Notch Effect Research Articles

Comparison of analytical and numerical methods for estimating notch strains**

AbstractIn fatigue assessments, local strains and stresses can be easily evaluated using accurate finite element analysis in a case of an individual fatigue‐critical notch or structural detail. In practical design and analysis of global models, the consideration of local notch effects using suitable estimation rules in the combination with linear elastic analysis is reasonable. Various notch rules exist but the current knowledge lacks understanding how applicable different notch rules are for estimating notch strains from elastic stresses. This work studies the Neuber′s rules for sharp and mild notches, Glinka′s equivalent strain energy density method, the correction of Neuber′s rule proposed by Sonsino for mild notches, as well as the Seeger‐Beste method. The application of different estimation rules for notch strains, applied to the elastic‐perfectly plastic steel material and to Ramberg‐Osgood material model for the aluminum material, including work hardening effect, was studied in this work by comparing the estimations with the corresponding experimental data and finite element analysis results. The Neuber′s rule for mild notches and Sonsino′s averaging method gave best correlations with the experimental data and numerical (finite element analysis) results and can be thus recommended for such analyses in compatible cases studied in this work.

Optimization of Welded Joints under Fatigue Loadings

In this paper, the notch effect in weldments has been investigated, and the optimal configuration of different types of welded joints has been analysed using the implicit gradient approach. By considering this implicit gradient method, it is possible to calculate the effective stress related to fatigue damage, with the effective stress being a continuous scalar function of the real stress tensor components, even in the presence of sharp edges. Hence, the search for the optimal configuration that maximises fatigue life can be tackled as the condition of minimum effective stress obtained by changing the weld shape and geometrical parameters. Both load-carrying cruciform joints and spot welds made of steel have been considered. The structural details have been studied by modelling actual shapes without any geometric simplification. Moreover, the same numerical procedure has been considered independently of the size, shape or load condition without imposing restrictive rules on the FE mesh.

Experimental studies on the static sharp notch effects during dynamic crack kinking/nucleation at the material interfaces

Dynamic fracture experiments on four bonded polymers using high-speed photography showed that different static sharp notches formed after the incident dynamic cracks met the material interfaces. In one scenario, an incident dynamic crack induced interfacial crack nucleation, and two convex notches formed after the interfacial crack propagated away. In another scenario, interface-induced crack kinking and a “head-to-tail” crack kinking pattern led to a concave notch with a singular stress field, which merits consideration in fracture mechanics modeling. In contrast, load-induced crack kinking did not cause the above scenarios. In another unique experimental phenomenon, a slightly curved/kinked dynamic crack only had a small local crack kinking angle, but its final crack direction was almost 90° to the initial crack direction over a long crack path.

Fatigue Behavior of Medium Entropy Alloys AlCrFe<sub>2</sub>Ni<sub>2</sub> and AlCrFe<sub>2</sub>Ni<sub>2</sub>Mo<sub>0.1 </sub>- A Comparison with Super Duplex Steel 1.4517

In the present study the notched fatigue behavior of two multi-phase medium entropy alloys (MEAs) AlCrFe2Ni2 and AlCrFe2Ni2Mo0.1 was characterized by three-point-bending (3-PB), along with a super-duplex steel 1.4517 as a reference material. An analytical approach for characterizing the fatigue notch factor (kf), based on grain size analysis in combination with finite element modelling (FEM) was used, relating the theory of critical distances (TCD) to the grain size of the material. To validate the approach, for the reference steel, the fatigue notch factor was also determined experimentally by comparing the fatigue behavior of notched and smooth specimens, resulting in an experimentally determined fatigue notch factor (kf) ~ 1.07. The numerically and analytically estimated notch effects increase with decreasing average grain size and vary between ~ 1.07 for the coarse-grained reference material – in very good agreement with the experimental results – and ~ 1.35 for the much more fine-grained AlCrFe2Ni2Mo0.1 medium entropy alloy. Note that these values are significantly lower than the stress concentration factor (kt) ~ 1.58, associated with the notch geometry. Fatigue endurance limits were measured at a fatigue stress ratio R ~ 0.1 (unidirectional stress), but were converted to fatigue amplitudes at R = -1 (σa, R-1, fully reversed stress), to be able to make due comparisons with available literature data, by using the elliptical relationship. The resulting fatigue endurance limit amplitudes for specimens surviving at least 2E+06 cycles for a minimum of three tested samples and including notch effects are σa, R-1 ~ 508 MPa for the AlCrFe2Ni2 alloy, σa, R-1 ~ 540 MPa for the AlCrFe2Ni2Mo0.1 alloy modification and σa, R-1 ~ 400 MPa for the reference super-duplex steel, putting the analyzed MEAs into a very competitive position compared to Cobalt containing multi-phase high or medium entropy alloys as well as commercially available steels.

