Fracture Energy Release Rate Research Articles

Study on translaminar fracture toughness under mixed mode I/II load for (0/45)° orientation unidirectional glass/epoxy composite

Mixed-mode translaminar fracture toughness behaviour is experimentally investigated using glass/epoxy composite laminate with (0/45)° orientation. Experimental investigation is conducted using Compact Tension Shear (CTS) mixed mode (I/II) fracture specimens having a/W = 0.5. The specimen plates of thickness 4.5 mm were carefully fabricated using hand lay-up technique. The experiments were conducted for seven loading angles varying from 0° (Mode-I) to 90° (Mode-II) with an increment of 15°. The translaminar fracture toughness and energy release rates were estimated for various loading angles based on the peak loads obtained by experiments. The results indicates that the energy release rate of glass/epoxy composite considered in the analysis is more in pure Mode-I loading than pure Mode-II loading, whereas mixed mode (I/II) loading conditions are in between.

Effect of loading rates on crack propagating speed, fracture toughness and energy release rate using single-cleavage trapezoidal open specimen under impact loads

The former studies indicate that loading rates significantly affect dynamic behavior of brittle materials, for instance, the dynamic compressive and tensile strength increase with loading rates. However, there still are many unknown or partially unknown aspects. For example, whether loading rates have effect on crack dynamic propagating behavior (propagation toughness, velocity and arrest, etc). To further explore the effect of loading rates on crack dynamic responses, a large-size single-cleavage trapezoidal open (SCTO) specimen was proposed, and impacting tests using the SCTO specimen under drop plate impact were conducted. Crack propagation gauges (CPGs) were employed in measuring impact loads, crack propagation time and velocities. In order to verify the testing result, the corresponding numerical model was established using explicit dynamic software AUTODYN, and the simulation result is basically consistent with the experimental results. The ABAQUS software was used to calculate the dynamic SIFs. The universal function was calculated by fractal method. The experimental-numerical method was employed in determining initiation toughness and propagation toughness. The results indicate that crack propagating velocities, dynamic fracture toughness and energy release rates increase with loading rates; crack delayed initiation time decreases with loading rates.

Prediction of axial load on variable graded composite tubes for crashworthy structure

Prediction of estimated load for crushing of fiber reinforced polymer (FRP) tubes presented with a simple mathematical equation on the basis of buckling theory and fracture mechanics approach. Buckling theory concept uses critical load carrying capacity of the FRP tubes and fracture mechanics concept uses the value of inter-laminar fracture energy release rate. Combination of above two concepts along with the mechanical and physical properties forms the prediction equation. The determined estimated loads from the prediction equation were compared with experimental quasi static axial compression test and comparison results show the good agreement.

On energy release rates in Peridynamics

This work is concerned with the calculation of fracture energy release rates in Peridynamics. The existing crack growth criterion and the related damage model in Peridynamics, e.g. the critical bond stretch in the prototype micro-elastic brittle (PMB) material model, are based on the energy release rate of an idealized infinite crack model. Therefore, applications of such damage model in Peridynamics to arbitrary fracture patterns, e.g. cracks with finite increment, kinked cracks, and penny-shaped cracks etc., are problematic, because that the idealized crack model assumes an infinitely large crack surface, and the crack growth direction is always assumed being along the direction of the old crack surface.In all engineering applications, we only encounter cracks of finite size. In this work, based on the celebrated Griffith theory that interprets the energy release rate as the surface energy density, we have systematically investigated the fracture energy release rate in Peridynamics for a number of finite crack models: two-dimensional (2D) plane strain finite size horizontal crack, 2D edge crack in a plate, 2D kinked crack, and three-dimensional (3D) penny-shaped crack.The highlights of this work are a set of elegant mathematical solutions: (1) We have proved that for 2D horizontal finite cracks, the energy release rate is exactly the same as that of 2D infinite large crack, i.e. Silling’s original result; (2) We have derived the exact expressions of the energy release rates as well as the related critical bond stretch formulas for 2D finite edge cracks and kinked cracks, and (3) We have found an asymptotic solution of the energy release rate for 3D penny-shaped cracks of finite size in Peridynamics, showing that Silling’s energy release formula for 3D crack model is only the zero-th order approximation of the exact solution.In addition, we have presented some numerical solutions of finite increment crack growths in Peridynamics, and discussed their implications, ramifications, and applications in nonlocal continuum fracture mechanics.

