Numerical analysis of effect of material and processing parameters on thickness distribution during superplastic die bulging of cavity sensitive materials

Abstract

The superplastic bulging of circular sheets clamped against axisymmetrical cylindrical dies has been analysed numerically by means of a rigid–viscoplastic finite element method, in which four node quadrilateral isoparametric elements are used with a Newton–Raphson non­linear solution scheme. Both effects of normal anisotropy and strain hardening in the material are considered and a modified Coulomb friction law is adopted. At the same time, the yield criterion suited for the superplastic forming process and the cavity damage evolution model deduced from continuum damage mechanics are applied to a finite element formulation. The influences of material parameters (the strain rate sensitivity exponent m, the strain hardening exponent n, the coefficient of normal anisotropy R) and processing parameters (pressure cycle, lubrication condition, die geometry) on the inhomogeneity of the thickness distribution are studied and discussed. A selection of the simulated results is compared with the experimental results, with good agreement.     

Ermittlung von Umformgrenzen beim Freiformschmieden

Determination of forming limits during open die forging The fundamentals of determining the forming limits during open die forging have been investigated in the research project “Vermeidung von Oberflächenfehlern beim Freiformschmieden” (“Prevention of surface defects during open die forging processes”) which was supported by the AiF (“Arbeitsgemeinschaft industrieller Forschungsvereinigungen”). The industrially produced material was analysed in the form of cast ingots of two high‐alloyed steels (1.2367 and 1.6957) by compression, tension and torsion tests. The tests showed that the sampling point has a small influence on the materials’ plasticity for the present dimensions of the ingots. Furthermore transformation and precipitation behaviour of the both steels have been determined and additional metallographic investigations have been made to find out reasons of variation of measurements for low forming temperatures. Forming limit diagrams are generated to predict the forming limits of open die forging processes. For this purpose, compression tests and numerical simulations of the compression tests and forging processes were made for crack‐critical temperatures. The points in time of crack initiation of the samples during the compression tests were determined by the acoustic emission analysis and show a high variation of measurements. Thus the forming limit diagrams also have high scatter, an unique forming limit cannot be determined. Instead of that a maximum allowed height‐reduction was determined and checked in open die forging tests in the laboratory under industrial conditions. The results show that the determined limits are very safe because no cracks were generated during the forging of both materials.     

差速器行星齿轮闭塞锻造成形工艺优化

运用DEFORM-3D软件对差速器行星齿轮的闭塞锻造成形过程进行有限元模拟，将其过程可视化，对成形中可能产生的缺陷进行预测，以降低工艺试验成本；通过分析模拟结果，为模具的选材、结构的优化提供依据。     

An experimental and numerical study of the effects of length scale and strain state on the necking and fracture behaviours in sheet metals

Within sheet metal forming, crashworthiness analysis in the automotive industry and ship research on collision and grounding, modelling of the material failure/fracture, including the behaviour at large plastic deformations, is critical for accurate failure predictions. In order to validate existing failure models used in finite element (FE) simulations in terms of dependence on length scale and strain state, tests recorded with the optical strain measuring system ARAMIS have been conducted. With this system, the stress–strain behaviour of uniaxial tensile tests was examined locally, and from this information true stress–strain relations were calculated on different length scales across the necking region. Forming limit tests were conducted to study the multiaxial failure behaviour of the material in terms of necking and fracture. The failure criteria that were verified against the tests were chosen among those available in the FE software Abaqus and the Bressan–Williams–Hill (BWH) criterion proposed by Alsos et al, 2008. The experimental and numerical results from the tensile tests confirmed that Barba's relation is valid for handling stress–strain dependence on the length scale used for strain evaluation after necking. Also, the evolution of damage in the FE simulations was related to the processes ultimately leading to initiation and propagation of a macroscopic crack in the final phase of the tensile tests. Furthermore, numerical simulations using the BWH criterion for prediction of instability at the necking point showed good agreement with the forming limit test results. The effect of pre-straining in the forming limit tests and the FE simulations of them is discussed.     

Effect of material plasticity on fatigue crack propagation under complex stress state

The maximum energy release rate criterion, i.e., G _max criterion, is commonly used for crack propagation analysis. However, this fracture criterion is based on the elastic macroscopic strength of materials. In the present investigation, a modification has been made to G _max criterion to implement the consideration of the plastic strain energy. This criterion is extended to study the fatigue crack growth characteristics of mixed mode cracks in steel pipes. To predict crack propagation due to fatigue loads, a new elasto-plastic energy model is presented. This new model includes the effects of material properties like strain hardening exponent n, yield strength σ_y and fracture toughness and stress intensity factor ranges. The results obtained are compared with those obtained using the commonly employed crack growth law and the experimental data.     

