Ductile Failure Criterion Research Articles

Numerical assessment of T-stub component subjected to impact loading

Since the partial collapse of the Ronan Point building in London in 1968, requirements for the avoidance of disproportionate collapse are addressed in the design codes. Despite these prescriptive requirements, the ability of steel connections to sustain large tensile forces whilst undergoing significant rotations has been questioned by recent studies and real evidences (as for example, the collapse of the World Trade Center in 2001).This paper describes the non-linear behaviour of a T-stub joint exposed to impact loads, by exploring a finite element model developed in ABAQUS software. The numerical model is validated against experimental results considering quasi-static loading and dynamic loading. A ductile failure criterion is implemented in the model, and the strain rate effect on the material behaviour is demonstrated in the enhancement of the force–displacement response. Finally, parametric studies, concerning the load magnitude, load application time and T-stub flange thickness, are performed. The results show that different dynamic loads have minor effect on the force displacement response, whilst the load application time has a larger effect. Moreover, it is also concluded that the force–displacement enhancement is less prominent for stiffer T-stubs.

Shear localization sensitivity analysis for Johnson–Cook constitutive parameters on serrated chips in high speed machining of Ti6Al4V

This research aims to investigate the influence of material constitutive parameters on the serrated chip formation during high speed machining (HSM) of Ti6Al4V alloys with finite element simulations and cutting experiments. The Johnson–Cook (JC) constitutive model and JC fracture model with an energy-based ductile failure criterion are adopted to simulate the HSM process. Five JC constitutive model parameters such as initial yield stress, hardening modulus, strain hardening coefficient, strain rate dependency coefficient, and thermal softening coefficient are included in this research. Shear localization sensitivity is novelly proposed to describe variations of serrated chips under different JC constitutive model parameters. Shear localization sensitivity is subdivided into chip serration sensitivity and chip bending sensitivity. The research finds that the influences of initial yield stress and thermal softening coefficient parameters on the chip serration and bending are much more prominent than those of the rest three JC constitutive model parameters. With initial yield stress or hardening modulus in JC constitutive model increasing, the chip serration sensitivity increases and the chip bending sensitivity decreases. However, the influences of the rest three parameters on chip serration sensitivity are opposite. High speed orthogonal cutting experiments of Ti6Al4V are carried out to validate the simulation results under different cutting speeds ranging from 50m/min to 3000m/min and fixed uncut chip thickness with 0.1mm. The results show that the serrated degree of chips increases with the cutting speed increasing until the chips become completely fragmented. The cutting speed break point of chip morphology from serrated to fragmented ones for Ti6Al4V is about 2500m/min. The average cutting force decreases with the cutting speed increasing, which is a prominent advantage for HSM. This paper can help to get deeper insights into the serrated chip formation mechanism in HSM.

A new approach to the determination of plastic flow stress and failure initiation strain for aluminum alloys cutting process

Abstracts Material flow stress in cutting is difficult to measure experimentally due to the complex deformation behavior involved. In this work, a finite element (FE) simulation of cutting and a theoretical flow stress model including plastic and failure criteria were developed to determine the flow stress during aluminum alloy (7075-T6) cutting process. In a stable plastic stage, the Johnson–Cook model considering the adiabatic temperature rise (ATR) was proposed to calculate the plastic flow stress, and the relative errors of the calculated and FE simulated stresses were less than 4%. In the ductile failure stage, an improved failure initiation criterion in terms of temperature, pressure and strain rate was proposed to determine the failure initiation strain in cutting. In addition, an energy-density based ductile failure criterion was used to predict the flow stress in the failure stage. By combining the proposed theoretical model results and the FE simulation results, the entire flow stress during cutting was obtained. The influence of the failure initiation strain of the chip layer on cutting performance was also discussed. In addition, a set of aluminum alloy (A2024-T351) orthogonal cutting simulations were performed to validate the effect of the failure initiation strain on the cutting process. The predicted variation trends of the failure initiation strain for the two types of aluminum alloys were similar, and the predicted forces and tool–chip contact lengths were compared with the measured values in Atlati et al. [9]. Finally, the prediction of the failure initiation strain and its influence on tool–chip contact behavior were validated indirectly.

