Showing papers on "Fracture mechanics published in 2011"

Strength failure and crack coalescence behavior of brittle sandstone samples containing a single fissure under uniaxial compression

Abstract: Uniaxial compression experiments were performed for brittle sandstone samples containing a single fissure by a rock mechanics servo-controlled testing system. Based on the experimental results of axial stress-axial strain curves, the influence of single fissure geometry on the strength and deformation behavior of sandstone samples is analyzed in detail. Compared with the intact sandstone sample, the sandstone samples containing a single fissure show the localization deformation failure. The uniaxial compressive strength, Young’s modulus and peak axial strain of sandstone samples with pre-existing single fissure are all lower than that of intact sandstone sample, which is closely related to the fissure length and fissure angle. The crack coalescence was observed and characterized from tips of pre-existing single fissure in brittle sandstone sample. Nine different crack types are identified based on their geometry and crack propagation mechanism (tensile, shear, lateral crack, far-field crack and surface spalling) for single fissure, which can be used to analyze the failure mode and cracking process of sandstone sample containing a single fissure under uniaxial compression. To confirm the subsequence of crack coalescence in sandstone sample, the photographic monitoring and acoustic emission (AE) technique were adopted for uniaxial compression test. The real-time crack coalescence process of sandstone containing a single fissure was recorded during the whole loading. In the end, the influence of the crack coalescence on the strength and deformation failure behavior of brittle sandstone sample containing a single fissure is analyzed under uniaxial compression. The present research is helpful to understand the failure behavior and fracture mechanism of engineering rock mass (such as slope instability and underground rock burst).

Lamellar Bilayers as Reversible Sacrificial Bonds To Toughen Hydrogel: Hysteresis, Self-Recovery, Fatigue Resistance, and Crack Blunting

Abstract: We report the extraordinary toughness, hysteresis, self-recovery, and persistent fatigue resistance of an anisotropic hydrogel with single-domain lamellar structure, consisting of periodical stacking of several thousands of rigid, hydrophobic bilayers in the ductile, hydrophilic polymer matrix. The stratified lamellar bilayers not only diffract light to exhibit magnificent structural color but also serve as reversible sacrificial bonds that dissociate upon deformation, exhibiting large hysteresis as an energy dissipation mechanism. Both the molecular dissociation and lipid-like mobile nature of bilayers dramatically enhance the resistance to crack propagation by suppressing the stress concentration at the crack tip with the formation of extraordinary crack blunting. This unique toughening phenomenon could allow deep insight into the toughening mechanism of the hydrogel-like soft materials such as biological soft tissues.

A time-discrete model for dynamic fracture based on crack regularization

Abstract: We propose a discrete time model for dynamic fracture based on crack regularization. The advantages of our approach are threefold: first, our regularization of the crack set has been rigorously shown to converge to the correct sharp-interface energy Ambrosio and Tortorelli (Comm. Pure Appl. Math., 43(8): 999–1036 (1990); Boll. Un. Mat. Ital. B (7), 6(1):105–123, 1992); second, our condition for crack growth, based on Griffith’s criterion, matches that of quasi-static settings Bourdin (Interfaces Free Bound 9(3): 411–430, 2007) where Griffith originally stated his criterion; third, solutions to our model converge, as the time-step tends to zero, to solutions of the correct continuous time model Larsen (Math Models Methods Appl Sci 20:1021–1048, 2010). Furthermore, in implementing this model, we naturally recover several features, such as the elastic wave speed as an upper bound on crack speed, and crack branching for sufficiently rapid boundary displacements. We conclude by comparing our approach to so-called “phase-field” ones. In particular, we explain why phase-field approaches are good for approximating free boundaries, but not the free discontinuity sets that model fracture.

