A Sigmoidal Model for Superplastic Deformation

Pan, Wei; Kröhn, K. Wieczorek K.-P.; Leen, Seán B.; Hyde, T H; Walloe, S.

doi:10.1243/146442005x10355

Cited by 8 publications

(17 citation statements)

References 10 publications

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“…5) and hence, the ductility of the material (Fig. 3) tends to have a sigmoidal shape function of both temperature and strain-rate, producing peaks of strain rate sensitivity [60]. Testing under these 'hot-zones' produced elongations in excess of 300% engineering strain with no observable necking (Fig.…”

Section: Identification Of Strain Rate/temperature Regime For Superplmentioning

confidence: 97%

Superplasticity in Ti–6Al–4V: Characterisation, modelling and applications

2015

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The processing regime relevant to superplasticity in the Ti-6Al-4V alloy is identified. The effect is found to be potent in the range 850-900°C at strain rates between 0.001/s and 0.0001/s. Within this regime, mechanical behaviour is characterised by steady-state grain size and negligible cavity formation; electron backscatter diffraction studies confirm a random texture, leaving grain-boundary sliding as the overarching deformation mechanism. Outside of the superplastic regime, grain size refinement involving recrystallisation and the formation of voids and cavities cause macroscopic softening; low ductility results. Stress hardening is correlated to grain growth and accumulation of dislocations. The findings are used to construct a processing map, on which the dominant deformation mechanisms are identified. Physically-based constitutive equations are presented which are faithful to the observed deformation mechanisms. Internal state variables are used to represent the evolution of grain size, dislocation density and void fraction. Material constants are determined using genetic-algorithm optimisation techniques. Finally, the deformation behaviour of this material in an industrially relevant problem is simulated: the inflation of diffusion-bonded material for the manufacture of hollow, lightweight structures.

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Section: Identification Of Strain Rate/temperature Regime For Superplmentioning

confidence: 97%

Superplasticity in Ti–6Al–4V: Characterisation, modelling and applications

2015

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“…Thus, the time variation of applied displacement u(t) was provided by Eq. . Afterwards, the true strain ε t and the true stress σ t evolutions were calculated from the value of displacement u(t) given by the previous equation Eqs.…”

Section: Experimental Investigation – Materials and Testingmentioning

confidence: 99%

Investigation of the mechanical behaviour of Ti–6Al–4V alloy under hot forming conditions: Experiment and modelling

Velay

Matsumoto

Sasaki

et al. 2014

Materialwissenschaft Werkst

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The present investigation aims at evaluating and understanding the formability of Ti-6Al-4V alloy under hot forming conditions (650°C ≤ T ≤ 750°C). To fulfil these objectives, it was necessary to establish accurate material models and predict microscopic material evolution depending on temperature and strain rate. Two kinds of microstructure were investigated, the first one considers a conventional grain size of the α-phase (3 μm) whereas a combined forging-rolling process is used to elaborate the second one and allows to obtain a very fine grain of the α-phase (0.5 μm). In this research work, we propose to investigate the capabilities of the titanium alloy under forming conditions quite different from those usually considered in superplastic forming process (lower temperatures and higher strain rates).

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“…strain-rate enhanced) [3]. The first disadvantage of equation (4), which also applies to equations (3) and (5), as a constitutive equation can be dealt with by introducing a constitutive equation with strain-rate-independent constants, such as the sigmoidal model of Pan et al [5], for example, as follows…”

Section: Constitutive Modelsmentioning

confidence: 99%

“…where a, b, c, andε a are temperature-dependent constants obtained from logarithmic plots of stress versus strain, as obtained from constant strain-rate tensile tests (see reference [5] for more details). Figure 5(a) shows a typical variation of m-value with strainrate from equation (6) compared with data from equation (4), and Fig.…”

Section: Constitutive Modelsmentioning

confidence: 99%

“…Figure 5(a) shows a typical variation of m-value with strainrate from equation (6) compared with data from equation (4), and Fig. 5(b) shows the correlation against measured uniaxial test data for the Ti-6242 material from reference [5]. However, this approach does not presently include microstructural effects such as grain growth hardening and is an empirical approach.…”

Section: Constitutive Modelsmentioning

confidence: 99%

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A superplastic forming limit diagram concept for Ti-6Al-4V

Krohn

Leen

Hyde

2007

Proceedings of the Institution of Mechanical Engineers, Part L:

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The current paper is concerned with the development of a simplified method for predicting failure due to plastic instability during the superplastic forming (SPF) of titanium alloys. The rationale is that a key factor in the process of reliable failure prediction is the incorporation of a mechanisms-based model, which includes microstructural effects, such as static and dynamic grain growth and associated hardening, and which is also independent of the forming strainrate. Existing methods for predicting plastic instability during conventional metal-forming are discussed along with previous attempts at predicting failure during SPF. It is shown that no easyto-interpret method, such as the forming limit diagram (FLD) in conventional forming, exists for SPF. Consequently, an SPFLD concept in a major strain (ε 1 ), minor strain (ε 3 ), and equivalent strain-rate space (ε eq ) is presented on the basis of uniaxial SP ductilities across a range of strainrates along with the Hill-Swift instability criteria and using finite element-predicted ε 1 -ε 3 -ε eq paths for key points on the forming blank to predict failure. The predicted results are validated against measured data for Ti-6Al-4V at different strain-rates. important benefit is the low flow stress normally associated with SP deformation. The technology requires significant investment into part and tool design, die manufacture, and process modelling. A number of key challenges prevent the more widespread exploitation of SPF.1. The requirement for a controlled, slow strainrate prevents rapid manufacture of mass-produced parts, so methods and/or materials are required to speed up the process. 2. The associated high temperatures, especially for titanium SPF alloys, represent hostile conditions for materials, tooling, equipment, and personnel. 3. Since only specific alloys display SP behaviour, often requiring pre-conditioning, these alloys are normally costly to produce and purchase and they are costly and difficult to characterize. 4. Finally, because of the non-linear, large deformation, viscoplastic nature of SP material behaviour, it is normally necessary to employ computational methods, such as finite element (FE) analysis, to predict industrial forming processes, and there are JMDA150

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A Sigmoidal Model for Superplastic Deformation

Cited by 8 publications

References 10 publications

Superplasticity in Ti–6Al–4V: Characterisation, modelling and applications

Superplasticity in Ti–6Al–4V: Characterisation, modelling and applications

Investigation of the mechanical behaviour of Ti–6Al–4V alloy under hot forming conditions: Experiment and modelling

A superplastic forming limit diagram concept for Ti-6Al-4V

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