Axisymmetric Specimens Research Articles

Damage accumulation and ductile fracture modeling of notched specimens under biaxial loading at room temperature

This paper presents the results of ductile fracture tests conducted on axisymmetric specimens with notch made from EN AW 2024 T351 aluminum alloy. Tests were conducted for five notch radius and seven cases of biaxial, proportional loading with tensile force and torsional moment. A model of damage accumulation and fracture based on variables of stress strain state and damage on a physical plane is proposed. The fracture criterion assumes that crack initiation will occur when a certain combination of normal and shear stress on the physical plane (elliptical criterion in the tensile stress zone and Coulomb criterion in the shear stress zone) reaches a critical value dependent on the value of the damage state variable on this plane. The damage accumulation law was formulated incrementally, and the increment of the damage state variable was made dependent on the increment of plastic deformations and stress values on the physical plane. This model was successfully verified by experimental tests and numerical simulations, which are presented in papers by Derpenski and Seweryn (2016a,b).

Brittle fracture of axisymmetric specimens with notches made of graphite EG0022A

The present paper summarizes the results of some numerical calculations carried out on the basis of a recent wide experimental research. The calculations are performed on axisymmetric specimens weakened by V notches consisting of a large bulk of different shapes. The specimens are subjected to multiaxial fracture loading (tension+torsion). Stress and strain fields in the whole specimens are evaluated herein by using the finite element method (FEM). Special attention is paid to the changing distribution of stresses induced by loading and notch shape. By taking advantage of the numerical calculations carried out in the present investigation, a new non-local fracture criterion for notched specimens under multiaxial loading is proposed and successfully employed and compared with some data taken from the recent literature.

Ductile fracture of EN-AW 2024 aluminum alloy specimens with notches under biaxial loading. Part 1 – Experimental research

This paper presents the results of the experimental studies on ductile fractures of axisymmetric specimens with circumferential notches. A range of notch root radii is considered. The specimens underwent proportional biaxial loading (tensile–torsion) until failure. The load was forced onto the specimens by elongation as well as angular movement and was controlled by a device for the non-contact measurement. The EN-AW 2024 T351 aluminum alloy was used in this research. Special attention was paid to the change in shape of the fracture surface, changing the force-elongation curve and torsional moment–torsional angle curve, which are dependent on loading.

Ductile fracture of EN-AW 2024 aluminum alloy specimens with notches under biaxial loading. Part 2 – Numerical research and ductile fracture criterion

This paper presents the results of the numerical modelling of axisymmetric specimens with circumferential notches. A range of notch rood radii is considered. The specimens underwent proportional biaxial loading. Stress and strain fields in whole specimens with notches were calculated using finite element analysis (FEM). Special attention was paid to changing distributions of stresses and plastic strains induced biaxial loading and notch radius. By taking advantage of numerical calculations, new ductile fracture criterion for notched specimens under biaxial loading was proposed.

Unusual plastic deformation and damage features in titanium: Experimental tests and constitutive modeling

In this paper, we present an experimental study on plastic deformation and damage of polycrystalline pure HCP Ti, as well as modeling of the observed behavior. Mechanical characterization data were conducted, which indicate that the material is orthotropic and displays tension-compression asymmetry. The ex-situ and in-situ X-ray tomography measurements conducted reveal that damage distribution and evolution in this HCP Ti material is markedly different than in a typical FCC material such as copper. Stewart and Cazacu (2011) anisotropic elastic/plastic damage model is used to describe the behavior. All the parameters involved in this model have a clear physical significance, being related to plastic properties, and are determined from very few simple mechanical tests. It is shown that this model predicts correctly the anisotropy in plastic deformation, and its strong influence on damage distribution and damage accumulation. Specifically, for a smooth axisymmetric specimen subject to uniaxial tension, damage initiates at the center of the specimen, and is diffuse; the level of damage close to failure being very low. On the other hand, for a notched specimen subject to the same loading the model predicts that damage initiates at the outer surface of the specimen, and further grows from the outer surface to the center of the specimen, which corroborates with the in-situ tomography data.

