Notch Crack Research Articles

Stress-Based Model for Calculating the Opening Angle of Notch Cracks in a Magnesium Alloy under Multiaxial Fatigue

This paper presents a model to calculate the opening angle of crack initiation in notched fractures subjected to multiaxial loading. To validate the proposed model, a study was performed on polished AZ31B-F magnesium alloy specimens under multiaxial high-cycle fatigue loading. The specimens exhibited a notch in the smaller cross-sectional area, which was created with a special drilling jig to promote the formation of fatigue cracks in this localized area of the specimen. The load paths used in the experiments and numerical analyses were proportional and non-proportional, resulting in different stress states in the crack front opening, which were determined by finite element analysis to validate the proposed model. To obtain more accurate numerical results for these estimates, these finite element analyses were performed using the nonlinear Chaboche plasticity model of ABAQUS® 2021 software. A sensitivity analysis was also performed to determine which load component—axial or torsional—has a greater influence on the fatigue strength and contributes significantly to the crack opening process. The results show that the type of load path and the stress level of each load component—axial and torsional—has a strong influence on the opening angle of the notch crack and the fatigue lifetime of the specimen. This result is confirmed not only by the experimentally determined fatigue strength, but also by a fractographic analysis performed on the surface of the specimens for both load paths. Moreover, the results show an acceptable correlation between the experimental results and the estimates obtained with the proposed model and the stresses obtained with the finite element analysis.

Effect of microstructure on impact fracture mechanism of a high-strength Ti-5Al-7.5V-0.5Si-0.25Fe-0.2O alloy

The impact property of high-strength Ti-5Al-7.5V-0.5Si-0.25Fe-0.2O alloy (Ti575) with trimodal microstructure (TM) and lamellar microstructure (LM) were investigated by combining instrumented Charpy U-notch impact test with microstructure characterization. Impact load-displacement curves illustrated that the higher impact toughness of LM (47.8 J/cm2) than TM (38 J/cm2) were attributed to both intrinsic toughening during crack initiation and extrinsic toughening during crack propagation. In crack initiation stage of LM, electron back-scattered diffraction (EBSD) evidenced the nucleation of numerous {10–12} <–1011> tensile twins in coarsened lamellar α (αl) in vicinity of the crack notch. The high intrinsic toughness of LM was due to the dynamic microstructure refinement and facilitation of prismatic/pyramidal slip induced by twins during impact. For TM in contrast, smaller-sized primary α(αp) and αl suppressed the nucleation of twins, exacerbated stress concentration and reduced plastic deformation near the crack notch. In crack propagation stage, the kinking, shearing of αl, crack deflection at αl/β interfaces and secondary crack in αl colony borders contributed to a tortuous crack path and large energy dissipation in LM, whereas crack could bypass αp and cut through thin αl in TM easily, resulting in a flat crack path and poor extrinsic toughness of TM. In summary, this work provided a basic understanding of the impact fracture mechanism of Ti575 with different microstructures.

Pressure reduction strategy based on a new CTOD model considering room temperature creep for X80 pipeline steel

The growing demand for energy consumption has led to the rapid development of high strength and high toughness pipeline steel technology, with fracture toughness being a crucial factor in evaluating the mechanical properties of pipeline steel. Despite experimental studies demonstrating that metallic materials, including pipeline steel, undergo creep at room temperature, the effects of room temperature creep (RTC) on pipeline steel fracture properties are still relatively unexplained. This study analyzes the impact of RTC on the fracture toughness of X80pipeline steel, using the X80pipeline steel base material as the research object. Firstly, the time-dependent change in crack notch opening displacement is added to the calculation formula for fracture toughness of three-point bending specimens, considering the effect of RTC. The test data is fitted to a power-law equation of the form, where k=0.01423 and m=-0.89651, with the improved formula indicating an incremental CTOD of approximately 0.0098 mm after 36 h of RTC for X80 pipeline steel. Secondly, a time-dependent CTOD model is proposed based on the ductile defect growth model, with the plastic part derived from the D-B model and the creep part obtained by fitting the test data. The study proposes a CTOD criterion for RTC and a pressure reduction strategy based on this criterion, providing a reference for quantitatively assessing the fracture toughness of pipeline steel under RTC conditions.

