Ductile Failure Criterion Research Articles

A Fully Coupled Thermomechanical Damage Analysis of Hot Closed Die Forging Using Finite Element Modeling

Advanced simulations are needed in the industry nowadays for reliable design of various machine parts. A complex computation is presented here to describe the whole manufacturing process, apart from the machining, of forged spur gear for a reverse transmission from a car gearbox. A coupled thermomechanical analysis was realized through the explicit finite element method, while the stress–strain analysis was conducted in all phases of the production with time- and temperature-dependent constitutive law. The influence of process parameters was assessed, and the magnitudes of forging load were compared for selected dimensions of intermediate product (blank) and its initial temperature (preheating). The numerical simulation was finished with the flash trimming along the circumference, so the temperature-dependent ductile failure criterion proposed by Johnson and Cook was accounted for as well.

Effect of Material Strength on Ductile Failure of Steel in Pressure Vessel Design

Abstract Pressure vessels and their components are commonly designed with the ASME Boiler and Pressure Vessel Codes. One of the requirements when pursuing the design by analysis route is to design these equipment against ductile local failure criterion provided in the codes. However, the ductile local failure criterion in the ASME codes only accounts for the stress triaxiality (T) as a stress state measure. Recent work has shown that ductile failure highly depends on the stress state characterized by both T and the Lode parameter L, which is related to the third deviatoric stress invariant. In this study, the effect of stress state characterized by both T and L is investigated for six different steel grades with different material strength levels. To establish the ductile failure loci for the six steel grades with respect to T and L, experiments were conducted on two different specimen geometries. The L parameter is controlled by the specimen configuration, where the round notched bar specimen corresponds to axisymmetric tensile conditions (L = −1) and the flat notched specimen corresponds to plane strain loading conditions (L = 0), whereas T is controlled by introducing a notch at the center of the specimens. A Lode sensitivity parameter (LS) is defined based on the experimental results and revealed that the steel grades with ultimate strength higher than a certain threshold value (450 MPa) exhibit sensitivity to the Lode parameter. The Lode sensitivity was quantified, and the results showed that the LS increases with increase in the ultimate strength of the steel grade. The results were incorporated to enhance the original ASME local failure criterion by accounting for T, L, and LS to accurately assess ductile failure in high-strength steels. The application of the enhanced failure locus in a design analysis of a pressure vessel made of a high-strength steel grade is demonstrated, which showed that the original ASME criterion, as compared to the enhanced criterion in this study, is not capable of predicting ductile failure and hence rendering a rather nonconservative design. It is concluded that the enhanced local failure criterion is recommended to be used for the design of pressure vessels and their components made of steel grades with an ultimate strength higher than the threshold value.

Analysis of flat-end milling forces considering chip formation process in high-speed cutting of Ti6Al4V titanium alloy

This paper proposes a unified numerical and analytical approach to predict flat-end milling forces considering the chip morphology and cutting force in high-speed cutting of titanium alloy (Ti6Al4V). A two-dimensional finite element (FE) model of the orthogonal cutting process is developed by applying a displacement-based ductile failure criterion. With this FE model, the segmented chip formation is analyzed. The mesh dimension is investigated as an effective factor in the chip segmentation. The numerical results demonstrate that the chip morphology is significantly affected from the mesh dimension while the average cutting force varies slightly with the mesh dimension. The mesh dependency of the chip morphology can be decreased by applying the non-local progressive damage model involving the intrinsic material length. An attempt is also made for modeling and prediction of cutting forces in high-speed flat-end milling. The milling force constants which are generally derived from experimental calibrations are required to predict the milling forces by using the unified mechanics of cutting approach. Here, the numerical FE simulations are carried out to characterize the milling force constants. The milling forces predicted analytically are validated by comparing with those obtained from the experimental study. Finally, the behavior of the milling forces can be effectively analyzed through the proposed approach based on the chip formation process.

