Notch Geometry Research Articles

Effects of voids and raster orientations on fatigue life of notched additively manufactured PLA components

In this study, the fatigue life of notched polylactic acid (PLA) samples fabricated through the fused deposition modeling (FDM) technique was studied experimentally and numerically. The volumetric method based on the theory of critical distance was employed for fatigue life predictions. The effects of influential process parameters including raster orientation and FDM-induced defects such as voids or gaps inside the parts were examined on the fatigue strength reduction factors and fatigue lives. Circular and elliptical-shaped notch geometries were considered with various dimensions. Fatigue tests were conducted on notched and un-notched samples at the load ratio of 0.1. Predicted results were compared with experimental fatigue test data. Results revealed that the raster orientation parameter had a substantial impact on fatigue strength reduction factors and fatigue lives. The stress concentrations induced by the FDM process on the surfaces and inside the parts for the samples with 90° raster angles acted similar to the sharp notches, resulting in no substantial difference in fatigue life of notched and un-notched 3D-printed samples. In contrast, un-notched 3D-printed specimens with 0° raster orientations possessed higher fatigue lives as compared to the notched samples. While the volumetric approach efficiently predicted the fatigue lives of the samples with 90° raster orientations, it moderately underpredicted the fatigue lives of the samples with 0° raster angles.

Determination of shear stresses in the measurement area of a modified wood sample

Abstract The purpose of the experiment was to determine the distribution of shear stresses in the measurement area of a natural and modified wood sample. Previous wood shear tests conducted on a typical Iosipescu specimen have shown that a complex stress state exists at the bottom of the notch. With transverse loading of the samples, flexure occurs and normal stresses arise from the bending moment and thus fibers are deformed. For the investigations oriented on shear, shear with stretching, and shear with compression, a special specimen was prepared which differed by notch geometry from a typical Iosipescu specimen. A new test machine is described in the article, which is equipped with special specimen holders to perform investigations in complex stress conditions. Crack patterns recorded for natural and modified wood are presented. For all tests, numerical finite element model simulations were performed to obtain stress distributions inside the specimens. The calculated stress distributions were visualized as contour line projections for natural and modified wood. Transverse shear strength values for the modified Iosipescu sample were found to exceed the magnitude of previously published ASTM D1037-87 test results. The test results proved that the strength properties of anisotropic materials in a complex state of stress can be assessed with great accuracy. This is very important in engineering applications.

An analytical stress field for bi-material V-notches with end hole: New solution and effects of higher order terms

Current manuscript develops an analytical stress solution for the bi-material V-notches with an end hole (VO). To do so, based on the Kolosov-Muskhelishvili’s approach, while appropriate potential functions are employed, the boundary conditions of the problem are imposed to the solution to reduce the number of unknown parameters. Subsequently, the analytical stress field is derived as an asymptotic series solution, where each term possessing a constant coefficient and an order of singularity. The order of singularity for each term is obtained from the characteristic equations of the problem which is dependent on the notch geometry and material combinations. The so-called least square method (LSM) is then used to compute the constant coefficients of the asymptotic series for several case studies. Special attention is given to the bi-material notch stress intensity factors (BNSIFs) and the coefficients of the higher order terms (HOTs) in the stress series expansion. The accuracy of the presented stress solution is verified by benchmarking the results with numerical values obtained from finite element (FE) method. In this process, several notch opening angles and notch radii are simulated using the three-point bend (3PB) specimen. The developed asymptotic stress solution is demonstrated to be capable of accurately evaluating the stress field around bi-material VO-notched structures.

