Continuum Damage Mechanics Theory Research Articles

Quantitative study on fatigue characteristics of warm mix recycled asphalt

The warm mix recycling technology of asphalt pavement can improve the utilization rate of solid waste in highway construction industry on a large scale, and reduce the emission of harmful gases ( NOX, CO2, benzopyrene, etc.) in the process of road construction. It is one of the effective ways to realize carbon neutrality in highway construction industry. The main purpose of this study is to systematically analyze the fatigue characteristics of warm mix recycled asphalt (WMRA) from the perspective of quantitative research, and to provide scientific basis for the popularization and application of this technology. Therefore, this study mainly evaluated the anti-fatigue characteristics of WMRA under different conditions based on the linear amplitude sweeping test ( LAS test). Based on the calculation and analysis of the commonly used fatigue judgment indexes ( stress-strain curve, phase angle-strain curve, S×N curve ( S is the ratio of the instantaneous modulus to the initial modulus of the material, which is often replaced by the virtual modulus in the LAS test, and N is the number of cyclic loadings.), virtual strain storage energy-strain curve), the peak strain of virtual strain storage energy is recommended as the fatigue judgment standard from the perspective of reliability and accuracy, and the peak strain of damage factor is proposed as one of the new fatigue judgment standards. In this paper, the nucleation of microcracks and the coalescence of microcracks are distinguished in the process of fatigue damage evolution, and the peak strain of virtual strain energy storage and the peak strain of damage factor are used as the judging indexes respectively. Finally, based on the theory of continuum damage mechanics, the loss modulus of WMRA is selected as the representative value of material properties to calculate the virtual modulus and damage factor, and the fatigue damage evolution model of WMRA based on the viscoelastic continuum damage model ( VECD model) was constructed. Based on this model, the anti-fatigue characteristics of WMRA with the reclaimed asphalt pavement ( RAP) content were analyzed.

Experimental Study and Creep-Fatigue Life Prediction of Turbine Blade Material DZ125 Considering the Nonholding Effect and Coupling Effect of Stress and High Temperature

Abstract In response to the problem of creep-fatigue interaction damage failure of aero-engine turbine blade material, based on the modified damage evolution model of Kachanov-Rabotnov and Chaboche, a creep-fatigue life prediction model for nickel-based superalloy DZ125 is constructed considering the nonholding effect and coupling effect of stress and high temperature with the nonlinear interaction and superposition of creep damage and fatigue damage according to the continuum damage mechanics theory. Simultaneously, the microfracture morphology of DZ125 was analyzed using a scanning electron microscope, revealing the micromechanism of creep-fatigue interaction. The research results manifest that the creep-fatigue life prediction model has a high life prediction ability within ±2.0 times the dispersion band of the prediction results. Concurrently, a large number of intertwined tearing edges, microcracks, and microvoids appear in the fracture morphology, and creep and fatigue interact with each other in the form of effective stress. The above research can provide theoretical support for predicting the lifespan of mechanical structures in a high-temperature environment.

Investigation on A Viscoelastic Creep Damage Constitutive Model for HTPB Propellant and Its Application in Finite Element Analysis

Solid rocket motor (SRM) is typically kept in storage for a significant portion of its lifespan. During storage, the propellant grain creeps under the action of gravity. To investigate the creep properties of hydroyl-terminated polybutadiene (HTPB) propellant under long-term loading, a creep damage constitutive model is developed based on the generalized Kelvin model and continuum damage mechanics theory. Parameters for this model are determined through creep tests conducted on HTPB propellant under various stress levels. Furthermore, to enable the application of the developed propellant constitutive model in the finite element analysis of SRM, the derived constitutive equation is transformed into an incremental form and integrated into the user subroutine UMAT of the finite element analysis platform ABAQUS. Subsequent to this, a three-dimensional SRM model containing the case, the insulator, and the propellant grain is established. The mechanical response of the grain under thermal and gravitational loads is calculated and analyzed. The results indicate that the stress concentration region in the grain is located at the stress release boot in the forward dome of the motor, where damage occurs. The methods employed in this paper and the conclusions drawn can serve as a reference for evaluating the structural integrity and storage lifespan of the SRM.

