Crack Growth Trajectory Research Articles

Fracturing behavior and mechanism of flawed disc specimens under compressive loading using geometry‐constraint‐based nonordinary state‐based peridynamics

AbstractA geometry‐constraint‐based nonordinary state‐based peridynamic (GC‐NOSBPD) model is developed to investigate the fracture characteristics of flawed brittle disc specimens under compressive loading as well as its fracturing mechanism. The bond‐associated horizon (BAH) size is directly defined based on the kinematic constraint (KC). This proposed model can well mitigate the numerical oscillation. The failure criteria based on the bond‐associated stress state are utilized to simulate the fracture of materials. Two stress effects can offer an insight into the fracturing mechanism of flawed specimens. The failure modes of flawed specimens are controlled by the tensile failure, and the crack growth trajectories acquired by the present numerical model are equivalent to those obtained by the experimental observations. The effects of size and crack inclination angles on the fracture toughness of brittle materials are assessed. The GC‐NOSBPD model is competent for evaluating the fracture damage of flawed brittle materials and understanding its failure mechanism.

Brittleness reduction of Al2O3–C refractories: Microstructure evolution and role of carbon fibers

Carbon fibers (Cf) were incorporated into Al2O3–C refractories to enhance their toughness in this work. The results indicated the 0.3 wt% Cf-adding improved the high-temperature bending strength to 1.93 MPa from 1.07 MPa, and led to a 55 % enhancement in thermal shock resistance. The above enhancement could attributed to the in-situ formed SiC coating which was observed on the carbon fiber's surface and strengthened the interface bonding between the carbon fiber and refractory matrix. A solid-liquid diffusion reaction was employed to describe the formation process of in-situ SiC layer on the carbon fibers. Furthermore, the wedge-splitting test with digital images was carried out to investigate the crack-growth trajectory during the splitting process. It was confirmed that Cf-adding could enhance the strength and reduce brittleness with the crack-bridging, pullout, and interlock behaviors of carbon fibers in the refractory matrix.

Fracture behavior of human cortical bone with high glycation content under dynamic loading

The present study simulates the fracture behavior of diabetic cortical bone with high levels of advanced glycation end-products (AGEs) under dynamic loading. We consider that the increased AGEs in diabetic cortical bone degrade the materials heterogeneity of cortical bone through a reduction in critical energy release rates of the microstructural features. To simulate the initiation and propagation of cracks, we implement a phase field fracture framework on 2D models of human tibia cortical microstructure. The simulations show that the mismatch between the fracture properties (e.g., critical energy release rate) of osteons and interstitial tissue due to high AGEs contents can change crack growth trajectories. The results show crack branching in the cortical microstructure under dynamic loading is affected by the mismatches related to AGEs. In addition, we observe cortical features such as osteons and cement lines can prevent multiple cracking under dynamic loading even with changing the mismatches due to high AGEs. Furthermore, under dynamic loading, some toughening mechanisms can be activated and deactivated with different AGEs contents. In conclusion, the current findings present that the combination of the loading type and materials heterogeneity of microstructural features can change the fracture response of diabetic cortical bone and its fragility.

Fatigue growth behavior of mode II crack in headed stud steel used in steel–concrete composite structures

The fracture mechanics method has been employed for fatigue performance evaluation of stud used in steel–concrete composite structures while the fatigue crack growth behavior in headed stud steel has not been systematically studied. The present work is proposed to investigate the fatigue growth behavior of mode II crack in headed stud steel and its welded joint. Compact tensile shear (CTS) specimens extracted from the base material (BM) and weld metal (WM) of stud are tested under mode II loading to investigate the fatigue crack growth (FCG) trajectories and rates with different stress ratio. The crack closure level and FCG threshold are determined and discussed. Results show that the crack deflection in BM meets both the MTS criterion and S-criterion, while crack deflection in WM does not meet the two criterions. The 2% compliance offset criterion in the origin ASTM method is suitable to determine the crack opening force both for BM and WM of stud. The low crack closure level in WM indicates the tensile residual stress in welded joint, resulting a more quickly fatigue crack growth rate (FCGR) in WM than that in BM. The calculation formulation of equivalent SIF range proposed by Borrego et al. is verified with the best normalization effects and is recommended to fit the FCGR model both for headed stud steel and its welded joint under mode II loading.

