Mixed Mode Fracture Tests Research Articles

Effect of grain morphology and interface on the toughness of nacre-like aluminas

Ceramic composites that are both tough and strong are needed for extreme environments, ranging from aerospace and nuclear, to medical applications. Bioinspired ceramic composites tackle this challenge by mimicking tough natural structures. Nacre-like aluminas (NLAs) are ceramics processed using advanced colloidal techniques to obtain a microstructure resembling the brick-and-mortar structure of nacre. NLAs can achieve flexural strengths up to 600 MPa and fracture toughnesses ranging from 5 MPa.m1/2 up to 16 MPa.m1/2 after crack propagation. These high values mainly rely on deflection mechanisms; these can operate at temperatures up to 1200°C and under impact testing. The fracture properties have been found to be highly dependent on the mortar composition and processing technique used. However, we still don't know how far we can extend the structural properties of NLAs by changing their mortar strength and brick morphology. In this study, we combine mode I wedge splitting testing and in situ synchrotron X-ray microtomography of mixed-mode SENB fracture testing along with a kinked crack analytical formulation to study the microstructure-properties relationship in NLAs having two mortar compositions/morphologies. We compare the toughness values obtained in mode I and II with deflection models and study the effect of mode-mixity on the NLA toughness. Our findings show the grain morphology strongly influences the fracture behaviour, with the longer grain material showing longer stable crack deflection which could be further optimised going forwards. By contrast the mortar properties which provide deflection and local toughening mechanisms may be nearing their optimal strength.

Determination of delamination-related material properties and sensitivities in a ply drop composite using a semi-numerical approach

The aims of this paper are to investigate damage initiation and propagation in the vicinity of a ply drop focusing on delamination, to extract delamination-related material properties without conducting classical single and mixed mode fracture tests, and to analyze the sensitivities of delamination evolution with respect to these material properties. Quasi-static tensile tests were conducted on the coupon level for a UD composite with a ply drop. A combined numerical/experimental approach was followed to identify the material properties associated with delamination evolution. For that purpose, a finite element model was created using the cohesive zone model. The delamination-related properties were characterized by fitting the numerical model to the experiments by calibrating the cohesive zone parameters such that the global coupon response and the delamination extent for different load levels were in good agreement. Based on the identified parameter set, a sensitivity analysis was carried out to raise awareness of the influence of material properties on damage evolution. Damage around the ply drop was governed by mode II delamination. Several sensitivities were found to be non-linear with respect to a variation of input parameters. The methodology can be used in future work focusing on different ply drop configurations, and the results so far can serve as a database for benchmark simulations of delamination evolution in the vicinity of ply drops.

Non-oscillatory fracture mode partition for interface crack under mixed-mode loading

The oscillatory crack-tip field in the classical interface fracture mechanics solution often leads to complications in identifying the mode mixity in bimaterial interface fracture problems. In this paper, a non-singular series solution for the continuum problem of a crack on the cohesive-spring interface under mixed-mode loading is presented and compared to the classical oscillatory solution. A Gaussian process regression model was also developed to enable quick evaluation of the phase angle for interface delamination characterization by using mixed-mode bending fracture test.

In-Plane Mixed-Mode Brittle Fracture Assessment of Harsin Marble Using HCSP Specimen

The primary objective of this manuscript is studying the effect of T-stress term (T) on the crack propagation angle (CPA) and fracture toughness of in-plane mixed mode loading by utilizing a generalized form of minimum strain energy density (SED) criterion. The generalized criterion considers the influence of the first non-singular term of the Williams stress field as well as the conventional stress intensity factors (SIFs). A specimen known as a holed-cracked square plate (HCSP) composed of white Harsin marble is used for a wide range of in-plane mixed-mode fracture studies. HCSP is a square plate containing two cracks that are placed along each other in the circumference of a hole at the center of the specimen. The experimental results from mixed-mode fracture test by using proposed geometry are then compared with the results obtained theoretically from the conventional and generalized form of SED. It is demonstrated that the generalized criterion which includes the T, is substantially in agreement with the experimentally observed in-plane mixed-mode fracture results when compared to the SED criterion.