Failure Criteria for Brittle Notched Specimens

Abstract Recently, new failure criteria were proposed for brittle materials to predict their failure loads regardless of the shapes of a notch or a crack in the material. This paper is to further evaluate the failure criteria for different shapes of notches and different materials. A circular hole, elliptical hole, or crack-like slit with a different angle with respect to the loading direction were considered. Double circular holes were also studied. The materials studied were an isotropic material such as polymethyl methacrylate (PMMA) as well as laminated carbon fiber composites. Both cross-ply and quasi-isotropic layup orientations were examined. The lamination theory was used for the composite materials so that they can be modeled as an anisotropic and homogeneous material. The test results were compared to the theoretical predictions using the finite element analysis with two-dimensional plane stress models. Both theoretical failure stresses agreed well with the experimental data for the materials and notch geometries studied herein.

Effect of ply orientation, staking sequence and notch geometry on the failure behaviour of glass fibre-reinforced epoxy composite laminates: A numerical investigation

A detailed numerical failure analysis was conducted for unidirectional glass fibre-reinforced epoxy composite laminates having an elliptical cut-out at the centre using Hashin’s damage model. The major axis, a, of the elliptical cut-out was fixed while the minor axis, b, was varied in such a way, that its upper extreme represented a situation of the plate with a circular hole, while the lower extreme of it represented the presence of a sharp crack in the structure. For angle ply cases, plies oriented along the material direction predicted an ever-increasing load replicating an elastic analysis without any damage accumulation. Such exceptionally higher stiffness and resistance to deformation were much anticipated, as the uni-axial tensile load was applied along fibre direction which shares a large portion of the load in comparison to the matrix material. While the plies oriented perpendicular to the direction of the material behaved as the weakest stack-up sequence in resisting uni-axial tensile load. Multi-angle hybrid composites predicted uneven failure behaviour. For the different combinations of multi-angle layups and minor axis, b, different trends for peak loads were observed. Interestingly, extension-shear coupling was observed for a few configurations which were marginally negligible for others. The variation of opening stress along the transverse direction predicts some very interesting observations. For the higher value of b, the opening stress decreases as we moved away from the irregularity. However, the situation of a plate with a sharp crack (b → 0) showed the effect of crack tip blunting. Near the vicinity of the sharp crack, the opening stress first dropped, then picked up, and again kept on decreasing as we move away. The drop in the stress near the vicinity of the sharp crack is attributed to the blunting of the crack tip.

Digital image correlation for accurate strain measurement on sharp notched specimens

Notch stress concentration and the notch effects in general, play a significant role in the field of structural mechanics. Also, the strain measurement in notches is still a challenge. In cases, when the notch geometry is not exactly defined e.g., weld joints etc., the measurement of strains in notches becomes even more important. Therefore, the present work focuses on the problem of strain measurement on notched specimens, especially on sharp notches (notches with small minimum radius) by using the digital image correlation method. Initial measurements were carried out on specimens with known stress concentration and the results were compared with the analytical and numerical solution. Multiple camera positions with respect to the specimen are compared and discussed. Minimum number of pixels per notch radius for accurate measurement was determined based on the measured data. This limitation is influenced by several effects. The presented work focuses deeper on the influence of postprocessing filter methods. Several possible solutions to overcome this limitation are presented. The obtained results and the knowledge gained by previous measurements were utilized by direct practical measurements, weld notch stress concentration measurement.

Optimization of notched tensile test specimen under plane strain condition

In the current paper, specimen notch geometries during plane strain tensile test for cold-rolled steel DC01 is studied and optimized using Response Surface Methodology (RSM) and the desirability approach. The notch angle (X°), notch width (d), and notch length (c) were the main geometry parameters considered in this study. The effects of these parameters on the strain state were expressed by self-defined metrics, namely the Plane Strain State Index (PSSI) and the Homogeneity Index (HI) as well as those were analyzed by ANOVA analysis. The quadratic mathematical models obtained by the RSM presenting the evolution of the PSSI and the HI depending on (X°, d, and c) are presented. Optimization of the geometry parameters to achieve the optimal PSSI and better HI was carried out by a desirability function.

