Fracture Energy Dissipation Research Articles

Tensile Fracture Initiation and Propagation of Granite and Gneiss at Wedge Splitting Tests: Part 2—Fracturing Studies Based on Digital Image Correlation and Thin Section Analysis

AbstractThe crack development in quasi-brittle granite and brittle gneiss under mode I loading condition was monitored using digital image correlation (DIC) technique during wedge splitting tests. The cracking behavior was studied on granite specimens that were split in one material direction, perpendicular to the rift plane, and gneiss specimens that were split in three different material directions, parallel and perpendicular to the foliation (along and across a lineation). The granite specimens had a saw cut 5 mm-wide notch and a blunt round notch in form of a 32 mm borehole. The gneiss specimens had a saw cut notch. The results from the DIC measurements revealed a meandering and branching crack path for the granite, whereas a smoother crack path for the gneiss with almost no branching. This behavior was confirmed by microscopy images from thin sections taken from specimens after testing. The thin sections showed that the fractures were prone to propagate across grains in the more coarse-grained granite than in the fine-grained gneiss, where the fractures propagated almost entirely along grain boundaries. The crack initiation occurred mainly in the corner of the saw cut notches and centrally in the round notch. However, the initiation locations in the granite were affected by the medium- to coarse-grained microstructure with grains preventing initiation and propagation which yielded displaced positions out from the ideal ones with respect to the highest stress in some cases. The crack opening displacement was determined along the crack path from the DIC measurements at 12 stages on each specimen of the advancing crack during the splitting progress. The critical crack opening displacement and length of the fracture process zone were assessed and the crack front position yielding the crack length along the tests was determined. The results showed a critical crack length when the deformations in the ligament (also called plastic hinge) affected the cracking process. The average crack velocity in gneiss during the test was more than twice as high as in the granite. This is attributed to a combined effect of the higher brittleness in the gneiss and the effect of a too large elastic energy in the specimen and test setup in relation to the dissipated fracture energy which made the initial crack propagation in the gneiss specimens nearly unstable. The strain energy release rate was calculated along the crack propagation and showed a lower value when the crack lengths were less than 40–60 mm. The calculation of the strain energy release rate was made on crack length measurements from DIC results. The results from the investigation were discussed in relation to the few other similar results found in the literature. The findings give an insight and understanding of the cracking process via both qualitative and quantitative results. Several used methods were novel or not used together in a single study as in this one.

Mode-I dynamic fracture evolution and energy dissipation of basalt fiber reinforced reactive powder concrete

Dynamic fracture experiments on basalt fiber reinforced reactive powder concrete (BFRRPC) were conducted using notched semi-circular bending (NSCB) specimens, aiming to investigate the Mode-I dynamic fracture characteristics. Based on the split Hopkinson pressure bar (SHPB) and digital image correlation (DIC) systems, this study focused on investigating the dynamic fracture toughness, fracture process zone (FPZ), crack propagation, fractal dimension of fracture path, and energy evolution of BFRRPC with different basalt fiber contents. The results show the basalt fiber break, pull-out and interface fracture in the matrix in the microscopic experiment results, which are the intrinsic reasons for the enhancement of fracture toughness in RPC due to the fiber presence. The increases in fracture toughness of BFRRPC range between 24.7 % and 42.7 %, with a notable enhancement observed when incorporating 1.0 % basalt fiber content. The crack and the FPZ tip of BFRRPC can be located effectively by the method of displacement-strain mixed calibration. The addition of 1.0 % basalt fiber content effectively delays the crack initiation in specimens, with crack initiation occurring earlier as the loading level increases. The CTOD and FPZ tip opening displacement have nothing to do with the loading level. Basalt fibers can lead to relatively lower and stable fractal dimensions of BFRRPC, effectively reducing the cracking degree and increasing the roughness of cracks. Basalt fiber effectively enhances the fracture energy of RPC. The dissipated energy is mainly composed of the energy consumed by the fracture (fracture energy) of BFRRPC, with the overall residual kinetic energy ratio (the ratio of residual kinetic energy to dissipated energy) generally below 1.90 %.