Comparison on crack propagation under tension at 150 °C of Mg-2Zn-1.5Mn alloy sheets with and without crack notch

Generally, edge crack of rolled magnesium alloy sheets initiates in the RD (rolling direction)-ND (normal direction) plane and then propagate in the RD-TD (transverse direction) plane. Hence, the Mg-2Zn-1.5Mn (ZM21) alloy sheets with and without crack notch were designed to carry out in-situ tensile experiments under 150 °C (the same temperature of rolling), with the aim to understand their crack propagation mechanism. The scanning electron microscopy (SEM) and electron backscattered diffraction (EBSD) techniques were utilized to reveal microstructural evolution in real time at designated displacements. The results show that the prismatic slip, basal slip, and extension twining play synergistic role in coordinating strain during the tensile process in ZM21 alloy sheet at 150 °C. In both tensile samples with and without crack notch, localized strain is mainly concentrated at relatively fine grain area and the grain boundaries or triple junctions of the grains with large basal Schmid factor (SF) difference, which eventually leads to severe surface roughening and subsequent crack initiation. Compared with the sample without crack notch, the pre-cracked sample exhibits severer deformation at the crack tip due to strain concentration. Strain gradient distribution is observed at the crack tip region in the pre-cracked sample. The crack propagation path of the sample with pre-crack is identified and the underlying mechanism is also discussed.

Fault diagnosis in rotors using adaptive neuro-fuzzy inference systems

Condition monitoring of rotor dynamic systems is emerging research in recent years. The proposed research is a condition monitoring methodology based on Adaptive Neuro-Fuzzy Inference Systems (ANFIS) to detect the open cracks in the single disk rotor-bearing system. Condition monitoring systems generally requires a large amount of processed data for a specific output. The proposed methodology uses the same input data to train two different ANFIS without compromising on the accuracy of the results. The response of rotor-bearing system is generated by using finite element model analysis and harmonic balance method. All simulations are programed in MATLAB programing software. The effects of open groove or wedge cracks (notch crack) on natural frequency and resultant operational response (nodal deflections) of rotor-bearing systems are analyzed. Response orbit at 3× resonance of first natural frequency is analyzed to diagnose the crack in rotor shaft. Resultant operational response (Absolute response due to crack) is recorded for various crack locations and crack depths. Continuous Wavelet Transforms (CWT) are used, to extract the features from operational deflection shape (from operational response) to detect the crack location and their severity (depth). Location of maximum CWT coefficients provides the close vicinity of crack and their magnitude provides the severity of crack. Crack as small as 1% of crack depth to diameter ratio can be identified by CWT. ANFIS are used as a machine condition monitoring methodology to diagnose the crack and predict the crack parameters (crack location and depth). Two Parallel ANFIS are trained to predict the crack parameters. ANFIS-1 is trained for crack location and ANFIS-2 is trained for crack depth. CWT coefficients, maximum response amplitude at the vicinity of crack, and first three natural frequencies are provided as input to both ANFIS-1 and ANFIS-2 for training. The trained condition monitoring methodology accurately detects (predict) the crack location (ANFIS-1) and crack depth (ANFIS-2) with root mean squared error of 0.0833 and 0.137916 respectively.

