Damage Evolution Model Research Articles

Phase-Field Modeling of Thermally-Grown Oxide and Damage Evolution in Environmental Barrier Coatings

Phase-Field Modeling of Thermally-Grown Oxide and Damage Evolution in Environmental Barrier Coatings

A novel continuum damage evolution model based on the concept of damage driving force for unidirectional composites

A novel damage evolution model for unidirectional (UD) composites is established in this paper in the context of continuum damage mechanics (CDM). It addresses matrix cracking and it is to be applied along with the damage representation established previously. The concept of damage driving force is employed based on the Helmholtz free energy. It is shown that the damage driving force can be partitioned into three parts, resembling closely three conventional modes of fracture, respectively. A damage evolution law is derived accordingly based on the newly obtained expressions of the damage driving force. The fully rationalised Tsai-Wu criterion is employed in the model for predicting the initiation of matrix cracking damage and fibre failure, assisted with the rationalised maximum stress criterion for identifying the damage modes. A mechanism is introduced to describe the unloading behaviour as a part of the proposed model. The predictions were validated against experimental results, showing good agreement with the experiments and demonstrating the capability and effectiveness of the proposed model.

Prediction of rotational bending fatigue life of bearing steel based on damage mechanics

Based on the theory of continuous damage mechanics, this paper proposes a fatigue damage evolution model and numerical calculation method considering the influence of vacuum chemical heat treatment process, and studies the rotational bending fatigue damage analysis and life prediction method of M50NiL bearing steel. Firstly, the constitutive model, fatigue damage evolution equation and material parameter calibration method in the theoretical model are given. Secondly, based on the ABAQUS platform, the damage mechanics-finite element numerical calculation method of fatigue damage analysis considering the influence of hardened layer is realized by writing the UMAT subroutine; then, the rotational bending fatigue test of M50NiL bearing steel treated by vacuum chemical heat treatment of quenching and tempering, carburizing and carbonitriding is carried out, and the influence of heat treatment process on fatigue performance is analyzed; finally, based on the proposed fatigue damage model and numerical calculation method, the rotational bending fatigue life of M50NiL bearing steel is predicted, and the results are compared with the experimental results to verify the correctness of the proposed method.

Study on the Deformation and Energy Evolution of Skarn With Marble Band of Different Orientations Under Cyclic Loading: A Lab‐Scale Study

ABSTRACTThe aim of this work is to investigate the deformation and energy characteristics of skarn with different interlayer inclination angles under cyclic loading. The skarn samples with marble bands of various orientations (i.e., 30°, 45°, 60°, and 75°) were chosen as the test material. It is revealed from the testing results that the presence of interlayers changes the geomechanical properties of the rock, rock peak strength, and elastic modulus increases with increasing the interlayer inclination angle. Additionally, the growth rate of input energy exhibits an inverted “V” pattern with respect to the interlayer inclination angle. In terms of damage modes, intact marble and skarn predominantly exhibit tensile damage, whereas interlayered rocks exhibit a combination of tensile and shear failure pattern. Finally, a damage evolution model defined by axial strain is proposed and expressed to fit the experimental data. The results in this work would provide a crucial theoretical basis for the safety assessment of underground engineering constructions.

Prediction of rotational bending fatigue life of bearing steel based on damage mechanics

Based on the theory of continuous damage mechanics, this paper proposes a fatigue damage evolution model and numerical calculation method considering the influence of vacuum chemical heat treatment process, and studies the rotational bending fatigue damage analysis and life prediction method of M50NiL bearing steel. Firstly, the constitutive model, fatigue damage evolution equation and material parameter calibration method in the theoretical model are given. Secondly, based on the ABAQUS platform, the damage mechanics-finite element numerical calculation method of fatigue damage analysis considering the influence of hardened layer is realized by writing the UMAT subroutine; then, the rotational bending fatigue test of M50NiL bearing steel treated by vacuum chemical heat treatment of quenching and tempering, carburizing and carbonitriding is carried out, and the influence of heat treatment process on fatigue performance is analyzed; finally, based on the proposed fatigue damage model and numerical calculation method, the rotational bending fatigue life of M50NiL bearing steel is predicted, and the results are compared with the experimental results to verify the correctness of the proposed method.

