Coupling effects of material properties and the bending angle on the springback angle of a titanium alloy tube during numerically controlled bending

The significant springback after the numerically controlled (NC) bending of a titanium alloy tube has an important influence on the precision of the shape and size of the bent tube. This springback depends on the material properties of the tube, the bending angle, and especially their coupling effects. The influence of some material properties and the bending angle on the springback angle in the NC bending of a TA18 tube were investigated using a three-dimensional (3D) elastic–plastic finite element model. Using multivariate and stepwise analyses, the coupling effects of the bending angle and the material properties on the springback angle during NC bending were revealed. It was observed that Young’s modulus, yield stress, the strain hardening coefficient and exponent, and the thickness anisotropy exponent, as well as interactions of these parameters with the bending angle, have a significant influence on the springback angle. The bending angle, yield stress, and hardening coefficient have positive effects on the springback angle, and Young’s modulus, the hardening exponent, and the thickness anisotropy exponent have negative effects. The influence of the material properties of the titanium alloy increases with the bending angle. Young’s modulus and the strain hardening coefficient and exponent have the greatest influence on the springback angle. The results will be very useful in predicting, compensating for and controlling the springback of titanium alloy tubes during NC bending.     

Mechanical anisotropy and stress–strain rate characteristics in superplastic deformation of titanium alloys

Abstract

Uniaxial tension and compression tests have been carried out on two titanium based alloys, Ti–6Al–4V in the form of extruded tubes and forged plates and Ti–3Al–10V–2Fe sheets, to study anisotropic behaviour during superplastic deformation. The following were observed: (i) originally round cross-section became elliptical after deformation; (ii) the flow stresses and strain rates were dependent on the orientation of the specimens; and (iii) the strain anisotropy became less severe as the strain rate increased. These characteristics of anisotropy were related to the original microstructure (e.g. the mechanical fibring of the α grains) and the microstructural evolution during superplastic deformation. New constitutive equations for describing anisotropic superplastic deformation have been proposed to explain the effect of strain rate or stress on anisotropy.     

材料参数对高强不锈钢管数控绕弯成形失稳起皱的影响

目的研究材料参数波动对管材数控绕弯成形失稳起皱的影响规律。方法基于ABAQUS有限元平台,建立了21-6-9高强不锈钢管数控绕弯成形过程三维弹塑性有限元模型,并验证了模型的可靠性;采用该模型模拟分析了材料参数波动对其数控绕弯成形过程失稳起皱的影响规律。结果随着厚向异性指数、屈服强度的增大或弹性模量、硬化指数的减小,弯管的起皱趋势增大,泊松比和强度系数对弯管起皱趋势的影响较小。结论材料参数对弯管起皱趋势影响的大小依次为:屈服强度、弹性模量、厚向异性指数、硬化指数、强度系数和泊松比。     

Mechanism of plastic void growth during superplastic flow

Abstract

Existing models for plastic hole growth have been re-evaluated in terms of their applicability to superplastic flow. The Cocks and Ashby model is modified to include more properly the effect of void shape, and the effect of simultaneous strain hardening is also discussed. Some new experimental data on the growth of artificial holes drilled in a sheet sample of Coronze 638 are presented and compared with data on the development of general cavitation damage in the same material without artificial holes. The difference between the two sets of results is explained in terms of a coalescence effect during general damage. Cavitation rates are found to be independent of strain in both sets of experiments. This result is explained by including the effect of strain hardening (brought about by strain enhanced grain growth) in the models.

MST/461     

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     

Influence of prior straining on superplastic behaviour of an Fe–Cr–Ni alloy

Abstract

The superplastic behaviour of a microduplex Fe–Cr–Ni (25·7Cr–6·6Ni) alloy was investigated in the as-worked, annealed, and prestrained conditions. In the early stages of deformation, flow stress depends significantly on strain, and also on the instantaneous microstructural state in the case of as-worked and annealed specimens. Under these conditions, the empirical parameters of the constitutive equation for superplastic deformation were found to depend systematically on strain. At 1000°C, strain hardening predominates, and this could be accounted for by grain growth and by the hardening produced by the noticeable dislocation activity. After suitable prestraining, steady-state deformation conditions may be attained; this may facilitate the collection of σ–ε data, which could then be used to assess the relative importance of the appropriate deformation mechanisms.