A general DBEM for mixed-mode cohesive crack problems

This work proposes a general dual boundary element method (DBEM) for cohesive mixed-mode crack problems. Local cohesive stiffnesses are defined to yield the boundary element nonlinear equations for any mixed-mode cohesive model in a direct way. The main novelty resides on the fact that the formulation can take into account all possible cohesive surface conditions: (i) contact, (ii) softening, (iii) unloading/reloading and (iv) complete failure, which may occur independently of the chosen cohesive model. Besides, the well-established Park–Paulino–Roesler (PPR) model was incorporated into DBEM methods. The tangent matrix of the discrete model is explicitly derived and the solution is sought by a proper degree-of-freedom (DOF) control method. The proposed formulation is validated reproducing mode I and mode II patch-tests. Some other relevant problems, including a mixed-mode fracture test, are also presented to demonstrate that the above conditions are essential to reproduce complex mixed-mode cohesive fractures. The results also shown that the control of a monotonically increasing DOF yields reliable solutions in problems with snap-back instabilities. In order to facilitate the validation of the method, predefined crack paths were assumed in the examples. Further developments may include incorporating arbitrary crack growth and damage-based cohesive models for fatigue crack growth analysis.

Direct cohesive law measurement under mixed-mode loading using semi-circular bend (SCB) specimens

The present paper suggests a new method to obtain pure mode and mixed mode traction-separation laws of adhesives using semi-circular bend (SCB) specimen by employing the digital image correlation (DIC) technique. This specimen was recently proposed by the same authors for fracture energy assessment of adhesives. This test method doesn't require any special apparatus or loading jig for mixed mode fracture tests ranging from pure mode I to pure mode II. Lower cost and higher precision than conventional methods are the most advantages of using SCB fracture tests. The primary drawback of this test method lies in its data reduction process. To address this limitation, this paper introduces a direct approach for measuring fracture energy and cohesive law parameters of the adhesive. In this method, substrate strains at the interface are used to calculate the cohesive stress applied to the adhesive layer at each desired section. Shear and normal separation values are obtained directly from DIC displacement results. The proposed method was applied to the SCB specimen subjected to pure modes I and II and for mixed-mode I/II cohesive laws. Four different SCB specimens were manufactured and tested to cover different mode mixities between pure mode I and pure mode II. The experimentally obtained cohesive laws were evaluated using finite element analysis (FEA). Good agreement between the experimental and numerical results were observed.

Determination of mode-II critical energy release rate using mixed-mode phase-field model

To overcome the harsh experimental conditions of obtaining the mode-II critical energy release rate GIIC, an easy and flexible method for determining GIIC is proposed based upon the mixed-mode fracture experiments and corresponding simulations using the mixed-mode phase-field model. In details, a mixed-mode fracture experiment is first conducted to determine the initial crack deflection angle. Subsequently, a range of phase-field numerical simulations are conducted through adjusting the value of GIC/GIIC to reproduce the experimental results so as to determine the value of GIIC with a known GIC. Three mixed-mode fracture tests (single edge cracked circular test, central crack rectangular tension test and compact tension shear test) of PMMA indicate that the determined GIIC is a stable material parameter independent of test and loading conditions. Meanwhile, the determined prediction of GIIC is compared with those in other references with a deviation of about 3.5%, which demonstrates that the proposed method can quantitatively and qualitatively obtain GIIC. Furthermore, the determined parameter GIIC is used to develop the mixed-mode phase-field model through using the mode-mixity factor (GIC/GIIC) to regular the relative proportions of volumetric and distortional crack driving energy, which results in better numerical results than the classical phase-field model (with relative deviation < 1.0%). Without the harsh conditions of the pure mode-II fracture experiment, the proposed method is of significant practice in the determination of GIIC.

