Central Notch Research Articles

Unifying acoustic emission and digital imaging observations of quasi-brittle fracture

Acoustic emission (AE) and digital image correlation (DIC) were used to characterize the fracture process zone (FPZ) in Berea sandstone, a quasi-brittle material with a maximum grain size of 1 mm. The complementary techniques of AE and DIC provide information on (i) damage throughout the volume, including AE locations and relative energy, and (ii) detailed DIC measurements of opening displacements associated with the FPZ. Three types of specimens were tested by three-point bending: center notch, smooth boundary, and large radius center notch. Experimental results indicate the following: (1) The length of FPZ is about 10 times longer than the maximum grain size. (2) The evaluation of energy based on the two different measurements, AE and DIC, is consistent with a linear softening law for the FPZ. (3) The fracture energy is estimated to be 120–140 J/m2, about seven times greater than the fracture energy based on linear fracture mechanics.

Fracture Response of Fine-Grained Cement-Based Composite Specimens with Special Inclusions

This paper concerns research into the importance of the interfacial transition zone around inclusions of selected materials in fine-grained cement-based composite. Tests were performed on eight sets of prismatic test specimens. The sets differed in the inclusion materials used, which were placed at midspan above the initial central edge notch. The first was a reference set without any inclusion, the second contained a steel inclusion, four more contained different types of rock inclusion, the seventh contained an inclusion of extruded polystyrene, and the last contained a space of the same dimensions as that occupied by the inclusions in sets 2 to 7. The test specimens were subjected to three-point bending fracture tests at the age of (usually) 28 days. The fracture response was analysed by means of fracture mechanics theory, and apparent mechanical fracture parameters (modulus of elasticity, fracture toughness and fracture energy) were evaluated. The conclusion shows that a possible relationship exists between the differences in the mechanical fracture parameters of specimens with/without an inclusion and the existence of the interfacial transition zone.

The effect of aging methods on the fracture toughness and physical stability of an oxirane/acrylate, ormocer, and Bis-GMA-based resin composites.

To determine the effect of aging methods on the fracture toughness of a conventional Bis-GMA-based resin composite (Filtek Supreme), an ormocer-based resin composite (Admira), and an experimental hydrophobic oxirane/acrylate interpenetrating network resin system (OASys)-based composite. A 25 × 5 × 2.8-mm stainless-steel mold with 2.5mm single-edge center notch, following ASTM standards [E399-90], was used to fabricate 135 specimens (n = 15) of the composite materials and randomly distributed into groups. For the baseline group, specimens were fabricated and then tested after 24-h storage in water. For the biofilm challenge, specimens were randomly placed in a six-well tissue culture plate and kept at 37°C with bacterial growth media (Brain Heart Infusion (BHI); Streptococcus mutans) changed daily for 15days. For the water storage challenge, specimens were kept in 5ml of deionized distilled autoclaved water for 30days at 37°C. μCT evaluation by scanning the specimens was performed before and after the proposed challenge. Fracture toughness (KIc) testing was carried out following the challenges. μCT surface area and volume analyses showed no significant changes regardless of the materials tested or the challenge. Filtek and Admira fracture toughness was significantly lower after the biofilm and water storage challenges. OASys mean fracture toughness values after water aging were significantly higher than that of baseline. Toughness values for OASys composites after biofilm aging were not statistically different when compared to either water or baseline values. The fracture toughness of Bis-GMA and ormocer-based dental resin composites significantly decreased under water and bacterial biofilm assault. However, such degradation in fracture toughness was not visible in OASys-based composites. Current commercial dental composites are affected by the oral environment, which might contribute to the long-term performance of these materials.

Notch failure in laminated composites under opening mode: The Virtual Isotropic Material Concept

Experimental and theoretical fracture investigations are performed on laminated glass/epoxy composite specimens with different numbers of ply and lay-up configurations weakened by central U-shaped notches of various tip radii and loaded under pure opening mode. Since the main purpose of this research is to evaluate the load-carrying capacity (LCC) of the U-notched glass/epoxy composite specimens, it is experimentally recorded by the testing machine and the failure behavior of the specimens is carefully observed. To predict the experimentally obtained LCCs or the last-ply-failure (LPF) loads theoretically, a novel concept, called Virtual Isotropic Material Concept (VIMC), is proposed and linked to two well-known stress-based brittle fracture models in the context of the linear-elastic notch fracture mechanics (LENFM), namely the maximum tangential stress (MTS) and the mean stress (MS) criteria. It is shown that both VIMC-MTS and VIMC-MS combined criteria can predict the experimental results well without the need for ply-by-aply failure analysis, the first-ply-failure (FPF) prediction, and the progressive damage modeling (PDM) etc. Thanks to both VIMC and LENFM, the LPF prediction is direct, rapid, and convenient, because only two distinct fracture parameters, namely the ultimate tensile strength and the trans-laminar fracture toughness of laminate are necessary for LPF prediction.