The Determination of the Elastoplastic and Phase-Field Parameters for Monotonic and Fatigue Fracture of Sintered Steel Astaloy™ Mo+0.2C

This paper presents a procedure for determining the elastoplastic parameters of phase-field fracture of sintered material. The material considered was sintered steel Astaloy™ Mo+0.2C of three densities: 6.5, 6.8 and 7.1 g/cm3. The stress–strain curve and Wöhler curve, which are experimentally obtained, are utilized for validation of the numerical simulations. For modelling of damage evolution, a CCPF (Convergence check phase-field) algorithm was used as a numerical framework. During calibration of the numerical parameters, two-dimensional as well as three-dimensional modelling was used. A comparison of different fatigue degradation functions known from the literature is also made. To improve the efficiency of numerical simulations of fatigue behaviour, the cycle skip technique is also employed.

Experimental study on damage of steel fiber reinforced concrete- and wood-filled GFRP tubes under axial compression

In order to reduce the self-weight of concrete structures and improve its corrosion resistance, it is an effective way to fill GFRP tubes with wood columns instead of part of concrete. However, concrete structures are prone to cracks, which will reduce the bearing capacity of the structure and affect the safety and applicability of the structure. Incorporating the steel fibers (SF) in concrete seems to be an excellent solution to limit crack propagation and improve the ductility of concrete structures. Based on the premise, in this paper, a new type of structure composite material of steel fiber reinforced concrete- and wood-filled GFRP tubes was developed. The mechanical properties, damage evolution process and crack fractal characteristics of steel fiber reinforced concrete- and wood-filled GFRP tubes under axial compression with different SF volume fractions (0 %, 1 %, 1.5 % and 2 %) were studied by acoustic emission (AE) technology. The finite element method (FEM) was established to simulate the test work and expand the analysis. The results showed that the bearing capacity and ductility of the specimens increased first and then decrease with the increase of SF content, and the specimens with 1.5 % volume fraction of SF showed the best mechanical properties. According to the characteristics of AE ringing counts, the damage process of the specimen was described by three marker events, which were concrete cracking, wood cracking and GFRP tube fracture. The incorporation of SF increased the intensity of AE signal and the proportion of shear cracks, and reduced the damage scale. The fractal dimension of concrete surface cracks had a good correlation with the degree of local damage and the complexity of crack propagation. The damage evolution model based on AE cumulative events and stress obeyed the two-parameter Weibull distribution. The incorporation of SF reduced the degree of damage, and the parameter m had a negative correlation with brittleness. In addition, the damage process of the specimens revealed by the FEM matched well with the experimental results. Additionally, the incorporation of SF made the stress distribution of each part of the specimen more uniform and avoided the phenomenon of stress concentration.

An ANN-based concurrent multiscale damage evolution model for hierarchical fiber-reinforced composites

In this paper, an ANN-based concurrent multiscale damage evolution model is proposed, which is able to investigate the complex failure behaviors of hierarchical fiber-reinforced composites. In the framework of the proposed model, yarn damage evolution laws at the mesoscale are indirectly derived from the microscale representative volume element (RVE), using artificial neural networks (ANNs) as a surrogate model. A homogenized characterization method is proposed to derive the homogenized damage variables. The homogenized strain and damage variables of the microscale RVE are taken as inputs and outputs in ANNs, respectively. The dataset is generated by combining clustering with the finite element simulation. A typical kind of plain-woven composite is adopted as a benchmark material for numerical implementation and experimental verification. The numerical predictions, including the tensile properties and damage evolution, are consistent with the results from quasi-static tension experiments.

