Damage Evolution Model Research Articles

Fatigue behaviors and damage mechanisms for Nb3Sn triple-helical structure at liquid nitrogen temperature

Nb3Sn triple-helical structure is the elementary structure in the superconducting cable of ITER magnets and undergoes prolonged fatigue loading in extreme environments leading to serious damage degradation. In this paper, the fatigue behaviors of the Nb3Sn triple-helical structure have been investigated by the strain cycling fatigue experiments at liquid nitrogen temperature. The results indicate that Nb3Sn triple-helical structures with short twist-pitches possess excellent fatigue damage resistance than that of long twist-pitches, such as longer fatigue life, slower damage degradation, and smaller energy dissipation. Meanwhile, a theoretical model of damage evolution has been established to reveal the effects of twist-pitches on fatigue properties for triple-helical structures, which is also validated by the present experimental data. Furthermore, one can see that the Nb3Sn superconducting wires in a triple-helical structure with the shorter twist-pitches have a larger elongation of helical structure and less cyclic deformation, which can be considered as the main mechanism of better fatigue damage properties for the triple-helical structures during the strain cycling processes. These findings provide a better understanding of the fatigue properties and damage mechanisms for Nb3Sn triple-helical structures in superconducting cables of ITER magnets.

Investigation on the off-axis tensile failure behaviors of 3D woven composites through a coupled numerical-experimental approach

Computational models with high precision and efficiency are in urgent need for the damage analyses of 3D angle-interlock woven composites which are widely accepted in composites industry. A novel concurrent multi-scale damage evolution modeling scheme is established based on a meso-scale representative volume cell (RVC) model and the multiphase finite element method to characterize the off-axis tensile response of carbon/epoxy composites. Modified Puck criterion and maximum shear stress criterion are adopted for fiber yarns. Parabolic yield criterion is adopted for the matrix. The fiber breakage, the inter-fiber fracture and matrix cracking are considered at mesoscopic level. To validate the proposed multi-scale damage model, off-axis tensile test is conducted with the help of 3D Digital Image Correlation (DIC) method. A reasonably good agreement is achieved between numerical predictions and experimental observations. Furthermore, the validated damage model is used to predict the tensile response of the composites considering full range on-axis and off-axis angles.

Particle filter-based damage prognosis using online feature fusion and selection

Damage prognosis generally resorts to damage quantification functions and evolution models to quantify the current damage state and to predict the future states and the remaining useful life (RUL). The former typically consists of a function describing the relationship between the damage state and a statistical feature extracted from the measured signals, thus the prognostic performance will strongly depend on the selection of a proper feature. Given the best feature may vary for different specimens or even at each time instant for the same specimen during damage progression, such selection is a challenging task but has received little investigation so far. In this context, this paper proposes a particle filter-based damage prognosis framework, which involves an online feature fusion and selection scheme. A prognostic model is considered for each feature, with a multivariate process equation, formulated using both a damage degradation function and a bias parameter, and a measurement equation linking the damage state and that feature considering a data-driven model and the bias. One PF is used to estimate the damage state, its evolution parameters, and the bias for each model. Then, at each step, the feature with the smallest estimated bias is selected as the best feature providing the most likely state vectors and is used to select the most likely samples of the damage state and growth parameters for predicting the RUL and for calculating the prior at the next step. The proposed prognostic framework is demonstrated by an experimental study, where an aluminum lug structure subject to fatigue crack growth is monitored by a Lamb wave measurement system.

Research on mesoscopic damage evolution models of TC4 titanium alloy under hot deformed process

Research on mesoscopic damage evolution models of TC4 titanium alloy under hot deformed process

New damage evolution law in plastic damage models for fiber‐reinforced cementitious composites

AbstractNowadays, fiber‐reinforced cement‐based composites (FRCC) can develop ductile behavior with high toughness when the matrix, fibers, and interface are optimally designed. These materials are promising solutions for constructing more resilient structures. In this context, the widespread use in large‐scale applications requires reliable models to predict the performance of FRCC structures. Usually, the studies on numerical modeling of FRCC apply the damage laws developed for quasi‐brittle concrete, making damage increase faster than really occurs in the presence of fibers. Therefore, the present paper proposes a new damage evolution model for FRCC based on energy dissipation concepts. It is assumed that the dissipated energy contributes fully to the evolution of the scalar damage and plastic strain variables, which is a technical advance from the previous works. The damage evolution is obtained with experimental envelopes of uniaxial stress–strain tests and the focal point from loading–unloading cycles. The results showed that the model accurately predicted experimental results using the damage‐plasticity framework. Furthermore, there are no empirical constants in the proposal, which means that it can be applied to any class of FRCC. An application regarding damage evaluation near a load transfer device in jointed plain cementitious pavements is presented. The damage distribution reveals that using FRCC materials has induced smaller damage values when compared with using conventional concrete. Consequently, cracking is reduced in such zones, increasing the structural life of the pavement.