Components of the Fracture Response of Alkali-Activated Slag Composites with Steel Microfibers

Knowledge of the mechanical and primarily fracture parameters of composites with a brittle matrix is essential for the quantification of their resistance to crack initiation and growth, and also for the specification of material model parameters employed for the simulation of the quasi-brittle behavior of structures made from this type of composite. Therefore, the main target of this paper is to quantify the mechanical fracture parameters of alkali-activated slag composites with steel microfibers and the contribution of the matrix to their fracture response. The first alkali-activated slag composite was a reference version without fibers; the others incorporated steel microfibers amounting to 5, 10, 15 and 20% by weight of the slag. Prism specimens with an initial central edge notch were used to perform the three-point bending fracture tests. Load vs. displacement (deflection at midspan) and load vs. crack mouth opening displacement diagrams were recorded during the fracture tests. The obtained diagrams were employed as inputs for parameter identification, the aim of which was to transfer the fracture test response data to the desired material parameters. Values were also determined for fracture parameters using the effective crack model, work-of-fracture method and double-K fracture model. All investigated mechanical fracture parameters were improved by the addition of steel microfibers to the alkali-activated matrix. Based on the obtained results, the addition of 10 to 15% of microfibers by weight is optimal from the point of view of the enhancement of the fracture parameters of alkali-activated slag composite.

Notch tip displacements of the concrete Brazilian disc test with central notch analysed by the concrete damaged plasticity model

A numerical parametric study has been performed on a Brazilian disc test with a central notch. In this study, the post peak crack initiation and propagation in this test is presented based on a concrete damaged plasticity model. The influence of the fracture energy Gf and the shape of the post peak tensile softening curve on the crack initiation were considered. Focus was placed on the notch tip displacements as to separate mode I and mode II displacements. For this, the nodal displacements were transformed based on the geometry (notch inclination angle), linear elastic fracture mechanical criteria, and plasticity conditions in order to help to distinguish the fracture modes. It was observed that, by choosing the right transformation angle, mode I and mode II fracture processes can be distinguished on such a test.

Multi-axial fatigue numerical crack propagation in cruciform specimens

Two cracks, initiated from the opposite tips of a central notch inclined by 45°, were considered in cruciform specimens made of Ti6246. A static load was applied to a cruciform arm while a cyclic load was applied along the other arm. Fatigue propagation of cracked specimens was performed by means of Dual Boundary Element Method (DBEM) and Finite Element Method (FEM) codes. For crack path assessment, the Minimum Strain Energy Density (MSED) and the Maximum Tensile Stress (MTS) criteria were adopted in DBEM and FEM approaches, respectively. Moreover, the J and M integrals’ formulations were used to evaluate the SIFs along the crack fronts for DBEM and FEM codes, respectively. Crack-growth rates were predicted by using a Walker law, calibrated on mode I fracture experimental data. A good agreement between numerical and experimental crack paths was obtained.

A new genus and species of extinct ground shark, †Diprosopovenator hilperti, gen. et sp. nov. (Carcharhiniformes, †Pseudoscyliorhinidae, fam. nov.), from the Upper Cretaceous of Germany

ABSTRACTWe describe a new genus and species of extinct ground shark, †Diprosopovenator hilperti, gen. et sp. nov. (Elasmobranchii, Carcharhiniformes), based on a single incomplete skeleton with dentition recovered from basinal marine late Cenomanian (Metoicoceras geslinianum ammonite zone) organic-rich deposits of northern Germany. The new carcharhiniform is characterized by a unique combination of dental morphologies, indicating close architectural resemblance to the family Scyliorhinidae (catsharks). However, the very distinct tooth root morphology readily separates the new taxon from all other scyliorhinids. The extinct Cretaceous carcharhiniform †Pseudoscyliorhinus (represented by †Ps. schwarzhansi and †Ps. reussi) shares tooth root morphologies and vascularization patterns with †Diprosopovenator, gen. nov. We hypothesize that these two sharks form part of an extinct group of carcharhiniforms characterized by a distinct root morphology (viz., low hemiaulacorhize roots with very flat and strongly flared basal faces protruding below the crown labially and mesiodistally and with a well-developed central labiobasal notch). Consequently, we propose a new family of Late Cretaceous carcharhiniforms, †Pseudoscyliorhinidae, fam. nov., to include the new taxon, as well as †Pseudoscyliorhinus. †Pseudoscyliorhinidae, fam. nov., shows a wide European distribution during the Late Cretaceous, ranging from the early Cenomanian to the late Campanian. The longevity of Scyliorhinidae, with a fossil record extending back into the Middle Jurassic, however, remains ambiguous and unresolved; therefore, it may be best to regard the assignment of fossil taxa to Scyliorhinidae as currently uncertain pending further taxonomic work.