A damage model for matrix cracks in composite laminates under fatigue loading based on continuum damage mechanics

A damage model for transverse matrix cracks in composite laminates under fatigue loading was presented in this paper. The model was prosed based on the theory of continuum damage mechanics (CDM) at macro level and could capture the ‘edge effect’ of matrix cracks in composite laminate under fatigue loading. To obtain the constitutive equation of UD lamina containing transverse matrix cracks, a polynomial Gibbs free energy function was derived, and a macro damage parameter was introduced to characterize the influence of matrix cracks on multidirectional stiffness properties of UD composite. To predict the initiation and evolution of matrix cracks, a previously deduced initial crack initiation life function and a Paris-like equation in terms of damage driving force were employed, respectively. Prediction results of two cross-ply laminates under fatigue loading with different stress levels were compared to the experimental results and prediction results obtained from previously proposed model. The comparison results indicate the presented model is more effective and reliable in predicting the initiation and evolution of matrix cracks and the corresponding stiffness degradation in composite laminates under fatigue loading.

A thermodynamically consistent strain difference-based nonlocal damage mechanics approach for failure analysis of quasi-brittle materials

The nonlocal integral approaches are established methods known for their effectiveness in dealing with the challenges of ill-posed behaviour and mesh sensitivity during the strain softening process, especially within classical continuum theories. The present work extends the strain difference-based nonlocal approach to continuum damage mechanics (CDM) theories for predicting the failure behaviour of quasi-brittle materials. The strain difference approach is adopted for two reasons: (i) it maintains physical realism and indirectly incorporates nonlocal effects while computing both the damage variable and the damage energy release rate, and (ii) the constitutive model maintains a symmetry nature in constructing the nonlocal part of the stiffness matrix, reducing the computational cost in strain-softening problems. The state and damage evolution equations for the present nonlocal approach are formulated within the thermodynamic framework. Numerical examples involving 2D and 3D cases are solved: (i) to study the influence of nonlocal parameter ‘α’ on the damage distribution while capturing the post-peak behaviours, (ii) to demonstrate the effectiveness of the present methodology by obtaining mesh-independent results and accurately predicting damage propagation paths, and (iii) to compare the experimental results and numerical structural response for coarse mesh, highlighting both computational efficiency and reduction of mesh-bias dependency. The results obtained by the strain difference-based nonlocal damage model agree well with the experimental results in the literature.

AC layer fatigue damage analysis and reflective cracking control of CRC + AC composite pavement

The current continuous reinforced concrete composite asphalt pavement (CRC + AC) design method in China does not consider the effect of the asphalt concrete (AC) layer on the longitudinal reinforcement rate of the continuous reinforced concrete (CRC) layer. To address such issues, a finite element model of CRC + AC using continuum damage mechanics theory and finite element method was established. The most unfavorable working condition and the location of the greatest damage by comparing the damage distribution under different working conditions were determined. To resolve the limitations of traditional design methods of CRC + AC composite pavement, criteria for the microcrack width of the CRC layer under different AC layer thicknesses were proposed, based on the combined effects of AC layer thickness and CRC layer microcrack width on the damage of the AC layer. The results suggest that the left lane vehicles braking and the right lane vehicles driving at a constant speed are the most unfavorable working conditions, with the greatest degree of damage found on the lane divider of AC layer. meanwhile, the microcrack width should be below 0.64 mm to mitigate the risk of Top-Down cracking and reflective cracking. Additionally, the CRC plate crack width control standards are provided for AC layer thicknesses ranging from 4 cm to 14 cm.

