Elastic Modulus Distribution Research Articles

Image driven deep learning method with FFT solver for predicting the microscale full field stress of stochastic boundary composites

AbstractA novel image‐driven deep learning approach embedded with model‐data‐knowledge information can directly predict the full field stress distribution and mechanical properties of composites solely based on initial scanning geometry images. The fiber spatial distribution and morphological features are identified by Scanning Electron Microscopy (SEM) initially. An effective random fiber generation algorithm is further utilized to generate images database comprising equivalent geometric models of various microstructures. Subsequently, the geometry model images database is analyzed by fast Fourier transform (FFT) to produce the database including the elastic modulus parameters and full field stress distributions of composites with distinct microstructures. Finally, an innovative image‐learning comprehensive paradigm uniting convolutional neural networks and convolutional autoencoders is elaborated systematically to learn the inherent laws of geometry images and field images. The results show that the proposed method have capacity to effectively and accurately predict the elastic modulus and full field stress distributions combined with error analysis even for stochastic boundary composites. The proposed methodology is a symbiosis of cutting‐edge image learning and non‐destructive testing techniques for composites, which can directly use the local non‐destructive or scanning images of composite structural components to quickly obtain field information and further predict damage evolution online.Highlights Proposing a novel deep learning approach combined with FFT directly to predict stress distribution of stochastic boundary composites solely based on micro‐images. Adopting equivalent geometric models dispersed by higher pixels mesh density considering extreme thin interface. Incorporate adaptive algorithms for streamlined training optimization. An innovative integration of deep learning and non‐destructive testing technology for the stress distribution and properties prediction online.

In-plane compressive properties and failure mechanisms of gradient Cf/ZrB2–SiC composites in high-temperature environment

The gradient Cf/ZrB2–SiC composites can exert the dual advantages of low-density and excellent heat resistance, but which have the complex mechanical properties due to the inhomogeneous geometry characteristics. The in-plane compressive behavior and failure analysis can examine the material integrity and the effect of inhomogeneous characteristics. The in-plane compressive elastic modulus distribution is expressed mathematically by using the superficial elastic modulus, back elastic modulus, and the gradient pore distribution. The superficial elastic modulus and the gradient pore distribution of the gradient materials were characterized by nanoindentation test and Micro-CT statistics. The back of the gradient materials is the porosity needled C/C composites without introducing ZrB2–SiC matrix, whose elastic modulus can be referenced from our previous work. The in-plane compressive experiments of the gradient materials in the high-temperature environment were also conducted to study the failure mechanisms. The strength of the gradient materials is further revealed by the temperature-dependent properties of carbon fibers and thermal residual stress release. The results indicate the gradient structure can effectively eliminate the delamination damage, but the high temperature drastically weakens the ability of needled fibers suppressing delamination damage in the high-porosity region of the gradient materials. This study can be helpful to the material design and evaluation of mechanical properties for the gradient Cf/ZrB2–SiC composites.

Corrosion characteristics and evaluation of galvanized high-strength steel wire for bridge cables based on 3D laser scanning and image recognition

The study investigates the corrosion behavior of galvanized high-strength steel wire, which significantly affects the bearing capacity and residual fatigue life of cables in cable-supported bridges. Through standardized salt spray accelerated corrosion tests, steel wires with varying corrosion degrees are obtained. Three-dimensional laser scanning technology reconstructs the corroded wire surface, while image recognition techniques extract geometric characteristics of corrosion pits. Fitting expressions are established to correlate the minimum cross-sectional area, maximum pit depth and dip angle, and mass loss ratio of the wire. Statistical analysis reveals log-normal distributions for the lengths of major and minor axes of corrosion pits over time. Fitting curves for elongation after fracture, nominal yield strength, and nominal ultimate strength, along with elastic modulus distribution, are derived for different mass loss ratios. Comparing corrosion grading criteria, the study quantitatively describes corrosion characteristic parameters for distinct corrosion grades. These insights enhance understanding of corrosion behavior and mechanical property degradation in high-strength steel wires, offering a quantitative framework for assessing and classifying corrosion extent based on measurable parameters.