Influence of manufacturing geometric defects on the mechanical properties of AlSi10Mg alloy fabricated by selective laser melting

The tensile behavior of bulk AlSi10Mg components, fabricated by selective laser melting (SLM), was investigated by uniaxial tensile testing and image-based finite element simulation. The initial morphological features of the structures were imaged by micro X-ray tomography. Moreover, the reconstructed model and as-designed model were compared to quantify the process-induced defects, which remained unavoidable due to complex manufacturing processes. The un-melted AlSi10Mg powders, sticking to the melting pool after condensation, intensified the deviation of side edges. Futhermore, the unevenly distributed process-induced defects resulted in anisotropic mechanical properties of AlSi10Mg alloy. Two finite element models were developed from X-ray tomography images and CAD model, which were simulated by finite element solver ABAQUS/Standard to discuss the effect of initial morphological features on the mechanical behavior of these samples. The geometric defects have slightly reduced Young's modulus and yield strength, but remarkably increased the equivalent plastic strain of the bulk structures. Furthermore, the ultimate strength and elongation, predicted by the image-based finite element model and the ductile failure criterion, was much lower than the values predicted by the as-designed model due to the influence of geometric defects.

Evaluation of different flow stress laws coupled with a physical based ductile failure criterion for the modelling of the chip formation process of Ti-6Al-4V under broaching conditions

During the machining of Ti-6Al-4V the changing deformation mechanisms produce a complex microstructure of segmented chips, which directly influenced tool-wear and process stability. Numerical simulation could give an insight into the physical phenomena involved in chip segmentation, but its accuracy is directly related to the reliability of the input parameters. In this work, therefore, three different flow stress law were evaluated coupled with a physical based ductile failure criterion, which depends on stress triaxiality and temperature. To this end, the flow stress laws were implemented in the finite element software AdvantEdge by programming user-defined subroutines. The resulting FEM models were compared with orthogonal cutting experimental tests (tubular/linear), analyzing different fundamental outputs (machining forces, temperatures in the workpiece and chip morphology). All the FEM models showed good agreement with the experimental results.

Ductile fracture predictions in small punch testing of cold-rolled aluminium alloy

The ductile fracture has been observed in large as well as small scales. Three chosen Lode and pressure dependent phenomenological ductile fracture criteria with cut-offs were calibrated for aluminium alloy EN AW 2024-T351 using an enhanced hybrid experimental–numerical technique. It consisted of calibrating all the material constants of fracture criteria altogether. This enabled ready determination of the cut-off related constant for one of those criteria. Moreover, a non-quadratic Lode dependent plasticity model was coupled with the ductile failure criteria to form the damage plasticity approach in the numerical analysis. The fracture criteria were calibrated using the standard – large – sized specimens including a non-standard upsetting test. The specimens used for the calibration of failure criteria are usually ten times larger than that of a specimen for the small punch test. The transferability of calibrated parameters was tested and fair predictability was observed for all numerical models when applied to small scales.

Notched specimen under compression for ductile failure criteria

Notched specimen was designed for testing in compression. It was manufactured from the aluminium alloy 2024-T351, which is widely used in the aerospace, aeronautical and automotive industry. The test, among others, was used for the calibration of three uncoupled ductile fracture criteria dependent on the first invariant of stress tensor and third invariant of deviatoric stress tensor. The yielding was described by three plasticity models dependent on the second invariant of deviatoric stress tensor – proposed by von Mises, dependent on the second and third invariants of deviatoric stress tensor, and the most complex yield criterion dependent on the first invariant of stress tensor and second and third invariants of deviatoric stress tensor. All models were implemented into Abaqus commercial finite element code using VUMAT user subroutine. The ductile fracture prediction was carried out by widely used element deletion technique for specimen under compression. In the aftermath, the results were compared to experiments to see the performance of complex plasticity models with uncoupled fracture criteria.

