Latham Fracture Criterion Research Articles

Analysis of extrusion characterization of Nd-Fe-B permanent magnet ring based on Normalized Cockcroft & Latham fracture criterion

The hot deformation behavior of hot-pressed Nd-Fe-B material was investigated using a Gleeble-3500 thermal simulation machine, with deformation of 50 %, temperatures ranging from 700 to 850 °C, and strain rates ranging from 0.01 to 1 s−1. A hyperbolic sine model was employed to establish a constitutive equation suitable for this material. In addition, the chosen fracture criterion and damage threshold in the simulations were validated against the experimental results. Then, a three-dimensional thermo-mechanical coupled model was developed to simulate the damage evolution of the material during the extrusion process. The effects of different extrusion processes and positions of the back pressure tool on the magnetic performance and forming quality of the material were investigated. The simulation results indicate that both the combined extrusion process and the back pressure tool located at the half of the workpiece will contribute to improve the uniformity of the magnetic properties, and effectively ensuring the regularity of the forming process at the top of the magnetic ring and suppressing the occurrence of cracks. The results of this paper will help to a better understanding of the deformation mechanism of Nd-Fe-B permanent magnet and provide a valuable theoretical guidance for the preparation of high-performance Nd-Fe-B magnetic rings.

Experimental and numerical study on the tensile ductility of an aluminium alloy with heat-affected zones

In the case of aluminium structures, welding may introduce weak zones, so-called heat-affected zones (HAZ), close to the weld. Such zones should be accounted for when predicting the overall behaviour of structures since the deformation tends to localise within such weak zones leading to the initiation of failure. Whereas the effect of welding on mechanical properties such as yield stress and work hardening is known, the ductility of a HAZ and how to model it in numerical simulations remain uncertain. To address this challenge, this article presents a combined experimental and numerical study on ductile fracture modelling of an aluminium alloy AA6063-T6 exposed to complex heat treatments. The first part includes preparation of specimens and uniaxial tension testing. A Gleeble machine is used to generate well-defined heat treatments involving high peak temperatures and heating rates. Subsequently, uniaxial tension tests at low and high strain rates are conducted. The results show the effect of the complex heat treatments on strength, strain-rate sensitivity, and fracture. The numerical part of this study concerns two widely used damage models, namely the Cockcroft–Latham fracture criterion and the Gurson–Tvergaard model. Calibration of material models and a parameter study are carried out based on analyses of the tension tests. To this end, a case study is conducted elaborating on the importance of the damage parameters within an idealised heat-affected zone and plane-strain tension. The main objective of this study is to obtain a more general understanding of ductile fracture modelling of aluminium alloys exposed to complex heat treatments representative of welding.

Assessment of the Susceptibility to Material Fracture in the Cross-Wedge Rolling Process with Concave Tools.

The internal cracking of forgings during the cross-wedge rolling (CWR) process is a serious limitation that prevents the correct implementation of this process. The phenomenon of material cracking in the CWR process reduces the technological and application possibilities of this highly efficient process, which can produce forgings with high geometric accuracy. This article presents the results of rolling forgings at different temperatures. An analysis of the results showed that the size of the resulting material fracture in the CWR process is related to the size of the ovalisation of the cross-section of the forging formed during rolling. On the basis of the observations made, it was proposed to realise the cross-wedge rolling process with concave tools. The use of tools with a concave geometry is intended to reduce the excessive flow of material in the rolling direction, which restrains the formation of the ovalisation of the cross-section of the forging. Numerical simulations were carried out comparing the rolling with flat tools and concave tools with different radii of the curvature. The results show that the use of concave tools reduces the ovality of the cross-section of the forging during rolling and reduces the value of the normalised Cockcroft–Latham (CL) fracture criterion.

