Notch Root Research Articles

Crystal plasticity-driven evaluation of notch fatigue behavior in IN718

The aim of this study was to establish a method for evaluating notch fatigue behavior through crystal plasticity finite element (CPFE) simulations based on the actual microstructure of the nickel-based alloy Inconel 718 (IN718). Initially, the equivalent plastic strain, εeps, which reflects the comprehensive slip at the grain scale, was employed to analyze the fatigue crack initiation mechanism of IN718, revealing that twinning and triple junctions of grain boundaries were high-risk locations for fatigue crack initiation. Next, fatigue simulations were performed on notched specimens using the CPFE model, with a material-level CPFE model particularly employed at the notch root. The increment of εeps, Δεeps, in a stable cycle was used as the fatigue damage control parameter and correlated with the fatigue life, Nf, revealing that the Δεeps-Nf relationship at material-level satisfied the form of the Mason-Coffin model. Finally, fatigue life prediction of IN718 notched specimens was carried out based on the Δεeps-Nf relationship, with the predicted results falling within the 2-fold scatter band, demonstrating good prediction accuracy.

Fatigue Life Prediction of a SAE Keyhole Specimen as a Subcase of Certification by Analysis.

To advance the technology of Certification by Analysis (CbA), as called for by the aerospace industry, the fatigue problems of SAE keyhole specimens are analyzed to demonstrate a subcase of CbA. First, phenomena identification and ranking table (PIRT) analysis is performed. Second, modeling of the key phenomena is conducted, and finally, verification and validation with the experimental results are achieved. In particular, the elastic/elastoplastic stress distributions in the keyhole specimens are obtained using the finite element method (FEM). Plasticity correction for stress/strain at the notch root is made using the modified Neuber's rule along with the Ramberg-Osgood equation. The low cycle fatigue (LCF) crack nucleation life is analytically predicted using the modified Tanaka-Mura model, a.k.a. the TMW model, given the material's elastic modulus, Poisson's ratio, Burgers vector, and surface energy, without the need for coupon fatigue data regression. The Tomkins equation is used to simulate plastic crack growth within the notch plastic zone. The above analytical life predictions are validated against the SAE keyhole specimen tests, becoming the first successful case of fatigue CbA at a sub-element level.

Evaluation of the fatigue life of AISI 347 specimens with small notches based on local strain considerations

The use of materials data for cyclic loading determined on unnotched specimens to predict the fatigue life of notched components has a long tradition, specifically when it comes to nuclear engineering. The basic principle is that the material behaviour of the unnotched specimens can be transferred to what the material is exposed to be in a notch root. This principle has been proven for large notches. However, what happens when the notch is relatively small? Can the fatigue life still be predicted on the grounds of what has been considered as the local strain or Neuber approach? A key reference in that regard is the Neuber equation or generally the load versus notch stress, notch strain – or any combination of those – relationship. In a larger study, unnotched and notched specimens from the metastable austenitic steel AISI 347 have been tested and characterized providing a database that may give some answers to the question raised above.The unnotched specimens considered here had a cross-section diameter of 10 mm while the notch radii of the notched components were only 0.5 and 0.35 mm, respectively. Notch radii of such dimensions will easily reach a fully plastic condition once the material has exceeded the yield limit, because the difference in load between yield start in the notch and full plastification is relatively small. This fully plastic state exceeds the validity of the Neuber equation and requires respective corrections. In this paper it is shown how such corrections can be obtained through a finite element analysis and how this applies to the cases mentioned above.