Cohesive zone modeling of I–II mixed mode fracture behaviors of hot mix asphalt based on the semi-circular bending test

Low temperature cracking is a major distress form of asphalt pavement. In this study, I–II mixed mode fracture test was conducted using cohesive zone modeling technique under −10 °C. Laboratory tests and virtual finite element modeling (FEM) tests were both conducted on semi-circular bending (SCB) specimens with the notch angle varying from 0 to 75° to yield the mixed fracture behaviors. Different loading rates, including 5 mm/min, 10 mm/min, 20 mm/min and 30 mm/min, were applied to investigate the influence of loading rate on the fracture resistance. Results indicated that the peak load increased with the increase of notch angle, which was caused by the increased alignment cracking area. Mode I critical stress intensity factor (KIC) decreased, while mode II critical stress intensity factor (KIIC) increased firstly and decreased subsequently from 1.25 MPa·m1/2 to 0.35 MPa·m1/2 with the increase of notch angle. Compared to KIC tested under the loading rate of 5 mm/min, KIC obtained at 30 mm/min increased by 12.6 %, 8.5 %, 8.4 %, 7.3 %, 7.4 % and 10.4 % for specimens with the notch angles of 0, 15°, 30°, 45°, 60° and 75°, respectively. For KIIC, the increments were 8.5 %, 8.4 %, 7.3 %, 7.4 % and 10.4 %, respectively. The mixity parameter, Me, was adopted to characterize the contribution of each fracture mode on the overall fracture behaviors. It was found that with the increase of notch angle, the mode II contribution on the overall fracture increased. However, the influence of loading rate on Me was very slight, indicating the loading rate could not play any impact on the respective contributions of mode I and II fracture on the overall fracture resistance. Moreover, a linear relationship was found between Me and the notch angle.

Numerical Modelling and Validation of Mixed-Mode Fracture Tests to Adhesive Joints Using J-Integral Concepts

The interest in the design and numerical modelling of adhesively-bonded components and structures for industrial application is increasing as a research topic. Although research on joint failure under pure mode is widespread, applied bonded joints are often subjected to a mixed mode loading at the crack tip, which is more complex than the pure mode and affects joint strength. Failure of these joints under loading is the objective of predictions through mathematical and numerical models, the latter based on the Finite Element Method (FEM), using Cohesive Zone Modelling (CZM). The Single leg bending (bending) testing is among those employed to study mixed mode loading. This work aims to validate the application of FEM-CZM to SLB joints. Thus, the geometries used for experimental testing were reproduced numerically and experimentally obtained properties were employed in these models. Upon the validation of the numerical technique, a parametric study involving the cohesive laws’ parameters is performed, identifying the parameters with the most influence on the joint behaviour. As a result, it was possible to numerically model SLB tests of adhesive joints and estimate the mixed-mode behaviour of different adhesives, which enables mixed-mode modelling and design of adhesive structures.

Mixed Mode Fracture Investigation of Rock Specimens Containing Sharp V-Notches.

This work aims to assess both experimentally and analytically the fracture behavior of rock specimens containing sharp V-notches (SV-notches) subjected to mixed mode I/II loading. To this end, firstly, several mixed mode fracture tests were conducted on Brazilian disk specimens weakened by an SV-notch (SVNBD sample), performed in their corresponding center and with various notch opening angles. Secondly, the fracture resistance of the tested samples was predicted using a criterion named MTS-FEM. This approach is based on the maximum tangential stress (MTS) criterion, in which the tangential stress is determined from the finite element method (FEM). Additionally, in the present research, the required critical distance is calculated directly from finite element analyses performed on cracked samples. Comparing the experimental results and the analytical predictions, it is shown that the fracture curves obtained from the MTS-FEM criterion are in agreement with the experimental results. These results are achieved without the need for the calculation of stress series expansion coefficients, as an additional advantage of the proposed approach.

