broad application prospects in the field of non-destructive testing. In this paper, we studied the coupling effect between highly nonlinear solitary waves in the one-dimensional particle chain and composite plate with matrix cracking. We based on the tensor internal variable damage model and the residual stiffness model, obtained the couple differential equation of the one-dimensional particle chain and the composite plate with matrix cracking. The fourth-order Runge-Kutta method is used to solve the differential equations, and the change law of the particle velocity, internal force, and displacement curve is obtained. This paper analyzed the influence of the damage amount and the geometric parameters on the reflected solitary waves of composite plates with different material properties. It is found that the reflected waves are sensitive to the thickness of the plate, the average distance between cracks, and the thickness of the damage layer. The research results of this paper have enriched and perfected the theory of nondestructive testing of solitary waves in the field of composite materials and provided broad application prospects for the practical application of one-dimensional particle chains.

Fatigue Behavior of Heavy-Haul Railway Prestressed Concrete Beams Based on Vehicle-Bridge Coupling Vibration.

Due to the demand for increasing trainload and enhancing some existing heavy-haul railways, the low reserve value of bearing capacity is a problem for the 32 m-span simply supported beam. The fatigue behavior of prestressed concrete beams in a heavy-haul railway loaded by 33 t and larger axle weight of trains was experimentally investigated. The experimental results of the fatigue behaviors, including fatigue deformation, crack propagation behavior, and strains of classical materials were obtained and analyzed. A fatigue behavior assessment model was established to investigate the residual stiffness and yield point degradation of the beams loaded by the trainload. The effects of train fatigue cycles and prestress loss on the residual stiffness and yield point degradation models of the beams were analyzed. The results indicated that the crack development process had three stages during the fatigue process: the derivative stage, gradual development stage, and fatigue failure stage. Trainload was the main external factor influencing the fatigue behavior of prestressed concrete beams. The increase in trainload accelerated the degradation rate of the residual stiffness of the beams and yield point, reducing the fatigue life. The prestressing strand was primarily used to delay the concrete cracking in the tension zone. When the beam was not cracked, the prestressed concrete beam showed good fatigue performance, and the degree of prestressing did not affect the fatigue life of the beams. When the maximum fatigue load exceeded the cracking load of the beam, prestress loss in beams became a critical issue that accelerated the degradation rate of fatigue strength and reduced fatigue life. The higher the fatigue damage degree, the more pronounced the effect of prestress loss on the fatigue strength of the beams. The fatigue failure of prestressed concrete beams occurred in the bottom tensile steel bar. Therefore, when the trainload of a heavy-haul railway is greater than the cracking load of the beam, it is recommended to strengthen the beam by prestressing and strictly control the trainload to avoid yield failure.

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.

Fatigue behavior of 2.5D woven composites based on the first-order bending vibration tests

The 2.5D woven composite material has good resistance to delamination and impact load. However, its fatigue behavior is lack of investigation. In this work, first-order bending vibration fatigue tests were conducted on cantilever beam specimens made of 2.5D woven composites under different nominal stress levels. Test results showed that rapid damage evolution and accumulation occurred in the woven composites under a high stress level. However, under a low stress level, crack growth showed arrest behavior. The square root of residual stiffness showed a linear relation with resonance frequency, so the normalized full-time domain curves can be used to characterize the residual stiffness. On that basis, a residual stiffness model for the studied vibration fatigue specimens under other stress levels was proposed. Besides, a formula of ɛ-N curve was established for guiding the design and analysis of the 2.5D woven composite. To further reveal the failure mechanism, a multi-scale model of the woven composite was proposed. Numerical results showed that the high interlaminar shear stress between the yarn and the matrix near the compressed surface of the specimen caused material damage. This was consistent with the observed fracture topography, which verified the applicability of the multi-scale model.

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.