Экспериментальная оценка адекватности численного моделирования межслоевой трещиностойкости слоистого стеклоэпоксикомпозита при комбинированной моде нагружения I/II

The reliability of numerical simulation of crack growth in a laminate glass-epoxy composite under mixed-mode loading by opening (mode I) and shear (mode II) of an interlayer crack is verified. According to the experimentally determined standard (DCB and ENF) and nonstandard (SLB and OLB) methods, the values of the parameters of interlayer crack resistance under individual and mixed-mode loading modes I and II calculated the exponent in the Benzeggagh-Kenane equation as a material constant of the laminate epoxy glass composite. Using this parameter and the ANSYS software package, within the framework of linear elastic fracture mechanics and the method of virtual crack closure, numerical finite element modeling of the growth of interlayer cracks in samples of a laminate glass-epoxy composite of the SLB and OLB types was carried out under a mixed-mode loading with a different fraction of modes. With the optimal number of elements in the finite element mesh per given length of the crack growth trajectory, numerical simulation provides sufficient accuracy of calculations of the limit load of the beginning of crack growth with a minimum amount of calculations and good agreement between the experimentally determined and calculated crack resistance parameters.

Effect of stiff substrates on enhancing the fracture resistance of Barium Titanate thin films

Damage tolerance of a thin film attached to a substrate is dependent on several parameters such as film thickness, film orientation, residual stresses, nature of interfaces, microstructure and defects present. Here we study the fracture resistance and crack growth trajectory in BaTiO3 thin films attached to elasticially stiff substrates using micromechanical experiments and finite element modeling. Microcantilever fracture tests are carried out on bi-layered systems of BaTiO3 film on Pt-Si and SrTiO3 substrates to study the effect of interfaces, texture and elastic mismatch on fracture toughness. The substrates in the bi-layers are chosen to force the crack to experience a shielding effect in terms of a decrease in the crack driving force. Experiments revealed an unexpectedly large increase in fracture toughness when the crack tip is closer to a stiffer substrate, qualitatively matching the predictions from the numerical model. The bi-layered films attached to the substrate showed 125% (on Pt-Si) and 160% (on SrTiO3) increase in fracture toughness compared to the free-standing films, for the first time, revealing the significant effect of elastic modulus of the substrate on improving the fracture resistance at such micrometer length scales.

Microstructural fatigue fracture behavior of glycated cortical bone.

The current study aims to simulate fatigue microdamage accumulation in glycated cortical bone with increased advanced glycation end-products (AGEs) using a phase field fatigue framework. We link the material degradation in the fracture toughness of cortical bone to the high levels of AGEs in this tissue. We simulate fatigue fracture in 2D models of cortical bone microstructure extracted from human tibias. The results present that the mismatch between the critical energy release rate of microstructural features (e.g., osteons and interstitial tissue) can alter crack initiation and propagation patterns. Moreover, the high AGEs content through the increased mismatch ratio can cause the activation or deactivation of bone toughening mechanisms under cyclic loading. The fatigue fracture simulations also show that the lifetime of diabetic cortical bone samples can be dependent on the geometry of microstructural features and the mismatch ratio between the features. Additionally, the results indicate that the trapped cracks in cement lines in the diabetic cortical microstructure can prevent further crack growth under cyclic loading. The present findings show that alterations in the materials heterogeneity of microstructural features can change the fatigue fracture response, lifetime, and fragility of cortical bone with high AGEs contents. Cortical bone models are created from microscopy images taken from the cortical cross-section of human tibias. Increased glycation contents in the cortical bone sample can change the crack growth trajectories.

A bond-based peridynamics model based on variable material properties for modeling elastoplastic behavior

Crack tip singularities and material discontinuities are taken to be the main challenges for analyzing cracks in fracture mechanics problems. Peridynamic (PD) theory has been recently introduced as a nonlocal extension of continuum mechanics capable of improved modeling of progressive damage and rupture in cracked structures. In this theory, the internal forces have been characterized by nonlocal interaction between the pairs of the material points whose displacements or displacement derivatives are discontinuous. Given that the bond-based PD (BB-PD) has not been satisfactorily employed for predicting ductile fracture, the main purpose of this work is to present a new PD plasticity model in conjunction with the Variable Material Property (VMP) method, aiming to provide the possibility of elastoplastic modeling in BB-PD. In the present work, the quasi-static loading has been selected for simulation and the von-Mises yield criterion has been utilized for describing the plastic deformation. The loadings are applied as the displacement is controlled and outputs from the PD model are compared with the results achieved from ABAQUS software based on the continuum mechanic assumptions. To validate the accuracy of the present formulation, two example problems of the plate with a central crack and a central hole subjected to tensile load are examined. The results of von-Mises stress, the plastic zone size, horizontal and vertical displacement, and equivalent plastic strain have been verified in comparison with the outputs calculated by the finite element method (FEM), evidencing good accuracy of the VMP-based PD elastoplastic model in predicting the desired parameters. To predict the formation of spontaneous cracks and crack growth trajectory, two more examples that include a plate with a central hole, as well as, a plate with two edge cracks and a double hole are discussed. The obtained results are in good agreement with those from the experiment and ABAQUS software.

