Numerical study of superplastic deformation with superimposed pressure for cavity sensitive materials

Abstract

The non-uniform deformation (necking and thinning) development and fracture of superplastic materials under both uniaxial tension and circular sheet bulging are numerically analysed by considering the effects of strain rate sensitivity and cavity growth with superimposed pressure. It is found that the fracture mode, which is controlled by both strain rate sensitivity and cavity growth rate, can be changed by superimposed pressure from fracture without external necking for cavity sensitive alloys at zero pressure to fracture with necking development or extensive thinning at pressure large enough to completely suppress cavity growth. Fracture mechanism diagrams are presented which enable prediction of the fracture mode to be made as a function of material parameters and pressure conditions for uniaxial tension and bulging.

MST/724     

孔洞敏感超塑性材料变形的数值分析

本文用两种数值方法,非线性长波分析和刚粘塑性有限元方法研究了孔洞敏感的超塑性材料在单向拉伸和园板涨形中的不均匀变形和断裂过程。分析表明,这种过程是不均匀几何失稳与内部孔洞长大的结合与相互作用的结果。材料的应变速率敏感性指数与孔洞长大速率通过不同的变形机理图控制着这种过程。叠加的静水压力能够改变孔洞敏感材料的断裂模式,从常压下没有宏观颈缩的孔洞断裂到无内部孔洞的外部颈缩断裂。     

Effect of stress state on cavitation and hole growth in superplastic AA 7475 aluminium alloy

Abstract

A study has been made of the growth of cavities and of artificial holes in AA 7475 alloy sheet material during both uniaxial and equibiaxial tensile straining, with the object of clarifying the effect of stress state on cavitation during superplastic flow. The growth rate of cavities with strain was observed to be lower for uniaxial tension than for equibiaxial tension. An analysis of artificial hole growth data supports these observations, and is consistent with the view that continuous cavity nucleation and cavity coalescence lead to an increase in the apparent cavity growth rate during superplastic flow.

MST/1149     

Superplastic deformation and postformed mechanical properties of high temperature titanium alloy IMI 834

Abstract

Superplastic forming is particularly attractive for high temperature Ti alloys because of the much lower forming stresses compared with those encountered during forging. The superplastic deformation parameters of IMI 834 sheet were obtained at 900, 940, and 990°C. At 990°C, IMI 834 shows low flow stresses, high values of strain rate sensitivity, and minimum strain anisotropy, however, 300% superplastic elongation was readily obtained at the lower forming temperature of 940°C but with a higher flow stress. A reduction in the room temperature and 600°C tensile properties with superplastic strain resulted from strain enhanced grain growth during superplastic deformation; this effect was greatest at 990°C. Aging of post 990°C superplastically formed material was studied. The creep performance of IMI 834 was found to be slightly reduced by superplastic forming. These properties and the changes in the microstructure and texture are compared with other Ti alloys under superplastic conditions.

MST/1822     

Failure analysis on gas pressure formed spherical domes of Pb–Sn eutectic alloy

Abstract

This paper addresses the issue of instability of deformation during gas pressure forming of superplastic sheets. With regard to fracture strain, the plastic behaviour of the spherical dome has been described in terms of the local effective stress and the effective strain. These quantities are equated to the uniaxial stress state. The limiting effective thickness strain is obtained utilising the relations between the strain rate sensitivity index and the fracture strain. The results are found to be in good agreement with the measured failure strains.     

Neck formation and cavitation in the superplastic Zn-22% Al eutectoid

The mechanical behaviour of the superplastic Zn-22% Al eutectoid is divisible into three distinct regions. Experiments show the deformation is quasi-uniform at intermediate strain rates in region II, but neck formation is important at low strain rates in region I. Extensive cavitation occurs in regions I and II, but fracture in region I is due to necking. The results provide strong evidence for a decrease in the true value of the strain rate sensitivity in region I.     

Effect of coalescence on cavity growth during superplastic deformation

Abstract

The accumulation of cavitation damage with increasing strain during the biaxial deformation of two superplastic aluminium-base alloys has been studied using densitometry and quantitative metallography. A model based on constitutive relationships for the diffusive and plastic growth of voids has been extended to account for cavity coalescence, a phenomenon commonly observed during superplastic deformation. Good agreement between the measured and calculated cavity growth rates was obtained for one alloy (AI 7475), while discrepancies observed for the second alloy (Supral 220) are explained in terms of the effects of continuous cavity nucleation.

MST/189     

Effect of two step strain rate on superplastic behaviour of Al–Zn–Mg–Cu–Zr alloy 7010 containing Sc

Abstract

A suitable thermomechanical process, different from the Rockwell route, before the superplastic deformation together with the utilisation of a ‘two step strain rate’ during the superplastic deformation has been employed to evaluate the total percentage elongation in a high strength Al–Zn–Mg–Cu–Zr alloy containing Sc. It is shown that the utilisation of a two step strain rate under appropriate combinations of temperature and strain rate results in superior values of elongations.     

