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This post was last edited by Shaobin Fluid on 2026-4-23 at 11:27. Titanium has a body-centered cubic (BCC) structure and is primarily used as a refractory metal in applications involving high temperatures and shock loads (i.e., in the electronics industry, cutting tool industry, chemical industry, as well as in medical and military fields). Tantalum exhibits good ductility at ambient temperatures as well as at low temperatures, along with excellent corrosion resistance (chemical inertness), which makes it suitable for use in the chemical industry in applications such as valves, heat exchangers, and bayonet heaters. As a biologically inert metal, tantalum can also be considered a suitable metal for biological applications, including orthopedic implants and hip replacements. The melting temperature of tantalum is about 3290 K, second only to rhenium (3453 K) and tungsten (3683 K). Due to its very high melting temperature, tantalum possesses high phase stability, which makes it a key candidate material for studying the plasticity of BCC metals. Instrumented micro/nano-indentation testing using depth sensing has become a method for characterizing plasticity (i.e., mechanical response). For example, the nanoindentation force-displacement response can be used to effectively evaluate the plastic deformation mechanisms at play, such as dislocation activity (nucleation and sliding), deformation twins, and phase transitions. In other words, in the instrumented indentation testing scheme, the indentation load P and the indentation depth h are recorded simultaneously, and from the obtained P(h), the indentation hardness and elastic modulus are derived. The indentation testing method has been widely used by researchers to study the plastic deformation mechanism of tantalum. For example, Goel et al. studied the twinning anisotropy of tantalum by using simulations of displacement-controlled nanoindentation tests via molecular dynamics (MD) simulations. They found that the critical Tresca stress in the deformation zone exceeded Ta’s theoretical shear strength ((shear modulus / 2π) = 10.03 GPa) for the (010) orientation, but was lower than it for the (110) and (111) orientations. Wang et al. studied the deformation twinning phenomenon during nanoindentation of nanocrystalline Ta (10–30 nm). The physical mechanism of deformation twinning in bcc nanocrystalline materials differs from that in face-centered cubic nanocrystalline metals. Experiment The starting material for this study was high-purity tantalum (with a minimum purity of 99.99%). Table 1 shows the chemical composition. High-purity tantalum is first forged by 50%, and then subjected to side forging with 50% deformation to disrupt the initial coarse grain structure. The forged tantalum was then annealed in a vacuum at 1250°C for 2 hours to obtain a fully recrystallized microstructure. Table 1: Chemical composition of the tantalum metal used in this study. Cut and install a cross-section with a thickness of 2 mm. To prepare for the testing, small square samples of each material were first mechanically ground and polished to 0.05 μm aluminum oxide powder. Then the sample is gently polished with colloidal silica to slightly etch it. Finally, to eliminate any deformation introduced during the mechanical polishing process, the sample was chemically polished in an appropriate chemical solution. In chemical polishing technology, the sample surface is immersed in a polishing solution, stirred for a few seconds or minutes, and then rinsed. The polishing solution dissolves the surface at a uniform rate, resulting in a completely flat and smooth surface. During chemical polishing, the externally applied current (i.e., electro-polishing) is replaced by a chemical oxidant. The cyclic indentation test for depth control was conducted at ambient temperature (24°C). Tests are conducted using a cone (Berkovich) indenter (see Figure 1). Figure 1: Schematic diagram of the Belković socket. The half-angle θ is equal to 65.3°, and the contact area can be expressed as a function of the indenter displacement on the sample surface h; here, c0 and Ck are constants determined by curve-fitting procedures using standard calibration samples of molten silicon. The indentation strain rate is defined as the ratio of the loading rate P& to the applied load P: According to the ‘Equation’, a proportionally controlled loading rate results in a relatively constant indentation strain rate. Therefore, in his research, multi-cycle indentation tests were conducted at constant strain-rate loading rates of 0.005, 0.05, and 0.5 mN/sec, which essentially correspond to approximate strain rates of 0.005, 0.05, 0.5, and 0.5 /sec. At each strain rate, 6 loading/unloading/reloading cycles with a depth interval of 300 nm were performed, and 3–5 indentation tests were carried out under each condition. During cyclic indentation, after loading to a predetermined depth, the sample is partially unloaded to a minimum force of Fmin = 0.1Fmax, and then reloaded. Thermal drift calibration was performed before testing (less than 0.05 nm/s). Results and Discussion Indentation load/displacement curve Figure 2 shows the indentation load-displacement curves obtained at different indentation strain rates of 0.005, 0.05, and 0.5 /sec. The instantaneous indentation strain rate is the ratio of the displacement rate (dh/dt) to the displacement (h). It can be seen that as the strain rate increases, the indentation load P increases at a constant h. The load-depth curve obtained from cyclic nanoindentation shows that the unloading-reloading