Fracture prediction of powder metallurgical Fe–Cu–C steel at elevated temperatures via finite element-aided hot tensile tests

Surface cracking induced by damage accumulation is a common quality problem during the hot processing of powder metallurgical (P/M) products. This study aims to clarify the damage and fracture of P/M Fe–Cu–C steel at elevated temperatures to propose its fracture criterion by combining hot tensile tests with finite element (FE) calculations. The results reveal that the FE-aided test accurately corrected the true stress and strain of the P/M steel during the Gleeble hot tensile testing. In addition, the flow behaviors and cracking tendency of the P/M steel strongly depended on the hot deformation parameters. The optimum hot processing window of P/M steel was proposed after determining the quantitative relationships between the damage and hot deformation parameters. Finally, a novel elevated temperature fracture strain model of the P/M steel was proposed based on the Zener–Hollomon parameter to construct its Cockroft and Latham fracture criterion coupling hot processing parameters. The constructed fracture criterion was further normalized and modified, and achieved an acceptable fracture predictive capability with a relative error of less than 5%, which was validated by powder forging experiments. This work provides essential information and a useful model for the fracture prediction of P/M Fe–Cu–C steel at elevated temperatures, helping to manage the surface cracking problems of P/M steel during hot processing.

Prediction of the Fracture of Metal in the Process of Screw Rolling in a Two-Roll Mill

We study the process of two-roll screw rolling of billets made of stainless steel in order to estimate the influence of the feed angle on the plasticity of the metal of rolling billets. Pilot rollings were simulated by using the DEFORM software. In the computer simulation, the normalized Cockroft–Latham fracture criterion is used to predict the so-called Mannesmann effect (axial fracture of a billet). The comparison of the results of pilot rollings with the data of computer simulations showed that this fracture criterion is an efficient tool for the investigation of screw rolling. A procedure is proposed for the prediction of fracture of the metal subjected to screw rolling.

Simulation Analysis and Research on Extrusion Process of Super Pipe Nozzle for Nuclear Power Station

In order to study nozzle forming process of super pipe for nuclear power plant, the numerical analog simulation has been carried out on hot extrusion nozzle forming process of super pipe forging using France Forge simulation software. The results show that the billet temperature drop is the fastest in contact with the mold, and the high temperature zone exist in the heart of the billet. During the forming process, the temperature of the billet is above 750℃, and is in the range of reasonable hot forming temperature of the hot extrusion nozzle. The axial stress extreme value happen from the intermediate stage of forming period, the maximum radial stress is 37.2MPa, produced in the nozzle connection transition zone near the inner surface; the radial stress extreme value happen from the latter stage of forming period, the maximum radial stress is 98.5MPa, appear in the inner surface near the nozzle tip edge, meanwhile the part strain is 1.61. According to Cockcroft & Latham fracture criterion, the above two parts have a tendency to crack. The actual product and inspection shows that there are cracks in the above positions.

A Theoretical and Experimental Analysis of Rotary Compression of Hollow Forgings Formed Over a Mandrel

The paper presents selected results of studies of the process of forming hollow stepped shaft forgings by rotary compression with rotary tools. The aim of the study was to determine whether rotary compression could be performed using an additional tool – a mandrel, which, when positioned in the cavity of the workpiece, could be used to shape the surface of the cavity. A theoretical analysis was based on finite element modeling using Simufact Forming software. During the simulations, distributions of deformation intensity, temperature, and the Cockroft–Latham fracture criterion were determined. Predictions were also made regarding phenomena such as slippage and deformation of forging pieces and material cracking, as potential impediments to the investigated process. Additionally, force parameters were determined during the forming of forgings. Numerical results were verified experimentally. Rotary compression tests for hollow forgings were carried out in a special forging machine designed by the present authors. The results were validated on the basis of the geometric parameters of formed forgings and the force parameters of the process. The results confirm that hollow stepped shaft forgings can be formed in the process of rotary compression using a mandrel. Forgings formed over a mandrel are characterized by greater precision and quality compared to freely formed blanks (without a mandrel).

