Notched Tensile Bars Research Articles

On determination of model parameters for strain based ductile tearing simulation

This technical note presents the effect of two options to determine model parameters of a strain-based damage model on ductile tearing simulation. Notched bar tensile test data are used to determine the parameters in the first option, whereas only smooth bar tensile data are needed in the second one. In this investigation, four material data are considered. By comparing the simulation results with experimental data, it can be shown that it is difficult to simulate both crack initiation and crack growth well using the first option. However, with the second option, good agreement can be achieved in the prediction of both crack initiation and crack growth in all cases. A possible reason for overestimating crack growth using the first option is discussed.

Simulation of ductile tearing during a full size test using a non local Gurson–Tvergaard–Needleman (GTN) model

Ductile tearing of a full size precracked pipe is experimentally investigated. In order to model and interpret the test, the pipe material is characterized using smooth and notched tensile bars and precracked C(T) specimens. This experimental database is used to fit the parameters of the non local Gurson–Tvergaard–Needleman (GTN) proposed in Zhang et al. (2018) and Chen et al. (2020). The model is used in finite element simulations using specific elements allowing for the control of strain/damage localization as well as volumetric locking. Mesh size independence is checked on notched tensile bars. The model is then able to represent the early stages of crack propagation in the pipe. In particular, experimentally observed crack branching is reproduced, whereas this appeared much more difficult to obtain using a local GTN model.

Integration of an adaptive cohesive zone and continuum ductile fracture model to simulate crack propagation in steel structures

Damage mechanics continuum criteria have been shown to provide an effective alternative to conventional fracture mechanics parameters to simulate ductile crack initiation in mild steel under large scale yielding and variable stress states. In this study, a damage mechanics initiation criterion, called the Stress Weighted Damage Model, is extended to simulate ductile crack propagation through an Adaptive Cohesive Zone model. The proposed approach regularizes the crack tip singularity using features of conventional cohesive zone methods, while adaptively updating the traction separation relationship to model crack propagation based on the continuum damage criterion. The proposed model is implemented in the finite element platform WARP3D and demonstrated using a set of fourteen coupon scale fracture experiments of two structural steels. The tests include Circumferentially Notched Tensile bars and sharp-cracked Compact Tension specimens, where the response is represented by load-deformation response and J-R curves, respectively. Comparisons with test results demonstrate that the combined Stress Weighted Damage Model and Adaptive Cohesive Zone approach can accurately simulate crack propagation with consistent mesh convergence. Examples are included to contrast the proposed model capabilities with a conventional (stress-based) Cohesive Zone model and the Gurson-Tvergaard model.

Mechanical Performance of Zr-Containing 354-Type Al-Si-Cu-Mg Cast Alloy: Role of Geometrical Discontinuities

The main objective of this study was to evaluate the performance of 354-type Al-Si-Cu-Mg cast alloys at both ambient (25 °C) and elevated temperatures (250 °C) through the addition of zirconium (Zr), nickel (Ni) and manganese (Mn). The motive behind these additions was to develop thermally stable alloys capable of resisting softening instigated by prolonged exposure at elevated temperatures and hence preserve acceptable mechanical properties. Another parameter affecting performance is geometry. Four different notch geometries were employed: two hole-type geometries and two types of V-notches (symmetric and asymmetric for each). The results reveal that the presence of asymmetric notches in the tensile test bars proved to be more deleterious than symmetric notches to the notch tensile strength and percentage elongation to fracture at both 25 °C and at 250 °C. The softening that took place during tensile testing at 250 °C rendered the alloys some ductility (in particular, the M1S (354 + 0.3 wt.% Zr), M2S (354 + 0.3 wt.% Zr + 2 wt.% Ni) and M3S alloys (354 + 0.3 wt.% Zr +0.75 wt.% Mn)), as a result, the notched tensile bars with asymmetric holes exhibited high strength values for these alloys compared to the tensile strength of unnotched bars subjected to similar heat treatment conditions owing to the presence of notches. The notch sensitivity ratios vary between 0.78 and 0.95 for asymmetric holes versus 0.7 and 0.85 for asymmetric V-notches at room temperature and 0.9 and 1.07 for asymmetric holes versus 0.7 and 0.92 for asymmetric V-notches at 250 °C.