Morfometrijsko-anatomski parametri interkondilarne jame kolena kod odraslih osoba u Srbiji

Objective: The aim of this investigation was to examine normal intercondylar notch morphometry in Serbian population and to determine whether there are gender differences in anatomical parameters of the intercondylar notch among asymptomatic subjects without structural change. Method: The study included Mr images of 90 patients (45 men and 45 women) receiving a 1,5-T knee scan at our radiological institute after the approval from the Ethics committee, which were taken in the period from 2010 to 2017. The knee was placed in the neutral position, and Mr images were obtained using conventional spin echo techniques. The morphology of the intercondylar notch (Ushaped and A-shaped notch) was measured for each knee. Results: The measurements of parameters for intercondylar notch geometry were obtained by analyzing coronal Mr images. U-shaped intercondylar notch was found in 46 patients (51.2%) and A-shaped intercondylar notch in 44 (48.8%). There was no significant difference in the shape incidence in Serbian population (p>0.05). According to the Notch width index (NWI) and the Notch shape index (NSI) criteria, we found U-shaped intercondylar notch with 24 men and 22 women and A-shaped intercondylar notch with 23 men and 21 women. There was no significant difference in incidence between the genders (p>0.05). Conclusion: We concluded that for all examined anatomical parameters of the intercondylar notch there were no significant differences in Serbian population. According to our findings in this study, we concluded that there was no sexual dimorphism for anatomical parameters of intercondylar notch in Serbian population.

Notch size influence on fatigue limit of steels pertinent to grain size

Fatigue limit of notched specimens is influenced by notch geometries and material microstructure. In this paper, seven groups of fatigue measurements on different steels with average grain size (G) from 8 to 64 μm were analyzed, and an explicit model was proposed to describe notch geometry effect on fatigue limit and its relation to G. Additionally, normal distribution theory was incorporated to consider the inevitable scatter of fatigue limit caused by material heterogeneity and machining/measurement errors. The result shows that the proposed model can predict fatigue limits of both notched and cracked specimens of various steels.

Localization of Plastic Deformation in Ti-6Al-4V Alloy

This article investigated the mechanical behavior of Ti-6Al-4V alloy (VT6, an analog to Ti Grade 5) in the range of strain rates from 0.1 to 103 s−1. Tensile tests with various notch geometries were performed using the Instron VHS 40/50-20 servo hydraulic testing machine. The Digital Image Correlation (DIC) analysis was employed to investigate the local strain fields in the gauge section of the specimen. The Keyence VHX-600D digital microscope was used to characterize full-scale fracture surfaces in terms of fractal dimension. At high strain rates, the analysis of the local strain fields revealed the presence of stationary localized shear bands at the initial stages of strain hardening. The magnitude of plastic strain within the localization bands was significantly higher than those averaged over the gauge section. It was found that the ultimate strain to fracture in the zone of strain localization tended to increase with the strain rate. At the same time, the Ti-6Al-4V alloy demonstrated a tendency to embrittlement at high stress triaxialities.

Narrow Notch Width and Low Anterior Cruciate Ligament Volume Are Risk Factors for Anterior Cruciate Ligament Injury: A Magnetic Resonance Imaging-Based Study.

The relationship between anterior cruciate ligament (ACL) injury and anatomical structures is still a topic of debate. The aim of this study was to compare knee geometry in demographically matched ACL-injured and ACL-intact athletes. We conducted a case-control study comparing 2 groups, each consisting of 55 professional athletes (44 men and 11 women): 1 group with complete ACL tears (cases) and 1 group with intact ACLs (controls). The groups were compared using magnetic resonance imaging (MRI) in terms of intercondylar notch geometry, tibial plateau characteristics, and ACL volume. Among cases and controls, we found the cases had lower notch width (20.24 ± 2.68 mm vs. 22.04 ± 2.56 mm, respectively) and notch width index (0.29 ± 0.03 vs. 0.31 ± 0.03, respectively). The mean ACL volume in the cases (1181.63 mm3 ± 326 mm3) was also lower than in controls (1352.61 mm3 ± 279.84 mm3). The parameters of tibial slope geometry were comparable between groups. In addition, women had lower ACL volume than men (1254 ± 310 mm3 vs. 890 ± 267 mm3, respectively) and higher medial posterior tibial slope (4.76 ± 2.6 vs. 6.63 ± 1.83, respectively). Among cases, women had narrower notch width than men (16.9 ± 2.42 mm vs. 21.08 ± 2.03 mm). However, notch width index was comparable between male (0.3 ± 0.02) and female (0.28 ± 0.03) cases. Our findings suggest that narrow notch width and low ACL volume may enhance the risk of ACL injury among athletes. There was no association found between posterior tibial slope and ACL injury between athletes with injured ACLs and controls. Further study is indicated.