Very High Cycle Fatigue Life Prediction of SLM AlSi10Mg Based on CDM and SVR Models

A novel fatigue evolution model considering the effect of defect size and additive manufacturing building direction based on the theories of continuum damage mechanics and its numerical implementation in ABAQUS is proposed in this paper. First, the constitutive model, fatigue damage evolution model and their parameter calibration methods are presented. Second, using the ABAQUS platform, the proposed model is implemented with user-defined subroutines. After that, based on the proposed model and its numerical implementation, the fatigue life of additively manufactured AlSi10Mg is predicted and its applicability is verified through experimental results. Finally, a support vector regression model is established to predict the fatigue life, and its results are compared to those of the numerical finite element method. The results show that the support vector regression model makes better predictions than the finite element method.

Study on the Deformation and Fracture Mechanisms of Plastic Metals Considering Void Damage

Fracture initiation in plastic metals is attributed to the development of voids. Analyzing the nucleation and growth processes of voids facilitates the study of plastic deformation and fracture mechanisms in metal materials. Uniaxial tensile tests were conducted on two high-quality carbon structural steels, and the microfracture surface morphology of the tensile specimens was observed by using a scanning electron microscope (SEM). From the perspective of vacancy condensation, the nucleation mechanism of voids in the absence of inclusions or particles was analyzed. Based on the continuum damage mechanics theory and the Rice–Tracy (R-T) model, a damage parameter considering the void volume fraction was derived, and a plastic potential function, hardening curve, and constitutive model for the plastic deformation process of the plastic metal material were established. Based on the uniaxial tensile test data of the two sheets of high-quality carbon steel, the strain range data in the hardening stage were converted into true stress–plastic strain data, and the established hardening curve was used to fit the true stress–plastic strain data. The results showed good agreement between the established hardening curve and the experimental results, which effectively reflected the deformation process of ductile fractures in plastic metal materials.

Continuous softening up to the onset of failure: A hyperelastic modelling approach with intrinsic softening for isotropic incompressible soft solids

This paper seeks to put forward an alternative notion for modelling the continuous softening in the finite deformation of incompressible isotropic rubber-like materials, up to the onset of failure. Based on the proposition that ‘there is no fundamental reason as to why the basic constitutive parameters of the (hyper)elastic state of a material cannot determine the natural evolution of softening and failure in that material’, the concept of hyperelasticity with intrinsic softening is posited. In contrast to the currently available theories of continuum damage mechanics and energy limiters, which superpose external parameters onto the basic hyperelastic model, the alternative approach presented here postulates that if a hyperelastic strain energy function accommodates a comprehensive set of constitutive parameters and has an appropriate functional form, it will intrinsically capture the observed continuous softening in the stress–deformation curves of soft solids, up to the onset of failure. Examples of this notion are presented using a specific hyperelastic model previously proposed by the author, applied here to extant datasets of a wide variety of isotropic incompressible soft solids, ranging from soft tissues to protein gels and 3D printed biomaterials, that include the softening behaviour. The favourable modelling results obtained via this approach are demonstrated. It is conferred that these results portend a versatile modelling tool for application to the whole-range deformation of soft solids, up to the onset of failure, and make the case for devising a unified theory for modelling both continuous and discontinuous softening in the finite deformation of rubber-like materials.

Experimental study and fretting fatigue life prediction in dovetail assembly considering stress–temperature nonlinear coupling effect

AbstractAs a paramount failure form of dovetail assembly, high‐temperature fretting fatigue seriously restricts the actual service life. Aiming at the problem of fretting fatigue life prediction of dovetail assembly of the aero‐engine compressor under the coexistence of stress and high temperature, based on D‐M contact theory and continuum damage mechanics theory, a fretting fatigue life prediction model considering stress–temperature nonlinear coupling effect is proposed in this paper by, respectively, introducing the fretting fatigue stress σfretting and the high‐temperature influence factor λ. Meanwhile, the judgment criterion of fretting fatigue crack initiation and failure is raised based on the strain–displacement method, and the fretting fatigue test is designed and carried out for experimental verification. The results show that the proposed fretting fatigue life prediction model has high life prediction ability, whose life prediction results are within ±1.7 times the error band, which can provide a theoretical reference for the structural design optimization and damage tolerance design of dovetail assembly.