Failure mechanism of circlular tunnel supported by concrete layers under uniaxial compression: Numerical simulation and experimental test

Under this study, particle flow code modeling and experimental testing were used to examine the failure behavior of a pre-holed rocklike specimen including concrete interlayers in uniaxial compression. Rectangular pre-holed gypsum samples with interlayer concrete have been made specifically for this purpose. The sample's measurements were 150 mm*150 mm*50 mm, and the hole's diameter was 20 mm. Changes were made to the concrete's length, location, and number. There were 0 and 20 mm between the concrete layer and the hole. The lengths of the concrete were 50, 100, and 150 mm. 20 mm thick concrete was used. This complex was quantitatively tested and simulated under uniaxial loading circumstances. 13 experiments in all have been performed. The findings show that concrete length, concrete layer number, and concrete circumstance all have an impact on the crack growth trajectory. Two tensile fractures started in the hole wall while it was in the middle of the concrete layer and spread parallel to the loading axis until coalescing with the sample edges. By increasing the distance between the concrete layer and the hole, more tensile cracks and oblique fractures occurred. By lengthening the concrete, the model's crack count was reduced. The shear bands at the hole were expanded by extending the distance between the concrete layer and the hole when the hole was encircled by two concrete layers. Additionally, by shortening the concrete, more shear bands were formed close to the hole. Longer concrete had higher young modulus, fracture initiation stress, ultimate strength, and absorbed energy. Additionally, the concrete layer's distance from the hole was increased, which diminished these mechanical qualities. By increasing the number of concrete layers, the concrete's young modulus, fracture initiation stress, ultimate strength, and absorbed energy were all raised. The results of the numerical simulation agree well with those of the experiments. Based on the results of this article, an innovative method and a unique technique can be proposed to install the concrete lining layers at different dimensions around the tunnel in such a way that the circular cross-section of the tunnel remains constant.

Study of the interaction mechanism of oppositely propagating cracks by dynamic photoelasticity and numerical simulation

The interaction mechanism of oppositely propagating cracks is an important basis for the study of rock fracture under dynamic loading. In this article, the stress field superposition and crack tip stress evolution are deeply investigated during the interaction of oppositely propagating cracks by using dynamic photoelastic experiment method and numerical simulation analysis. Obtained results indicate that the cracks interaction process is accompanied by the deflection of the crack, and the deflection of the cracks is mainly affected by the shear stress field at the crack tip. According to the difference of the crack deflection characteristics, the interaction process of the oppositely propagating cracks can be divided into two stages. The Stage I: the non-interlaced stage and Stage II: the interaction stage after the mutual staggered. It includes the period of Stage I that the oppositely propagating cracks are not interlaced with each other; the Stage II is the interaction period after the oppositely propagating cracks are interlaced with each other. The effects of stress intensity factor K I, stress intensity factor K II and far-field T stress on crack propagation process should be comprehensively considered when predicting the crack growth trajectory. The interaction of the stress field between cracks is the main factor determining the crack propagation trajectory. In addition, the vertical spacing between cracks also has a significant effect on the fracture behavior of oppositely propagating cracks. When the vertical distance between the two cracks is large, the local stress fields at the crack tip cannot overlap and interfere with each other, and the oppositely propagating cracks will expand independently of each other.

Influence of age-related changes on crack growth trajectories and toughening mechanisms in human dentin.