A new time-frequency domain simulation method for damage accumulation and life prediction of composite thin-wall structures under random cyclic loadings

A time-frequency domain simulation method has been developed to predict the lifetime and simulate the damage evolution of composite thin-wall structures subjected to random fatigue loading. Simulation method contains two main parts: (1) structural response based on the power spectral density loading, and (2) damage progression according to residual stiffness model of material. Simulation is proceeded based on step-by-step update of material properties in time domain. For each step fundamental frequency is calculated to determine the degradation ratio of frequency. Time corresponding to the critical degradation ratio of frequency is defined as the lifetime. The method presented in this paper presents a possible solution for practical engineering applications of composite thin-wall structures subjected to the random fatigue loadings and can be applied to other similar thin-wall structure with more complex features.

Fatigue Modeling for Carbon Fiber/Epoxy Laminated Composites Considering Voids’ Effect

In this article, experimental tests under static tensile loadings and tension-tension cyclic loadings were conducted for T300/924 unidirectional laminated composites at different porosity levels. On the basis of the experimental tests, a physical-based residual stiffness model for porous CFRP composites was put forward. The present model describes the deterioration of composites under cyclic loading in perspective of the initiation and propagation of cracks in the matrix, and is capable of capturing the effect of voids on fatigue behaviors of the composites. Lastly, the stiffness degradations of laminates with different void contents under various stress levels were predicted, and the predicted stiffness reduction as well as fatigue life of the material agreed well with the experimental data.

Fatigue Behavior of Aramid Fiber Reinforced Rubber Matrix Sealing Composites

This paper presents an experimental and theoretical study of aramid fiber reinforced rubber sealing composites (AFRC). The fatigue performance of AFRC with different stress amplitudes and fiber mass fractions was tested, and the residual strength of AFRC after different fatigue cycles was conducted. The fracture morphology of AFRC samples with different fiber mass fractions, stress amplitudes and fatigue cycles were observed by scanning electron microscope (SEM), and the fatigue damage modes of AFRC were discussed. The experimental results were analyzed and predicted by fatigue life model, residual stiffness model and residual strength model. It was found that the results predicted by theoretical model agreed well with that measured by experimental results, which indicated that the proposed model gave an advantage in evaluating the fatigue behavior of AFRC without further morphological experiments.

A frequency domain approach in residual stiffness estimation of composite thin-wall structures under random fatigue loadings

Based on the constant-amplitude fatigue experiment, a new residual stiffness model combining with power spectral density is proposed to adapt random stress states. The random loading process can be divided into multi-level variable amplitude loadings. All stiffness degradation increments can be integrated to obtain the stiffness degradation by using a numerical integral method. Fatigue damage accumulation of composite thin-wall structures subjected to random cyclic loadings is investigated by using the proposed method, which is also verified by random vibration tests with limited-bandwidth excitation. The influence of local stiffness damage on the fundamental frequency of the experiment specimen is calculated by using finite element method, which is in good agreement with the experimental results. The life predictions based on the proposed residual stiffness model are more conservative in comparison of that with linear damage accumulation rule.

Random fatigue damage accumulation analysis of composite thin-wall structures based on residual stiffness method

The damage accumulation and life prediction for C/SiC composite panels subjected to random vibration loading was studied by using the residual stiffness model in combination with critical failure stiffness ratios in the different stress levels. According to the results of stiffness degradation and material S-N curves for constant-amplitude fatigue loadings, a new residual stiffness model was established and extended to adapt random stress states by using an equivalent damage ratio algorithm in time domain. The stiffness degradation and material S-N curves were obtained by using constant amplitude fatigue experiments. Random vibration tests with limited-bandwidth excitation were conducted to verify the prediction model. Good agreement is observed compared with the results of 2D plain-woven C/SiC composite panel subjected to random vibration loadings.

Fatigue characterization of T300/924 polymer composites with voids under tension‐tension and compression‐compression cyclic loading

AbstractFibrous polymer composites exhibit excellent properties such as high specific stiffness/strength and good fatigue performance. However, as inherent defects of polymer composites, voids have been reported to have an impact on their load‐bearing properties including fatigue resistance. In the interest of safety, the effect of voids on fatigue behaviours of composites should be understood and quantified. In this article, the effect of voids on the fatigue of T300/924 composites was evaluated in terms of their fatigue life, stiffness degradation, and cracks propagation under tension‐tension and compression‐compression loadings. The failure probability was assessed by Weibull distribution. Furthermore, crack measurement and fractographic analysis reveal that the effect of voids on the failure mechanisms of the material under various loading configurations could be different. Lastly, an analytical residual stiffness model was proposed, and a good correlation was obtained between the experimental data and the prediction results.

