Notched Round Bar Research Articles

Fracture toughness using strain energy density for aluminum alloys with notched round bars

ABSTRACT This paper introduces a refined method for measuring the fracture toughness of aluminium alloys using notched round bar (NRB) specimens. By incorporating plasticity effects and empirical adjustments, a model based on strain energy density (SED) is proposed. The refined values were validated against experimental data for aluminium 6061-T6 and 2011-T6 alloys. The results demonstrate that the proposed method yields fracture toughness values closely matching the experimental results, underscoring its potential for standardisation and practical applications in material testing and engineering design.

Radiation and thermal embrittlement of RPV steels: the links of embrittlement mechanisms, fracture modes and microcrack nucleation and propagation properties. Part 1. Strategy, program and methods of experimental and numerical studies

Further development of local approach models is considered from viewpoint of links of local brittle fracture properties with embrittlement mechanisms and fracture modes for RPV steels. Strategy and program of experimental and numerical investigations have been developed that allows one to find how various embrittlement mechanisms and fracture modes are connected with the conditions of nucleation and propagation of microcracks resulting in brittle fracture of RPV steels. The experimental and numerical investigations are performed for 2Cr-Ni-Mo-V steel and A533 steel used for RPVs of WWER and PWR types. RPV steels are studied in the following states: (1) initial (as-produced); (2) thermally embrittled by a hardening mechanism; (3) thermally embrittled by a non-hardening mechanism; 4) irradiated. Experimental studies include testing specimens of different geometry (smooth and notched round bars, and cracked compact tension specimens), which allows us to obtain characteristics of brittle fracture under various stress triaxialities. Numerical studies performed with the probabilistic brittle fracture model Prometey aim to obtain the brittle fracture properties on micro- and macroscales for all the investigated states of the materials.Part 1 of the paper presents information concerning the investigated materials, the used procedures and methods. Part 2 gives the test results of smooth round bars of the investigated materials in various states and the stress-strain curves determined over wide temperature range. The experimental results for various specimens from the investigated steels in various states are represented and compared with the results predicted with the Prometey model in Part 3.

Radiation and thermal embrittlement of RPV steels: the links of embrittlement mechanisms, fracture modes and microcrack nucleation and propagation properties. Part 3: Brittle fracture modelling and analysis of the link of microcrack nucleation and propagation properties and embrittlement mechanisms

Radiation and thermal embrittlement of RPV steels are studied from viewpoint of links of brittle fracture properties on micro- and macroscales. Brittle fracture properties on macroscale (such as fracture toughness and fracture stress) and the critical parameters controlling nucleation and propagation of microcracks are determined on the basis of the probabilistic brittle fracture model Prometey. The experimental and numerical investigations are performed for 2Cr–Ni–Mo-V steel and A533 steel used for RPVs of WWER and PWR types. RPV steels are studied in the following states: (1) the initial (as-produced) state; (2) the thermally-embrittled state modelling hardening mechanism of embrittlement; (3) the thermally-embrittled state modelling non-hardening mechanism of embrittlement; (4) the irradiated state. The test results of various specimens (smooth and notched round bars and cracked compact tension specimens) from the investigated steels in various states are represented over brittle fracture temperature range. Brittle fracture modelling is performed with the Prometey model for all the above specimens, and the experimental and numerical results are compared. On the basis of the obtained results the links between embrittlement mechanisms, fracture modes and microcrack nucleation and propagation properties are found.

Experiment and prediction of the strain-range dependent ultra-low-cycle fatigue based on micromechanical cyclic void growth model

Under severe seismic action, the local stress concentration region in steel structures is prone to the ultra-low-cycle fatigue (ULCF) under high triaxiality and irregular cyclic deformation with intensively varying strain amplitudes. It emphasizes the necessity of the jointed effects of the stress triaxiality and strain range incorporated in the ULCF life prediction. Given the limited relevant studies in terms of the underlying micro-mechanisms, this paper focuses on experimental and modeling studies of the combined effects of stress triaxiality and strain range on the ULCF failure, based on Gurson-Tvergaard-Needleman (GTN) microvoid evolution theories. Monotonic tensile tests on three types of notched round bars suggest that fracture strain decreases with increasing triaxiality. Cyclic tests on two types of notched bars under various strain ranges confirm the combined effects of stress triaxiality and strain range. Given a specific triaxiality, the ULCF damage accumulation rate increases linearly as the tensile plastic strain range ramps up. For the same tensile plastic strain range, higher triaxiality results in a greater damage accumulation rate. In the modeling studies, the consistency of the GTN and uncoupled damage models has been proven in terms of ULCF failure of structural steel. Based on GTN theories, a new micromechanical cyclic void growth model (GCVGM) is proposed, considering the detailed processes of void nucleation, growth, and coalescence under monotonic and cyclic loadings. Moreover, the joint effects of stress triaxiality and strain range can be explicitly described within a unified framework, without additional empirical assumptions. Based on experimental and simulation results, the proposed GCVGM shows significant advantages over conventional models in accurately predicting ULCF failure under various loading protocols, with low average errors of 2.73 % and −0.91 % for two types of notched bar specimens, respectively.

