Fracture Surface Energy Research Articles

Temperature-dependent fracture strength and the effect of oxidation for ZrB2-SiC ceramics

Using the stress distribution of the body containing a spherical inclusion, the stress intensity factor at the tip of the annular flaw emanating from the inclusion is formulized. Since the thermal expansion coefficient of matrix and inclusion is not matched, the residual stress is also taken into account. Introducing into the proposed temperature-dependent fracture surface energy or fracture toughness, the temperature-dependent fracture strength for ZrB2-SiC is obtained. The influence of oxidation on the fracture strength is also discussed and the analysis reveals that the oxidation has significant effect on the fracture strength under some circumstances. The calculated results are compared with the experimental data and they have very good consistency.

Investigations on fracture toughness and fracture surface energy of 3D random fibrous materials at elevated temperatures

In this study, model Ⅰ fracture toughness of three-dimensional random fibrous (3D RF) materials with a porosity of 83% is investigated from room temperature to 1273 K by performing experiments with compact tension (CT) specimens in the through-the-thickness (TTT) and in-plane (IP) directions. The experiments show that the fracture toughness in the TTT and IP directions increases from 0.0842 to 0.1162 MPa·m1/2 and 0.4292–0.6767 MPa·m1/2, respectively, with increasing temperature until a critical temperature (1073 K and 1223 K, respectively) is reached, following which the fracture toughness decreases from 0.1162 to 0.0819 MPa·m1/2 and from 0.6767 to 0.6170 MPa·m1/2, respectively. The significant changes at elevated temperatures are directly attributed to the viscous flow of the crack tip. In addition, a viscous flow contribution to the fracture surface energy of the 3D RF material is identified at high temperatures. The curves of the fracture surface energy versus temperature data for the TTT and IP directions can be partitioned into sections by fitting with experimental observations. Based on the two fitted curves, we calculate the activation energy of the viscous flow in the TTT and IP directions as 220.3 kJ/mol and 892.2 kJ/mol, respectively.

Variational interface zone model for modeling of fluid induced fracture propagation

AbstractA novel variational framework for an interface zone model is developed and extended to poroelasticity. As was previously promoted in [1,2], the total energy of the system is composed by the bulk potential and fracture surface energy. In contrast to the phase‐field method, the fracture surface is approximated directly along the edges of the finite elements in terms of interface zero‐thickness finite elements. By introducing a new degree of freedom c (damage field) on the interface level, the solution is found by the minimization of the total potential energy with respect to the displacements and the damage field. An elastic interface constitutive law allowing for a normal and tangential displacement opening is adopted in the pre‐fracture regime. Assuming, that a crack propagates according to the Griffith's criterion of brittle fracture, fracture initiates and propagates in normal opening mode. Biot's theory is applied both to the bulk and interface elements for the simulation of fluid driven fracture in fully saturated materials. The pressure field within the interfaces is averaged between the pressure at the bulk element faces. Pressure continuity is enforced by means of a penalty functional. The flow within the fracture is modeled by the cubic law taking the displacement and damage variables into account. A number of numerical benchmark tests, which include comparisons with experimental results and analytical solutions, are performed to demonstrate the performance of the model. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A novel approach to improve flexural strength of Al2O3‐20 wt% ZrO2 composites by oscillatory pressure sintering

AbstractIn this communication, Al2O3‐20 wt% ZrO2 composites (ZTA) were prepared by a novel oscillatory pressure sintering (OPS) process. An almost perfectly full density of 99.94% and a relatively high flexural strength of 1145 MPa can be achieved for the OPS‐fabricated specimen, which were higher than those prepared by pressureless sintering (98.24% and 682 MPa) and hot pressing (99.53% and 990 MPa). The enhancement of flexural strength of the OPS‐fabricated specimen was correlated with its smaller flaw size and higher fracture surface energy. It was suggested that OPS was an effective approach to fabricate ZTA composites with ultrahigh density and high strength.

Finite element modeling of debonding mechanisms in carbon fiber reinforced polymer‐strengthened reinforced concrete continuous beams

This paper presents three‐dimensional (3D) and two‐dimensional (2D) finite element models to analyze strengthened reinforced concrete (RC) continuous beams with carbon fiber reinforced polymer (CFRP) which has become familiar technique in the last decade. Experimental results in the literature showed that two different debonding failure modes, either by interfacial debonding of fiber reinforced polymer (FRP) or by concrete cover separation may occur. This study takes the two possible debonding failure modes into account by considering two cohesive surfaces; the first is inserted in the adhesive layer, whereas the second is inserted between the reinforcing steel and the concrete cover. The proposed cohesive surfaces take the slippage into account considering the cohesive surface fracture energy. The numerical models are verified utilizing five symmetrical RC continuous beams available in the literature. The numerical results of 3D and 2D models for the plated beams (beams strengthened with FRP plates) agreed well with the experimental results. Additionally, the effect of the CFRP plate length, and the parameters of the cohesive surfaces on the behavior and debonding failure modes (in the adhesive layer and between the reinforcing steel and the concrete cover) of CFRP‐strengthened RC continuous beams are investigated.