A new method for preparation of functionalized graphene and its epoxy nanocomposites

Organic solvents are often used to prepare epoxy/graphene nanocomposites. In this study a graphene precursor is developed, which in epoxy at 200 °C is able to directly exfoliate into three classes of graphene platelets: large, single-layer sheets, medium sized sheets with 5.2 ± 1.95 nm in thickness, and smaller 0.5–1.0 nm thick sheets of 200–500 nm in lateral dimension, with a Raman ID/IG ratio of 0.177. The yield of single-layer graphene is 41.45%. Due to oxygen-containing groups on the surface, these sheets are named functionalized graphene platelets. Platelet films of ~10 μm in thickness have an electrical conductivity of 978.65 ± 79.44 S/cm. A percolation threshold of electrical conductivity is observed at 0.80 vol% for epoxy/graphene nanocomposites. The composites show highly improved mechanical and dynamic thermo-mechanical properties. At 1.03 vol%, the nanocomposite has a fracture energy release rate of 850.78 ± 58.00 J m−2 corresponding to an increase of 170.61% over neat epoxy.

Experimental-numerical failure analysis of the c-Al0.66Ti0.34N-M2 steel system applying instrumented indentation and extended finite element method

An experimental-numerical methodology for failure analysis of the c-Al0.66Ti0.34N/Interface/M2 steel coating system is proposed here. This c-Al0.66Ti0.34N coating was deposited by the arc-PVD technique. The values of the elastic modulus, the fracture energy release rate and the nano-hardness of the coating were obtained by nanoindentation. Normal and shear stress limits of the interface, as well as the adhesive and cohesive critical loads, were measured with the scratch test method. A finite element analysis, using the experimental mechanical properties, was carried out to understand the relationship between the irreversible work vs. depth curve and the mechanical failure evolution of the coating-substrate system, associating the pop-in with nucleation, crack growth and cracking pattern. Extended finite element method (XFEM) was applied for modeling of the mechanical behavior of the coating; the cohesive zones approach was applied for modeling the interface and the Ramberg-Osgood law for modeling the substrate. This approach proposes an experimental-numerical methodology for failure analysis of hard coatings (monolithic body) allowing to calculate fracture energy of the coating material and to model cracking patterns caused by contact mechanics. This work is the first step to answer questions about multi-scale approaches for multi-functional multi-layer coatings to push their enhancements and further applications.

Computing critical energy release rates for fracture in atomistic simulations

We describe a method for computing critical energy release rates for crack propagation in atomistic models and apply it to simulations of fracture in Ni. Our method relies on independent calculations of crack surface area and energy dissipated during fracture. We show that the critical energy release rate for fracture in Ni increases linearly with model size due to increasing energy dissipated through plastic deformation. We conclude with a discussion of prospects for direct comparisons of critical energy release rates computed from atomistic simulations to ones obtained from experiments.

Crack evolution in diamond-like carbon films on steel substrates during nano-indentation

Fracture behaviors of thin hard diamond-like carbon (DLC) films were investigated considering the effects of plastic deformation of steel substrates. Nano-indentation tests for DLC films on SUS304 and M50 steels were conducted. The nucleation and propagation of film cracks were analyzed using the extended finite element method (XFEM). The ultimate tensile strength, fracture energy release rate and toughness of the films were evaluated. Results showed that cracks in DLC films on M50 steel substrates nucleated on the top surface of the films during nano-indentation; however, the first crack initiated at the bottom surface of DLC films on SUS304 steel because of its low yield strength. Large plastic deformation of the steel substrate was generated under nano-indentation, leading to consequent high tensile stress that concentrated first at the bottom surface of the films due to the film bending effect.

