Rate-controlling deformation mechanisms in drawn tungsten wires

Figures & data

Figure 1. Ductile-to-brittle transition temperatures (squares, left ordinate) and mean widths of elongated grains (circles, right ordinate) of doped drawn wires (according to A.J. Opinsky, L. Sama and L. Seigle (1958), see [12]).

Table 1. Composition of the sintered rod representing the starting point of the wire series investigated in this study.

Element	Al	Cr	Fe	K	Mo	Nb	Ni	Si	Ti	V
Content in wt. ppm	10.1 ± 0.2	2.1 ± 0.1	8.1 ± 0.2	67.1 ± 4.6	0.6 ± 0.1	0.6± 0.1	1.5± 0.1	0.1± 0.1	0.1± 0.1	0.5± 0.1

Notes: The element concentrations were measured using glow discharge mass spectroscopy (GD-MS). The column for potassium is highlighted since GD-MS is not the ideal method to measure the potassium content. The manufacturer however guarantees a potassium concentration above $65\mathrm{w}\mathrm{t}.\mathrm{p}\mathrm{p}\mathrm{m}$.

Table 2. Diameters and accumulated drawing strains of the tungsten wires investigated.

Wire diameter d in $\mu \mathrm{m}$	16	41	150	490	950
Accumulated drawing strain φ	10.8	9.0	6.4	4.0	2.7

Figure 3. Temporal stress evolution during a repeated stress relaxation experiment performed on a drawn tungsten wire with a diameter of $150\mu \mathrm{m}$ at room temperature. The inset shows the temporal stress decay $\mathrm{\Delta }\sigma$ during the five relaxation cycles performed. For better visibility, only every fifth measured data point is drawn. The dashed lines represent the fitted stress decays following Equation (15(15) $\mathrm{\Delta }\sigma =\sigma \left(t\right)-\sigma (t=0)=-\frac{k_{\mathrm{B}}T}{V_{\mathrm{r}}}\ln (1+\frac{t}{c_{\mathrm{r}}}),$(15) ).

Figure 2. Temporal evolution of true strain (left y-axis) and stress (right y-axis) during a strain-rate jump test performed on a tungsten wire with a diameter of $16\mu \mathrm{m}$. Dashed vertical lines mark the times at which a strain-rate jump was performed. The two zoomed insets show jumps from low to high (green, left side) and from high to low strain rate (red, right side).

Figure 4. Mean maximum stresses ${\sigma }_{\mathrm{m}\mathrm{a}\mathrm{x}}$ (black symbols, from RSRE) and yield strengths ${\sigma }_{\mathrm{Y}}$ (blue symbols, from RSRE and SRJT) and the difference ${\sigma }_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\sigma }_{\mathrm{Y}}$ (red symbols) as a function of the accumulated drawing strain φ.

Table 3. Maximum stresses, yield stresses and the difference between both for the wires investigated in the course of this study.

Wire diameter	Accumulated drawing strain	Yield stress	Maximum stress
d in $\mu \mathrm{m}$	φ	${\sigma }_{\mathrm{Y}}$ in $\mathrm{M}\mathrm{P}\mathrm{a}$	${\sigma }_{\mathrm{m}\mathrm{a}\mathrm{x}}$ in $\mathrm{M}\mathrm{P}\mathrm{a}$	${\sigma }_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\sigma }_{\mathrm{Y}}$ in $\mathrm{M}\mathrm{P}\mathrm{a}$
16	10.8	$3140\pm 68$	$4378\pm 50$	$1238\pm 30$
41	9.0	$2690\pm 74$	$3960\pm 69$	$1270\pm 41$
150	6.4	$2037\pm 47$	$2989\pm 26$	$952\pm 41$
490	4.0	$1716\pm 44$	$2157\pm 23$	$442\pm 12$
950	2.7	$1585\pm 64$	$1892\pm 64$	$307\pm 14$

Figure 5. Effective activation volume $V_{\mathrm{e}\mathrm{f}\mathrm{f}}$ in $b^3$ as a function of the relaxation stress ${\sigma }_0$.

Figure 6. Strain-rate sensitivities from RSRE (filled symbols) and from SRJT (empty symbols) as a function of the relaxation and jump stress, respectively.

