Mixed Mode Fracture Criterion Research Articles

Mixed mode I/II and I/III fracture toughness investigation for preplaced aggregate concrete mixtures: Experimental study and theoretical prediction

AbstractIn this paper, mixed mode I/II and I/III fracture toughness of preplaced aggregate concrete was studied using an edge‐notched disc bend specimen. The results showed the dependency of the fracture toughness value on the mode mixity. The values of modes I, II, and III fracture toughness were obtained to be equal to , , and , respectively. Several theoretical fracture criteria were examined for predicting the trends of experimental data in the tested preplaced aggregate concrete material. The 3D averaged strain energy density criteria provided the best predictions for the KIIIc/KIc ratio. Mixed mode I/III fracture toughness data were between the predicted envelopes of the maximum tensile stress and 3D maximum tangential strain theories. The generalized maximum tangential stress criterion provided accurate predictions for pure mode II and mixed mode I/II fracture data among the investigated mixed mode fracture criteria. By comparing the preplaced aggregate concrete fracture results with those of other types of concrete, it is observed that preplaced aggregate concrete has acceptable and in‐the‐range fracture resistance.

Mode I/II cracking behavior of additively manufactured interpenetrating phase composites (IPC), an experimental and theoretical study

An interpenetrating phase composite (IPC) material combines the advantages of being made from materials for an intended behavior. 3D-printed parts have received attention for rapid prototyping of complex structures; however, their porous inherent makes them susceptible to cracking. Polymer adhesives can be used to overcome these issues to increase their strength and durability. In this paper, IPCs were developed using 3D-printed scaffolds and epoxy resin matrix, and their fracture behavior was examined. The samples were printed with 25, 50, 75, and 100 infill percentages and tested in the full range of mode I-II fracture. From the results, the promising behavior of IPCs can be seen. Where the 3d printed samples with 100, 75, 50, and 25 infills show 2.4, 1.8, 0.8, and 0.3 MPa√m mode-I fracture toughness, IPCs made from samples with 75, 50, and 25 infills, show 2.0, 2.2 and 2.7 MPa√m, respectively. The same trends are also seen in the full range of mode I-II fractures. The generalized maximum tangential stress (GMTS) criterion accurately predicted KIIc/KIc ratios among the investigated mixed-mode fracture criteria. The evaluations indicated that the discrepancy between the measurements is mainly due to the sign and magnitude of the T-stress parameter.

Application of modified fracture criteria incorporating T-stress for various cracked specimens under mixed mode I-II loading

Accurate assessment of fracture behavior and life prediction of cracked materials based on the mixed mode fracture criteria is of utmost importance in fracture mechanics. In this study, the modified fracture criteria incorporating T-stress for mixed mode I-II cracks were comprehensively reviewed. Additionally, a comparative analysis was conducted between the experimental results obtained from five different cracked configurations and the theoretical predictions according to these modified criteria. Moreover, a brief discussion was held regarding the effect of T-stress on both crack initiation angle and fracture toughness, accompanied by providing some suggestions. The results revealed that the predictive accuracy of modified criteria exhibited noticeable variations across different cracked configurations due to the significant disparities in both the sign and magnitude of T-stress around the crack tip. However, it was observed that the predicted curves based on the modified fracture criteria for the semi-circular bend and edge-crack triangular specimens had remarkable similarities owing to their similar biaxial stress ratio B. When the mode II loading dominated, the generalized maximum tangential stress, generalized minimum strain energy density and generalized averaged strain energy density criteria were suitable for the semi-circular bend, edge-crack triangular, central crack rectangular and short bend beam specimens with positive T-stresses, whereas the maximum tangential strain, generalized maximum tangential stress and generalized maximum tangential strain energy density criteria could provide better theoretical predictions for central cracked Brazilian disk specimens having a negative T-stress.