Effect of direct-quenching and tempering on hydrogen-induced delayed fracture resistance of high-strength bolt steel

This investigation attempts to explore the potential significance of controlled forging, i.e., direct-quenching at two different finish-forging temperatures of ∼930 °C (B8H sample) and ∼780 °C (B8L sample), and tempering at 600 °C in improving the hydrogen-induced delayed fracture (HIDF) resistance of a 1300-MPa-grade high-strength bolt steel by constant load tensile testing using circumferentially notched round bar specimens and hydrogen thermal analysis. The microstructural characteristics of the tested samples were analyzed and their influences on HIDF were discussed. The results showed that the B8L sample demonstrated a considerably increased HIDF resistance expressed by critical notch delayed fracture stress of 1825 MPa and a decreased hydrogen embrittled index of as low as 21% compared with those of 1675 MPa and 27% for the B8H sample, although the former exhibited slightly higher strength and absorbed hydrogen content. Scanning electron microscopy observation of the fracture surface demonstrated that the B8L sample prevented the brittle intergranular fracture with smaller quasi-cleavage facet and decreased area fraction of the brittle crack initiation zone compared with the B8H sample. The increased resistance to HIDF of the B8L sample is primarily because of its fine microstructure with increased number of finely distributed V-rich nanoscale MC precipitates and decreased dislocation density. It is proposed that controlled forging coupled with V-microalloying is a feasible and economical way to further increase the HIDF resistance of high-strength bolt steel.

The cyclic GTN model for ULCF fracture analysis of Q355 steel

The cyclic GTN (C-GTN) model, built upon the GTN model, considers the influence of cyclic loadings on the evolution of microvoids, enabling the prediction of ULCF fracture in materials. In this study, the C-GTN model was calibrated for Q355 steel based on tests on notched round bar specimens reported in the literature. Following existing four tests on single-edge notched plate (SENP) specimens subjected symmetric cyclic loadings, additional four ULCF tests were conducted on SENP specimens with asymmetric cyclic loadings. ULCF fracture was observed in these tests and ULCF lives of these SENP specimens were obtained. Mesh sensitivity was investigated for the ULCF fracture analysis of the SENP specimens with the C-GTN model. After balancing the computational accuracy and cost, the ULCF fracture analysis of the SENP specimens were conducted using finite element models with a mesh size of 0.2 mm at the notch tip. ULCF lives predicted by the C-GTN model agree very well with test results for all SENP specimens. The agreement validated the applicability of the C-GTN model for the ULCF fracture analysis of Q355 steel. The increase of the void volume fraction and the degradation of its critical value played dominant roles in the ULCF fracture of V-notched and U-notched SENP specimens respectively.

Cyclic Void Growth Model Parameter Calibration of Q460D Steel and ER55-G Welds after Exposure to High Temperatures

When high-strength steel is heated to high temperatures and then cooled naturally, its ductility decreases. In earthquake-prone areas, it is necessary to evaluate the ultra-low cycle fatigue fracture (ULCF) behavior of high-strength steel structures after a fire if these structures are used continuously. However, the ULCF fracture model of high-strength steel subjected to high temperatures followed by natural cooling has not been deeply studied. In view of this, twelve notched, round bar specimens fabricated from Q460D steel and ER55-G welds were heated to 900 °C followed by natural cooling and then cyclic loading experiments and finite element analyses (FEA) were performed on these specimens. The fracture deformation obtained from the experiments was used in the FEA to calibrate the damage degradation parameter of a Cyclic Void Growth Model (CVGM) of Q460D steel and ER55-G welds under this condition. The calibrated values were 0.30 and 0.20, respectively. The calibrated CVGM was employed to predict the number of cycles and the force and displacement at the fracture moment of the notched round bar specimens. The predicted results aligned closely with the experimental results, indicating that CVGM is effective in predicting the fracture of Q460D steel and ER55-G welds following exposure to 900 °C and subsequent natural cooling.