Investigation of the tensile-shear failure of asphalt concrete base (ACB) construction materials using a non-linear cohesive crack model and critical crack threshold analysis

The American Society for Testing and Materials (ASTM) has recommended ASTM D8044, an international standard test using Semi-Circular Disc Bend (SCB) specimens, to test only the tensile fracture toughness (mod I) of Asphalt Composite (AC) materials. However, AC materials are exposed to not only tensile stresses but also both compressive and shear stresses under wheel load. Thus, one of the main objectives of this study is to develop a new approach for the mixed mode I-II (tension and shear) testing of AC materials by using the SCB geometry. This study deals with a comparative assessment of the fracture toughness of AC materials by using the results of experimental, analytical, and Linear Elastic Fracture Mechanics (LEFM) and Non-LEFM (NEFM) numerical analyses done on the SCB specimens. The numerical analyses of the stress distribution and the cohesive crack growth were performed using the fracture mechanics program FRANC2D. Experimental results showed that the notched cracks opened at a 30° inclination angle (β) and kept opening up to β of 45°. The mode I fracture toughness (KIC) value of Asphalt Concrete Base (ACB) specimens was found at 0.37 MPa√m. On the other hand, the KC value was found to be 0.44 MPa√m for the 30° inclined crack and 0.40 MPa√m for the β = 45° inclined notch crack.The critical crack length for the mode-I loading was found to be 2–2.5 mm using the experimental and Critical Crack Threshold (CCT) analytical analysis, and it was found to be 2.5–3 mm using the NEFM-based cohesive crack analysis. Moreover, the NEFM-based cohesive crack analyses showed the critical crack length was between 3 mm and 7 mm for the mixed mode (I-II) condition, in which the notch cracks are inclined at 30° and 45°. The feasibility of the SCB test proposed by ASTM and AASHTO standards in determining the mixed mode I-II (tensile-shear) fracture toughness value of ACB specimens, which is an important parameter in determining the strength of materials, was verified by comparing the experimental results with LEFM and NEFM numerical analyses. As a result, experimental and numerical analysis results showed that the SCB test could be an appropriate geometry to determine the mixed mode I-II fracture toughness of AC materials when the crack is inclined at 30°. It is believed that this study would be evaluated as initial research on the use of SCB geometry for AC materials not only for mode I test but also for mixed mode loading tests and for the establishment of an international standard test.

Improving toughness of medium-Mn steels after friction stir welding through grain morphology tuning

• The FSW steel showed a higher toughness than the TIG-welded steel and base material. • Morphology tuning by FSW eliminates a weak prior γ boundary and improves the toughness. • The preserved γ R grains after FSW contribute to the improved toughness by active TRIP. This work demonstrated the viability of friction stir welding for the welding of medium-Mn steels when used as cryogenic vessel materials for liquefied gas storage. We used an intercritically annealed Fe-7Mn-0.2C-3Al (wt.%) steel with a dual-phase ( α ′ martensite and γ R retained austenite) nanolaminate structure as a base material and systematically compared its microstructure and impact toughness after friction stir and tungsten inert gas welding. The friction stir welded specimen exhibited a large amount of γ R phase owing to a relatively low temperature during welding, whereas the tungsten inert gas welded specimen comprised only the α ′ phase. Furthermore, the friction stir welded steel exhibited a tuned morphology of nanoscale globular microstructure at the weld zone and did not exhibit any prior austenite grain boundary due to active recrystallization caused by deformation during welding. The preserved fraction of γ R and morphological tuning in the weldment improved the impact toughness of the friction stir welded steel at low temperatures. In the steel processed by tungsten inert gas welding, the notch crack propagated rapidly along the prior austenite grain boundaries—weakened by Mn and P segregations—resulting in poor impact toughness. However, the friction stir welded steel exhibited a higher resistance against notch crack propagation due to the slow crack propagation along the ultrafine ferrite/ferrite ( α / α ) interfaces, damage tolerance by the active transformation-induced plasticity from the large amount of γ R , and enhanced boundary cohesion by suppressed Mn and P segregations. Graphical Abstract .