Experimental investigation of reciprocally supported element (RSE) lattice honeycomb domes structural behaviour

The honeycomb configuration of the many Diamatic dome patterns available is particularly convenient for reciprocally supported element (RSE) transformation. This is due to there being only three lattice bar elements intersecting at any apex, irrespective of the number of the bar elements used to form the crown polygon. RSE transformation effort therefore is both reduced and simplified compared to some RSE forms. To inform the understanding of the structural behaviour of honeycomb RSE lattice domes, a study comparing structural modelling predicted behaviour with monitored behaviour in the laboratory was carried out. This investigation focused on the structural behaviour of a RSE lattice honeycomb dome structure under applied static loading. The first part of the study included configuration processing, structural modelling and analysis. The second part involved manufacture, construction and monitored behaviour of the dome in the laboratory. The creation of the selected RSE honeycomb lattice structure together with the structural modelling and experimental outputs are presented and discussed. Predicted displacements and stresses are compared under varying applied loading, boundary support conditions and connection stiffnesses. The locations of the onset of local yielding is considered and discussed. The applied loading did not exceed the tube yield stress according to the von Mises ductile material failure criterion indicating that the dome behaviour observed was elastic.

Modeling Forming Limit in Low Stress Triaxiality and Predicting Stretching Failure in Draw Simulation by an Improved Ductile Failure Criterion

Modeling Forming Limit in Low Stress Triaxiality and Predicting Stretching Failure in Draw Simulation by an Improved Ductile Failure Criterion

Calibration of the Ductile Failure Criterion for Nickel-Based Superalloys taking into Account the Localization of the Strain

Abstract Static tension test allows characterization of material strength properties. This simple test provides input data for numerical calculation of structural components made of the tested alloy. Elastic, plastic and failure behavior of the structural component in question is simulated, using, for example, the FEM package, based on parameters obtained as the result of tensile testing. When using the results of the tensile test for modeling the material failure it is important to estimate correctly plastic strain corresponding to failure. It is common practice to use elongation of the specimen gage part for the calculation of failure strain. On the other side, the most popular ductile failure criterion used by engineers performing numerical simulation of the material’s behavior relies on the equivalent plastic strain as the criterial quantity. Those two parameters can differ significantly. In order to calculate the equivalent plastic strain correctly, we have to remember about strain localization (necking) appearing during tensile tests and take into account the fact that during tensile testing we have three non-zero strain tensor components. Ignoring this fact, and using only elongation as the criterial quantity can lead to enormous simulation error. This error is analyzed in this paper for nickel based superalloy tested at elevated temperatures.

Predicting Sheet Forming Limit of Aluminum Alloys for Cold and Warm Forming by Developing a Ductile Failure Criterion

In this study, the forming limit of aluminum alloy sheet materials is predicted by developing a ductile failure criterion (DFC). In the DFC, the damage growth is defined by Mclintock formula, stretching failure is defined at localized necking (LN) or fracture without LN, while the critical damage is defined by a so-called effect function, which reflects the effect of strain path and initial sheet thickness. In the first part of this study, the DFC is used to predict forming limit curves (FLCs) of six different aluminum sheet materials at room temperature. Then, the DFC is further developed for elevated temperature conditions by introducing an improved Zener–Hollomon parameter (Z′), which is proposed to provide enhanced representation of the strain rate and temperature effect on limit strain. In warm forming condition, the improved DFC is used to predict the FLCs of Al5083-O and failure in a rectangular cup warm draw process on Al5182 + Mn. Comparison shows that all the predictions match quite well with the experimental measurements. Thanks to the proposal of effect function, the DFC needs calibration only in uniaxial tension, and thus, provides a promising potential to predict forming limit with reduced effort.

Structural modelling investigation of reciprocally supported element lattice honeycomb domes

Reciprocally supported element (RSE) lattice honeycomb dome structures have the ability to support considerable loading via their composition of interconnected closed circuits of elements. Distinctively, these dome structures use only three elements in each circuit. To understand the structural behaviour of these RSE lattice domes, a structural modelling investigation was carried out. Global linear elas- tic analysis was considered where the behaviour of the structure under the application of loading on selected elements was monitored. The aim of the modelling was to investigate the influencing factors to monitor for model calibration as well as to compare predicted structural behaviour output with future monitored behaviour in laboratory experiments involving the manufacture and construction of an RSE lattice honeycomb dome structure. The creation of the selected RSE honeycomb lattice structures together with the structural modelling findings are presented and discussed. Predicted displacements and stresses were compared under varying boundary support conditions. The von Mises ductile material failure criterion showing the onset of local yielding is considered.

