Continuum Damage Research Articles

A continuum damage mechanics model for fatigue degradation and failure of short fiber reinforced composites

The present study is concerned with the development and implementation of a continuum damage mechanics model describing the degradation and failure of short fiber reinforced composites subjected to static and fatigue loads. Towards a numerically efficient formulation, the model is defined entirely on the macroscopic scale, although being motivated by microstructural considerations. Based on experimental observations, an anisotropic linear elastic formulation is adopted as a base formulation. The elastic model is coupled with a damage formulation assuming that damage is driven by the approach of a state point in strain space to a Tsai-Hill type failure envelope. The model is implemented as a user defined subroutine into a finite element formulation. As a numerically highly efficient alternative, an enhanced Wöhler-Miner type post-processing procedure is proposed. Both numerical approaches are found in good agreement with experimental data obtained in coupon experiments as well as in experiments on specimens with more complex geometry and loading conditions.

Evaluation of Linear Amplitude Sweep data analysis techniques and failure criteria for High Polymer-Modified binders

High Polymer Modified Binders (HiPMBs) have gained attention for their resilience to environmental and traffic stressors, yet their fatigue cracking resistance remains insufficiently explored. Even though the Linear Amplitude Sweep (LAS) test is an AASHTO standardized procedure, various data analysis techniques and failure criteria can be found in the literature. It is unclear whether they produce divergent results and whether any of them provide better insights into bitumen behavior. The research showcased in this paper aimed to assess the factors affecting the evaluation of HiPMBs' fatigue life through the LAS test. Additionally, asphalt concrete was produced with bitumen previously tested and subjected to Push-Pull (PP) fatigue cracking evaluation for direct comparison. Results show significant differences between analysis methods, regardless of the failure criteria applied. The methods that rely on the Viscoelastic Continuum Damage (VECD) analysis were affected by the inaccuracy of the material integrity function fitting. The failure criterion significantly impacts the ability to detect the benefits of the high polymer content, which becomes increasingly noticeable for failure criteria different from those suggested in the AASHTO specification. Meanwhile, the Fatigue Resistance Energy Index (FREI) approach has a great advantage of not being tight to the VECD formulations and was able to capture the differences between the Neat Binders (NBs) and the HiPMBs. As for the corresponding binders' performance on the HMA level, similarities in the ranking were noticed; however, no full agreement was recognized.

Towards Characterizing Continuum Damage in Glass Fibre-Reinforced Composite

Towards Characterizing Continuum Damage in Glass Fibre-Reinforced Composite

Effects of a Complex Environment on Fatigue and Self-Healing Characterization of Asphalt Composites Containing Rock Asphalt.

In recent years, asphalt pavement has been subjected to varied environmental conditions during its service life, conditions that predispose it to deformation and cracking. To enhance the performance of asphalt pavement, rock asphalt has been selected as a modifier due to its good compatibility with virgin asphalt binder and its ability to improve the fatigue cracking resistance of asphalt mixtures. Although scholars have conducted some studies on rock asphalt mixtures, research on the fatigue and self-healing performance of these mixtures under conditions such as ultraviolet (UV) aging and freeze-thaw remains limited. This paper presents findings from a study that employs a combined fatigue-healing test to assess the impact of such complex environmental factors on the fatigue and self-healing properties of fine aggregate matrix (FAM) mixtures containing three types of rock asphalts, i.e., Buton, Qingchuan (QC), and Uintaite Modifier (UM). The analysis of fatigue-healing test results, grounded in viscoelastic continuum damage (VECD) theory, indicates that rock asphalt can extend the fatigue life of FAM mixtures, albeit with a concomitant decrease in their self-healing capabilities. The study further reveals that UV aging, freeze-thaw, and UV aging-freeze-thaw conditions all led to a diminution in the fatigue and self-healing properties of FAM mixtures. However, FAM mixtures containing rock asphalt demonstrated greater resilience against these reductions. Atomic force microscope (AFM) results indicate that UV aging reduced the number of bee-structures and enlarged their area, whereas the incorporation of rock asphalt enhanced the uniformity of these structures' distribution, thereby improving the fatigue cracking resistance of FAM mixtures. Fourier transform infrared spectroscopy (FTIR) analysis reveals that while UV aging increased the carbonyl and sulfoxide indices within the asphalt binder, rock asphalt is effective in mitigating this effect to a certain degree, thereby enhancing the aging resistance of FAM mixtures.

