Axisymmetric Specimens Research Articles

Analysis of Liquefaction in Tailings Deposits by Fem Modeling of Undrained Cyclic Triaxial

In this article, a numerical calibration procedure for undrained cyclic triaxial tests is presented to evaluate the liquefaction potential in sand and silt samples from mining tailings in northern Chile. The numerical modeling of an axisymmetric specimen involved two stages: isotropic consolidation using the Hardening Soil Small (HSS) model and a cycling phase employing the UBC3D-PLM model to simulate the onset of liquefaction using the criterion that the excess pore pressure ratio Ru should exceed 0.8. The results demonstrate that the UBC3D-PLM modeling calibrated with experimental data from cyclic triaxial tests effectively represents the excess pore pressure in both sandy and silty soils from mining tailings. The accuracy of the modeling decreases when a single set of parameters is applied to the same soil at different cyclic stress ratios (CSR), highlighting the need for specific calibrations for each loading.

Extraction of Equivalent Stress Versus Equivalent Plastic Strain Curve of Necking Material in Tensile Test Without Assuming Constitutive Model

Abstract An algorithm for extracting the equivalent stress versus equivalent plastic strain curve of a necking material in tensile test is proposed (the curve is called here the equivalent-plastic (EP) stress–strain (SS) curve). The presented algorithm traces the force–elongation curve via iterative finite element (FE) simulations without assuming a constitutive model and is suitable for a general-purpose FE solver available to a general audience. In the FE simulation and experiment, a slightly tapered geometry was employed around the specimen center to stably initiate necking there. The proposed algorithm and mentioned necking initiation method have been applied to extracting the EP SS curve of a high-strength steel material using an axisymmetric specimen. Because necking was initiated stably in simulation at the specimen center for a range of mesh sizes, the convergence of the extracted EP SS curve with the mesh size could be successfully verified. The EP SS curve of the tested material was extracted up to an EP strain of 0.85 with average strain intervals of approximately 2.5 mili-strain. The error values were less than 0.2 and 0.1% after four and seven FE simulations, respectively. The presented algorithm and necking initiation method in simulation can also be used for simultaneously quantifying the fracture EP strain of a necking material in the tensile test.

Service-life assessment of aircraft integral structures based on incremental fatigue damage modeling

The Ottosen–Stenström–Ristinmaa (OSR) incremental fatigue damage model is adapted for fatigue-life assessment of integral airframes milled from 7050-T7451 aluminum plates. For validation, variable-amplitude high-cycle fatigue experiments are conducted for circumferentially notched, axisymmetric specimens, and for a geometry similar to an aircraft fuselage frame, with flanges, stiffeners, and web panels. We also describe how the parameters of the OSR model can be modified to account for surface roughness, and for setting acceptable failure probability.

Simulations of complex crack paths using a robust and cost-efficient continuous–discontinuous approach

Prediction of complex crack propagation is necessary to guarantee performance in service of critical parts of transport vehicles despite the presence of a crack. In cases where linear fracture mechanics assumptions are not valid, e.g. for ductile rupture, this prediction may require continuous–discontinuous strategies to insert a strong discontinuity (i.e. a crack) into a continuous model based on a scalar variable related to material degradation. These strategies still face difficult challenges regarding robustness and cost-efficiency, in particular for 3D problems. To overcome these challenges, it is useful to consider the different ingredients that constitute a continuous–discontinuous strategy and try to optimize each of them. With this perspective, this work addresses the simulation of crack initiation and propagation in ductile metals and proposes new contributions to some rarely addressed points: (i) a simple geometrical approach to initiate realistic crack shapes in 3D meshes, (ii) a new 3D insertion criterion to minimize the number of transfer operations, (iii) a pragmatic remeshing procedure to refine only Active Process Zones, and (iv) an equilibrium recovery method meant to improve the convergence rate after the insertion of a discontinuity.The effectiveness of these new ingredients is demonstrated in 2D axisymmetric, 2D plane strain, and 3D cases in the case of test specimens used to characterize ductile failure in metals. This includes axisymmetric specimens exhibiting cup-cone fracture, plane strain specimens with slant fracture, and pre-cracked CT-like specimens with crack blunting and large crack propagation.