A rate-dependent crack bridging model for dynamic fracture of CNT-reinforced polymers

Carbon nanotubes (CNTs) improve the fracture toughness of polymer-based matrix composites by bridging the crack growth path. This research presents a finite element (FE) rate-dependent crack bridging model of Mode-I dynamic crack growth in CNT-reinforced polymers accounting for rate of loading and rapid crack growth. Two distinct CNT bridging and matrix cracking damage mechanisms are taken into account in the fracture process zone (FPZ) accounting for the dissipation of fracture energy. A viscoelastic-viscoplastic material model is adapted for the matrix phase to capture the strain rate effects. The crack in the matrix phase is modeled using cohesive zone elements characterized by experimental data. A rate-dependent traction-separation law obtained from CNT pull-out simulation at relevant crack opening speeds is used to simulate the CNT bridging in the FPZ. Considering the given traction-separation law as a constitutive equation, the CNTs are replaced with non-linear spring elements to facilitate the FE simulation of crack bridging with numerous CNTs in the FPZ. The proposed rate-dependent FE model for crack bridging enables the study of the effect of key CNT factors such as length, orientation, waviness, volume fraction, and agglomeration on fracture energy dissipation at various crack speeds. The developed model can simultaneously consider the interactive effects of all CNT parameters which is useful for considering all processing-induced uncertainties in analyzing the effects of CNTs on the dynamic fracture toughness of nanocomposites.

Experimental Study on Acoustic Emission Features and Energy Dissipation Properties during Rock Shear-Slip Process.

The features of rock shear-slip fracturing are closely related to the stability of rock mass engineering. Granite, white sandstone, red sandstone, and yellow sandstone specimens were selected in this study. The loading phase of "shear failure > slow slip > fast slip" was set up to explore the correlation between fracture type, acoustic emission (AE) features, and energy dissipation during the rock fracturing process. The results show that there is a strong correlation between fracture type, energy dissipation, and AE features. The energy dissipation ratio of tension-shear (T-S) composite, shear, and tensile types is 10:100:1. The fracture types in the shear failure phase are mainly tensile and TS composite types. The differential mechanism of energy dissipation of different rocks during the shear-slip process is revealed from the physical property perspectives of mineral composition, particle size, and diagenetic mode. These results provide a necessary research basis for energy dissipation research in rock failure and offer an important scientific foundation for analyzing the fracture propagation problem in the shear-slip process. They also provide a research basis for further understanding the acoustic emission characteristics and crack type evolution during rock shear and slip processes, which helps to better understand the shear failure mechanism of natural joints and provides a reference for the identification of precursors of shear disasters in geotechnical engineering.

Fracture behavior of 3D-printed thermoplastics—A dilemma of fracture toughness versus fracture energy

The Material Extrusion (ME) technique in 3D printing facilitates the production of thermoplastic materials with diverse cellular or lattice-like infill geometries, enabling the creation of lightweight, high-performance materials. This study investigates the influence of infill geometry and relative density on the fracture behavior of 3D-printed thermoplastics produced through ME. Polylactic acid (PLA) is used as the model material, with unit cell geometries-square, triangle, and Kagome-and relative densities ranging from 0.4 to 0.8 explored. Tensile tests are first conducted to determine in-plane elastic moduli in two orthogonal directions, accounting for unit cell anisotropy. These results are employed in effective fracture energy calculations. Compact tension fracture tests follow, quantitatively characterize crack growth characteristics in both directions. In both tests, digital image correlation method is used to measure full field strain distributions. Three significant findings emerge. First, there is a power scaling relationship between Elastic Modulus and relative density across all unit cells, with Kagome exhibiting the highest correlation constant. Triangle and Kagome unit cells show negligible orthotropic responses in perpendicular directions for varying relative densities. Second, the relationship between nondimensional fracture toughness and relative density follows a similar scaling law, with minor variations depending on unit cell type. The correlation factor slightly dependens on unit cell geometry but remains around 3 across the the examined relative density range. Third, considering the dissipation of inelastic fracture energy, both triangle and Kagome unit cell geometries demonstrate an order of magnitude higher effective fracture energy (i.e., crack growth resistance) compared to the square unit cell. This is associated with toughening mechanisms such as crack deflection and bifurcation. These findings highlight the disparity between fracture toughness and effective fracture energy in assessing the fracture resistance of 3D-printed thermoplastics, clearly demonstrating that fracture toughness alone is insufficient for a comprehensive assessment. The proposed scaling laws provide predictive insights into the fracture toughness of polymeric materials produced via the ME method.