Effect of U-shaped notches on nozzle performance and jet flow structures

In nacelle design, optimization of nozzle shape is crucial for flow control. To understand the effect of nozzle shape on its aerodynamic performance and jet flow structures, the numerical experiment is performed using the dual separate flow reference (DSFR) nozzle released by the Aero Systems Engineering (ASE) FluidDyne Laboratory. A pair of U-shaped notches are made on the nozzle. The results show that the discharge coefficient and thrust angle increase with the size of the notches in all the simulated operating conditions. The notches induce a pair of streamwise vortices, which enhance turbulent mixing and decrease turbulent kinetic energy in the mixing layer.

The Effect of Notch and Molecular Weight on the Impact Fracture Behavior of Polycarbonate.

The impact protection applications of polycarbonate (PC) products are gradually increasing. Due to the high sensitivity of PC to notches, research on notch impacts has become very important. In this paper, the impact performance of PC with two different molecular weights under different notch states was investigated. Three notch size factors, namely notch tip radius, notch angle, and notch center depth, were selected to design orthogonal experiments and research impact toughness. Subsequently, a single-factor study was conducted on the impact radius at the tip of the notch, which was the most important factor affecting the impact performance. Research shows that the brittle-ductile-transition tip radius of high-molecular-weight PC is 0.15 mm, and it has a higher impact toughness than low-molecular-weight PC during the brittle fracture process. The brittle-ductile-transition tip radius of lower molecular weight is 0.25 mm, while low-molecular-weight PC has a higher impact toughness during the ductile fracture process. The brittle and ductile fracture mechanisms of PC with different molecular weights were analyzed by observing the stress changes and cross-sectional morphology.

Investigation of the effect of ball-burnishing treatment applied to Al 7075-T6 alloy on mechanical and crystallographic properties

ABSTRACT In this study, the mechanical, microstructural, and crystallographic effects of ball-burnishing applied to Al 7075-T6 alloy at 0.15–0.30 mm penetration depth, 0.15–0.30–0.60 mm/rev changing feed rates and 100–200 rpm range were investigated. After the ball-burnishing processes were carried out in different parameters, surface roughness measurements were applied to determine the surface qualities, and hardness and impact energy tests were applied to characterise the mechanical properties. Dislocation density and texture coefficient values were calculated by determining the crystallographic properties using X-ray diffraction. It has been determined that the ball-burnishing process directly affects the surface roughness, depending on the increasing rotational speed and feed rate. As a result of microstructural investigations, the average grain size decreased with increasing amount of deformation on the sample surface. At 200 rpm ball-burnishing parameter, the surface hardness of the sample increased by approximately 41% compared to the initial state and was measured as 265 HV2. It was determined that the ball-burnishing process did not positively affect the impact of the toughness of the alloy. The reason for this is that the roughness and scratches on the surface caused by the ball-burnishing process have a notch effect, increasing the crack formation and propagation speed.

Displaced sigmoid notch fracture and higher patient age are associated with distal radioulnar joint subluxation.

Distal radius fractures (DRFs) are frequently associated with distal radioulnar joint (DRUJ) instability. The purpose of this study is to evaluate the effect of the sigmoid notch and ulna styloid fracture types on DRUJ subluxation following closed reduction and casting of DRFs via calculating radioulnar ratio (RUR) on postreduction computed tomography (CT) images. In our study, postreduction CT images of 202 patients with distal radius fractures were evaluated retrospectively. CT images were evaluated for RUR, sigmoid notch fracture, and ulna styloid types. Sigmoid notch fractures were classified as nondisplaced in the sigmoid notch fractures (NDS) and displaced sigmoid notch (DS) fractures; ulna styloid fractures were grouped as the proximal half ulna styloid (PHUS) and distal half ulna styloid (DHUS) fractures. The mean age of Rozental type 3b (62.8 years) was significantly higher among others. The mean RUR value was significantly higher in Rozental type 3a in compared to type 1a and type 2 fractures. PHUS fractures were more common with DS fractures than DHUS fractures. DS fractures and higher patient age are associated with DRUJ subluxation on postreduction CT images following DRFs. DS fractures are seen more commonly with PHUS fractures than DHUS. Patients with PHUS should be carefully assessed for sigmoid notch fractures and DRUJ congruency. These findings could be helpful for preoperative decision making in the treatment of DRFs.