A phase-field model for ductile fracture at finite strains and its experimental verification

In this paper, a phase-field model for ductile fracture previously proposed in the kinematically linear regime is extended to the three-dimensional finite strain setting, and its predictions are qualitatively and quantitatively compared with several experimental results, both from ad-hoc tests carried out by the authors and from the available literature. The proposed model is based on the physical assumption that fracture occurs when a scalar measure of the accumulated plastic strain reaches a critical value, and such assumption is introduced through the dependency of the phase-field degradation function on this scalar measure. The proposed model is able to capture the experimentally observed sequence of elasto-plastic deformation, necking and fracture phenomena in flat specimens; the occurrence of cup-and-cone fracture patterns in axisymmetric specimens; the role played by notches and by their size on the measured displacement at fracture; and the sequence of distinct cracking events observed in more complex specimens.

Visualizing shear bands in 3-D using axisymmetric sample: An experimental study

In this study a qualitative description of the occurrence of shear bands produced by a sudden impact on an axisymmetric specimen made of medium carbon steel 0.45% C is given. A simple experiment was developed aimed at producing a pinch shear stress in the front side of the test sample in order to visualize shear bands in 3-D. Curve fitting using MATLAB was employed based on the points taken from the images of the front section of the test sample. The predictions of the curve fitting suggests a hyperbolic section leading to the conclusion that within the sample there is a double cone region of material where the shear band region is located on its outer surface. The formation of the shear band is explained by the fact that the interaction of the stress wave front with the free surface of the test sample produces reflection waves that attenuate the incoming stress wave inwards leading to a stress gradient in the plane of the front side of the specimen that causes shear localization. Also, the progressively increasing cross sectional area of the test sample causes the expansion of the wave front, which also results in a stress gradient in the normal direction of the front side of the specimen. So the formation of shear bands depends not only on the impact momentum and strain rates but also on the sample’s geometry.

Multiaxial fatigue strength of severely notched titanium grade 5 alloy

The multiaxial fatigue strength of severely notched titanium grade 5 alloy (Ti-6Al-4V) is investigated. Experimental tests under combined tension and torsion loading, both in-phase and out-of-phase, have been carried out on axisymmetric V-notched specimens considering different nominal load ratios (R = -1, 0). All specimens are characterized by a notch tip radius less than 0.1 mm, a notch depth of 6 mm and a notch opening angle equal to 90 degrees. The experimental data from multiaxial tests are compared with those from pure tension and pure torsion tests on un-notched and notched specimens, carried out at load ratio ranging from R = -3 to R = 0.5. In total, more than 160 new fatigue data are examined, first in terms of nominal stress amplitudes referred to the net area and then in terms of the local strain energy density averaged over a control volume surrounding the V-notch tip. The dependence of the control radius on the loading mode is analysed showing a very different notch sensitivity for tension and torsion. For the titanium alloy Ti-6Al-4V, the control volume is found to be strongly dependent on the loading mode.

Effects of particles and solutes on strength, work-hardening and ductile fracture of aluminium alloys

The influence of particles and solutes on the strength, work-hardening behaviour and ductile fracture of four different aluminium alloys in the as-cast and homogenised condition is investigated in this paper. These alloys contain different types and volume fractions of particles, i.e. constituent particles and dispersoids, in addition to elements in solid solution. Tensile tests on smooth and notched axisymmetric specimens are performed to determine the work-hardening curves and the ductile fracture characteristics of the alloys. A laser-based extensometer is used to continuously measure the logarithmic strain to failure in the minimum cross section of the specimens. Finite element simulations of the test specimens are used to determine the work-hardening curves to failure. Both the J2 flow theory and the Gurson model are used to describe the stress–strain behaviour of the materials, where the latter accounts for material softening due to void growth. The microstructure of the alloys is characterised by optical and scanning electron microscopy, and fractography is performed to investigate the fracture modes. While the damage and failure mechanisms are similar in the four alloys, the failure strain depends markedly on the stress triaxiality and the yield stress. The trend is that the failure strain decreases linearly with increasing yield stress for the investigated alloys.