Interfacial debonding mechanism of magnesium phosphate cement onto old concrete substrates under freeze-thaw conditions

The interface created by the repair of damaged ordinary Portland concrete (OPC) structures using magnesium phosphate cement (MPC) is prone to cracking and debonding under freeze-thaw (F-T) conditions and may even cause engineering disasters. In this study, the entire debonding process, moisture migration and debonding mechanism of the MPC-OPC composite interface under F-T actions were investigated and a novel mixed mode fracture criterion was established. The primary findings are drawn as follows: (i) The interfacial crack initiates and propagates along the interface or kinks into the MPC side during F-T actions, depending on the position and thickness of the localized interface F-T damage zone (IFDZ) close to the interface on the MPC side; (ii) The net suction force causes capillary and film water in the mesopores and micropores to migrate to the freezing macropores inside the interface layer, whereas the increase in the liquid pressure caused by the water-ice phase transition causes crack initiation in the macropores and even the interface layer damage; (iii) The stiffness difference between MPC and OPC increases as the molar ratio of magnesia and phosphate (M/P) or the mass ratio of water to cement (W/B) of MPC increases, and the interface debonding mode shifts from propagating along the interface to kinking into the MPC side.

Fracture parameters and crack initiation Assessment Employing Mixed-mode I/II Fracture Criterion in Laminate Composites Using Digital Image Correlation Method

The present study aims to have fracture parameters, such as stress intensity factors (SIFs) and J-integral, as well as the crack initiation angle, extracted through the utilization of a novel mixed-mode (I/II) fracture criterion founded on the maximum energy release rate (MERR) and maximum tangential stress (MTS). The digital image correlation (DIC) method is employed in the analysis of crack behavior. Of note, several key findings are highlighted by our research. Results show a slight decrease in the mode I stress intensity factor (KI) with an increase in the crack inclination angle (φ). Interestingly, a bell-shaped curve characterizes the mode II stress intensity factor (KII), with its peak occurring at φ = 45. Comparison of experimental outcomes with finite element (FE) based modeling reveals consistent trends in both KI and KII from both sources. The comparison of experimentally determined crack initiation angles with predictions from the MERR and MTS criteria offers insightful observations. For φ ≤ 30, both criteria closely match experimental outcomes, as the crack initiation corresponds to φ. However, for φ > 30, these criteria underestimate the crack initiation angles, leading to a slower decrease in kink angles compared to observations. Further analysis involves a comparison between the two criteria and experimental results. Here, MERR emerges as being more accurate in prediction than MTS. Lastly, Simpson's rule is employed to calculate the J-integral, contributing to a comprehensive understanding of crack behavior. The reliability of the new mixed-mode fracture criteria and the DIC method in evaluating crack tip conditions and predicting minor kink angles is established by our study. Not only is understanding enhanced by our findings, but practical applications in predicting crack initiation and behavior in complex materials are also offered.

An experimental study and theoretical evaluation on the effect of specimen geometry and loading configuration on recorded fracture toughness of brittle construction materials

Geometry and loading condition of cracked specimens may affect the fracture toughness results and hence the evaluation of differences in measured fracture toughness values is necessary for many construction materials. In the absence of standard methods for measuring the general mode fracture resistance of asphaltic concrete materials, in this study the fracture toughness values for such materials were measured and compared by means of three different test specimens and methods. All three fundamental fracture modes (i.e. pure I, pure II, and pure III) and related mixed-mode loading cases (i.e. I/II and I/III) were evaluated. The test specimens were edge-notched disc bend (ENDB), edge-notched diametrically compressed disc (ENDC), and semi-circular bend (SCB). During the experimental program the specimens made of asphaltic concrete were tested at two temperatures of −5 and −25 °C and analyzed using the linear elastic fracture mechanics (LEFM) principles. Also, several theoretical frameworks were compared and examined to evaluate their applicability and accuracies for predicting the trends of experimentally obtained test data. The results showed that the geometry and loading configuration can significantly affect the measured fracture toughness values under pure mode II and pure mode III. The value of mode I fracture toughness measured by three specimens was almost the same (with small differences of 4%) and equal to 0.68 MPa√m. At pure mode II, the fracture toughness evaluated by the ENDB specimen was about 20% higher than that of the SCB specimen (with averages of 0.83 and 0.68 MPa√m for the ENDB and SCB samples, respectively). For pure mode III case, the measured fracture toughness by the ENDC specimen was approximately 60% higher than that of the ENDB specimen (with averages KIIIc = 0.62 MPa√m for the ENDC and 0.42 MPa√m for the ENDB specimen). Among the investigated mixed mode fracture criteria, the GMTS criterion provided accurate predictions for KIIc/KIc ratios. Also, 3D-MTSN, and 3D-MTSED criteria were more precise than others for mode I/III predictions. The evaluations indicated that the discrepancy between the measurements is mainly due to sign and magnitude of T-stress parameter.