METHODOLOGY FOR PREDICTING THE MATERIALS ELASTIC MODULUS OF PRODUCTS PRODUCED BY LAYER-BY-LAYER CLADDING WORKING UNDER THREE-POINT BENDING CONDITIONS

The work is devoted to the investigation of the influence of technological filling density on the distribution of elastic modulus when printing functional parts by the layer-by-layer deposition modeling (FDM) method in terms of stiffness under three-point bending conditions, in an elastic isotropic setting. The structure of the product is considered as a set of the body of the outer shell formed during printing by the outer perimeters and the inner body, which is directly the technological filling. The data of experimental studies of elasticity modulus distribution for both the outer shell and the inner structure are given, the nomogram of elasticity modulus distribution is obtained, allowing in general to estimate the functionality of the part in the aspect of providing the required elasticity modulus in calculations.

Composition-dependent brittleness and ductility of the multicomponent phase (Fe, Cr)23(C, B)6 in Fe–Cr–B–C alloys: First-principles calculations and modeling

(Fe, Cr)23(C, B)6, as a strengthening phase in Fe–Cr–B–C alloys, has not been reported on the relationship between its properties and composition over the entire composition range. (Fe, Cr)23(C, B)6 tends to exhibit brittleness, which is difficult to regulate through traditional experiments. The mechanical properties of (Fe, Cr)23(C, B)6 phase in Fe–Cr–B–C alloy have been studied by first principles calculation. With the help of CALPHAD method, the distribution of elastic constant, modulus, hardness and fracture toughness in the whole component space was obtained, so that the suitable component with good wear resistance and strong toughness was obtained. The mechanical properties of (Fe, Cr)23(C, B)6 phase is better in the range of ∼0.4–0.6 at. % B and ∼0.5–0.7 at. % Cr. The mechanism of these differences is explained in terms of state density, bond length, population analysis and differential charge density, as the addition of boron and the increase in chromium content led to a significant increase in the formation of covalent bonds between metals and non-metals, in which these bonds play a decisive role. The combination of the first principles calculation and the CALPHAD model provides a feasible model for constructing the composition-property relationship of medium entropy compounds.

On the soft tissue ultrasound elastography using FEM based inversion approach.

Elastography is a medical imaging modality that enables visualization of tissue stiffness. It involves quasi-static or harmonic mechanical stimulation of the tissue to generate a displacement field which is used as input in an inversion algorithm to reconstruct tissue elastic modulus. This paper considers quasi-static stimulation and presents a novel inversion technique for elastic modulus reconstruction. The technique follows an inverse finite element framework. Reconstructed elastic modulus maps produced in this technique do not depend on the initial guess, while it is computationally less involved than iterative reconstruction approaches. The method was first evaluated using simulated data (in-silico) where modulus reconstruction's sensitivity to displacement noise and elastic modulus was assessed. To demonstrate the method's performance, displacement fields of two tissue mimicking phantoms determined using three different motion tracking techniques were used as input to the developed elastography method to reconstruct the distribution of relative elastic modulus of the inclusion to background tissue. In the next stage, the relative elastic modulus of three clinical cases pertaining to liver cancer patient were determined. The obtained results demonstrate reasonably high elastic modulus reconstruction accuracy in comparison with similar direct methods. Also it is associated with reduced computational cost in comparison with iterative techniques, which suffer from convergence and uniqueness issues, following the same formulation concept. Moreover, in comparison with other methods which need initial guess, the presented method does not require initial guess while it is easy to understand and implement.

Exploring Advanced Functionalities of Carbon Fiber-Graded PEEK Composites as Bone Fixation Plates Using Finite Element Analysis.

This study aims to address the challenges associated with conventional metallic bone fixation plates in biomechanical applications, such as stainless steel and titanium alloys, including stress shielding, allergic reactions, corrosion resistance, and interference with medical imaging. The use of materials with a low elastic modulus is regarded as an effective approach to overcome these problems. In this study, the impact of different types of chopped carbon fiber-reinforced polyether ether ketone (CCF/PEEK) functionally graded material (FGM) bone plates on stress shielding under static and instantaneous dynamic loading was explored using finite element analysis (FEA). The FGM bone plate models were established using ABAQUS and the user's subroutine USDFLD and VUSDFLD, and each model was established with an equivalent overall elastic modulus and distinctive distributions. The results revealed that all FGM bone plates exhibited lower stress shielding effects compared to metal bone plates. Particularly, the FGM plate with an elastic modulus gradually increased from the centre to both sides and provided maximum stress stimulation and the most uniform stress distribution within the fractured area. These findings offer crucial insights for designing implantable medical devices that possess enhanced mechanical adaptability.