Investigations on the chip formation mechanism and shear localization sensitivity of high-speed machining Ti6Al4V

This study develops a combined numerical and experimental approach to get deeper insights into chip formation mechanism for high-speed machining of titanium alloy Ti6Al4V. The numerical investigation of high-speed machining is implemented with the aid of finite element analysis software Abaqus/Explicit, in which the Johnson-Cook (JC) fracture model with an energy-based ductile failure criterion is adopted. Meanwhile, the experiments of high-speed orthogonal cutting are carried out to validate the numerical results. The cutting speeds are selected ranging from 50 to 3,000 m/min, and the uncut chip thickness is fixed at 0.1 mm. The variables investigated include the serrated degree and serrated frequency of chips in addition to the cutting force. The results show that both the serrated degree and serrated frequency have positive correlations with the cutting speed. An important regularity for the transformation of chip morphology from serrated to unit at a critical cutting speed has been achieved, and the critical value for Ti6Al4V is about 2,500 m/min. The research also finds that the cutting force decreases with the increasing cutting speed, while its fluctuant frequency and amplitude increase sharply. Furthermore, the influences of JC fracture constants (the five constants in JC fracture model) on chip formation are investigated based on the finite element method, which is the main original and innovative highlight of this study. The shear localization sensitivity is firstly proposed to describe the influences of JC fracture constants on the chip formation process. When the JC fracture constants decrease, the shear localization sensitivity is positive which means that the serrated degree increases and vice versa. The sensitivity analyses indicate that the influences of initial failure strain D 1 and exponential factor of stress triaxiality D 2 on chip formation process are more conspicuous than the rest three ones. This paper is enticing from both the engineering and the analytical perspectives aimed at predicting the evolution of serrated chip formation and chip morphology transformation in metal cutting process.

Geometry and grain size effects on the forming limit of sheet metals in micro-scaled plastic deformation

In micro-scaled plastic deformation or micro-forming process, workpiece usually consists of only a few grains in deformation zone. The so-called size effect thus exists and the material deformation behaviors are quite different from the conventional ones in macro-scaled. Size effect affects the deformation capability or the forming limit of sheet metals. To explore this effect, uniaxial tensile tests of different-shaped specimens were conducted to obtain the left-hand-side forming limit diagram of sheet metals from macro to micro-scaled. The deformation process was recorded by a digital camera and the limit strains of different deformation conditions were measured using the digital image correlation method. The left-hand-side forming limit diagrams under different thickness-to-grain-size ratio conditions were then constructed. The experimental results show the existence of the significant size effect and the forming limit decreases with the thickness-to-grain-size ratio. However, the scatter of forming limit gets much worse if there are only one or two grains over the thickness of material. To analyze how the size effect affects the ductile fracture in micro-forming, Oyane׳s ductile failure criterion was modified to model the forming limit in micro-scaled plastic deformation. Through calculation, the modified criterion is found to be able to model the decrease of forming limit caused by size effect. The revised Oyane criterion can then be used to analyze the forming limit of sheet metals in micro-scale.

Influence of elastic and plastic support on the energy absorption of the extruded aluminium tube using ductile failure criterion

Thin-walled structures like crash tubes may be used as energy absorption members in automobile chassis. There have been a lot of investigations into the behaviour of these parts on the frontal crash. The main task of previous researches has been to predict the energy absorption and maximum impact force in shell structure. The energy absorption and maximum impact force depend on many parameters such as boundary conditions, the history of plastic deformation during metalworking, geometry, material, and impact energy (mass and velocity of striker). In this paper, the crash behaviour of a circular tube made of the extruded aluminium alloy EN AW-7108 T6 is studied. In this study, by creating elastic and plastic boundary conditions instead of rigid boundary conditions on the bottom of a crash box, the stress–strain sensitivity effect on box behaviour during a crash is considered. In addition, the effect of elastic and plastic boundary conditions on the energy absorption of circular tubes under impact force is numerically investigated. The ductile failure criterion is employed to accurately obtain crashworthiness simulation results. Results reveal that the use of elastic boundary can change deformation mode and decrease the maximum impact force.

Relation between Ductile Fracture Locus and Deformation of Phases in Ti–6Al–4V Alloy

Failure criteria based on ductility associated with triaxiality are often used to define the strength of metal alloys as a function of the load modalities. However a discussion of the results with regards to the microstructural evolution and the behavior of the different phases is still not investigated, especially in multi-phase alloys. In this paper a ductile failure criterion was calibrated on α/β titanium alloy (Ti–6Al–4V). The applied approach is based on different experimental tests supported by numerical analyses carried out by detailed FE models. Specimens were tested on a multiaxial test system to investigate the failure induced by different states of stress triaxiality. Results have been discussed with regards to the textures induced in the lattice of the α-phase and β-phase, which are a direct consequence of the rotations associated with the dissipative plastic strains. Schmid factors at failure have been also calculated to determine which slip system have been activated by the different load modalities. The proposed approach could be also extended to steel.