An Experimental Investigation of the Influence of the State of Stress on the Ductile Fracture of 2024-T351 Aluminum

Abstract This paper investigates the influence of stress state on the equivalent plastic fracture strain in 2024-T351 aluminum alloy. Eighteen unique stress states at failure—with triaxialities ranging from 0.388 (compressive) to −0.891 (tensile) and Lode parameters ranging from −0.978 to 1.000—are explored through mechanical experiments on 2024-T351 aluminum specimens with various geometries under multiple loading conditions. These include tension tests of plane stress (thin), plane strain (thick), and axisymmetric specimens, as well as pure shear and combined axial–torsional loading on thin-walled tubes. Using a hybrid numerical–experimental approach, the dependence of fracture strain on stress triaxiality and Lode parameter is quantified for each experiment. Fracture strains are measured using three-dimensional digital image correlation. Equivalent plastic fracture strain for 2024-T351 generally increases with stress triaxiality (moving toward a more compressive state). Fracture strain decreases modestly as the Lode parameter decreases from 1 to 0, although there is a significant increase in ductility as the Lode parameter decreases below −0.8. Compression–torsion tests extend the data’s stress-space coverage well into the compressive triaxiality region (up to 0.388) and to Lode parameters approaching −1. This experimental program provides the most extensive set of ductile fracture data from a single 12.7-mm-thick 2024-T351 aluminum plate in the literature. These data can be used to calibrate ductile fracture models used in finite element simulations of dynamic events such as bird strikes, automotive collisions, and debris containment.

Incremental fatigue damage modeling of 7050-T7 aluminum alloy at stress-raisers

The Ottosen–Stenström–Ristinmaa (OSR) incremental fatigue damage model, based on an moving endurance surface centered around a backstress, is adapted for high-cycle fatigue at stress-raisers in AA7050-T7 specimens. Fatigue experiments are carried out for circumferentially-notched, axisymmetric specimens subjected to constant-amplitude (CA) load. The OSR model parameters are fitted to CA fatigue data, showing fair agreement for one set of model parameters across different stress ratios, stress concentration factors, uniaxial stress and biaxial stress. To demonstrate predictive capability, the fatigue life is integrated for an aircraft load spectrum (TWIST), and compared with experimental fatigue life data for holeplate specimens in the literature.

Local crack growth evaluation in a fully lamellar Ti-6Al-4V alloy using an electrothermal Crack-Tip marking technique

Local crack growth properties within microstructural components are often anisotropic and difficult to measure, especially in materials like titanium alloys, that do not respond well to conventional, stress-ratio-based crack tip marking techniques. A method is described to extract a 3D anisotropic crack growth model from a common triplet colony type in titanium alloys, consisting of three grain-orientation variants of alpha-phase sharing a common 1¯21¯0 plane, parallel to a 111 (octahedral) plane from a parent beta grain. A fatigue crack growth test was run using a novel axisymmetric specimen (Pettit, 2021) of Ti-6Al-4V with an extremely coarse, fully lamellar microstructure. The microstructure consisted of ∼ 10 mm diameter beta grains, one of which had spanned nearly the entire specimen cross section of crack growth, and had decomposed to multiple regions of triplet basketweave microstructure during colony from above the beta transus. During pauses in the test, a succession of crack fronts was recorded on the fracture surface using a novel electrothermal crack tip marking technique (Pettit, 2021; Pettit, 2019) as the crack propagated through these colonies. Crack growth data was then extracted from post-test microscopy to obtain local crack growth rates. The position of the crack front on successive cycles and the fracture surface topography were correlated to local microstructural features using electron backscattered diffraction analysis following minimal polishing of the fracture surface. A numerical model was developed in Franc3D to quantify local crack driving forces. Local triplet-colony crack growth data was fit to a 3D anisotropic crack growth model. Both the crack growth rate and the fracture morphology in the triplets were strongly dependent on the crack orientation relative to the triplet axis. Crack propagation in a direction normal to the octahedral plane was estimated to grow 2.88x faster than crack growth within the octahedral plane at the same crack driving force. The methodology described appears promising for local crack growth evaluation.