Research on the effect of thermal treatment on the crack resistance curve of marble using notched semi-circular bend specimen

The crack resistance curve is widely used to describe the complete fracture process of quasi-brittle materials. In the paper, the crack resistance curves of thermally treated marble were tested through the notched semi-circular bend specimens. The acoustic emission (AE) and digital image correlation (DIC) techniques were used to monitor the fracture behaviors of the specimens during the test. The AE results indicated that the crack will initiate from the notch when the axial load is less than the peak load. And, when the axial load reaches the peak load, the DIC results demonstrated that there exists a large fracture process zone (FPZ) in front of the crack notch. The effect crack length was calculated by the compliance method, which is coincided with the DIC results. The amplitude of the crack resistance curves decreases with the increase of treatment temperature, which suggested that the fracture resistance of the specimen declines due to thermal treatment. Based on the K-resistance curves, the initial fracture toughness, unstable fracture toughness, and fracture toughness when FPZ is fully formed have been determined for the thermally treated specimens. The results showed that these parameters both decrease in the increase of treatment temperature. Moreover, The FPZ length first increases and then decreases with the increase of normalized crack length and the critical and maximum non-dimensional FPZ length tends to increase with the increase in treatment temperature.

Axial behavior of circular steel tube with localized penetrating corrosion simulated by artificial notch

Aiming to assess the compressive performance degradation of circular steel tube with localized penetrating corrosion, 26 specimens with artificial notch were tested by considering the corrosion type, corrosion length and corrosion orientation. The experimental results indicated that notch orientation shows the most remarkable effect on the failure model of the tubes. The close of crack notch which would result in the double peak in the load–displacement curve is beneficial for the post-buckling behavior of the tubes. Decreasing the orientation angle of notch would increase the reduction in the compressive resistance of the tubes whilst the type of hole notch is much more favorable than crack notch. Based on the test results, the reduction factors for the compressive resistance of circular short steel tubes with slim localized penetrating corrosion are described by a semi-empirical formula. The parametric analysis confirms that the proposed design formula predicts the compressive resistance of the circular tube with slim localized penetrating corrosion well.

Stress-based structural topology optimization for design-dependent self-weight loads problems using the BESO method

This article aims to propose an approach to the stress-based topology optimization of continuous elastic bi-dimensional structures subjected to design-dependent self-weight loads using the Bi-directional Evolutionary Structural Optimization (BESO) method. Topology optimization is developed through the minimization of P-norm von Mises stress while satisfying a volume constraint. To implement the algorithm, a consistent sensitivity analysis including design-dependent loads has been developed by the adjoint method. A series of tests has been performed to explore and validate the method through three numerical examples: an L-bracket; a doubly supported beam with one pre-existing crack notch; and a cantilever beam. Comparison between traditional compliance minimization and stress minimization analyses, including design-dependent self-weight loads, shows that the method is an effective way to reduce the maximum stress.

Structural characterization of semiconductor multi-layer pad

Structural mechanics and mechanical reliability issues are becoming more and more challenging in the semiconductor industry due to the continuous trend of the device dimensional shrinkage and simultaneous increased operative temperature and power density. As main consequence of the downsizing and more aggressive operative conditions, the mechanical robustness assessment is now having a central role in the device engineering and assessment phase. The risk of mechanical crack in the brittle oxide layers, which are embedded in pad stacks, increases during the device manufacturing processes such as the electrical wafer testing and during wire bonding. This risk increases with the presence of intrinsic mechanical stress in individual layers resulting from the metal grain growth mechanisms, the stack layers’ interfacial mismatches in coefficients of thermal expansion and the temperature stress induced by doping diffusion and film deposition. The current trend of innovation in the electronic industry is going over the semiconductor material itself and it is now impacting the improvement of the Back-End of Line. Key actors are becoming the interactions between the semiconductor die and the device packaging such as adhesion layers, barriers and metal stacks. In the present work, different pad structures have been structurally analyzed and benchmarked. The experimental characterization of the pad structures has been done through a flat punch nano-indentation to investigate on the mechanical strength and the crack propagation. The considered mechanical load reproduces the vertical impact force applied during wire bonding process to create the bond-pad electrical interconnection. The obtained testing results have been compared to finite element models to analyze the stress distribution through the different layers’ stacks. Scope of this work is to demonstrate the validity of the proposed integrated numerical/experimental methodology, showing the impact of the metal connections layouts by the analysis of the stress notch factors and crack propagation behaviour.