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.

Characterisation and damage modelling of oxide/oxide composites considering temperature dependence

Continuous fibre reinforced ceramic matrix composites (CMCs) are increasingly being employed in safety critical applications. As a result, their use in these applications requires the adoption of appropriate design methodologies that are able to consider their complex non-linear mechanical behaviour. In this paper, a simple but robust formulation for continuum damage model, thermodynamically consistent and written under plane stress condition, is proposed for a laminated 2D woven composite material. This model is implemented via the Classical Laminate Theory (CLT) extended to non-linear behaviour to predict the behaviour of different stacking sequences. In-plane tensile tests were performed on an oxide/oxide composite up to 1000 °C to fully identify the model. The procedure is described and used on tests at room temperature before being extended higher temperature tests. Finally, the law and its coupling with the CLT are validated by means of tests on quasi-isotropic and cross-ply laminates at different temperatures.

Mesoscopic simulation of uniaxial compression fracture of concrete via the nonlocal macro–meso-scale consistent damage model

To capture the uniaxial compression fracture of concrete composite is still a great challenging problem. To this end, the newly proposed nonlocal macro–meso-scale consistent damage (NMMD) model is extended to simulate uniaxial compression fracture of concrete composites. In the NMMD model, a mesoscopic structure composed of material point pairs is attached to each material point. A decomposition scheme suitable for masonry-like materials is adopted to decompose the elongation quantity of point pairs. The topologic damage is defined as the weighted summation of mesoscopic damage in neighboring material point pairs driven by the decomposed elongation quantity. The physically-based energetic degradation function is employed to bridge the geometric discontinuity in solids and the energy dissipation, and thus the topologic damage is integrated into the framework of continuum damage mechanics. The Monte-Carlo method and two-phase random field model are employed to generate stochastic circular and irregular aggregates representing the meso structure of concrete, respectively. The interface transition zone is prescribed by reducing the critical value of interface point pairs. Numerical results indicate that both the crack patterns and stress–strain curves of the uniaxial compression experiments on concrete panels can be well captured by the proposed NMMD model without mesh size sensitivity. The influence of horizontal constraints on the top and bottom surfaces is investigated and shown to have an effect on the crack patterns, strength and deformation capability of the specimen. The necessity of decomposition is also illustrated.

Lifetime assessment of deep-sea manned cabin with PMMA pressure-resistant hull prior to micro-cracks

Fully-transparent cabin type, utilized in manned submersibles, is typically constructed using viscoelastic PMMA (polymethyl methacrylate) material. Accurate fatigue life assessment of manned cabin is of paramount importance to ensure structural safety. In this study, a calculation process for evaluating the fatigue life of PMMA manned cabins based on a continuum damage mechanics model combined with the viscoelastic constitutive relationship of the PMMA material in response to the absence of related specification is proposed. Fatigue tests of PMMA material are performed for determination of damage evolution model parameters and the calculation process is validated by the fatigue test data. Tailored subroutines are then developed by using ABAQUS software tool, respectively for structural analysis of a typical manned cabin with PMMA pressure-resistant hull, openings, hatches and penetration plates and simulating trapezoidal loading history acting on manned cabin. Subroutine coupling is accordingly employed to conduct parametric analysis on fatigue crack initiation life of the fully-transparent manned cabin with consideration of different outside pressure level and operation time and valuable results are obtained for identifying key areas of concern. This study intends to contribute to further cabins safety enhancement, as well as to design optimization and fatigue analysis of underwater structures involving PMMA materials.

