Notched Round Bar Research Articles

Study on cyclic constitutive model and ultra low cycle fracture prediction model of duplex stainless steel

This paper calibrates micromechanical fracture models for duplex stainless steel in order to study its fracture behaviour under seismic loading, characterized by large strain ultra low cyclic conditions. In this investigation, smooth round bars and notched round bars were subject to monotonic and cyclic loading. Monotonic and cyclic loading constitutive models were calibrated against smooth round bar test tests. The fracture toughness parameters of the void growth model (VGM), the stress modified critical strain (SMCS) model and the cyclic void growth model (CVGM) were calibrated against the notched round bar tests. Furthermore, the skeleton curve, hysteresis loop and characteristic length of duplex stainless steel were also investigated. The test results indicate that duplex stainless steel exhibits cyclic hardening behaviour under cyclic loading, and the subsequent numerical simulation successfully captured this behaviour. The toughness parameters of duplex stainless steel are generally higher than those for carbon steel grades Q345B and Q460, which demonstrates that duplex stainless steel has better toughness. All the experimental results provide useful data for the prediction of ultra low cycle fatigue (ULCF) fracture of duplex stainless steel.

Modeling of plasticity and fracture behavior of X65 steels: seam weld and seamless pipes

A non-associated/associated flow rule coupled with an anisotropic/isotropic quadratic yield function is presented to describe the mechanical responses of two distinct X65 pipeline steels. The first as a product of the cold-rolling forming (UOE) process also known as seam weld pipes and the second as a result of high temperature piercing process called seamless tube manufacturing. The experimental settings consist of a wide range of sample types, whose geometric characteristics represent different state of stresses and loading modes. For low to intermediate stress triaxiality levels, flat specimens are extracted at different material orientations along with notched round bar samples for high stress triaxialities. The results indicate that despite the existing differences in plasticity between materials due to anisotropy induced processes, material failure can be characterized by an isotropic weighting function based on the modified Mohr–Coulomb (MMC) criterion. The non-associated flow rule allows for inclusion of strain directional dependence in the definition of equivalent plastic strain by means of scalar anisotropy (Lankford) coefficients and thus keeping the original capabilities of the MMC model.

Hydrogen embrittlement behavior of high strength bainitic rail steel: Effect of tempering treatment

Abstract The present study was attempted to evaluate the effect of tempering treatment on the hydrogen embrittlement (HE) behavior of a novel bainitic rail steel by using slow strain rate test (SSRT) with notched round bar specimens. The microstructure of the as-hot rolled rail steel mainly consists of granular bainite and ~9 vol% martensite. It was found that tempering treatment could increase the HE resistance and decrease the susceptibility to HE of the as-hot rolled bainitic rail steel except at temper embrittlement temperature of ~400 °C, and excellent HE properties could be obtained when tempered at 500 °C at less expense of strength and ductility. The enhanced HE properties are ascribed mainly to the gradual decomposition of blocky M/A constituents as well as the tempering of the martensite. It is thus suggested that suitable tempering after hot rolling could be applied to enhance the HE properties as well as to obtain maximum mechanical properties, and thus to guarantee the safety of bainitic steel rails in service.

Mode III Notch Fracture Toughness Assessment for Various Notch Features

In the present paper, two stress-based failure criteria are proposed to predict the notch fracture toughness for three different notch features under pure mode III loading. These criteria are developed based on the two well-known failure concepts of the point-stress and the mean-stress previously used for predicting brittle fracture in notched members under various loading conditions. The validity of the criteria is verified through the comparison of their theoretical predictions with a bulk of test data reported in the open literature on mode III fracture of graphite notched round bars. Very good agreement is shown to exist between the experimental and theoretical results. Moreover, the comparison revealed that the mean-stress criterion is more accurate than the point-stress criterion in predicting mode III brittle fracture of V-notches and semicircular notches.