MST/125     

Asymptotic and finite element analyses of mode III dynamic crack growth at a ductile-brittle interface

In this work, dynamic crack growth along a ductile-brittle interface under anti-plane strain conditions is studied. The ductile solid is taken to obey the J ₂ flow theory of plasticity with linear isotropic strain hardening, while the substrate is assumed to exhibit linear elastic behavior. Firstly, the asymptotic near-tip stress and velocity fields are derived. These fields are assumed to be variable-separable with a power singularity in the radial coordinate centered at the crack tip. The effects of crack speed, strain hardening of the ductile phase and mismatch in elastic moduli of the two phases on the singularity exponent and the angular functions are studied. Secondly, full-field finite element analyses of the problem under small-scale yielding conditions are performed. The validity of the asymptotic fields and their range of dominance are determined by comparing them with the results of the full-field finite element analyses. Finally, theoretical predictions are made of the variations of the dynamic fracture toughness with crack velocity. The influence of the bi-material parameters on the above variation is investigated.     

Superplasticity and superplastic forming processes

Abstract

Superplasticity, first observed some seventy years ago, remained a scientific curiosity until about twenty years ago. It is now recognized as a property which can be utilized in forming processes. There are two types of superplastic behaviour, known as fine–grained (or fine–structure) and internal–stress superplasticity. Fine–grained superplastic materials have a strain–rate sensitivity exponent of 0·5, and deform principally by a grain–boundary sliding mechanism. In this paper the microstructural features important in the development of fine structure super plasticity are discussed, and phenomenological equations for describing superplastic flow are presented. The superplastic properties of fine–grained materials can be optimized by promoting grain–boundary sliding and inhibiting slip. A number of fine–grained superplastic materials have been developed for commercial use, and their number is increasing. Internal–stress superplastic materials can have a strain–rate sensitivity exponent as high as unity, i.e. they can exhibit Newtonian viscous behaviour. Internal stresses can be generated by thermal cycling in materials that consist of two phases, or are anisotropic in their thermal–expansion coefficients, or are polymorphic. No commercial applications have yet been found for the superplastic forming of materials by generating internal stress.

MST/169     

Studies on the fracture mechanics parameters of weldment with mechanical heterogeneity

The fully plastic solutions of welded centre-cracked strip for plane stress problem were carefully investigated with the fully plastic finite element method. It was introduced for assessing the fracture mechanics parameters of weldment with mechanical heterogeneity that there existed an equivalent yielding stress and equivalent strain hardening exponent in the vicinity of crack tip keeping the assessment of fracture mechanics parameters of weldment in the same way as the homogeneous material. The equivalent yielding stress and equivalent strain hardening exponent of various matched weldment were computed and the effect of weld metal width were calculated and discussed on equivalent yielding stress and equivalent strain hardening exponent near crack tip. The engineering approach was given for estimating the fracture mechanics parameters of weldment with mechanical heterogeneity in elastic-plastic range.     

Crack growth on elastic-plastic bimaterial interfaces

Finite element calculation based on finite strain theory is carried out to simulate the crack growth on bimaterial interfaces under the assumption of small scale yielding and plane strain condition. The modified Gurson's constitutive equation and the element vanish technique introduced by Tvergaard et al. are used to model the final formation of an open crack. The crack growths in homogeneous material and in bimaterials are compared. It is found from the calculation that the critical macroscopic fracture toughness for crack growth J _IC is much lower in bimaterials than in homogeneous material. For bimaterial cases, the J _IC of a crack between two elastic-plastic materials which have identical elastic properties with different yield strength is lower than that of a crack between an elastic-plastic material and a rigid substrate. It seems that the difference in yield strength between the dissimilar materials has more significant influence on the void nucleation and crack growth than the difference in hardening exponent.     