Investigation of the Near-Tip Stress Field of a Notch Terminating at a Bi-Material Interface.

The article deals with the problem of a sharp corner, the tip of which is located on the bi-material interface. The paper presents a qualitative and quantitative description of singular stress fields occurring in the tip area of such a stress concentrator. The qualitative description was obtained by solving the problem of the plane theory of elasticity with appropriately defined boundary conditions. To obtain a quantitative description, it was necessary to determine the values of generalised stress intensity factors (GSIFs). The GSIFs were determined using the developed analytical-numerical method. The calculations were made for various load variants (uniaxial/biaxial tension load, shear load) and notch positions (single/double edge-notched plate, centre-notched plate). Additionally, the impact of notch geometry (height and opening angle) and relative stiffness (Young’s moduli ratio of both components of bi-material) on GSIFs was investigated. It has been noticed that with a decrease in the relative stiffness and an increase in the notch angle or its height, the normalised GSIFs values increased. The obtained results were compared with the data available in the literature and their satisfactory agreement with those presented by other scientists was found.

Association of femoral intercondylar notch geometry with risk of anterior cruciate ligament injury in a black patient population

BackgroundAnterior cruciate ligament (ACL) injuries can significantly affect the productivity and quality of life of the individual. Certain factors such as notch width and notch width index that predispose to such an injury can be screened for to help in injury prevention strategies. MethodologyConsecutive cases of anterior cruciate ligament injury in male patients and age- and gender-matched controls were recruited for the study. The anthropometric characteristics of patients in both groups was noted. The notch width (NW) and notch width index (NWI) were measured. The mean values of the anthropometric characteristics and the notch width and notch width indices of both groups were compared using independent t-test at a p-value of <0.05. The frequency of the various femoral notch morphologies was also noted in both groups. ResultsThe mean notch width index in the control group was significantly higher than among cases of ACL injury (p = 0.01). patients with ACL injuries were 9.75 times more likely to have stenotic femoral notch than those without. No statistically significant relationship was established between the anthropometric characteristics of both groups, and the NW, NWI and femoral morphology. ConclusionACL injured patients tend to have a narrower femoral notch. Study DesignCase-control study; Level of evidence, III

The Master S-N curve approach for fatigue assessment of welded bridge structural details

The verification of the Master S-N curve approach using an equivalent structural stress parameter, has been carried out for welded joints with different geometries, thickness and loading modes, mainly representative of pressure vessels and piping components. The application of the Master S-N curve to a new field requires the reassessment of the relevant fatigue data, due to different manufacturing conditions, detailing techniques across industries and typical loading modes. In this paper, the referred verification will be further extended by means of available fatigue strength data from large-scale tests of typical bridge structural details, mainly based on girder-type specimens. The reassessment can allow the consideration of loading modes and stress conditions closer to those which develop in actual girder steel bridges. An approach based on experimental S-N data is also useful because it can take into account residual stresses, construction misalignments, local notch and weld bead geometry effects in the estimated fatigue lives. In this manner, the aim is to reassess the robustness and effectiveness of the equivalent-structural stress technique combined with the Master S-N curve approach through the finite element numerical modelling of large-scale tests of welded bridge details subjected to in-plane and out-of-plane loading. The approach is applied to four fatigue test setup programs representative of welded bridge details, which were used as the basis for the establishment of the current nominal S-N curves available in American codes. A performance comparison with the nominal and the hot-spot stress method is carried out. The method proved to collapse nearly 300 datapoints of fatigue failures of welded bridge details into a narrow scatter band.