Damage mechanisms in the ultra-low cycle fatigue loading

Predicting extreme limit states in steel structures using finite element simulations requires an understanding of the fracture mechanisms themselves and the relationship of various models to these mechanisms. Aiming at addressing dominant damage mechanisms in the Ultra-Low-Cycle Fatigue (ULCF) regime which occurs during earthquakes, circumferentially notched tensile bars were subjected to cyclic loadings with large displacement amplitudes. Two weld metals from rutile and basic classifications and two different grades of structural steels were selected to determine the role of microstructural features in the response of materials to ULCF conditions. Scanning Electron Microscopy (SEM) technique equipped with 3D measurement software was employed to describe fracture surfaces quantitatively. Moreover, further analyses of hysteresis loops, as well as the structure of the materials beneath the fracture surfaces, provided a better insight into various micromechanisms of damage such as internal cracks involved in ULCF failures. To consider the contribution of all these mechanisms in final failures, fracture surfaces were characterized using “Developed Interfacial Area Ratio” parameter. These results were served to suggest a model for predicting the cyclic life of materials when exposed to ULCF loadings.

Predicting embrittlement of polymer glasses using a hydrostatic stress criterion

ABSTRACTIn this study, the aging‐induced embrittlement of three polymer glasses is investigated using a previously developed hybrid experimental–numerical method. The evolution of yield stress of unnotched tensile bars upon aging is coupled to the evolution of embrittlement of notched tensile bars using a numerical model combined with a critical hydrostatic stress criterion that determines the onset of failure. The time‐to‐embrittlement of notched tensile bars with a different notch geometry is predicted and in good agreement with the experimentally determined value. Next to that, the approach is extended to three polysulfone polymers, and it is shown that the value of the critical hydrostatic stress correlates well with the polymers entanglement density: : polymers with a denser entangled network display higher values, that is, a higher resistance against incipient cavitation. © 2019 The Authors. Journal of Applied Polymer Science published by Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 136, 47373.

Modelling the strain rate dependent hardening of constructional steel using semi-empirical models

The importance of modelling the strain rate dependent material behaviour increases since structural components more and more have to be designed against extreme events. With growing usage of numerical programmes, good models become necessary. The goal of the ongoing research project is to find reasonable models for simulations concerning steel constructions. This paper discusses various models to describe the strain rate dependent hardening of mild steel. In this context, high speed tensile tests were performed and evaluated. Four commonly used material models and a new model were introduced and calibrated to the test results: The Johnson-Cook model, a modified Johnson-Cook model by Huh and Kang, the Cowper-Symonds model and a combined Johnson-Cook/Cowper-Symonds model. These four models do not describe the observed behaviour of constructional steels satisfactorily. Unlike these models, a newly introduced model is able to describe both a yield plateau and the slope of the strain hardening, both as a function of the strain rate. The quality of the approximations is discussed and further investigated by performing notched bar tensile tests and simulations. Finally, recommendations are given on the basis that the modelling of a yield plateau and the negative strain rate sensitivity of the strain hardening is necessary for modelling structural components under extreme events.

Estimating fracture toughness of various matrix structured ductile iron using circumferentially notched tensile bars

In this experimental study, circumferentially notched tensile (CNT) specimens with various notch root radii of 0.05, 0.1, 0.16, 0.25, 0.4, and 0.8 mm were employed to investigate the influence of matrix structure on the fracture toughness of 1.03% Cu, 1.25% Ni, and 0.18% Mo alloyed ductile iron. The assayed matrix structures in this study were ferritic, pearlitic/ferritic, pearlitic, tempered martensitic, lower and upper ausferritic. The microstructures were obtained by several heat treatment processes. The microstructures and morphology of broken surfaces of CNT specimens were also examined by the optical and scanning electron microscopes. It was observed that for the steady-phased (ferritic, pearlitic/ferritic, and pearlitic) matrixes, the increasing rates of fracture toughness under the applications of different notch tip radii were lower than that of the tempered martensitic, lower and upper ausferritic matrixes. It was also inferred that lower values of fracture toughness were obtained by the applied rapid method.