paths overlap, and the unloading path is purely elastic. However, at the slowest strain rate (0.005/sec), as shown in Figure 3, by enlarging a portion of the unloading-reloading path, it is clear that they do not overlap but rather form an open jaw. The open jaw indicates that the sample behavior during reloading is softer compared to the previous unloading path. The difference between the unloading path and the reloading path increases as the cyclic indentation depth increases. Figure 4a shows a single loading/unloading cycle (Cycle #3) at a strain rate of 0.005/s and the depth ； The corresponding surface indentation hardness is the indentation load divided by the projected area of the indenter, as shown in Figure 4b. Figure 5 shows the typical relationship between indentation hardness and indentation depth at three different strain rates. As shown in the figure, as the indentation depth decreases, the indentation hardness increases, clearly demonstrating the indentation size effect (ISE). The size effect of indentation hardness may arise from the strong plastic strain gradients that naturally occur in microscale indentations, or from the effect of dislocation starvation, which forces intense plastic deformation to take place within a very small volume of originally defect-free crystalline material at the nanoscale. Figure 2: Load-deepness curve obtained by cyclic indentation. Unloading is performed at depths of approximately 300, 600, 900, and 1200, as well as 1800 nm. Figure 3: The enlarged unloading-reloading section from Figure 2 (strain rate of 0.005/sec) shows the differences between the two paths. This difference increases as the unloading depth increases. Figure 4: a) Indentation load versus depth for a single loading/unloading cycle (strain rate: 0.005/s), b) Surface indentation hardness versus depth for a single loading/unloading cycle (strain rate: 0.005/s). Figure 5: Relationship between indentation hardness and indentation depth at different strain rates. In the graph, ISE can be clearly observed, with larger scatter points in the shallow pits. Figure 6 shows the curves of 2 Hind versus indentation depth 1h at different indentation strain rates. Figure 6: Square of hardness versus reciprocal of depth for pure tantalum at different indentation strain rates. Indentation strain rate sensitivity: If hardness is directly related to flow stress (σ), then hardness can depend on the strain rate through a power-law relationship: where B is a constant, m is the strain rate sensitivity, and ε̇ is the instantaneous indentation strain rate, defined as dh/dt. Take the logarithm of both sides of the equation, 4, and simplify the expression: Thus, for many materials, there is a linear relationship between the logarithm of hardness and the logarithm of strain rate, with a slope equal to the strain rate sensitivity m. The slope of each curve in Figure 7 gives the strain rate sensitivity (m-value) at a specific depth. Figure 8 shows the variation of m with indentation depth h. The m-value is consistent with the reported strain rate sensitivity of Ta in the thermally activated state (i.e., 0.037–0.075). It can also be seen that m is a depth-dependent phenomenon, showing an increasing trend as the indentation depth decreases. Figure 7: ln (H) versus ln(ind ε&) curves obtained at different indentation depths. The slope of each curve gives m values. Figure 8: Depth dependence of m. It can be seen that as the indentation depth increases, the m value decreases rapidly from 0.0531 at a depth of 300 nm to 0.0109 at a depth of 1800 nm. Work hardening behavior and the activation amount H/Er can be used as indicators of work hardening. An increase in the H/Er value indicates an enhanced work hardening reaction. Er is a simplified version of Young’s modulus; it is a function of Young’s modulus Es and Poisson’s ratio, as well as of Young’s modulus Ei and Poisson’s ratio vi. Figure 9 shows the relationship between the hardness-to-decreased-modulus ratio and indentation depth at different strain rates. The distribution of the data clearly shows that shallow notches exhibit a greater average work hardening than deep notches, which may be due to the presence of gnd. The apparent activation volume V*, which is the product of Burger’s vector (b) and the activation area (∆a), can be calculated from the change in hardness relative to the indentation strain rate. The activation volume essentially describes the thermally activated motion of dislocations through obstacles in crystalline solids, which occurs at the elastoplastic interface that expands under the indenter. The slope of the activation volume varies with hardness, reflecting a transition in deformation dynamics. As shown in Figure 10, as the hardness increases (moving toward shallower indentations), the activation volume decreases, maintaining a bilinear behavior. Figure 9: Changes in H/Er and indentation depth at different indentation strain rates. Figure 10: Changes in activation volume and hardness. Conclusion 1. At the minimum strain rate of 0.005/sec, softening (creep) is significant. 2. In the cyclic indentation tests of pure tantalum, the indentation size effect, the ISE value, and the strain rate sensitivity m can be observed. 3. The observed dependencies of H and V* on indentation depth indicate that both the average flow stress and average plastic strain around small indentations are higher than those around deep indentations. The strain rate sensitivity m and activation volume V* are depth-dependent phenomena, exhibiting different plastic deformation mechanisms in shallow indentation and volume indentation.