Constitutive model of interfacial bond-slip between steel fibers and concrete matrix after exposing to high temperature

In the current study, the bonding properties between two kinds of steel fiber with different shapes and concrete matrix after exposing to high temperatures are investigated experimentally and theoretically. A total of 55 samples were prepared and divided into five groups, subjected to different temperatures ranging from 25 °C to 800 °C, then the residual fiber pull-out strength was measured after naturally cooling down to room temperature. The results of the fibers pulling-out experiment and microstructure analysis show that the bond-slip property of hooked-end steel fiber is better than that of straight steel fiber at any temperature. The influence of temperature on the fiber-pulling performance is mainly due to the change of microstructure in the cement matrix. With the increase of temperature, the cracks of the matrix gradually increase, and the fiber will degrade after 800 °C. According to experimental analysis, a new elastic-plastic constitutive model of bond-slip is developed within the thermodynamic framework. A unified yield function is proposed to describe the pull-out process of fibers of different shapes, which only needs to determine the hardening characteristics. Combined with the principle of free energy dissipation, a damage evolution model of the interface after exposing to high temperature is proposed. The model requires several parameters with definite physical meanings to be obtained from the experiment. Compared with the experimental results, the model proposed in this paper is reliable and provides a basis for further research on the mechanical properties of fiber-reinforced concrete after high temperatures.

Calculation of the recombination radii between various point defects and defect clusters in nickel via kinetic Activation Relaxation Technique

The recombination radii between various point defects and defect clusters are essential input parameters for mathematical and computational models of radiation-induced damage evolution. In this work, such recombination radii is calculated by the kinetic Activation Relaxation Technique (k-ART)—an off-lattice, self-learning kinetic Monte Carlo algorithm—in conjunction with molecular dynamics simulations. We found vacancy clusters exhibit larger average recombination radii with interstitials than single vacancies, reaching as large as 2.2a0 (a0 is the lattice parameter of nickel). Such recombination enhancement can be attributed to the intensified distortion near cluster surfaces. Unlike vacancy clusters, free surfaces feature smaller recombination radii than single vacancies. Their recombination radii are correlated with the angle between surface normal and <110> directions. Finally, the recombination radii of interstitial clusters are larger than vacancy clusters and strongly depends on the cluster configurations. Overall, the recombination radii of most internal defect clusters range from ∼2a0 to ∼2.4a0. Because previous research has found that recombination radii affect the density-size distribution of point defect clusters but not the fraction of a particular defect, our analysis suggests that given an accurate initial estimate of cluster density-size distributions, choosing a uniform recombination radius for different clusters in object kinetic Monte Carlo simulations should be sufficient to predict subsequent microstructural evolution.

Experimental and numerical study of step-path failure in jointed rocks

To study the failure process and mechanism of step-path failure in jointed rocks, experimental and numerical methods are conducted. In the damage evolution model, the previous damage field is introduced into the following finite element calculation. Based on this way, the initiation, propagation and coalescence of cracks can be simulated and presented. According to the results of numerical simulations and physical experiments, the brittle fractures caused by tensile stress may be the main reason of step-path failure, which interact with natural discontinuities to form macroscopic shear planes. Shear cracks also play an important role in the process of step-path failure, which can accelerate the process of step-path failure. Additionally, the proposed damage evolution model has a good agreement with the test results. According to the test and numerical results, the stability of jointed rocks by step-path failure is discussed, and the possible slides due to step-path failure are classified and analyzed, and the corresponding criterion and protective measures are also given. These results are expected to improve the understanding of step-path failure in rocks and can be used to analyze the stability of rock structures and rock masses, such as the slopes tunneling construction or, excavated underground openings.