Ductile damage modelling with locking‐free regularised GTN model

SummaryThe major goal of this work is to develop a robust modelling strategy for the simulation of ductile damage development including crack initiation and subsequent propagation. For that purpose, a Gurson‐type model is used. This model class, as many other damage models, leads to significant material softening and must be used within a large deformation framework due to the ductile character of the materials. This leads to 2 main difficulties that should be dealt with carefully: mesh dependency and volumetric locking. In this work, a logarithmic finite strain framework is adopted in which the Gurson‐Tvergaard‐Needleman constitutive law is reformulated. Then a nonlocal formulation with regularisation of hardening variable is applied so as to solve mesh dependency and strain localization problem. In addition, the nonlocal model is combined with mixed “displacement‐pressure‐volume variation” elements to avoid volumetric locking. Thereby, a mesh‐independent and locking‐free finite strain framework suitable for the modelling of ductile rupture is established. Attention is paid to mathematical properties and numerical performance of the model. Finally, the model parameters are identified on an experimental database for a nuclear piping steel. Simulations of standard test specimens (notched tensile bars and compact tension and single edge notched tensile cracked specimens) are performed and compared to experimental results.

Notch bluntness effects on fracture toughness of a modified S690 steel at 150 °C

This paper addresses the effect of blunt defects on the structural integrity assessment of steels. Smooth tensile, notched bar tensile and multi-specimen single edge notched bend tests with various notch acuities have been performed and show an increase in effective ductile fracture toughness with increasing notch radius. A ductile fracture model has been shown to be capable of predicting the specimen responses including the local variation of ductile crack extension through the thickness. An empirical fit developed to describe the effect of notch radius on cleavage fracture toughness has been examined and found to be also capable of describing the effect of notch radius on ductile fracture toughness.

Towards designing anisotropy for ductility enhancement: A theory-driven investigation in Mg-alloys

Plastic anisotropy is often invoked to rationalize low formability in strongly anisotropic materials. Analysis based on homogenization theory suggests, however, that certain forms of plastic anisotropy may hinder ductile damage under any triaxial stress state or loading orientation. Here, a proof-of-concept is demonstrated in the case of Mg alloys. Two textures produced by severe plastic deformation of Mg-3Al-1Zn alloy, while keeping the grain sizes nearly the same, are compared with the well-known rolling texture in terms of their anisotropy–ductility correlations at room temperature. For each material, the 3D plastic anisotropy is characterized using tensile and compression specimens whereas the ductility is determined using smooth and round notched tensile bars. A simple micromechanical model is proposed to rationalize the trends. The main finding suggests that plastic anisotropy can be altered to aid ductility. Perspectives for how to harness anisotropy in material design are presented.

Effect of thermal ageing of CF8M on multi‐axial ductility and application to fracture toughness prediction

AbstractThis paper proposes a method to predict the thermal ageing effect on fracture toughness of CF8M cast stainless steel. The proposed method is based on multi‐axial fracture strain combined with finite element damage analysis to simulate ductile tearing. Multi‐axial fracture strain loci of un‐aged and aged CF8M are determined by analyzing notched bar tensile test. It is shown that the thermal ageing effect on multi‐axial fracture strain loci can be characterized by one constant. It is further shown that J‐resistance curves of un‐aged and aged CF8M can be predicted well from finite element damage analysis using multi‐axial fracture strain loci. Implication of present results to practical application of crack assessment of aged cast stainless steels is discussed.

Possibility to Estimate Fracture Toughness of Ductile Steel Materials from Small Punch Test Data

This paper presents a procedure to predict fracture toughness of steel material using small punch test (or notched small punch test) and finite element (FE) damage analysis. Tensile property can be determined from setting the constitutive equations and can be validated by comparing the small punch (SP) test data with FE results applying the determined tensile property. FE damage analysis used in this paper is based on the strain-based fracture model. Material constants in the model are normally determined from analyzing notched bar tensile tests. To determine these material constants from SP test instead of notched bar tensile tests, simplified model (with only one material constant) can be introduced and used in the simulations. SP test and notched small punch (NSP) test are simulated via FE damage analyses using the tensile property and simplified strain-based fracture model. NSP simulation results are sensitive to element size. However, SP simulation results are not sensitive to element size. Compact tension (C(T)) test is also simulated and it can be found that the proper element size for C(T) simulation is four times of that for NSP simulation to predict cracking initiation toughness.

Investigation of Thermal Aging Effect on Fracture Toughness of Cast Stainless Steels Using Experimental and Numerical Approach

This paper investigates effect of thermal aging on reduction of fracture toughness of CF8 M cast stainless steel. To predict fracture toughness of un-aged and aged materials by numerical analyses, finite element damage analysis is used in conjunction with strain-based fracture model. The strain-based fracture models for un-aged and aged CF8 M are determined from notched bar tensile test data and finite element analysis of it. It is found that the effect of thermal aging on material ductility can be quantified with introducing the concept of thermal aging constant. Using the method in this paper, J-resistance curves for un-aged and aged CF8 M can be predicted and compared with experimental test data.

