Impact Response and Microstructural Evolution of Biomedical Titanium Alloy under Various Temperatures

Figures 2(a) through (c) present the stress-strain curves of Ti-alloy specimens deformed at strain rates of 8 × 10² s⁻¹, 3 × 10³ s⁻¹, and 8 × 10³ s⁻¹, respectively, at temperatures between 25 °C and 900 °C. In general, it is observed that the flow stress increases with increasing strain rate but decreases with increasing temperature. It can also be seen that for a constant strain rate, the flow stress increases with increasing strain initially but then reduces as the strain is increased further. Table I summarizes the yield stress, fracture strain, and maximum stress for each of the current specimens. The results show that the yield stress and the maximum stress both increase with increasing strain rate but decrease with increasing temperature. At the lowest strain rate of 8 × 10² s⁻¹, the specimen fractures only at a deformation temperature of 25 °C. However, when the strain rate is increased to 8 × 10³ s⁻¹, all the specimens fracture, irrespective of the temperature conditions. Hence, the results show that Ti alloy fractures more readily at higher strain rates or lower temperatures. Table I also shows that for a constant temperature, the fracture strain increases with increasing strain rate, which suggests that the fracture toughness of the alloy is enhanced at higher strain rates. Finally, it is observed that for a given strain rate, the fracture strain reduces with increasing temperature at temperatures lower than 700 °C but increases significantly at a deformation temperature of 900 °C. This tendency implies that an increasing deformation temperature is accompanied by a significant change in the microstructure of the Ti alloy, particularly at temperatures between 700 °C and 900 °C.

Figure 2(d) compares the experimental stress-strain data obtained for the current Ti alloy under various temperature and strain rate conditions with those presented in the literature for α-phase Ti alloy and Ti-6Al-4V alloy tested under broadly equivalent conditions.[20‐22] It can be seen that the flow stress of the current biomedical Ti alloy is greater than that of the α-phase Ti alloy under both temperature and strain-rate conditions and is higher than that of the Ti-6Al-4V alloy tested at 725 °C and 3.7 × 10³ s⁻¹. However, the flow stress of the Ti-6Al-4V alloy deformed at 25 °C and 3.4 × 10³ s⁻¹ is slightly higher than that of the current Ti alloy under similar loading conditions (i.e., a temperature of 25 °C and a strain rate of 3 × 10³ s⁻¹).

The stress-strain curves in Figure 2 show signs of both work hardening and work softening as the deformation strain is progressively increased. Figure 3 plots the work- hardening rate, i.e., the slope of the stress-strain curves (∂σ/∂ε), against the deformation temperature as a function of the strain rate at true strains of 0.1 and 0.2. For an engineering material, the work-hardening rate represents the net result of the competing effects of work hardening (induced by the strain and strain rate) and work softening (induced by the testing temperature and the deformation-heating effect). Overall, a negative rate of work hardening indicates that the deformation is dominated by a work-softening mechanism. Figure 3 shows that for the current Ti alloy, the work-hardening rate increases with increasing strain rate at a constant temperature, which indicates a greater resistance to plastic deformation under higher strain-rate loading conditions. However, the temperature rise caused by the deformation heat produced under high-strain-rate loading reduces the work-hardening rate as the true strain increases under constant temperature conditions. For a constant strain rate, the work- hardening rate decreases with increasing temperature at temperatures lower than 700 °C but increases significantly (particularly at a higher true strain) when the deformation temperature is increased to 900 °C. Generally speaking, the greater thermal energy associated with a higher deformation temperature enhances the ability of dislocations to overcome short-range barriers. Therefore, the work-hardening rate decreases with increasing temperature at temperatures lower than 700 °C. However, at temperatures higher than the β-transus temperature of the current Ti alloy, i.e., 785 °C, the microstructural transition from α + β phase to pure β phase results in an increased work-hardening rate.