Auxetic Properties of the Stiffest Elastic Bodies as a Result of Topology Optimization and Microstructures Recovery Based on Homogenization Method

Herein, several semianalytical formulae for the optimal distribution of elastic moduli in 2D or 3D domains occupied by nonhomogeneous, least compliant bodies are presented and three different methods for recovering microstructures predicted by the isotropic material design method are proposed, which is a stress‐based variant of topology optimization for isotropic bodies. In all five presented variants of the topology optimization of elastic bodies, the numerical implementation of these formulae requires only the use of any algorithm of searching for the minimum of functional in multidimensions without any constraints, even box constraints on design parameters. For each variant considered, the formulae defining this functional are defined analytically. All results concern the design of composite structures that maximize their stiffness (equivalently minimize their compliance) while satisfying a certain isoperimetric condition introducing the upper limit of the available material resource. The article pays special attention to the fact that the stiffest, heterogeneous isotropic elastic material has almost always auxetic properties. Based on the asymptotic homogenization method and adopted bending‐free lattice model, an algorithm for the numerical recovering of nonhomogeneous isotropic microstructure in the entire domain occupied by the plate is proposed, with a fairly easy‐to‐implement ability to model an auxetic behavior.

Determining the Spectrum of Eigenvalues and Eigenfunctions for the Bernoulli–Euler Equation with Variable Coefficients by the Peano Method

The paper considers the problem of determining the natural frequencies and eigenwaves of transverse vibrations for the Bernoulli–Euler equation with variable coefficients. Such problems arise both in the case of complex geometry of a vibrating solid and in the case of functionally graded materials or the accumulation of damage in a classical elastic material. Solutions of boundary value problems are constructed using the expansion in Peano series. Under broad assumptions, the uniform convergence of Peano series is shown and estimates of the residual terms are obtained. Examples of the numerical implementation of the proposed procedure are given for bending vibrations of a rod with certain parameters of a variable cross section (geometric heterogeneity) and elastic modulus distribution (physical heterogeneity). Numerical examples are focused on assessing the geometric and elastic properties of samples in an experimental study of the fatigue strength of alloys during high-frequency cyclic tests based on the general principle of point resonant loading. The method proposed for solving problems of resonant vibrations for the Bernoulli–Euler equation can be used in the design of new promising cyclic test schemes and mathematical modeling of fatigue failure processes under high-frequency resonant vibrations.

Postfire performance of pultruded wood-cored GFRP sandwich beams

Wood-cored sandwich components have been extensively used in constructions of buildings and bridges. However, the existing studies on the postfire behavior of these components are very limited. This study aims to quantitatively evaluate the postfire residual properties of the pultruded wood-cored GFRP sandwich (PWGS) beams. This paper mainly comprises three parts: (i) review of fire experiment of the PWGS beams; (ii) postfire bending experiments conducted on the PWGS beams with different fire scenarios and (iii) numerical study on thermal and postfire thermomechanical responses. It was found the failure modes mainly depended on the number of exposed sides and the fire damage degree. For the three-sided fire-exposed specimens (except for the one with a 25 mm-thick calcium silica board), the progressive tension rapture of the charred fibers was the dominant failure mode. The other specimens, however, exhibited the brittle in-plane shear failure of the web. Moreover, after cooling down from 250 °C to 20 °C, the GFRP and wood exhibited 68 % and 35 % of recoveries of elastic modulus respectively. A three-dimensional thermal model with kinetic thermophysical sub-models considering heat transfer, water evaporation and decomposition was developed. The developed thermal model accurately predicted the temperature responses and charring profiles. Furthermore, a thermomechanical model considering the material damage was developed to accurately predict the elastic modulus distribution, postfire residual bending capacity and failure modes. This study provides the basis for the retrofit and the reinforcement of the fire-damaged PWGS beams. In the future, study on the fire resistance of the PWGS components in fire will be required.