A ductile failure criterion for predicting sheet metal forming limit

This study proposes a new Ductile Failure Criterion (DFC) to predict forming limits for sheet metal forming. In this criterion, damage growth is defined by a modified McClintock formula, stretching failure is defined at Localized Necking (LN) or Fracture without LN, and the critical damage is defined as a function of strain path and initial sheet thickness. The failure definition removes the uncertainty of Post-Necking (P-N) deformation while the critical damage definition reflects the findings of many micromechanical studies. The observed strain path and sheet thickness effects on the critical damage are represented by an effect function, which can be phenomenologically determined by a set of critical tests. With the help of the determined effect function, the proposed criterion only needs a calibration at uniaxial tension. The proposed criterion is validated by calculating limit strains under linear, bilinear and strongly non-linear strain paths for different sheet materials, which include data from Numisheet 2008 and 2014 Benchmark studies. Comparison shows that the calculations and failure predictions are in good agreement with the experimental observations and comparable with the best results from benchmark participants.

Force prediction in blow-out preventer shearing of drill pipes

Abstract An accurate prediction of blow-out preventer (BOP) drill pipe shearing is of critical importance in the applications of offshore drilling equipment. To simulate the shear process, a ductile failure criterion is clearly needed. In this paper, we employ an extended Mohr-Coulomb (EMC) criterion, which makes validated predictions for shear fracture by including the stress triaxiality T and Lode parameter L. This criterion has six parameters to be calibrated either by experimental tests or by numerical simulations. Here, we present a micromechanics model to calibrate the undetermined parameters via a void coalescence mechanism, and predict the forces for pipe shearing by finite element analyses. The shear force profile for the case where the EMC criterion parameters are micromechanically determined agrees with that for the case where the parameters are experimentally determined. This paper demonstrates the predictive capability of a micromechanics-based ductile fracture model in conjunction with the EMC criteria for BOP drill pipe shearing.

Numerical modeling on compressive behaviors of 3-D braided composites under high temperatures at microstructure level

This paper reports a numerical modeling on the compressive behaviors of 3-D braided carbon/epoxy composites with different braided angles under high temperatures at microstructure level. The coupling effect of temperature and braided angle on the compressive failure mechanisms and damage morphologies have been calculated with finite element method (FEM) and compared with experimental results. In the FEM model, the imperfect interfacial bonding and the fibers with waviness were introduced into the FEM model. The ductile/brittle transition temperature was investigated and the ductile failure criterion was employed in the FEM model at high temperatures. It was found that braided angle affects the compressive failure. The compressive failure changes from ductile to brittle when the braided angle changes from larger to smaller one. The high temperature has almost no influence on the damage mode but it leads to the failure modes more ductile. The thermal stress improves the longitudinal compressive properties. The higher temperature and larger braided angle lead to the ductile behaviors of the 3D braided under longitudinal compression.

A study on the performance of ductile failure models under different range of stress triaxiality states with experimental validation

In this work, experimental tests were carried out, under different loading conditions, in order to assess different ductile failure criteria, namely based on GTN, Johnson-Cook or Lemaitre models and to establish new proposals for improvement. Corresponding characterization for damage parameters is performed by an inverse analysis procedure, using reference experimental tests. Numerical simulations of a cross-shaped component are considered for the damage models, and results show a similar trend related with the experimental fracture evidence.

Constitutive modeling for Ti-6Al-4V alloy machining based on the SHPB tests and simulation

A constitutive model is critical for the prediction accuracy of a metal cutting simulation. The highest strain rate involved in the cutting process can be in the range of 104–106 s–1. Flow stresses at high strain rates are close to that of cutting are difficult to test via experiments. Split Hopkinson compression bar (SHPB) technology is used to study the deformation behavior of Ti-6Al-4V alloy at strain rates of 10–4–104s–1. The Johnson Cook (JC) model was applied to characterize the flow stresses of the SHPB tests at various conditions. The parameters of the JC model are optimized by using a genetic algorithm technology. The JC plastic model and the energy density-based ductile failure criteria are adopted in the proposed SHPB finite element simulation model. The simulated flow stresses and the failure characteristics, such as the cracks along the adiabatic shear bands agree well with the experimental results. Afterwards, the SHPB simulation is used to simulate higher strain rate(approximately 3×104 s–1) conditions by minimizing the size of the specimen. The JC model parameters covering higher strain rate conditions which are close to the deformation condition in cutting were calculated based on the flow stresses obtained by using the SHPB tests (10–4–104 s–1) and simulation (up to 3×104 s–1). The cutting simulation using the constitutive parameters is validated by the measured forces and chip morphology. The constitutive model and parameters for high strain rate conditions that are identical to those of cutting were obtained based on the SHPB tests and simulation.