The stress-strain curves presented in Figure 2 indicate that the strain rate has a significant effect on the flow stress of Ti alloy. In order to analyze the strain-rate effect on the mechanical behavior of the deformed alloy under different loading conditions, Figure 4(a) illustrates the relationship between the flow stress and the strain rate as a function of the temperature at true strains of 0.1 and 0.2, respectively. In general, it is apparent that the flow stress increases with increasing strain rate at both values of the true strain. Furthermore, for a given temperature, the flow stress increases more significantly at higher strain rates (i.e., 3 × 10³ and 8 × 10³ s⁻¹), while for a given strain rate, the stress increases more gradually at higher temperatures.

The literature contains many experimental investigations into the mechanical response of engineering materials subjected to dynamic loading. The results typically reveal that a significant increase in flow stress occurs at strain rates higher than 10³ s⁻¹. This phenomenon is thought to indicate a change from a thermally activated control of the dislocation movements at low strain rates to a viscous-drag control mechanism at higher strain rates.[23] However, in their study of copper alloy, Follansbee and Kocks[24] suggested that the increased flow stress at strain rates higher than 10³ s⁻¹ was caused, not by a transformation of the deformation mechanism from thermally activated flow to viscous drag, but by an enhanced rate of dislocation generation. The same argument was also advanced by Lee et al.[25] and Zerilli et al.[26] in their studies of 304L stainless steel and oxygen-free high conductivity (OFHC) copper, respectively.

The strain-rate effect can be quantified via the strain-rate-sensitivity parameter, β, defined by the following equation:[27] where the compressive stresses σ ₁ and σ ₂ are obtained from tests conducted at average strain rates of \( \ifmmode\expandafter\dot\else\expandafter\.\fi{\varepsilon }_{2} \) and \( \ifmmode\expandafter\dot\else\expandafter\.\fi{\varepsilon }_{1} \), respectively, and are calculated at the same value of compressive plastic strain. Figure 4(b) illustrates the variation of the strain-rate sensitivity of the current Ti alloy with the temperature as a function of the strain rate at true strains of 0.1 and 0.2, respectively. It is observed that the strain-rate sensitivity increases with increasing strain and strain rate but decreases with increasing temperature. Furthermore, at lower strain rates (8 × 10² to 3 × 10³ s⁻¹), an approximately linear relationship is found between the strain-rate sensitivity and the temperature. However, at higher strain rates (3 × 10³ to 8 × 10³ s⁻¹), the Ti alloy is more strain-rate sensitive at lower temperatures for both values of the true strain.

Assuming that the plastic deformation of the Ti alloy is a thermally activated process, the strain rate can be expressed in the form of the following Arrhenius equation:[28] where \( \ifmmode\expandafter\dot\else\expandafter\.\fi{\varepsilon }_{0} \) is the frequency factor, \( \Delta G^{*} \) is the activation energy required to induce plastic flow, k is the Boltzmann constant, and T is the absolute experimental temperature. The activation energy associated with the dynamic deformation of the current Ti alloy is given by the following equation:[29,30] where \( \nu ^{*} \) is the activation volume and can be obtained from the following equation:[31]

For the current Ti alloy, sufficient activation energy to trigger the plastic-flow process is obtained at particular combinations of the current strain, strain rate, and temperature conditions. Figure 2 has shown that the flow stress varies as a function of the strain, strain rate, and temperature. Therefore, a correlation can be obtained between the activation energy and the flow stress under equivalent loading conditions, as shown in Figure 5. The results indicate that the flow stress is inversely related to the activation energy. In other words, at activation energies lower than 20 kJ/mole, the flow stress increases significantly as the activation energy decreases. In general, the role of the activation energy is to assist dislocations in overcoming short-range barriers to movement. In the current case, moving a dislocation requires more stress during plastic deformation, particularly under high-strain-rate and low-temperature loading conditions because Ti alloy is known to have a low activation energy.[32]