An Efficient Methodology towards Mechanical Characterization and Modelling of 18Ni300 AMed Steel in Extreme Loading and Temperature Conditions for Metal Cutting Applications

A thorough control of the machining operations is essential to ensure the successful post-processing of additively manufactured components, which can be assessed through machinability tests endowed with numerical simulation of the metal cutting process. However, to accurately depict the complex metal cutting mechanism, it is not only necessary to develop robust numerical models but also to properly characterize the material behavior, which can be a long-winded process, especially for state-of-stress sensitive materials. In this paper, an efficient mechanical characterization methodology has been developed through the usage of both direct and inverse calibration procedures. Apart from the typical axisymmetric specimens (such as those used in compression and tensile tests), plane strain specimens have been applied in the constitutive law calibration accounting for plastic and damage behaviors. Orthogonal cutting experiments allowed the validation of the implemented numerical model for simulation of the metal cutting processes. Moreover, the numerical simulation of an industrial machining operation (longitudinal cylindrical turning) revealed a very reasonably prediction of cutting forces and chip morphology, which is crucial for the identification of favorable cutting scenarios for difficult-to-cut materials.

Crack growth threshold testing using flat-bottom hole specimens

This study benchmarks a relatively new axisymmetric specimen concept for use in threshold testing, where the crack initiates and grows from the corner of a flat-bottomed circular hole in a cylindrical specimen while the bottom of the hole is cyclically loaded with a flat-ended plunger. The Flat-Bottom Hole (FBH) specimen is configured so the stress intensity naturally decreases as the crack grows radially outward at constant cyclic load, favoring self-centering, highly circular crack growth, and thus enabling tightly repeatable results especially for threshold testing. Because the specimen achieves K-shedding without load shedding, the opening at every point along the crack is constantly increasing during constant load amplitude growth, minimizing the threat of remote closure. Contrary to most conventional specimens, the circular crack front makes no intersection with a free surface, resulting in a crack front of uniform constraint and, where applicable, a uniform crack closure state. In practice, the specimen can be made quite small in size compared to other specimens of similar function.Two configurations are described, one for ambient testing, and one for elevated temperature testing. The K-solution and displacement solution obtained using FRANC2D are presented. Test results include data for Ti 6A-4V forging and Inconel 718 forging.

Complex study of the Portevin-Le Chatelier effect by uniaxial tension of axisymmetric specimens with ring concentrators of various geometries

In order to assess the influence of the geometry of the concentrators on the spatio-temporal inhomogeneities of the plastic flow of aluminum-magnesium alloys, uniaxial tension tests of axisymmetric specimens with ring concentrators of various geometries were carried out. The test program includes 4 groups of concentrators: a groove with a radius of 5 mm, a groove with an angle of 157 ° and a nose radius of 5 mm, a groove with an angle of 140 ° and a nose radius of 5 mm, and a groove with an angle of 140 ° and a nose radius of 5 mm. It is of interest to detect the effect of intermittent flow, which manifests itself in the form of load discontinuities in the loading diagram. An increase in the sharpness of the annular concentrator, and, consequently, an increase in the degree of stress concentration, leads to an increase in the bearing capacity of the samples (maximum perceived load), but deformation reserves decrease (maximum deformation at the time of destruction), and also affects the manifestation of the Portevin-Le Chatelier effect.

Modeling the effect of notch geometry on the deformation of a strongly anisotropic aluminum alloy

In this study, an elastic-plastic model with yielding described by a newly proposed orthotropic yield criterion was used to model the unusual deformation of a strongly textured AA6060 alloy. Available experimental data from tension tests and results of crystal plasticity simulations were used to determine the anisotropy coefficients involved in the yield criterion. Virtual material tests using a recent polycrystalline model were performed to obtain flow stresses for loadings where experimental data were not available. The capability of the elastic-plastic model to account for the distinct anisotropy of the material is demonstrated through comparison of finite element simulations and experimental tests on both smooth and notched axisymmetric specimens of the AA6060 alloy. Specifically, for the smooth specimen, the model predicts that the minimum cross-section evolves from a circle to an ellipse while for the notched specimens, the minimum cross-section evolves from a circular shape to an approximately rectangular, or rhomboidal shape, respectively as observed in the experiments. This model can be easily implemented in finite element codes, requires reduced CPU time compared to crystal plasticity finite element simulations, and can be applied in simulations of large-scale structural applications.