Notch effect in tension-tension fatigue of short glass fibre reinforced polyphenylene sulfide composites

An experimental investigation of the fatigue behaviour of plain and notched specimens made of 40 % wt. short glass fibre-reinforced PolyPhenylene sulfide is presented. To this end, plain and V-notched specimens (with notch root radius ranging from 0.2 mm to 10 mm) were produced by injection moulding, and the final geometries were obtained by means of two different technological processes (i.e., directly after the injection moulding process and by machining them from injected plates). To investigate the effect of notch root radius and fibre orientation, tension–tension fatigue tests were carried out in load control mode, and the experimental results were reanalysed in terms of net stress amplitude defining the traditional stress-life curves. During the fatigue tests, the damage evolution was monitored using a travelling microscope to define the number of cycles spent for fatigue crack nucleation. Furthermore, the fracture surfaces were observed at the microscopic level to investigate the damage mechanisms and the actual fibre orientation was evaluated by computed tomography analysis. Then, by employing coupled finite element analysis of the injection moulding process and the structural behaviour, four different approaches available in the open literature were used to correlate the geometrical and/or manufacturing process effects in the fatigue strength of the considered material.

A novel model considering combined effects of as-built roughness and notch for multiaxial fatigue life prediction of L-PBF Ti6Al4V

Additive Manufacturing (AM) has emerged as a promising manufacturing technology. However, there is still a lack of effective methods for evaluating the influence of as-built roughness, especially for notched components under complex fatigue loading. In this paper, a method based on damage mechanics for multiaxial fatigue life prediction is proposed for addressing the individual and combined effect of as-built surfaces and macro notches. Chaboche material model is coupled with a damage variable to describe the elastic–plastic deformation around the notch. The effect of as-built roughness is integrated into the damage evolution law developed by Chaudonneret, taking into account the degree of roughness, the orientation-dependent effect, and the variation of roughness effect with stress levels. The proposed model is numerically implemented by UMAT and validated through experimental data from literature under four types of fatigue loading including axial, torsion, in-phase axial-torsion and 90° out-of-phase axial-torsion. The predicted results agree well with the experimental values and the combined effect of the as-built roughness and notch is well analyzed.

Probabilistic notch fatigue assessment under size effect using micromechanics-based critical distance theory

Geometrical discontinuities are inevitable in engineering structures due to various functional requirements, which often yield complex stress–strain state and thereby significantly impact their fatigue performances. In this study, crystal plasticity theory is coupled with traditional critical distance theory for notch effect modelling considering microstructural heterogeneity. Specifically, microstructural and geometrical size effects on critical distance and fatigue performance are studied based on Sub-modelling approach. In addition, critical distance theory is coupled with Weibull distribution for probabilistic fatigue life evaluation of notched components. The developed method is verified and compared by using experimental data of GH4169 alloy. The findings demonstrate that the evaluated P-S-N curves exhibit strong agreement with tested data and geometrical size effect poses larger influence than the grain size effect on critical distance and fatigue life.

An enhanced stress field intensity approach for fatigue life assessment combining notch and size effect

The notch characteristics of engineering components significantly impact their fatigue lives. Accurately analyzing the notch effect and size effect is of great significance for structural integrity evaluation, which provides insights into the extent of fatigue failure in engineering structures. In this paper, a new method is proposed for determining the fatigue failure region based on actual elastic–plastic stress distribution under various notch geometries and applied loads. It considers the complex mechanical behavior of the plastic effect and stress relaxation near the notch root. Furthermore, a novel weight function is employed to consider the relative stress gradient at all points within the fatigue failure region. Finally, an enhanced stress field intensity approach is developed to predict notch specimens fatigue lives utilizing experimental lives of smooth specimens. Additionally, the effectiveness of the proposed method is analyzed by predicting the fatigue lives of three distinct materials notched specimens with varying geometries and applied loads. The prediction absolute errors of the proposed approach are compared with those of the other traditional notched fatigue analysis methods. The comparative results indicated that the performance of the proposed method outperforms the other methods.

Bending stresses in straight bars with a transverse centre hole: A case of beneficial notch effect?

The article investigates by finite elements the bending stresses around a centre transverse circular hole in straight bars with rectangular or circular cross-section. Four loading conditions are considered, pure bending and three variants of three-point bending (load concentrated on the bar surface above the hole, load directly applied to the hole as uniform pressure, load applied to the hole through a connecting pin). Mostly, the hole diameter is one-third of the section height and one-twentieth of the beam length. Holes of one-fourth and one half of the section on several beam lengths are also investigated for the flat bar in three-point bending to appraise the sensitivity to aspect ratios. The results show that, in all cases, the notch effect is mildly detrimental to the stress distribution and can even be beneficial in comparison with the unperforated bar. This is because the hole increases the stresses around the neutral axis, where the stresses are naturally low, thus taking away stresses from the surface where the bending stresses are naturally highest. The design of pivoted flexural machine elements like levers, yokes and balance arms can take advantage from this evidence.