Effect of plastic deformability and fracture behaviour on interfacial toughening mechanism at Fe/Ni interfaces

Fracture at interface causes plastic deformation in the vicinity region. Conventional plastic energy dissipation theory indicates that ductile vicinity toughens the interface by absorbing plastic deformation energy. However, the microstructure in the vicinity directly affects local plastic deformability and fracture behaviour, implying a more complicated toughening mechanism. In this study, the effect of microstructure and hardness on fracture behaviour of Fe/Ni interface was investigated. By experimental approach, interfaces with and without dynamic recrystallization (DRX) were fabricated by controlling the bonding conditions. It showed that compression-induced plastic deformation is the main source of the hardening behaviour in the vicinity. Moreover, the interfaces with hardened DRX vicinities exhibited improved fracture toughness, which is inconsistent with the plastic energy dissipation theory. To clarify this observation, the crystal plasticity finite element method (CPFEM) approach was employed to distinguish the effects of plastic deformation and interfacial microstructure. The result showed that although higher plastic deformability in the vicinity absorbs more dissipated plastic energy, severe stress concentration at the interface leads to early fracture and poor toughness. On the other hand, the interfacial hardened DRXed grains disperse interfacial stress distribution and provide potential sub-crack sites. A combined result of uniform plastic deformation and fracture energy dissipation is responsible for the improved toughness at interfaces with DRXed grains.

A rate-dependent cohesive zone model for dynamic crack growth in carbon nanotube reinforced polymers

Carbon nanotubes (CNTs) enhance the fracture toughness of polymer-based matrix composites by dissipating the fracture energy through the pull-out deformation damage mechanism. The rate-dependent behavior of the matrix phase and the CNT/matrix interface affects the contribution of CNTs in enhancing the fracture toughness under dynamic loading and rapid crack growth. A continuum-based finite element (FE) model is utilized in this research to analyze the CNT pull-out damage mechanism. The influence of CNTs on the dynamic fracture behavior of polymer-based composites is studied taking into account the crack opening speed and loading rate effects. The matrix phase is treated as a viscoelastic-viscoplastic material and a new rate-dependent cohesive zone model (CZM) is proposed for modeling the behavior of interface between the CNTs and matrix. The rate-dependent traction-separation laws for the cohesive zone elements are established at different pull-out or crack opening speeds. The proposed rate-dependent FE model of pull-out mechanism facilitates the investigation of the effective factors of CNTs, including length, orientation, and waviness, on fracture energy dissipation at different pull-out speeds. Developed model is very suitable for very long CNTs where atomistic-based molecular dynamics and molecular mechanics methods are associated with difficulties and are more costly and time-consuming.

Fracture characteristics and energy dissipation law of shale under water-based impact loads