Influence of stress state on plastic flow and ductile fracture of three 6000-series aluminium alloys

In this study, the plastic flow and ductile fracture of three 6000-series aluminium alloys commonly used for crash components in the automotive industry are characterised experimentally and the observations are related to microstructural features. The three alloys are used in the cast and homogenised condition after artificial ageing to temper T6 to ensure isotropic behaviour. Tension tests on smooth and notched axisymmetric specimens are carried out to reveal the stress–strain behaviour, ductility and fracture mechanisms of the materials for different stress states. Through the use of optical and scanning electron microscopes, the initial microstructure of the alloys and the fracture surfaces of the tension test specimens are investigated. The work-hardening of the alloys is analysed up to large strains. Whereas the ductility of two of the alloys falls into the trend of previous experimental data on 6000-series aluminium alloys, where the strain to failure decreases linearly with increasing yield stress, the third alloy stands out by combining high strength with high ductility. The excellent properties of the latter alloy are assumed to be due to a favourable size distribution of constituent particles.

Dynamic Strength of AZ31B-4E and AMX602 Magnesium Alloys Under Shock Loading

Free surface velocity histories for two magnesium (Mg) alloys are obtained from planar shock compression experiments. Symmetric plate impacts at velocities of approximately 400, 600, 800, and 1000 m/s are reported, where axisymmetric cylindrical specimens (flat-faced discs) are launched in single stage light gas guns. The studied specimens have been produced from an equal channel angular extrusion process for Mg AZ31B-4E and from a hot extrusion of consolidated powder prepared via a spinning water atomization process for Mg AMX602. The present studies focus on the region of the velocity profiles spanning the Hugoniot elastic limit through the plastic rise up to the Hugoniot state, as opposed to wave reflection, release and spall studied previously in these materials. A semi-analytical method is invoked to extract inelastic constitutive response information from particle velocity histories. The only parameters entering the procedure are fundamental thermoelastic properties—notably including elastic constants up to order three—and the ratio of plastic work to energy storage of defects generated in the crystal lattice. Plastic shock velocities are not available from the present data; these are estimated from the initial bulk modulus, its pressure derivative, and known shock velocities in conventional Mg AZ31B. Shear stress, plastic strain, plastic strain rate, temperature, and dislocation density are computed outcomes. Results demonstrate similar trends in extracted behaviors for the two alloys, whereby maximum strength in the plastic shock front increases with increasing impact velocity in each material. Strain rate sensitivity appears to be greater in AZ31B-4E than AMX602. Flow stress on the Hugoniot is calculated as 295 to 336 MPa for AZ31B-4E and 163 to 293 MPa for AMX602. Maximum flow stress in the plastic rise, as extracted from tests with maximum impact velocity, is on the order of 700 MPa for each alloy.

A Numerical Study on Ductile Failure of Porous Ductile Solids With Rate-Dependent Matrix Behavior

Abstract This work examines the effects of loading rate on the plastic flow and ductile failure of porous solids exhibiting rate-dependent behavior relevant to many structural metals. Two different modeling approaches for ductile failure are employed and numerical analyses are performed over a wide range of strain rates. Finite element unit cell simulations are carried out to evaluate the macroscopic mechanical response and ductile failure by void coalescence for various macroscopic strain rates. The unit cell results are then used to assess the accuracy of a rate-dependent porous plasticity model, which is subsequently used in strain localization analyses based on the imperfection band approach. Strain localization analyses are conducted for (i) proportional loading paths and (ii) non-proportional loading paths obtained from finite element simulations of axisymmetric and flat tensile specimens. The effects of strain rate are most apparent on the stress–strain response, whereas the effects of strain rate on ductile failure is found to be small for the adopted rate-dependent constitutive model. However, the rate-dependent constitutive formulation tends to regularize the plastic strain field when the strain rate increases. In the unit cell simulations, this slightly increases the strain at coalescence with increasing strain rate compared to a rate-independent constitutive formulation. When the strain rate is sufficiently high, the strain at coalescence becomes constant. The strain localization analyses show a negligible effect of strain rate under proportional loading, while the effect of strain rate is more pronounced when non-proportional loading paths are assigned.