Effect of Interface Form on Creep Failure and Life of Dissimilar Metal Welds Involving Nickel-Based Weld Metal and Ferritic Base Metal

For dissimilar metal welds (DMWs) involving nickel-based weld metal (WM) and ferritic heat resistant steel base metal (BM) in power plants, there must be an interface between WM and BM, and this interface suffers mechanical and microstructure mismatches and is often the rupture location of premature failure. In this study, a new form of WM/BM interface form, namely double Y-type interface was designed for the DMWs. Creep behaviors and life of DMWs containing double Y-type interface and conventional I-type interface were compared by finite element analysis and creep tests, and creep failure mechanisms were investigated by stress-strain analysis and microstructure characterization. By applying double Y-type interface instead of conventional I-type interface, failure location of DMW could be shifted from the WM/ferritic heat-affected zone (HAZ) interface into the ferritic HAZ or even the ferritic BM, and the failure mode change improved the creep life of DMW. The interface premature failure of I-type interface DMW was related to the coupling effect of microstructure degradation, stress and strain concentrations, and oxide notch on the WM/HAZ interface. The creep failure of double Y-type interface DMW was the result of Type IV fracture due to the creep voids and micro-cracks on fine-grain boundaries in HAZ, which was a result of the matrix softening of HAZ and lack of precipitate pinning at fine-grain boundaries. The double Y-type interface form separated the stress and strain concentrations in DMW from the WM/HAZ interface, preventing the trigger effect of oxide notch on interface failure and inhibiting the interfacial microstructure cracking. It is a novel scheme to prolong creep life and enhance reliability of DMW, by means of optimizing the interface form, decoupling the damage factors from WM/HAZ interface, and then changing the failure mechanism and shifting the failure location.

Evaluation of the fatigue resistance of butt-welded joints in towers of wind turbines — a comparison of experimental studies with small scale and component tests as well as numerical based approaches with local concepts

Wind turbines must endure a high number of load cycles during their service lifetime. Therefore, the fatigue strength verification plays an important role. Butt-welded joints are one of the most common structural details in the tower structure of wind turbines. In general, the nominal stress method is used for their fatigue verification. The Eurocode 3 part 1–9 is the current design standard for this field of application and defines the fatigue resistance by pre-defined FAT-classes. This paper presents recent results of fatigue tests on small-scaled specimens and large components with transverse butt welds to discuss the validity of the FAT-class. In addition, results from numerical simulations for the verification with the effective notch stress and the crack propagation approach are used for comparison. For this purpose, macroscopic measurements of the weld seam geometry and a 3D scan were used for a realistic consideration of the notch effect in the simulation. Based on the consistency between the numerical results and the fatigue tests, the influence of the seam geometry on the fatigue resistance was worked out. Furthermore, a prediction of the fatigue strength of butt-welded joints with plate thicknesses up to 80 mm was carried out.

Atomistic details of grain, crack, and notch effect on the mechanical behavior and fracture mechanisms of monolayer silicon carbide

Recently, sp2-hybridized single-layer SiC, analogous to graphene, has received much attention in nanoelectronics and nanoelectromechanical systems because of its remarkable thermal, electrical, and mechanical properties. However, the unique properties and related applications strongly depend on the growth of a single-crystal and large-area two-dimensional SiC. The majority of synthesized SiC monolayers exhibit a natural polycrystalline structure, comprising single-crystalline grains with diverse sizes and orientations. Moreover, the emergence of structural defects, including cracks and notches, poses challenges that are difficult to overcome during both the fabrication and subsequent processing stages. In this paper, we explore the atomistic details of grain, crack, and notch effect on the mechanical behaviors and fracture mechanisms of single-layer SiC using molecular dynamics simulations. Increasing grain size from 2 nm to 35 nm gradually increases the elastic modulus and fracture strength, which fits well with the inverse Pseudo Hall-Petch relationship. However, an anomalous trend of decreasing as well as increasing fracture strain is observed with the increasing grain size. For polycrystalline SiC with a 2 nm grain size, the elastic modulus and fracture strength are roughly 87% and 41% of those observed in single-crystalline SiC. Notably, when comparing the impact of rectangular crack and circular notch defects, the circular notch exhibited a more pronounced effect in diminishing mechanical behavior under both armchair and zigzag orientational loading. The circular notch produces considerable amorphization around the notch, but the rectangular crack does not show any significant dislocation or amorphization around the crack. The critical stress intensity factor, energy release rate, radial distribution function, and potential energy per atom are calculated to explain all the fracture properties. The effect of temperature and strain rate is also investigated for all the defect-induced samples. Overall, our results provide new insight and understanding of the mechanical behavior and fracture mechanisms of polycrystalline, crack- and notch-induced SiC, and set a standard for making and designing new nanodevices and nanostructures made of SiC.

