Blunt Notches Research Articles

Accurate comparison of the fracture toughness of ultra-thick polycrystalline diamond plates by ISO standard method

Due to the difficulty in preparing ultra thick diamonds, current research on the mechanical properties of diamonds mostly focuses on thin samples, which cannot represent the true mechanical properties. In this study, DC arc plasma jet chemical vapour deposition method was used to deposit ultra-thick diamond plate measuring Ø125 mm × 6.5 mm. The size of 18 mm × 4 mm × 3 mm sample were prepared. The samples with dimensions of 18 mm × 4 mm × 3 mm were prepared. For the first time, fracture toughness test samples meeting the ISO 15732 requirements were prepared by using the single-sided beam pre-crack method. The accurate fracture toughness of ultra-thick diamond with pre-crack was obtained using the three-point bending method, 6.5 MPa·m1/2. Samples with sharp or blunt notch by laser cutting were used for comparison. The sharp notch sample had a value similar to that of the pre-crack sample, 6.3 MPa·m1/2. The value of the blunt notch sample was relatively large, 7.5 MPa·m1/2. The effects of defects and grain size on fracture toughness and the reasons for the differences in test results for different notches were analyzed. Overall, obtaining accurate fracture toughness values of ultra-thick diamond by ISO standard is crucial for industrial applications.

Initiation and growth of fatigue cracks in sheets with U-shaped notches in the first and mixed modes of fracture

Initiation and growth of fatigue cracks in sheets with U-shaped notches in the first and mixed modes of fracture

Asymptotic stress field for the blunt and sharp notches in bi-material media under mode III loading

Abstract This study introduces a novel approach to analyze the stress and displacement fields around blunt notches in bi-material media, focusing on mode III loading conditions. The eigenfunction expansion method is used to derive a simplified yet accurate solution, satisfying the boundary conditions for bi-material blunt V-notches. The robustness of the proposed asymptotic solution is validated through several finite element analyses, encompassing a range of notched geometries such as blunt V-notches, VO-notches, and circular holes. Notably, it is demonstrated that when the notch tip radius approaches zero, the solution coincides with the existing sharp V-notch model, illustrating the robustness of the methodology.

Sensitivity analysis of notch shape on brittle failure by using uni-bond dual-parameter peridynamics

The brittle failure of components weakened by sharp or blunt notches is a topic of active and continuous research. Notches created during the design and manufacturing of structural components give rise to localized stress concentrations, which can generate a crack leading to catastrophic failure or to a shortening of the assessed structural life. To investigate how notches influence the fracture and bearing capacity of brittle materials by using peridynamics (PD), an extended uni-bond dual-parameter peridynamic (UDPD) model that can overcome the fixed Poisson’s ratio in bond-based PD and address the attenuation effect of the nonlocal PD force is developed. The expressions of normal stiffness and tangential stiffness with elastic modulus and Poisson’s ratio are derived and rewritten. Additionally, the critical microstrain energy density for the extended UDPD model is given to judge the fracture initiation, and the validity and accuracy of the proposed model are verified by four examples. Ultimately, six typical types of notches, i.e., rectangular notches, sharp V notches, U notches, blunt V notches, keyhole notches, and VO notches, were selected and investigated in brittle plates with four different tip radii to study the notch sensitivity of brittle failure to notch shape by using the extended UDPD model. The results show that the crack path and bearing capacity of the structure are sensitive to the notch shape and the tip radius of the notch, and a blunt notch with a larger tip radius (U notch, blunt V notch, keyhole notch, and VO notch, tip radius ρ⩾2mm) offers better performance in terms of structural safety than a sharp notch or a notch with a smaller tip radius.