Multiaxial low-cycle fatigue life model for notched specimens considering small sample characteristics

PurposeSufficient sample data are the necessary condition to ensure high reliability; however, there are relatively poor fatigue test data in the engineering, which affects fatigue life's prediction accuracy. Based on this, this research intends to analyze the fatigue data with small sample characteristics, and then realize the life assessment under different stress levels.Design/methodology/approachFirstly, the Bootstrap method and the principle of fatigue life percentile consistency are used to realize sample aggregation and information fusion. Secondly, the classical outlier detection algorithm (DBSCAN) is used to check the sample data. Then, based on the stress field intensity method, the influence of the non-uniform stress field near the notch root on the fatigue life is analyzed, and the calculation methods of the fatigue damage zone radius and the weighting function are revised. Finally, combined with Weibull distribution, a framework for assessing multiaxial low-cycle fatigue life has been developed.FindingsThe experimental data of Q355(D) material verified the model and compared it with the Yao’s stress field intensity method. The results show that the predictions of the model put forward in this research are all located within the double dispersion zone, with better prediction accuracies than the Yao’s stress field intensity method.Originality/valueAiming at the fatigue test data with small sample characteristics, this research has presented a new method of notch fatigue analysis based on the stress field intensity method, which is combined with the Weibull distribution to construct a low-cycle fatigue life analysis framework, to promote the development of multiaxial fatigue from experimental studies to practical engineering applications.

Mechanisms of void nucleation on neat and Glass Syntactic PolyPropylene using in situ synchrotron radiation tomography

The mechanisms of void nucleation of a hollow glass syntactic foam during tensile loading were studied in depth. Flat-notched geometries, cut-out from neat and Glass Syntactic PolyPropylene (GSPP), were investigated by in situ microtomography. Notched specimens with two notch root radii, 4 mm and 0.15 mm named respectively N4 and N0.15, to set initial triaxial stress state in the minimum cross section, were observed. Tomographic data sets, with a resolution of 1.3μm, from stepwise tensile loading, at the SOLEIL synchrotron radiation facilities, were retrieved from the notched zone. In addition, they allowed gathering both the width and thickness evolution in the minimum cross section, and the notch opening displacement during the tests.In line with literature, neat PolyPropylene (PP) showed crazes concentration at the specimen core in N4 specimen, whereas, in N0.15 specimen, they were located at the notch root. In isolated Hollow Glass Microspheres (HGM), mechanisms of crazing and debonding were correspondingly highlighted in the PP matrix and at the poles of HGM. Finally, in GSPP, decohesion follows the same trend as in neat PP, i.e. at the specimen core and near the notch, respectively in N4 and in N0.15 geometry. Scenarios of void nucleation and propagation were outlined. The initiation of the brittle crack in the GSPP is mainly due to the matrix-HGM decohesion followed by the coalescence of near neighbouring caps.

Modeling hydrogen diffusion in precipitation hardened nickel-based alloy 718 by microstructural modeling

Abstract Environmentally assisted cracking can significantly affect the performance of high strength alloys and limit material selection to minimize the risk of subcritical crack growth in service. UNS N07718 is widely used in marine service applications and under a variety of conditions, such as: alternate immersion, different levels of cathodic protection, and freely corroding galvanic couples, because of its demonstrated corrosion and fracture resistance in these environments. In this work we developed a representative model of the material microstructure including the metal grains, the material texture, and the precipitates along the grain boundaries and within the grains. The microstructural model was subjected to the boundary conditions identified at the notch root of a fracture mechanics sample and the results are used as input for a simulation of hydrogen diffusion from the surface of the notch, assuming the material has been introduced to a hydrogen producing environment. The diffusion of hydrogen was modeled by Fick’s law and included both hydrostatic stress and mobile dislocation velocity as driving forces. The influence of immobile dislocations was also modeled to account for the irreversible trapping. The results show that hydrostatic stress and immobile dislocation trapping can significantly alter the highest concentration of hydrogen and its location within the microstructure towards the fracture process zone. Mobile dislocation velocity has a small influence in determining the hydrogen distribution near the fracture process zone.

Dynamic shear resistance and its dependence on geometrical imperfection of high entropy Cantor alloy and BJAM 316L stainless steel

This paper examines the adiabatic shear resistance of recently popular Cantor alloy and Binder Jetting Additive Manufacturing (BJAM) 316L, with emphasis on their dependence on geometrical imperfection. A series of shear tests were conducted by using the long Split Hopkinson bar and shear compression specimen (SCS). Both alloys present strain rate dependent shear behaviour with the large dynamic shear failure strain of about 104 %–132 %. Microstructural characterizations reveal that both Cantor and BJAM 316L alloys fail by adiabatic shear band. Introduced by the varying notch root radius, the sharpness significantly affects the dynamic shear resistance of the Cantor and BJAM 316L alloys. The linear functions are proposed to describe the drop of critical strain and energy density with the designed inverse root radius.