The Numerical Experimental Investigation on Damage Zone of Surrounding Rock of Deep Tunnel Based on the Elastic-Plastic-Brittle Constitutive Model

A particular elastic-plastic-brittle constitutive model, considering the heterogeneity of rock and the features of deep engineering, is presented, in which the multiple yield criteria based on stress space and ductile failure criteria based on strain space are adopted, and the numerical method is FEM. Through the simulation of the compression test of rock samples, the results show that the present model is rational and accurate. The elastoplastic damage mechanism of the surrounding rock mass of deep tunnel is studied and through the display of centralization, extension and transfer of stresses, it is shown that the present model can be used to predict reliably the whole process of formation of broken zone.

Modeling the ductile fracture behavior of an aluminum alloy 5083-H116 including the residual stress effect

In this work, the plasticity and ductile fracture behaviors of an aluminum alloy 5083-H116 are studied through a series of experiments and finite element analyses. A recently developed stress state dependent plasticity model, the I1–J2–J3 plasticity model, is implemented to describe the plastic response of this material. Furthermore, a ductile failure criterion based on a damage parameter defined in terms of the accumulative plastic strain as a function of the stress triaxiality and the Lode angle is established. The calibrated I1–J2–J3 plasticity model and ductile failure model are utilized to study the residual stress effect on ductile fracture resistance. A local out-of-plane compression approach is employed to generate residual stress fields in the compact tension specimens. Fracture tests of C(T) specimens having zero, positive and negative residual stresses are conducted. The numerical results, such as load–displacement curves and crack front profiles, are compared with experimental measurements and good agreements are observed. Both experimental and finite element results show significant effect of residual stress on ductile fracture resistance.

Ductile fracture locus of Ti–6Al–4V titanium alloy

The simulation of ductile fracture in real components is becoming a strategic issue in numerical simulations. Numerical simulations of crashes, forming processes, impacts and fractures are reliable only if carried out with an accurate material calibration. The topics involved in this kind of simulation require a complete calibration of both the true stress–strain curve and the failure. The focus of this work is the accurate calibration of the constitutive relations of the titanium alloy Ti–6Al–4V. The approach proposed is based on different experimental tests supported by numerical simulations performed by means of detailed FE models. The Bao–Wierzbicki ductile failure criterion is calibrated using a total of 11 specimens. These specimens are tested on a multiaxial test machine to investigate the failure at different stress triaxialities. Furthermore, the sensitivity to the mesh size and the assessment of the calibration accuracy are analysed in detail on different components in order to verify the geometry transferability.

Calibration of Constitutive Law and Ductile Failure Criterion for Very Thin Rectangular Al2024-T3 Aluminum Alloy Specimen

Thin plate structures are common in many industrial products and in particular they can be found as skins in sandwich panels. In order to develop complex FE analysis which involve the damage of these structures, it’s crucial the knowledge of constitutive law and damage criterion of the material they are made. In this paper a complete characterization of both constitutive material law and damage criterion for very thin rectangular Al2024-T3 aluminum alloy specimen plate has been done. The specimens have been cut, using a water jet machine, directly from sandwich panel skins in order to take into account the modification of mechanical behavior due to the manufacturing process. A complete experimental campaign of tensile tests has been done and an accurate virtual testing methodology has been subsequently applied (by means on Finite Element Models) in order to numerically reproduce the tests. The calibration of a fitted constitutive law and of three ductile failure criteria allows the numerical model to reproduce the experimental tests with good agreement up to failure.

Numerical simulation of the slant fracture of a helicopter's rotor hub with ductile damage failure criteria

ABSTRACTThe main rotor hub is one of the most critical components in helicopter structures. Thus, to assess the behaviour of the component, a fatigue test until failure has been carried out on a real Ti–6Al–4V hub. A fracture mechanics analysis is used to estimate the critical crack dimensions. Subsequently, the slant fracture due to a propagating fatigue crack has also been simulated numerically with an explicit finite element model, using the Bao–Wierzbicki ductile damage criterion. Fracture toughness and failure calibration of Ti alloy have been carried out to obtain reliable results. The numerical fracture surface obtained has been compared with the experimental one.