Creep-fatigue damage behavior of a titanium alloy at room temperature: Experiments and modeling

In this paper, the creep-fatigue failure mechanism and damage behavior of a Ti-6Al-3Nb-2Zr-1Mo titanium alloy at room temperature were quantitatively investigated with a series of fatigue and creep-fatigue tests. Based on experimental data and continuum damage mechanics theory, a phenomenological creep-fatigue damage model applicable to Ti-6Al-3Nb-2Zr-1Mo titanium alloy at room temperature is proposed that can describe the stress dependence of the interaction between fatigue damage and creep damage. The proposed model can consider the mutual effects of fatigue damage and creep damage at room temperature. Remarkably, the previous damage models proposed based on creep-fatigue experiments at high temperatures cannot accurately characterize the creep-fatigue damage behavior of titanium alloys at room temperature. Creep damage accumulates at a fast rate and dominates the damage evolution in the initial stage, and fatigue damage predominates in the late stages. The fatigue life is significantly reduced by creep damage at room temperature. Moreover, fatigue and creep damage promote each other.

A frequency‐dependent high‐cycle fatigue damage model and its application in crack nucleation of marine riser from corrosion pits

AbstractBased on the continuum damage mechanics theory, a frequency‐dependent high‐cycle fatigue damage evolution model was established. According to the fatigue results of API X80 steel, the frequency‐dependent damage evolution parameters were regressed. Using the available riser mechanical model, the user subroutine of high‐cycle fatigue damage evolution was compiled, and the accelerating effect of corrosion pits on fatigue crack initiation of the marine riser was analyzed. The results show that a single corrosion pit at the surface can reduce crack nucleation life by more than 80%. In a double corrosion pits' case, the stress interference between pits significantly affects the crack nucleation. Circumferential double pits can produce a fatigue crack earlier than the single pit, but the effect of axial double pits is just the opposite. When the spacing reaches a certain distance, the stress interference disappears, and the crack nucleation life approaches that of a single pit case.

Investigation on the Differences in the Failure Processes of the Cortical Bone under Different Loading Conditions

Cortical bone is a transversely isotropic material, and the mechanical properties may be related to the loading direction on the osteon. Therefore, analyzing the differences in the failure processes of cortical bone under different loading conditions is necessary to explore the measures for reducing the incidence of fracture. In this study, to investigate the effects of different loading directions on the fracture performance in the cortical bone, a numerical method that could simultaneously simulate the failure processes in the cortical bone structure under compression and bending loads was established based on continuum damage mechanics theory. The prediction accuracy and feasibility of the numerical method were first verified by comparing with the corresponding experimental results. Then, the differences in the failure process and fracture performance of the same cortical bone structure under compression and bending loads were investigated. The simulation results indicated that for the same structure, the slip-open failure mode appeared under compression load, and the crack propagated along a certain angle to the loading direction; the tension-open failure mode appeared under bending load, and the crack propagated along the direction perpendicular to the loading direction. Meanwhile, the fracture load was greater and the fracture time was later in the compression than in the bending condition. These phenomena stated that discrepant failure processes and fracture patterns occurred in the same cortical bone structure under different loading conditions. The main reason may be related to the tension-compression asymmetry and transversely isotropic characteristics in the cortical bone material. The fracture simulations in the cortical bone under different loading conditions could improve the prediction accuracy in bone biomechanics and provide the prevention method for cortical bone damage and fracture.