Modelling of the blanking process of high-carbon steel using Lemaitre damage model

This paper presents a methodology to model a blanking process using a continuum mechanical damage model. A variant of the Lemaitre model, in which the quasi-unilateral conditions are taken into consideration to modify the damage behavior under compressive stress states, is selected as material model. S45C high-carbon steel is analyzed experimentally. To characterize the damage behavior of the material, notched round bar tensile tests with three different notch radii (6 mm, 10 mm, and 20 mm) using image analysis are performed. Using digital image processing, the strain at the deformation zone can be computed for the load–strain curves. Those curves are used as an objective function to determine the parameters of the Lemaitre damage model. The experimental results are compared with the results of the FE analysis of the tensile test. The identified model parameters are used in numerical investigations of axisymmetric blanking. The effect of the model's extension to quasi-unilateral damage evolution is discussed. The crack progress in high-carbon steel sheet during blanking and the final sheared part morphology are predicted and compared with the experimental results. Sheared surface and burr height obtained by the analysis coincide with the results of the blanking experiment.

Constitutive analysis of pressure-insensitive metals under axisymmetric tensile loading: A stress triaxiality-dependent plasticity damage model

In this paper, by separately characterizing the influence of stress triaxiality (ratio of hydrostatic stress to von Mises stress) on the stress response to plastic deformation and to damage evolution, the constitutive equation of the pressure-insensitive metal under axisymmetric tensile loading is defined as a new stress triaxiality-dependent plasticity damage model. For this purpose, experimental testing and finite element modelling are performed based on smooth and notched round bars, machined from a high-strength rail steel. The test results show that mechanical behaviour of both types of tensile specimens can be closely simulated based on the same constitutive equation calibrated following the classical J2 flow theory; even though stress triaxiality and damage evolution generated in these two types of specimens are very different. Such an issue is investigated by implementing the new constitutive model to finite element modelling of smooth and notched specimens using the ABAQUS user subroutine VUMAT. It is found that the rates of both damage-free stress response to deformation and damage evolution increase with increasing stress triaxiality. Also, the increase of damage-free stress response to deformation, caused by the increase of stress triaxiality, is offset by the decrease of stress due to the increase of damage evolution. This results in the constitutive equation insensitive to the change of stress triaxiality.

Metal plasticity and ductile fracture modeling for cast aluminum alloy parts

In this study, plasticity and ductile fracture properties were characterized by performing various tension, shear, and compression tests. A series of 10 experiments were performed using notched round bars, flat-grooved plates, in-plane shear plates, and cylindrical bars. Two cast aluminum alloys used in automotive suspension systems were selected. Plasticity modeling was performed and the results were compared with experimental and corresponding simulation results; further, the relationships among the stress triaxiality, Lode angle parameter, and equivalent plastic strain at the onset of failure were determined to calibrate a ductile fracture model. The proposed ductile fracture model shows good agreement with experimental results.

Ductile tearing analysis of TC128 tank car steel under mode I loading condition

The objective of the present work is to incorporate the effect of post-failure softening on fracture initiation modeling of steel alloy TC128 commonly used in railroad tank car manufacturing. The fracture initiation process is determined through a comprehensive mechanical tests, which includes tensile tests on standard dog-bone specimens, flat specimens with circular cutouts and central hole, notched round bars, punch indentation tests on circular blanks and special flat shear specimens. Ductile fracture toughness usually referred to as resistance curve is measured from two types of typical fracture mechanics specimen geometries: the compact tension C(T) and the three-point bending SE(B). Post-failure softening is then coupled with the constitutive model to describe ductile fracture propagation. It turns out that in the absence of softening in fracture, the crack growth rate increases with little resistance opposite of what has been observed in fracture response of typical steels. On the other hand, the post-failure softening algorithm increases the ductile resistance behavior of the material more realistically, compared to experiments and provides additional information regarding the state of stress governing the fracture process.