Mode I fracture evaluation of carbon fiber reinforced polymer/steel interfaces subject to freeze-thaw cycling

In order to increase the durability database and have a better understanding of the degradation mechanism, the effect of freeze-thaw cycling on the mode I fracture energy release rate of CFRP (Carbon Fiber Reinforced Polymer)/steel interface is studied by using wedge driving test method. Previous studies show that moisture plays an important role in freezing-thawing cycling, therefore the relationship between moisture and mode I fracture energy release rate of CFRP/steel interface is studied. Because the interfacial moisture content cannot be measured directly, a finite element simulation is established to predict the moisture distribution of the interface based on water uptake tests of component materials. The results show that the mode I fracture energy release rate of CFRP/steel interface decreases nonlinearly with apparent relative humidity. The change of failure mode from debonding within the CFRP layer to adhesive failure long the interface is also observed.

An end notched flexure specimen model for mode-II fracture of high-temperature superconductor tapes with thermal effect

End notched flexure (ENF) experiment using three-point bending beam specimen is a very convenient test configuration to evaluate the mode-II fracture toughness of composites. High-temperature superconductor (HTS) tapes are multi-layered composite that have been widely used in magnets and cables. HTS tapes are manufactured at room temperature ([Formula: see text][Formula: see text]300 K) but are used in the liquid-nitrogen temperature (77 K) environment. The large temperature change leads to large shear stress which may cause delamination of HTS tapes. In this paper, a closed-form expression of energy release rate (and therefore the stress intensity factor) for mode-II fracture of HTS tapes with thermal effect is developed based on the end notched flexure specimen. Results show that HTS tapes in working condition are prone to delaminating. Increasing the thickness of Hastelloy layer can reduce the energy release rate of mode-II cracking thus increase the interface strength. In the design of HTS tapes, the silver and copper layers are used to enhance the stretch of the HTS tapes. While silver and copper layers will increase the energy release rate for mode-II crack. This fact indicates that thicker silver and copper layers are not always good from the fracture mechanics point of view. The results of thermomechanical model and fracture criterion model of this research are useful for determining mode-II fracture toughness of superconducting composites for high-temperature applications.

Three dimensional finite element simulations of hydraulic fracture height growth in layered formations using a coupled hydro-mechanical model

In this paper, we treat the important problem of hydraulic fracturing in the presence of elastic modulus and stress contrast in layered rock systems encountered in petroleum resources development using a fully coupled 3D hydro-mechanical model. First, the model is validated by simulating a laboratory hydraulic fracturing experiment dealing with the influence of stress contrast. Good agreements in the distribution of fracture aperture, injection pressure and fracture footprint have been achieved. Then, numerical analyses are performed to investigate the influence of in-situ stress and formation layer properties, such as Young's modulus and fracture energy release rate on the height growth and containment of hydraulic fractures. Comparing the results of simulations using conventional thickness-weighted Young's modulus to those from explicit modeling of layers' Young's moduli, it is found given that for the same amount of injection volume, the thickness-weighted modulus generates a higher injection pressure. Explicit modeling of the layers influences the hydraulic fracture aperture distribution in the pay zone as well as in the surrounding layers. A relatively large fracture aperture is observed in the layer with the lower Young's modulus. Also, the hydraulic fracture tends to propagates mainly in the lower Young's modulus layers which could facilitate containment of the hydraulic fracture by limiting height growth in the stiffer layers. When considering the influence of stress contrast on height growth, the conventional equilibrium height model produces a relatively large aperture and overestimates the fracture height. Simulations using typical injection rate, fluid viscosity, and in-situ stress, show stress contrast larger than a certain value, for example 30% of the in-situ minimum horizontal stress, can effectively inhibit height growth. When the payzone is bounded by ductile layers, the injection pressure is higher and the corresponding aperture at the injection point is larger than those obtained using uniform rock properties.