Simulating delamination growth accounting for fracture directionality using a cohesive element approach

Experiments have shown that the critical energy release rate (ERR) can vary as a function of the delamination in-plane propagation direction, relative to the bounding plies, and out-of-plane direction towards which it tends to grow, often referred to as delamination directionality. Despite the experimental evidence, delamination directionality is typically neglected in simulations. A cohesive element formulation is proposed that can simulate delamination growth while accounting for delamination directionality. The simulated fracture process is defined via piecewise-linear, independent, Mode I, II, and III traction separation laws (TSLs) and a directional mixed-mode fracture criterion. Mixed-mode loading conditions are simulated by scaling the pure mode TSLs based on the fracture criterion and the calculated mode-mixity. The same scaling concept is used in partially damaged material points to ensure that a change in fracture process (e.g. decrease/increase in critical ERR due to a variation in delamination directionality) is captured while preventing spurious delamination growth or healing and minimizing history dependence.

Crack density estimation method for composite laminates based on discrete form stiffness degradation models

Matrix cracking of composite laminates leads to stiffness degradation and dominates the medium leakage of liner-less composite vessels. A stiffness degradation model can be established through the machine learning method, which provides only discrete form equivalent moduli data without explicit analytical results. This paper further explored the use of the discrete form data set of stiffness degradation in the crack density estimation for composite laminates by using an iterative process. Furthermore, different mixed-mode fracture criteria were discussed. The results showed that Benzeggagh-Kenane (B-K) criterion and the power law criterion are more appropriate in mixed-mode crack density analyses.

An extended peridynamic model for analyzing interfacial failure of composite materials with non-uniform discretization

This work presents an extended ordinary state-based peridynamic model and approaches to analyze the fracture behavior of composite materials considering interfacial failure. An interface force term is introduced to characterize the interaction among different compositions in composite materials, which enables naturally the non-uniform discretization to be conveniently adopted, especially where sharp interfaces exist. The calculation of force states in different compositions is independent of each other, and the use of non-uniform discretization can improve computational efficiency significantly. Further, inspired by the cohesive zone model (CZM), the deformation coefficient and degradation behavior of interface bonds are derived by using the traction-separation law, and a mixed-mode fracture criterion for interface bonds based on the bond energy density is established as well. Validation of the proposed model and approach is established through a classical rectangular plate example, and then the proposed model is employed to analyze the failure of typical composites including laminated glass and concrete. The results show good agreement with corresponding experimental observations and it indicates that the proposed extended peridynamic model can accurately and efficiently capture and describe the fracture of composite materials with sharp interfaces.

A review of mixed mode I-II fracture criteria and their applications in brittle or quasi-brittle fracture analysis

Fracture criteria play a very important role in predicting crack propagation behavior and life evaluation of cracked bodies. In this paper, mixed mode I-II fracture criteria in the framework of linear elastic fracture mechanics and their applications in brittle or quasi-brittle fracture analysis are systematically reviewed. Meanwhile, the advantages and shortcomings of these criteria are briefly discussed. Furthermore, the effects of T-stresses on brittle fracture characteristics are also studied and some suggestions are given to select appropriate fracture criteria. The results show that different types of fracture criteria differ greatly in predicting the crack propagation behavior, and a suitable criterion can be chosen according to the crack types, loading modes and failure characteristics. Tension-based fracture criteria are applicable for the opening cracks under tensile-based failure, but not for the closed cracks under shear-based failure. T-stresses around the crack tip have significant effects on crack initiation angle, fracture resistance and crack tip plastic zone, which should be introduced into the classical fracture criteria only determined by singular terms for providing more accurate predictions. Moreover, the variable fracture process zone radius can be further considered in these modified criteria considering stress intensity factors and T-stresses, which are not only suitable for brittle materials, but also for plastic materials under small scale yielding. This review will contribute to the development of mixed mode fracture criteria.