조선 해양 구조물용 강재의 소성 및 파단 특성 III: 파단 변형률에 관한 실험적 연구

This is the third of several companion papers dealing with the derivation of material constants for ductile failure criteria under hydrostatic stress. It was observed that the ultimate engineering stresses and elongations at fracture from tensile tests for round specimens with various notch radii tended to increase and decrease, respectively, because of the stress triaxiality. The engineering stress curves from tests are compared with numerical simulation results, and it is proved that the curves from the two approaches very closely coincide. Failure strains are obtained from the equivalent plastic strain histories from numerical simulations at the time when the experimental engineering stress drops suddenly. After introducing the new concept of average stress triaxiality and accumulated average strain energy, the material constants of the Johnson-Cook failure criterion for critical energies of 100%, 50%, and 15% are presented. The experimental results obtained for EH-36 steel were in relatively good agreement with the 100% critical energy, whereas the literature states that aluminum fits with a 15% critical energy. Therefore, it is expected that a unified failure criterion for critical energy, which is available for most kinds of ductile materials, can be provided according to the used materials.

Finite element simulation of high-speed machining of titanium alloy (Ti–6Al–4V) based on ductile failure model

AJ ohnson-Cook material model with an energy- based ductile failure criterion is developed in titanium alloy (Ti-6Al-4V) high-speed machining finite element analysis (FEA). Furthermore, a simulation procedure is proposed to simulate different high-speed cutting processes with the same failure parameter (i.e., density of failure energy). With this finite element (FE) model, a series of FEAs for titanium alloy in extremely high-speed machining (HSM) is carried out to compare with experimental results, including chip morphol- ogy and cutting force. In addition, the chip morphology and cutting force variation trends under different cutting con- ditions are also analyzed. Using this FE model, the ductile failure parameter is modified for one time, afterword, the same failure parameter is applied to other conditions with a key modification. The predicted chip morphologies and cutting forces show good agreement with experimental results, proving that this ductile failure criterion is appropriate for titanium alloy in extremely HSM. Moreover, a series of relatively low cutting speed experiments (within the range of HSM) were carried out to further validate the FE model. The predicted chip morphology and cutting forces agree well with the experimental results. Moreover, the plastic flow trend along an adiabatic shear band is also analyzed.

Failure criterion for aluminium tubes during warm hydroforming and in crash applications

A quantitative failure criterion was developed for aluminium (Al) tubes. The developed criterion is based on the critical damage value as calculated from the Cockroft and Latham ductile failure criterion and can be used to determine the forming limit during warm hydroforming or for failure during a crash. As-extruded, fully annealed, and T6-tempered Al 6061 tubes were tested to evaluate the effect of heat treatment conditions and forming temperature. To assess the formability of the Al 6061 tubes, uniaxial tensile tests and hydraulic bulge tests were performed in the temperature range of 25—300°C. The measured flow strength was used in finite element (FE) simulations for the tube hydroforming process. A commercial finite element method (FEM) code, DEFORM2DTM, was used to calculate the damage values and strains at various locations in the hydroformed tube. Based on the results of both the experimental and FEM analysis, a failure criterion, which is based on the forming limit and ductile fracture criterion, was developed. Using the critical damage value as a quantitative measure, the formability and also the critical damage value of the as-extruded tube is 50 per cent lower than that of the fully annealed tube. The developed failure criterion predicts well the observed failures during hydroforming for a hexagonal-shaped prototype part. Moreover, the failure criterion can be used to predict the crash performance of the hydroformed part, which has variations in the amount of prior deformation and in thickness. The benefit of the proposed failure criterion is that it can be used to predict both the forming limit of the tube during hydroforming and the behaviour of hydroformed tubes during a crash.

Optimized thick-wall cylinders by virtue of Poisson's ratio selection: Part 1: Isochoric pressure application

The principal stress distributions in thick-wall cylinders due to variation in the Poisson's ratio are predicted using analytical and finite element methods. Analyses of appropriate brittle and ductile failure criteria show that under the isochoric pressure conditions investigated that auextic (i.e. those possessing a negative Poisson's ratio) materials act as stress concentrators; hence they are predicted to fail before their conventional (i.e. possessing a positive Poisson's ratio) material counterparts. The key finding of the work presented shows that for constrained thick-wall cylinders the maximum tensile principal stress can vanish at a particular Poisson's ratio and aspect ratio. This phenomenon is exploited in order to present an optimized design criterion for thick-wall cylinders. Moreover, via the use of a cogent finite element model, this criterion is also shown to be applicable for the design of micro-porous materials.