Non-Contact Evaluation of Deformation Characteristics on Automotive Steel Sheets

Non-Contact Evaluation of Deformation Characteristics on Automotive Steel Sheets

New approach to low-cycle fatigue lifetime prediction for deep-rectangular notched components with finite residual thickness: Experiment and simulation

The introduction of notches in engineering components often has detrimental effects on fatigue behavior. Current research on finite residual thickness is extremely limited, especially when dealing with more complex geometric shapes of notches. In this study, the low-cycle fatigue (LCF) life of cylindrical components with deep-rectangular notches were predicted based on the theory of critical distance (TCD) and the total stress field (TSF) method. The results indicated that the presence of stress concentration near the notch accelerated the initiation and propagation of cracks. Furthermore, finite element method (FEM) was conducted, revealing the need to comprehensively consider the stress distribution across the residual thickness zone (RTZ) for notched specimens. Through numerical method improvement and geometric modeling optimizations, the accuracy of fatigue lifetime prediction has been refined to within a margin of ± 1.5. Comparative simulations on notched specimens with various ratio of notch depth to residual thickness were conducted, characterizing the fatigue process zone (FPZ) near the notch root under LCF loading for Q345R steel, indicating that characteristic material parameter d* exhibits minimal fluctuations with changes in the notch size, while the corresponding local stress levels display a logarithmic upward trend, substantiating that fatigue lifetime decreases with larger notch sizes.

The experimental and numerical investigation of fracture behaviour in PMMA notched specimens under biaxial loading conditions – Tension with torsion

This paper presents the results of experimental fracture test of flat PMMA specimens under biaxial loading condition tension with torsion (proportional). The specimens were made in two thicknesses: 5 and 15 mm and were weakened with V-type edge notches with different root radii: 0.5; 2 and 10 mm. Thanks to the ARAMIS 3D 4 M non-contact vision system, measurement of the elongation and twist angle were recorded. During experimental part all of the deformation processes were observed using PHANTOM cameras. Obtained records made it possible to precisely indicate the moment of crack initiation (tensile force and torsional moment values). Using the microscopic observations the location of crack initiations were determined. Results obtained for biaxial loading were compared with those obtained for uniaxial tension and torsion. Based on experimental data the numerical calculation with FEM were carried out. The principal stress and plastic strain distribution under critical load, were obtained. The points of occurrence of stress maxima and plastic strain were indicated, which were taken as potential crack initiation sites. On the basis of the stress and plastic strain values measured at the critical points, a stress–strain fracture criterion was formulated, which was then positively verified. Additionally, new form of stress–strain fracture criterion was proposed. The bilinear form of the fracture criterion can be successfully used to predict fracture in PMMA flat specimens, regardless of the notch root radius, type of load or element thickness.

Notched Tensile Fracture of a Fe-15Mn-0.6C-2Al Twinning Induced Plasticity Steel at Room Temperature

The tensile fracture behavior of an Al-bearing TWIP steel was investigated by conducting a series of tensile tests on smooth and notched specimens with different notch geometries, focusing on the effects of evolution of the stress triaxiality and the effective strain during deformation. The flow curve and digital image correlation (DIC) analysis evidenced suppression of dynamic strain aging due to Al addition, and therefore, the effects of local inhomogeneous deformation associated with Portevin-Le Chatelier (PLC) band on fracture could be excluded. The smooth specimen fractured with negligible necking despite the absence of PLC bands. As a result, the effective strain was uniform through the gage section and the stress triaxiality (<i>η</i>) of ~0.33 was nearly unchanged over the entire cross-section up to the maximum load. This led to the fracture surface of the smooth specimen being entirely covered with fine equiaxed dimples. For notched specimens, the fracture strain was drastically reduced with decreasing notch radius, indicating the high notch susceptibility of the steel. The effective strain of the notched specimens was the highest at the edge of the notch root, regardless of the notch radius, so cracks first developed at the surface of the notch root. Although the <i>η</i> at the center of the notched specimens (0.40~0.48 depending on the notch radius) was higher than that of the smooth one, the center of the fracture surface of all notched specimens exhibited dimple features that were very similar to the smooth one, even in size. In contrast, in spite of the same <i>η</i> of ~0.33, fractography at the edge of the notched specimens revealed a fracture mode transition from dimple fracture to void sheet fracture to quasi-cleavage fracture as the notch radius decreased. The present results were rationalized in terms of the local evolution of stress triaxiality and effective strain during deformation, which were analyzed using the finite elemental method and DIC technique. It can be said that the fracture mode of TWIP steel, showing limited necking, was more influenced by the distribution and/or gradient of stress traiaxiality and effective strain rather than their local absolute values - that is, the severer their gradient is, the easier the quasi-cleavage fracture occurs.