Hydrogen embrittlement behavior of high strength rail steels: A comparison between pearlitic and bainitic microstructures

The present study was attempted to evaluate the hydrogen embrittlement (HE) behavior of two high strength rail steels with pearlitic and bainitic microstructures by using slow strain rate test (SSRT) with notched round bar specimens. The results show that the bainitic rail steel with a mixed microstructure of bainite, tempered martensite and M/A constituents exhibits superior mechanical properties in comparison with the pearlitic rail steel. The results of SSRT revealed that the bainitic rail steel is more susceptible to HE than the pearlitic rail steel, which is ascribed mainly to the higher strength level and the microstructural characteristics of the bainitic rail steel. The attempt of re-tempering treatment of the as-received bainitic rail steel exhibits no notable improvement in the resistance to HE at no expense of strength. It is thus suggested that further efforts concerning obtaining low susceptibility to HE besides obtaining excellent combination of strength and toughness should be conducted to guarantee the safety service of the bainitic steel rails.

Time dependent voiding mechanisms in polyamide 6 submitted to high stress triaxiality: experimental characterisation and finite element modelling

Double notched round bars made of semi-crystalline polymer polyamide 6 (PA6) were submitted to monotonic tensile and creep tests. The two notches had a root radius of 0.45 mm, which imposes a multiaxial stress state and a state of high triaxiality in the net (minimal) section of the specimens. Tests were carried out until the failure occurred from one of the notches. The other one, unbroken but deformed under steady strain rate or steady load, was inspected using the Synchrotron Radiation Computed Tomography (SRCT) technique. These 3D through thickness inspections allowed the study of microstructural evolution at the peak stress for the monotonic tensile test and at the beginning of the tertiary creep for the creep tests. Cavitation features were assessed with a micrometre resolution within the notched region. Spatial distributions of void volume fraction ( $\mathit{Vf}$ ) and void morphology were studied. Voiding mechanisms were similar under steady strain rates and steady loads. The maximum values of $\mathit{Vf}$ were located between the axis of revolution of the specimens and the notch surface and voids were considered as flat cylinders with a circular basis perpendicular to the loading direction. A model, based on porous plasticity, was used to simulate the mechanical response of this PA6 material under high stress triaxiality. Both macroscopic behaviour (loading curves) and voiding micro-mechanisms (radial distributions of void volume fraction) were accurately predicted using finite element simulations.

Effect of loading orientation on fatigue behaviour in severely notched round bars under non-zero mean stress bending-torsion

This paper studies the effect of different loading orientations on fatigue behaviour in severely notched round bars under pulsating in-phase combined bending-torsion loading. Bending moments are applied in three different planes with respect to the notch root considering two bending moment to torsion moment ratios. Complementary, beach-marking tests are also performed for different loading scenarios to evaluate the crack shape changes during the crack growth. After fatigue testing, specimen surfaces are examined by scanning electron microscopy to identify the main failure micro-mechanisms. Fatigue life is predicted via the Coffin-Manson model, and the notch effect is evaluated using the Equivalent Strain Energy Density concept. Overall, experimental and predicted lives are very reasonably correlated. Furthermore, initiation sites, initiation angles and surface crack paths are successfully predicted from the principal stress field at the notch.

Fatigue life assessment of notched round bars under multiaxial loading based on the total strain energy density approach

The main purpose of this paper is the fatigue assessment in lateral U-shaped notched round bars under bending-torsion loading. Despite its importance in the context of mechanical design, very little work has been done in this field. The fatigue life prediction model relies on the assumption that both the smooth and the notched samples fail when a critical value of the total strain energy density is reached. The modus operandi, in a first instance, consists of developing a fatigue master curve that relates the total strain energy density and the number of cycles to failure using smooth specimens subjected to strain-controlled conditions. In a second stage, the total strain energy density of the notched samples is computed from representative hysteresis loops obtained through a three-step procedure: reduction of the multiaxial stress state to an equivalent stress state using a linear-elastic finite-element model; definition of an effective stress range on the basis of the Theory of Critical Distances; and generation of a hysteresis loop applying the Equivalent Strain Energy Density concept in conjunction with the calculated effective stress range. The comparison between the experimental and the predicted lives has shown a very good correlation, with all points within a factor of 2.