Mixed mode failure curve for an interface crack between single crystal silicon and silicone rubber

An interface crack between single crystal silicon (SC-Si) and silicone rubber was examined. Mixed mode fracture tests were performed on Arcan-type specimens at different mode mixities. It was observed during the tests that silicone rubber underwent large deformations before crack propagation. Nonlinear finite element analyses (FEAs) of the fracture tests were carried out in Abaqus. A cubic (anisotropic), linear elastic material model was used for SC-Si, while a Mooney–Rivlin (hyperelastic) model was used for the silicone rubber. The virtual crack closure technique (VCCT) which has been adopted for large deformations was employed to determine the energy release rates from the FEAs. A mixed mode failure criterion was obtained from the energy release rate data.

Mixed mode fracture of geometrically similar FRUHPC notched beams with the localizing gradient damage model

A localizing gradient damage model is proposed in this paper to capture the mechanisms underlying the fracture of fiber reinforced ultra-high performance concrete (FRUHPC): (i) an initially expanding damage process zone due to the formation of numerous fine cracks, each widening up slowly due to the fiber bridging effect; (ii) a gradual formation of a localized macroscopic crack, when at least one of the fine cracks has opened up sufficiently to trigger a fiber pull-out process. Restricting to tensile-shear dominated failures in monotonic loadings, the simplest form of damage model is adopted, where an isotropic damage variable is driven by a strain-like variable. The performance of the proposed localizing gradient damage model is first demonstrated by comparing the damage evolution process against the corresponding intensity of acoustic emission (AE) events obtained experimentally, for a notched FRUHPC beam in three-point bending. It was shown that the model is able to reproduce the slightly widening fracture process zone (FPZ) during strain hardening, as well as the eventual localized damage process zone during strain softening. Specifically, during strain hardening, the proposed localizing gradient damage model predicts an energy dissipation bandwidth that compares well with the AE energy maps, together with a consistent propagation of crack front. With a correct description of the underlying damage mechanisms, the predictive capability of the proposed model is next demonstrated through the mixed mode fracture of a series of geometrically similar FRUHPC notched beams. Since the specimens are of the same casting batch as those in the three-point bending test, the numerical material parameters calibrated earlier are adopted directly for the mixed mode fracture tests. Without any further undue calibrations, the localizing gradient damage model is shown to predict well the structure responses and size effect of the series of geometrically similar FRUHPC notched beams in mixed mode fracture.

A study on the effects of internal architecture on the mechanical properties and mixed-mode fracture behavior of 3D printed CaCO3/ABS nanocomposite samples

PurposeThe purpose of this study was to investigate the effects of CaCO3 nanoparticles on the mechanical properties, and mixed-mode fracture behavior of acrylonitrile butadiene styrene 3D printed samples with different internal architectures.Design/methodology/approachThe nanocomposite filaments have been fabricated by a melt-blending technique. The standard tensile, compact tension and special fracture test samples, named Arcan specimens, have been printed at constant extrusion parameters and at four different internal patterns. A special fixture was used to carry out the mixed-mode fracture tests of Arcan samples. Finite element analyses using the J-integral method were performed to calculate the fracture toughness of such samples. The fractographic observations were used to evaluate the mechanism of fracture at different concentrations of nanoparticles.FindingsThe addition of CaCO3 nanoparticles has resulted in a significant increase in the fracture loading of the samples, although this increase was not consistent for all the filling patterns, being more significant for samples with linear and triangular structures. According to the fractographic observations, the creation of uniformly distributed microvoids due to the blunting effect of nanoparticles and 3D stress state at the crack tip in the samples with linear and triangular structures justify the enhancement in the fracture loading by the addition of CaCO3 nanoparticles in the matrix.Originality/valueThere is a significant gap in the knowledge of the effects of different nanoparticles in the polymer samples produced by the fused filament fabrication process. One of such nanoparticles is an inorganic CaCO3 nanoparticle that has been frequently used as nanofillers to improve the thermomechanical properties of thermoplastic polymers. Here, experimental and numerical studies have been conducted to investigate the effects of such nanoadditives on the mechanical and fracture behavior of 3D printed samples.