Numerical simulation of surface roughness effects on low-cycle fatigue properties of additively manufactured titanium alloys

Additive manufacturing (AM) is a complex process involving a multiscal physical phenomena (solid–liquid-gas), often resulting in poor surface quality. Although surface treatments such as polishing or chemical treatment can improve surface quality, localized sub-grain stress concentrations induced by surface roughness anomalies are still easily formed, which can lead to the reduction and dispersion of fatigue properties in AM alloys. In this study, a numerical simulation model is proposed to study the association between surface roughness and fatigue properties of AM alloys. Based on the continuum damage mechanics modeling framework, an idealised grain/grain boundary model is generated by employing the Voronoi tessellation meshing technology. The numerical simulations are performed for the model with different surface geometric states. The correlation between surface roughness geometric features and fatigue properties is analyzed and discussed. A parameter “G” which comprehensively considers the influence of the maximum surface height (Rz) and correlation length (Lcor) is proposed to quantify the influence of surface roughness geometric features on the fatigue properties of AM alloys. This finding can be of great significance in improving the surface integrity of components to increase service life.

A tensorial energy-release-rate based anisotropic damage-plasticity model for concrete

This paper proposes an anisotropic damage model for concrete to capture its plasticity and damage behavior effectively. Utilizing the framework of continuum damage mechanics, the model considers the influence of plastic Helmholtz free energy on damage evolution. This approach explicitly deduces damage-related thermodynamic forces without resorting to assumptions such as strain equivalence or energy equivalence. The proposed model employs tensile and compressive damage tensors to describe the development of anisotropic damage in concrete. The solution for plastic strain utilizes the empirical plasticity model. Furthermore, a unified evolutionary criterion for isotropic and anisotropic damage is also established, incorporating damage yield functions and orthogonal flow laws. Numerical simulations are conducted to validate the model’s ability to reproduce typical nonlinear behaviors of concrete structures under various load conditions.

Combined effect of random porosity and surface defect on fatigue lifetime of additively manufactured micro-sized Ti6Al4V components: An investigation based on numerical analysis and machine learning approach

Surface defects and internal porosities resulting from the additive manufacturing process contribute to a scatter in fatigue lifetime, increasing uncertainty in applications such as aerospace engineering. This study proposes a combined approach of machine learning and finite element modelling to explore the interaction between random porosity distribution and high surface roughness on the fatigue lifetime of micro-sized additively manufactured parts. To achieve this, a high-fidelity finite element model is constructed with randomly distributed porosities and surface defects. A fatigue lifetime estimation model, developed using a combination of continuum damage mechanics and the theory of critical distance, is then applied to predict lifetime using effective stress extracted from simulations. A total of 1200 simulations are conducted using these models to examine the interaction effects of subsurface porosity and surface defects on localized stress distribution and fatigue lifetime. Subsequently, two machine learning algorithms, Support Vector Regression and Kernel Ridge Regression, are employed to estimate fatigue lifetime, accounting for the effects of randomly distributed subsurface porosities and surface defects. Eighty percent of the developed finite element models are employed to construct an input dataset, incorporating geometrical features of pores, and to train the algorithms, while the remaining 20% are reserved for verification purposes. The observed results demonstrate that the combined effect of random porosity and surface defects increases fatigue scatter behaviour, leading to greater uncertainty in lifetime prediction. Furthermore, the machine learning algorithms exhibit promising prediction performance.

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.