Anisotropic (Continuum Damage Mechanics)-based multi-mechanism model for semi-crystalline polymer

In this work, the anisotropic damage of semi-crystalline polymers is investigated. The model, developed within a thermodynamic framework, includes the following features: (i) the degree of crystallinity; (ii) the hydrostatic pressure effect; and (iii) the damage anisotropy. The adopted tensorial damage variable is based on the Continuum Damage Mechanics approach under the energy equivalence assumption. For the quantification of the anisotropy, a parameter called “shape factor” is defined as the ratio between the void mean diameter and the void mean height. This parameter is linked to the main axial and the main radial damage components. Experimental data taken from the recent literature using the tomography technique were selected to assess the model capability. Finite element simulations of notched round bar specimens subjected to tensile test stopped at three key loading stages are systematically compared with experimental data. The proposed model was able not only to accurately simulate the macroscopic response of the material, but more interestingly, to reproduce the spatial distribution of the shape factor. This demonstrates the anisotropy effects of the material under study induced at different stages of the deformation.

Observations by in-situ X-ray synchrotron computed tomography of the microstructural evolution of semi-crystalline Polyamide 11 during deformation

This study deals with the cavitation of semi-crystalline Polyamide 11 during deformation. The link between the microstructural evolution and the material macroscopic behaviour is demonstrated thanks to tensile tests on small notched round bars using in-situ X-ray synchrotron computed tomography (SRCT). 3D rendering, image processing and both qualitative and quantitative data analyses are at the heart of this work so as to provide a comprehensive description of micro-mechanisms occurring in the material throughout the tensile tests. Whitening appeared whilst only few microvoids were observed via the tomographic scans in the central part of the specimen where the stress triaxiality is the highest. Significant stages – chronologically, denotching, renotching and a final denotching phase, resulting in the elongation of the central part of the specimen – are detailed. Corresponding evolution of the morphologies (in terms of growth and prolate and oblate shapes) of the void cloud, as well as of the individualized voids within the latter, are discussed.

Effect of size on necking of dynamically loaded notched bars

The influence of material inertia on neck development in a notched round bar is analyzed numerically. Dynamic axisymmetric calculations are carried out for isotropically hardening elastic-viscoplastic solids so that both material strain rate sensitivity and material inertia are accounted for. The focus is on the effect of bar size on whether the notch triggers necking or necking initiates away from the notch. The governing equations are presented in non-dimensional form and two key non-dimensional groups that involve both material and loading parameters are identified. For both non-dimensional groups, with all parameters fixed except for bar size, it is found that for sufficiently small bars, the notch triggers necking, whereas for sufficiently large bars necking ultimately occurs away from the notch. With material properties fixed, for one non-dimensional group the transition to necking away from the notch corresponds to increasing imposed velocity whereas for the other non-dimensional group this transition takes place for decreasing imposed strain rate. Both these transitions correspond to increasing bar size. The results indicate that this transition is governed by material inertia but the bar size at which it occurs depends on the material properties, particularly strain hardening and strain rate hardening.

Voiding mechanisms in semi-crystalline polyamide 6 during creep tests assessed by damage based constitutive relationships and finite elements calculations

Notched round bars made of a semi-crystalline polymer, polyamide 6, were submitted to creep tests. In order to study the microstructural evolution of the material during creep deformation, these tests were stopped at two characteristic creep times: i) the end of the secondary creep stage, ii) the onset of the failure during the tertiary creep stage, allowing 3D through thickness Synchrotron Radiation Tomography (SRT)-inspections. This SRT-technique allowed features of the damage to be assessed at a micrometre resolution within the notched region, such as spatial distributions of void volume fraction and void heights and diameters. These deformation mechanisms have already been observed and studied during steady strain rate loading and a multi-mechanism model coupled with damage formulation proposed to simulate notched specimens submitted to tensile loads. This model, based on porous visco-plasticity, was used here to simulate the creep behaviour of this PA6 material. The optimization procedure has led to a set of material coefficients capable of reproducing both macroscopic behaviour (creep curves) and damage micro-mechanisms. The level of maximum damage within the material and the spatial distributions of void volume fraction obtained numerically were compared successfully to experiments and the Cauchy stress tensor has been proved to be related to the void deformation mechanisms.