Numerical and experimental analysis of the notch effect on fatigue behavior of polymethylmethacrylate metal based on strain energy density method and the extended finite element method

Abstract This work investigates the effect of the notch on fatigue behavior by combining two methods: the extended finite element method (XFEM) and the averaged strain energy density (ASED) method, which considers the combined action of bending and shear loading. The ASED method has already been proven accurate for assessing the failure of components in the presence of sharp and blunt notches, and several results are available in the literature for different materials. These results were compared with those obtained from the experimental tests reported here. The main purpose of this study was twofold: The first part is an experimental study of fatigue in rotary bending of specimens weakened by U and V notches made of polymethyl-methacrylate (PMMA) material. Two values for the radius were used for the U-notches (0.2 and 2 mm) and two angles for the V-notches (20° and 140°). The second part of the study consisted of performing several simulation tests using the Cast3m software for different angles and radii. The local approach based on the mean value of the ASED acted over a finite-sized volume surrounding the highly stressed regions. The maximum principal stress located at the notch edge defined the center of the control volume. If the notch is blunt, the control volume assumes a crescent shape with its width measured along the notch bisector line. When the notch is considered pointed (V-notched) or is a crack, the control volume becomes a circle with its center at the notch tip. The presence of geometric discontinuities in structures affects their lifetime by reducing it, producing a high concentration of local energy around the notch tip. Good convergence was obtained between the numerical simulation and experimental results for the ASED in a finished zone surrounding the notch tip.

Blunt notch effect on the fatigue response up to 109 cycles of selective laser melting Ti6Al4V specimens

AbstractIn this paper, the influence of a blunt notch on the VHCF response of SLM Ti6Al4V specimens is investigated. Ultrasonic fully reversed tension–compression tests up to 109 cycles were carried out on unnotched specimens and specimens with a blunt notch. Unnotched specimens show a slightly larger fatigue response, with limited differences. All fatigue failures originated from defects, which are bigger in unnotched specimens, mainly due to the different risk volume of the tested specimens and the related size effect. Interactions between notch, stress gradient, and defect size distribution must be considered to properly assess the influence of notch on the VHCF response.

Experimental stress determination of blunt notches under combinations of modes I and II loading

An appropriate evaluation of the stress field for designing new or optimizing existing engineering structures is required. The primary goal of this paper is to use the digital image correlation (DIC) approach to ascertain the stress field around the root of various blunt notches. At first, extensive tests were performed using the Brazilian Disc (BD) specimen containing three distinct notches (U, VO, and Keyhole) under diverse loading conditions, including pure mode I, pure mode II, and mixed-mode I/II. The displacement fields output from the DIC experiments were employed as the input data for a computer program, and the coefficients of the stress and displacement fields were then determined utilizing the over-deterministic technique. Afterward, the computed coefficients were used to calculate the analytical stress field around the notch root by considering singular and higher-order terms for each notch type. Subsequently, the finite element (FE) method was employed to verify the accuracy of the stress field obtained from the DIC experiments. In addition, the influence of some major parameters such as notch opening angle, notch tip radius, and geometry on the stress distribution was investigated. This study validated the efficiency of the DIC approach in determining the unknown stress coefficients of rounded notches, especially the first non-singular term of the stress expansion, which is revealed to have a considerable impact on appraising the exact stress field around the notch curvature.

Critical distance-based fatigue life evaluation of blunt notch details in steel bridges

Orthotropic steel deck (OSD) is applied on many bridges around the world, but its drawback of being prone to fatigue has been a concern due to the damages observed. Fatigue cracks initiated from the blunt notch details in rib-to-floor beam connections have a different fatigue behavior compared to welded connections and deserve to be investigated further. To study the effect of notch radius on the fatigue performance of blunt notch detail, 27 specimens with different geometries were manufactured and tested with fatigue loads. The fatigue lives of specimens and their crack initiation locations were investigated, and the prediction on the fatigue life of notched specimens based on the theory of critical distance (TCD) was also conducted. For notched specimens made of S355, the predicted fatigue life using the TCD method is in good agreement with the experimental results. Also, it is found that the point method has higher accuracy compared to the line method and the use of one calibration curve of notched specimens could provide enough accuracy compared to the case when two calibration curves of notched specimens are used. By modifying the mathematical description of the stress distribution near the notch root, a new formulation of the critical distance-fatigue life relationship is here proposed and validated with the experimental results.