Study on the Weibull distribution function-based stochastic damage evolution law for uniaxial compression in high-performance concrete with full aeolian sand

The issues of environmental degradation due to natural sand overextraction are becoming increasingly severe. In desert regions, utilizing aeolian sand as a substitute for natural sand in construction projects facilitates the resource economization and the effective management of desertification. The concrete industry is expected to significantly contribute to this objective, as high-performance concrete with full aeolian sand (FA-HPC) has demonstrated excellent mechanical properties. However, current researches have yet to establish a rational damage evolution law for uniaxial compression in FA-HPC from the perspective of damage characteristics. In this study, uniaxial compression tests were conducted on FA-HPC with different mixture proportions. Simultaneously, the stress-strain behavior was examined, and acoustic emission (AE) signals were collected and localized. Based on the Weibull distribution function-based stochastic damage evolution law for uniaxial compression, regression analyses of the stress-strain and AE cumulative ringing count for FA-HPC were performed. Damage evolution model for effective stress and damage variable were established and validated with experimental data to confirm their applicability. The scale and shape parameters of the model were predicted using the mixture proportions as independent variables. The results show that the rationality of the damage evolution law assumption was validated through AE source localization. The goodness of fit values for damage variable and effective stress equation range from 0.87 to 0.98, with the ascending segment and the vicinity of the peak point closely matching the experimental data, indicating that the Weibull distribution function-based stochastic damage model for uniaxial compression is applicable for FA-HPC. The predicted values of the damage evolution model parameters based on the mixture proportions align well with the measured values, achieving a goodness of fit of 0.99, thereby guiding the study of FA-HPC's compressive characteristics prior to the formation of primary cracks. Notably, there remains a need to propose corrective equations to enhance the correlation between regression curves and experimental data in the late failure stages of FA-HPC in future research, achieving precise predictions by considering the interactions of multiple factors.

Novel integration of PSO-enhanced damage mechanics and finite element method for predicting medium–low-cycle fatigue life in perforated structures

In this research, we introduce an innovative approach that combines the Continuum Damage Mechanics-Finite Element Method (CDM-FEM) with the Particle Swarm Optimization (PSO)-based technique, to predict the Medium-Low-Cycle Fatigue (MLCF) life of perforated structures. First, fatigue tests are carried out on three center-perforated structures, aiming to assess their fatigue life under various strengthening conditions. These tests reveal significant variations in fatigue life, accompanied by an examination of crack initiation through the analysis of fatigue fracture surfaces. Second, an innovative fatigue life prediction methodology is applied to perforated structures, which not only forecasts the initiation of fatigue cracks but also traces the progression of damage within these structures. It leverages an elastoplastic constitutive model integrated with damage and a damage evolution model under cyclic loads. The accuracy of this approach is validated by comparison with test results, falling within the three times error band. Finally, we explore the impact of various strengthening techniques, including cross-sectional reinforcement and cold expansion, on the fatigue life and damage evolution of these structures. This is achieved through an in-depth comparative analysis of both experimental data and computational predictions, which provides valuable insights into the behavior of perforated structures under fatigue conditions in practical applications.

Effects of freeze-thaw cycles on fatigue performance of asphalt mixture and a fatigue-freeze-thaw damage evolution model