The analysis of lock forming mechanism in the clinching joint

In this study, the effect of the process parameters of the clinching process on the joinability of advanced high-strength steel was investigated using finite element analysis (FEA). The effect of die geometrical parameters on the achieved joint lock size and maximum forming force has been determined. It has been determined that the die groove width is the most important parameter affecting the material flow effect and energy consumption of the joining process. From the result, the die radius, die depth, and die groove shape were mainly affected by the joinability of advanced high-strength steel H320LA.     

CRACK EXTENSION UNDER MIXED-MODE LOADING IN AN ANISOTROPIC MODE–ASYMMETRIC MATERIAL IN RESPECT OF RESISTANCE TO FRACTURE

Abstract— Recently, a crack path fracture criterion was proposed by Kfouri and Brown, based on maximum energy release rates at the tip of short kinks emanating from an existing crack when the main crack is subjected to mixed-mode loading. Assuming a ‘mode asymmetry’ in respect of the fracture resistances of the material, K_Ir, and K_IIr, for pure mode I and pure mode II, respectively, i.e., K_IIr, differing from K_Ir, generally, the modified criterion proposed that the resistance to fracture is a function of the ratio q (=k₂/k₁) of the mode II to the mode I stress intensity factors at the tip of the kink. The aim of the present paper is to extend the modified criterion by presenting it in a form that takes into account material fracture resistance anisotropy in addition to the fracture resistance mode asymmetry previously described. Note however that the material's elastic properties are still assumed to be isotropic. A short FORTRAN computer program has been written to predict the kink angle under mixed-mode loading for cracks in materials with mode asymmetry and material anisotropy with respect to their fracture resistance properties, and the inclination angle, θ, defining the direction of the main crack in the material. The values of four parameters, r₀, r₉₀, s and θ, described in the text, characterising the material fracture resistance asymmetrical and anisotropic properties and the orientation of the main crack, are prompted by the program, which provides, almost instantaneously, the kink angles under various loading modes and much additional relevant information. The effects of the variation of these parameters, treated singly or in combination, and the discontinuous “catastrophic” character of many of the responses at certain “transition” values of the parameters, are illustrated further. In the discussion it is recognised that the translation of the results of the analysis of a highly idealised situation to actual practical problems on real materials encountered in practice, is not straightforward but, notwithstanding, since material fracture resistance anisotropy and fracture resistance mode asymmetry may well be present in the real world, the possible influence of these factors perhaps needs to be taken into account in studies on crack paths.     

Some studies on wrinkling limit of commercially pure aluminium sheet metals of different grades when drawn through Conical and Tractrix dies

This paper deals with the wrinkling limit diagrams of annealed three different grades of commercially pure sheets namely ISS 19000, ISS 19600 and ISS 19660 having thickness of 2.00 mm when deep drawing into cylindrical cups through Conical and Tractrix dies using a flat bottomed punch. It is well established that, the use of either a Conical die or a Tractrix die can enhance the limiting draw ratio compared with that obtainable in a conventional drawing operation. When a Conical or a Tractrix die is employed the need for a hold down or clamping ring is eliminated. However, this enhances the propensity of the blank to fail by wrinkling or buckling, particularly in the early stages of a drawing process in which thin sheet blanks are used. It is proved by these researchers and others that the onset of wrinkling takes place when the ratio of strain increments (dε _r /dε _θ ) or the ratio of strain (ε _r /ε _θ ) reaches a critical value during the drawing process. These values which could be determined experimentally over which the wrinkling takes place has been shown in the form of wrinkling limit diagrams for the above three different grades. An attempt is also made to develop the wrinkling theory that predicts the wrinkling based on results obtained in the form of wrinkling limit diagrams established for the above grades.     