The influence of temperature and preheating time in extrudate quality of solid-state recycled aluminum

Recovering waste metal without the need for remelting in solid-state recycling of metal chips can create green production. The overall process of solid-state recycling should be run at the lowest possible cost to remain competitive. High temperature and prolonged preheating time for billet’s homogenization in hot extrusion to consolidate the chips conflicts with the aim of minimizing energy usage. Therefore, optimizing the effect of preheating temperature and time prior to hot extrusion is important. This study investigates the effects of preheating temperature and preheating time on the extrudates’ quality. Milling chips of AA6061 were cold compacted and hot extruded through a flat-face die using preheating temperatures of 400, 500, and 550 °C for 1–6 h of preheating time. The mechanical and physical properties and microstructure of the extruded profiles were compared. The results revealed that higher acceptable strength and ductility were obtained at 500 °C with 2 h of preheating time. On top of that, temperature increase was the main criterion that results in the highest tensile strength; nevertheless, it was subjected to trade-off in ductility. The profile extruded at 500 and 550 °C had gained a close tensile strength. The study includes the prediction of the chip’s welding quality through the damage evolution on the extrudate’s structure. It was implemented with the help of DEFORMTM 3D finite element method (FEM) software, and the normalized Cockcroft and Latham (C & L) fracture criterion was chosen. The results of the simulations were compared and validated by the experimental results.

Fracture behaviour of aluminium alloy sheet under roller hemming process

Roller hemming is a tendency for hemming flexibility. While for aluminium alloy sheets, fracture happens easily. According to comparison of flat surface straight line flanging and limit strain under necking theory, the failure mode of aluminium alloy sheet under roller hemming is ductile fracture, with the aid of analysis of cross-section of the fracture location. Then ductile fracture criterion critical parameter is determined by simulation and experiments of uniaxial tensile test. Consequently, forming limit strain curve at fracture could be calculated from the assumptions including stress–strain curve, plane-stress condition, linear strain path, Deformation Theory of Constitutive Equation, Cockcroft–Latham fracture criterion, etc. Finally, the feasibility of ductile fracture criterion and bending effect on roller hemming process are analysed.

An efficient method for the identification of the modified Cockroft–Latham fracture criterion at elevated temperature

The paper presents the theoretical part of a method for the identification of the modified Cockroft–Latham ductile fracture criterion at elevated temperature. Quite a general viscoplastic model is adopted to describe material behavior. The original criterion is path-dependent and involves stresses. Therefore, the identification of constitutive parameters of this criterion, as well as many other ductile fracture criteria, is rather a difficult task that usually includes experimental research and numerical simulation. The latter is impossible without a precisely specified material model and boundary conditions. It is shown in the present paper that for a wide class of material models usually used to describe the behavior of materials at elevated temperatures, the criterion is significantly simplified when the site of fracture initiation is located on traction-free surfaces. In particular, this reduced criterion solely depends on two in-surface logarithmic strains. Since there are well-established experimental procedures to measure surface strains, the result obtained can be considered as a theoretical basis for the efficient method for the identification of the modified Cockroft–Latham ductile fracture criterion at elevated temperature.

Development of a Competitive Technology to Make Wire for Metal Cord

A method is proposed for developing an efficient technology to make high-quality wire for the production of metal cord. Experimental data and results obtained from modeling in DEFORM software are used to determine the limiting value of the Cockcroft–Latham fracture criterion. That value is then used to calculate the limiting drawing ratio for wire rod when the drawing operation is performed without an intermediate heat treatment. The new technology developed for making the wire has made the metal cord a more competitive product.

Study on the Effect of Tool Geometrical Parameters on Cutting Forces Based on Finite Element Method

Based on finite element software DEFORM-3D, a three-dimensional oblique cutting model for aerospace aluminum alloy was built. The material’s flow stress behavior was described with Johnson-Cook constitutive equation. The separation of the chips with the workpiece was realized by the combination of adaptive remeshing technique and separation criterion. The material’s failure was defined by adopting Cockcroft & Latham fracture criterion. The tool-chip friction model was the combination of a Coulomb friction model and shear (sticking) friction model. To validate the finite element model, cutting tests were conducted. The effects of tool geometrical parameters such as flank wear, cutting edge inclination and corner radius on cutting forces were analyzed by three-dimensional oblique finite element model.