Experimental and first-principles calculation study on influence of stacking faults on hardness and anisotropy of M7C3 carbides

M7C3 often exhibits stacking faults (SFs). However, the influence of SFs on carbide properties are rarely studied. To explore effects of SFs, the carbide hardness, elastic modulus, and distribution of hardness and elastic modulus in the grain were analyzed using nanoindentation technology. The SFs structure of M7C3 carbides was analyzed using transmission electron microscopy (TEM). First-principles calculations revealed the influence mechanism of SFs on carbide hardness. The results showed that high-density SFs improved the carbide hardness by approximately 2 GPa. Uneven distribution of SFs leads to uneven hardness and elastic modulus of M7C3 carbides. The SFs disrupt the ordered arrangement of C-Cr bonds, which reduces the anisotropy of Cr7C3. The change in carbide strength was not due to the change in bond strength. Instead, the lattice distortion caused by the change in the C-Cr bond angle in Cr7C3-SFs increased the deformation resistance of the crystal and improved the hardness of Cr7C3.

Using Adhesive Micropatterns and AFM to Assess Cancer Cell Morphology and Mechanics.

The mechanical properties of living cells reflect their physiological and pathological state. In particular, cancer cells undergo cytoskeletal modifications that typically make them softer than healthy cells, a property that could be used as a diagnostic tool. However, this is challenging because cells are complex structures displaying a broad range of morphologies when cultured in standard 2D culture dishes. Here, we use adhesive micropatterns to impose the cell geometry and thus standardize the mechanics and morphologies of cancer cells, which we measure by atomic force microscopy (AFM), mechanical nanomapping, and membrane nanotube pulling. We show that micropatterning cancer cells leads to distinct morphological and mechanical changes for different cell lines. Micropatterns did not systematically lower the variability in cell elastic modulus distribution. These effects emerge from a variable cell spreading rate associated with differences in the organization of the cytoskeleton, thus providing detailed insights into the structure-mechanics relationship of cancer cells cultured on micropatterns. Combining AFM with micropatterns reveals new mechanical and morphological observables applicable to cancer cells and possibly other cell types.

Numerical analysis on mechanical difference of sandstone under in-situ stress, pore pressure preserved environment at depth

Deep in-situ rock mechanics considers the influence of the in-situ environment on mechanical properties, differentiating it from traditional rock mechanics. To investigate the effect of in-situ stress, pore pressure preserved environment on the mechanical difference of sandstone, four tests are numerically modeled by COMSOL: conventional triaxial test, conventional pore pressure test, in-situ stress restoration and reconstruction test, and in-situ pore pressure-preserved test (not yet realized in the laboratory). The in-situ stress restoration parameter is introduced to characterize the recovery effect of in-situ stress on elastic modulus and heterogeneous distribution of sandstone at different depths. A random function and non-uniform pore pressure coefficient are employed to describe the non-uniform distribution of pore pressure in the in-situ environment. Numerical results are compared with existing experimental data to validate the models and calibrate the numerical parameters. By extracting mechanical parameters from numerical cores, the stress-strain curves of the four tests under different depths, in-situ stress and pore pressure are compared. The influence of non-uniform pore pressure coefficient and depth on the peak strength of sandstone is analyzed. The results show a strong linear relationship between the in-situ stress restoration parameter and depth, effectively characterizing the enhanced effect of stress restoration and reconstruction methods on the elastic modulus of conventional cores at different depths. The in-situ pore pressure-preserved test exhibits lower peak stress and peak strain compared to the other three tests, and sandstone subjected to non-uniform pore pressure is more prone to plastic damage and failure. Moreover, the influence of non-uniform pore pressure on peak strength gradually diminished with increasing depth.

Phase formability and nanomechanical properties in nanostructured multi-principal element alloys: Combinatorial and data-driven studies

The identification of multi-principal element alloys with optimal properties from a vast composition space is a daunting task, particularly for high-entropy alloys (HEAs) composed of five or more elements. Despite increasing theoretical and experimental investigations, the majority of HEAs are developed through a time-consuming trial-and-error approach. Here we demonstrate a combinatorial and data-driven methodology based on a composition gradient TiZrHfNbTa library. Using synchrotron X-ray diffraction and high-speed nanoindentation, we characterized the phase formability and mechanical properties, respectively. We correlated the compositions with the distributions of structures, elastic moduli, and hardness in the TiZrHfNbTa system and proposed a kinetic phase formation criterion based on critical cooling rates. Moreover, we evaluated high-throughput data extrapolation models including the volume fraction of triple junctions, the Hall-Petch relationship, and machine learning. Our methodology opens up new avenues to the accelerated discovery of multi-principal element alloys by revealing relationships among compositions, phase formability, and mechanical properties.