The characteristics of dynamic fracture toughness and energy release rate of rock under impact

To investigate the characteristics of rock fracture toughness and dynamic energy release rate, impact experiments were conducted in large single cleavage semicircle compression (LSCSC) specimens. Fracture toughness and energy release rate of three sandstones were investigated and a drop-weight device was applied. Crack length and crack propagation velocity were corrected by fractal method, and fracture surface morphology was obtained by scanning electron microscope. The dynamic stress intensity factor (DSIF) was acquired from the finite element model established in the ABAQUS. The DSIF history was acquired, and the initiation and propagation toughness were determined according to the measuring result of fracture time. It shows that, for a material, propagation toughness is related to its Young’s modulus, and the higher the Young’s modulus or wave impedance is, the larger the propagation toughness is. For black sandstone, the energy release rate increases rapidly with crack length, whereas for green and red sandstones, it increases slightly under a same speed impact.

A three-phase model of the single-fiber composite fragmentation test to evaluate viscoelasticity, stress distribution and interface fracture toughness

ABSTRACTA three-phase model of the single-fiber composite fragmentation test is proposed to evaluate viscoelasticity, stress distributions and interface fracture toughness. Based on the three-parameter standard linear solid model, a unit cell is established under periodic boundary conditions to study viscoelasticity considering the interface effect. Under the thermal residual stress and the tensile load, a three-dimensional (3D) theoretical cylinder model is utilized to predict the stress distributions in radial, hoop and axial directions for fiber, interface and matrix. The results are in good agreements with finite element method (FEM) results. Especially, we discuss the effects of the fiber shape on the mechanical behavior. Classic shear-lag theories are compared to modify the axial stress distributions. For the fragmentation test, two basic failure modes are studied in the proposed model. Based on accurate stress distributions, the energy-balance scheme takes into account all strain energies, the failure consumption, the friction consumption and the applied load work to calculate interface fracture energy release rate, results of which is consistent with other models. Furthermore, we study the effects of friction coefficients and radial debonded locations. Using the softening and failure model of the interface, the debonding process is simulated for zero-thickness and thick interfaces, respectively.

Mode I fracture evaluation of CFRP-to-concrete interfaces subject to aggressive environments agents: Freeze-thaw cycles, acid and alkaline solution

The long-term durability of the interface between FRP (fiber reinforced polymer) and concrete is crucial to the safety of FRP strengthened concrete structures. Some experimental works have been carried out to investigate the effect of environmental factors on model II fracture behavior of the FRP-to-concrete interface. However, fewer efforts have been made to estimate interfacial durability under mode I loading. This study evaluates the mode I fracture energy release rate of CFRP (carbon fiber reinforced polymer)-to-concrete interface subjected to freeze-thaw cycling, acid attack, and alkali attack. Significant decrease of fracture energy release rate is observed after environmental conditioning. With the increase of freeze-thaw cycles and soaking time, the failure mode of the specimen changes from tensile failure of concrete to adhesive failure along the interface. Test results also confirm that the durability of the CFRP-to-concrete interface can be improved by application of silane coupling agent under freeze-thaw cycling and alkaline condition.

Effect of Morphology of Calcium Carbonate on Toughness Behavior and Thermal Stability of Epoxy-Based Composites

In this study, the modification of an epoxy matrix with different amounts of cube-like and rod-like CaCO3 nanoparticles was investigated. The effects of variations in the morphology of CaCO3 on the mechanical properties and thermal stability of the CaCO3/epoxy composites were studied. The rod-like CaCO3/epoxy composites (EP-rod) showed a higher degradation temperature (4.5 °C) than neat epoxy. The results showed that the mechanical properties, such as the flexural strength, flexural modulus, and fracture toughness of the epoxy composites with CaCO3 were enhanced by the addition of cube-like and rod-like CaCO3 nanoparticles. Moreover, the mechanical properties of the composites were enhanced by increasing the amount of CaCO3 added but decreased when the filler content reached 2%. The fracture toughness Kic and fracture energy release rate Gic of cube-like and rod-like CaCO3/epoxy composites (0.85/0.74 MPa m1/2 and 318.7/229.5 J m−2, respectively) is higher than the neat epoxy (0.52 MPa m1/2 and 120.48 J m−2).