连续变截面直接挤压成形技术研究

实现晶粒细化的传统塑性加工工艺所需工序多且要求较高,为了解决这些问题,本文提出了一种能够实现金属材料制备及成形一体化的挤压成形新工艺——连续变截面直接挤压成形技术.对不同工艺条件的连续变截面挤压成形过程的数值模拟研究表明:当模角由90°增大至140°时,塑性区范围明显扩大,金属流动均匀性随之提高;模口处轴向拉应力数值减小了20%,降低了表面产生开裂的可能性;模角为90°时变截面型腔处存在死区缺陷,且流线折叠倾向较严重,模角为140°时成形过程中坯料与型腔间易出现空隙.分析认为,本文条件下模角为120°的情况比较理想.     

Bivariate Dispersion Control Charts for Monitoring Non‐Normal Processes

Multivariate control charts are well known to be more sensitive to the occurrence of variation in processes with two or more correlated quality variables than univariate charts. The use of separate univariate control charts to monitor multivariate process can be misleading as it ignores the correlation between the quality characteristics. The application of multivariate control charts allows for the simultaneous monitoring of the quality characteristics by forming a single chart. The charts operate on the assumption that process observations are normally distributed, but in practice this is not always the case. In this study, we examine and present multivariate dispersion control charts for detecting shifts in the covariance matrix of normal and non‐normal bivariate processes. These control charts, referred to as SMAX, QMAX, MDMAX and MADMAX, rely on dispersion estimates, such as the sample standard deviation (S), interquartile range (Q), average absolute deviation from median (MD) and median absolute deviation (MAD), respectively. We compare the performances of these charts to the existing multivariate generalized variance |S| and RMAX charts for bivariate processes using normal and non‐normal parent distributions. The average run length (ARL) measure is used for the evaluation and comparison of the charts. A real life and simulated datasets are used to demonstrate the application of the charts. Copyright © 2016 John Wiley & Sons, Ltd.     

Experimental investigation on constitutive behaviour of superconducting powder BSCCO

As a superconducting material, Bi 2233/Ag tape needs high-critical transport current density J _c, which is influenced by the uniform deformation and density of BSCCO powder in filaments during the forming process. The aim of this paper is to investigate the constitutive behaviour of BSCCO powder. The modified Drucker–Prager/Cap model is introduced to describe the constitutive behaviour of BSCCO powder. A series of cyclic loading experiments for BSCCO powder in a cylinder die were carried out. Based on the experiments, the relationships between the radial stress and the axial stress were obtained, and the parameters in the constitutive model were calculated. By pushing the compact powder from the die, the coefficient of friction between the BSCCO powder and the cylinder die was determined. Finally, the modified Drucker–Prager/Cap model is proposed and used to simulate the confined compression test of BSCCO powder.     

陶瓷成型技术及应用

由于对陶瓷材料的性能要求的提高,传统的成型方法制备的陶瓷已经不能完全满足现代工业的需求,随着学科间交流的广泛,各种新的陶瓷成型工艺不断涌现。本文以制品形状为分类标准,综述了国内外目前研究活跃的多种干法成型、湿法成型方法,并讨论了今后陶瓷成型工艺的发展趋势。     

Predicting whether a material is ductile or brittle

In this paper we discuss the various models that have been used to predict whether a material will tend to be ductile or brittle. The most widely used is the Pugh ratio, $G/K$, but we also examine the Cauchy pressure as defined by Pettifor, a combined criterion proposed by Niu, the Rice and Thomson model, the Rice model, and the Zhou-Carlsson-Thomson model. We argue that no simple model that works on the basis of simple relations of bulk polycrystalline properties can represent the failure mode of different materials, particularly where geometric effects occur, such as small sample sizes. Instead the processes of flow and fracture must be considered in detail for each material structure, in particular the effects of crystal structure on these processes.     

Extended temperature–entropy (T–s) diagrams for aqueous lithium bromide absorption refrigeration cycles

Temperature–entropy (T–s) diagrams have the unique capability of being able to quantify processes in terms of both the first and second laws of thermodynamics. Although use of generalised T–s diagrams has been made to indicate or represent generalised absorption cycles, with the exception for NH₃/water systems, these diagrams have not been specifically tailored to scale to quantify LiBr/water systems. The main barrier for this is that the diagram needs to represent the necessary properties of both the refrigerant (water) and of the solution (LiBr/water). This paper describes the use of the T–s diagram of water extended with additional curves to represent real and ideal LiBr/water absorption cycles. An explanation is provided on several methods available, including details of the thermodynamic justification of the method that was used, to construct the extended diagrams. Finally, the extended T–s diagram is provided with the representation of a real single-effect LiBr/water absorption refrigeration cycle. This should prove to be a valuable tool for design and research engineers to study and optimise LiBr/water chillers.     

