Analytical modeling of hot behavior of Ti-6Al-4V alloy at large strain

Tchein, Gnofam Jacques; Jacquin, Dimitri; Aldanondo, Egoitz; Coupard, D.; Gutierrez-Orrantia, Esther; Girot, F.; Lacoste, Éric

doi:10.1016/j.matdes.2018.11.025

Cited by 15 publications

(15 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here, 𝑫 ̃ * and 𝑾 ̃ * are given by: 𝑫 ̃ * = sym(𝐂 ̃𝑒𝛀 ̃𝑒) + 𝑹 𝑒 𝑫 ̅ 𝑝 𝑹 𝑒 𝑇 , 𝑾 ̃ * = skew(𝐂 ̃𝑒𝛀 ̃𝑒) + 𝑹 𝑒 𝑾 ̅̅̅ 𝑝 𝑹 𝑒 𝑇 (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) where 𝐂 ̃𝑒 = 𝑽 𝑒 𝑇 𝑽 𝑒 and, in the next equation, 𝑪 ̅ 𝑒 = 𝑭 𝑒 𝑇 𝑭 𝑒 are the elastic right Cauchy-Green tensors, and 𝑫 ̅ 𝑝 and 𝑾 ̅̅̅ 𝑝 are defined below:…”

Section: Constitutive Model 21 Updated Kinematicsmentioning

confidence: 99%

“…It can be seen in (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) that the rate of deformation tensor due to plastic deformation, 𝑫 ̅ 𝑝 , depends on both the slip and void growth based plastic deformations, but the spin tensor only depends on the deformation due to slip, because void growth does not change the shape of the lattice.…”

Section: Constitutive Model 21 Updated Kinematicsmentioning

confidence: 99%

“…The definition of 𝑳 ̃ given in (2)(3)(4)(5)(6)(7)(8)(9)(10)(11) along with 𝑫 ̃= sym(𝑪 ̃𝑒𝑳 ̃) can be used to get 𝑫 ̃= 𝑽 𝑒 𝑇 𝒅𝑽 𝑒 in which the value of 𝒅 can then be substituted from (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17) to get:…”

Section: Constitutive Model 21 Updated Kinematicsmentioning

confidence: 99%

See 2 more Smart Citations

A multiscale constitutive model for metal forming of dual phase titanium alloys by incorporating inherent deformation and failure mechanisms

Asim¹,

Siddiq²,

McMeeking³

et al. 2022

Modelling Simul. Mater. Sci. Eng.

View full text Add to dashboard Cite

Ductile metals undergo a considerable amount of plastic deformation before failure. Void nucleation, growth and coalescence is the mechanism of failure in such metals. α–β titanium alloys are ductile in nature and are widely used for their unique set of properties such as specific strength, fracture toughness, corrosion resistance and resistance to fatigue failures. Voids in these alloys have been reported to nucleate on the phase boundaries between α and β phase. Based on the findings of crystal plasticity finite element method investigations of the void growth at the interface of α and β phases, a void nucleation, growth, and coalescence model has been formulated. An existing single-phase crystal plasticity theory is extended to incorporate underlying physical mechanisms of deformation and failure in dual phase titanium alloys. Effects of various factors [stress triaxiality, Lode parameter, deformation state (equivalent stress), and phase boundary inclination] on void nucleation, growth and coalescence are used to formulate a phenomenological constitutive model while their interaction with a conventional crystal plasticity theory is established. An extensive parametric assessment of the model is carried out to quantify and understand the effects of the material parameters on the overall material response. Performance of the proposed model is then assessed and verified by comparing the results of the proposed model with the RVE study results. Application of the constitutive model for utilisation in the design and optimisation of the forming process of α–β titanium alloy components is also demonstrated using experimental data.

show abstract

Section: Constitutive Model 21 Updated Kinematicsmentioning

confidence: 99%

Section: Constitutive Model 21 Updated Kinematicsmentioning

confidence: 99%

See 1 more Smart Citation

A multiscale constitutive model for metal forming of dual phase titanium alloys by incorporating inherent deformation and failure mechanisms

Asim¹,

Siddiq²,

McMeeking³

et al. 2022

Modelling Simul. Mater. Sci. Eng.

