Damage Evolution Model Research Articles

Method to assess the interplay of slope, relative water depth, wave steepness, and sea state persistence in the progression of damage to the rock layer over impermeable dikes

The objective of this research was to develop a new methodology to assess the progression of damage to sloped coastal structures such as revetments, dikes, and mound breakwaters by applying dimensional analysis. The adequacy of the derived functional relationship was verified with the same experimental data (rock layer over impermeable dikes under irregular waves and four dike slopes) originally used to obtain the Van de Meer stability formula. The method addresses the epistemic uncertainty of the damage evolution model and its dependence on the experimental design and technique, the non-dimensional incident sea-state characteristics at the foot of the slope, relative water depth, relative wave height, wave steepness, sea-state persistence, and number of waves. It is specific to each dike slope. Specifically, the scarcity of experimental data in shallow water conditions are considered. Accordingly, the sigmoid function is proposed as an alternate model to quantify the progression. In the current state of knowledge, it is uncertain how the formulas based on lab-experiments perform for real-world design conditions. More research in the form of further test series is thus necessary to explore this new approach in greater depth.

Damage Evolution of Concrete Piles Mixed with Admixtures in Marine Corrosion and Freeze-Thaw Environment

Marine corrosion and freeze-thaw environment will bring serious damage to marine concrete structures, leading to affect the safety and service life of structures. With the help of artificial climate and environment simulation laboratory, the variation of the compression strength and elastic modulus of concrete with the number of freeze-thaw cycles and corrosion time under the corrosion and freeze-thaw environment is studied. The results show that both of them firstly increase and then decrease with corrosion time. When the corrosion time is 270 d and the freeze-thaw time is 90 times, the strength of concrete decreases by 13% and the elastic modulus decreases by 5%. Then, based on the theory of damage mechanics, the damage evolution and constitutive model of concrete under the marine corrosion and freeze-thaw environment are established. Compared with the experimental results, it is found that the model can well describe the damage evolution characteristics of concrete under marine corrosion and freeze-thaw environment. Finally, a numerical model is established on the basis of elastic modulus and strength degradation model of concrete under marine corrosion and freeze-thaw environment. Elevated pile caps of concrete pile component are taken as an example to analyze the process of damage, and the change rules of displacement, deformation, and damage of concrete pile are obtained.

Evaluation of fatigue performance of cement-treated composites based on residual strength through discrete element method

Fatigue damage is the process of material fatigue failure caused by cyclic loading, and the development of damage degrades the material properties. This paper aims to investigate the fatigue degradation law of cement-treated base (CTB) materials using a discrete element method (DEM) simulation technique. A fatigue evolution model was adopted to characterize the time-dependent fatigue damage under cyclic loading. Virtual semi-circular bending (SCB) fatigue and residual strength tests at different fatigue stages were performed on mesoscale DEM model to evaluate the fatigue damage of CTB material. With residual strength variable, the fatigue damage model was established to reveal the accumulation of damage. The results show that the residual strength evolution nearly appears an exponential correlation with the fatigue stages. In the first stage, the strength degradation is stable and appears as approximately linear. At about 80% of the fatigue life, the degradation rate is significantly accelerated. The residual strength degradation rate is related to the initial stress level and decreases with the increase of stress ratio. At the same fatigue life stage, the greater residual strength attenuation will be generated with a lower load level. The fatigue damage evolution model indicates the fatigue damage accumulation approximately linearly in the early stage and rapidly in the late stage. The late fatigue stage has the main contribution to fatigue failure. The degradation law demonstrates the lower the load level is, the more the damage accumulation at the same fatigue life stage will be, and the corresponding critical damage is greater. Moreover, based on the strength degradation law, a prediction model is established to evaluate the residual fatigue life of pavement base material.

An energy-based damage model for red-bed sandstones subjected to drying–wetting cycles

A series of experiments is performed to determine the damage behaviour and energy evolution of red-bed sandstones subjected to drying–wetting (D–W) cycles. The experimental results reveal that accompanied by the strain increases, the input energy density gradually increases, the elastic energy density increases slowly first, then increases linearly, and reaches the maximum value at the peak strength, then gradually decreases. The dissipated energy density continuously increases and then maintains a steady-state level before it finally increases rapidly. Furthermore, with the increase in the number of D–W cycles, all three energy densities of specimens present a linear downward trend. According to the damage variable defined by the energy principle, the damage evolution models of the uniaxial compression strength (UCS) and peak strain of the D–W specimen are established, which can well characterise the evolution of the UCS and peak strain of rocks after different numbers of D–W cycles.