X-FEM in isogeometric analysis for linear fracture mechanics

Abstract: The extended finite element method (X-FEM) has proven to be an accurate, robust method for solving problems in fracture mechanics. X-FEM has typically been used with elements using linear basis functions, although some work has been performed using quadratics. In the current work, the X-FEM formulation is incorporated into isogeometric analysis to obtain solutions with higher order convergence rates for problems in linear fracture mechanics. In comparison with X-FEM with conventional finite elements of equal degree, the NURBS-based isogeometric analysis gives equal asymptotic convergence rates and equal accuracy with fewer degrees of freedom (DOF). Results for linear through quartic NURBS basis functions are presented for a multiplicity of one or a multiplicity equal the degree.

The effect of carbon nanotubes on the fracture toughness and fatigue performance of a thermosetting epoxy polymer

Abstract: Multi-walled carbon nanotubes, with a typical length of 140 μm and a diameter of 120 nm, have been used to modify an anhydride-cured epoxy polymer. The modulus, fracture energy and the fatigue performance of the modified polymers have been investigated. Microscopy showed that these long nanotubes were agglomerated, and that increasing the nanotube content increased the severity of the agglomeration. The addition of nanotubes increased the modulus of the epoxy, but the glass transition temperature was unaffected. The measured fracture energy was also increased, from 133 to 223 J/m2 with the addition of 0.5 wt% of nanotubes. The addition of the carbon nanotubes also resulted in an increase in the fatigue performance. The threshold strain-energy release-rate, G th, increased from 24 J/m2 for the unmodified material to 73 J/m2 for the epoxy with 0.5 wt% of nanotubes. Electron microscopy of the fracture surfaces showed clear evidence of nanotube debonding and pull-out, plus void growth around the nanotubes, in both the fracture and fatigue tests. The modelling study showed that the modified Halpin–Tsai equation can fit very well with the measured values of the Young’s modulus, when the orientation and agglomeration of the nanotubes are considered. The fracture energy of the nanotube-modified epoxies was predicted, by considering the contributions of the toughening mechanisms of nanotube debonding, nanotube pull-out and plastic void growth of the epoxy. This indicated that debonding and pull-out contribute to the toughening effect, but the contribution of void growth is not significant. There was excellent agreement between the predictions and the experimental results.

Microstructural characteristics and toughness of the simulated coarse grained heat affected zone of high strength low carbon bainitic steel

Abstract: The correlation of microstructural characteristics and toughness of the simulated coarse grained heat affected zone (CGHAZ) of low carbon bainitic steel was investigated in this study. The toughness of simulated specimens was examined by using an instrumented Charpy impact tester after the simulation welding test was conducted with different cooling times. Microstructure observation and crystallographic feature analysis were conducted by means of optical microscope and scanning electron microscope equipped with electron back scattered diffraction (EBSD) system, respectively. The main microstructure of simulated specimen changes from lath martensite to coarse bainite with the increase in cooling time. The deterioration of its toughness occurs when the cooling time ranges from 10 to 50 s compared with base metal toughness, and the toughness becomes even worse when the cooling time increases to 90 s or more. The MA (martensite–austenite) constituent is primary responsible for the low toughness of simulated CGHAZ with high values of cooling time because the large MA constituent reduces the crack initiation energy significantly. For crack propagation energy, the small effective grain size of lath martensite plays an important role in improving the crack propagation energy. By contrast, high misorientation packet boundary in coarse bainite seems to have few contributions to the improvement of the toughness because cleavage fracture micromechanism of coarse bainite is mainly controlled by crack initiation.

Predicting crack propagation with peridynamics: a comparative study

Abstract: The fidelity of the peridynamic theory in predicting fracture is investigated through a comparative study. Peridynamic predictions for fracture propagation paths and speeds are compared against various experimental observations. Furthermore, these predictions are compared to the previous predictions from extended finite elements (XFEM) and the cohesive zone model (CZM). Three different fracture experiments are modeled using peridynamics: two experimental benchmark dynamic fracture problems and one experimental crack growth study involving the impact of a matrix plate with a stiff embedded inclusion. In all cases, it is found that the peridynamic simulations capture fracture paths, including branching and microbranching that are in agreement with experimental observations. Crack speeds computed from the peridynamic simulation are on the same order as those of XFEM and CZM simulations. It is concluded that the peridynamic theory is a suitable analysis method for dynamic fracture problems involving multiple cracks with complex branching patterns.