Table 4. Strain-rate sensitivities and activation volumes of different tungsten materials at room temperature.

Material	Logarithmic strain accumulated during cold-working	Mean grain size	Type of test	Activation volume		Strain-rate sensitivity	Source
	φ	$〈L〉$ in $\mu \mathrm{m}$		Type	V in $b^3$	m
High-purity single crystal	0	–	SRE${}^{\mathrm{a}}$ , tensile test	Effective	14.1	$14.6\mathrm{M}\mathrm{P}\mathrm{a}$${}^{\mathrm{b}}$	[37]
Single crystal	0	–	SRJT, nanoindentation	Apparent	6	$0.024\pm 0.004$	[38]
Flattened wire	3.6	1	SRJT, tensile test	Apparent	10.3	–	[13]
Ultrafine-grained disk	4.3	0.5	SRJT, nanoindentation	Apparent	5	–	[38]
Coarse-grained plate	?	5.4	SRJT, nanoindentation	Apparent	8	0.021	[39]
Cold-rolled plate	2.5	0.516	SRJT, tensile test	Apparent	15	0.030	[40]
	2.9	0.447				0.028
	3.3	0.404				0.026
	4.0	0.256				0.018

${}^{\mathrm{a}}$ Only one relaxation cycle was performed and evaluated for each sample in this study, thus the experiment is called stress relaxation experiment.

${}^{\mathrm{b}}$ Brunner & Glebovsky [37] determined the strain-rate sensitivity of the tungsten single crystal via stress relaxation experiments. They used the following definition of the strain-rate sensitivity: $r=\mathrm{\partial }\mathrm{\Delta }\tau /\mathrm{\partial }(-\dot{\tau })$, where r is the strain-rate sensitivity, $\mathrm{\Delta }\tau$ the stress drop during the relaxation cycle and $\dot{\tau }$ the stress rate during the relaxation cycle. Hence, r has the dimension of a stress.

Table 5. Activation volumes and strain-rate sensitivities of grain boundary sliding and the kink-pair mechanism.

	Activation volume in $b^3$	Strain-rate sensitivity m
Grain boundary sliding [41]	1	0.5
Kink-pair mechanism	$10\dots 100$ [16]	see equation (5(5) $V=\frac{k_{\mathrm{B}}T}{m\sigma }.$(5) )

L.L. Seigle and C.D. Dickinson, Refractory Metals and Alloys: Effect of Mechanical and Structural Variables on the Ductile-Brittle Transition in Refractory Metals, Interscience, New York, 1963.

 Google Scholar

D. Brunner and V. Glebovsky, Analysis of flow-stress measurements of high-purity tungsten single crystals, Mater. Lett. 44 (2000), pp. 144–152.

 Web of Science ®Google Scholar

D. Kiener, R. Fritz, M. Alfreider, A. Leitner, R. Pippan, and V. Maier-Kiener, Rate limiting deformation mechanisms of BCC metals in confined volumes, Acta. Mater. 166 (2019), pp. 687–701.

 Web of Science ®Google Scholar

O. Boser, The temperature dependence of the flow-stress of heavily-deformed tungsten, J. Less-Common Met. 23 (1971), pp. 427–435.

 Google Scholar

J. Kappacher, A. Leitner, D. Kiener, H. Clemens, and V. Maier-Kiener, Thermally activated deformation mechanisms and solid solution softening in W-Re alloys investigated via high temperature nanoindentation, Mater. Des. 189 (2020), pp. 108499.

 Web of Science ®Google Scholar

S.W. Bonk, Plastische Verformungsmechanismen in hochgradig kaltgewalzten, ultrafeinkörnigen Wolframblechen, Ph.D. Thesis, Karlsruher Institut für Technologie, Karlsruhe, 2018.

 Google Scholar

Y.M. Wang, A.V. Hamza, and E. Ma, Temperature-dependent strain rate sensitivity and activation volume of nanocrystalline Ni, Acta. Mater. 54 (2006), pp. 2715–2726.

 Web of Science ®Google Scholar

H. Conrad, Thermally activated deformation of metals, J. Met. 16 (1964), pp. 582–588.

 Google Scholar