Stiffness Degradation Rule Research Articles

Fatigue Analysis of Composite Bolted Joints under Random and Constant Amplitude Fatigue Loadings.

This paper attempts to analyze the random fatigue life and failure modes of joints using two calculation methods. Three kinds of tests were carried out, which were the static test, constant amplitude fatigue test and the random fatigue test, and four kinds of joints were designed. After the static test, the joint was subjected to a constant amplitude fatigue test by selecting different percentages of load according to the static strength. In order to predict the random fatigue life more precisely, two calculation methods were carried out, which were the linear cumulative damage method and the equivalent loading finite element method. Based on the linear cumulative damage hypothesis, the fatigue life of the joint was established as a function of the load amplitude, and then, the random life prediction was calculated by the amplitude distribution of the random loading. Another method was the equivalent loading method, which was to obtain the equivalent constant amplitude fatigue loading of the random loading spectrum. The finite element model was established based on the stiffness and strength degradation rule. The equivalent random life and fatigue failure modes of the joint were modeled. The two life prediction methods show good agreement with the fatigue experimental result, and all prediction results were included in a scatter band of the factor of 2.

Experimental study on seismic performance of Chinese traditional mortise and tenon joints with different lengths that tenons pull out of mortise

This paper presents the results of a study on seismic performance of mortise-tenon joints with different lengths that tenons pull out of joints. Three 1:3.52 scaled mortise-tenon joint specimens were fabricated: one with through-tenon joints, one with half-tenon joints, and one with dovetail joints. Seismic data of the joints, such as hysteretic curves, skeleton curves, stiffness degradation rules, and energy dissipation capacity curves, were obtained by low-cycle reversed loading test. The influence of lengths that tenons pull out of joints on the mortise-tenon joints was analyzed. The seismic performance of three types of mortise-tenon joints was compared. The results showed that all hysteretic loops are z shaped. The seismic performance of the through joint was the best among three types of mortise tenon joint. The length that the tenon pulls out of the joint significantly affected the performance of the mortise and tenon joints.

Simplified Evaluation of Shear Stiffness Degradation of Diagonally Cracked Reinforced Concrete Beams.

Shear cracking in concrete box-girder bridges, which could cause excessive deflection during the serviceability limit state, cannot be effectively avoided by code-guided design. While elastic shear deformation only accounts for a small proportion of total deformation for un-cracked reinforced concrete (RC) beams, the magnitude of after-cracking shear deformation becomes comparable to flexural deformation for RC beams. However, there is still a lack of practical models to predict the after-cracking shear deformation of RC beams. First, six thin-webbed I beams were tested to investigate the shear stiffness degradation mechanism and the decrease ratio. Then, a very simple truss strut angle formula, which is the crucial parameter for shear stiffness, was established. Furthermore, a stiffness degradation rule for partially cracked beams was proposed considering the influence of concrete tension stiffening, which is essential for predicting the development process of after-cracking shear deformation. Finally, directly measured shear strains were used to validate the proposed shear stiffness model. The results showed that the shear stiffness drops to about 30~40% of the original stiffness after the first diagonal crack, and the remaining shear stiffness is only about 10% of the original one when the stirrup yields. Increasing the stirrup ratio is a more effective method to control shear stiffness degradation for diagonally cracked RC beams. Also, the proposed shear stiffness model well captures the main features of the shear stiffness degradation, and it provides a relatively accurate prediction of the equivalent shear stiffness at the post-cracking stage.

A novel creep-fatigue life evaluation method for ceramic-composites components

A novel progressive creep-fatigue damage analysis method based on multiscale information was proposed to accurately predict the service life of SiC/SiC composites and their structural components under complex mechanical loads and external environments. First, the strength degradation of SiC fibers involving five damage mechanisms and degradation of the properties of the interface under high-temperature fatigue loading were described quantitatively based on experimental results. Subsequently, a micromechanical model incorporating the global load sharing model, two-parameter Weibull model, shear-lag model, property degradation models of various constituents, and the effect of the braiding angle was utilized to calculate the volume fraction of broken fibers. The fatigue life of 3D 4-directional SiC/SiC composites was predicted and exhibited a trend similar to that of the experimental data. The rupture life of the SiC/SiC composites was calculated considering the stress transfer among microscopic constituents and the influence of creep slow crack growth on the fiber strength. The volume fraction of broken fibers obtained in these micromechanical models was used to perform a gradual strength degradation in the novel progressive creep-fatigue damage analysis method. Microscopic constituents damage and macroscopic property degradation were quantitatively linked in this step. This infuses the micro information into the traditional phenomenological progressive damage method. The gradual stiffness degradation rules were derived from the fitting of the residual elastic modulus obtained from the fatigue and creep experiments. Finally, the damage evolution and service life of SiC/SiC turbine blades were simulated and evaluated as a preliminary validation of the entire process.