Experimental and theoretical model study on the dynamic mechanical behavior of sintered NdFeB

Sintered neodymium iron boron (NdFeB) is a widely applied permanent magnet, whose dynamic mechanical properties restrict the further development of its application. In order to provide a theoretical basis for the application of NdFeB in the shock field, the dynamic mechanical behavior of sintered NdFeB was studied experimentally and theoretically in this paper. First, the Split Hopkinson Pressure Bar (SHPB) experiments under different strain rates were carried out. The dynamic process was captured by a high-speed camera, and the strain data measured by oscilloscope was processed with the three-wave method. Combined with the electron microscope analysis of the recovered samples, the dynamic failure process and characteristics of NdFeB under high-speed impact were explored, which provided an experimental basis for the following theoretical research. Given the theoretical deficiency of the dynamic mechanical properties of sintered NdFeB and the assumption of microcracks with uniform distribution and no friction, a theoretical model of damage evolution process of brittle materials was established based on the dynamic crack growth criterion. Combining the damage evolution model with Zhu-Wang-Tang (ZWT) constitutive model, the damage constitutive model of sintered NdFeB was established, whose validity was verified by the comparison with the experimental data.

On the Hybrid Modeling of Phenomenological Damage Evolution in Low Carbon Steels During Equal Channel Angular Extrusion Process

On the Hybrid Modeling of Phenomenological Damage Evolution in Low Carbon Steels During Equal Channel Angular Extrusion Process

A mesoscale fatigue progressive damage model for 3D woven composites

A mesoscale fatigue progressive damage model (FPDM) is proposed for fatigue life prediction and failure behavior assessment of 3D woven composites (3DWC). The Hashin's fatigue criteria and the maximum tensile/shear stress criteria are used as damage activation criteria for the yarn and resin-rich matrix, respectively. A fatigue damage evolution model is developed based on Fang's static-load damage evolution model, where the damage irreversibility and compressive crack closure effect are considered. The UserMat subroutine and APDL language in ANSYS are employed to implement the fatigue process of 3DWC. The results show that all predicted fatigue lives are within two-fold error band.

Study on damage evolution and constitutive model of sandstone under the coupled effects of wetting-drying cycles and cyclic loading

A constitutive model for damage is proposed to describe the deformation and strength characteristics of sandstone under the coupled effects of wetting-drying cycles and cyclic loading. First, the microparameters of sandstone were calibrated by wetting-drying cycles and uniaxial compression tests. Subsequently, a discrete element model of the specimen was established by numerical simulation software (PFC2D), and a cyclic loading test was performed to obtain relevant test data. Second, assuming the microdamage of the sample is described by the Weibull distribution, the macrodamage can be described by a mechanical model. Based on the Lemaitre strain equivalence hypothesis, the coupled damage variable of the specimens was derived. Finally, the constitutive model of damage of sandstone under the coupled effects of wetting-drying cycles and cyclic loading was derived from the statistical mechanics theory of damage. In addition, the damage evolution process of sandstone under the coupled effects of wetting-drying cycles and cyclic loading was validated by an analysis of the microscopic force field and calculations of the damage variable. Compared with the existing models, the constitutive model proposed in this paper can better reflect the stress-strain relationship and damage evolution of sandstone under the coupled effects of wetting-drying cycles and cyclic loading.

An irreversible bilinear cohesive law considering the effects of strain rate and plastic strain and enabling reciprocating load

The commonly used bilinear cohesive law doesn’t consider the effects of strain rate and plastic strain, but it is well known that strain rate and plastic strain can greatly affect materials’ mechanical response. In this paper a new bilinear cohesive law is proposed that can handle these two effects and enables reciprocating load. Compared with the commonly used bilinear cohesive law, one difference in the new bilinear cohesive law is that normal traction and tangential traction are always coupled even when normal traction is negative. And after combined with finite thickness modeling method of cohesive element, this new bilinear cohesive law can solve problems like penetration, force discontinuity and increase of compliance. For damage evolution model, the difference between monotonically increasing effective separation and monotonically increasing damage factor is explained. The influence of strain rate (or opening speed) on stiffness, fracture strength and critical energy release rate is referred from literature. Based on zero plastic strain damage factor model, a Generalized Damage Factor Model (GDFM) is proposed that can cover all materials from zero plastic strain to full plastic strain by changing only one parameter. A Bilinear Cohesive Law Update Method (BCLUM) is proposed to make this new bilinear cohesive law handle reciprocating load, which includes the update of local coordinate system and bilinear cohesive law parameters. A single cohesive element analysis is presented first to show some basic differences among different bilinear cohesive laws, and then Tapered Double Cantilever Beam (TDCB) and Mixed Mode Bending (MMB) analyses are used to verify the proposed law.