Room-Temperature Creep Testing of Grade 2 CP Titanium Plate Using Notch Tensile Samples

Commercially pure (CP) Titanium has a unique behavior in that creep can occur at room temperature. In addition, many materials exhibit an effect from a notch on mechanical properties. This paper shall review 2000-h room-temperature creep data generated using notched tensile bars from Grade 2 CP Titanium at loads which were between 30 and 50% of the notch yield strength. The results shall be compared to previously generated data (Dennies and Kupkovits in J Fail Anal Prev 14(4):437–442, 2014).

中炭素鋼の延性破壊に及ぼす応力三軸度と組織異方性の影響

A method for accurately predicting ductile fracture is desired to achieve efficient process optimization. The critical value of the Cockcroft & Latham equation as a typical model of uncoupled damage criteria is formulated taking into consideration the stress triaxiality and microstructural anisotropy. The medium-carbon steel S45C is used as a specimen material. Notched bar tensile test, taper anvil compression test, and torsion test are designed and conducted so as to represent different stress triaxiality states. These material tests are carried out while changing the direction of specimen relative to the rolling direction. Furthermore, tensile-compressive combined loading test is performed to confirm the applicability of the formulated critical value. The result shows that the proposed damage critical value has an advantage over the constant critical value in predicting the occurrence of fracture accurately.

Determination of Burst Pressure of API Steel Pipes using Stress Modified Critical Strain Model

This paper presents a technique which can be used to determine the burst pressure of defective steel pipes using non-linear finite element (FE) analysis. The technique uses stress modified critical strain (SMCS) failure criterion to study the effect of gouge defects on maximum working pressure of API X65 steel pipes. The procedures in determining the model parameters using 3-D, homogeneous isotropic elastic-plastic material model with large deformation finite element analyses from notched tensile bars were systematically discussed. The relationship between burst pressure and gouge depth was proposed. The burst pressure estimated then was compared to experimental data from the literature for validation showing overall good agreements.

Criteria to predict the embrittlement of polycarbonate

A direct correlation is found between the time evolution of the yield stress in unnotched tensile bars and that of the impact energy measured using notched tensile bars. In both cases a master curve can be constructed with an Arrhenius type of shift function, using the same activation energy. Combining these experimental findings with numerical simulations lead to a maximum hydrostatic stress as a criterion to predict the onset of failure, s h . Where aging kinetics is not dependent on the polymer’s molecular weight, embrittlement is, and for higher molecular weights a higher s h is found. Moreover, for high polymers we observe a more stable craze extension and crack propagation after cavitation, causing the computed impact energies to underestimate the experimental ones for all but the lowest molecular weight polymers. Because the maximum in hydrostatic stress under the notch, s h , increases with the polymer’s age, defined by the value of the state parameter Sa, and given the proportionality between Sa and the yield stress, sy, an alternative failure criterion is proposed which is a molecular weight dependent critical value of the evolving yield stress, sy,c. It predicts a product’s increased sensitivity to damage under the influence of progressive aging as enhanced by temperature.

On the mechanism of quench cracking in Rene 95 nickel-based superalloy

The mechanism of quench cracking in the nickel-based superalloy Rene 95 has been investigated. Rapid cooling of notched tensile bars loaded with fixed grips was used to mimic a quench. Failures occurred by brittle intergranular fracture in air, but by rupture and at higher stress in vacuum. The brittle intergranular fracture in air was recognized as dynamic embrittlement. Nickel-plating of sufficient thickness was found to eliminate cracking when Rene 95 was water-quenched from above the γ′ solvus temperature.

Fracture in Thin Oxide Films

ABSTRACTIn thin film systems, failure often occurs via fracture mechanisms, with either through thickness cracking or interfacial delamination leading to failure of the device or layer. Measuring the stress at which fracture occurs in these thin film systems requires testing methods amicable to both the small scale of the films as well as the complex relationship between the mechanical properties of the film and the substrate. This paper will cover two oxide film systems, a piezoelectric ceramic (PZT) on platinum and passive oxide films (primarily Cr2O3) on stainless steels. Both will be tested with a bulk method (bulge testing in the case of PZT and circumferentially notched tensile bars for the stainless steel) and then with a nanoindentation method developed for testing fracture for hard coatings on soft substrates. The differences in stresses required for failure between the bulk and the nanoscale tests will be discussed in terms of differences in flaw population.