Fatigue life estimation of stranded copper conductors using the method based on the fatigue damage evolution model

ABSTRACT To consider the effects of plastic damage caused by compaction procedure on the tensile fatigue life of stranded copper conductors, the fatigue life estimation method based on the fatigue damage evolution model was applied to estimate the tensile fatigue life of stranded copper conductors with two different compaction degrees. The macroscopic and mesoscopic elastic-plastic constitutive models of TU2 oxygen-free copper material based on mixed hardening theory and two-scale theory were constructed and the user defined material subroutines (UMAT) for these two models were programmed. The estimation results were compared with fatigue test results and verified the good applicability and accuracy of the applied method on the tensile fatigue life estimation of stranded copper conductors. The effects of the plastic damage caused by the compaction procedure on the tensile fatigue life of stranded copper conductors were obtained.

Damage evolution and failure characteristics of red sandstone with prefabricated crack under coupled dry–wet cycle-fatigue loading

Dry-wet cycle and fatigue loading both severely affect the stability of hydraulic engineering. In this paper, the deterioration process of red sandstone under coupled dry–wet cycle-fatigue loading was investigated from three aspects of deformation, energy, and damage. And the variation law of crack propagation mode of the samples was revealed. The results showed that the elastic modulus and the deformation modulus had a negative correlation with the number of dry–wet cycles, while the maximum strain and the residual strain were the opposite. Coupled damage variable was defined based on porosity and dissipated energy density, and a damage evolution model was established. With the increase of dry–wet cycles, the failure characteristics of the samples evolved from predominantly wing cracks to anti-wing cracks.

Estimation of cohesive zone model parameters for glass/Elium composites with different processing temperature

Important estimates were made of the cohesive zone mode (CZM) characteristics used to predict the fracture of Elium composites processed at various temperatures in this study. First, tests for the end notched flexure (ENF) and double cantilever beam (DCB) on composites processed at different temperatures (24°C, 50°C, and 80°C) were performed. Based on the experimental results, the numerical models of damage evolution were developed. And six pairs of cohesive parameters (cohesive strength and cohesive stiffness) to the specified fracture energy release rates were obtained. Then, a Tsai approach was developed to predict the cohesive strength of the Elium composite with various process temperatures based on the obtained parameters. In order to predict the delamination behavior of the Elium composite, the obtained cohesive parameters were then used to a numerical model of short beam shear (SBS). The peak force of the simulations was discovered to be consistent with the outcomes of the tests. The findings served as a reference for damage assessments of Elium composites processed at various temperatures.

A progressive damage model for quasi-static tension of 2D woven composites and FEM implementation

We tested the quasi-static tension behavior of the high-strength glass fiber four-Harness stain woven composite, Kevlar fiber plain woven composite, and their laminated hybrid composite. Their representative volume element models are established based on mesoscopic cross-section photographs combined with voxel mesh. A progressive damage model for predicting the damage initiation and evolution of the 2D woven composites is proposed. The crimping effect of plain-woven composites has been considered. The 3D Hashin and the maximum stress criterion are used as the fiber yarn and matrix's damage initiation criterion, respectively. The exponential model is used as the damage evolution model of the fiber yarn. A combination of exponential and reverse tangential damage models has been proposed to describe the damage evolution of the matrix. The proposed damage model is realized using user-defined subroutine UMAT and VUMAT. Abaqus/Standard performs the uniaxial tensile simulation of the two kinds of 2D woven composites with UMAT. Abaqus/Explicit solver simulates the laminated hybrid composite with VUMAT. The simulation results highly agree with the experiment results.

Fatigue failure and energy evolution of double-stepped fissures contained marble subjected to multilevel cyclic loads: a lab-scale testing

The instability of rock mass induced by the deterioration and failure of rock bridge is often encountered in hard rock engineering. Under engineering disturbance, a steep and gentle stepped sliding surface is prone to forming along the rock bridges between the intermittent rock joints, which directly controls the rock mass instability modes. In order to reveal the influence of fissure angle on the fatigue deterioration and energy evolution mechanism of stepped double-flawed hard rock, the multilevel cyclic loading mechanical test were carried out on flawed marble samples with fissure angle of 10°, 30°, 50°, and 70° angles. The testing shows that rock strength, fatigue lifetime, peak strain and dissipated energy increase with increasing fissure angle and the increase rate of them becomes sharply in the high cyclic level. In addition, the increase of dissipated energy accelerates with the increase of cyclic loading level, and shows a sudden increase trend in the last cyclic loading stage. When the joint fissure angle is 10°, the dissipated energy is the smallest and the dissipated energy is the largest at 70°. Moreover, a damage evolution model based on dissipated energy is established to describe the characteristics of damage accumulation. The model is in good agreement with the experimental data and reflects the nonlinear characteristics of damage accumulation.