To study the effect of freeze-thaw (FT) cycles on the fatigue performance of composite crumb rubber modified asphalt mixtures (CCRMA), a semicircular bending fatigue test based on the digital image correlation technique (DIC) was used to measure the fatigue life (Nf) of CCRMA and SBS modified asphalt mixtures (SBSMA) and the horizontal strain (Exx) of the DIC deformation field under repeated loading. The variation laws of Nf, Exx and the damage factor (D) defined based on Exx were analyzed under FT cycle conditions. In addition, considering the important influence of FT cycles on the Nf and damage evolution characteristics of asphalt mixtures, based on the classical Chaboche damage evolution model, the influence of FT cycle was considered, a fatigue-freeze-thaw damage evolution model that reflects the effects of FT cycling variables and stress levels on asphalt mixtures was constructed. The results indicate that the Exx peak of asphalt mixture shifts forward with increasing FT cycle number. After 20 FT cycles, the Nf of CCRMA decreased by 73.4 %, 62.1 %, and 75.1 %, while that of SBSMA decreased by 76.5 %, 58.6 %, and 74.6 % at stress ratios of 0.2, 0.3, and 0.4, respectively. The fatigue-freeze-thaw damage evolution model predictions were in agreement with experimental results, with the goodness of fit (R2) of all Nf prediction models being greater than 0.9. With the exception of a few outliers, the relative error between the measured and predicted Nf for the two asphalt mixtures was within 15 %. This indicates that the model can effectively predict the Nf and damage evolution laws of asphalt mixtures at different stress levels after an arbitrary number of FT cycles. The related research results provide a theoretical basis for predicting the Nf of new roads in cold regions under FT cycles.

Multi-scale modeling of damage evolution for particle-filled polymer composites

In this study, a multi-scale modeling framework that spans from molecular chains to macroscopic structure was proposed for a typical particle-filled polymer composite (HTPB propellants). The cohesive zone model (CZM) is utilized in the RVE model of HTPB propellants to capture the debonding phenomena at the AP/HTPB interface. For the HTPB matrix, a free energy function based on the Gaussian chain network is employed. To depict the chain scission behavior, the phase fracture (PF) method along with gradient-damage theory is introduced. Subsequently, microscale fracture behavior under uniaxial tensile load was investigated based on the constructed RVE model, and a phenomenological macroscopic damage model was developed correspondingly. In this developed model, two damage factors related to the debonding of AP/HTPB interface and the growth of voids in matrix are introduced respectively. Thus, it can not only predict the macroscopic stress–strain response, but also can give the microscopic damage evolution information. Overall, this multi-scale modeling framework can offer us a deeper insight into the microstructural changes and the resulting macroscopic mechanical behavior of HTPB propellants.

Study on fatigue characteristics of red sandstone under extremely high stress in the hydro-chemical environment

To study the failure of red sandstone under extremely high stress during the service life of tunnels, an in-depth study was conducted on the mechanical properties of red sandstone under uniaxial loading and cyclic loading and unloading processes at different pH values using the AG-250kNIS electronic precision material testing machine and MTS815 mechanical testing machine. The results show that as the acidity and alkalinity increase, the peak stress under uniaxial loading decreases and the axial strain increases,The peak stress at failure is 9.40, 12.37, 7.18, and 5.36 MPa, respectively, accounting for 74.19%, 68.91%, 40.38%, and 36.21% of the uniaxial compressive strength; The number of cycles significantly decreases during cyclic loading and unloading fatigue failure, and the stress required for sandstone failure gradually decreases. The peak strength and elastic modulus of sandstone show a decreasing trend, indicating that the hydrochemical environment plays an accelerating role in rock degradation. During the cyclic loading and unloading process of sandstone, there is a continuous increase in dissipated energy and finally a sudden increase, the Ud/U and Ue/U ratios at the peak point of sandstone in the natural state are 0.399 and 0.601, respectively, while the overall elastic energy shows an increasing trend; and a damage evolution model was established based on dissipative energy, which can better describe the degradation process of red sandstone.

Study on quasi-static tensile mechanical properties of biomimetic helicoidal composite laminates

Abstract Numerous biomaterials exhibit intricate helicoidal structures renowned for their exceptional toughness. This study drew inspiration from the collagen fiber structure found in the scales of coelacanths to design composite laminates featuring double helicoidal layup configurations with varying pitch angles. A damage evolution model with damage initiation and linear stiffness degradation based on the Hashin failure criterion was used to describe the damage behavior of the materials. The impact of varying pitch angles on the quasi-static tensile properties of double helicoidal composite laminates is investigated. The results show that the magnitude of the pitch angle has a significant effect on the tensile properties of the laminates, and the tensile modulus of double composite laminates is highest when the pitch angle is 90°.