Effects of initial overload on the fatigue crack initiation and growth in notched plates

This paper studies the initial overload effects on the stages of the crack initiation and its growth under fatigue loads in v-notched plates. V-notched samples made of aluminum alloy 2024-T3 were overloaded with different values. These specimens went under fatigue loads with various constant amplitudes and their fatigue behaviors were investigated. Numerical analysis in finite element software with a proper crack growth law was used to estimate the crack initiation cycles to reach a specified length and also crack growth rates and propagations. The superposition principle was employed for considering the effects of the applied and residual stresses on the stress intensity factor ranges. For validation, the estimated results were compared with experimental data which showed good agreement. Results show that the crack initiation lives were increased significantly after an overload cycle due to retardation of micro-cracks creation around the notch root. Compressive residual stresses in comparison with the tensile stresses are dominant in the affected area by the overloads.

Local ratcheting and stress relaxation at notch root of CP-Ti specimen under cyclic loading: Experiment and simulation

Damage and crack always origin from notch, and it is necessary to understand the local ratcheting and stress relaxation at notch root for commercially pure titanium (CP-Ti). Symmetric strain-controlled cyclic test for smooth CP-Ti specimen is conducted to determine the cyclic constitutive relationship based on the combined hardening model. Asymmetric force-controlled cyclic test combined with Digital Image Correlation (DIC) technology is conducted to reveal local ratcheting strain distribution at notch root of CP-Ti specimen, while the distributions of stress, local stress ratio, and local hysteresis curve at notch root are obtained by finite element (FE) simulation. It is found that plastic zone, local ratcheting and stress relaxation at notch root area change significantly with cyclic load levels. In the low stress amplitude region with the mean nominal stress lower than 87 MPa, the small-scale yield occurs, and the notch root is in a state of plastic shakedown. With the mean nominal stress increasing to 96 MPa in the transition region, the notch root is in a state that exceeds the plastic shakedown limit but the continuous ratcheting progress is not found. In the high stress amplitude region with the mean nominal stress higher than 104 MPa, the plastic zone significantly expends, and the notch root is in a continuous ratcheting progress state, accompanied by stress relaxation. For a specific structural configuration, the local ratcheting at notch root is affected by both the load level and the cyclic deformation characteristics of the material. In the high stress amplitude region, the reverse yield occurs at the notch root during unloading, which promotes continuous ratcheting progress and stress redistribution, resulting in stress relaxation. The higher the load level, the larger the ratcheting strain rate, and the lower the stress relaxation rate.

Comparison between slow strain rate test and constant load test on notched specimens for HSLA steels HE susceptibility evaluation