Continuum Damage Mechanics Approach for Modeling Cumulative-Damage Model

In this study, we propose a novel cumulative-damage model based on continuum damage mechanics under situations where the mechanical components are subjected to variable loading. The equivalent completely reversed stress amplitude accounting for the effect of mean stress, stress gradients, loading history, and additional hardening behavior related to nonproportional loading paths on high-cycle fatigue under variable loading is elaborated. The effect of mean stress, stress gradients, loading history, and additional hardening behavior related to nonproportional loading paths is considered by averaging the superior limit of the intrinsic damage dissipation work in the critical domain. We developed a novel cumulative-damage model by introducing the equivalent completely reversed stress amplitude into the damage-evolution model. For better comparison, existing cumulative-damage models, including the Palmgren–Miner law, corrected Palmgren–Miner law, Morrow’s plastic work interaction rule, and Wang’s rule, were employed to predict the fatigue life under variable loading. The proposed model performed better, considering the error scatter band obtained by plotting the predicted and experimental fatigue life on the same coordinate system. The model precisely predicts fatigue life under variable loading and easily identifies its material constants.

MULTIPLE IMPACT COMPRESSIVE PROPERTIES AND CONSTITUTIVE MODEL OF ULTRA-HIGH TOUGHNESS CEMENTITIOUS COMPOSITES

The mechanical properties of ultra-high toughness cementitious composites (UHTCC) under multiple impacts were studied using an 80-mm split Hopkinson pressure bar (SHPB). The evolution law of the stress-strain curve under different numbers of impacts was analyzed and compared with that of other fiber reinforced concrete. The experimental results show that under multiple impact loads, the strain rate increased exponentially with the increase of the number of impacts due to damage accumulation. The peak strength of UHTCC decreased linearly with the strain rate, while the peak strain and cumulative energy absorption increased gradually. The single energy absorption value increased first and then decreased with the increase of the number of impacts. The thermal activated damage evolution (TADE) model could only describe the mechanical response of UHTCC upon the first impact, but could not reflect the evolution law of the mechanical properties under multiple impacts. Comparatively, the damage evolution model based on Weibull distribution could well reflect the cumulative damage evolution law and the stress-strain curves of UHTCC under multiple impacts. According to the calculation of the damage degree, the sample could be considered to have been completely damaged after the third impact. However, the sample could still be kept as a whole by the bridging effect of the PVA fibers. It demonstrated its good crushing resistance capacity.

Study on the Damage Model of Coal Rock Caused by Hydraulic Pressure and Electrical Impulse in Borehole

The purpose of this study is to study the damage and fracturing effects of high-voltage discharge on coal-rock mass under the action of hydrostatic pressure. Based on the traditional damage evolution model and the change of the effective bearing area and stress around the microcrack of coal-rock mass on a microscopic scale, the expression of macroscopic damage variation of coal-rock mass under the action of electrohydraulic coupling was derived, and its damage constitutive relation was established. The high-voltage pulse water shock stress test of coal-rock mass under the conditions of different water pressures and voltages was carried out, and its damage numerical model was established by the ABAQUS/XFEM. The damage variable values of coal-rock mass with different electrohydraulic parameters were compared to characterize the generation and expansion of internal macroscopic cracks. From the results, it is shown that the damage variable based on the effective bearing area and stress around the crack can represent the morphology and expansion change of crack of coal-rock mass with different electrohydraulic parameters clearly and quantitatively. Different hydrostatic pressures and discharge voltages have influence on the damage variables of coal-rock mass, but different influencing degrees cause different damages on coal-rock mass. The damage of coal rock can be characterized by the change of the effective bearing area and stress around microcracks in coal body. So, stress testing and numerical simulation have verified the correctness of the damage model.