Combined static-cyclic multi-axial crack propagation in cruciform specimens

Two cracks, initiated from the opposite tips of a 45° inclined central notch, were considered in cruciform specimens made of Ti6246. A static load was applied along one arm of the specimen and a cyclic load (R = −1) was applied along the other arm. Crack propagation was carefully monitored by optical means for different ratios of static to cyclic load. The observed crack propagation was simulated using two numerical tools, involving two different mixed-mode crack propagation prediction methods. The experimental evidence shows that there is a switch in crack propagation direction from orthogonal to the cyclic load at low static load levels to orthogonal to the static load for high static load levels. Both numerical procedures were able to predict this switch, albeit at slightly different static to cyclic load ratios.

Visual detection of a cohesionless crack in rock under three-point bending

Crack initiation and propagation in rock involve the development of a nonlinear zone around the crack tip called fracture process zone. The existence of fracture process zone influences the fracture behavior and therefore it must be carefully investigated. This zone is normally idealized as a cohesive zone whose mechanical properties are difficult to measure. In this study, a relatively simple approach is proposed to identify the properties of the cohesive zone and the length of the cohesionless crack in a sandstone specimen under three-point bending. Two types of specimens were tested: beams with center notch and with smooth boundary. The digital image correlation (DIC) was utilized to obtain the opening displacement around the position where the fracture initiated. For a small length of a horizontal section around the specimen center, the material is considered to be in the state of uniaxial tension and its behavior is interpreted by the cohesive zone model.The proposed approach discusses three types of opening displacement distribution patterns (I), (II), (III). Pattern (I) is related to tensile loading of the material, pattern (II) suggests the development of material softening within the cohesive zone and pattern (III) indicates the development of the cohesionless crack. These displacement patterns together with the appropriate reference loadings are used to identify the length of the cohesionless crack. For example, observation of pattern (III) is consistent with the development of the cohesionless crack when the reference loading is the beginning of experiment. Further, the proposed method is useful for measuring the critical crack opening displacement and the fracture energy.

Modelling of cracking of the ceramic foam specimen with a central notch under the tensile load

In this contribution, open cell ceramic foam structures composed of regular/irregular shape cells and containing a macroscopic central notch/crack were investigated in terms of their cracking upon the tensile loading and their strength was predicted using the FE simulations. The developed model of the real ceramic foam specimen containing a central notch/crack was subjected to a tension, resulting in a failure beginning at the tip of the notch. The work discusses an approach how to predict the critical failure load and also the crack path in the foam structure. Various cell irregularity and size of the macroscopic notch was considered in the investigations. Predictions of the foam structure cracking were performed using the beam element based FE model having characteristics of the real foam structure and by utilization of the stress criterion which considers failure of particular struts, when the maximum stress on them reaches the tensile strength of the ceramic material. Outputs from simulations were compared with available experimental observations and with an estimation of the critical failure load calculated using the developed analytical model.

Alternative approach to model ductile fracture by incorporating anisotropic yield function

Due to the texture formed in cold/hot rolled forming process, anisotropy is a key issue not only in modeling of plastic deformation but also in characterization of fracture behavior. In this study, an anisotropic ductile fracture criterion is developed by introducing anisotropic parameters into the weight function of an uncoupled shear ductile fracture criterion. The proposed anisotropic ductile fracture is applied to describe the anisotropic characteristics in the ductile fracture of AA6082-T6. Ductile fracture behavior of AA6082 is experimentally investigated at the different loading conditions: shear by in-plane torsion test, uniaxial tension by specimens with a central hole, plane strain tension by notched specimens, and the balanced biaxial tension by the Nakajima test. In-plane torsion and tension tests with a central hole and notch are conducted along three directions: rolling direction, diagonal direction and transverse direction. Specimen deformations during the tests are recorded and fracture strains are measured by digital image correlation approach. The measured fracture strains are then utilized to calibrate the parameters in the proposed ductile fracture criterion. With the calibrated ductile fracture criterion, the fracture locus and anisotropic ductile fracture in various loading conditions are predicted and compared with experimental measurement and those predicted by linearly transformed anisotropic fracture model to investigate the predictability of the proposed ductile fracture criterion. The comparison demonstrates that the anisotropic fracture of AA6082 is predicted by the proposed criterion with good agreement in the different loading directions of shear, uniaxial tension, plane strain tension, and the balanced biaxial tension. Considering the high accuracy of the proposed ductile fracture criterion, it is expected that the proposed anisotropic ductile fracture criterion can improve the reliability of failure prediction in metal forming for materials with strong directionality in fracture.