A fatigue damage and residual strength model for unidirectional carbon/epoxy composites under on-axis tension-tension loadings

Fibre-reinforced composites experience a degradation of stiffness and strength during fatigue life. Understanding the reduction of these properties is fundamental to establish a reliable fatigue life prediction methodology. This work investigates the loss of stiffness and strength in advanced unidirectional carbon/epoxy laminates under on-axis tension-tension loads. A phenomenological stiffness-based fatigue model is formulated within the framework of continuum damage mechanics, where damage is described by the reduction of the in-plane longitudinal stiffness. The particularity of the model is to assume that the ultimate strain remains constant after fatigue damage. Thus, the residual strength model and the S-N curves are deduced from the residual stiffness model. This assumption reduces the experimental characterization of phenomenological-based approaches. The experimental challenges found in the fatigue experiments are also discussed. The accuracy of the model is verified by comparing the experimental data with the derived S-N curves.

Fatigue behaviors of 2.5D woven composites at ambient and un-ambient temperatures

In-depth understanding of the fatigue behavior of woven composites at un-ambient temperatures is critical for their engineering applications, especially in aero-engine. Here, fatigue tests were conducted on 2.5D woven composites at an ambient temperature (AT) and an un-ambient temperature (U-AT) to investigate the fatigue characteristics and related damage mechanism. Results show that the fatigue life of this material at U-AT has a sudden increase phenomenon, alongside an abnormal behavior existing in residual strength. Additionally, the gradual right shift of the hysteresis loop was exhibited, which unambiguously reveals that during the cyclic loading, the samples were stretched alongside the increase in inclination of warp, causing the strengthening of mechanical properties in warp direction. The fatigue failure locations were mostly located on the intersection of warps and wefts, which is similar with the static fracture locations. Finally, based on the test data, fatigue life and residual stiffness models taking temperature into account were established.

A residual strain model for progressive fatigue damage analysis of composite structures

A residual strain model was presented based on the fatigue-accumulated damage mechanisms of composite materials. By combining the proposed residual strain model with a residual stiffness model, the gradually degraded material properties due to the damage in fatigue cycles were characterized. Accompanying the residual strain based gradual material degradation model with a micromechanics-based sudden material degradation rule for describing the stiffness degradation in one fatigue cycle and an extended maximum strain criterion for evaluating failure of materials, a progressive fatigue damage model (PFDM) of a typical double-lap three-bolt joint made of T800 carbon/epoxy composites was developed. Compared with the residual strength model in a traditional PFDM, the residual strain model has consistent parameters with those in the residual stiffness model, which could be determined by nondestructive experiments. Fatigue tests of the double-lap three-bolt joint specimens under a stress ratio R=−0.2 and three-level load ratios q=0.7, 0.8, 0.9 were performed. Good consistency between the experimental results and numerical predictions of the PFDM validates the efficiency of the proposed residual strain model and PFDM in accurately predicting the residual strength and fatigue life of composite structures.

A new fatigue failure theory for multidirectional fiber-reinforced composite laminates with arbitrary stacking sequence

Fatigue failure is one of the most important failure types of fiber-reinforced composites. In this paper, a new fatigue failure theory for multidirectional fiber-reinforced composite laminates with an arbitrary stacking sequence is developed, by combining nonlinear residual strength and residual stiffness models with the recently improved Puck’s failure theory which includes the in situ strength effect. This fatigue theory can predict the fatigue life, residual strength and residual failure envelope of fiber-reinforced composite laminates under multidirectional loadings. For these predictions it is necessary to recalculate the fatigue lives of laminae after each cycle since the stresses in the laminae change due to stiffness degradation. It is also necessary to account for the nonlinear accumulation of damage at the new stress level in the laminae resulting from stiffness degradation. This is achieved by using the concept of equivalent cycle. The theoretical predictions are in good agreement with available experimental results.