A micromechanics-based non-local damage to crack transition framework for porous elastoplastic solids

The failure process of ductile porous materials is simulated by representing the damage nucleation, growth and coalescence stages up to crack initiation and propagation using a physically-based constitutive model. In particular, a non-local damage to crack transition framework is developed to predict the fracture under various loading conditions while minimising case-dependent calibration process. The formulation is based on a discontinuous Galerkin method, making it computationally efficient and scalable. The initial stable damage process is simulated using an implicit non-local Gurson-Tvergaard-Needleman (GTN) model ensuring solution uniqueness beyond the onset of softening. Once the coalescence criterion is satisfied, which can physically arise before or during the softening stage, a cohesive band is introduced. Within the cohesive band, a void coalescence-based governing law is solved, accounting for the stress triaxiality state and material history, in order to capture the near crack tip failure process in a micromechanically sound way. Two coalescence models are then successively considered and compared. First, with a view to model verification towards literature results, a numerical coalescence model detects crack initiation at loss of ellipticity of a local model, and the crack opening is governed by ad-hoc parameters of the GTN model. Alternatively, the Thomason criterion is used to detect crack nucleation during the softening stage while the Thomason coalescence model governs the crack opening process. This latter model is able to reproduce slant and cup-cone failure modes in plane-strain and axisymmetric specimens, respectively.

Dynamic Behaviour of a High-Strength Structural Steel at Low Temperatures

The main objective of this experimental study is to determine the effect of low temperatures on the mechanical behaviour of Strenx 960 Plus high-strength structural steel at different strain rates and stress triaxialities. For this purpose, a comprehensive experimental campaign was designed to characterise the material at a wide range of temperatures and loading rates. The stress triaxiality was varied by testing specimens with different geometry. First, to determine the ductile-to-brittle transition temperature, instrumented Charpy V-notch impact tests were carried out at a range of temperatures from + 20 °C down to − 90 °C. The impact energy dropped gradually with decreasing temperature, but a clear transition temperature could not be identified. A fractography study exhibited a clear dimple structure, revealing predominantly ductile fracture at all temperatures. Then, uniaxial tension tests on smooth and pre-notched axisymmetric specimens under both quasi-static and dynamic loading rates were carried out at room temperature and low temperatures. These tests were conducted to characterise the rate-dependence of the stress–strain behaviour and the failure strain. The results revealed that under quasi-static conditions the flow stress increased with decreasing temperature, while the failure strain was nearly independent of the temperature. Dynamic tensile tests using the same specimen geometries were conducted in a split Hopkinson tension bar at + 20 °C and − 40 °C. The material exhibited a positive strain rate sensitivity at all investigated temperatures. This experimental study reveals that the Strenx 960 Plus steel retains its ductility at temperatures as low as − 40 °C. Brittle failure could not be observed even with combined high strain rate, high stress triaxiality and low temperature.

Ductile fracture of notched aluminum alloy specimens under elevated temperature part 1 – Experimental research

This paper presents the results of experimental fracture tests of axisymmetric specimens with circumferential notches under elevated temperature conditions. Five different radii at the notch root and four temperature levels were used for the tests. Specimens used in research were made of the EN-AW 2024T3 aluminum alloy. It was observed that elevated temperature increases the ductility of the tested material. For the adopted aluminum alloy, only at 300 °C was a significant decrease of material hardening obtained. The effect of the notch shape and elevated temperature on the decrease of the critical force value is also presented. On the basis of binary image conversion, the influence of elevated temperature on the size, quantity and distribution of dimples on the fracture surfaces was determined. Obtained results show the elevated temperature decrease material properties, such as Young modulus, yield point, ultimate strength, gauge length elongation.