Critical reinforcement size for cavity nucleation during superplastic deformation of metal matrix composites

Abstract

A high strain rate superplastic composite Al–Cu–Mg/Si₃N_4p has been investigated to estimate the critical particle size for cavity nucleation. Specimens superplastically deformed to a strain of 0.2 at 773 K contained no liquid phase whereas those deformed at 783 K contained liquid phase. The critical particle size, i.e. the smallest size to nucleate a cavity, obtained experimentally was 0.5 µm dia. for deformation at 773 K and 0.4 µm for deformation at 783 K. The critical particle size for deformation at 773 K can be estimated accurately using Stowell's equation for critical strain rate. However, for deformation at 783 K when liquid phase was present, the predicted critical strain rate was much lower than the experimental strain rate for critical particle size for cavity nucleation. It is suggested that the actual critical strain rate was increased by an increase in diffusivity at the interfaces and grain boundaries due to the presence of liquid phase.     

The stress-strain rate behaviour of superplastic Zn-Al eutectoid alloy

The stress-strain rate behaviour of a superplastic Zn-22% Al alloys was investigated by the differential strain rate and constant load cycling tests on an Instron machine. A region with a rate sensitivity approaching unity was observed at low strain rates. On increasing the strain rate, a transition to the superplastic region occurred through an intermediate region of lower m (0.35). These observations are interpreted in terms of a transition from diffusional creep to superplastic flow with a threshold stress for superplastic deformation.     

Superplasticity in an alulllinium alloy 2124/SiCp composite

Abstract

The superplastic potential of an aluminium alloy 2124/SiC_p composite, fabricated by powder metallurgy techniques, has been investigated. Instead of any special thermomechanical processing or hot extrusion, simple warm rolling has been employed to obtain a fine grained structure before superplastic testing. Constant strain rate tests were performed to characterise the superplastic behaviour of the composite. All tests were performed in air at temperatures of 743–783 K and in the strain rate range 10^-3-10^-1 S^-l. A maximum elongation of 425% was achieved at a temperature of 763 K and a strain rate of 8.3 × 10^-2 S^-1. The highest value obtained for the strain rate sensitivity index (m) was 0.41. Differential scanning calorimetry was used to ascertain the possibility of any partial melting in the vicinity of optimum superplastic temperature. These results suggested that no liquid phase existed where maximum elongation was achieved and deformation took place entirely in the solid state. Optical and electron microscopy were used to examine the materials microstructure before and after superplastic testing.     

The fracture process in a fine-grained superplastic 7475 Al alloy

In order to contribute towards alloy design and therefore an improvement in fracture toughness of engineering materials in general, the effect of temperature, strain rate and strain level on the superplastic deformation, cavity nucleation and growth, and fracture behaviour are studied in an important rate-sensitive structural engineering material, 7475 Al, in the light of current models and thinking. The efficacy of hydrostatic pressure in reducing cavitation during superplastic deformation is considered.     

Response of titanium alloys to high strain rate deformation

Abstract

The stress-strain response of samples of Ti64 and Ti550 at strain rates from 10^?1 s^?1 to 10³ s^?1 and samples of Ti811 and Ti153 at a strain rate of 10³ s^?1 have been assessed. It has been found that the influence of the imposed strain rate on the stress-strain response of Ti64 and Ti550 alloys is very similar – in both alloys the yield stress increases with increase of strain rate and the energy absorbed to fracture increases. At high strain rates localised deformation occurs in the form of shear bands in Ti64 and Ti550 but no shear banding was seen in Ti811 and Ti153. The fracture surfaces of Ti64 and of Ti550 show an increased tendency to brittle failure and an increase in necking with increase of strain rate. The influence of alloy microstructure and composition on the response to changes in imposed strain rate are discussed in terms of adiabatic heating and the factors controlling the flow stress in these alloys.     

An analysis of deformation and failure in rectangular tensile bars accounting for void shape changes

A three-dimensional finite deformation study of necking and failure in rectangular tensile bars is carried out using a constitutive relation for porous material plasticity. The fully dynamic formulation accounts for void nucleation and growth along with thermal and rate effects, but here focus is on quasi-static response with a specified initial void volume fraction. The constitutive relation takes into account void shape changes and associated void rotations for three-dimensional voids. The constitutive update is carried out using a generalized rate tangent scheme for an elastic-viscoplastic solid. The sensitivity of necking and failure patterns to the aspect ratio of the rectangular bar is investigated with focus on the plane strain limit and a square tensile bar. The calculations predict the well-known slant fracture in plane strain tension and the emergence of a cup-cone like failure region for a square cross-section. Details are provided for the development of porosity in the bar with a square cross-section, including void shape changes and void rotations. The numerical examples show the capability of a constitutive relation for porous plasticity that can model details of void evolution, thus paving the way for advanced analyses of ductile failure under arbitrary loadings.