Fracture Resistance of Alkali Activated Concrete under the Mixed Mode I/II Load Conditions

Nowadays, traditional concrete mixture uses as a binder well known Portland cement. However, the production of the Portland cement is not environmentally friendly, due to high production of CO2 in the fabrication process. In recent years, there are some trends to use secondary materials as a binder or as replacement of aggregate in the process of making the concrete mixture. This modified material uses alkali reaction in the hardening of fresh mixture, therefore an alkali activated concrete (AAC) term is used. This AAC is then used in formwork as it was traditional concrete, due to similar properties. Despite the use of advanced material, standards for structural design do not provide any instruction for practical application. Subsequently, the knowledge of fracture of this material is limited. The fracture mechanical properties help to perform advanced structural analysis, especially when some of the structural elements have a crack. The load presence on the structure can be divided into tensile, shear, and into combination of tension and shear. Therefore, it is necessary to perform test, which covers mixed mode I/II loading conditions. One of the tests usually used for the evaluation of fracture resistance of concrete is the Brazilian disc test with a central notch. This contribution evaluates the fracture resistance of alkali activated concrete, which will be used as a possible replacement for traditional structural concrete with cement binder, subjected to mixed mode I/II loading. The generalized maximum tangential stress (GMTS) criterion was used for the evaluation of the fracture resistance curve.

Relationship between Fracture Toughness and Specimen Thickness for Quasi-isotropic Titanium/Epoxy Laminates

Abstract The fracture properties like toughness of the trans-laminar fracture was calculated for the Titanium/epoxy laminate in a series of center notched quasi isotropic IM7/8552 which is of 3mm and 9mm scaled specimen thickness. The main objective of the paper was to find out that there is a toughness of the fracture change in the transition laminate thickness. The center notches of the specimens with 12.8mm and 25.6mm was found out that there is no dependency on specimen thickness. The potential causes are discussed with the compared discrepancy of the previous literature.

The influence of polygonal cavity on fracture behaviour of concrete

In this work, the influence of polygonal cavity on fracture behaviour of cement composite (concrete) is investigated. Specimens of the nominal dimensions 40 × 40 × 160 mm with polygonal cavity of 8 × 8 × 40 mm were provided with an initial central edge notch with a depth 12 mm, which was made by diamond blade saw. To determine the influence of polygonal cavity on fracture behaviour, fracture tests were conducted via three-point bending. The aim of this work is to analyse the behaviour of such specimen by means of finite element method (FEM) principles in Ansys, Inc. software. For this reason, a simplified 2D model was created for plane strain conditions and based on the fracture test configuration. The crack propagation assessment was based on generalized fracture mechanics approaches using a criterion of an average value of tangential stress determined in dependence on the polar angle θ. Results of numerical analysis indicates that the actual crack depth must be greater than it supposed. In other words, diamond blade saw damage the specimen more than expected.

On crack propagation in homogeneous and composite materials under mixed mode loading conditions

The direction of crack propagation under mixed mode loading conditions is investigated by FEM simulation in comparison with delamination experiments performed in the 4 point bending mode. Composites consisting of aluminum nitride attached to copper by active metal brazing were delaminated with use of a central notch for crack initiation. The main crack line propagated along the interface direction. However, SEM micrographs revealed that the crack line propagating along the interface is subjected to bifurcation. Small cracks digress from the main delamination line under kinking angles of 90° until they are stopped at the copper substrate. The observed behavior of crack propagation is studied by Linear Elastic Fracture Mechanics and by nonlinear Finite Element Analysis. In fact, the bifurcation angle of 90° can be considered as an indication for dominant influence of geometrical nonlinearities at the crack tip. Finite Element Analysis is performed in two stages starting from macroscopic level and then the analysis of crack tip behavior is continued on a microscopic level. On the macroscopic level, the whole experimental setup is simulated in order to derive an approximation of the stress distribution around the crack tip. Thereafter, the analysis is further extended on microscopic level, whereby local mesh refinement is continued until the element size approaches the dimension of the lattice constant. Thus, high stress values at the crack tip lead to considerable amounts of material rotation. Consequently, the observed direction of crack extension may be derived from the maximum hoop stress criterion.