Shale fracture and energy dissipation are the basis of reservoir fracturing effect evaluation. The damage and fracture mechanism of shale under dynamic impact load is the key scientific concern of reservoir fracturing. To study the law of fracture, fracture propagation and energy dissipation of shale under dynamic impact, dynamic tests of water-based impact load under different impact velocities were carried out using impact rock breaking test platform based on air cannon. Topological and fractal theory, Weibull distribution model, space vector geometry method and Griffith fracture mechanics theory were used to systematically study the effects of impact velocity on fracture development and expansion, fragment mass and size distribution, damage degree of abutment residual and energy dissipation transformation. Scanning electron microscopy (SEM) was used to observe the micromorphology of the impact fracture surface. The results demonstrated that an increase in impact velocity led to the formation of a network fracture featuring main fractures, cavity fissure, bedding fractures, and crushing zones, thereby enhancing the fracture’s capability to penetrate bedding. The apparent fracture network connectivity, topology structure and fractal dimension were positively correlated with impact velocity. The residual height of the shale decreased, resulting in an escalation of the damage degree from mild (0.43) to severe (0.75), while the average penetration angle decreases from 81.00° to 63.52°. The area of new surface experiences rapid initial growth followed by a more gradual increase, with dissipative energy showing a more pronounced increase compared to crushing energy. The micro-fracture mode underwent an evolution from brittleness to toughness and a transition from low energy consumption to high energy consumption. The propagation, reflection, and superposition of stress waves within the rock mass gave rise to a complex stress zone, ultimately causing the rock mass to break. These findings lay the groundwork for developing a stress-damage-energy-failure combined model for shale subjected to dynamic impact loads, thereby enhancing the development of intricate networks in shale reservoir and improving the effective extraction of shale gas.

OVERVIEW OF STUDIES ON EXTERNAL CONFINEMENT OF R/C COLUMNS USING UNIAXIAL GEOGRID

It has been established in the literature that using uniaxial geogrid as internal confinement for reinforced concrete (R/C) columns would improve the strength and ductility characteristics of the column. However, the potential of using uniaxial geogrid as external confinement remains largely unexplored. The aim of the study is to assess the effectiveness of utilizing uniaxial geogrid as external confinement as compared to FRP external confinement, as well as various configurations of internal confinement, including uniaxial geogrid and stirrups. The assessment encompasses the analysis of axial load-displacement behavior, identification of failure modes, and evaluation of structural ductility through metrics such as fracture energy and energy dissipation. Test results indicate significant benefits associated with external confinement using uniaxial geogrid, including strength, ductility, and energy capacity. This study contributes to the progression of knowledge by illustrating the efficacy of uniaxial geogrid as an external confinement method for reinforced concrete columns. Additionally, it offers valuable comparative insights into different confinement techniques, informing the selection and design of optimal strategies for reinforced concrete structures.

OVERVIEW OF STUDIES ON EXTERNAL CONFINEMENT OF R/C COLUMNS USING UNIAXIAL GEOGRID

It has been established in the literature that using uniaxial geogrid as internal confinement for reinforced concrete (R/C) columns would improve the strength and ductility characteristics of the column. However, the potential of using uniaxial geogrid as external confinement remains largely unexplored. The aim of the study is to assess the effectiveness of utilizing uniaxial geogrid as external confinement as compared to FRP external confinement, as well as various configurations of internal confinement, including uniaxial geogrid and stirrups. The assessment encompasses the analysis of axial load-displacement behavior, identification of failure modes, and evaluation of structural ductility through metrics such as fracture energy and energy dissipation. Test results indicate significant benefits associated with external confinement using uniaxial geogrid, including strength, ductility, and energy capacity. This study contributes to the progression of knowledge by illustrating the efficacy of uniaxial geogrid as an external confinement method for reinforced concrete columns. Additionally, it offers valuable comparative insights into different confinement techniques, informing the selection and design of optimal strategies for reinforced concrete structures.

An interlaminar fatigue damage model based on property degradation of carbon fiber-reinforced polymer composites

Interface delamination is a significant damage mechanism in fiber-reinforced polymer (FRP) laminated composites caused by interlaminar normal and shear stresses. This is due to the low interlaminar properties including interface stiffness and strength that continuously degrade to cause fatigue crack nucleation and growth. In this respect, an interlaminar fatigue damage model is proposed to accurately address the reliability aspect of the FRP composite materials and structures. The model considers a damage process that consists of two stages: (1) fatigue damage evolution due to interlaminar properties degradation to the onset of crack nucleation. A cyclic cohesive zone model with a bilinear softening behavior is introduced along with the fatigue life model to capture the mean stress effect of the interface. This is followed by (2) the crack nucleation process leading to the physical separation/debonding of the interface material point, as governed by the cycle-dependent fracture energy dissipation. The mechanical prediction of the interlaminar fatigue damage process is illustrated through finite element simulation of a mixed-mode flexural test of a carbon fiber-reinforced polymer (CFRP) composite beam subjected to fatigue loading. The results indicate that the interlaminar normal and shear crack opening displacement increases exponentially with the larger number of load cycles. In addition, the high-stress gradient is limited to the interface crack front zone with the normal and shear stress peaks at 69.2 and 16.5 % of the respective interlaminar strength. Moreover, controlled interlaminar crack growth is initially foreseen at 7.0 × 10-6 mm/cycle, followed by an abrupt crack “jump” at 287,000 load cycles.