Stenotic Intercondylar Notch as a Risk Factor for Physeal-Sparing ACL Reconstruction Failure: A Case-Control Study.

Introduction:Identifying risk factors is crucial for developing strategies that minimize reinjury after anterior cruciate ligament reconstruction (ACLR). This study aims to determine whether certain features of intercondylar notch geometry are associated with failure of physeal-sparing ACLRs in skeletally immature athletes.Methods:Nine failed physeal-sparing ACLRs were compared with a control subject group of 15 age- and sex-matched intact physeal-sparing ACLRs. Notch width index (NWI), notch angle (NA), and intercondylar notch roof inclination angle (RA) were measured on preoperative MRIs.Results:Median NWI was smaller in the failed ACLR versus control subject group in coronal (0.23 versus 0.27; P < 0.05) and axial planes (0.25 versus 0.27; P = 0.055). Median NA was smaller in the failed ACLR versus control subject group in coronal (49.6 versus 61.0°; P < 0.05) and axial planes (48.6° versus 54.9°; P < 0.05). Median RA was steeper in the failed ACLR versus control subject group (132.0° versus 125.7°; P < 0.05).Conclusion:NWI, NA, and RA were associated with ACLR failure in skeletally immature patients undergoing physeal-sparing reconstruction. A smaller, narrower, and steeper notch may predispose these patients to reinjury.

Kf Evaluation in GFRP Composites by Thermography

Since the presence of a notch in a mechanical component causes a reduction in the fatigue strength, it is important to know the kf value for a given notch geometry and material. This parameter is fundamental in the fatigue design of aeronautical components that are mainly made of composites. kf is available in the literature for numerous types of notch but only for traditional materials such as metals. This paper presents a new practice, based on thermographic data, for the determination of the fatigue notch coefficient kf in composite notched specimens. The innovative aspect of this study is therefore to propose the application on composite materials of a new thermographic procedure to determine kf for several notch geometries: circular, U and V soft and severe notches. It was calculated, for each type of notch, as the ratio between the fatigue limits obtained on the cold and hot zone corresponding to the smooth and notched specimen, respectively. Consequently, this research activity provides, for the first time, a little database of kf for two particular typologies of composite materials showing a fast way to collect further values for different laminates and notch geometries.

Tensile and compressive quasi-static behaviour of 40% short glass fibre - PPS reinforced composites with and without geometrical variations

In this work, a comprehensive experimental investigation was carried out to characterise the quasi-static tensile and compressive behaviour of notched and plain specimens made of 40% wt. glass fibre-Polyphenylenesulphide (40GF-PPS) short fibre reinforced composite.To this end, plain and notched specimens (with notch radius ranging from 0.25 mm to 10 mm) were manufactured with two different fibre orientation angles (0° and 90°) and tested under tension and compression, allowing to observe the effect of the notch root radius and the notch geometry. In addition, a careful analysis was carried out both at the macroscopic and microscopic level to compare the fracture behaviour of plain and notched specimens. Finally, a Generalised-Stress-Intensity-Factor-based approach was adopted to correlate the tensile strength of notched specimens. On the contrary, the compressive strength of the notched samples was rationalised in terms of the nominal net-stress, thanks to the limited notch sensitivity exhibited by the material during the compression tests.

A simplified Navarro-Rios model to predict fatigue limits in notched components.