Influence of Processing Route on the Work-Hardening and Ductile Fracture of an AA6060 Aluminium Alloy

Tensile tests on smooth and notched axisymmetric specimens were carried out to determine the large strain work-hardening curves and the ductile fracture characteristics of an AA6060 aluminium alloy for three different processing routes. The alloy was processed in three subsequent steps: 1) casting and homogenization, 2) extrusion, and 3) cold rolling and heat treatment to obtain a recrystallized grain structure. After each processing step, the material was tested after natural ageing for more than one week. A laser-based extensometer was used to continuously measure the average true strains to failure in the minimum cross-section of the specimens and the true stress-strain curves were calculated. Since these curves are influenced by necking, they do not represent the correct work-hardening of the material. Accordingly, finite element (FE) simulations of the tensile tests on the smooth axisymmetric specimens were conducted to determine the work-hardening curves to failure, using an optimization tool that interfaced with the nonlinear FE code and the experimental stress-strain curves as objectives. The microstructure of the alloy was characterized after the three processing steps by optical and scanning electron microscopy, and fractography was used to investigate the failure mechanisms.

Local Measurement of Stress–Strain Behaviour of Ductile Materials at Elevated Temperatures in a Split‐Hopkinson Tension Bar System

ABSTRACTA split‐Hopkinson tension bar system is modified to allow for measuring the stress–strain behaviour of ductile materials at large strains, high strain rates and elevated temperatures. The specimen is heated by induction, and a pyrometer provides a laser‐based temperature measurement that controls the testing temperature in a feed‐back loop. A high‐speed digital camera system and an edge detection algorithm are used to obtain local measures of strain after necking of the axisymmetric specimens. Using the local strain measurements and Bridgman's analytical formulas, it is feasible to find the equivalent stress–strain curve to fracture for different levels of strain rate and temperature. Thermal and thermo‐mechanical finite element simulations of the test set‐up are used to evaluate the validity of the proposed experimental method.

Multiaxial fatigue strength of severely notched cast iron specimens

The present work deals with multiaxial fatigue strength of severely notched cast iron (EN-GJS400). Circumferentially V-notched specimens are tested under combined tension and torsion loading, both in-phase and out-of-phase, with two nominal load ratios, R=−1 and R=0. All axis-symmetric specimens are characterized by a constant notch tip radius (less than 0.1mm), a notch depth of 4mm and a V-notch angle of 90°. The results from multiaxial tests are discussed together with those obtained under pure tension and pure torsion loading from notched specimens with the same geometry. Altogether more than eighty new fatigue data (10 Wöhler curves) are summarised in terms of normal and shear stresses. Afterwards, all fatigue strength data are given also in terms of the local strain energy density averaged over a material-dependent control volume surrounding the V-notch tip. The dependency of the control volume size as a function of the loading mode is investigated showing the necessity to introduce for the cast iron EN-GJS400 a different value of the control volume radius under tension and under torsion.

Multiaxial fatigue resistance of shot peened high-strength aluminum alloys

This paper is aimed at investigating multiaxial fatigue of shot peened Al-7075-T6 alloy. Plain axi-symmetric specimens were subjected to combined in-phase tension and torsion loading, under nominal load ratio R=0.05 and biaxiality ratio λ=τa/σa=2. The results from multi-axial tests are discussed together with those obtained under pure tension and pure torsion loading. Fatigue crack initiation sites have been investigated through scanning electron microscopy fractography and the role of surface roughness on fatigue resistance has been analyzed. The initial and the stabilized residual stress profiles were used to discuss the improvement in the fatigue response in the hypothesis of crack initiation and early crack propagation as fatigue controlling parameters. For this purpose, several multiaxial fatigue criteria were used to account for the residual stress field. The Crossland and the Findley fatigue criteria incorporating stabilized residual stresses as mean stresses were found to predict the fatigue strength with a relative error lower than 15% within the entire fatigue life interval, for all the material variants and the loading conditions considered.