Predicting failure initiation at V-notch tips in an AISI 4340 alloy by a continuum damage model

Predicting the fracture in quasi-brittle structures composed of steel alloys near V-notch tips presents a significant challenge. We investigate to which extent the continuum damage approach predicts the failure load FcExp when applied to experiments performed on AISI 4340 alloy specimens tempered at two different temperatures and containing three different V-notch opening angles loaded to fracture under a four-point bending configuration.A series of experiments was performed for the characterization of the material parameters and fracture surface (including triaxiality) for the continuum damage model coupled with the J2 theory of plasticity. Subsequently, this model was implemented within a finite element framework to compute the predicted failure load, termed FcFE. Sensitivity analyses were performed to identify the influence of notch radii and the representation of the supports on FcFE.A strong correlation was observed between FcFE and FcExp for all configurations for both tempering temperatures, with predicted loads falling within the range of experimental observations for all V-notch angles. Additionally, a linear relationship was identified between the increase of FcFE and V-notch radii. These non-linear analyses have also revealed that for these high-strength steel specimens, it is crucial to model supports as linear elastic, as rigid supports led to underestimated FcFE.The presented methodology has shown to be superior in predicting failure loads in these quasi-brittle steel structures compared to other more simplified linear approaches.

Prediction of fretting fatigue lifetime of aluminium alloy treated with Friction Stir Processing using continuum damage mechanics

In the aviation industry, fretting fatigue represents a significantly hazardous form of fatigue failure, thus warranting substantial research attention. A key area of focus lies in enhancing the fretting fatigue resistance of aluminium alloys. This study investigates the feasibility of using Friction Stir Processing (FSP) to enhance fretting fatigue lifetime. After FSP, large-size inclusions in the Base Material (BM) are shattered, clustered inclusions are dispersed, and the preferred orientation of inclusions is disrupted. Consequently, areas of stress concentration, damage concentration and merging of hazardous zones become less, and the peak values of stress, stress triaxiality, and damage are decreased with 6–10 %. Compared to BM, the results show that the fretting fatigue lifetime of Friction Stir Processed (FSPed) material is increased by 50.1 %. Hence, FSP could emerges as a highly promising surface treatment technique for enhancing fretting fatigue performance.

Effect of Case Depth and Hardness Distribution on the Rolling Contact Fatigue Performance of G20CrNi2MoA Carburized Steel

This study aims to investigate the effects of the case depth and hardness distribution of carburizing on the rolling contact fatigue (RCF) properties of G20CrNi2MoA steel under deeper carburizing conditions. Four groups of specimens of different case depths are prepared and subjected to RCF tests. A 2D finite element model based on continuum damage mechanics is developed to further analyze these two factors. As the depth of the carburized case increases, the RCF life first increases and then decreases. The optimum case depth is approximately one‐quarter of the thickness of the specimen. A gentler hardness distribution due to a change in the diffusion process parameters ensures a minimal increase (8%) in the RCF performance. The proper case depth has a more notable effect on the RCF life compared with those of the gentle or steep hardness distribution. It is expected that the results can help to promote a better understanding of the heat treatment process of carburized bearings and ensure more reliable carburized bearings are produced.

Development of a novel continuum damage mechanics‐based machine learning approach for vibration fatigue assessment of fastener clip subjected to high‐frequency vibration

AbstractThis paper proposes a novel method based on continuum damage mechanics (CDM) and machine learning (ML) models to evaluate the vibration fatigue behavior of W1‐type railway fastener clips subjected to high‐frequency vibration. Firstly, static and fatigue tests are conducted on 60Si2Mn spring steel to acquire elastic modulus, tensile strength, and P‐S‐N curves. Subsequently, a CDM model is established, and numerical simulations are performed under various working conditions to obtain the fatigue characteristics of the clips. Finally, the ML model is trained using numerical simulation results, thereby establishing a mapping model between the working conditions and fatigue characteristics. The developed ML model demonstrates high accuracy in predicting the vibration fatigue life of the clips. Moreover, the Shapley Additive Explanations (SHAP) algorithm is employed to elucidate the ML model, revealing that the vibration frequency has a greater impact on the fatigue life of the clips compared to the vibration displacement.