Portable Generator to Detect Cracks on Large Steel Structures: An Application of Inductive Thermography

The demand of non-destructive methods to detect cracks caused by fatigue or brittle behavior in large steel structures has increased in the last years. Thermography based on electromagnetic induction is a promising method to detect cracks in weld seams and notches. This paper presents a portable experimental setup, which allows to perform in situ crack detection tests on large steel structures. The success of this configuration is based on the use of a highly efficient switched H-Bridge circuit, which can generate a square-wave output voltage with a fundamental frequency up to 100 kHz. Due to the low losses and the low necessary DC-link voltage, the circuit can be supplied by a lithium-ion battery, which allows a small and light setup. The generated square-wave output voltage supplies an air coil resulting in a high frequent triangle current. The induced electromagnetic field caused by the current signal generates eddy currents in the steel structure. Due to an increased current density of the eddy currents in the crack area, there is a measurable temperature increase near the crack. The resulting temperature field is visualized and recorded with an infrared (IR) camera, which shows in real time the occurrence of cracks.

Laser Shock Peening of SiCp/2009Al Composites: Microstructural Evolution, Residual Stress and Fatigue Behavior.

SiC particle reinforced aluminum alloy has a wide application in the aerospace industries. In this study, laser shock peening (LSP), an advanced surface modification technique, was employed for SiCp/2009Al composite to reveal its microstructure, microhardness and residual stress evolution. After peening, high densities of dislocations were induced in the aluminum substrate, and stacking faults were introduced into the SiC particle. The microhardness was increased from 155–170 HV to 170–185 HV, with an affected depth of more than 1.5 mm. Compressive residual stresses of more than 200 MPa were introduced. The three-point bending fatigue of the base material, laser peened and milled after laser peened specimens with artificial crack notch fabricated by a femtosecond laser was investigated. The average fatigue lives of laser peened and milled after laser peened specimens were increased by up to 10.60 and 2.66 times, compared with the base material. This combined fundamental and application-based research seeks to comprehensively explore the applicability of LSP on metal matrix composite.

Analysing mixed mode (I–II) fracturing of concrete discs including chevron and straight-through notch cracks

Pre-existing cracks in concrete material and discontinuities in concrete structures are seldom subjected to pure tensile loading (mode I); rather, they are subjected to compressive, shear (mode II) or mixed mode loading (mode I-II). Cracked Chevron Notched Brazilian Disc (CCNBD) and Semi-Circular Brazilian (SCB) specimens including chevron notch and straight-through cracks were used in this research to analyse mixed mode fracturing of concrete. Both the experimental and numerical results showed that the crack initiation angle (θ) was found dependent on the crack inclination angle (β). Moreover, CCNBD specimens with chevron notch crack geometry was found more suitable than the SCB geometry with straight-through notch crack to analyse mixed mode fracturing behaviour of plain concrete. However, using CCNBD or SCB specimens straight-through notch cracks may be more useful for testing the fracturing properties of coarse-grained concrete as sharp chevron cracks reduce the possible Fracture Process Zone (FPZ) size in front of the notch crack tip. Further analyses showed that the critical crack length is found as 13 mm (dimensionless notch length (α) = 0.5). Thus, it is understood that the unstable crack propagation starts between the initial chevron notch crack and final chevron notch crack length and it shows all experiments were done accurately. This outcome would be useful for concrete researches to obtain the yield point by using the relative analysis for finding where the unstable crack propagation starts.

Influence of Notch Sensitivity and Crack Initiation Site on Low Cycle Fatigue Life of Notched Components under Multiaxial Non-proportional Loading

A series of strain-controlled multiaxial low cycle fatigue (LCF) tests under proportional and non-proportional loading conditions have been conducted on notched specimens. Cylindrical bars of Al 6061 aluminum alloy and AISI 316L stainless steel with four values of stress concentration factors referred to the net section Kt,n were employed. The experimental results evidenced a reduction of fatigue life due to non-proportional loading. Furthermore, the crack initiation site has been detected to be moved from the notch tip in the case of steel for high values of notch radius under non-proportional loading. Stress concentration factor evaluated in the elastic field Kt,n has been included in the Itoh-Sakane parameter to evaluate the fatigue life, returning a general underestimation of fatigue life especially for high values of Kt,n. Material notch sensitivity and crack initiation position have been taken into account to further modify the model, improving the original results and showing a better assessment.