A new numerical implementation of a second-gradient model for plastic porous solids, with an application to the simulation of ductile rupture tests

An interesting second-gradient model for plastic porous solids, extending Gurson (1977)’s standard first-gradient model, was proposed by Gologanu et al. (1997) in order to settle the issue of unlimited localization of strain and damage and the ensuing mesh sensitivity in finite element calculations. Gologanu et al. (1997)’s model was implemented in a finite element code by Enakoutsa (2007), Enakoutsa and Leblond (2009). The implementation however rose two difficulties: (i) the number of degrees of freedom per node was awkwardly large because of the introduction of extra nodal degrees of freedom representing strains; (ii) convergence of the global elastoplastic iterations was often very difficult.A new implementation solving these problems is presented in this work. An original procedure of elimination of the nodal degrees of freedom representing the strains permits to reduce the number of degrees of freedom per node to its standard value. Also, the convergence issue is solved through use of normally integrated linear elements instead of more customary subintegrated quadratic ones.As an application, 2D numerical simulations of experiments of ductile rupture of a pre-notched and pre-cracked axisymmetric specimen and a CT specimen are performed. The calculations are pursued without difficulties up to a late stage of the rupture process, and the results are mesh-independent. Also, a good agreement between experimental and computed load–displacement curves is obtained for values of the parameters governing void coalescence compatible with those suggested by micromechanical numerical simulations, which could never be achieved in calculations based on Gurson (1977)’s standard model.

Recent Developments in Brittle and Quasi-Brittle Failure Assessment of Graphite by Means of SED

Brittle fracture of polycrystalline graphite under tension, in-plane shear and torsion loading is studied experimentally and theoretically using prismatic and axisymmetric specimens weakened by sharp and rounded-tip V-notches. The main purpose is twofold. First, to provide a new set of experimental data from notched samples made of isostatic polycrystalline graphite with different values of notch opening angles and root radii, which should be useful to engineers engaged with static strength analysis of graphite components. At the best of authors' knowledge, data from notch specimens are very scarce in the literature for this material. Second, to apply a fracture criterion based on the strain energy density (SED) averaged over a well-defined control volume surrounding the notch tip, extending what was made by the present authors for in-plane tension-shear loading conditions in notched specimens made of other materials. Good agreement is found between the experimental data related to the critical loads to failure and the theoretical assessments based on the constancy of the mean SED over the material-dependent control volume.

An experimental study on the deformation and fracture modes of steel projectiles during impact

Previous investigations of the penetration and perforation of high-strength steel plates struck by hardened steel projectiles have shown that under certain test conditions the projectile may fracture or even fragment upon impact. Simulations without an accurate failure description for the projectile material will then predict perforation of the target instead of fragmentation of the projectile, and thus underestimate the ballistic limit velocity of the target plate. This paper presents an experimental investigation of the various deformation and fracture modes that may occur in steel projectiles during impact. This is studied by conducting Taylor bar impact tests using 20mm diameter, 80mm long, tool steel projectiles with three different hardness values (HRC 19, 40 and 52). A gas gun was used to fire the projectiles into a rigid wall at impact velocities ranging from 100 to 350m/s, and the deformation and fracture processes were captured by a high-speed video camera. From the tests, several different deformation and fracture modes were registered for each hardness value. To investigate the influence of material on the deformation and fracture modes, several series of tensile tests on smooth axisymmetric specimens were carried out to characterise the mechanical properties of the three materials. To gain a deeper understanding of the various processes causing fracture and fragmentation during impact, a metallurgical investigation was conducted. The fracture surfaces of the failed projectiles of different hardness were investigated, and the microstructure was studied for each hardness value.