A new simple specimen for mixed-mode (I/II) fracture and fatigue tests: Numerical and experimental studies

In the present investigation, a simple and efficient specimen geometry for conducting mixed mode (I/II) static fracture tests and fatigue crack growth studies has been proposed. No additional complicated fixtures are needed for loading the specimen and it can be used for both metallic and non-metallic materials. Large number of finite element analyses and mixed mode fracture experiments have been conducted. Present results of the experimental studies have been compared with widely used mixed mode (I/II) fracture criteria in terms of fracture toughness. The present experimental results are in very good agreement with the selected mixed mode (I/II) fracture criteria. Results of the present investigation clearly recommend the proposed specimen geometry as a useful mixed mode (I/II) specimen for fracture and fatigue studies.

Application of a micro-model for concrete to the simulation of crack propagation

The PeriDynamics (PD) model of material fracture can simulate the nucleation and propagation of cracks naturally with a simple bond breakage criterion. Combined with its advantages in multi-scale, the crack characteristics of concrete can be simulated from micro-scale. Therefore, the micro-calculation model of concrete was established by the spherical growth model based on the MATLAB-ABAQUS co-simulation method. Meanwhile, combined with the plastic softening characteristics of concrete, a quasi-plastic damage fracture constitutive model for concrete was established. Finally, the mode-I fracture test and two typical mixed-mode fracture tests were simulated by this model, and the PD-FEM (finite element method) method was used to reduce the calculation cost, in which the cracking regions were set as the PD model and other regions were set as the FEM model. The results show that the crack initiation and propagation of different calculation samples can be well described by the calculation model. Moreover, the proposed material model can better reflect the comprehensive mechanical behavior of concrete, and the crack path of the specimens is consistent with the test results. For the simulation of the I-II (tension shear) mixed fracture test, the crack paths of different calculation samples with small shear load are obviously different, and the range of crack paths can be predicted by the simulation of calculation samples. Furthermore, for the calculation samples with large shear load, the crack path and macro-behavior of different calculation samples are close to each other.

Fracture characterization and modeling of Gyroid filled 3D printed PLA structures

Abstract Polylactic acid (PLA) is a commonly used biodegradable material in medical and increasingly in industrial applications. These materials are often exposed to various flaws and faults due to working and production conditions, and increasing the demand for PLA for various applications requires a full understanding of its fracture behavior. In addition to ABS, PLA is a widely used polymeric material in 3D printing. The gyroid type of filling is advantageous for overcoming the relatively higher brittleness of PLA in comparison with conventional thermoplastic polymers. In this study, the effects of various filling ratios on the fracture toughness of 3D printed PLA samples with gyroid pattern were investigated numerically and experimentally for pure mode I, combined mode I/II, and pure mode II. Two-dimensional finite element modeling was created, and the two-dimensional functions of stress intensity coefficients were extracted in loading mode I, mode I/II, and mode II at varied filling ratios of the gyroid PLA samples. Mixed-mode fracture tests for 3D printed PLA samples with a gyroid pattern at various filling ratios were performed by using a specially developed fracture testing fixture. The results showed that the amount of fracture toughness of the samples under study in tensile mode was much higher than those values in shear mode. Also, as the percentages of the filling ratios in the samples increased, both tensile and shear fracture toughness improved.

Endowing explicit cohesive laws to the phase-field fracture theory

One of the fundamental but unsolved problems in the phase-field theory is how to obtain the energy density expression based on an arbitrary cohesive law. In this paper, we propose a phase-field model with the energy density determined by the cohesive law with an arbitrary form, which builds a rigorous link between the phase-field theory and the cohesive zone theory. Using the proposed method, the energy density in the phase-field model for any cohesive law can be determined from a unified formula. As examples, we derive the explicit energy density expressions for the linear, exponential, polynomial, and Cornelissen cohesive laws. Five numerical examples are presented to show the effectiveness of the proposed method, including a uniaxial tension test for mode-I failure, a uniaxial compression test for mode-II failure, a mixed-mode fracture test, the mode-I failure in a wedge splitting test, and the mixed-mode failure of an L-shaped panel. In the first three numerical examples, the predicted mode-I, mode-II and mixed-mode cohesive laws are extracted and compared with the target analytical cohesive laws. Excellent agreements are observed. In the last two numerical examples, the predicted global responses and the crack paths are in good agreement with the experimental results.