Ductile fracture of notched aluminum alloy specimens under elevated temperature part 2 – Numerical modelling and fracture criterion

Paper presents the results of the numerical modelling of axisymmetric specimens with circumferential notches made of aluminum alloy EN-AW 2024 T3 under elevated temperature. A range of notch rood radii (rK = 0.5, 2, 4, 8, 30 mm) is considered. The specimens underwent monotonic uniaxial loading at elevated temperature 20, 100, 200 and 300 °C. Stress and strain fields in whole specimens were calculated using finite element analysis (FEM). Axisymmetric finite element mesh model built of four-node elements with a bilinear shape function was used in simulations. The aim of these calculations were to determine the location of maximum stress and plastic strain in the specimen depending on the notch radius and the elevated temperature. Significant attention was paid to influence on distributions of stresses and plastic strains under uniaxial loading, elevated temperature and notch radius. It has been shown that the location of maximum stresses and plastic strains depends only on the notch radius where their value depends both on the notch radius and on the temperature. The main aim of these research was to develop new ductile fracture criterion for notched specimens taking into account elevated temperature and uniaxial loading. In this criterion assumed that the fracture initiation occurs when the normal stress on this physical plane reaches the critical value, depending on the isotropic damage state variable ω, generated by plastic flow of the material (depending on the temperature).

Tensile and fatigue properties of 17-4PH martensitic stainless steels in presence of hydrogen

Effects of hydrogen on slow-strain-rate tensile (SSRT) and fatigue-life properties of 17-4PH H1150 martensitic stainless steel having an ultimate tensile strength of ~1GPa were investigated. Smooth and circumferentially-notched axisymmetric specimens were used for the SSRT and fatigue-life tests, respectively. The fatigue-life tests were done to investigate the hydrogen effect on fatigue crack growth (FCG) properties. The specimens, tested in air at ambient temperature, were precharged by exposure to hydrogen gas at pressures of 35 and 100 MPa at 270°C for 200 h. The SSRT properties of the H-charged specimens were degraded by hydrogen, showing a relative reduction in area (RRA) of 0.31, accompanied by mixed fracture surfaces composed of quasi-cleavage (QC) and intergranular cracking (IG). The fatigue-life tests, conducted under wide test frequencies ranging from 10-3 Hz to 10 Hz, revealed three distinct characteristics in low- and high-cycle regimes and at the fatigue limit. The fatigue limit was not degraded by hydrogen. In the high-cycle regime, the hydrogen caused FCG acceleration with an upper bound ratio of 30, accompanied by QC surfaces. In the low-cycle regime, the hydrogen caused FCG acceleration with a ratio of ~100, accompanied by QC and IG. The ordinary models such as process competition and superposition models hardly predicted the H-assisted FCG acceleration; therefore, an interaction model, successfully reproducing the experimental FCG acceleration, was newly introduced.

Brittle fracture analysis of Dissimilar Metal Welds between low-alloy steel and stainless steel at low temperatures

Dissimilar Metal Welds (DMW) between low-alloy steel (A533 steel) and austenitic 316L stainless steel are widely used within the French nuclear power plants where they connect the main components to the primary circuit pipes. In these DMW, the welding process and the post-weld heat-treatment generate a hard thin layer of carburized martensite and austenite in the vicinity of the fusion line (FL), resulting in a heterogeneous microstructure with high mechanical properties gradient, hence potentially, a higher sensitivity to brittle fracture in the hard layer. The present study aims to evaluate the brittle behavior of the DMW at low temperatures and more particularly of the interface between the carburized martensite and austenite (MA interface). Fracture toughness tests were carried out at temperatures between - 120°C and -50°C, with a precrack tip located on the ferritic side near the FL (i.e., between the ferritic steel and the stainless steel buttering). The analysis of the fracture behavior of the DMW was based on a SEM examination of CT (Compact Tension) specimens fracture surfaces. Coupled with a 2D plane strain numerical simulation of the tests, the results show that the presence of austenite in the fatigue precrack front and subsequent ductile tearing towards FL produced higher solicitations on the hard layer and caused intergranular fracture on the MA interface, resulting in lower toughness values for the specimen. To model the brittle behavior of the MA interface, a stress based criterion was used. Tensile tests on axisymmetric specimen, which were machined to initiate intergranular fracture in the MA interface and tested at -170°C, were used to define a threshold stress (σth), below which brittle fracture cannot occur. Then, a criterion to evaluate the brittle fracture risk of the DMW was proposed and applied to the CT specimen.