Dentin microstructure undergoes changes with age and its materials properties degrade over time. In the present study, we investigate the coupled influence of increased filled tubules and decreased materials properties on the fracture behavior of human dentin. We assume degraded materials properties are linked with increased advanced glycation end-products (AGEs) crosslinks in dentin tissue. We use morphological data of human molars to create 2D and 3D models of dentin microstructure, and utilize a phase field fracture framework to study crack growth trajectories. We construct aged dentin samples (i.e., filled tubules and degraded properties) and compare the fracture results with the samples without age-related changes. The simulations show an increase in the number of filled tubules can deactivate the toughening mechanisms such as crack deflection and microcracking. In addition, filled tubules have adverse impacts on the ability of peritubular dentin to shield microcracking. We further show how the dentinal tubules' orientations affect the crack surface growth. We also investigate that an increase in the AGEs level can result in increased brittleness. The developed model and findings of the present study provide region-dependent information on crack growth trajectories as well as more understanding of crack surface growth at the presence of filled tubules.

Fatigue behavior and digital image correlation monitoring of steel plates with mixed-mode edge cracks repaired with CFRP materials

In recent years, carbon fiber reinforced polymer (CFRP) has been widely used to improve the fatigue behavior of steel structures, while most relevant studies were focused on steel components with mode I cracks. This study aims to investigate the fatigue behavior of steel plates with mixed-mode I/II edge cracks patched with CFRP sheets or plates. A total of eleven specimens were fabricated and tested. A digital image correlation (DIC) system was employed as a non-contact measurement to monitor the fatigue crack propagation. Post-processed displacement fields were used to calculate stress intensity factors (SIFs) near the crack tips. Experimental results showed that double-sided CFRP repairing could significantly improve the fatigue life of edge-cracked specimens, especially those with mode I crack rather than mixed-mode I/II crack. Corresponding finite element (FE) analyses were conducted, and good consistency was achieved with test results of crack growth trajectories and fatigue lives. Further FE analysis considered three parameters: load application angle, CFRP layer number, and initial damage level.

Bifurcation and propagation of mixed mode fatigue crack in steel plates repaired with prestressed CFRP laminates

The mixed-mode crack propagation model was proposed to predict crack growth trajectory of a central cracked tensile steel plate with prestressed carbon fiber-reinforced polymer (CFRP) reinforcement through verification of previous experiments. A sensitivity analysis of different parameters including CFRP fiber orientation, initial crack geometry, and prestress level was conducted to investigate CFRP repairing efficiency by using a combination of the programs FRANC3D and ABAQUS. The results show that the applied loading direction primarily governs the bifurcation angle of crack propagation. Increasing prestress level of CFRP along the applied loading direction can achieve ten-fold repairing efficiency of damaged steel structures.

A generalized model for dynamic mixed‐mode fracture via state‐based peridynamics

AbstractA generalized model is developed to investigate dynamic crack propagation in isotropic solids under mixed‐mode I/II conditions using state‐based peridynamics. The critical stretch and the critical strain energy release rate (ERR) are related within the state‐based peridynamic framework to construct a computational model capable of capturing fracture energy of the kinked cracks. A novel formulation is presented to predict crack growth trajectory and pattern by combining the traditional expression of ERR and the peridynamic states of the crack opening and sliding displacements. The proposed model is used to predict dynamic fracture behavior in polymethyl methacrylate (PMMA) and soda‐lime glass using various test specimens, including cracked semi‐circular bending (SCB), cracked rectangular plate, and single edge‐notched tensile (SENT) specimens, and under different dynamic loading conditions. The developed model is examined against the numerical and experimental data available in the literature, and a very good agreement is observed.

Residual stress influence on fatigue crack propagation of CFRP strengthened welded joints

In order to take into account the influence of welding residual stresses on fatigue crack growth, thermo-elastic-plastic finite element models of steel cruciform welded joints were developed by the ABAQUS software. The distribution and magnitude of longitudinal and transverse residual stresses were obtained in consideration of different welding currents and speeds. Uniaxial tensile fatigue tests on cracked cruciform joints strengthened with carbon fiber reinforced polymer were conducted. The coupling actions of residual stresses and fatigue loads were applied to subsequently simulate fatigue crack propagation via using the Extended Finite Element Method. Good agreement between the simulated and theoretical transverse residual stresses at the weld toe along the plate thickness direction verifies the accuracy of numerical results. The welding speed has a greater impact on residual stresses than the welding current. The stiffness ratio of carbon fiber reinforced polymer and steel plate is larger, and a better reinforcement effect will be achieved. Whether specimens repaired or not, it significantly decreases the fatigue life of cracked welded joints in the presence of residual stresses, but the fatigue crack growth trajectory is almost unchanged.