Notch structural stress theory: Part II predicting total fatigue lives of notched structures

Notch fatigue problems are among the most common topics for the reliability analysis and structural design of mechanical engineering components. In previous work, we proposed the Notch Structural Stress (NSS) method based on fracture mechanics for reflecting the notch effect on fatigue crack propagation lives. However, like other regular fatigue assessing procedures, NSS also cannot accurately predict the fatigue life of notched structures with slower stress gradients due to the inconsistent slope of their S-N curves. This paper presents the Theory of Notch Structural Stress (TNSS) for predicting total fatigue lives of notched structures, which overcomes the life prediction limitations caused by slope differences in S-N curves and constructs a life-predicting frame suitable for different notch types even including plain and sharp notches. Compared with the often-used stress-concentration-assessing procedures, TNSS provides a more effective consolidation of the S-N data from different notch types, mostly since it takes both Initiation and Propagation state resistance into account at the same time.

Evaluation of damage and failure analysis of CPVC pipes

In this paper, the work we have carried out has focused on the failure analysis of CPVC (chlorinated polyvinyl chloride) pipes. We stimulated the damage by notch effect and evaluated its properties using models available in the literature, specifically, the linear damage of Miner, the normalized damage and the unified theory. Burst tests allowed us to obtain ultimate pressure and time parameters for the virgin specimens and the residual parameters for the damaged ones. Then, we analyzed the effect of defect on the mechanical behavior of the studied structures; we found that the mechanical properties of the material were lost as defects increased. An observation and analysis of the pressure drop and thereafter the residual ultimate resistance brings out acceleration from it around the critical depth. Then, an evaluation of the static damage of the studied CPVC pipes was made according to model based on the experimental results of the burst tests and on the modification of the unified theory concepts and the static damage. Indeed, we evaluated the static damage of blank and notched tubes using mainly burst pressure parameters.

Fatigue life analysis based on the groove angle reduction in the butt welding of excavator booms

This study analyzes the effect of changes in groove angle on the fatigue strength of the V-groove butt weld joint made of SM490A steel used in excavators. Butt-type specimens with different groove angles of 40° and 30° were manufactured by CO2 welding at a speed of 300 mm/min on a 13.5 mm thick steel plate. Four-point bending fatigue tests were conducted at room temperature with a frequency of 5 Hz and stress ratio of R = 0.1, and fatigue limits were set to 2 × 106 cycles. The high-cycle fatigue life of VG40 was approximately 7% higher than that of VG30. The stress concentration coefficient calculated using the effective notch stress method was 1.62 for the VG40, and 1.78 for the VG30, with an approximate difference of 9%. This decrease in fatigue life was caused by stress concentration due to the notch effect at the weld root, which was attributed to the adjacent backplate. Although the fatigue life decreased slightly owing to the improvement angle of the welded part, no difference was observed in microstructure and hardness. Therefore, it was confirmed that a sound weld was formed. The results of this study can be used as important basic data for determining the V-groove angle.

Mechanical analysis of new-type arc-cone anchor for CFRP strand wires

Conventional anchors tend to produce ‘notch-effect’ at the tensile end due to stress concentration when anchoring prestressed CFRP strand cables. A new-type arc-cone anchor was designed with the purpose of optimizing the stress distribution in the anchor zone in this study. The ‘arc-cone’ model was proposed to represent the mechanical characteristics of the anchor, and the numerical simulation and experiments were carried out. The effect of the design factors on the anchoring performance was discussed, involving the arc-cone radius, the anchoring length, and the end hole wall thickness. The failure mode, the ultimate load, the anchoring efficiency coefficient as well as the stress distribution were ascertained with the consideration of the effect of the abovementioned design factors. The research results show that the extrusion stress on the barrel decreases with respect to both the wall thickness and the anchor length. The larger the radius of the arc-cone is, the larger the slip of the CFRP strand wire is. The proposed anchor configuration inversely changes the stress distribution from the tensile end to the free end, alleviates the ‘notch effect’ existing in the anchoring zone of conventional anchors, and consequently, improves the anchoring efficiency for CFRP strand wires.