Numerical simulation of creep notched bar of P91 steel

Numerous components designed for use at elevated temperatures now exhibit multiaxial stress states as a result of geometric modification and material inhomogeneity. It is necessary to anticipate the creep rupture life of such components when subjected to multiaxial load. In this work finite element analysis has been performed to study the influence of different notches, namely blunt and medium notches on the stress distribution across the notch throat during the creep exposure. Within the FE model, a ductility exhaustion model based on the Cocks and Ashby model was utilized to forecast the creep rupture time of notched bar P91 material. The lower and upper bound of creep ductility are employed in the FE analysis. Different notch specimens have different stress and damage distribution. It is shown that for both types of notches, the von Mises stress is lower than the net stress, indicating the notch strengthening effect. The accumulation of creep damage in the minimum cross-section at each element across the notch throat increases over time. The point at which damage first occurs is closer to the notch root for the medium notch than for the blunt notch. The long-term rupture life predicted for blunt notch specimens appears to be comparable to that of uniaxial specimens. The upper bound creep ductility better predicts the rupture life for medium notches.

Additive effect of micro-damage zones from nano-scale crack tip and nano-grains for fracture toughness measurements of 3Y-TZP zirconia ceramics

A nano-scale crack tip around 500 nm wide introduced by femtosecond laser still affects the accuracy of fracture toughness KIC measurements of 3Y-TZP zirconia ceramics with average grain size G from 200 to 500 nm. A simple formula was proposed to estimate the additive effect of crack-tip damage zones from an infinitely sharp crack to a nano-scale blunt notch. The error in fracture toughness measurements is less than 8 % if the nano-scale crack-tip width < 0.5·G. The intrinsic KIC can be deduced from the simple formula if the nano-scale crack tip > 0.5·G. This study shows the same KIC was deduced from two different sets of 3Y-TZP measurements with nano- and micro-scale notches of 500 nm and 18 µm wide. Furthermore, the simple formula specifies the relation between the fracture toughness KIC and intrinsic strength ft via grain size G, which means KIC can also be estimated from ft and G without testing pre-cracked specimens. KIC values of 3Y-TZP from specimens with and without pre-cracks were compared.

Evolution of Crack Propagation Rate in Notched Specimens Using XFEM Method under Bending Load Condition

The crack initiation and propagation often occur in structures subjected to fatigue loads and their privileged sites it is the geometric discontinuity in particular the notches. The geometric configuration of the notches always leads to disturbances of stress fields in the vicinity of the notch end as a consequence of the effects on the crack initiation site and on the crack rate. The present study is interested to the evolution of crack speed propagation in the notched specimens subjected to bending. The specimens chosen are made of PMMA material containing two opposite notches U or V that presented two different parameters, a radius for U-notch and angle for V-notch. The variations taken into account for the sharp notches (V-notch) going from the small angle to the large angle, which are 30°; 45°, 90°, and 140°, and for blunt notches (U-notch) the radius takes the different values 0.5, 1, 1.5, and 2 mm. The fracture brittle behavior adapted to this material led to predict the Fatigue crack growth using a modified form of Paris’s law with the equivalent stress intensity factor (ΔKeq) relying on extended finite element method (XFEM) in order to follow the interaction between the notch and the crack on one side and study the evolution of crack growth rate to another side. The variations, which brought to these parameters entailed an influence on the crack propagation speed, which was born at the end of notch of component as well as the variations of equivalent notch intensity stress factors (ΔKeq). The variations made to the parameters of notches have a huge influence on the crack propagation rate.