The stress-strain curves presented in Figure 2 have shown that the plastic flow is affected not only by the strain rate but also by the temperature. The temperature effect is shown more clearly in Figure 6(a), which plots the variation of the true stress with the temperature as a function of the strain rate. It can be seen that the flow stress drops rapidly as the temperature is increased from 25 °C to 500 °C, reduces more slowly as the temperature is increased to 700 °C, and then falls abruptly as the temperature is further increased to 900 °C. The variation in flow stress with increasing temperature is the result of microstructural changes, i.e., changes in the grain size, the number of dislocations, the volume and composition of phase, and so forth. In the current Ti alloy, the softening resistance observed at temperatures between 500 °C and 700 °C is thought to be the result of a strengthening effect prompted by the formation of α phase as the temperature is increased at temperatures lower than the β-transus temperature (785 °C). The temperature effect can be quantified via a temperature-sensitivity parameter, b _a , defined as |(σ ₂ − σ ₁)/(T ₂ − T ₁)|.[33,34] Figure 6(b) shows the correlation between the temperature sensitivity of the Ti alloy and the temperature as a function of the strain and strain rate. It can be seen that the highest temperature sensitivity occurs at 500 °C, while the lowest occurs at 700 °C. It is also apparent that for a constant temperature, the temperature sensitivity increases with increasing strain rate. Thus, it can be inferred that the strain-rate-induced strengthening effect is restrained by the temperature effect. This restraining effect is particularly pronounced at higher strain rates at temperatures of 300 °C and 500 °C, respectively. Comparing the temperature sensitivity at true strains of 0.1 and 0.2, respectively, for a fixed strain rate, it can be seen that the temperature-sensitivity parameter has a higher value at a true strain of 0.2 than at 0.1 for temperatures of 300 °C and 500 °C. However, at a higher temperature of 700 °C, the temperature-sensitivity parameter has an approximately equal value at true strains of 0.1 and 0.2, respectively. Finally, at the highest temperature of 900 °C, the temperature-sensitivity parameter has a lower value at a strain of 0.2 than at 0.1. These results reveal that the temperature effect is more pronounced in specimens subjected to large deformations at low temperatures.

In the high-strain-rate tests performed in this study, the same heating rate and holding time were applied in every case, i.e., a heating rate of 2/3 °C/s until the specified testing temperature was attained and a holding time of 15 minutes. Figure 7 shows the initial undeformed microstructures of Ti-alloy specimens heated to each of the current testing temperatures. The grain sizes of the undeformed, heated specimens were measured using a linear intercept method and were found to be 36, 39, 44, 47, and 51 μm in the specimens heated to temperatures of 25 °C, 300 °C, 500 °C, 700 °C, and 900 °C, respectively. The macromechanical behavior of the deformed Ti-alloy specimens is closely related to the microstructural changes induced by the applied strain rate and temperature-loading conditions. Figures 8 and 9 present diffraction patterns and TEM micrographs of the Ti alloy deformed at a true strain of 0.2 under various strain-rate/temperature conditions. The diffraction patterns in Figures 8(a) and (b) reveal the presence of elongated α phase within the β matrix of the Ti alloy deformed at 25 °C. The micrographs presented in Figures 8(c) through (f) and Figures 9(a) through (f) reveal that the dislocation density increases with increasing strain rate but decreases with increasing temperature. Furthermore, it can be seen that the amount of α phase increases with increasing temperature at temperatures lower than 700 °C. Observing the dislocation structures, it is found that the dislocation cells are large and have thin walls composed of tangled dislocations in the specimen deformed at a strain rate of 8 × 10² s⁻¹ and a temperature of 25 °C (Figure 8(c)). However, at the same deformation temperature, when the strain rate is increased to 8 × 10³ s⁻¹, the dislocation cell size reduces, and the cell walls become thicker (Figure 8(d)). Under this higher strain rate condition, the dislocation density increases, and the greater number of dislocations tangled at the cell walls suppresses dislocation movement. In other words, as the number of tangled dislocations within the cell wall increases, the force required for the dislocations to overcome the barriers formed by these tangled dislocations also increases. Correlating the stress-strain curves in Figure 2 with the increased dislocation density observed at higher strain rates in Figure 8(d), it can be inferred that the flow stress increases as a result of an increasing dislocation density. Although previous research[20] reported the presence of both twins and twin interactions in α-phase titanium alloy deformed at a high strain rate of 3 × 10³ s⁻¹ , no evidence of twinning was found in the current biomedical Ti alloy in the high-strain-rate tests performed at room temperature.