Modelling pre-fatigue, low-velocity impact and post-impact fatigue behaviours of composite helicopter tail structures under multipoint coordinated loading spectrum

This paper aims to numerically study progressive pre-fatigue, low-velocity impact (LVI) and post-impact fatigue (PIF) damage behaviours of a full-scale composite helicopter tail structure under multipoint coordinated loading spectrum. A mixed progressive damage algorithm incorporating residual strength and stiffness degradation rules and failure criteria is developed for progressive fatigue and LVI damage analysis of plain-weave (PW) and unidirectional (UD) composites. Novel global–local​ FE modelling technique is proposed for parallel computation and real-time data transferring of global–local FE models in progressive pre-fatigue, LVI and PIF damage modelling of helicopter composite tail structure. The numerical predictions from this work agree well with experimental data from previous literature, indicating that the mixed algorithm and global–local FE modelling technique can effectively analyse the impact damage tolerance of large full-scale composite aircraft structures.

Continuum damage dynamics of a large-scale flexible multibody system comprised of composite beams

Herein, a continuum damage dynamic model of a large-scale flexible multibody system comprising composite beams is proposed based on the framework of the absolute nodal coordinate formulation. To accurately model the continuum damage dynamics of a multibody system, the Hashin criterion is adopted to describe damage initiation during dynamics. A type of nonlinear evolution law is used to characterize the value of material damage. Furthermore, a material stiffness degradation rule is introduced to describe the process of structural damage. A formulation for the damage element elastic force and its Jacobian are derived based on the second Piola–Kirchhoff stress tensor. Two dynamic numerical examples, including a deployment dynamic analysis of the spatial beam structural unit, are conducted to verify the availability and applicability of the proposed model.

Cyclic behavior of semi-rigid precast concrete beam-to-column subassemblages with rapid assembly connections

In this paper, the semi-rigid precast beam-to-column joint subassemblages based on corbel-shoe connection system with rapid assembly characteristics were proposed and experimentally investigated. Four full-scaled interior and exterior beam-to-column joints were prepared and tested under cyclic loading keeping a fixed axial compression ratio at 0.5. It was demonstrated that the tested beam-to-column specimens failed characterized by flexural failure of beam end instead of the column or joint core. The arch-like load-displacement curves and stable hysteretic behavior were captured. The proposed precast beam-to-column subassemblages could not only provide ease of construction process but perform well under simulated earthquake action. The similar bearing capacity, stiffness degradation rule and energy dissipation capacity between precast and monolithic joints provided evidence in support of this. Also, the ductility of precast interior and exterior subassemblies (3.8 and 3.3) was 15.2% and 23.1% higher than that of the monolithic counterparts (3.2 and 2.6). The degenerated four-linear restoring force model was proposed and verified. Moreover, the structural performance evaluation and semi-rigid characteristics of tested specimens were discussed.

Experimental study on seismic behavior of precast concrete beam-column joints using UHPC-based connections

Ultra-high performance concrete (UHPC) with high bond characteristics with reinforcing bars could significantly shorten the lap splice length of rebars. UHPC-based rebar lap splice connections offer larger tolerance and simpler operation than traditional rebar connection approaches, which could ease and accelerate the on-site construction process of precast concrete structures. This paper characterizes the seismic behavior of precast beam-column joints where the longitudinal rebars of columns are connected using UHPC with a lap length of 15 times rebar diameter (15db). Full-scaled cyclic tests on two precast joints and two corresponding monolithic joints to compare were carried out keeping a high axial compression ratio (n) at 0.5. It was demonstrated that the beam-column subassemblies failed characterized by flexural failure of beam end instead of the column or joint core. The arch-like load–displacement curves and stable hysteretic behavior were still captured considering the p-delta effect. The proposed precast beam-column joints with UHPC-based connections could achieve similar bearing capacity, ductility and stiffness degradation rule to the monolithic counterparts. The degenerated four-linear restoring force model was presented and verified. Moreover, the numerical simulation was also performed, and the predicted structural behavior was in agreement with the experimental results.