Deformation and fracture of impulsively loaded sandwich panels

Light metal sandwich panel structures with cellular cores have attracted interest for multifunctional applications which exploit their high bend strength and impact energy absorption. This concept has been explored here using a model 6061-T6 aluminum alloy system fabricated by friction stir weld joining extruded sandwich panels with a triangular corrugated core. Micro-hardness and miniature tensile coupon testing revealed that friction stir welding reduced the strength and ductility in the welds and a narrow heat affected zone on either side of the weld by approximately 30%. Square, edge clamped sandwich panels and solid plates of equal mass per unit area were subjected to localized impulsive loading by the impact of explosively accelerated, water saturated, sand shells. The hydrodynamic load and impulse applied by the sand were gradually increased by reducing the stand-off distance between the test charge and panel surfaces. The sandwich panels suffered global bending and stretching, and localized core crushing. As the pressure applied by the sand increased, face sheet fracture by a combination of tensile stretching and shear-off occurred first at the two clamped edges of the panels that were parallel with the corrugation and weld direction. The plane of these fractures always lay within the heat affected zone of the longitudinal welds. For the most intensively loaded panels additional cracks occurred at the other clamped boundaries and in the center of the panel. To investigate the dynamic deformation and fracture processes, a particle-based method has been used to simulate the impulsive loading of the panels. This has been combined with a finite element analysis utilizing a modified Johnson–Cook constitutive relation and a Cockcroft–Latham fracture criterion that accounted for local variation in material properties. The fully coupled simulation approach enabled the relationships between the soil-explosive test charge design, panel geometry, spatially varying material properties and the panel's deformation and dynamic failure responses to be explored. This comprehensive study reveals the existence of a strong instability in the loading that results from changes in sand particle reflection during dynamic evolution of the panel's surface topology. Significant fluid–structure interaction effects are also discovered at the sample sides and corners due to changes of the sand reflection angle by the edge clamping system.

The influence of the drawing parameters and temperature rise on the prediction of chevron crack formation in wire drawing

The objective of the present work is to predict the formation of chevron crack in copper wire drawing process. The first part of this paper is to determine the chevron crack formation initiated by a central burst inside the wire material using experimental tests. These results are compared with results from a series of numerical simulations using the Cockcroft–Latham fracture criterion. The second part of this work concerns the determination of a curve that divides the chevron and safe zones for a better wire drawing process. The conditions of central burst defects formation along the wire axis depend on drawing parameters and friction coefficient between the die and the wire. The friction coefficient is defined as a linear function of temperature rise which is measured close to the wire-die interface. The obtained results show that the friction coefficient depending on temperature rise during wire drawing has an impact on the damage of copper wire.

3D Numerical Simulation and Optimization of Processing Parameters in Fine Blanking of Back Plate of Brake

Due to the limitation of 2D simulation in fine blanking, finite element software DEFORM-3D was used to simulate the 3D model of Back Plate. In this article the Normalized Cockroft&Latham fracture criterion was chosen to simulate the blanking process. The distribution and developing trend of the hydrostatic stress, equivalent stress in the fine blanking process are predicted. When the die radii are between 0.4mm and 0.6mm, burnished surface improves. It shows that the ideal blanking clearance value is 0.6% of the material thickness. The results indicate that FE numerical simulation could effectively optimize fine blanking process and offer basis for quality improvement.

Chip Formation and Cutting Performance Investigation on Titanium Alloy Machining

First, a 2D orthogonal cutting model for titanium alloy is constructed by finite element method in this study. The cutting tool is incrementally advanced forward from an incipient stage of tool-workpiece engagement to a steady state of chip formation. Cockroft and Latham fracture criterion [1] is adopted as a chip separation criterion. By changing the settings of cutting variables such as cutting speed, depth of cut and tool rake angle to investigate the chip formation process and the variation of cutting performance during titanium cutting simulation. The changes of chip type, cutting force, effective stress/strain and cutting temperature with different cutting condition combinations are thus analyzed. The result demonstrates that the serrated chip type is obviously produced when cutting titanium alloy. Next, water-based and oil-based cutting fluids are employed in conjunction with proper cutting parameter arrangements to perform up-milling experiments. By measuring the cutting force, surface roughness and tool wear to investigate the effect of these combinations of milling variables on the variation of cutting performance for Ti-6Al-4V. The chip shape and cutting force obtained from the experiment are compared with those calculated from simulation. It is shown that there is a good agreement between simulation and experimental results.