However, Figures 8(c) and (d) suggest that the presence of α phase in the matrix also contributes to the strengthening effect observed in the deformed alloy at temperatures lower than 700 °C. Specifically, the α phase presents a barrier to dislocation movements, causing the dislocations to pile up at the phase boundary. It seems reasonable to assume that the amount of precipitated α phase has a direct effect on the mechanical behavior of the Ti alloy.[35,36] As the deformation temperature is increased, the thermal energy of the dislocations is also increased, and, hence, their ability to overcome short-range barriers is enhanced. Therefore, at a strain rate of 8 × 10² s⁻¹ and a temperature of 300 °C, the dislocation cells have a looser structure and the dislocation density is reduced. Furthermore, a greater amount of α phase is precipitated (Figure 8(e)). However, for the same deformation temperature, but at an increased strain rate of 8 × 10³ s⁻¹, both the dislocation density and the cell-wall thickness are increased (Figure 8(f)).

At higher temperatures of 500 °C and 700 °C, the number of dislocations decreases. As a result, at a strain rate of 8 × 10² s⁻¹, the dislocation density is lower than that observed at 25 °C or 300 °C under the same strain rate, as shown in Figures 9(a) and (c), respectively. Fewer dislocations and no cell substructures are found in the specimens tested at 500 °C and 700 °C, respectively, because the higher temperature accelerates the annihilation of the dislocation substructures. However, at equivalent temperatures, but at a higher strain rate of 8 × 10³ s⁻¹, the dislocation-multiplication phenomenon is not significantly restrained by the higher temperature conditions. As a result, large dislocations and cell structures are still formed at temperatures of 500 °C and 700 °C, as shown in Figures 9(b) and (d), respectively. Comparing the cell substructures formed at a strain rate of 8 × 10³ s⁻¹ in Figures 8(d) and (f) and 9(b) and (d), it is apparent that the cell size increases and the cell walls become thinner as the temperature is increased. Furthermore, in comparing Figures 8(e), 9(a), and 9(c) at a strain rate of 8 × 10² s⁻¹, it is observed that the amount of α phase precipitated in the β matrix at 500 °C and 700 °C is greater than that formed at 300 °C. The increased amount of α phase increases the resistance to dislocation movements and causes a greater accumulation of tangled dislocations at the α-phase boundary. Accordingly, plastic deformation is suppressed, and the mechanical strength of the alloy is increased. As shown previously in Figure 6(a), an obvious resistance to thermal softening occurs at a temperature of 700 °C. It is thought that the presence of α phase in the matrix dominates the high-temperature strength characteristics of Ti alloy at temperatures lower than the β-transus temperature, i.e., 785  °C.[37] However, at higher temperatures, i.e., 900 °C, the microstructures of the specimens deformed at strain rates of 8 × 10² s⁻¹ and 8 × 10³ s⁻¹ contain subgrains and a very low number of dislocations (Figures 9(e) and (f), respectively). Furthermore, since the temperature is higher than the β-transus temperature, the β matrix contains no α phase. The combined effects of thermal activation assistance at higher deformation temperatures and the absence of α phase reduce the intensity of the driving force required to produce dislocation movements, and, hence, the flow stress reduces considerably at temperatures ranging from 700 °C to 900 °C, as evidenced in Figure 2.