The assessment of hydrogen embrittlement (HE) susceptibility in high-strength steels, intended for use in subsea components that are exposed to cathodic protection for corrosion control, is of great importance. Therefore, the present study investigates the behavior of AISI 4340 steel with hardness of 32, 36 and 40 HRC. The investigation involves employing slow strain rate test (nSSRT) and constant load test (CLT) on notched specimens with three different notch root radii. These tests were carried out under two different levels of cathodic protection (−1100 and −950 mVAg|AgCl) in a 3.5 % wt NaCl aqueous solution. The outcomes from the tests on notched specimens were compared with the hydrostatic stress profile obtained through finite element analysis (FEA). Additionally, the post-test fracture surfaces were analyzed using scanning electron microscopy (SEM). The test results revealed a higher hydrogen embrittlement index (HEI) with increasing material hardness and the applied cathodic potential. Moreover, a smaller notch radius was associated with a higher HEI. A clear correlation was observed between HEI and the extent of intergranular fracture in the test samples. Furthermore, the results from the nSSRT tests were correlated with the threshold stress (σth) obtained from CLT. It was evident that a relationship of σth = 90 %σnSSRT_min could be employed for a faster determination of this parameter.

A two-point fatigue strength assessment for surface-hardened notched components under consideration of residual stresses based on the local strain approach

The “Guideline non-linear” of the German Research Association for Mechanical Engineering provides a fatigue strength assessment for machine components based on the local strain approach. Currently, this assessment is limited to homogeneous components and without the possibility to consider residual stresses. The methods are thus inadequate for surface-hardened components, where the presence of material inhomogeneity and the introduced residual stresses significantly impacts fatigue life and the potential failure origin. In the following paper, an adaptation of the proof of structural durability of the guideline is shown, that firstly includes a two-point assessment and the estimation of load cycles to crack initiation at two failure-relevant points simultaneously. This enables the consideration of inhomogeneous material states, since the failure of surface-hardened components may initiate from the notch root as well as from the transition area between the low-strength core material and the high-strength surface layer. Secondly, the consideration of the residual stress state for both failure-relevant points is also introduced as part of the adapted fatigue strength assessment.

Assessing notch fatigue performance of aluminium alloy AA2024-T4 after uni-axial and equi-biaxial tensile pre-straining: Experimental observations and predictive models

This study delves into the effect of different tensile pre-straining (uni-axial and equi-biaxial pre-strain) modes on the notch fatigue performance of AA2024-T4. By conducting a series of fully reversed stress-controlled high cycle fatigue (HCF) experiments, pre-strained samples demonstrated notable improvements in HCF resistance, surpassing those without pre-strain. A stress-based fatigue life prediction approach, namely the theory of critical distance (TCD), is applied. We propose an experimentally validated physics-based method for predicting notch fatigue life in the HCF regime, utilising the cyclic plastic zone (CPZ) concept and TCD’s point method. The CPZ commonly plays a significant role in both crack initiation and propagation at the notch roots, thereby altering the stress in the vicinity under cyclic loading. However, TCD considers a linear-elastic stress field around the notch root for fatigue life calculation. The model successfully predicts HCF life based on experimental results and gives better prediction than the conventional TCD approach in terms of prediction accuracy, which falls within a range of ± 2 the experimental results for all the pre-strain conditions.

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.

Effect of Hydrogen on Fatigue Life and Fracture Morphologies of TRIP-Aided Martensitic Steels with Added Nitrogen

The effects of hydrogen on the tensile properties, fatigue life, and tensile and fatigue fracture morphologies of nitrogen-added ultrahigh-strength transformation-induced plasticity (TRIP)-aided martensitic (TM) steels were investigated. The total elongation and number of cycles to failure (Nf) of the hydrogen-charged TM steels decreased with the addition of nitrogen; in particular, adding 100 ppm of nitrogen decreased the total elongation and Nf of the TM steels. The quasi-cleavage cracking around the AlN occurred near the sample surface, which is the crack propagation region, although dimples appeared at the center of the fracture surface in the tensile samples. The initial fatigue crack initiated at the AlN precipitate or matrix/AlN interface, located at the notch root. During crack propagation, new cracks were initiated at the AlN precipitates or matrix/AlN interfaces, while quasi-cleavage crack regions were observed around the AlN precipitates. The decrease in the total elongation and Nf of the hydrogen-charged TM steel with 100 ppm of added nitrogen might be attributable to the crack initiation around the AlN precipitates formed by a large amount of hydrogen trapped at the AlN precipitates and matrix/AlN interfaces, and to the dense distribution of AlN, which promoted crack linkage.

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

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.