Burst Ductility of Zirconium Clads: The Defining Role of Residual Stress

Closed end burst tests, using room temperature water as pressurizing medium, were performed on a number of industrially produced zirconium (Zr) clads. A total of 31 samples were selected based on observed differences in burst ductility. The latter was represented as total circumferential elongation or TCE. The selected samples, with a range of TCE values (5 to 35 pct), did not show any correlation with mechanical properties along axial direction, microstructural parameters, crystallographic textures, and outer tube-surface normal (σ 11) and shear (τ 13) components of the residual stress matrix. TCEs, however, had a clear correlation with hydrostatic residual stress (P h), as estimated from tri-axial stress analysis on the outer tube surface. Estimated P h also scaled with measured normal stress (σ 33) at the tube cross section. An elastic–plastic finite element model with ductile damage failure criterion was developed to understand the burst mechanism of zirconium clads. Experimentally measured P h gradients were imposed on a solid element continuum finite element (FE) simulation to mimic the residual stresses present prior to pressurization. Trends in experimental TCEs were also brought out with computationally efficient shell element-based FE simulations imposing the outer tube-surface P h values. Suitable components of the residual stress matrix thus determined the burst performance of the Zr clads.

Dynamic rupture and crushing of an extruded tube using artificial neural network (ANN) approximation method

A numerical study of the crushing of thin-walled circular aluminum tubes has been carried out to investigate the crashworthiness behaviors under axial impact loading. These kinds of tubes are usually used in automobile and train structures to absorb the impact energy. Previous researches show that thin-walled circular tube has the highest energy absorption under axial impact amongst different structures. In this work, the crushing between two rigid flat plates and the tube rupture by 4 and 6 blades cutting tools is modeled with the help of ductile failure criterion using the numerical method. The tube material is aluminum EN AW-7108 T6 and its length and diameter are 300 mm and 50 mm, respectively. Using the artificial neural network (ANN), the most important surfaces of energy absorption parameters, including the maximum displacement of the striker, the maximum axial force, the specific energy absorption and the crushing force efficiency in terms of impact velocity and tube thickness are obtained and compared to each other. The analyses show that the tube rupture by the 6 blades cutting tool has more energy absorption in comparison with others. Furthermore, the results demonstrate that tube cutting with the help of multi-blades cutting tools is more stable, controllable and predictable than tube folding.

A Comparison between cutting and folding modes of an extruded aluminum alloy tube during impact using ductile failure criterion

Thin-walled structures like crash boxes may be used as energy absorbers in the automotive chassis. There have been lots of investigations about the behavior of these parts during frontal crashes. Previous researches show that thin-walled circular tube has the highest energy absorption among different structures. In this study, cutting and folding modes of extruded aluminum tubes (EN-7018 T6) with 50 mm diameter, lengths of 300 and 400 mm and thicknesses of 2, 2.5 and 3 mm are compared when axial impacts with velocities of 6, 8 and 10 m.s-1 are applied to them. Cutting tools of 4 and 6 blades are used to provide the cutting mode. Effective parameters of energy absorbers including crush force efficiency, specific energy absorption and maximum axial load are modeled numerically with the help of Hooputra’s ductile damage criterion and are compared to each other for three cases of aluminum tube folding between two rigid plates and tube rupture by using 4 and 6 blades cutting tools. The analyses show that the tube rupture by the 6 blades cutting tool is better than the other two in the case of energy absorption. Furthermore, the results demonstrate that tube cutting with the help of multi-blades cutting tools is more stable, controllable and predictable than tube folding.