View full text Add to dashboard Cite

show abstract

“…A considerable amount of literature has been recently published on the superplasticity of titanium alloys. The most popular Ti-based alloy widely used for SPF is Ti-6Al-4V [9,10,11,12,13,14,15,16,17,18,19,20,21,22]. Zhou et al [22] studied the superplastic tensile behaviour of Ti-6Al-4V alloy with an initial β-grain size of 6μm and α-phase volume fraction of 62%.…”

Section: Introductionmentioning

confidence: 99%

Superplasticity of Ti-6Al-4V Titanium Alloy: Microstructure Evolution and Constitutive Modelling

et al. 2019

View full text Add to dashboard Cite

Determining a desirable strain rate-temperature range for superplasticity and elongation-to-failure are critical concerns during the prediction of superplastic forming processes in α + β titanium-based alloys. This paper studies the superplastic deformation behaviour and related microstructural evolution of conventionally processed sheets of Ti-6Al-4V alloy in a strain rate range of 10–5–10–2 s–1 and a temperature range of 750–900 °C. Thermo-Calc calculation and microstructural analysis of the as-annealed samples were done in order to determine the α/β ratio and the grain size of the phases prior to the superplastic deformation. The strain rate ranges, which corresponds to the superplastic behaviour with strain rate sensitivity index m ˃ 0.3, are identified by step-by-step decreasing strain rate tests for various temperatures. Results of the uniaxial isothermal tensile tests at a constant strain rate range of 3 × 10−4–3 × 10−3 s−1 and a temperature range of 800–900 °C are presented and discussed. The experimental stress-strain data are utilized to construct constitutive models, with the purpose of predicting the flow stress behaviour of this alloy. The cross-validation approach is used to examine the predictability of the constructed models. The models exhibit excellent approximation and predictability of the flow behaviour of the studied alloy. Strain-induced changes in the grain structure are investigated by scanning electron microscopy and electron backscattered diffraction. Particular attention is paid to the comparison between the deformation behaviour and the microstructural evolution at 825 °C and 875 °C. Maximum elongation-to-failure of 635% and low residual cavitation were observed after a strain of 1.8 at 1 × 10−3 s−1 and 825 °C. This temperature provides 23 ± 4% β phase and a highly stable grain structure of both phases. The optimum deformation temperature obtained for the studied alloy is 825 °C, which is considered a comparatively low deformation temperature for the studied Ti-6Al-4V alloy.

show abstract

“…Different microstructures need different forming conditions, usually fixed by optimizing the deformation temperature and strain rate, in order to reduce the flow stress and maximize the elongation. Knowledge about the flow behaviour is necessary to optimise the conditions of superplastic deformation, as it depends on so many factors [10,[23][24][25][26][27][28][29][30][31][32][33][34][35][36]. Modelling of the flow behaviour at tensile tests is conducted to find the relation of stress versus temperature and strain-rate.…”

Section: Introductionmentioning

confidence: 99%

Modelling approach for predicting the superplastic deformation behaviour of titanium alloys with strain hardening/softening characterizations

Mosleh

Mestre-Rinn

Khalil

et al. 2019

Mater. Res. Express

View full text Add to dashboard Cite

This paper introduces an approach for modelling the flow behaviour of different titanium alloys (VT6, OT4-1 and VT14 alloys by Russian specifications) in superplastic deformation temperature and strain rate ranges. The initial microstructure parameters (d V , , , a b a b ) before starting the deformation test were included in the constructed model for each alloy. The investigated alloys have different initial microstructures and flow behaviour characteristics. The isothermal uniaxial tensile deformation tests were performed at the superplastic deformation temperature and strain rate ranges of each alloy. The VT6, OT4-1 alloys were characterized by strain hardening effect during the deformation test, while VT14 alloy was characterized by strain softening effect. A comparison study between the experimental and modelled data was performed. The general equation of the constructed models was affected by the flow behaviour of the investigated alloys. The comparison results proved the good capability of the constructed models to predict the flow behaviour of the studied alloys. The correlation coefficient R was 0.98, 0.95 and 0.97 for VT6, OT4-1 and VT14, respectively. The predictability of the constructed model was assessed by the cross-validation technique, which ascertained the quality of the constructed model.

show abstract

Analytical modeling of hot behavior of Ti-6Al-4V alloy at large strain

Cited by 15 publications

References 25 publications

A multiscale constitutive model for metal forming of dual phase titanium alloys by incorporating inherent deformation and failure mechanisms

A multiscale constitutive model for metal forming of dual phase titanium alloys by incorporating inherent deformation and failure mechanisms

Superplasticity of Ti-6Al-4V Titanium Alloy: Microstructure Evolution and Constitutive Modelling

Modelling approach for predicting the superplastic deformation behaviour of titanium alloys with strain hardening/softening characterizations

Contact Info

Product

Resources

About