The shear behaviors of concrete-gypsum specimens containing double edge cracks under four-point loading conditions

In this investigation, the fracture behavior of concrete-gypsum samples consisting of edge joints (planer and echelon joints) under four-point bending tests has been investigated using numerical simulation and experimental testing. For this purpose, concrete and gypsum rectangular samples with a dimension of 30 cm * 15 cm * 5 cm have been prepared. These slabs have edge notches in their volume. The lengths of these notches vary by 2 cm in increments of 2 cm, from 2 cm to 6 cm. The slabs were attached with glue. This complex was tested and simulated numerically under four-point loading conditions. The results indicate that the crack growth trajectory is affected by the type of slab material. The strength of samples is controlled by notch length. Numerical simulation outputs are in good accordance with experimental test results.

Three-dimensional non-planar crack growth analysis using enriched finite elements

The paper presents computational mixed mode non-planar fatigue crack growth analyses using Fracture and Crack Propagation Analysis System (FCPAS), which employs enriched crack tip finite elements to calculate the mixed mode stress intensity factors (SIFs) and utilizes from other sub-modules to predict the evolving crack growth trajectories and the resulting fatigue crack growth lives. Numerical applications on different problems selected from the literature; a hollow shaft, an H-shaped specimen and cylindrical rods containing cracks with different initial orientations and sizes and subjected to different fatigue loading types are presented. Comparisons of results from the numerical analyses with the corresponding data from the literature agree well in terms of computed SIFs, predicted evolving crack paths and crack propagation lives.

Finite Element Simulation of a Crack Growth in the Presence of a Hole in the Vicinity of the Crack Trajectory.

The aim of this paper was to present a numerical simulation of a crack growth path and associated stress intensity factors (SIFs) for linear elastic material. The influence of the holes’ position and pre-crack locations in the crack growth direction were investigated. For this purpose, ANSYS Mechanical R19.2 was introduced with the use of a new feature known as Separating Morphing and Adaptive Remeshing Technology (SMART) dependent on the Unstructured Mesh Method (UMM), which can reduce the meshing time from up to several days to a few minutes, eliminating long preprocessing sessions. The presence of a hole near a propagating crack causes a deviation in the crack path. If the hole is close enough to the crack path, the crack may stop at the edge of the hole, resulting in crack arrest. The present study was carried out for two geometries, namely a cracked plate with four holes and a plate with a circular hole, and an edge crack with different pre-crack locations. Under linear elastic fracture mechanics (LEFM), the maximum circumferential stress criterion is applied as a direction criterion. Depending on the position of the hole, the results reveal that the crack propagates in the direction of the hole due to the uneven stresses at the crack tip, which are consequences of the hole’s influence. The results of this modeling are validated in terms of crack growth trajectories and SIFs by several crack growth studies reported in the literature that show trustworthy results.

On the influence of different in-plane biaxial loading conditions over FCG lives

In-plane biaxial loading conditions have a strong influence over fatigue crack growth trajectories and lives. Under equal and proportional loadings on both axes, pure mode I propagation occurs. Mixed mode conditions were simulated using different biaxial load ratios, and mode II propagation can be introduced when different loading phases or mean load values are used. Using an automatic algorithm, different in-phase and out-of-phase loading conditions were simulated in a cruciform specimen. Fatigue life is proportional to initial notch angle β, but inversely proportional to the load phase shift ϕ. The present results increase mixed mode fatigue crack propagation understanding.

Damage analysis of human cortical bone under compressive and tensile loadings

Developing advanced fracture tools can increase the understanding of crack growth trajectories in human cortical bone. The present study investigates fracture micromechanics of human cortical bone under compressive and tensile loadings utilizing a phase field method. We construct two-dimensional finite element models from cortical microstructure of a human tibia cross section. We apply compression on the cortical bone models to create compressive microcracks. Then, we simulate the fracture of these models under tension to discover influential parameters on microcracks formation and post-yielding behavior. The results show that cement lines are susceptible sites to damage nucleation under compression rather than tension. The findings of this study also indicate a higher accumulation of initial damage (induced by compression) can lead to a lower microscopic stiffness as well as a less resistant material to damage initiation under tension. The simulations further indicate that the post-yielding properties (e.g., toughness) can be dependent on different variables such as morphological information of the osteons, the initial accumulation of microcracks, and the total length of cement lines.