The correlation between the microstructural evolution of the Ti alloy and its macromechanical response can be quantified by measuring the dislocation density and the amount of α phase within the matrix. In this study, the dislocation density, ρ, was determined using the analytical formula proposed by Ham,[38] i.e., ρ = 2n/Lt, where n is the number of intersections between a dislocation and a random set of lines of length, L, and t is the foil thickness. In performing the analysis, the dislocation density was calculated for the specimens deformed at a strain of 0.2 under each of the current strain-rate/temperature conditions. Figure 10 reveals that the square root of the dislocation density increases linearly with the flow stress, which implies that the combined effect of the strain rate and the temperature determines the correlation between the dislocation density and the flow stress. Quantitative measurements of the amount of α phase precipitated in the β matrix were obtained via X-ray diffraction. Figure 11 presents the X-ray diffraction profiles of the Ti alloy deformed at temperatures ranging from 25 °C to 900 °C at a constant strain rate of 8 × 10² s⁻¹. It can be seen that peaks corresponding to α phase \( {\left( {10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}1} \right)} \) are present only in the profiles corresponding to temperatures of 700 °C or lower and are particularly strong at temperatures of 500 °C and 700 °C. The amount of α phase in the β matrix was estimated quantitatively by computing the α-phase intensity, I _α , in accordance with the following equation:[39] where I{200} _β is the base reflection intensity, i.e., the intensity of the pure β matrix.

Figure 12 plots the variations of the dislocation density, the α-phase intensity, and the flow stress with the deformation temperature as a function of the strain rate at a true strain of 0.2. The results show that for a given strain rate, the flow stress and the dislocation density decrease as the temperature increases. It is also observed that the intensity of the α phase increases with increasing temperature below the β-transus temperature. The precipitated α phase not only imposes barriers to dislocation motion but also acts as the origin of dislocation multiplications. Therefore, an increased amount of α phase induces the generation of additional dislocations and leads to an obvious softening resistance effect (particularly at a temperature of 700 °C).

Figure 12 confirms that the presence of α phase in the β matrix results in a strengthening effect in the current Ti alloy at temperatures lower than 700 °C. However, Figure 13 shows that the fracture strain decreases with an increasing amount of α phase at temperatures lower than 700 °C. The microstructural observations presented in Figures 8 and 9 reveal that the formation of α phase causes the accumulation of dislocations at the phase boundaries, resulting in extreme stress concentrations. Thus, cracks form more readily within the microstructure, and, hence, the fracture strain reduces. However, at temperatures higher than the β-transus temperature, α phase is not precipitated in the matrix, and, hence, the fracture strain increases.

Fractographic analysis reveals that the current specimens fracture as a consequence of adiabatic-shear band formation. The fracture states presented in the right-hand column of Table  1 show that the formation of adiabatic-shear bands is strongly dependent on both the strain rate and the temperature. At the lowest temperature of 25 °C, all three specimens fracture as a result of adiabatic shearing. However, at temperatures between 300 °C and 700 °C, adiabatic shearing takes place only at strain rates higher than 3 × 10³ s⁻¹, while at the highest temperature of 900 °C, adiabatic-shear bands are formed only at the highest strain rate of 8 × 10³ s⁻¹. Overall, the results indicate that the tendency toward adiabatic shearing increases with increasing strain rate and reducing temperature.

Figure 14(a) presents a low-magnification micrograph of a specimen tested at a temperature of 25 °C and a strain rate of 8 × 10³ s⁻¹. It can be seen that the specimen fails in a catastrophic manner along a plane orientated at an angle of 40 to 50 deg to the compression axis. Figure 14(b) shows the fragmentation features of the failed specimen. Figures 14(c) and (d) present optical micrographs of the transverse sections (i.e., perpendicular to the compression axis) of sheared specimens deformed at a strain rate of 8 × 10³ s⁻¹ under temperatures of 25 °C and 900 °C, respectively. The micrographs show that adiabatic-shear bands propagate along a circular path on the transverse section of each specimen. Interestingly, double localized shear bands are formed in the specimen tested at a strain rate of 8 × 10³ s⁻¹ and a temperature of 900 °C, as shown in Figure 14(d). The formation of this double shear band can be attributed to the change in the deformed microstructure from a mixed α + β phase at temperatures lower than the β-transus temperature to a single β phase at higher temperatures.