     

Cavitation behaviour in fine grain 3Y-TZP during tensile and compressive superplastic flow

Studies of cavitation in Y-TZP during superplastic flow have been made for both tensile and compressive deformation conditions. It was observed that the morphologies of cavities near the fracture faces of tensile specimens varied markedly with testing conditions and in most cases differed from those near the gauge heads. Two quite different forms of cavitation behaviour were observed leading to high and low strains to failure, respectively. For optimum conditions of superplastic flow, of high temperature/low strain rate (low stress), when large elongations were observed, cavities were either spherical or elongated parallel to the tensile axis. Those near the fracture face interlinked in a plastic (necking) mode to give transverse cavities and subsequent failure. At high strain rate/low temperature (high stress), transverse intergranular cracking played a dominant role in failure at low elongations. For intermediate conditions of temperature/strain rate, elongated cavities developed parallel to the tensile axis, but near the fracture face these usually interlinked by transverse cracking. These conditions were associated with intermediate elongations to failure. For the assessment of cavity growth mechanisms, artificial pores were introduced into fine grain Y-TZP specimens and changes in their shape and size during tensile or compressive deformation were investigated. Results show that the change of pore volume, in the superplastic regime, is controlled by plastic deformation of the matrix and can be described by the relationship of dR/d = ;R, where is the true strain, the cavity growth rate parameter and R is the radius of the pore.     

Quantitative analysis on the onset of necking in rate-dependent tension

Quantitative analysis on the onset of necking of Zn–5%Al alloy at 340 °C in rate-dependent tension is developed based on Hart’s criterion, through accurately measuring the values of the strain hardening index (n) and the strain rate sensitivity index (m). A critical relation of strain rate to uniform strain is derived and then is verified to be an essential mechanical parameter for characterizing the capability of uniform deformation of rate-dependent materials. The prediction of the onset of necking at specific strain paths with strain rates, tensile velocities and loads agrees well with the critical relation, which suggests the validity of instability analysis in this study. The critical relation indicates that the onset of necking is dependent only on the final values of strain and of strain rate in tension, and is independent of strain path, deformation condition or strain history, which is of great significance for the increase of formability and the reduction of forming time in superplastic forming process. Additionally, it is proved that the tension at constant load is a very effective approach for precisely establishing the critical relation, due to not involving test data at others strain paths.     

Flow stress,strain rate,strain relationships in superplastic deformation

The superplastic deformation of materials has commonly been characterized by the strain rate sensitivity, m, determined from two-dimensional, flow stress against strain rate plots. For material in which flow stress varies with strain or because of microstructural changes due to time at a high temperature, superplastic deformation must be characterized with respect to a three dimensional plot in which strain or time is the third axis. Techniques for generating the necessary plots are indicated and a simple experimental method for determining the suitability of a given material to a particular forming operation is described.     

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.     

Localized strain and heat generation during plastic deformation in nanocrystalline Ni and Ni–Fe

Room temperature tensile testing was performed on a coarse-grained polycrystalline Ni (32 μm), a nanocrystalline Ni (23 nm) and two nanocrystalline Ni–Fe (16 nm) electrodeposits at two strain rates of 10^?1 and 10^?2/s. Strain localizations and local temperature increases were simultaneously recorded during tensile testing. For all materials, higher loads or higher strain rate generally resulted in higher peak temperature with the highest temperatures recorded in the fracture regions. The maximum temperature for the nanocrystalline materials was just over 80 °C, which is significantly below the reported temperatures for the onset of thermally activated grain growth. Therefore, the previously reported grain growth observed on similar materials after tensile deformation is likely not thermally activated but a stress-induced phenomenon. Despite the wide grain range from 16 nm to 32 μm, all samples exhibited similar strain localization behavior. Local strain variations initiated in the early stage of macroscopic uniform deformation, subsequent necking and fracture took place in the region of initial strain localization. While the coarse-grained polycrystalline Ni exhibited little strain rate sensitivity, gradually increased strain rate sensitivity was observed for the 23 nm Ni and the two 16 nm Ni–Fe samples, suggesting that both dislocation-mediated and grain-boundary-controlled mechanisms were operative in the deformation of the nanocrystalline Ni and Ni–Fe samples.     

Cavitation and fracture in the superplastic Al-33% Cu eutectic alloy

Experiments were conducted on the Al-33% Cu eutectic alloy in both an annealed and an as-extruded condition. For both conditions, the relationship between flow stress and strain rate is sigmoidal with maximum ductilities occurring at intermediate strain rates in the superplastic Region II. Specimens fail by necking at the faster strain rates in Region III, but the severity of necking is reduced with decreasing strain rate and the necks are very diffuse in Region II. There is extensive internal cavitation in the fractured specimens, especially at lower strain rates and in the vicinity of the fracture tip. It was observed that cavities form preferentially on the- interphase boundaries. It is shown by calculation that the observed change from small rounded cavities to large cavities elongated along the tensile axis is reasonably consistent with the theories of cavity growth in fine-grained superplastic alloys