Parameters prediction of cohesive zone model for simulating composite/adhesive delamination in hygrothermal environments

In this paper, moisture parameters of adhesive SY-14M-III and composite T800/AC531 were firstly measured, which were used for the following moisture diffusion investigations. Then, double cantilever beam (DCB) tests and end notched flexure (ENF) tests were conducted in four environments, and relevant progressive damage models considering cohesive zone models were established. The results show that the models are efficient by comparison of experimental and numerical results, and eight pairs of cohesive parameters (interface strength and interface stiffness) corresponding to the specified fracture energy release rates were obtained. Finally, a modified Tsai prediction method of cohesive zone model for simulating composite/adhesive delamination in hygrothermal environments was proposed based on an assumption of the composite/adhesive moisture diffusion process, which can be as a reference or basic data for numerical analysis of adhesively bonded composite structures.

Energy Budget of Intermediate‐Depth Earthquakes in Northern Chile: Comparison With Shallow Earthquakes and Implications of Rupture Velocity Models Used

AbstractWe calculate well‐resolved corner frequencies and radiated energies for a set of 96 earthquakes divided into two clusters located in the same tectonic setting but with different depths in northern Chile. Fifty‐three shallow events with a mean depth of 20 km are analyzed, along with 43 intermediate‐depth earthquakes with a mean depth of 110 km. We deduce and compare their static (stress drop Δσ) and dynamic (rupture energy EG and radiation efficiency ηR) source parameters and test the implications of different common assumptions on their depth dependence, such as stress drop invariance, strain drop invariance, or constant rupture velocities. Our data show that, in this zone of Chile, most of these models imply higher rupture velocities at depth than for shallow earthquakes. In these cases, high stress drop, high fracture energy release rate, and higher radiation efficiency are observed for intermediate‐depth earthquakes, suggesting short and impulsive ruptures.

Analyses of Energy Release Rate for Interface Fracture of Elastic Multilayered under Four-Point Bending

Analyses of Energy Release Rate for Interface Fracture of Elastic Multilayered under Four-Point Bending

Effects of surface crack on the mechanical properties of Silica: A molecular dynamics simulation study

In this paper, fracture mechanism and the effects of surface crack on the mechanical properties (modulus and strength) of silica glass are studied through reactive all-atom molecular dynamics (MD) simulations. Tapered surface cracks of different length ranging from 0.25 to 10.0 nm are created by deleting atoms to study the crack length effects. Interatomic interactions are modeled with state-of-the-art reactive force field ReaxFF and fracture energy release rate is determined from discretized atomistic J-integral approach. Simulation results indicate that surface cracks have no effect on fiber modulus, however, fiber strength is significantly affected by surface crack. With the increase in crack length, strength decreases and MD predicted strength-crack length response is in good agreement with theoretical prediction. MD simulations project that about 35 nm size crack could reduce glass fiber strength to 3.5 GPa, which is experimentally observed fiber mean strength. MD simulations show that there is no inelastic process zone with cavities in front of the crack tip. Fracture mode is brittle type where crack growth initiates through Si-O bond breakage and it propagates through sequential bond ruptures.

Intermediate temperature fracture resistance evaluation of cement emulsified asphalt mortar

Cement emulsified asphalt mortar (CEAM) as part of the slab track system is subjected to various combinations of repeated train loading and varying environmental conditions leading to fatigue cracking. In this respect, this research examined the fatigue cracking resistance behavior of CEAM through various testing methods applying fracture mechanics. Experimental tests conducted (i.e. indirect tensile (IDT) strength and semicircular bending (SCB)) showed that the fracture parameters (i.e. displacement at fracture, fracture energy, and critical strain energy release rate) could properly evaluate the fatigue performance of CEAM and distinguish additives’ impact at intermediate temperature. Furthermore, correlation analysis was employed to investigate the effect of test-related factors (e.g. specimen size, specimen thickness, notch length, and loading rate) on the assessed fracture parameters and specifying the most suitable parameter for fatigue cracking resistance evaluation of CEAM. According to the results, although the displacement at fracture and fracture energy were capable to assess the fatigue cracking behavior of CEAM, they exhibited to be specimen size dependent. Additionally, results of experiments conducted on CEAM specimens possessing various sizes and geometries along with the correlation analysis indicated that the critical strain energy release rate (Jc) is a potentially feasible parameter to recognize the fatigue cracking resistance of CEAM as a material parameter as it is independent of specimen size and geometry.