The application value of shear wave dispersion and shear wave elastography combined with serological indicators in the evaluation of liver fibrosis

Objective: To explore the application value of shear wave dispersion (SWD) and shear wave elastography (SWE) combined with serological indicators in the evaluation of liver fibrosis. Methods: A total of 219 patients with liver disorders who underwent liver biopsy were prospectively collected in Huashan Hospital, Fudan University from January 2021 to September 2022, including 130 males and 89 females, aged from 18 to 76 (42±12) years. All patients underwent SWD and SWE examinations before liver biopsy. Serological indicators including alanine aminotransferase(ALT), aspartate aminotransferase(AST), alkaline phosphatase(ALP)) and γ-glutamyl transpeptadase (GGT) were also collected. Based on pathological diagnosis of liver fibrosis stage (from S0 to S4), the distribution of dispersion slope and liver elastic modulus at different fibrosis stages were analyzed in all patients. All patients were divided 7: 3 into training set (156 cases) and validation set (63 cases) in chronological order. In training set, factors influencing liver fibrosis≥S2 stage and S4 stage were analysed using binary logistic regression. The predictive models were established for diagnosing liver fibrosis≥S2 stage and S4 stage by using R language, and the models were evaluated by the area under curve (AUC) and calibrated for validation. Results: The dispersion slope and elastic modulus increased with the severity of fibrosis, with statistically significant differences in different fibrosis stages (both P<0.001). In training set, dispersion slope, elastic modulus, ALT, AST, and GGT were influential factors in liver fibrosis≥S2 stage and S4 stage(both P<0.05), and prediction models were constructed based on these indicators. In training set, the AUCs of the predictive model, SWD and SWE for diagnosingliver fibrosis≥S2 stage were 0.743 (95%CI: 0.665-0.821), 0.709 (95%CI: 0.628-0.790) and 0.725 (95%CI: 0.647-0.804), respectively; for diagnosing liver fibrosis S4 stage, the AUCs were 0.988 (95%CI: 0.968-1.000), 0.908 (95%CI: 0.852-0.963) and 0.974 (95%CI: 0.945-1.000), respectively. In validation set, the AUC of the predictive model, SWD and SWE for diagnosing liver fibrosis≥S2 stage were 08.735 (95%CI: 0.612-0.859), 0.658 (95%CI:0.522-0.793) and 0.699 (95%CI:0.570-0.828), respectively; for diagnosing liver fibrosis S4 stage, the AUC were 0.976 (95%CI: 0.937-1.000), 0.872 (95%CI: 0.757-0.988) and 0.948 (95%CI: 0.889-1.000), respectively. The calibration curves of the prediction models were consistent in the training and validation sets. Conclusion: The predictive model of SWD and SWE combined with serological indicators is helpful in the diagnosis of stage of liver fibrosis non-invasively.

Distribution of microstructure, elastic modulus and residual stress near the interface in laser repaired GH4169 superalloy

As an emerging additive manufacturing technology, Direct Energy Deposition (DED) shows great potential for repairing or remanufacturing high-value components, such as aero-engine turbine blades. Through the utilization of Direct Laser Deposition (DLD), a specific form of DED, GH4169 superalloy powder can be cladded onto a GH4169 substrate to mimic the repairing of aerospace components. The microstructure, mechanical properties, and their distribution characteristics near the interface under different DLD process parameters are comprehensively studied. Combining Electron Backscatter Diffraction (EBSD), data stitching technique, and first-principles, the grain orientation and the elastic stiffness matrix of each phase are determined, based on which the distribution of elastic modulus and residual stress in a relatively large and complex area are analyzed. The results indicate that the DLD process parameters, such as linear energy density, significantly affect the grain size, grain growth direction and residual stress, but much less on the elastic modulus. Furthermore, the microstructure presents significant nonuniformity near the interface, and the elastic modulus presents anisotropy at the microscale, but almost isotropy at the macroscale, without noticeable value differences among the cladding zone, the heat-affected zone (HAZ) and the substrate. This study could shed light on the DLD process optimization for improving the microstructure and mechanical properties of laser-repaired components.

