High-Temperature Scanning Indentation: A new method to investigate in situ metallurgical evolution along temperature ramps

Abstract

A new technique, High-Temperature Scanning Indentation (HTSI), is proposed to investigate metallurgical evolution occurring during anisothermal heat treatments. This technique is based on the use of high-speed nanohardness measurements carried out during linear thermal ramping of the system with appropriate settings. A specific high-speed loading procedure, based on a quarter sinus loading function, a creep segment and a three-step unloading method, permits the measurement of elastic, plastic and creep properties. The indentation cycle lasts one second to minimize thermal drift issues. This approach enables quasi-continuous measurements of elastic modulus and hardness as a function of temperature in much shorter times than previous techniques. The HTSI technique is validated on fused silica and pure aluminum. The application to cold-rolled aluminum undergoing thermal cycling highlights the potential of the HTSI technique to investigate in situ thermally activated mechanisms linked with microstructural changes such as viscoplasticity, static recovery and recrystallization mechanisms in metals. Results on aluminum were confirmed using Electron Back-Scattering Diffraction measurements.

Graphic abstract

Appendix: The model of Loubet

Contact depth ${{\varvec{h}}}_{{\varvec{c}}}$ versus contact area relation

The hardness of a material is defined as the ratio of the applied load $P$ divided by the projected contact area ${A}_{\text{c}}$ (see Eq. 6).

The contact area can be geometrically determined from the contact depth. For a perfect conical indenter,

$${A}_{\text{c}}={C}_{0}{h}_{\text{c}}^{2}$$

(16)

with ${C}_{0}$ a geometrical constant. For a Berkovich indenter, ${C}_{0}=24.56$. However, the contact depth is not directly measured and has to be calculated from the tip displacement measurement. This measurement does not account for pile-up or sink-in phenomena.

Plastic depth ${{\varvec{h}}}_{{\varvec{r}}}^{\boldsymbol{^{\prime}}}$

Loubet’s model is based on indentation measurements made on an elastic, perfectly plastic material. More specifically, he considers that the depth underneath the tip is purely plastic. Consequently, he relates the indentation depth to a plastic depth, named ${h}_{\text{r}}{^{\prime}}$, with the following expression:

$${h}_{\text{r}}{^{\prime}}=h-\frac{P}{S}.$$

(17)

The plastic depth is presented in Figs. 10 and 11. Figure 11 shows the intersection between the displacement axis and the linear fit with the S slope.

Figure 10

Schematic representation of the contact geometry between a conical indenter and some material, defined in Loubet’s model. $h$ is the measured indentation depth, ${h}_{\text{r}}{^{\prime}}$ is the plastic depth, ${h}_{0}$ is the tip defect and ${h}_{\text{c}}$ is the contact depth.

Figure 11

Schematic load–displacement curve of a material. ${h}_{\text{r}}$ is the persistent depth, and ${h}_{\text{r}}{^{\prime}}$ is the plastic depth.

Figure 12

Determination of the tip defect from the stiffness–displacement curve made on fused silica using CSM mode.

Tip defect

When carrying out real experiments, the tip is never perfect. Therefore, the real contact area is underestimated if considering a perfect tip (see Fig. 10). The hatched purple area is a perfect tip contact area without defects. Because the real tip is slightly round, the purple zone should be added to the perfect contact area to obtain the real contact area. Therefore, to solve this issue, a tip defect term ${h}_{0}$ is added in the contact depth expression when calculating the tip contact.

$${h}_{\text{r}}{^{\prime}}=h-\frac{P}{S}+{h}_{0}.$$

(18)

This term could be easily determined when plotting stiffness against depth changes for a homogeneous material such as fused silica during calibration of the system with CSM measurements (see Fig. 12). For a perfect tip, this term should be $S\left(h\right)=bh$. When there is a tip defect, the equation becomes $S\left(h\right)=b(h-{h}_{0})$, and ${h}_{0}$ can be determined. Let us note that the obtained value of ${h}_{0}$ depends on the load frame stiffness determined by calibration.

At low depth, the term ${h}_{0}$ allows us to be more precise in the calculation of the contact area. At large depths, the error between the ideal contact area and the real contact area becomes negligible.

Consideration of pile-up

Pile-up [46] can occur when performing indentation measurements. This effect increases the real contact area, so if not considered, the Young’s modulus and hardness will be overestimated. Therefore, Loubet defined the contact depth using

$${h}_{\text{c}}=\alpha {h}_{\text{r}}{^{\prime}}$$

(19)

with $\alpha =1.2$ from experimental results [54, 55]. This value was experimentally determined on gold by Bec et al. [55]. It was also validated theoretically for perfectly elastic materials [56] and numerically for perfectly plastic materials [56] in the case of a conical indenter. It is worth noting that when pile-up occurs, ${h}_{\text{c}}$ could be higher than the maximum depth.

Looking to Eq. 19, the condition for sink-in is not forbidden. Loubet’s model could also been applied to materials that presents sink-in. Guillonneau et al. [57] show that Oliver and Pharr’s model and Loubet’s model give the same results on fused silica, which presents sink-in.

Independence to the load frame stiffness ${{\varvec{S}}}_{{\varvec{L}}{\varvec{F}}}$

Equation 18 can be rewritten using $u$, the raw displacement of the tip instead of $h$, and the displacement corrected from the load frame stiffness when performing a nanoindentation experiment:

$${h}^{\prime}_{\text{r}}=u-\frac{P}{{S}_{\rm LF}}-\frac{P}{S}+{h}_{0}.$$

(20)

Therefore,

$$\frac{1}{K}=\frac{1}{S}+\frac{1}{{S}_{\rm LF}}$$

(21)

with $K$ the global stiffness.

Therefore,

$${h}^{\prime}_{\text{r}}=u-\frac{P}{K}+{h}_{0}.$$

(22)

We can deduce from this expression that even if an error is made in the frame stiffness calculation, it will not change the plastic depth value because the elastic part of the displacement $P/S$ (where $S$ is not well calculated if ${S}_{\rm LF}$ is not well estimated) is removed from u to calculate ${h}^{\prime}_{\text{r}}$. Therefore, with the use of Loubet’s model, ${h}^{\prime}_{\text{r}}$, ${h}_{\text{c}}$ and hardness $H$ are independent of the load frame stiffness. This point is particularly interesting when performing experiments at low penetration depths for materials with high $E/H$ ratios.