Analysis of Electrical Resistivity Characteristics and Damage Evolution of Soil-Rock Mixture under Triaxial Shear.

Construction of engineering structures in geomaterials with soil-rock mixture (S-RM) is often a challenging task for engineers. When analyzing the stability of the engineering structures, the mechanical properties of S-RM often receive the most attention. To study the mechanical damage evolution characteristics of S-RM under triaxial loading conditions, a modified triaxial apparatus was used to conduct shear test on S-RM, and the change of electrical resistivity was measured simultaneously. The stress-strain-electrical resistivity curve and stress-strain characteristics under different confining pressures were obtained and analyzed. Based on the electrical resistivity, a mechanical damage model was established and verified to analyze the damage evolution regularities of S-RM during shearing. The results show that the electrical resistivity of S-RM decreases with increasing axial strain and that the differences in decrease rates correspond to the different deformation stages of the samples. With the increase in loading confining pressure, the stress-strain curve characteristics change from a slight strain softening to a strong strain hardening. Additionally, an increase in rock content and confining pressure can enhance the bearing capacity of S-RM. Moreover, the derived damage evolution model based on electrical resistivity can accurately characterize the mechanical behavior of S-RM under triaxial shear. Based on the damage variable D, it is found that the damage evolution process of S-RM can be divided into a non-damage stage, a rapid damage stage and a stable damage stage. Furthermore, the structure enhancement factor, which is a model modification parameter for the effect of rock content difference, can accurately predict the stress-strain curves of S-RMs with different rock contents. This study sets the stage for an electrical-resistivity-based monitoring method for studying the evolution of internal damage in S-RM.

Effects of fiber and rubber materials on the dynamic mechanical behaviors and damage evolution of shotcrete under cyclic impact load

Dynamic loads in underground construction environments can significantly damage supporting structures. The mechanical behavior of shotcrete under high strain rate impact has received significant attention. However, few researchers have investigated the performance degradation law, damage evolution process, and failure mode of shotcrete under cyclic impact load. This study utilized the split Hopkinson pressure bar (SHPB) to conduct cyclic impact loading experiments on shotcrete reinforced with copper-plated steel fiber (CSF), basalt fiber (BF), polypropylene fiber (PF), and rubber particles (RP). The addition of reinforcing materials significantly improved the dynamic mechanical properties of shotcrete. Under cyclic impact, the stress-strain curves of reinforced shotcrete basically coincided in the elastic deformation stage. As the content of the reinforcing materials increased, the dynamic mechanical properties of the shotcrete improved. The performance of fiber-reinforced shotcrete improved under the compaction effect caused by the first impact. Only rubber shotcrete sustained 6 impacts under cyclic constant impact pressure. Based on the ultrasonic velocity obtained by non-destructive testing, a cumulative damage evolution model during cyclic impact was established. The incorporation of RP effectively slowed down the damage evolution rate and increased the shotcrete's bearing capacity for cumulative damage. This paper conducted a comprehensive comparative analysis and concluded that the addition of rubber particles at a content level of 5% was the most cost-effective option to enhance the dynamic mechanical properties of shotcrete. The findings provide a theoretical reference for underground engineering supporting structures subject to long-term cyclic dynamic loading.

Investigation of the heat energy and multi‐level load on subsurface fatigue damage evolution via multi‐scale method

AbstractThe relationship between heat energy and initial fatigue life of different metals under multi‐level loading stress and elevated temperature is introduced. The fatigue damage evolution model was established from the microscopic and mesoscopic perspectives to explore the fatigue damage and the crack initiation location at elevated temperature. Based on the method of continuous damage mechanics, the influence of multi‐level loads on fatigue cracking life and heat energy on strain energy of distribution were investigated. The mathematical model is verified by the experimental data. The model has important engineering significance for predicting the service life of parts at elevated temperature.