Meso-scale size effects of material heterogeneities on crack propagation in brittle solids: Perspectives from phase-field simulations

Brittle solids are often toughened by adding a second-phase material. This practice often results in composites with material heterogeneities on the meso scale: large compared to the scale of the fracture process zone but small compared to that of the application. The specific configuration (both geometrical and mechanical) of this mesoscale heterogeneity is generally recognized as important in controlling crack propagation behavior and, subsequently, the (effective) toughness of the composite. Here, we systematically investigate how dynamic brittle fracture navigates through a linear array of mesoscale inclusions. Using a variational phase-field (PF) approach, we compute the apparent crack speed and fracture energy dissipation rate to compare crack propagation (and the resulting toughening) under Mode-I loading for various configurations of inclusions. We identify an interplay between the size of inclusion and that of the K-dominant zone in the presence of elastic heterogeneity: matching these two sizes gives rise to the best toughening outcome for a given area fraction of inclusions. We discuss mechanisms that rationalize this observation and the importance of the length scale parameter used in PF models in interpreting simulation results. Our work sheds physical insight into the interaction between size effects and material properties, thereby opening a venue for the rational design of functional (architected) composites for dynamic fracture applications.

Toughing epoxy nanocomposites with Graphite-Nanocellulose layered framework

Epoxy nanocomposites hold immense promise for advanced high-performance applications in coatings, adhesives, and fiber-reinforced composite matrices. However, their widespread use is hindered by low fracture toughness, attributed to highly cross-linked network structure. Here, this study presents a synergistic manufacturing strategy combining ultrasonic graphite-nanocellulose assembly and bidirectional freeze casting to fabricate epoxy nanocomposites with remarkable layered architectures. Subsequent infiltration and curing with epoxy prepolymer produce nanocomposites exhibiting a fracture toughness 4.67 times higher than pure epoxy. Both experimental and theoretical analyses demonstrate the nanocomposite's superior crack propagation resistance, attributable to a range of synergistic toughening mechanisms. These include robust interfacial bonding and mechanical interlocking, which arise from fiber pull-out/flake fracture effects, effectively impeding crack growth. Additionally, the distinctive layered architecture promotes tortuous crack pathways, optimizing fracture energy dissipation. This work offers pivotal insights into structure–property relationships, paving the way for the design of next-generation nanocomposites with tailored, superior mechanical performance.

Peanut shaped auxetic cementitious cellular composite (ACCC)

Auxetic cementitious cellular composites (ACCCs) exhibit desirable mechanical properties (e.g., high fracture resistance and energy dissipation), due to their unique deformation characteristics. In this study, a new type of cementitious auxetic material, referred to as peanut shaped ACCC, has been designed and subsequently architected using additive manufacturing techniques. Two peanut shaped ACCCs specimens with different pseudo-minor axes have been tested under uniaxial compression with Digital Image Correlation (DIC) to assess their compressive behavior, peak strength, Poisson’s ratio, and energy dissipation capacity. Additionally, cyclic tests were conducted to investigate their compressive resilience properties, further elucidated through microstructural analysis using a digital optical microscope. The mechanical test results were also compared with those of previously developed elliptical-shaped ACCCs. Furthermore, a numerical model was used to simulate the mechanical behavior of peanut shaped ACCCs under uniaxial compression, and showed a good agreement with the experimental data. The auxetic behavior observed in peanut shaped ACCCs arises from the rotation of sections facilitated by fiber bridging at the ligament of adjacent holes within the cementitious unit cell. In comparison to elliptical-shaped ACCCs, peanut shaped ACCCs can exhibit a slightly more negative Poisson's ratio and mitigate stress concentration. The reduction of stress concentration enables peanut shaped ACCCs to dissipate substantial energy, showcasing enhanced ductility and toughness. In cyclic tests, peanut shaped ACCCs exhibit superior recoverable deformation elasticity, attributed to robust fiber bridging capacity. The exceptional mechanical properties exhibited by peanut shaped ACCCs offer a scalable solution for developing energy-absorbent and multifunctional cementitious materials for smart infrastructure.