Discrete‐Continuum Duality of Architected Materials: Failure, Flaws, and Fracture

Abstract3D nano‐ and micro‐architected materials are resilient under compression; their susceptibility to flaws and fracture remain unexplored. This work reports the fabrication and tensile‐to‐failure response of hollow alumina nanolattices arranged into 5 µm octet‐truss unit cells. Some specimens contained through‐thickness center notches oriented at different angles to the loading direction, with a length‐over‐sample‐width ratio of 0.45. In situ tensile experiments reveal that for all orientations, failure initiates at the notch root, followed by instantaneous crack propagation along lattice planes orthogonal to extension. A tensile strength of 27.4 ± 0.7 MPa is highest for unnotched samples and decreases as notch orientation varies from 0° to 90° to its minimum, 7.2 ± 0.4 MPa; their specific tensile strength is ≈4 × higher than that for all other low‐density materials. Finite element simulations reproduce observed strengths and failure mechanisms: initial cracks always initiate at the nodal junctions with highest stress concentrations by tearing of alumina walls at the nodes. Subsequent crack propagation shifts maximum stress concentration to the nodes along lattice plane orthogonal to the loading direction. A modified analytical fracture model based on the effective notch length predicts tensile strengths consistent with experiments. These findings imply that continuum fracture mechanics can predict failure in nano‐architected materials, which helps develop advanced materials through informed architectural design.

Impact Analysis of Pocket Damper Seal Geometry Variations on Leakage Performance and Rotordynamic Force Coefficients Using Computational Fluid Dynamics

In this paper, different notch and partition wall arrangements of a fully partitioned pocket damper seal (FPDS) are investigated using computational fluid dynamics (CFD). The CFD model is derived for a baseline FPDS design reflecting the full sealing configuration with a structured mesh. Steady-state simulations are performed for eccentric rotor position and different operational parameters. The results are validated using experimental cavity pressure measurements. In transient computations, rotor whirl is modeled as a circular motion around an initial eccentricity using a moving mesh technique. Different whirl frequencies are computed to account for the frequency-dependent behavior of damper seals. The stiffness and damping coefficients are evaluated from the impedances in the frequency domain using a fast Fourier transform. The validated model is then transferred to varying designs. In addition to the baseline design, six different notch arrangements with constant clearance ratio were modeled. Moreover, two partition wall design variations were studied based on manufacturability considerations. Predicted leakage as well as frequency-dependent stiffness and damping coefficients are presented and the impact of geometry variations on these parameters is discussed. The results suggest that a single centered notch is favorable and indicate considerably higher effective damping for a design with staggered partition walls. A rounded partition wall design with significantly eased manufacturing reveals good performance.

Comparison of Double- and Single-Bonded Repairs to Symmetrical Composite Structures

The object of this study is an experimental analysis of the repair of a laminate composite damaged by central circular notch. The effects of the repair technique used, single or double patch, the nature of the patch and its stacking sequence, were highlighted. The main results show that the performance of the repair depends on several parameters, namely the nature of the patch and its stacking sequence, the technique repair used.

The Application of Full-Field Techniques to Estimate both Tensile and Fracture Properties: an Investigation into Modifications to Standard Sample Geometries

This paper investigates modifications to the Brazilian disk and compact tension C(T) standard test geometries to allow full-field extraction of elastic tensile and toughness properties. A central notch has been introduced in the Brazilian disk to allow for the extraction of fracture properties, while the C(T) sample has been lengthened to allow for the extraction of tensile properties. Full-field displacements, measured on samples prepared from PMMA (Polymethyl methacrylate) using digital image correlation are analysed under the assumption of linear elasticity. First, the Virtual Fields Method is applied to estimate Young’s Modulus (E) and Poisson’s Ratio (v). These tensile properties are then used to determine estimates for the peak stress intensity factor (SIF) prior to fracture through a non-linear least squares field fitting approach. Test results show that a modified disk sample performed well in both analysis approaches with relative errors obtained as: 2.1% in E, 12.9% in v and 1% in SIF. A modified C(T) sample obtained relative errors of: 1.5% in E, 40.2% in v and 1% in SIF. Furthermore it is shown that field fitting approaches are less sensitive to error in v than error in E. The presented evidence aims to guide future experiments utilizing full-field techniques to study material properties in the framework of fracture mechanics, in particular in applications where limited material for obtaining tensile properties is available.