An experimental and numerical investigation on low velocity impact response of GLAREs

Glass fiber aluminum laminates (GLAREs) are a type of fiber metal laminates (FMLs) that are widely used in the aviation industry. The present article aimed to carry out the numerical and experimental study of the damage mechanism initiation and development in the FMLs subject to low velocity impact. In the experimental part, the drop weight impact test was conducted at four energy levels of 8, 11.5, 15, and 18.5 J on the GLARE laminates. The first crack in the aluminum layer was observed at 18.5 J in the lower aluminum layer. In the numerical simulation, the user-material subroutine VUMAT, including the three-dimensional Hashin damage initiation criterion and the modified progressive damage evolution model, was coded and implemented in the ABAQUS/Explicit finite element package to predict damage initiation and development. The numerical simulations were validated by the experimental results in terms of force–time, force–displacement, and absorbed energy-time curves. The optical microscopy (OM) and scanning electron microscopy (SEM) images of the specimen cross-section were produced to detect the FML damage pattern. The numericalsimulation andexperimentalresults showed to be in good agreement.

A Strain Rate-Dependent Damage Evolution Model for Concrete Based on Experimental Results

There are various definitions of damage variables from the existing damage models. The calculated damage value by the current methods still could not well correspond to the actual damage value. Therefore, it is necessary to establish a damage evolution model corresponding to the actual damage evolution. In this paper, a strain rate-sensitive isotropic damage model for plain concrete is proposed to describe its nonlinear behavior. Cyclic uniaxial compression tests were conducted on concrete samples at three strain rates of 10−3s−1, 10−4s−1, and 10−5s−1, respectively, and ultrasonic wave measurements were made at specified strain values during the loading progress. A damage variable was defined using the secant and initial moduli, and concrete damage evolution was then studied using the experimental results of the cyclic uniaxial compression tests conducted at the different strain rates. A viscoelastic stress-strain relationship, which considered the proposed damage evolution model, was presented according to the principles of irreversible thermodynamics. The model results agreed well with the experiment and indicated that the proposed damage evolution model can accurately characterize the development of macroscopic mechanical weakening of concrete. A damage-coupled viscoelastic constitutive relationship of concrete was recommended. It was concluded that the model could not only characterize the stress-strain response of materials under one-dimensional compressive load but also truly reflect the degradation law of the macromechanical properties of materials. The proposed damage model will advance the understanding of the failure process of concrete materials.

Predicting failure pressure of reinforced thermoplastic pipes based on theoretical analysis and experiment

Because they transport high-temperature and high-pressure oil and gas, the pressure-carrying capacity of reinforced thermoplastic pipes (RTPs) needs to be high. This study develops two analytical models to estimate deformation and stresses in RTPs with any number of layers under internal pressure based on their nonlinear mechanical behaviors. The Hashin–Yeh failure criterion and the damage evolution model of composite materials are combined, and changes due to deformation are introduced to the winding angle to analyze the progressive failure of RTPs. The modeling covered stress analysis, failure evaluation, and material degradation. By comparing their results with those of the finite element model (FEM) and experiments, the advantages and disadvantages of the two theoretical models are determined. The stress distribution and failure pressure calculated by them were in good agreement with those obtained by the FEM and the experiments. However, the accuracy of calculation of the proposed model (model-Ⅰ) was clearly better than that of homogenization model (model-Ⅱ), and its results of failure pressure and the failure sequence were more accurate. Model-I was thus used to obtain the optimal range for the winding angle of the fiber’s, and to discuss the influence of diameter-to-thickness (D/t) ratios on the first-ply failure (FPF) pressure and burst pressure.

A model and simulation strategy for fatigue damage evolution of copper films

A damage model and simulation strategy are developed to simulate fatigue damage evolution and predict fatigue life of metallic films. The fatigue damage model is established based on the collective effect of current all micro/nanoscale cracks within material in a homogenized way, and block cycle jump method is used in the simulation strategy, which can speed up fatigue damage evolution simulation for metallic films reasonably. Based on numerical study, fatigue damage evolution and life of the smooth and notched specimens for copper films subjected to various stress levels are numerically analyzed and compared with the corresponding experimental results. It shows that the developed damage model and simulation strategy can be used to simulate the fatigue damage evolution and predict fatigue life for metallic films reasonably.

Investigation of Microcrack Propagation and Energy Evolution in Brittle Rocks Based on the Voronoi Model.