Study of Damage Mechanism and Evolution Model of Concrete under Freeze–Thaw Cycles

Researching the mechanical characteristics of concrete subjected to the freeze–thaw cycle is crucial for building engineering in cold climates. As a result, uniaxial compression tests were performed on concrete samples exposed to various freeze–thaw (F–T) cycles, and the measurements of the pore size distribution, porosity, and P-wave velocity of the saturated concrete samples were obtained, both before and after being exposed to the F–T cycles. Concrete’s F–T damage mechanism and damage evolution model were thoroughly examined. Using rock structure and moisture analysis test equipment to observe the T2 spectrum, the results showed that the F–T cycles can cause the internal structure of the samples to deteriorate. Porosity and F–T cycles have a positive correlation, although P-wave velocity has a negative correlation with the F–T cycles. As the F–T cycles increased, the specimens’ peak strength and elastic modulus steadily declined, while the peak strain clearly exhibited an increasing trend. A microscopic F–T damage model that takes into account the pore size distribution was developed, based on the relative changes in the pore structure distribution (PSD), before and after the F–T cycles. The concrete sample damage evolution law under various F–T cycles was examined using the following metrics: total energy, pore size distribution, static and dynamic elastic moduli, porosity, and P-wave velocity. Uniaxial compressive strength (UCS) and peak strain tests were used to evaluate the accuracy of the pore size distribution damage model, as well as that of five other widely used damage models.

Research on the static and dynamic tensile damage mechanism of concrete based on fuzzy sets

The quantitative analysis of microscopic damage mechanisms in concrete and the formulation of damage evolution equations using mathematical theory and computerized tomography (CT) imaging are still emerging fields. The test data from CT scans have yet to be fully exploited. This study proposes a method for quantitatively characterizing mesoscale damage evolution in concrete. By segmenting CT images from static and dynamic tensile tests, we define metrics such as the aggregate rate, mortar rate, and porosity to examine the damage progression under both stress conditions. We then establish a damage evolution model based on porosity changes. Our findings reveal that crack growth in concrete is slower under static tension, with cracks navigating around aggregates towards weaker regions. Conversely, under dynamic loads, cracks propagate more rapidly and directly through aggregates, following paths of quicker energy dispersion. Static loading results in less aggregate damage than does dynamic loading, with a notable increase in porosity and a more varied change in the mortar rate. The damage to the finer components of concrete increases as the crack-adjacent region diminishes. Damage is generally more extensive under static loading than under dynamic loading. The proposed porosity-based damage evolution model effectively describes concrete damage under static tension, leveraging CT technology to enhance the universality of the research and offering a microscopic-level theoretical foundation for studying concrete mechanical properties.

Tensile damage evolution of unidirectional ceramic matrix composites under thermal stress

Ceramic matrix composites (CMCs) have been widely used in aerospace thermal-structures due to their excellent high-temperature performance. It is essential to understand the damage evolution of CMCs. However, in previous research work, the effect of thermal stress induced damage during CMCs fabrication on tensile response was often ignored. A damage evolution model that considers axial and radial thermal stresses to predict tensile response of unidirectional ceramic matrix composites was proposed in this study. The average relative errors between the current prediction and experimental data in the literature were calculated as 1.64 % and 1.91 %, validating this approach. Meantime, the damage evolution laws of interface debonding and the critical stress of matrix cracking in the Budiansky–Hutchinson–Evans (BHE) model were corrected to satisfy the discontinuous interfacial shear stress. According to the experimental data, the current model predicted critical stresses of matrix cracking better than the BHE model, with error rate reductions of 6.52 % and 15.38 %.