Microstructural evolution during nitriding, finite element simulation and experimental assessment

A finite element simulation of nitriding is proposed in this paper, using the analogy between diffusion and heat conduction, to overcome the shortcomings of the classical internal oxidation model in predicting the kinetics of layer growth and nitrogen distribution during nitriding. To verify the model, a typical gas nitriding has been carried out on an axisymmetric specimen. Treated specimen has been characterized using optical microscopy (OM), scanning electron microscopy (SEM), micro-hardness and X-Ray diffraction (XRD) measurements. It was found that the so-called diffusion zone can be divided into two parts with different influence on the mechanical characteristics including residual stress and hardening. First layer which is a two phase region of ferritic matrix and γ′ (Fe4N) makes further improvement with respect to the second layer which is a solid solution of nitrogen in ferrite. The formation of that two phase region, which is not predicted by classical model, can be efficiently recognized by the proposed model. It is also proved that the model has the ability to consider the geometry dependency of layer growth and formation in nitriding.

Effect of Multiaxial Stress State on Morphology and Spatial Distribution of Voids in Deformed Semicrystalline Polymer Assessed by X-ray Tomography

Cavitation in the semicrystalline polymer polyamide 6 has been studied in terms of 3D void morphology and distribution in the notched region of axisymmetric specimens using synchrotron radiation tomography at submicrometer resolution. Ex-situ (interrupted and unloaded) tests at different stages of straining reveal damage initiation in form of penny-shaped crazes at maximum load. An in-situ (under load) test confirms the damage morphology at maximum load. When a neck appears and extends within the notch, the penny-shaped crazes extend in height, resulting in a volume change. Final failure is seen to occur from the specimen interior via coalescence of several voids resulting in large cavities. The multiaxial stress state generated by the axisymmetric notch causes crazes/cracks that are larger in diameter than those occurring during necking of an initially smooth specimen. The distribution void volume fraction as a function of the radius is measured via image analysis, showing a damage maximum at the specimen center that decreases toward the specimen border. This distribution was found to be consistent with that of the stress triaxiality ratio.

Brittle fracture of sharp and blunt V-notches in isostatic graphite under torsion loading

Brittle fracture of polycrystalline graphite under torsion loading is studied experimentally and theoretically using axisymmetric specimens weakened by sharp and rounded-tip V-notches. The main purpose is twofold. First, to provide a new set of experimental data from notched samples made of isostatic polycrystalline graphite with different values of notch opening angles and root radii, which should be useful to engineers engaged with static strength analysis of graphite components. At the best of authors’ knowledge, data from notch specimens under torsion are not available in the literature for this material. Second, to apply to the torsion loading case a fracture criterion based on the strain energy density (SED) averaged over a well-defined control volume surrounding the notch tip, extending what was made by the present authors for in-plane tension-shear loading conditions in notched graphite specimens. Good agreement is found between the experimental data related to the critical loads to failure and the theoretical assessments based on the constancy of the mean SED over the material-dependent control volume.

Effect of Strain Rate on the Stress-Strain Behavior of Sand

Drained triaxial compression tests on crushed coral sand were performed from near-static strain rates to very high strain rates (up to approximately 1,800%/s). Experiments were performed on dry, vacuum-confined axisymmetric specimens at two different confining pressures (98 and 350 kPa) and two different densities (Dr approximately 36 and 60%). A gravity drop weight loading system was used to generate high strain rates. High-speed film photographs of the specimen were taken through the flat sides of a square triaxial cell. By using digital image analysis techniques, strains were locally measured near the center of the specimen to obtain the most uniform assessment. Stress-strain relationships are presented. The following effects were observed with increasing strain rates: the elastoplastic stiffness increased significantly; the failure shear strength increased moderately; the axial strain at peak stress decreased significantly; and volumetric strains became more dilatant. Unusual behavior was observed at ...