Assessing the integrity of steel structural components with stress raisers using the Theory of Critical Distances

This paper assesses and evaluates the detrimental effect of standard and complex geometrical features on the static strength of samples made of Q460 steel. The experimental results generated by testing four types of notched specimens were analyzed using the Theory of Critical Distances (TCD). The considered configurations included uniaxial tension tests on standard notched round bars and double-side U-notched flat plate specimens. In particular, our attention was focused on the fracture behavior of two specimens containing complex geometrical features subjected to pure-shear and tensile-shear local stress states. The common feature of these two notched specimens was that cracks were seen to initiate, within the material, away from the stress raisers, even though obvious stress concentrations existed at notch tip. The performed validation exercise confirms the accuracy and reliability of the linear-elastic TCD in estimating the fracture initiation position and static strength of standard notched round bars and double-side U-notched flat plate specimens. In the meantime, the linear-elastic method proposed in this paper can also be used as an effective approach to assess the fracture behavior of metallic components having complex geometry.

V-Notched Bar Creep Life Prediction: GH3536 Ni-Based Superalloy Under Multiaxial Stress State

In this study, creep experiments on smooth and circumferential V-type notched round bars were conducted in GH3536 Ni-based superalloy at 750 °C to identify notch strengthening effect in notched specimens. FE analysis was carried out, coupled with continuum damage mechanics (CDM), to analyze stress distribution and damage evolution under multiaxial stress state. The creep deformation of smooth specimens and the rupture life of both smooth and notched specimens showed good agreement between experimental results and FE analysis predictions; the creep rupture life for the notched specimen was successfully predicted via the “skeletal point” concept. Both creep damage analysis and the observed fracture morphology suggest that creep rupture started first at the root in the V-type notched specimens, and shifted to the region close to the notch root when the notch was relatively shallow compared to U-type notched specimens.

Three dimensional quantification of anisotropic void evolution in deformed semi-crystalline polyamide 6

The evolution of voids has been used as an efficient indicator of the volume changes occurring during deformation for polymers which undergo high levels of plasticity. This has to be taken into account in determining the constitutive models for these polymers. Void growth during uniaxial stretching of a semi-crystalline polyamide 6 has been studied using 3D image analysis of tomography data. Tests on axi-symmetrical notched round bars have been stopped at: (i) the maximum net stress; (ii) the end of the stress softening stage; (iii) the onset of the final failure. Local synchrotron tomography has been performed so as to observe voids in a predetermined volume of interest around the minimum net section. The shape of the voids was found to be cylindrical. Mathematical morphology analysis was used to identify 3D voids, allowing the void diameter and height histograms to be obtained. An anisotropic shape factor parameter was defined as the ratio between the void diameter and the void height. This shape factor was found to evolve with the degree of deformation. The principal strain components of the voids were calculated and plotted, showing anisotropy and a heterogeneous distribution. The irreversible void growth noted as plastic dilation was also found to be heterogeneous in the deformed net section.

Fracture behavior under torsion of notched round bars made of gray cast iron

The purpose of this paper is twofold and therefore it has been divided in two parts. In the first part, experimental results of 25 gray cast iron notched specimens tested under torsion loading are provided. V-notch (with an opening angle of 120°) geometry is considered with root radii ranging from 0.1 to 2.0mm. Plots of torque loads versus twist angles are recorded for all notch root radii tested. Such results can help in evaluating numerical and theoretical models for fracture of notched components under mode III loading. The second part of the paper deals with an analysis of the experimental results by using the Strain Energy Density criterion. Because of the mode III loading conditions, a non-conventional application of such criterion is carried out, showing a good agreement between the experimental results and the theoretical fracture assessments and it is used to justify the link between nominal and local fracture approaches.