Three-dimensional finite element analysis of multi-stage hot forming of railway wheels

Three-dimensional finite element analyses has been carried out using DEFORM 3D software on multi-stage hot forming of railway wheels involving the processes of upsetting, forging, and punching of wheels. Thermal analysis related to heating the blank in furnace and all intermediate heat transfer stages between deforming operations have been conducted. Rigid viscoplastic finite element method has been utilized for coupled thermo-mechanical analysis of the processes. Modeling of punching the wheel bore has been carried out using Cockcroft and Latham fracture criterion. Evolution of thermo-mechanical parameters at selected points within the workpiece has been studied in detail. The method of simulating the effects of various process parameters has been explained using relevant mathematical relations. This study shows that design, optimization, and analysis of process perturbations for multi-stage railway wheel manufacturing process can be done efficiently in three-dimensional finite element simulations instead of conventional time and cost intensive trials. It might be necessary to use the results of finite element analysis in shop-floor to enhance productivity and reduce wheel rejection.

Numerical modelling of magnesium die-castings using stochastic fracture parameters

Quasi-static material tests using specimens cut from a generic cast component are performed to study the behaviour of the high-pressure die-cast magnesium alloy AM60 under different stress states. The experimental data set is applied to establish a validated probabilistic methodology for finite element modelling of thin-walled die-castings subjected to quasi-static loading. The test specimens are modelled in the explicit finite element (FE) code LS-DYNA using shell elements. The cast magnesium alloy AM60 is modelled using an elasto-plastic constitutive model including a high-exponent, isotropic yield criterion, the associated flow law and isotropic hardening. To simulate fracture, the Cockcroft–Latham fracture criterion is adopted, and the fracture parameter is chosen to follow a modified weakest-link Weibull distribution. Comparison between the experimental and predicted behaviour of the cast magnesium specimens gives very promising results.

Perforation resistance of five different high-strength steel plates subjected to small-arms projectiles

Thin plates of high-strength steel are frequently being used both in civil and military ballistic protection systems. The choice of alloy is then a function of application, ballistic performance, weight and price. In this study the perforation resistance of five different high-strength steels has been determined and compared against each other. The considered alloys are Weldox 500E, Weldox 700E, Hardox 400, Domex Protect 500 and Armox 560T. The yield stress for Armox 560T is about three times the yield stress for Weldox 500E, while the opposite yields for the ductility. To certify the perforation resistance of the various targets, two different ballistic protection classes according to the European norm EN1063 have been considered. These are BR6 (7.62 mm Ball ammunition) and BR7 (7.62 mm AP ammunition), where the impact velocity of the bullet is about 830 m/s in both. Perforation tests have been carried out using adjusted ammunition to determine the ballistic limit of the various steels. In the tests, a target thickness of 6 mm and 6 + 6 = 12 mm was used for protection class BR6 and BR7, respectively. A material test programme was conducted for all steels to calibrate a modified Johnson–Cook constitutive relation and the Cockcroft–Latham fracture criterion, while material data for the bullets mainly were taken from the literature. Finally, results from 2D non-linear FE simulations with detailed models of the bullets are presented and the different findings are compared against each other. As will be shown, good agreement between the FE simulations and experimental data for the AP bullets is in general obtained, while it was difficult to get reliable FE results using the Lagrangian formulation of LS-DYNA for the soft core Ball bullet.

Structural behaviour of Al–Si die-castings: Experiments and numerical simulations

Abstract Axial crushing and three-point bending tests have been performed in order to establish an experimental database of the behaviour of generic high-pressure die-cast (HPDC) Al–Si alloys. The experimental data are used to obtain a validated methodology for finite element modelling of thin-walled cast components subjected to quasi-static loading. The HPDC structural components are modelled in the non-linear explicit FE-code LS-DYNA using shell elements. The behaviour of the cast aluminium alloys are described using the classical J 2 flow theory and the Cockcroft–Latham fracture criterion, which is coupled with an element erosion algorithm available in LS-DYNA. The comparison of the experimental and predicted behaviours of HPDC components gives promising results. The use of the fracture criterion of Cockcroft and Latham seems to be an effective approach to predict failure in HPDC components. A novel modelling approach is outlined accounting for different material properties through the thickness, thus incorporating the effects of a fine-grained surface layer and a central region that possesses lower ductility.