Delamination propagation manipulation of composite laminates under low-velocity impact and residual compressive strength evaluation

The poor delamination resistance of laminated composites is always regarded as a potential threat to the service safety of the primary load-bearing structure. However, delamination is inevitable during low-velocity impact (LVI) events, as a result, the residual compressive strength of laminates is significantly reduced. Discrete interleaving is a novel strategy to enhance the damage tolerance of these composites, yet the damage mechanism of laminates modified by this method is more complicated. In this paper, we investigated the delamination failure mechanism of quasi-isotropic laminates through thermal deply experiment, and proposed a discrete interleaving scheme based on its damage characteristics. Accordingly, a series of LVI and compression-after-impact (CAI) tests were conducted to validate the design philosophy. Besides, the damage constitutive relation and evolution model applicable to discrete interleaved laminates were explored in detail, a numerical model embedded strain-rate-dependent progressive damage criterion and modified cohesive zone model was established to further study the damage mechanism. Experimental and numerical results exhibit excellent alignment. The results demonstrate that the CAI strength is enhanced by 16.48 % according to the proposed discrete interleaving method. The main reason is attributed to the employed method can manipulate the delamination propagation during the low-velocity impact loading, and then maneuver the compressive failure mode of laminates to achieve a favorable benign failure (implying higher CAI strength).

Salt freezing-thawing damage evolution model based on the time-dependent hydration reaction incorporating rice husk ash and recycled coarse aggregate

Rice husk ash (RHA), an abundant agricultural by-product, has led to significant environmental pollution due to current treatment methods. To achieve resource utilization, the feasibility of RHA recycled concrete subjected to the salt freezing-thawing resistance was assessed, including the macroscopic properties, microstructure and sustainability, and an evolutionary model of salt freeze-thaw damage was established based on the time-dependent hydration reaction of the cement paste. The results indicate that RHA particles effectively retard damage by limiting chloride ion diffusion and preventing salt crystallization, while deteriorating the concrete performance due to reduced hydration products at high RHA replacement ratios. The established salt freeze-thaw damage evolution model has an R2 as high as 0.9817, which indicates that the model fits with high accuracy and can capture the performance variations of different types of RHA recycled concrete under extreme environmental conditions. Additionally, the synergistic preparation of concrete using RHA with a 20 % replacement ratio and recycled coarse aggregate (RCA) with a 50 % replacement ratio reduces the total global warming potential (GWP) by 16.65 %, which means that it has the potential to advance low-carbon sustainable development in the construction industry while meeting the engineering requirements. This research is expected to provide a theoretical reference for applying and promoting biobased low-carbon concrete with RHA in saline-alkali cold areas.

Study on the damage mechanism and evolution model of preloaded sandstone subjected to freezing–thawing action based on the NMR technology

Abstract Investigating the damage degradation of rock during the freezing and thawing process is more consistent with the actual engineering environment, considering its internal initial damage. In this study, the effects of initial damage from preloading and subzero-temperature freezing–thawing on microscopic and macroscopic mechanical properties of sandstone were studied based on the nuclear magnetic resonance (NMR) technique. The results show that the P-wave velocity of the sample decreased, while the porosity increased as the initial damage level increased. The distribution of T2 signal intensity exposed to the low-temperature freezing–thawing–saturation treatment was rather larger than that under normal temperature conditions for samples with different levels of initial damage from preloading, indicating that the low-temperature freezing–thawing condition would promote the porosity and have an obvious increase in damage. A continuum damage model considering subzero-temperature freezing–thawing damage from different pore sizes was finally introduced to describe the damage evolution mechanism of sandstone. The research results can be used to quantitatively evaluate the damage evolution mechanism of sandstone treated by subzero-temperature freezing–thawing without mechanical tests. Furthermore, the analysis and research results show that the damage variables of sandstone obtained by the NMR theory were lower than those of classical rock mechanics theory.