Experimental and theoretical study on large ductile transverse deformations of rectangular plates subjected to shock load due to gas mixture detonation

The main purpose of this study is to show that metal plate forming by direct application of gas mixture detonation loads can be considered as an alternative high‐velocity forming method for structures instead of a conventional one. Therefore, in this investigation, a series of experimental tests have been conducted on aluminium alloy and mild steel plates with different thicknesses to examine large ductile transverse deformations of rectangular plates with clamped edge conditions subjected to gas mixture detonation loading. The main aim of the experimental section is to investigate the effects of predetonation pressures of acetylene (C₂H₂) and oxygen (O₂) gasses and different mixture ratios on the dynamic response of specimens. The permanent deflections of plates have widely varied from 21.66 up to 56.31 mm. In theoretical analysis, according to an upper bound solution and energy method, theoretical models have been presented by assuming a zero‐order Bessel function of the first kind in the x and y directions for a transverse displacement profile to predict permanent deflections. To account for material strain rate sensitivity, a Cowper–Symonds model has been used, whereas the material coefficients of this equation are constant values or functions of plate thickness. A comparison of the present models with Jones' theoretical model shows that a good agreement with experimental results can be obtained when constant values are used for material coefficients in the Cowper–Symonds equation.     

Standard free energy change of formation per unit volume: a new parameter for evaluating nucleation and growth of oxides, sulphides, carbides and nitrides

 The present paper introduces a thermodynamic parameter, the standard free energy changes of formation of oxide, sulphide, carbide and nitride per unit volume, as a criterion for comparing the formation tendency of these compounds. The diagrams for the standard free energy change of formation of common oxides, sulphides, carbides and nitrides per unit volume vs temperature have been calculated and established based on the available thermodynamic data. It is believed that these diagrams can provide better explanations to some oxidation phenomena including the effects of reactive elements on the selective oxidation of Cr₂O₃ and Al₂O₃. Received: 12 September 1997 / Accepted: 16 September 1997     

Effect of mechanical properties on wrinkling limit diagrams for Aluminum 5086 alloy annealed at different temperature

This article deals with the wrinkling limit diagrams for Aluminium 5086 alloy sheets having thickness of 2.00 mm annealed at three different temperatures namely 200, 250 and 300 °C. The study pertains to deep drawing into cylindrical cups through conical die using a flat bottom punch. When a conical die is employed, the need for a hold down or clamping ring is eliminated. However, this enhances the propensity of the blank to fail by wrinkling or buckling, particularly in the early stages of a drawing process in which thin sheet blanks are used. It is proved by these researchers and others that the onset of wrinkling takes place when the ratio of strain increments (dε_r/dε_θ) or the ratio of strain (ε_r/ε_θ) reaches a critical value during the drawing process. These values which could be determined experimentally over which the wrinkling takes place has been shown in the form of wrinkling limit diagrams for the above grade at different annealed temperatures. An attempt is also made to develop the wrinkling theory that predicts the wrinkling based on results obtained in the form of wrinkling limit diagrams established for the above grade at different annealed temperatures. Further it was observed that the annealed sheets having high n-value, high R-value and high UTS/σ_y ratio improve the resistance against wrinkling.     

Two-parameter fracture criterion (Kρ,c-Tef,c) based on notch fracture mechanics

A two-parameter fracture criterion has been proposed to predict fracture conditions of notched components. This criterion includes the critical notch stress intensity factor K _ρ,c , which represents fracture toughness of a material with a notch of radius ρ, and the effective T-stress. The effective T-stress T _ef has been estimated as the average value of the T-stress distribution in the region ahead of the notch tip at the effective distance X _ef . These parameters were derived from the volumetric method of notch fracture mechanics. The results of numerical T _ef,c -stress estimation are compared to the T _ef,c -stress results obtained from experimental analysis. The material failure curve or master curve K _ρ,c = f(T _ef,c ) has been established as a result of the notched specimen tests. A large T _ef,c range was covered from −0.80 σ _Y to +0.19 σ _Y using SENT, CT, RT (roman tile) and DCB specimens. It was shown that the notch fracture toughness is a linear decreasing function of the T _ef,c -stress. The use of the material failure curve to predict fracture conditions was demonstrated on gas pipes with the surface notch.