Variational approach to interface element modeling of brittle fracture propagation

The paper proposes a variational approach to model brittle fracture propagation based on zero-thickness finite elements. Similar to the phase-field model for fracture, the problem of a fractured structure is variationally formulated by considering a minimization problem involving bulk and fracture surface energies. With the help of a damage variable used as an additional degree of freedom, the fracture propagates according to the values of the minimizers of the total potential energy. This damage variable is restricted to dimensionally reduced interface elements inserted between element boundaries. Crack opening is predicted when the elastic energy within the interface surface exceeds the critical energy release rate. The solution of the discretized system of equations is performed in a staggered scheme, solving first for the displacement field and then searching for the solution for the updated nodal damage variables. Selected numerical examples, including re-analyses of laboratory tests characterized by rather complex crack paths, are presented to demonstrate the performance of the proposed variational interface model.

Modeling the temperature and test rate dependent fracture strength of zirconia and alumina single crystal fibers

Abstract In this paper, based on the Griffith fracture theory, the slow crack growth theory and the temperature-dependent fracture surface energy model, a temperature and test rate dependent fracture strength model for zirconia and alumina single crystal fibers was established. As a comparison, the other one based on the temperature-dependent free surface energy was also deduced and discussed. These models were verified by comparison with the experimental data of the two types of ceramic single crystal fibers. Good agreement between the model predictions and the experimental data was obtained. Moreover, based on the present model and the existing material parameters, the influencing factor analysis for these ceramic single crystal fibers were systematically conducted. Some new findings regarding their high temperature fracture strengths were provided for the first time.

A Theoretical Model for Predicting Fracture Strength and Critical Flaw Size of the ZrB2-ZrC Composites at High Temperatures

This work shows a new rational theoretical model for quantitatively predicting fracture strength and critical flaw size of the ZrB2-ZrC composites at different temperatures, which is based on a new proposed temperature dependent fracture surface energy model and the Griffith criterion. The fracture model takes into account the combined effects of temperature and damage terms (surface flaws and internal flaws) with no any fitting parameters. The predictions of fracture strength and critical flaw size of the ZrB2-ZrC composites at high temperatures agree well with experimental data. Then using the theoretical method, the improvement and design of materials are proposed. The proposed model can be used to predict the fracture strength, find the critical flaw and study the effects of microstructures on the fracture mechanism of the ZrB2-ZrC composites at high temperatures, which thus could become a potential convenient, practical and economical technical means for predicting fracture properties and material design.

Determining fracture strength and critical flaw of the ZrB2–SiC composites on high temperature oxidation using theoretical method

Abstract In this work, based on the Griffith energy method and the sensitivities of the thermal-physical properties of materials to temperature, a theoretical method for studying the temperature dependent fracture strength and critical flaw size of the ZrB2–SiC composites on high temperature oxidation is proposed by using a temperature dependent fracture surface energy model. The combined effects of temperature, microstructure and oxidation damage are taken into account by this method. The method can be easily used to predict fracture strength of the composites and its key control mechanism by using some basic material parameters. The predictions are in good agreement with experimental reports. The theoretical method can become a potential convenient and practical technical means for determining temperature and oxidation dependent fracture strength and critical flaw of the ZrB2-SiC composites developed for aerospace applications related to hypersonic flight.

Fracture surface energy and toughness of inorganic glasses

A simple model is proposed to predict the fracture surface energy (γ) and the fracture toughness (KIc) of glasses from their nominal compositions. The theoretical values are compared with the experimental ones, as obtained by means of self-consistent methods such as the Single Edge Pre-crack Beam (SEPB) and Chevron Notch (CN) ones, when available. A remarkable agreement is observed for ionocovalent glasses. This corroborates previous investigations showing that crack tip is nearly atomically sharp. In the case of metallic glasses, the theoretical values are much smaller than the experimental ones, which support the occurrence of crack tip plasticity and shielding effect.

Development of a detailed 3D FE model for analysis of the in-plane behaviour of masonry infilled concrete frames

This paper detailed the development of a numerical model for simulating the nonlinear behaviour of the concrete masonry infilled RC frames subjected to in-plane lateral loading. The ABAQUS finite element software was used in the modeling. Nonlinear behaviour as well as cracking and crushing of concrete and masonry blocks were simulated using the Concrete Damaged Plasticity (CDP) model. The cohesive element method combined with hyperbolic Drucker-Prager and shear and tensile failure criteria were used to capture the possible failure mechanisms in mortar joints. Concurrent with the finite element modeling, an experimental study was also conducted and results of masonry infilled RC frame specimens incorporating infill openings and interfacial gaps were used to validate the model. The validation showed that the model can accurately simulate the behaviour and predict the strength of masonry infilled RC frames. A sensitivity study was subsequently conducted where the influence of mortar joint failure surface parameters, mortar dilatancy, and fracture energy on the lateral behaviour of infilled RC frames was investigated. Results showed that the in-plane behaviour of infilled RC frames was significantly affected by the input parameters of mortar failure surface and dilatancy and less affected by those of mortar fracture energy.