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

Ductile fracture prediction of additively manufactured Ti-6Al-4 V alloy based on void growth and coalescence of a unit-cell model

In this work, we have studied the fracture mechanism and proposed a micromechanical method with a unit cell model to predict the ductile fracture of additively manufactured (AMed) Ti-6Al-4 V alloy. The tensile experiments with smooth round bars and notched round bars were conducted to investigate the mechanical properties and ductile fracture behavior of materials. The proposed unit-cell model was validated by quasi-static tensile fracture tests to predict the ductile failure of titanium alloy manufactured by laser power bed fusion (L-PBF) under different stress states, which include a wide range of stress triaxialities. An equivalent initial void fraction was introduced to evaluate the ductile behavior of the titanium alloy. Our investigation shows that the stress states significantly influence the void coalescence behavior of AMed Ti-6Al-4 V alloy, and the fracture locus of L-PBF fabricated Ti-6Al-4 V alloy under different stress states was successfully predicted by the proposed unit-cell model under proportional loading. Our study provides useful guidance for the future design and application of metal materials for additive manufacturing.

Continuous damage model for structural steels and weld metals under ultra-low-cyclic loading

For the fracture problem of structural steel under strong earthquakes, a continuous damage model which comprehensively considers the influence of stress triaxiality and Lode parameter was proposed in this paper. According to the variation law of Mises stress under cyclic loading, this model decomposes the effective cumulative plastic strain into isotropic hardening and kinematic hardening components, assuming a linear proportional relationship between the fatigue damage induced by these two components. The basic mechanical properties and constitutive relationships of five common Chinese structural steels and four corresponding weld metals were investigated. The fracture failure tests for both notched round bar specimens and pure shear specimens subjected to monotonic tensile and ultra-low-cyclic loading were thoroughly examined on these materials. The continuous damage model parameters were calibrated by means of test results and complementary finite element simulations. Experimental and numerical simulation results indicate that Q690 high strength steel exhibits cyclic softening behavior, whereas the other steels show cyclic hardening characteristics. For pure shear specimens, plane strain specimens and shear energy dissipation cover plates, the continuous damage model was adopted to simulate and analyze the damage development and fracture failure process of the specimens. The predictions for crack initiation, crack propagation and fatigue life are consistent with experimental results, lending further credibility to the model. The calibrated continuous damage model of various steels provides an effective means for analyzing the ULCF fracture failure of structural steel under intense earthquakes.

Fracture prediction and damage evolution of Q690 HSS under various stress states

The high strength and light weight of the high strength steel (HSS) make it extensively used. However, the reduction in ductility often leads to prominent fracture issues. The Q690 steel, with a yield strength greater than 690 MPa, is one type of Chinese HSS, and its fracture behavior, especially under complex stress states, is a growing concern. Therefore, this study tests a series of monotonic tensile specimens of Q690 HSS with various stress states to obtain the fracture results. Subsequently, a new Lode-dependent enhanced Lemaitre (NLEL) model is proposed. This model integrates the damage effect of the Lode parameter into the original Lemaitre model, enhancing the accuracy of fracture prediction specifically under shear-dominated stress scenarios. Comparative analysis among the Lemaitre model, NLEL model, and another Lode-dependent enhanced Lemaitre (LEL) model reveals that the proposed NLEL model delivers more comprehensive fracture prediction across all tested specimens, including smooth round bars, notched round bar, flat grooved plates, pure-shear plates as well as tensile-shear plates. Furthermore, this study delves into the analysis of damage evolution under representative stress states and initiates discussions regarding the coupled damage model.

Mechanical properties and constitutive model of filling medium in hot casting socket at elevated temperatures

Hot casting sockets have been commonly applied in the prestressed structures to anchor steel cables. However, the study on the fire behaviour of hot casting sockets is limited, particularly in relation to the thermo-mechanical properties of the filling medium. This paper experimentally investigates the mechanical properties of a zinc copper alloy (employed as the filling medium) at varying target temperatures. A comprehensive range of stress–strain curves are obtained by using a digital image correlation measurement system. The elastic modulus, proportional limit, effective yield strength and ultimate strength are presented and compared to those of steel cables. It is found that the strain hardening effect diminishes as the temperature increases. Reduction factors of elastic modulus, effective yield strength and ultimate strength of the zinc copper alloy are smaller than those of steel cables at elevated temperatures, indicating the vulnerability of the filling medium in fire scenarios. Mathematical formulas of reduction factors of mechanical properties are proposed. Furthermore, a novel constitutive model is proposed by modifying the Johnson-Cook model. Parameters involved in the stress–strain relationship are determined by the smooth round bar test results, whereas those in the failure criterion are determined by the notched round bar test results. Finally, the modified constitutive model is applied in a finite element model, and the numerical results have good agreement with the test results.