The onset of unstable fracture and crack deflection of AA7085 in mixed mode I + II loading

The current study focuses on the planar mixed mode fracture of AA7085. A loading device based on the concept given by Richard et al. has been developed for inducing planar mode-mixity in compact tension and shear (CTS) specimens. The CTS specimens extracted from the AA 7085 plate were subjected to mixed mode quasi-static loading after pre-cracking the specimens by fatigue loading under mode-I conditions. The desired pre-cracking length was achieved after performing an extended finite element method (XFEM) based fatigue crack growth simulation. Different mode-mixity has been introduced in the specimens by changing the orientation of the loading device with respect to the loading axis of the machine. Experimentally observed crack deflection was compared with the angles predicted by different planar mixed mode fracture criteria, namely MTS, Richards, and strain energy density. Equivalent stress intensity factors proposed at the onset of unstable fracture have been determined using different criteria and compared with each other. A new equivalent stress intensity factor for mixed mode has been proposed from Shah's equation of fracture locus. It has been found that the equivalent stress intensity factor based on Shah's equation of fracture locus is suitable for the alloy being investigated. The fracture morphology of the fractured specimen was inspected in a field emission scanning electron microscope. Both inter-granular and dimpled ductile fracture was observed in the specimens irrespective of the mode-mixity. Extended finite element simulation was performed to determine tangential stress distribution at a distance around the crack tip.

Mixed mode (I/III) fracture studies using a new specimen setup

In the present work, mixed mode (I/III) fracture studies have been investigated using a new specimen and an out-of-plane loading fixture that can be used with the conventional uniaxial universal testing machines. The proposed specimen is a single edge cracked circular (SECC) specimen which can be employed on both metallic and non-metallic materials under static and fatigue loads. A large number of three-dimensional finite element analyses have been performed on the proposed specimen setup to demonstrate the efficacy of the proposed setup. Experimental fracture studies have also been performed under mixed mode (I/III) loading conditions. The present experimental results are in very good agreement with the available mixed mode (I/III) fracture criteria. Experimental results indicate that the pure mode III fracture toughness is nearly 1.46 times greater than that of the mode I. This has been found due to an increase in the inelastic region around the crack tip in pure mode III and is in accordance with the published results. Detailed analyses of the fractured surfaces have also been carried out. It has been demonstrated that the fractured surfaces become more rough as the mode III component increases. Preliminary results of mixed mode (I/III) fatigue crack growth studies on Al 7075-T6 using the metallic SECC specimen have also been presented. The results of the present study confirm that the proposed specimen setup can be used to study the mixed mode fracture behavior of linear elastic materials under static and fatigue loading.

A comprehensive study on ring shape specimens under compressive and tensile loadings for covering the full range of I+II fracture modes of gypsum material

Using ring-shape specimens containing two aligned cracks on the internal surface of the ring, two test configurations subjected to tensile or compressive loads namely (i) diametrically compressed ring (DCR) and (ii) diametrically tensile ring (DTR) specimens were suggested to investigate the full mixed-mode I/II fracture problem. The fracture parameters, including modes I and II stress intensity factors and T-stress, were determined numerically for these two test specimens with different crack lengths and crack angles. Also, the ability of the specimens was examined by conducting experimental fracture tests on gypsum material. In addition, the direction of fracture kinking was investigated both experimentally and theoretically. The experimental results were then compared and predicted using the mixed mode fracture criteria such as maximum tangential stress (MTS) and generalized maximum tangential stress (GMTS). The normalized fracture toughness (KIIc/KIc) ratios of the tested DCR and DTR specimens were about 0.72 and 0.95, respectively. Such difference was related to the considerable effect of T-stress values and it was shown that the GMTS criterion provides more accurate predictions for the test results of both DCR and DCT samples compared to the MTS criterion.