Effects of non-linearity and thixotropy in linear amplitude sweep testing for the evaluation of self-healing of bituminous binders

Linear amplitude sweep tests have been demonstrated to have good potential in being used for the evaluation of self-healing properties of neat and polymer-modified bituminous binders. Past research works, however, have neglected the effects of material non-linearity and thixotropy. This implies that the whole material integrity loss is attributed to damage and all restoration to self-healing, thus resulting in the possible overestimate of both damage and self-healing when evaluating the fatigue performance of materials. In the study described in this paper, specific experimental and analytical methods were adopted with the purpose of separating non-linearity and thixotropy in LAS healing tests. Non-linearity was assessed by means of multiple strain sweep tests carried out to determine the material non-linear viscoelastic moduli at specific testing temperatures. Thixotropy was considered by coupling self-healing LAS testing with a purposely defined test in which loading was applied to the undamaged material after a rest period equal to that applied in self-healing tests. Obtained results were processed by means of an analytical approach based on the simplified viscoelastic continuum damage model. Quantification of self-healing included the determination of material integrity and damage parameters recovered after the rest period. Such parameters, calculated by excluding time-dependent and non-linear biasing effects, can be used as straightforward indicators of the self-healing potential of neat and polymer-modified bituminous binders. Moreover, obtained results substantiate the concept that time–temperature superposition is still applicable when non-linearity is incorporated into the simplified viscoelastic continuum damage model.

A Numerical Method for Unstable Propagation of Damage in Fiber-Reinforced Plastics with an Implicit Static FE Solver

Finite element analyses of the propagation of damage such as fiber compressive failure and delamination have greatly contributed to the understanding of failure mechanisms of fiber-reinforced plastics owing to extensive studies on methodologies using Continuum Damage Mechanics and Fracture Mechanics. Problems without the need for consideration of inertia, such as Double-Cantilever Beam tests, are usually solved by implicit FE solvers, and explicit FE solvers are appropriate for phenomena that progress with very high velocity such as impact problems. However, quasi-static problems with unstable damage propagation observed in experiments such as Open-Hole Compression tests are still not easy to solve for both types of solvers. We propose a method to enable the static FE solver to solve problems with unstable propagation of damage. In the present method, an additional process of convergence checks on the averaged energy release rate of damaged elements is incorporated in a conventional Newton–Raphson scheme. The feasibility of the present method was validated by two numerical examples consisting of analyses of Open-Hole Compression tests and Double-Cantilever Beam tests. The results of the analyses of OHC tests showed that the present method was applicable to problems with unstable damage propagation. In addition, the results from the analyses of DCB tests with the present method indicated that mesh density and loading history are not significantly influential to the solution.

Phenomenological modeling of aging and rejuvenation on asphalt binder fatigue characteristics

Recycling agents (RAs) have been explored as additives to enhance the properties of recycled asphalt binders. Despite extensive research on RAs, a critical knowledge gap exists regarding their impact on fatigue cracking of asphalt binders, especially considering the aging processes. This study aims to comprehensively investigate the effects of recycling agents on the fatigue properties of asphalt binders, with a specific focus on the influence of aging and rejuvenation. The current Linear Amplitude Sweep (LAS) test analysis procedure is utilized to assess the fatigue properties, and the efficacy of existing LAS test-based indices is evaluated. Furthermore, a novel index based on the simplified viscoelastic continuum damage (S-VECD) theory framework is proposed to monitor changes in fatigue properties with aging and rejuvenation. A total of 26 recycled binder blends are studied and the results demonstrate that the proposed index consistently tracks the effects of aging and rejuvenation in recycled binder blends containing recycling agents. Additionally, cross-scale assessments are conducted by correlating the proposed index with mixture performance, specifically the Indirect Tensile-Cracking Test parameter (CTindex). The findings indicate that the proposed index exhibits a correlation with the CTindex after 1-day Long Term Aging testing and effectively captures the aging sensitivity across different scales.