Unstable stress-triaxiality development and contrasting weakening in two types of high-strength transformation-induced plasticity(TRIP) steels: Insights from a new compact tensile testing method

The impact of high stress triaxiality on work hardening in transformation-induced plasticity (TRIP) steel has been widely acknowledged, particularly through measurements of the austenite fraction. Understanding this TRIP behavior is crucial for predicting material fracture in press-forming processes. However, the actual flow stresses under high-stress-triaxiality conditions remain largely undetermined. To address this gap, we developed a new tensile testing method using tiny notched round bars to investigate stress-triaxiality-induced work hardening in TRIP steels. The specimens were analyzed using two-dimensional micrometry to allow finite element analyses to identify the flow stress. Additionally, we conducted in situ tensile tests in which their crystal lattice stresses were monitored using synchrotron X-ray diffraction (XRD) to realize mechanism analyses of the unexpected work-hardening behavior identified by the developed tensile testing method. Our combined approach revealed a mutual, unstable increase in the flow stress and stress triaxiality in the TRIP-aided bainitic ferrite steel, which reduced the hardening exponent coefficients and thus induced a higher stress triaxiality. In contrast, the TRIP-aided martensitic steel exhibited a weakening behavior, characterized by a significant decrease in the hardening exponent coefficients in the case of the sharpest notch. XRD analyses showed that microstructural heterogeneity led to an extraordinarily high hydrostatic stress in the austenite phase, accounting for these contrasting behaviors. This finding challenges the established consensus on TRIP steels and suggests the need for a revised framework for their application in press-forming, taking into account stress-triaxiality conditions.

A cyclic GTN model for ultra-low cycle fatigue analysis of structural steels

Ultra-low cycle fatigue (ULCF) is a critical concern in the seismic design of steel structures due to its adverse effects on the ductility and energy dissipation capacity of steel connections. The Gurson-Tvergaard-Needleman (GTN) model, a well-accepted micromechanical fracture model, cannot be applied directly to ULCF analysis, as it requires proper estimation of the effects of cyclic loadings on the ductile fracture of materials. In this paper, a cyclic GTN (C-GTN) model was proposed for the ULCF prediction of materials, in which the evolution of microvoids during ULCF loadings was addressed for tensile and compressive half load cycles, respectively, and the effect of the cumulative plastic strains on the material’s resistance to ductile fracture was considered by the reduction of the critical void volume fraction for void coalescence. Then, a VUMAT subroutine was programmed for the C-GTN model, in which the cyclic hardening behavior of materials was simulated with the Voce-Chaboche model. Finally, the C-GTN model was calibrated for the G20Mn5QT cast steel based on previous tests on notched round bar specimens of the material. The applicability of the C-GTN model and the VUMAT subroutine were validated in the ULCF analysis of double-hole plate specimens of the G20Mn5QT cast steel.

Effect of stress triaxiality on the hydrogen embrittlement micromechanisms in a pipeline steel evaluated by fractographic analysis

Hydrogen gas, as an energy carrier, is expected to play an important role in the storage and transport of energy produced by renewable sources. The transport of hydrogen gas can be managed through the use of existing pipeline networks. However, the uptake of hydrogen in steel structures is known to cause a degradation of mechanical properties, a phenomenon called hydrogen embrittlement (HE). In this study, the hydrogen-assisted ductility loss of an API 5L X70 pipeline steel is investigated. The influence of hydrogen on mechanical behavior is evaluated by tensile tests on uncharged and hydrogen charged specimens. These tests are performed on notched round bar specimens with different notch radii, allowing for a range of positive stress triaxialities to be examined. Notched samples are more embrittled than unnotched specimens after hydrogen charging. Hydrogen signatures in the form of fisheyes and quasi-cleavage are detected on the fracture surface. Fisheyes initiate primarily at segregation bands in the steel for all specimen geometries. Fisheyes can also be linked to different inclusion types present in the steel, depending on notch geometry. For unnotched as well as the least sharply notched specimens tested in this study, the embrittlement can be correlated with the area fraction of fisheyes on the fracture surface.