Damage behavior of Nb3Sn/Cu superconducting strand at room temperature under asymmetric strain cycling

In this study, damage evolution of Nb3Sn/Cu superconducting strand was investigated under asymmetric strain cycling. The results of the fatigue tests indicate that higher strain ranges and peaks can accelerate damage evolution, and damage evolution occurs seriously at the early fatigue stage. Based on the stiffness degradation rule of composites, two independent plastic damage evolution equations of the Nb3Sn sub-elements and Cu matrix were derived to obtain stiffness degradation and fatigue life by considering the effect of strain range and strain peak, respectively, and the accumulated plastic strain of Nb3Sn/Cu superconducting strands was obtained by deriving the total damage evolution equation. The proposed model was verified and validated by studying the fatigue behavior of Nb3Sn/Cu superconducting strands under asymmetric strain cycling. A good agreement between the analytical model and experimental data irrespective of the strain range and strain peak shows that the analytical model can not only predict the stiffness degeneration and accumulated plastic strain, but also describe the fatigue life of Nb3Sn/Cu superconducting strands under asymmetric strain cycling.

Experimental and numerical study on the seismic performance of rocking steel frames with different joints under earthquake excitation

A rocking steel frame is proposed in this paper, which can reduce the plastic deformation of the main structural components under strong earthquake actions and can be easily repaired after earthquakes. Three 1:2 testing steel frames (buckling-restrained braced steel frame, rocking steel frame with rigid beam-column joint and rocking steel frame with semi-rigid beam-column joint) are designed and manufactured. The pseudo-static tests on the three specimens are carried out respectively. The hysteretic curves, skeleton curves, stiffness degradation rules and other parameters of the three specimens are compared and analyzed to study the seismic performance and damage characteristics of the rocking steel frame. The effect of beam-column joint form on the seismic performance of the rocking steel frame is investigated. In addition, the corresponding numerical analysis and modelling methods are introduced. The results indicate that the rocking structure can effectively reduce the damage of beams and columns. The RBS (rigid beam-column joint with reduced beam section) on the beam end can effectively transfer plastic hinge to the beam end, thus protecting the beam-column joints. It can be also concluded from the results that compared with rigid beam-column joint, semi-rigid beam-column joint has greater superiority and better seismic performance, which can protect the main components more effectively.

Fatigue damage model of woven glass-epoxy fabric composite materials

Based on the Stiffness degradation rule of woven glass fiber composite under fatigue loading, a phenomenological fatigue damage model containing two material parameters in which first is directly proportional to the fatigue life and second is inversely proportional to fatigue loading level is presented in this paper by analyzing damage development effects with very nice result as fatigue modulus is inversely proportional to fatigue strain. Experimental data from Tensile Fatigue Test were employed to verify the model, and the results show that the model can describe the damage evolution of woven glass-epoxy composite laminates under different fatigue loading by verifying the predicted fatigue life of composites. Degradation of Young’s Modulus at different loading cycles, damage development corresponding to Normalized life, its accumulation subjected to constant amplitude fatigue loading including its verifications are well discussed.

Hysteretic Behavior of Steel Reinforced Concrete Columns Based on Damage Analysis

With the aim to model the seismic behavior of steel reinforced concrete (SRC) frame columns, in this research, hysteresis and skeleton curves were obtained based on the damage test results of SRC frame columns under low cyclic repeat loading and the hysteretic behavior of the frame columns was further analyzed. Then, the skeleton curve and hysteresis loops were further simplified. The simplified skeleton curve model was obtained through the corresponding feature points obtained by mechanical and regression analysis. The nonlinear combination seismic damage index, which was developed by the test results and can well reflect the effect of the loading path and the number of loading cycle of SRC frame columns, was used to establish the cyclic degradation index. The strength and stiffness degradation rule of the SRC frame columns was analyzed further by considering the effect of the accumulated damage caused by an earthquake. Finally, the hysteresis model of the SRC frame columns was established, and the specific hysteresis rules were given. The validity of the developed hysteresis model was verified by e comparison between the calculated results and the test results. The results showed that the model could describe the hysteresis characteristics of the SRC frame columns under cyclic loading and provide guidance for the elastoplastic time-history analysis of these structures.