Many methods have been proposed to predict fatigue failure in the presence of notches, among which is the Navarro-Rios model. This model is based on short-crack fracture mechanics. Specifically, the model analyses the capacity of the crack, which is formed at the notch root by cyclic loading, to overcome successive microstructural barriers such as grain boundaries. This model provides a fairly reasonable explanation of crack growth from a notch under cyclic loading and has been successfully used for many years to predict the fatigue limit in some notched geometries, as shown in several published works. However, the application of this model is not easy, mainly for two reasons: the first is that to build the equations of the model, it is necessary to know the stress field generated by a dislocation in the vicinity of the specific notch, which is a complicated elasticity problem except for very simple notch geometries. The second is related to the resolution of the equations of the model, which are singular integral equations that are difficult to solve except for very simple cases. This work shows a simplified version of the Navarro-Rios model, which allows us to overcome these two difficulties. First, the elastic problem of a dislocation near a notch is simplified to that of a dislocation in an infinite medium, which has a known analytical solution. Second, the study of the equilibrium at the crack line is simplified by using the elastic stress at the midpoint of the crack line instead of using the full stress gradient. After this simplification, the singular integral equation has a known and simple solution. This simplified Navarro-Rios model is applied to some notched geometries and provides similar fatigue limit predictions to those of the classic Navarro-Rios model. It is also compared with results in the literature, where it provides similar predictions to the experimental fatigue limits. The simplified Navarro-Rios model can be a relatively simple alternative to critical distance models for predicting the fatigue limit in notched solids.

Validation of the ductile fracture modeling of CGI at quasi-static loading conditions

Fracture modeling and experimental validation of Compacted Graphite Iron (CGI) specimens loaded under quasi-static conditions at room temperature are considered. Continuum damage mechanics coupled to plasticity is adopted to describe the evolution of damage. The damage production is based on a recently developed rate dependent damage evolution law, where the damage–plasticity coupling is modeled based on a damage driving energy that involves both stored energy and plasticity contributions. To describe ductile fracture accounting for stress triaxiality on the damage initiation, the inelastic contribution to the damage driving energy is controlled by the Johnson-Cook failure criterion. Three different damage models are defined based on elastic/inelastic damage driving energies. The damage models are validated against experiments on a set of notched specimens made of CGI with different notch geometries, where the global force-displacement curves and corresponding strain fields are obtained using digital image correlation technology. It is shown from the testing and the simulations that plastic strains generally need to be accounted for in order to properly describe the different failure processes of the CGI specimens. In addition, the ductile damage model is shown to more accurately predict the experimental force-displacement response as compared to the more simplistic stress drop, element deletion technique.

Determination of Fracture Toughness of Mode I Fractures from Three-Point Bending Tests at Elevated Confining Pressures

Fracture toughness is one of the key parameters for the characterization of brittle rock fracturing. Yet, constraints on it mainly rest on measurements performed at ambient pressure, although rock fracturing frequently occurs at elevated pressures even in geotechnical applications. To address the lack of a generally accepted evaluation procedure for tests at elevated pressure we explored the conditions for initiation and propagation of mode I fractures in samples subjected to bending at elevated pressure by numerical modeling and analytical considerations of the involved angular moments. We derived an evaluation procedure and applied it to experimental observations for specimens with either a chevron or a single-edge notch of four different rocks (a granite, a limestone, a marble and a sandstone) subjected to three-point bending at confining pressures up to 30 MPa. Two sealing methods were considered. Specimens were either varnished or jacketed by a rubber tube, differing in whether pressure is allowed to build up inside the pre-fabricated notch or not, respectively. Irrespective of notch geometry and sealing method, the determined toughness values increase significantly with confining pressure. The apparent toughness determined for jacketed specimens is, however, larger than that for varnished specimens, for which toughness seems to reach a plateau with increasing pressure. The similarity of the pressure dependence of the toughness determined for varnished, i.e., uniformly pressurized, samples with that of other physical properties suggests that it is controlled by the closure of pre-existing micro-cracks; the absence of pressure dependence beyond some tens of MPa suggests that non-linearity effects may not be as severe at depths beyond a few kilometers as previously discussed. Our study points to the necessity of resolving numerical issues associated with compressed fractures and of further improving experimental facilities for the determination of fracture toughness at elevated pressure.