Mixed-mode I/II fracture properties of selectively laser sintered polyamide

Additive manufacturing (AM) is a topical field today and has received the attention of many researchers. However, further research is needed to overcome the many challenges facing AM, especially in the mixed-mode fracture. The results presented in this paper are framing the experimental data obtained for mixed-mode I/II fracture properties of laser sintered polyamide. The experiment was carried out on Semi-Circular Bend (SCB) specimens manufactured from polyamide PA2200 using EOS Formiga P100 laser sintering machine. To achieve the full range of fracture toughness values, from pure mode I to pure mode II, five crack orientations of the SCB specimens (0, 15, 30, 45 and 54°) were considered. Further, crack initiation angle and crack paths of SCB specimens have been assessed in order to identify the fracture phenomena (interlayer and/or intralayer fracture). The main fracture properties (fracture toughness, crack initiation angles and crack paths) were compared with the theoretical predictions of three mixed-mode fracture criteria (Maximum Tensile Stress-MTS, Maximum Energy Release Rate-Gmax and Equivalent Stress Intensity Factor-ESIF). The results underline differences between theoretical approaches and experimental data, especially due to the interlayer fracture phenomenon. However, it was obtained that the Gmax and ESIF criteria show the best match with the experimental data.

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.

Three-Dimensional analysis of mixed mode Compact-Tension-Shear (CTS) Specimens: Stress intensity Factors, T-stresses and crack initiation angles

In order to characterize the crack tip stress field in three-dimensional fatigue and fracture problems, stress intensity factor and T-stress solutions are usually necessary. In this paper, extensive three-dimensional (3D) finite element models are constructed for Compact-Tension-Shear (CTS) specimen, which is one of the most widely used specimens for fatigue and fracture tests under mixed-mode I&II loading. In-plane and out-of-plane geometric dimensions including varying crack depths ratios (a/W = 0.3, 0.5 and 0.7) and thicknesses ratios (B/W = 0.1, 0.3 and 0.5) are considered under different loading angles (β = 0°, 15°, 30°, 45°, 60°, 75° and 90°). The results of stress intensity factors (KI,KII and KIII) and T-stresses (T11 and T33) along the crack front are computed and analyzed. The combined effects of geometric dimensions and loading angles on these fracture parameters have been illustrated. The solutions of the parameters are then described using empirical formulae by fitting numerical results with the least-squares method. Solutions obtained have been used to predict the crack initiation angles for CTS specimens based on mixed-mode fracture criteria including the maximum tangential stress (MTS) criterion, the generalized MTS (GMTS) criterion, the strain energy density (SED) criterion and the generalized SED (GSED) criterion. Solutions are useful for fracture and fatigue problems of mixed-mode I&II, such as analysis of the constraint effects on fracture toughness and propagation path of fatigue crack.

Fracture Modeling of the Bi-Block Ballastless Track System Resulting from Early-Aged Relative Humidity during the Construction Process