Surface Structure and Stability of Partially Hydroxylated Silica Surfaces.

Surface energies of silicates influence crack propagation during brittle fracture and decrease with surface relaxation caused by annealing and hydroxylation. Molecular-level simulations are particularly suited for the investigation of surface processes. In this work, classical MD simulations of silica surfaces are performed with two force fields (ClayFF and ReaxFF) to investigate the effect of force field reactivity on surface structure and energy as a function of surface hydroxylation. An unhydroxylated fracture surface energy of 5.1 J/m2 is calculated with the ClayFF force field, and 2.0 J/m2 is calculated for the ReaxFF force field. The ClayFF surface energies are consistent with the experimental results from double cantilever beam fracture tests (4.5 J/m2), whereas ReaxFF underestimated these surface energies. Surface relaxation via annealing and hydroxylation was performed by creating a low-energy equilibrium surface. Annealing condensed neighboring siloxane bonds increased the surface connectivity, and decreased the surface energies by 0.2 J/m2 for ClayFF and 0.8 J/m2 for ReaxFF. Posthydroxylation surface energies decreased further to 4.6 J/m2 with the ClayFF force field and to 0.2 J/m2 with the ReaxFF force field. Experimental equilibrium surface energies are ∼0.35 J/m2, consistent with the ReaxFF force field. Although neither force field was capable of replicating both the fracture and equilibrium surface energies reported from experiment, each was consistent with one of these conditions. Therefore, future computational investigations that rely on accurate surface energy values should consider the surface state of the system and select the appropriate force field.

Production of nanoparticles during experimental deformation of smectite and implications for seismic slip

Nanoparticles and amorphous materials are common constituents of the shallow sections of active faults. Understanding the conditions at which nanoparticles are produced and their effects on friction can further improve our understanding of fault mechanics and earthquake energy budgets. Here we present the results of 59 rotary shear experiments conducted at room humidity conditions on gouge consisting of mixtures of smectite (Ca-montmorillonite) and quartz. Experiments with 60, 50, 25, 0 wt.% Ca-montmorillonite, were performed to investigate the influence of variable clay content on nanoparticle production and their influence on frictional processes. All experiments were performed at a normal stress of 5 MPa, slip rate of 0.0003≤V≤1.5 ms−1, and at a displacement of 3 m. To monitor the development of fabric and the mineralogical changes during the experiments, we investigated the deformed gouges using scanning and transmission electron microscopy combined with X-ray powder diffraction quantitative phase analysis. This integrated analytical approach reveals that, at all slip rates and compositions, the nanoparticles (grain size of 10–50 nm) are partly amorphous and result from cataclasis, wear and mechanical solid-state amorphization of smectite. The maximum production of amorphous nanoparticle occurs in the intermediate slip rate range (0.0003≤V≤0.1 ms−1), at the highest frictional work, and is associated to diffuse deformation and slip strengthening behavior. Instead, the lowest production of amorphous nanoparticles occurs at co-seismic slip rates (V≥1.3 ms−1), at the highest frictional power and is associated with strain and heat localization and slip weakening behavior. Our findings suggest that, independently of the amount of smectite nanoparticles, they produce fault weakening only when typical co-seismic slip rates (>0.1 ms−1) are achieved. This implies that estimates of the fracture surface energy dissipated during earthquakes in natural faults might be extremely difficult to constrain.

Room Temperature SiC-SiO2 Wafer Bonding Enhanced by Using an Intermediate Si Nano Layer

In this work, compared with the direct wafer bonding by surface activated bonding (SAB) at room temperature, SiC-SiO2 wafer bonding was effectively enhanced by using a Si nano layer deposited on SiO2 such as improvement of fracture surface energy and reduction of bonding void. A uniform seamless bonding in bonded region was confirmed by interface analysis. The strong bonding confirmed the strong bonding of SiC-Si in previous research and also demonstrated a strong adhesion of Si nano layer deposited on SiO2 substrate, which is different from direct wafer bonding of Si-SiO2 by SAB. The possible mechanism of strong adhesion was investigated by molecular dynamic simulation.