Stress, deformation and damage fields near the tip of a crack in a damaged nonlinear material

The stress, strain, displacement and damage fields near the tip of a crack in a power-law hardening material with continuous damage formation under antiplane longitudinal shear loading are investigated analytically. The interaction between a major crack and distributed microscopic damage is considered by describing the effect of damage in terms of a damage variable D. A deformation plasticity theory coupled with damage and a damage evolution law are formulated. A hodograph transformation is employed to determine the singularity and angular distribution of the crack-tip quantities. Consequently, analytical solutions for the antiplane shear crack-tip fields are obtained. Effects of the hardening exponent n and the damage exponent m on the crack-tip fields are discussed. It is found that the present crack-tip stress and strain solutions for damaged nonlinear material are similar to the well-known HRR fields for virgin materials. However, damage leads to a weaker singularity of stress, and to a stronger singularity of strain compared to that for virgin materials, respectively. The stress associated with damage always falls below the HRR field for virgin material; but the distribution of strain associated with damage lies slightly above the HRR field for r/(J/0) > 1.5 while the difference becomes negligible when r/(J/0) > 2. The limiting distributions of stress and strain may indeed be given by the HRR field.     

Effects of microstructure on superplastic behaviour of nickel based superalloy NK17CDAT

Abstract

The superplastic behaviour of nickel based superalloy NK17CDAT( Astroloy) has been studied using torsion testing. The evolutions of stress and average grain size are found to follow the same classical behaviour as other nickel based alloys under similar conditions. The superplastic flow is characterised by a strain rate sensitivity exponent of 0·5 and a grain size sensitivity exponent of 3. Modelling of this alloy can be considered using a combination of microscopic mechanisms, namely, those of Gittus, Coble, and dislocation glide–climb.

MST/1135     

A damage related thermo-viscoplastic constitutive model of metallic materials under high rate deformation

Abstract

A constitutive model considering the effects of strain hardening, strain rate hardening, thermal softening and material damage softening is suggested. In order to take the effect of material damage into account, a strain softening term is added in Johnson–Cook flow stress law. The model can predict the overall deformation process of metallic materials at high strain rates and a simple way is provided to determine the coefficients of softening term.     

On the evaluation of parameters of the constitutive equation for 7475 Al alloy

From the mechanical data on 7475 Al alloy, it is evident that flow stress is significantly dependent on the strain during superplastic flow. This is due to its ability to strain-harden during superplasticity. The rate of increase in the flow stress is much higher at 457° C than at 517° C. This gives rise to non-unique values for the parameters of the constitutive equation. At 457° C, whereas the stress exponent (n) and activation energy for superplastic flow at 1 × 10^–4 sec^–1 increase only slightly with strain, the grain size sensitivity parameter (p) and structure parameter (A) decrease significantly with strain. These changes in the constitutive parameters are associated with dislocation activity occurring within the grain interior, leading to grain elongation without significant changes in the grain size, through the parameter, (b/d) ^p , of the constitutive equation.     

Evaluation of the tensile properties of a material through spherical indentation: definition of an average representative strain and a confidence domain

In the present article, a new method for the determination of the hardening law using the load displacement curve, F–h, of a spherical indentation test is developed. This method is based on the study of the error between an experimental indentation curve and a number of finite elements simulation curves. For the smaller values of these errors, the error distribution shape is a valley, which is defined with an analytic equation. Except for the fact that the identified hardening law is a Hollomon type, no assumption was made for the proposed identification method. A new representative strain of the spherical indentation, called “average representative strain,” ε _aR was defined in the proposed article. In the bottom of the valley, all the stress–strain curves that intersect at a point of abscissa ε _aR lead to very similar indentation curves. Thus, the average representative strain indicates the part of the hardening law that is the better identified from spherical indentation test. The results show that a unique material parameter set (yield stress σ _y, strain hardening exponent n) is identified when using a single spherical indentation curve. However, for the experimental cases, the experimental imprecision and the material heterogeneity lead to different indentation curves, which makes the uniqueness of solution impossible. Therefore, the identified solution is not a single curve but a domain that is called “solution domain” in the yield stress–work hardening exponent diagram, and “confidence domain” in the stress–strain diagram. The confidence domain gives clear answers to the question of uniqueness of the solution and on the sensitivity of the indentation test to the identified hardening laws parameters.     