Effect of Eccentricity Difference on the Mechanical Response of Microfluidics-Derived Hollow Silica Microspheres during Nanoindentation.

Hollow microspheres as the filler material of syntactic foams have been adopted in extensive practical applications, where the physical parameters and their homogeneity have been proven to be critical factors during the design process, especially for high-specification scenarios. Based on double-emulsion droplet templates, hollow microspheres derived from microfluidics-enabled soft manufacturing have been validated to possess well-controlled morphology and composition with a much narrower size distribution and fewer defects compared to traditional production methods. However, for more stringent requirements, the innate density difference between the core-shell solution of the double-emulsion droplet template shall result in the wall thickness heterogeneity of the hollow microsphere, which will lead to unfavorable mechanical performance deviations. To clarify the specific mechanical response of microfluidics-derived hollow silica microspheres with varying eccentricities, a hybrid method combining experimental nanoindentation and a finite element method (FEM) simulation was proposed. The difference in eccentricity can determine the specific mechanical response of hollow microspheres during nanoindentation, including crack initiation and the evolution process, detailed fracture modes, load-bearing capacity, and energy dissipation capability, which should shed light on the necessity of optimizing the concentricity of double-emulsion droplets to improve the wall thickness homogeneity of hollow microspheres for better mechanical performance.

Insight into the fracture energy dissipation mechanism in elastomer composites via sacrificial bonds and fillers.

Most tough elastomer composites are reinforced by introducing sacrificial structures and fillers. Understanding the contribution of fillers and sacrificial bonds in elastomer composites to the energy dissipation is critical for the design of high-toughness materials. However, the energy dissipation mechanism in elastomer composites remains elusive. In this study, using a tearing test and time-temperature superposition, we investigate the effect of fillers and sacrificial bonds on the energy dissipation of elastomer composites consisting of poly(lipoic acid)/silver-coated Al fillers. We found that the fillers and sacrificial bonds mutually enhance both the intrinsic fracture energy and the bulk energy dissipation, and moreover the sacrificial bonds play a more important role in enhancing fracture toughness than the fillers. It is unreasonable to rely solely on the loss factor for bulk energy dissipation. The addition of sacrificial bonds results in a chain segment experiencing greater binding force compared to the addition of fillers. This suggests that the chain segment consumes more energy during its movement. By calculating the length of the Kuhn chain segment and the Kuhn number, it is evident that the addition of sacrificial bonds results in a greater binding force for the chain segment than the addition of fillers, and this enhanced binding force increases the energy consumption during the motion of the chain segment.

High-strength electrospun ceramic ultrafine fibers based on in-situ polymer-derived technology

Improving the mechanical strength of electrospun ceramic ultrafine fibers (UFs) is crucial for both structural and functional applications. Herein, we report a facile strategy of in-situ embedding ZrO2 nanocrystals (NCs) in polycarbosilane-derived silicon carbide (SiC) UFs. The morphology, chemical composition, mechanical properties, and cross-section morphologies of single UFs are characterized to investigate the effects of introducing ZrO2 NCs. Notably, a single ZrO2 NCs/SiC UF with an average ZrO2 NCs size of 4.5 ± 1.3 nm possesses optimum mechanical performance, it exhibits about 371.3% increase in tensile strength and 6 times improvement in fracture energy when compared with SiC UFs. The uniformly distributed ZrO2 NCs increase the fiber density that reduce the internal defects, which improve the strength of SiC UF. The enhanced fracture energy can be attributed to the efficient fracture energy dissipation mechanism related to the NCs size. This work provides a viable strategy for designing ceramic fibers with enhanced mechanical properties.