Temperature dependent first matrix cracking stress model for the unidirectional fiber reinforced ceramic composites

Based on a kind of equivalence between heat energy and fracture energy, assuming that there is a constant maximum storage of energy that includes both heat energy and fracture energy, a new temperature dependent fracture surface energy model is developed. Using the new model and the classical ACK theory, a temperature dependent first matrix cracking stress model is obtained for the fiber reinforced ceramic composites. According to the model, the temperature dependent first matrix cracking stress of materials can be easily predicted using some basic material parameters such as matrix fracture surface energy and Young’s modulus. The model is verified by comparison with experimental data of SiC fiber reinforced reaction-bonded Si3N4 composites at different temperatures. Good agreement is obtained between predicted and experimental data of first matrix cracking stress. The dependency of first matrix cracking stress on fracture surface energy and interfacial shear strength is systematically analyzed.

Temperature dependent fracture strength model for the laminated ZrB2 based composites

In this work, a new temperature dependent fracture strength model for the laminated ZrB2 based composites is developed by employing a temperature dependent fracture surface energy model and the classical fracture theories. The model unifies the effects of temperature, temperature dependent residual stresses owing to added reinforced particles and laminated structures, microstructures and laminated structures on the strength of laminated ZrB2 based composites into a single theory. Using the model, the effects of microstructures and laminated structure parameters on the strength of composites and their evolutions with temperature are studied in detail. The micro and laminated structure parameter optimizations for improvement of the material strength are discussed. The model is verified at different temperatures by comparison with experimental data of different laminated ZrB2 based composites. Excellent agreement is obtained between the model prediction and the experimental data.

Irreducible specific energy of new surfaces creation in materials with crack-type macro defects under pulse action

The study of destruction of samples with crack-type macro defects in shockwave microsecond duration range mode with amplitude up to 1 GPa was carried out using the magnetic pulse method of pressure pulse creation. The result analysis held on the basis of computer modeling of stressed condition and thermodynamic approach. The relation between the surface fracture energy and the material parameter, such as the energy accumulation time required for destruction, was revealed.

Effect of saturated fluid on the failure mode of brittle gas shale

To understand the influence of fluid saturation on the failure mode of gas shale, a series of triaxial compression tests under the quasi-static loading conditions were conducted using the GCTS (Geotechnical Consulting and Testing System) under different conditions (dry, water saturation, and slickwater saturation). The results showed that the rupture of dry shale samples was accompanied by a transient release of energy, which formed into the main splitting crack. Simultaneously, high-energy tension-type acoustic emission (AE) events were detected around the peak stress. Shale saturated with fluid decreased the strength and increased deformation. The presence of a “step” disturbance was clear in the expansion stage before rupture, and low-energy shear rupture events were detected repeatedly. This indicates that there were internal microslips and distributed micro-cracks to form, which maintained the overall integrity of the cores. Based on the analysis above, two failure modes were discovered: transient main crack failure mode for dry shale and distributed micro-failure mode for shale saturated with fluid. The effect of fluid saturation on the failure mode of shale was clear. This effect can increase the pore pressure; reduce fracture-surface energy; enhance the softening effect caused by water-absorbing clay, which reduced the effective stress on crack surfaces; promoted rock shear slip inside the rock; and changed the energy release characteristic and fracture mode of the shale under a stress condition, which were conducive to the formation of a crack network. The experimental results showed that saturated slickwater had a stronger effect on the failure mode of brittleness gas shale than that of saturated water.

High-entropy alloy particle reinforced Al-based amorphous alloy composite with ultrahigh strength prepared by spark plasma sintering

An Al0.6CoCrFeNi high-entropy alloy (HEA) particle reinforced Al65Cu16.5Ti18.5 amorphous alloy composite was prepared by spark plasma sintering (SPS). There is an interdiffusion (ID) layer between the HEA particle and the matrix. The yield strength of the composite is as high as 3120±80MPa, which was attributed to the combined action of the stable propagation of cracks, the significant increase of fracture surface energy, and the relative low content of sintering defects in the matrix.

Delamination fracture toughness of UHMWPE fibers/polyurethane laminates interleaved with carbon nanotube‐reinforced polyurethane films

The main cause for failure of composite laminates is delamination under shear or transverse loading. A common approach to prevent such failure is to introduce a discrete interleaf at the midplane of the laminate in order to increase its fracture toughness and, consequently, its resistance to delamination. Accordingly, a study of Mode I fracture toughness of ultra‐high molecular weight polyethylene fibers/polyurethane matrix composite laminates interleaved with thin polyurethane films reinforced with either untreated or functionalized carbon nanotubes is presented here. The results show that—depending on the surface treatment of the carbon nanotubes—the introduction of an interleaf at the midplane of the laminate generates a significant improvement of the Mode I initiation and propagation fracture toughness compared to the non‐interleaved laminates and to laminates interleaved with un‐reinforced polyurethane films. The Mode I fracture toughness results correlate with the “trouser‐leg” fracture surface energy of the films. Copyright © 2016 John Wiley & Sons, Ltd.