Study on Restoring Force Performance of Corrosion Damage Steel Frame Beams under Acid Atmosphere

In order to study the restoring force characteristics of corroded steel frame beams in an acidic atmosphere, based on different corrosion damage degrees, tests on the material properties of 48 steel samples and six steel frame beam specimens with a scale ratio of 1/2 under low cyclic repeated loading were conducted. According to the test results, the relationship between the weight loss rate and the mechanical properties of corrosion damage steel was obtained by numerical regression analysis, and the hysteresis curves and skeleton curves of the corroded steel frame beams were also obtained. The simplified trilinear skeleton curve model of the corroded steel frame beams and the expression of the corresponding feature points were determined by analyzing the failure process. The strength and stiffness degradation rule of the steel frame beam was analyzed furtherly. The hysteresis rule was established by introducing the cyclic degradation index which considers the effect of different corrosion degrees, and finally the restoring force model based on the corroded steel frame beams in an acidic atmospheric environment was established. Comparison with the test results show that the skeleton curve and the restoring force model established in this paper can accurately describe the seismic performance of corrosion damaged steel frame beams and can provide a basis for the seismic calculation analysis of corroded steel structures in an acidic atmosphere.

Fatigue damage simulation of tension-tension loaded glass/polyester fiber composites with thickness tapering effects

This study evaluates the capability of a progressive damage method in predicting the fatigue failure in glass/polyester fiber composite materials. Residual material properties in different failure modes have been obtained from testing fatigue-loaded specimens to their ultimate limits. A numerical tool utilizes the experimentally obtained values to simulate the process of damage in more complex models with high interlaminar shear stresses. The tool accounts for fatigue damage through stiffness and strength degradation rules without relying on prior calibration/modifications. Benchmark ply-drop problems under constant and variable amplitude fatigue loadings are simulated and compared against experimental results. Verification case studies show that the numerical tool can predict damage initiation and final fatigue life, successfully.

A progressive damage model for predicting damage evolution of laminated composites subjected to three-point bending

Based on the Hashin-type failure criteria and cohesive zone method, a new progressive damage model with a set of gradual stiffness degradation rules was developed to investigate the flexural behavior and the damage evolution of laminated composites subjected to three-point bending. Eight kinds of failure modes were considered for damage evolution in the present model. Compared the analysis results of the present model and Linde's model with the results of three-point bending experiments, it was found that both stiffness and the maximum strength obtained from the present model were in accordance with experimental results. The relative errors of stiffness and the maximum strength between the present model and the experiments were −0.35% and 0.75%, respectively. The degradation stages of the load-deflection curve after the ultimate load can be well predicted by the present model with relative load errors less than 12.5% and relative deflection errors less than 8.5% for four characteristic points of the degradation stages. Both final predicted failures and damage evolution were in good agreement with the damage micrographs observed from the failed specimens.

A three-dimensional progressive damage FE model for GFRP composites under monotonic loading

An anisotropic non-linear 3-D progressive damage constitutive model for composite materials under monotonic loading (both tension and compression) was presented. It was implemented in a 3-D solid finite element of a commercial FEA code. Material non-linearity was taken into account, based on experimental data at the ply level. Puck's failure theory for general 3-D stress state was also implemented for the determination of the failure onset of each ply along with new, simple stiffness degradation rules for the simulation of the mechanical behaviour of the damaged ply, including a very limited number of fitting parameters. The parameters were derived by comparing the simulation results against experimental data of [±45]S and 60° off-axis uni-directional coupons in tension. The model was validated by comparing its results to experimental data of glass/epoxy continuous fibre reinforced composite laminates of various lay-ups under axial, static, tensile and compressive loading. The effect of the FE mesh and the load increment was investigated. It was proven that 6 layers of FE per UD ply across the thickness direction were enough to capture the 3-D stress state effects in all cases. The FE model width was proven to have an important influence on the predictions. The failure modes predicted by the FE analysis were also compared against photos of failed specimens. The results of the MD laminates simulated were very good and the failure modes predicted were in good agreement with the damage observed on the failed coupons.