Topology optimization of multi-morphology composite lattice structure with anisotropy properties

Compared with the single-morphology lattice structures, multi-morphology composite lattice structure shows the potential to achieve a broad spectrum of customizable mechanical properties by modify the architectural feature of substructures. Inspired by Sigmoid mathematical function, a new parametrical design method for composite lattice structure was presented by combining the two cell lattice structs with complementary spatial distribution of elastic modulus based on previous studies. The results indicate that the unique anisotropy control strategy of elastic modulus is achieved by changing the design variables. Moreover, instead of altering the volume fraction of single-morphology lattice structure, the elastic constants of new composite lattice structure can be modified under a constant volume fraction by adjusting the design parameters. To further enhance the structural stiffness of composite lattice infilling structures, we propose a novel stiffness optimization approach based on the principal stress direction. This anisotropy control strategy enables the optimal distribution of design variables in the lattice-infill structures. Finally, the numerical results show that the proposed approach improves global stiffness compared to traditional approaches.

Mechanical Behavior and Low-Cycle Fatigue Performance of a Carburized Steel for GTF Engines

Using nanoindentation technology to analyze the hardness and elastic modulus distributions of the local microzones within materials, it can be determined that the case-carburized specimen is a composite of the carburized case and the pseudo-carburized material in the core. The overall mechanical behavior of the case-carburized material is much closer to that of the completely carburized material, indicating that the carburized case dominates the case-carburized material. Stress fatigue tests conducted on carburized tubular specimens, pseudo-carburized solid specimens, and case-carburized solid specimens showed that the fatigue performance of the completely carburized material is slightly lower than that of the pseudo-carburized specimens due to lower plasticity. However, the fatigue performance of the case-carburized specimens is significantly better than that of the two homogeneous materials. This could be attributed to the graded material behavior and the larger compressive residual stress in the carburized case, which are the primary positive factors for improving the fatigue life of case-carburized materials. SEM fractographs revealed that the fatigue nucleation in the case-carburized specimen initiates from the transition zone rather than from the surface of the specimens as observed in the homogeneous materials. Low-cycle fatigue evaluation of ultra-high-power gear transmission systems should focus on the influences of the carburized case.

Revealing the length-scale dependence of the spatial mechanical heterogeneity and shear transformation zone size in metallic glassy films

Mechanical heterogeneity in metallic glasses at the nanoscale has been widely investigated but remains to date not well understood. In this study, metallic glassy films with an ultra-smooth and defect-free surface were prepared via a magnetron sputtering method. Grid nanoindentation tests were conducted to study the statistical distributions of hardness, elastic modulus, and yield stress, as well as their spatial fluctuation at varying indentation depths. The results revealed locally “strong” and “weak” regions with a characteristic length of 5–10 μm uniformly distributed at an indentation depth of 50 nm. The spatial mechanical heterogeneity was shown to be greatly suppressed with increasing indentation depth. Using the statistical law of yield shear stress, the shear transformation zone (STZ) size was determined and was found to rapidly increase with increasing indentation depth. Along the planar direction, mechanical heterogeneity and STZ size were shown to be independent of the length scale.

Degradation Mechanism of Coal Gangue Concrete Suffering from Sulfate Attack in the Mine Environment.

Recycling coal gangue as aggregate to produce concrete in situ is the most effective way to solve the problem of deposited coal gangue in mines. Nevertheless, the mine environment underground is rich in sulfate ions, posing a threat to the durability of coal gangue concrete (CGC). Hence, the degradation process of sulfate-attacked CGC is investigated. A series of tests is performed to evaluate its variation law of mass, dynamic elastic modulus, compressive strength and sulfate ion distribution. Meanwhile, the microstructure and phases of sulfate-attacked CGC are identified by scanning electron microscopy, X-ray diffraction and thermogravimetric analysis. The results indicate that the residual compressive strength ratio of CGC is higher than that of normal concrete after a 240 d sulfate attack, implying a superior sulfate resistance for CGC. Additionally, the higher the sulfate concentration, the more severe the degradation. Except for the secondary hydration of CGC itself, the diffused sulfate ions also react with Ca(OH)2, forming gypsum and ettringite; this plays a positive role in filling the pores at the early stage, whereas, at the later stage, the generated micro-cracks are detrimental to the performance of CGC. In particular, the proposed sulfate corrosion model elucidates the degradation mechanism of CGC exposed to a sulfate-rich environment.