A study of inclined impact in polymethylmethacrylate plates

The penetration and perforation of a polymethylmethacrylate (PMMA) plate is investigated experimentally and numerically. Two combined failure criteria are used in the numerical analyses: ductile failure with damage evolution and tensile failure. The measured mechanical properties of PMMA are input to the analysis. The determination of the damage evolution parameter in this material is calibrated by simulating and replicating shear localization results obtained in confined PMMA cylinders. The numerical simulation based on these parameters is tested by comparing the numerical trajectory prediction to actual trajectories of inclined impacts of projectiles. The first comparison is qualitative and shows that the numerical simulation predicts ricochet of a projectile impacting at an angle of inclination 30° as reported by Rosenberg et al. (2005) [1]. Additional successful comparison with experimental results of inclined impact of a 0.5″ AP projectile on 3 PMMA plates is reported. The contribution of each failure criterion to the projectile trajectory is studied, showing that the ductile failure criterion enforces a straight trajectory in the initial velocity direction while the tensile failure criterion controls the deflection and ricochet phenomenon. The numerical analyses are further used to study the effect of the angle of inclination on the trajectory and kinetic energy of the projectile. The effect of the projectile mass and impact velocity on the depth of penetration (DOP) was investigated too. It is found that the ricochet phenomenon happens for angles of inclination of 0° < α ≤ 30°. The projectile perforates the plate for 50° ≤ α ≤ 90°, thus defining a failure envelope for this experimental configuration. For normal impact ( α = 90°) the DOP scales linearly with the projectile's mass and can be fitted by a square polynomial with the impact velocity.

A Study to Predict Failure in Biaxially Stretched Sheets of Aluminum Alloy 2024-T3

The 2024-T3 aluminum alloy is extensively used for making aircraft parts. This alloy has a relatively low ductility at room temperature, and is generally heat-treated before forming. The present study experimentally and numerically analyzes the formability of AA2024-T3 sheets subjected to biaxial stretching. The aim of this study is to provide an appropriate criterion to accurately predict sheet failure, which will allow for the optimization of the stretching operations, and provide the means to evaluate when heat treatment can be avoided. The fracture process of AA2024-T3 stretched sheets is experimentally analyzed, obtaining the FLD at fracture. A selection of classical ductile failure criteria (integral and local criteria) is implemented in ABAQUS, and their capability to predict sheet failure is studied in detail. It is found that the local criteria, in particular Treca's criterion, provide a better description of the failure process than the integral criteria. Finally, the influence of bending strains in the initiation of failure is also discussed.

Dodecahedric Mutually Supported Element Space Structure: Experimental Investigation

Circuits of mutually supported elements (MSEs) can produce novel 3-dimensional spatial structures. In the creation of a circuit, the basic concept is that the primary members rely on each other for support. These novel structural arrangements may give rise to complexity in the configuration geometry and structural behaviour due to the creation of an eccentricity between elements. An experimental programme was designed to aid understanding of the primary behaviour of structures composed of MSEs. This investigation concentrated on the structural performance, under applied static loading, of a dodecahedric MSE space structure. The main objectives of the experimental investigation were to confirm behaviour as being linear elastic within a predermined appied load range, to understand the distribution of stress and the displacements of the structural elements, later to be compared with that predicted by numerical modelling. Displacements of closed MSE circuits with different spatial orientations were considered. Differences in the recorded strains were also considered. The experiment highlighted the difficulties associated with monitoring MSE circuits, particularly support stiffness and displacements of circuits with arbitrary 3-dimensional spatial orientations. The recorded strains were complex in nature in as far as they included the effects of axial forces, bi-axial bending, shear and torsion. It was found that the maximum applied load did not cause yield of the material according to the von Mises ductile material failure criterion.

Development of stress-modified fracture strain for ductile failure of API X65 steel

The present paper proposes ductile failure criteria in terms of true fracture strain (the equivalent strain to fracture) as a function of the stress triaxiality (defined by the ratio of the hydrostatic stress to the equivalent stress) for the API X65 steel. To determine the stress-modified fracture strain, smooth and notched tensile bars with four different notch radii are tested, from which true fracture strains are determined as a function of the notch radius. Then detailed elastic–plastic, large strain finite element analyses are performed to estimate variations of stress triaxiality in the tensile bars, which leads to true fracture strains as a function of the stress triaxiality, by combining them with experimental results. Two different failure criteria are proposed, one based on local stress and strain information at the site where failure initiation is likely to take place, and the other based on averaged stress and strain information over the ligament where ductile fracture is expected. As a case study, ligament failures of API X65 pipes with a gouge are predicted and compared with experimental data.