Study on impact fatigue test and life prediction method of TC18 titanium alloy

To study the impact fatigue properties of TC18 titanium alloy and propose a new damage model for the impact fatigue life prediction of material, the impact fatigue test method and the impact response measurement scheme are designed. The impact fatigue tests are then implemented on a drop hammer impact test machine to obtain the fatigue lives and impact responses of the tested specimens under different impact conditions. A new impact damage model is proposed based on the theory of continuum damage mechanics considering the effect of strain rate. The calibration method of material parameters is presented, and the parameters of the impact damage model are obtained according to the test data of TC18. Afterward, the numerical implementation of impact damage calculation is established, and an ABAQUS user-defined subroutine is used to realize the finite element numerical simulation of impact fatigue damage accumulation. Finally, the damage evolution of TC18 under tensile impact fatigue loading is simulated and the corresponding fatigue life is predicted. The errors between the calculated impact fatigue lives and the experimental lives are less than 25%, which demonstrates the good validity and applicability of the proposed damage model and the numerical method.

Multi‐scale analyses on mechano‐electric degradation of film interconnects in flexible electronics

AbstractIn flexible electronics, the fatigue reliability of film interconnects will directly affect the stability of the entire device. Since the thickness of the film material is usually much smaller than its length and width, the fatigue of film interconnects exhibits significant size effects. To evaluate the reliability of film interconnects, based on the theory of continuum damage mechanics, a multi‐scale damage model considering length‐scale effect is established. For the convenience of the model application in damage prediction of film interconnects, a multi‐scale mechano‐electric degradation model is further proposed. Validation with experimental data shows that the model can predict the fatigue life and resistance changes of not pre‐stretched films well. For pre‐stretched films, the proposed model is also applicable to thicker films without debonding or damage localization. The proposed model is expected to provide a facile approach for fatigue life prediction of flexible electronic devices with coplanar mesh structures.

Study on the process of intervertebral disc disease by the theory of continuum damage mechanics

BackgroundRecently, more and more people suffer from low back pain triggered by lumbar degenerative disc disease. The mechanical factor is one of the most significant causes of disc degeneration. This study aims to explore the biomechanical responses of the intervertebral disc, and investigate the process of disc injury by the theory of continuum damage mechanics. MethodsA finite element model of the L4–L5 lumbar spine was developed and validated. The model not only considered changes in permeability coefficient with strain, but also included physiological factors such as osmotic pressure. Three loading conditions were simulated: (A) static loads, (B) vibration loads, (C) injury process. FindingsThe simulation results revealed that the facet joints shared massive stresses of the intervertebral discs, and prevented excessive lumbar spine movement. However, their asymmetrical position may have led to degeneration. The von Mises stress and pore pressure of annulus fibrosus showed significantly different trends under static loads and vibration loads. The von Mises stress of nucleus pulposus was not sensitive to vibration loads, but its pore pressure was conspicuously influenced by vibration loads. The injury first appeared at the posterior centre, and then, it gradually expanded along the edge of the intervertebral disc. With an increase in the loading steps, the damage rate of the intervertebral disc increased logarithmically. InterpretationThe variation in the biomechanical performance of the intervertebral disc could be attributed to the periodic movement of internal fluids. This study might be helpful for understanding the mechanism of intervertebral disc degeneration.

Constitutive and damage model for the whole-life uniaxial ratcheting behavior of SAC305

With the wide application of SAC305 solders in electronic packaging, it is important to examine their reliability. In this study, uniaxial ratcheting experiments were carried out on SAC305 solders with varying loading rates, mean stresses, and stress amplitudes at room temperature. Based on the unified creep–plasticity constitutive model applicable to SAC305 solders, a nonlinear continuum damage mechanics model was established to simulate the whole-life ratcheting behavior. The damage variable was extracted from the elastic modulus decline of the unloading section during the cyclic loading process, and its evolution was based on the damage dissipation potential, which was derived from the theory of continuum damage mechanics. In addition, the normalized life was used to correct the evolution of the damage variable. For a more accurate description of their evolution, the energy method was used to modify the damage evolution parameters under different loading conditions. Finally, the uniaxial ratcheting behavior of SAC305 solder could be accurately described by the modified damage-coupled constitutive model under different loading conditions.