Numerical model of cumulative damage evolution of offshore wind turbine grouted connection under cyclic axial load

GCs in OWTs are exposed to fatigue loads that can lead to damage of the grout before ultimate limit state is reached. A uniaxial and fatigue compression test of high strength grout material were carried out to obtain the compressive strength, failure mode, fatigue life and load-displacement relationship of test cubes. A uniaxial and fatigue tests were carried out on GCs specimens to study the damage evolution of the GCs. The fatigue test on GC was done by applying six incremental amplitude cyclic load ranges of 30%–80% of ultimate load on the GC. The scalar damage degradation parameter (SDEG) from the result of the numerical simulation was used to estimate a damage index which measured the cumulative damage evolution. The cumulative damage evolutions were influenced by the cyclic load amplitude. The larger the load amplitude, the higher the damage index accumulated. The numerical simulation results compared with the DNV code method showed that the DNV code predicted lower damage values for fatigue loads ratio of up to 0.725 and predicted higher damage values beyond the 0.725 loads ratio for the GC. The proposed numerical model predicted the laboratory test results of the grout cube and the grouted connections.

Investigation of fatigue failure and energy characteristics of rock exposed to complicated stress disturbance paths: Cyclic stress amplitude effect

AbstractTo deeply reveal the differences in geomechanical responses of rock during mining exposed to complicated stress disturbance of excavation unloading and cyclic loading conditions, cyclic triaxial fatigue loads with four cyclic stress amplitude (CSA) (60, 100, 130, and 160 MPa) were performed on deeply buried rock. Results show that rock deformation, energy evolution, and failure modes are all influenced by the CSA. Additionally, it is found that all the strain energy increases with increasing CSA during rock failure. Especially, the dissipated energy increases greatly at the confining stress unloading stage (CSUS) than the fatigue loading stage (FLS), indicating the influence of unloading on rock damage accumulation. Moreover, a damage evolution model reflecting a first slow and then quick increase pattern was established using the dissipated energy. Finally, a transition failure mode from the dominant tensile‐shear to pure shear is found. It is suggested that much more energy needs to be consumed to induce shear cracks than tensile cracks.

Research on Algorithm of Corrosion Fatigue Damage Evolution of Stay Cables and Structural Mechanical Behavior with Cable Fracture

From the point of view of material multiscale analysis, the deterioration of the fatigue properties of the cable is due to the micro-damage inside the strand. To describe the damage failure process of the cable as accurately as possible, many micro damage details need to be implanted in the strand model. However, with the increase of the number of wires in the cable body, this modeling method will produce a large number of elements in the finite element model of the stay cable, which makes the calculation cannot be completed iteratively. Based on this, a time-step adaptive simulation method for corrosion fatigue damage evolution of stay cables was proposed in this paper. In this method, the corrosion fatigue damage evolution model was implanted in the local part of the strand model, and a damage variable was used to comprehensively consider the evolution behavior of distributed micro-damage in the strand, which satisfies the calculation accuracy and realizes the simulation of the whole process of fatigue deterioration of the stay cable, greatly improving the calculation accuracy and convenience. Then taking an in-service cable-stayed bridge as an example, the stress of the main beam and the local spatial stress of the main beam under the special condition of the cable damage failure were studied by combining the rod model with the local model, which provides data reference for the replacement of the cable of the cable-stayed bridge with a long construction life.

Experimental and numerical investigations on damage evolution of concrete under sulfate attack and freeze-thaw cycles

The macro-microstructure tests of concrete under the alternating action of salt freezing (ASF) were conducted to investigate the macro-mechanical properties and microstructure pore evolution patterns of concrete. Combined with CT scanning and 3D pore model reconstructing technologies, we present the evolution equation of concrete porosity and the quantitative relation between the fractal dimension of concrete pores and the macroscopic strength under the ASF. Then, a macro-microscopic damage evolution model of concrete was proposed to study the structural performance evaluation of an aqueduct. The results show that the compressive strength (fc), splitting tensile strength (ft), and relative dynamic modulus (Erd) of concrete specimens under the ASF show a decreasing trend as a whole, and the mechanical properties of concrete gradually decrease with the increase of sulfate solution concentration. With the increase of the cycles of salt freezing alternation, the pore fractal dimension of the concrete gradually decreases and the porosity gradually increases. After the cycle of 8 times, the pore fractal dimension decreases by 6.06%, and the porosity increases by 7.30% compared with the initial state. The porosity of concrete is negatively correlated with the strength, while the fractal dimension of the pore structure is positively correlated with the strength. When the ASF reaches 8 times, the maximum compressive stress and tensile stress of the groove body are 9.48 MPa and 3.13 MPa, respectively, which appear at the ends of the lower chord. The displacements of the bottom and side wall plates are 0.384 mm and 3.289 mm, respectively. The penetrating cracks appear at the junction, and the structure severely deteriorates.