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On thermoplastic shear instability in the machining of a titanium alloy (Ti-6Al-4V)

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Abstract

A thermal model for the thermoplastic shear instability in the machining of a titanium alloy (Ti-6Al-4V) is developed. It is based on the analysis of the shear-localized chip formation process and the temperature generated in the shear band due to various heat sources (primary, preheating, and image) in machining. The temperature in the shear band was determined analytically using the Jeager’s classical stationary- and moving-heat-source methods. Using Recht’s classical model of catastrophic shear instability (thermal softening vs strain hardening), the onset of shear localization was determined. The shear stress in the shear band is calculated at the shear-band temperature and compared with the value of the shear strength of the bulk material at the preheating temperature. If the shear stress in the shear band is less than or equal to the shear strength of the bulk material, then shear localization is imminent. The cutting speed at which this occurs is taken as the critical speed for the onset of shear localization, which continues at all speeds above this value. In the case of titanium alloys, this speed is rather low, indicating shear localization practically at all conventional cutting speeds. The effect of the depth of the cut on the onset of shear localization was also considered, as it may affect the heat transfer from the shear-localized region, i.e., between the segments in the chip, to the rest of the chip and preheating of the segment. For example, there can be a significant difference in the thermal aspects of shear localization in ultraprecision machining (where the depths of cuts are a few micrometers or less) compared to conventional machining (where the depths of cuts are several hundred micrometers). This is because of the differences in the distances between the segments as well as the energy inputs in each case.

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Abbreviations

a o :

depth of cut, mm

a :

thermal diffusivity of the conducting medium, m2/s

c :

specific heat, J/kg °C

l s :

width of the main shear plane, mm

Q l :

heat liberated per unit length of the instantaneous infinitely long line heat source, J/cm

q l :

heat liberation intensity of a continuous infinitely long line heat source, W/cm

q pl :

heat liberation intensity of a plane heat source, W/cm2

r i :

distance between point M and the line heat source (a segment of the plane heat source), mm

t oi :

time when the heat source segment (regarded as a line heat source) begins to work, s

t h :

maximum time of operation of the four heat sources, s

t o :

time required for a chip segment to move along the main shear plane through a distance l s, s

v s :

velocity of the chip segment moving along the direction of the main shear plane, m/s

v s2 :

equivalent sliding speed along the secondary shear plane, m/s

v o :

cutting speed, m/s

v c :

sliding speed of the chip segment along the tool rake face, m/s

w :

width of the moving plane heat source, mm

X, Y :

coordinates of point M in the moving coordinate system in X and Y directions

α :

rake angle of the cutting tool, deg

ɛ :

true strain of the material

θ M :

temperature rise at any point M in the conduction medium, °C.

φ :

shear angle of the primary shear plane

φ′ :

shear angle of the secondary shear plane

λ :

thermal conductivity, W/m °C

ρ :

density, kg/m3

t or τ :

time of observation or the time of the moment when the temperature rise is concerned, s

σ′ :

true stress in the shear band at the shear band temperature, MPa

σ :

yield stress of the bulk material near the shear band at the preheating temperature, MPa

σ y :

true stress at yield point, MPa

ɛ y :

true strain at yield point

\(\overline {\theta _1 } ,\overline {\theta _2 } ,\overline {\theta _3 } ,\overline {\theta _4 } \) :

temperature rise in the primary shear plane caused by each of the four primary heat sources, respectively, °C

\(\overline {\theta '_1 } ,\overline {\theta '_2 } ,\overline {\theta '_3 } ,\overline {\theta '_4 } \) :

temperature rise in the primary shear plane caused by each of the preheating effects of the four primary heat sources, respectively, °C

\(\overline {\theta _{11} } \) :

temperature rise in the primary shear plane caused by the image of the first primary heat source, °C

\(\overline {\theta '_{11} } \) :

temperature rise in the primary shear plane caused by the preheating effect of the image of the first primary heat source, °C

Σθ primary :

temperature rise in the primary shear plane caused by the four primary heat sources (including the image heat source of the first primary heat source), °C

Σθ preheating :

temperature rise in the primary shear plane caused by the preheating effect of the four primary heat sources (including image heat source of the first primary heat source), °C

\(\Sigma \bar \theta \) :

temperature rise in the primary shear plane caused by the four primary and the preheating effect of the four primary heat sources including the image heat sources, °C

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Authors and Affiliations

  1. the Mechanical and Aerospace Engineering Department, Oklahoma State University, 74078, Stillwater, OK

    Ranga Komanduri (Regents Professor and Endowed Chair in Engineering) & Zhen-Bing Hou (Visiting Professor)

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  1. Ranga Komanduri
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  2. Zhen-Bing Hou
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Komanduri, R., Hou, ZB. On thermoplastic shear instability in the machining of a titanium alloy (Ti-6Al-4V). Metall Mater Trans A 33, 2995–3010 (2002). https://doi.org/10.1007/s11661-002-0284-1

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