Drying-induced cracks are an important issue for bi-block ballastless track system consisting of foundation, precast sleepers, and cast-in-place track slab, which not only significantly affects the comfortableness and safety of rapid transit railway but also reduces the service life of ballastless track. In order to explore its damage mechanism, this work presents an evolution model of relative humidity (RH) in the CRTS I bi-block ballastless track system by considering the actual construction sequence and environmental conditions to simulate the crack propagation induced by nonuniform RH field. Firstly, based on the node coupling technique, a three-step transfer process of RH is designed to separately investigate the influence of the construction sequence on the early humidity field in the foundation, sleepers, and cast-in-place track slab, and then the nonuniform distribution of early humidity field in the ballastless track system is determined. Subsequently, the formation mechanism of shrinkage crack in the system is analyzed, and the crack propagation path is predicted by using the mixed-mode fracture criterion. The results show that the maximum relative humidity gradient (RHG) appears at the interface between the track slab and the sleeper after concreting the cast-in-place track slab, which causes the maximum principal stress due to the drying shrinkage property of concrete materials. When the maximum principal stress exceeds the tensile strength of the interface, an interface crack will be generated and converted to a splayed crack with an initial angle of about 45° at the sleeper corner, which will be further propagated under the action of drying shrinkage deformation and finally forms a transverse through-wall crack in the track slab. The simulated crack propagation path agrees with the observed one at the site well, and thus the results are beneficial to understand the formation mechanism of through-wall crack in the track slab and further guide the construction design of the bi-block ballastless track system.

A Discussion on the Forms of Planar Mixed-Mode Fracture Criteria

For the mixed-mode fracture on an original crack plane, the fracture criteria are usually based on the coupling of K I/K IC and K II/K IIC. Extended to general potential fracture planes, they become K I (θ)/K IC and K II (θ)/K IIC. Specifically, three forms have been widely used: linear, elliptical, and quadratic forms. The question of how these criteria perform is addressed by this research. This study does not intend to provide a general assessment but focused on only one case in which an analytical solution can readily be obtained. Specifically, we considered the performance of these criteria under Mode I loading, namely, K I ≠ 0, K II = 0. The analytical solution for fracture initiation angle under each of the three mixed-mode criteria were presented, where the results demonstrated that only the elliptical form yielded accurate results. That is, under Mode I loading, the initiation of pure Mode I fracture takes precedence that agrees well with standard results. What’s more, the mathematical requirements are obtained for the applicable mixed-mode fracture criteria.

Mixed-mode fracture in a soft elastomer

We present an experimental study on mixed-mode crack propagation in thin sheet specimens of a soft silicone elastomer. To introduce mixed-mode loading, we adopted the widely applied pure shear fracture testing geometry, but oriented the initial crack at an inclined angle relative to the direction perpendicular to the external tensile loading. Because of the inclined angle, locally the crack tip was subjected to both tensile and shear loading even though the global loading was tensile, thus resulting in a mixed Mode-I and Mode-II condition for the crack. Altering the inclined angle led to different degrees of mode-mixity and hence different crack propagation trajectories. Using a particle tracking method, we were able to measure the nonlinear deformation fields throughout the entire course of crack propagation. Based on the measured deformation fields, we used J-integral to calculate the energy release rate during crack propagation and found that the results were insensitive to the tangent direction of the crack trajectory, suggesting that the fracture toughness was approximately mode independent. Moreover, the tangent direction of the crack trajectory, when plotted in the reference configuration, was observed to be perpendicular to the direction of maximum principal stretch. The experimental results pave the way for establishing quasi-static mixed-mode fracture criteria for soft silicone elastomer, which has not yet been well understood in the literature.

Mechanics of a pressurized penny-shaped crack in a poroelastic halfspace

This paper examines the axisymmetric problem of a penny-shaped crack located in a poroelastic halfspace that is modelled by Biot poroelasticity. The paper first examines the axisymmetric problem of the mechanics of fluid injection over a circular area within a halfspace that would create the skeletal stress state necessary to initiate fracture. The triggering of the fracture is assumed to create an axisymmetric penny-shaped crack whose surfaces will be subjected to fluid pressure. The mechanics of the penny-shaped crack in terms of its potential to extend in an axisymmetric fashion is examined by formulating the poroelastic mixed boundary value problem and solving the coupled Fredholm integral equations of the second-kind obtained through successive applications of integral transform techniques. The analysis of the poroelasticity problem of fluid-injection into the crack gives rise to time-dependent skeletal stress intensity factors (SIFs) at the crack tip; these are combined with a mixed-mode brittle skeletal fracture criterion to establish the injection pressures that can lead to the extension of the penny-shaped crack in a self-similar fashion.