Structural hierarchies define toughness and defect-tolerance despite simple and mechanically inferior brittle building blocks

Abstract: Mineralized biological materials such as bone, sea sponges or diatoms provide load-bearing and armor functions and universally feature structural hierarchies from nano to macro. Here we report a systematic investigation of the effect of hierarchical structures on toughness and defect-tolerance based on a single and mechanically inferior brittle base material, silica, using a bottom-up approach rooted in atomistic modeling. Our analysis reveals drastic changes in the material crack-propagation resistance (R-curve) solely due to the introduction of hierarchical structures that also result in a vastly increased toughness and defect-tolerance, enabling stable crack propagation over an extensive range of crack sizes. Over a range of up to four hierarchy levels, we find an exponential increase in the defect-tolerance approaching hundred micrometers without introducing additional mechanisms or materials. This presents a significant departure from the defect-tolerance of the base material, silica, which is brittle and highly sensitive even to extremely small nanometer-scale defects.

Phase field modeling of crack propagation

Abstract: Fracture is a fundamental mechanism of materials failure. Propagating cracks can exhibit a rich dynamical behavior controlled by a subtle interplay between microscopic failure processes in the crack tip region and macroscopic elasticity. We review recent approaches to understand crack dynamics using the phase field method. This method, developed originally for phase transformations, has the well-known advantage of avoiding explicit front tracking by making material interfaces spatially diffuse. In a fracture context, this method is able to capture both the short-scale physics of failure and macroscopic linear elasticity within a self-consistent set of equations that can be simulated on experimentally relevant length and time scales. We discuss the relevance of different models, which stem from continuum field descriptions of brittle materials and crystals, to address questions concerning crack path selection and branching instabilities, as well as models that are based on mesoscale concepts for crack tip ...

Toughening of epoxy using core–shell particles

Abstract: An epoxy resin, cured using an anhydride hardener, has been modified by the addition of preformed core–shell rubber (CSR) particles which were approximately 100 or 300 nm in diameter. The glass transition temperature, T g, of the cured epoxy polymer was 145 °C. Microscopy showed that the CSR particles were well dispersed through the epoxy matrix. The Young’s modulus and tensile strength were reduced, and the glass transition temperature of the epoxy was unchanged by the addition of the CSR particles. The fracture energy increased from 77 J/m2 for the unmodified epoxy to 840 J/m2 for the epoxy with 15 wt% of 100-nm diameter CSR particles. The measured fracture energies were compared to those using a similar amount of carboxyl-terminated butadiene-acrylonitrile (CTBN) rubber. The CTBN particles provided a larger toughening effect when compared to CSR particles, but reduced the glass transition temperature of the epoxy. For the CSR-modified epoxies, the toughening mechanisms were identified using scanning electron microscopy of the fracture surfaces. Debonding of the cores of the CSR particles from the shells was observed, accompanied by plastic void growth of the epoxy and shell. The observed mechanisms of shear band yielding and plastic void growth were modelled using the Hsieh et al. approach (J Mater Sci 45:1193–1210). Excellent agreement between the experimental and the predicted fracture energies was found. This analysis showed that the major toughening mechanism, responsible for 80–90% of the increase in fracture energy, was the plastic void growth.

Mechanical behaviour of strain hardening cement-based composites under impact loading

Abstract: This paper describes the material behaviour of a strain hardening cement-based composite (SHCC) at high strain rates. The results of highly dynamic spall experiments using a Hopkinson bar at strain rates 140–180 s −1 are arrayed against the results of quasi-static uniaxial tensile tests at strain rates of 0.001 s −1 . This comparison is based on the values of tensile strength, Young’s modulus, and fracture energy of the specimens. In addition, the experimental results of SHCC are related to the characteristic values of other concrete types. Differences in material behaviour are explained by the phenomena of crack formation and fibre pullout resistance.