Probability fatigue life prediction of pin-loaded laminated composites by continuum damage mechanics-based Monte Carlo simulation

Predicting the failure probability of composite laminates under fatigue loading has many uncertainties, such as material properties, loading, boundary conditions, etc. In this paper, the failure probability of pin-loaded composite laminates is investigated. For this purpose, the continuum damage mechanics (CDM) theory has been combined with Monte Carlo Simulation (MCS) as a physics of failure tool to predict the failure of composite laminates in different directions (fibers, matrix, and shear) to calculate the probability of failure of the composite laminates under fatigue loading. Therefore, the failure function will be formed using the CDM theory and random variables identified. Finally, using the MCS, the failure probability will be obtained and the failure probability graphs extracted.

Compressive properties and underlying mechanisms of nickel coated carbon nanotubes modified concrete

Nickel coated multi-walled carbon nanotubes (Ni-MWCNTs) having exceptional mechanical properties, thermal conductivity and dispersibility can effectively overlap in cementitious matrix, thus forming an enhanced and thermal conductive network. They are therefore a promising nanofiller for modifying cement and concrete materials. This paper studies the compressive properties of reactive powder concrete (RPC) filled with different aspect ratios of Ni-MWCNTs, including strength, toughness, Young's modulus and Poisson’s ratio. It is concluded that the incorporation of 0.06 vol.% Ni-MWCNTs with an aspect ratio of 1500 maximally increases the compressive strength and toughness of RPC by 20.24%/20.39 MPa and 43.89%/56.35 (N·m), respectively. However, Young's modulus and Poisson's ratio of Ni-MWCNTs modified composites do not significantly be improved. Besides, a constitutive model of Ni-MWCNTs reinforced RPC under uniaxial compression is established based on the continuum damage mechanics theory, reasonably predicting the relationship between compressive strength and deformation of composites. The modification mechanism of Ni-MWCNTs is also investigated through the temperature distribution monitoring inside composites, Scanning Electron Microscope (SEM) observation and energy dispersive x-ray spectrometry (EDS) analysis of Ni-MWCNTs reinforced RPC. The thermal conductive network formed by Ni-MWCNTs in matrix reduces the temperature difference and improves the temperature uniformity inside composites, thereby decreasing thermal stresses, primary cracks and defects of composites. Furthermore, the incorporation of Ni-MWCNTs makes the RPC microstructures dense, decreases the average CaO to SiO2 ratio, and inhibits the development of cracks inside RPC, thus achieving effective enhancement to RPC.

Coupled FEA Model with Continuum Damage Mechanics for the Degradation of Polymer-based coatings on Drug-Eluting Stents.

Drug-Eluting Stents (DES) are commonly used in Coronary angioplasty procedures to reduce the phenomenon of restenosis. Numerical simulations are proven to be a useful tool to the Bioengineering community in computing the mechanical performance of stents. BioCoStent is a research project aiming to develop a DES with retinoic acid (RA) coating, in the frame of which FEAC is responsible for the in silico numerical simulation of the coating's degradation in terms of Finite Element Analysis (FEA). The coatings under study are poly(lactic-co-glycolic acid) (PLGA) and polylactide (PLA). The FEA is based on the Continuum Damage Mechanics (CDM) theory and considers a mechanistic model for polymer bulk degradation of the coatings. The degradation algorithm is implemented on the NX Nastran solver through a user-defined material UMAT subroutine. This paper describes the developed numerical model to compute the degradation of biodegradable coatings on DES. The transient numerical model provides useful insight into the critical areas with regards to the scalar damage of the coatings. The FEA results present a complete degradation of polymers after several weeks.