Fracture Parameters and Cracking Propagation of Cold Recycled Mixture Considering Material Heterogeneity Based on Extended Finite Element Method.

Cold recycled mixture (CRM) has been widely used around the world mainly because of its good ability to resist reflection cracking. In this study, mixed-mode cracking tests were carried out by the designed rotary test device to evaluate the cracking resistance of CRM. Through the finite element method, the heterogeneous model of CRM based on its meso-structure was established. The cracking process of CRM was simulated using the extended finite element method, and the influence of different notch lengths on its anti-cracking performance was studied. The results show that the mixed-mode fracture test method can effectively evaluate the cracking resistance of CRM by the proposed fracture parameters. The virtual tests under three of five kinds of mixed-cracking modes have good simulation to capture the cracking behavior of CRM. The effect of notch length on the initial crack angle and the crack propagation process of the CRM is mainly related to the distribution characteristics of its meso-structure. With the increase of the proportion of Mode II cracking, the crack development path gradually deviates, and the failure elements gradually increase. At any mixed-mode level, there is an obvious linear relationship between the peak load, fracture energy, and the notch length.

Determining a Lower Bound Mixed Mode Failure Curve for An Interface Crack Between Single Crystal Silicon and Silicone Rubber

AbstractAn interface crack between single crystal silicon (SC-Si) and silicone rubber is examined. The first term of the asymptotic solution for this interface crack is derived. Mixed mode fracture tests were performed on Brazilian disk specimens at different mode mixities. Finite element analyses (FEAs) of these tests were carried out in abaqus. A cubic (anisotropic) material model is used for SC-Si. Two different material models were used for silicone rubber: a linear elastic model for the asymptotic solution and a Mooney–Rivlin (hyperelastic) model for the FEA. The FEAs showed that large deformations were relegated to a small region surrounding the crack tip. Hence, a K-dominate region exists in which linear elastic fracture mechanics (LEFM) may be used. From the FEAs of the Brazilian disk specimens, energy release rates were determined using the virtual crack closure technique (VCCT) and displacement extrapolation (DE) methods which were corroborated by J-integral values evaluated using the contour integral method. Elsewhere, it was demonstrated that properly implemented, the VCCT method may be used for interface cracks. A mixed mode failure criterion is obtained from the energy release rate data. The SC-Si failed before the interface crack propagated. Hence, the failure curve obtained in this study should be considered as a lower bound of the critical energy release rate for this material pair.

Mixed mode fracture tests and inversion of FPZ at crack tip of overlying strata in underground coal gasification combustion cavity under real-time high temperature condition

Measuring the fracture parameters of rock materials under real-time high temperature is of great significance for accurately evaluating the stability and safety of high-temperature underground tunnels. At present, the related research is focused on the fracture properties of rocks after treatment with high temperature. To this end, we independently developed a set of testing apparatus with effect of THMC coupling of high temperature and high pressure. Using this equipment, a serious of mixed mode I ± II fracture experiments of overlying strata (red sandstone) in combustion cavity under real-time high temperature conditions (20–700 °C) are carried out. And, the variations of fracture toughness, fractal dimension of fracture trajectory and fracture initiation angle with respect to temperature and notch angle are clarified. In addition, in order to predict the fracture process and fracture behavior of red sandstone at real-time high temperature, the experimental fracture envelopes are compared with that predicted by traditional fracture criterion. It is concluded that the fracture process zone (FPZ) size at the crack tip plays a crucial role in the effectiveness of the fracture criterion, and it is temperature-dependent. Finally, based on the generalized tangential stress criterion (GMTS), the effective FPZ sizes of red sandstone under different high temperature conditions are determined by using particle swarm optimization (PSO) algorithm combined with least square method. The research results of this paper are of great significance for evaluating the stability and safety of overlying strata (red sandstone) in combustion cavity.