On the applicability of digital image correlation method in extracting the higher order terms in stress field around blunt notches

Accurate and deep understanding of the stress field has a key role in designing and optimizing the engineering structures. The main objective of the present article is to experimentally investigate the stress field around various blunt notches by means of the digital image correlation (DIC) method. First, several mode I tests were conducted using two types of specimens, namely single edge notch tension (SENT) and single edge notch bending (SENB), each consisting of three different notches (U, VO, and Keyhole). Then, the optical method of DIC was used to determine the stress field around the notch tip by calculating the coefficients of singular and higher-order terms (HOTs) for each notch type. To do so, the output displacement field of the DIC measurements was considered as input data for a computer program, and the coefficients of the stress field were calculated by the least square method (LSM) and an over-deterministic approach. Moreover, the effects of several geometry parameters like notch opening angle and notch tip shape on the stress distribution around the notch were discussed in detail. Finally, the precision of the calculated notch stress intensity factors (NSIFs) and the coefficients of HOTs were studied by comparing the DIC results with those obtained from the finite element (FE) analysis. It is also shown that HOTs of stress field have considerable contribution in more precise determination of the stress field around notches.

Asymptotic stress field around the blunt and sharp notches in bimaterial media under mixed mode I/II loading

This paper provides a simple approximate solution for the stress and displacement fields around the blunt notches in bimaterial media under in-plane loading. The Kolosov-Muskhelishvili's method is used to determine the stress and displacement components according to the complex potential functions. Then, by imposing the boundary conditions of bimaterial blunt V-notches, the asymptotic solutions of the stress and displacement fields are obtained. Due to the convenient selection of the boundary conditions, the solution is shown to be the same as the one proposed by Williams’ for sharp V-notches, in case the notch tip radius becomes zero. Finally, finite element method is employed to benchmark the precision of the suggested asymptotic solution. Some sample examples are selected, and the results obtained by the proposed analytical solution are compared with the numerical results of the finite element method. It is demonstrated that the proposed stress field is not only applicable to obtain the stress distribution around the blunt V-notches but also is suitable for stress field calculation around some other types of bimaterial notches.

Static and fatigue behavior in presence of notches for polyamide 12 (PA12) additively manufactured via Multi Jet Fusion™ process

Static, fatigue and notch sensitivity tests were performed on Multi Jet Fusion™ (MJF) Polyamide 12 (PA12) specimens in unnotched conditions or with blunt/sharp notches. Stress concentration factors, and potential applicability of theory of critical distances (TCD) were investigated. Fracture surfaces were comparatively analyzed for quasi-static, fatigue and cryogenic failures. Stress-Life curves were determined and MJF-PA12 showed static and fatigue properties comparable to conventional PA12. The blunt notch had limited impact on fatigue strength, with failure onsetting from internal defects. The sharp notch showed low fatigue notch sensitivity but reduced static strength and fatigue life, with failure onsetting from notch tip.

A Structural Stress Approach Accounting for Notch Effects on Fatigue Propagation Life: Part I Theory

This paper presents the Notch Structural Stress method for reflecting the notch effect on fatigue crack propagation lives, which is based on a closed-form stress solution along the ligament and an analytical KⅠ solution for the crack propagating under notch effect. Besides that, the validity of the proposed method is further verified by carrying out the double V-notch fatigue tests and reanalyzing the blunt notch fatigue tests reported in the literature. Compared with the often-used stress procedures, the Notch Structural Stress parameter provides a more effective consolidation of the S-N data from different notch angles, notch types, and load types.

Modelling fracture process zone width and length for quasi-brittle fracture of rock, concrete and ceramics

The crack-tip fracture process zone (FPZ) length with distributed cohesive stresses is commonly modelled for quasi-brittle fracture of heterogeneous solids. This study highlights the crack-tip blunting effect from FPZ width since FPZW > FPZL at the peak fracture load. Both FPZ width and length are linked to the microstructure (grain size for rock and ceramics, aggregate size for concrete, atomic diameter for single crystal silicon), providing a fresh perspective on quasi-brittle fracture phenomena. Importantly, FPZW at the peak fracture load bridges the gap between the fracture toughness KIC and tensile strength ft, i.e. KIC ↔ FPZW ↔ ft. The influence of a blunt notch on quasi-brittle fracture can also be explained by a widened FPZW. A closed-form model containing both FPZW and FPZL (approximately FPZW/FPZL ≈ 2 at the peak fracture load) is used to analyse experimental data of rock, concrete and ceramic with macro-/micro-sized FPZ, and single crystal silicon with FPZ-like critically stressed atomic bonds in front of atomic scale defects.