A generalized weight function for cracks emanated from sharp and blunt V-notches

This paper presents a generalized weight function which applicable to cracks initiated from V-notches with sharp or blunt tips. The proposed function is based on the composition solution of the weight function of an edge crack in a semi-infinite plate. For obtaining the proper relation, two correction factors are used to express the effects of the notch depth, root radius, and opening angle. Each factor can be applied separately to present only the effects of the notch depth or root radius to improve solutions that proposed in the earlier studies. This method can be used for studying the effects of the notch parameters and loading conditions on the stress intensity factors of the notch cracks. The accuracy of the proposed function was verified by comparing the results with finite element data for a case study.

Stress Intensity Factors for Cracks Emanating from a Notch under Shear-Mode Loading

The influence of the notch geometry on the stress intensity factor at the front of the emanating cracks is well known for the opening loading mode. The critical length of the crack corresponding to a vanishing of the influence of the notch stress concentration can be approximately expressed by the formula aI,c = 0.5ρ(d/ρ)1/3, where d and ρ are the depth and radius of the notch, respectively. The aim of the paper was to find out if this formula could be, at least nearly, applicable also to the case of shear mode loading. The related numerical calculations for mode II and III loading were performed using the ANSYS code for various combinations of notch depths and crack lengths in a cylindrical specimen with a circumferential U-notch. The results revealed that, for mode II loading, the critical length was much higher than that predicted by the formula for mode I loading. On the other hand, the critical lengths for mode I and mode III were found to be nearly equal.

Shear Mode Stress Intensity Factors for Serrated Crack Fronts

The paper is related to experiments on near-threshold fatigue cracks under shear modes II, III and II+III in bcc metals. Cylindrical bars with circumferential cracked notch were loaded by shear force. In-plane precracks with microtortuous geometry were created by compressive cyclic loading in mode I to measure the effective values of the remote crack driving force. Fatigue cracks in bcc metals loaded under remote shear modes II, III and II+III always grew by creation of local tongues loaded in mode II and their coalescence. Therefore, serrated precrack fronts of a linear roughness identical to those of the real fronts were modeled and the related local stress intensity factors k2 were calculated. Since such FEM calculation for various values of roughness were time consuming, a further task was to identify a lowest number of isolated teeth that produces k2 components identical with those created by the continuously serrated crack front. The results reported in this article reveal that this condition is fulfilled by only two isolated teeth.

Experimental and calculation challenges of crack propagation in notches – From initiation to end of lifetime

Notches reduce significantly the lifetime of cyclically loaded components due to their stress concentration and early crack initiation. In this work the initiation and crack growth behaviour of cracks in notches has been studied with the direct current potential drop technique. Due to the notch geometry and semi-elliptical shape of the starting crack, significant differences between the crack length determination by the Johnson equation and the real crack length have been observed. By means of numerical simulations for single and multiple crack initiation sites, a calibration function for determining the crack length from the potential drop has been developed. The calibration function results in a good agreement between the estimated and measured changes of the potential drop and permits a quite accurate estimation of the crack initiation life time.

Distribution of Aspect Ratio of Fatigue Crack at Notch Root Depending on Crack Initiation Point of Annealed Steel, JIS S45C

Aspect ratio of crack is one of key factors of fatigue strength prediction in engineering design and civil structures using fracture mechanics. Their empirical shapes are changed by stress concentration. However, it was not clear how stress concentration affects empirical results including crack shape and size. In this study, in order to investigate the relationship between stress concentration and crack geometry, the aspect ratio of cracks at notch root was observed and discussed. We succeeded to capture two important relationships which are between stress concentration and crack shape, and between crack initiation point at notch root and crack shape, respectively.