Ductile fracture of LYP225 steel: Effects of stress states and loading histories

This paper presents the experimental and modeling studies of the ductile fracture initiation of LYP225 steel, considering the stress state and loading history dependency. The monotonic material tests, including the notched round bars (NRBs), flat grooved plates (FGPs), and the shear plates (SPs), confirm the prominent stress state dependency of the ductile fracture. The increased stress triaxiality will significantly reduce the fracture strain, and the shear effect quantified by the Lode angle parameter will degrade the deformability under similar triaxiality. The Hosford-Coulomb fracture criterion can well characterize the relationship between fracture strain and stress state variables. Regarding the cyclic loading, a generalized expression of the cut-off region is proposed to consider the temporarily frozen damage accumulation under compression applied. In addition, the premature cyclic fracture initiation predicted by the monotonic fracture criterion highlights the necessity of considering the loading history effect. Based on the plastic strain memory surface, a reduced factor is introduced for the lower damage accumulation rate under cyclic loading. By comparing the testing and predicted plastic deformation corresponding to fracture initiation, the proposed fracture model is validated under different stress states and loading protocols, as indicated by the low average percentage errors of 4.02% for monotonic loading and 16.7% for cyclic loading.

Miniature specimen tests and fracture model of heat affected zone material

AbstractThe paper investigates the mechanical properties of the heat affected zone (HAZ) material near welds and compares the properties to those of the base metal and weld materials. A dedicated experimental set‐up was designed and manufactured to test miniature specimens with a cross‐section width in the range of 1 mm to 2.5 mm and a parallel gauge length of less than 10 mm. To identify the HAZ of the welded connections, a macro‐etching technique was adopted, and the shape and size of the HAZ were measured. Afterwards, miniature specimens were extracted from the base metal, weld and HAZ in both the longitudinal and transverse directions of the weld, and subsequently tested in the specialised experimental set‐up. The miniature specimens not only included the normal rectangular plate‐type specimen, but also the notched round bar and grooved plane strain types of specimens. Hence, the stress‐strain curve and fracture strains under various stress states were obtained from the tests. The validity of the Lode angle Modified Void Growth Model (LMVGM) was investigated using the experimental data, and the fracture loci of the base metal, weld and HAZ in both the longitudinal and transverse directions were identified.

Stress Intensity Factor Solutions for Eccentric Annular External Cracks in Notched Round Bars under Tensile Loading

In this paper, stress intensity factor (SIF) solutions of eccentric annular external cracks in elliptical notched round bars under tension loading have been obtained from 3D finite element analysis, along with their relation to the energy release rate obtained with the J-integral contour. The analysis variables have been the ligament diameter, its eccentricity, and the elliptical notch aspect ratio. The maximum SIF increases with the ligament eccentricity, the presence of the notch (compared to when the bar is smooth), and the elliptical notch axial semi-axis (for the same notch depth); it decreases with the ligament diameter. For external cracks, eccentricity induces bending of the bar subjected to tensile loading, which can produce partial and full contact of the crack surface, relevant phenomena in terms of the SIF value at the different points of the crack front.

Fracture prediction of Fe-SMA under monotonic and low cycle fatigue loading

A total of 18 Fe-SMA notched round bars were tested to study their monotonic and low-cycle fatigue (LCF) fracture behavior, followed by FE simulation to calibrate necessary parameters for void-growth-model (VGM) and cyclic-void-growth model (CVGM). Subsequently, Fe-SMA shear-panel-type and bar-type dampers are considered for further validation. The CVGM is shown to predict the LCF fracture of these Fe-SMA dampers with good accuracy under large strain amplitudes, but may underestimate their LCF resistance under small strain amplitude. A phenomenological modified CVGM is developed to provide a more accurate and consistent fracture prediction for Fe-SMA under a spectrum of strain amplitudes.

A new ductile fracture model for Q460C high-strength structural steel under monotonic loading: Experimental and numerical investigation

Tensile fracture static tests on nine specimens covering different stress states were performed to investigate the ductile fracture behavior of Chinese Q460C high-strength structural steel (HSS). Based on combining the Rice-Tracey model and Xue model, the new model considering the effect of stress triaxiality and Lode angle was proposed to predict ductile fracture of Q460C HSS. Furthermore, the stress softening criterion was incorporated into the new fracture model to simulate the fracture propagation of Q460C HSS better. The material parameters of the proposed fracture model for Q460C HSS were identified using MATLAB optimization code. The VUMAT subroutine was developed to perform ductile fracture simulations for each specimen, and the fracture simulation results show satisfactory agreement with the experimental results. In addition, the five existing ductile fracture models were also selected to compare the prediction accuracy of the new model. The comparative results show that the new model has better accuracy and is more suitable for predicting fracture initiation and propagation of Q460C HSS. Finally, the applicability of the new model in predicting the fracture of Q460 HSS was furtherly verified by successfully simulating the existing fracture tests of the notched round bar specimens and the bolted connections.