High Impact Resistance of 2D MXene with Multiple Fracture Modes.

Two-dimensional (2D) transition metal carbides/nitrides (MXenes) are promising nanomaterials due to their remarkable mechanical and electrical properties. However, the out-of-plane mechanical properties of MXene under impact loading remain unclear. Here, particular impact-resistant fracture behaviors and energy dissipation mechanisms of MXene were systemically investigated via molecular dynamics (MD) simulation. Specifically, it was found that the specific penetration energy of MXene exceeds most conventional impact-resistant materials, such as aluminum and polycarbonate. Two kinds of novel energy dissipation mechanisms, including radial fracture and crushed fracture under different impact velocities, are revealed. In addition, the sandwiched atomic-layer structure of MXene can deflect cracks and restrain their propagation to some extent, enabling the cracked MXene to retain remarkable resistance. This work provides in-depth insights into the impact-resistance of MXene, laying a foundation for its future applications.

Buckling collapse of reinforced thermoplastic pipes (RTPs) with initial imperfections subject to external pressure

In the present study, the collapse behavior of RTPs was analyzed by an experimentally-verified numerical method, in which the eccentricity directions, the combinations of eccentricity and initial ovality are considered. Eigenvalue analysis and Riks analysis were combined to simulate the progressive failure of composites during the collapse, which was conducted by a continuum damage model based on Hashin failure criterion and fracture energy dissipation. The stress analysis showed that the hoop stress of composites is much higher than that of isotropic layers both in the elastic and progressive failure phases. Because of this, thick composites always play important roles in bearing external pressure. Except the experimentally observed O-/U-type collapse modes, the C-type collapse mode was observed and simulated for the first time. They all go through the uniform contraction-collapse-large deformation process, and have the same failure modes of composites. However, different from the O-/U-type collapse modes, the cross-sectional deformation of the C-type collapse is not symmetrical and has a moving maximum-displacement point. The collapse pressure decreases linearly as the increase of the eccentricity and the initial ovality. The effect of eccentricity directions can be concluded as: more dispersed eccentricity distribution makes composites contribute more to the pressure resistance.

Bamboo as a substitute for plastic: Underlying mechanisms of flexible deformation and flexural toughness of bamboo at multiple scales

To develop bamboo-based products by weaving, winding and molding for promoting "bamboo as a substitute for plastic", it is urgent to fully understand the underlying mechanisms of flexible deformation and flexural toughness of bamboo at multiple scales. In this study, we quantified the micro deformation and strain of bamboo cells at different curvatures by in situ high-resolution field emission scanning electron microscopy (FE-SEM) and X-ray micro-computed tomography (Micro-CT) to analyze its flexible deformation at cellular and nano scales. The toughening mechanism embodied in fracture morphology was quantitatively calculated using mathematical models at macro and cell-wall scales. Results showed that bamboo possessed both excellent flexible deformation and flexural toughness in the longitudinal direction with the variation of fiber contents in the radial direction of bamboo culm. Flexible deformation of bamboo was achieved through synergistic cellular deformation between tensile sclerenchyma fibers (SFs) and compressible parenchyma cells (PCs) adapted to external stress distribution. SFs with greater tensile strain (0.027) bore the load even after the PCs broke (0.019), while the PCs in the compression layer acted as a buffer through plastic deformation. Meanwhile, the cell-wall sublayer wound by microfibrils at different angles, demonstrated significantly different Young's modulus and fracture modes verified by a mathematical model. Multiwalled fiber pullout and crack deflection were the main toughening mechanisms in bamboo at macro- and cellular scales. Multiwalled fibers pullout energy contributed the most to fracture energy dissipation, accounting for 46.0∼77.5%, whereas the weak intercellular interface effectively promoted crack deflection, reduced the local stress and delayed bamboo failure.