Effect of Interfacial Debonding on the Strength of Composite Structure-Similarity Scale Model for the Wing-Box

Based on the wing-box structure, a model was established to analyze the strength of the scale model for the composite wing. Firstly, different failure criteria were set to determine damage onset of the components. The continuum damage variables were adopted in the stiffness degradation rule. Secondly, the interface elements were placed along the interface between the beam flange and the skin to investigate the effects of bonding strength on the ultimate load-carrying capacity of the wing-box. The failure modes of the wing-box structure were studied by using the nonlinear finite element method. The effect of flange’s width on the strength of wing-box was discussed based on the prediction method. The results indicated that the ultimate load-carrying capacity varied distinctly with the change of flange’s width. However, the bonding strength had limited effect on the model strength as the flange’s width increases to the critical value. The research methods and results of the study can serve as reference for the strength analysis on the scale model of composite wing as well as the determination of principles adopted in the design of the scale model for wing spar.

Static Tensile Properties Simulation of Plane Woven-Reinforced Laminates with Hole Damage

According to the structural difference between the unidirectional and the bidirectional laminate ply, the traditional 3-D (three-dimensional) Hashin failure criteria and the corresponding stiffness degradation rules were amended for damage tolerance simulation analysis of plane woven-reinforced laminates. Based on 3-D finite element technique, a secondary development was carried out on ANSYS software platform, a cumulative damage model was established, and the simulation analysis program for damage tolerance analysis of plane woven-reinforced laminates with hole damage was developed by use of APDL (ANSYS Parametric Design Language). In order to study the influence of different hole diameters on damage tolerance of plane woven-reinforced laminates, two kinds of G803/BMP316 plane woven-reinforced laminates with different hole diameters were selected as the analysis and verification object, and residual tensile strength and damage extension process of the damaged laminates were predicted and analyzed in the simulation. The simulations results are close to the experimental results, and visually present the situation of damage extension in each ply. It provides an effective tool for the damage tolerance analysis of plane woven-reinforced laminates with hole damage.

Study on the Tensile Strength in X-Cor Sandwich by Using Finite Element Method

In the tensile strength analysis, the failure criterion and materials stiffness degradation rule were proposed and the X-cor sandwich’s failure modes were also clarified. According to the failure criterion we used the elements with stiffness degradation and their distributions in the finite element model to simulate the types and propagation path of the failure and the failure mechanisms of X-cor sandwich were explained. The finite element analysis indicates during the tension firstly the interfaces between resin regions and Z-pin tips fail and the failure mode is Z-pin pull-out from the face-sheets. The finite element simulated results are in good agreement with the experimental results, the error range is -11.6%~9.7%. The comparison results show the failure criterion and stiffness degradation rule are reasonable and this method can be used to predict the X-cor sandwich’s tensile strength.

A New Method for Analyzing X-Cor Sandwich’s Shear Strength

The finite element software was used to get the X-cor sandwich’s shear strength. During the shear strength analysis, the failure criterion and materials stiffness degradation rules fitting for the analysis of X-cor sandwich’s failure mechanism were proposed and the X-cor sandwich’s failure process and modes were also clarified. According to the failure criterion we used the elements with stiffness degradation and their distributions in the finite element model to simulate the types and propagation path of the failure and the failure mechanisms of X-cor sandwich under shear were explained. The finite element analysis indicates during the shear firstly the resin regions fail and then the multiple failure modes of Z-pin pull-out from the face-sheet, Z-pin shear off and Z-pin buckling all exist. The propagation paths of the failure elements are dispersive. By contrasting the finite element results and test results the values are consistent well and the error range is -10.4%~7.4%. The comparison results show that the failure criterion and stiffness degradation rules are reasonable and this method can be used to predict the X-cor sandwich’s shear strength.