The cracking of rock mass under compression is the main factor causing structural failure. Therefore, it is very crucial to establish a rock damage evolution model to investigate the crack development process and reveal the failure and instability mechanism of rock under load. In this study, four different strength types of rock samples from hard to weak were selected, and the Voronoi method was used to perform and analyze uniaxial compression tests and the fracture process. The change characteristics of the number, angle, and length of cracks in the process of rock failure and instability were obtained. Three laws of crack development, damage evolution, and energy evolution were analyzed. The main conclusions are as follows. (1) The rock’s initial damage is mainly caused by tensile cracks, and the rapid growth of shear cracks after exceeding the damage threshold indicates that the rock is about to be a failure. The development of micro-cracks is mainly concentrated on the diagonal of the rock sample and gradually expands to the middle along the two ends of the diagonal. (2) The identification point of failure precursor information in Acoustic Emission (AE) can effectively provide a safety warning for the development of rock fracture. (3) The uniaxial compression damage constitutive equation of the rock sample with the crack length as the parameter is established, which can better reflect the damage evolution characteristics of the rock sample. (4) Tensile crack requires low energy consumption and energy dispersion is not concentrated. The damage is not apparent. Shear cracks are concentrated and consume a large amount of energy, resulting in strong damage and making it easy to form macro-cracks.

A Two-phase Constitutive Model with Damage for Tungsten Heavy Alloy

Tungsten heavy alloy is a kind of two-phase alloy composed of high-strength tungsten phase and binder phase with good-plasticity. Its mechanical properties and damage evolution are affected by both phases. The static and dynamic mechanical tests of 92.5W-4.9Ni-2.1Fe-0.5Co are carried out. According to the characteristics of stress-strain curves, KHL model is selected as the constitutive model of the material. Then, combined with Eshelby equivalent inclusion theory and Mori Tanaka mean field theory, the stress-strain relationship of each phase in tungsten heavy alloy is studied by introducing representative volume element (RVE). The damage evolution model considering the strain rate effect is proposed, and according to the different loading states, a two-phase constitutive model with damage is established. By compiling the UMAT subroutine, the test conditions of different strain rates are calculated in ABAQUS software. The simulation results are in good agreement with the test results, and the validity of the proposed model is verified.

Damage development during the strain induced phase transformation of austenitic stainless steels at low temperatures

The strain-induced martensitic transformation greatly affects the plastic behavior of the metastable austenitic stainless steels. The martensitic transformation continuously changes the initially homogeneous material into a strongly heterogeneous bi-phase one. In addition to the hardening behavior, this phenomenon would influence the damage growth and load-carrying capacity of the material during the plastic deformation. In this study, plastic behavior of the material AISI 304 including the hardening and damage growth, has been examined at low temperature; where a high rate of martensitic transformation affects the microstructure strongly. Experimental analysis and microscopic observations have been performed for evaluating the martensite content and damage growth. In addition, based on the continuum damage mechanics, a simplified damage evolution model has been proposed to capture the effect of phase transformation on the damage growth rate explicitly. The results show that the damage initiates with a considerable rate in early stages of transformation, however at higher levels of transformation, damage growth rate decreases until a sudden fracture. The presented model properly predicts the observed damage behavior.

In-situ synchrotron X-ray tomography investigation of damage mechanism of an extruded magnesium alloy in uniaxial low-cycle fatigue with ratchetting

This paper elucidates the relationship between the primary deformation processes and associated damage mechanisms operating in an extruded AZ31 Mg alloy under uniaxial low-cycle fatigue with an occurrence of ratchetting. Different mean stresses and stress amplitudes were prescribed to study twinning/detwinning-dominated (TDD), twinning/detwinning and slip-dominated (TDSD), and slip-dominated (SD) cyclic deformations, respectively. In each case, the damage was examined by synchrotron radiation micro-computed tomography and scanning electron microscopy. The plastic deformation mechanism for each load case was then characterized by electron backscatter diffraction and transmission electron microscopy. Profuse twins were detected in the TDD and TDSD samples, while more complex structures and higher dislocation densities were found in the TDSD and SD samples where dislocation slip was plentiful. The TDSD sample had the most damage initiation sites owing to the transgranular damage caused by twins and the intergranular damage induced by the combined effect of <c+a> dislocations and twins, followed by the TDD sample because of the low dislocation density, while the SD sample had the fewest due to the lack of twins. Shear linkage between the isolated cracks was observed only in the TDSD sample. This provides rich evidence for the modelling of damage evolution of extruded Mg alloys.