Stress distributions in orthotropic solids with blunt notches under in-plane shear loadings

The present work is devoted to the analysis of the stress distributions in orthotropic solids weakened by blunt notches and loaded under in-plane shear. In particular, using Lekhnitskii's approach, new closed form equations are derived for the stress components, explicitly accounting for the notch geometrical features, namely the notch radius and the opening angle, in conjunction with the elastic material properties.Three main geometries are considered, described using proper conformal mappings: lateral symmetric hyperbolic notches, parabolic notches and hyperbola-like notches in plates loaded under in-plane shear. Appropriate complex potential functions are introduced in the analytical formulation and analytical expressions for the whole stress fields are derived, taking advantage of free-of-stress boundary conditions along the notch edge.Eventually, the very good accuracy of the new solutions is proved against numerical results, as obtained from a number of two-dimensional finite element analyses carried out on plates with rounded notches under shear, also discussing the main features of the mode II stress fields in notched plates.

Notch fatigue of Cu50Zr50 metallic glasses under cyclic loading: molecular dynamics simulations

Molecular dynamics simulation is performed to simulate the tension–compression fatigue of notched metallic glasses (MGs), and the notch effect of MGs is explored. The notches will accelerate the accumulation of shear transition zones, leading to faster shear banding around the notches’ root causing it to undergo severe plastic deformation. Furthermore, a qualitative investigation of the notched MGs demonstrates that fatigue life gradually becomes shorter with the increase in sharpness until it reaches a critical scale. The fatigue performance of blunt notches is stronger than that of sharp notches. Making the notches blunter can improve the fatigue life of MGs.

Nanofibril-mediated fracture resistance of bone

Natural hard composites like human bone possess a combination of strength and toughness that exceeds that of their constituents and of many engineered composites. This augmentation is attributed to their complex hierarchical structure, spanning multiple length scales; in bone, characteristic dimensions range from nanoscale fibrils to microscale lamellae to mesoscale osteons and macroscale organs. The mechanical properties of bone have been studied, with the understanding that the isolated microstructure at micro- and nano-scales gives rise to superior strength compared to that of whole tissue, and the tissue possesses an amplified toughness relative to that of its nanoscale constituents. Nanoscale toughening mechanisms of bone are not adequately understood at sample dimensions that allow for isolating salient microstructural features, because of the challenge of performing fracture experiments on small-sized samples. We developed an in situ three-point bend experimental methodology that probes site-specific fracture behavior of micron-sized specimens of hard material. Using this, we quantify crack initiation and growth toughness of human trabecular bone with sharp fatigue pre-cracks and blunt notches. Our findings indicate that bone with fatigue cracks is two times tougher than that with blunt cracks. In situ data-correlated electron microscopy videos reveal this behavior arises from crack-bridging by nanoscale fibril structure. The results reveal a transition between fibril-bridging (∼1 μm) and crack deflection/twist (∼500 μm) as a function of length-scale, and quantitatively demonstrate hierarchy-induced toughening in a complex material. This versatile approach enables quantifying the relationship between toughness and microstructure in various complex material systems and provides direct insight for designing biomimetic composites.

On notch fracture mechanics

Different stress distributions for an elastic behavior are presented as analytical expressions for an ideal crack, a sharp notch and a blunt notch. The elastic plastic distribution at a blunt notch tip is analyzed. The concept of the notch stress intensity factor is deduced from the definition of the effective stress and the effective distance. The impacts of the notch radius and constraint on the critical notch stress intensity factor are presented. The paper ends with the presentation of the crack driving forceJρfor a notch in the elastic case and the impact of the notch radius on the notch fracture toughnessJρ,c. The notch fracture toughnessJρ,cis a measure of the fracture resistance which increases linearly with the notch radius due to the plastic work in the notch plastic zone. If this notch plastic zone does not invade totally the ligament, the notch fracture toughnessJρ,cis constant. This occurs when the notch radius is less than a critical one and there is no need to use the cracked specimen to measure a lower bound of the fracture resistance.