Two-parameter characterization of the near-tip stress fields for a bi-material elastic-plastic interface crack

A particular case of interface cracks is considered. The materials at each side of the interface are assumed to have different yield strength and plastic strain hardening exponent, while elastic properties are identical. The problem is considered to be a relevant idealization of a crack at the fusion line in a weldment. A systematic investigation of the mismatch effect in this bi-material plane strain mode I dominating interface crack has been performed by finite strain finite element analyses. Results for loading causing small scale yielding at the crack tip are described. It is concluded that the near-tip stress field in the forward sector can be separated, at least approximately, into two parts. The first part is characterized by the homogeneous small scale yielding field controlled by J for one of the interface materials, the reference material. The second part which influences the absolute value of stresses at the crack tip and measures the deviation of the fields from the first part can be characterized by a mismatch constraint parameter M. Results have indicated that the second part is a very weak function of distance from the crack tip in the forward sector, and the angular distribution of the second part is only a function of the plastic hardening property of the reference material.     

Microstructural evolution and plastic stability during superplastic flow in a 7475 aluminium alloy

Abstract

Superplastic behaviour and microstructural evolution were examined at 788 K for strain rates in the range 2 × 10^-4–2 × 10^-3 s^-1 in a 7475 aluminium alloy of nominal composition Al–(1·2–1·9)Cu–(5·2–6·2)Zn–(1· 9–2·6)Mg (wt-%). In addition, the variation of the strain hardening and plastic stability parameters with strain was investigated based on experimental grain growth and cavitation data. The strain hardening parameter at 2 × 10^-4 s^-1 was high over a wide range of strain because of the high grain growth rate. Decrease in the strain hardening parameter due to cavitation was negligible. The highest plastic stability parameter was attained at 2 × 10^-4 s^-1, although the strain rate sensitivity was the lowest for the strain rate range investigated. This demonstrates the influence of grain growth on high plastic stability during superplastic deformation.     

A micro‐mechanical damage model based on gradient plasticity: algorithms and applications

As soon as material failure dominates a deformation process, the material increasingly displays strain softening and the finite element computation is significantly affected by the element size. Without remedying this effect in the constitutive model one cannot hope for a reliable prediction of the ductile material failure process. In the present paper, a micro‐mechanical damage model coupled to gradient‐dependent plasticity theory is presented and its finite element algorithm is discussed. By incorporating the Laplacian of plastic strain into the damage constitutive relationship, the known mesh‐dependence is overcome and computational results are uniquely correlated with the given material parameters. The implicit C¹ shape function is used and can be transformed to arbitrary quadrilateral elements. The introduced intrinsic material length parameter is able to predict size effects in material failure. Copyright © 2002 John Wiley & Sons, Ltd.     

Elastic-plastic analysis of an arbitrarily-oriented mode III crack touching an interface

In this paper we investigate a semi-infinite crack terminating at an arbitrarily oriented interface between two elastic-plastic materials under an anti-plane shear loading. An analytical solution is first developed for general power-law hardening materials under a mode III loading. If both materials have the same hardening exponent, the formulation results in a nonlinear eigenequation which can be solved numerically. The stress singularities are determined as a function of two material constants: the hardening exponent n and parameter G which represents the relative resistance of the two materials. In addition to the power of the singularity, the stress, strain and displacement asymptotic fields are also determined. If the hardening exponents are not the same, the leading order terms of an expansion model ensure the stress continuity across the interface. The results show that the stress singularity mainly depends upon the material having the larger hardening exponent, with the highest stresses in the material having the smaller hardening exponent. By taking the hardening exponent n , the perfectly plastic bimaterial problem is studied. It has been found that if the crack lies in the less stiff material, the entirely plastic asymptotic fields around the crack tip can be determined. On the other hand, if the crack lies in the stiffer material, the crack-tip fields are partially elastic and partially plastic. For both cases, unique asymptotic fields can be determined explicitly. For those cases when the materials present a strain hardening property, different mathematical models are established.