Awardee: Ir Prof Alfonso H W Ngan

There have been enormous interest in and demand for accurately measuring the mechanical properties of soft materials using nanomechanical test platforms including nanoindentation, atomic force microscopy and optical tweezers.

The rate-jump method is a general method for accurately measuring the intrinsic elastic modulus of materials. It does so by introducing a jump in the rate of the test force or sample displacement during an unloading process in any nanomechanical test platform. This method is based on rigorous theoretical foundation^1,2 as follows. During an unloading process, the deformation of a specimen can be generally described as viscoelastic without plasticity which has been consumed in the preceding loading process prior to unloading (Figure 1a). With a sudden change in the load rate applied at a certain time point during unloading, a step change in the corresponding deformation rate will result (Figure 1b). However, in any viscoelastic material law for the specimen, any viscous or dashpot units (linear or nonlinear) will not respond to the jump in the load rate, and only the elastic (spring) units will respond. As a consequence, the specimen response during unloading obeys the following equation:

where ∆σ̇_ij is the jump in the stress rate, ∆ε̇_kl is the jump in the strain rate, and c_ijkl is the elastic constant of the viscoelastic material law with the dashpot units ignored. Equation (1) implies that the response of a viscoelastic specimen to a rate jump can be obtained by solving a linear elastic problem with the same geometry and linear elastic elements as the original viscoelastic problem, but with the viscous units ignored. Equation (1) involves the effective elastic modulus c_ijkl of all the linear elastic units of the viscoelastic model, which can be measured in the following manner:

(i) in any test geometry, establish the relation between the applied force F and specimen displacement δ for a purely elastic specimen; then

(ii) make the substitutions F → ∆F ̇ and δ → ∆δ ̇ into the relation, which will involve the elastic modulus of the specimen.

Thus, measuring ∆δ ̇ for the ∆F ̇ applied during unloading will allow measurement of the elastic modulus of the specimen, even though it is viscoelastic during the unloading.

Figure 1: Principle of the rate-jump method; (a) General viscoelasticity during
unloading (b) A jump in loading rate leading to a jump in displacement rate, or
vice versa, during unloading

Traditional methods of nanomechanical testing are based primarily on the Hertzian and Oliver-Pharr models³, which assume purely elastic behaviour of the specimen during quasi-static loading or unloading. While these methods may be suitable for hard materials, for soft materials their severe creep/viscoelasticity does not meet the purely elasticity assumption. Consequently, the measurement that results during quasi-static loading or unloading will be affected by the load rate. Another traditional method is dynamic force spectroscopy based on oscillatory loading, but the storage and loss modulus measured this way are dependent on the test platform as well as the loading frequency. Furthermore, certain specimens are sensitive to vibrational loading. These include biological cells which may be preferentially killed by oscillations at specific frequencies⁴, or metals like aluminium, where small oscillatory loadings may trigger subgrain formation, thus altering the microstructure of the test sample to be measured⁵.

The current ISO standard on instrumented indentation for metallic materials (ISO 14577) based on the Oliver-Pharr model is applicable only to the condition that the creep factor C_creep⁶ is < 0.1. While this protects the standard against situations of significant creep during the unloading process, the applicability of the standard is limited. One may think that a long load hold and/or a fast unload may be used to make the condition C_creep < 0.1 satisfied, but the test settings to meet this cannot be known a priori. Therefore, practically, one will have to do a few trial runs on the sample to get the correct conditions for C_creep < 0.1. However, if the allowable region for measurement is limited (say, a small region in a heterostructured sample), this may not be feasible. The rate-jump method offers an easy solution to the problem, by correcting the unloading stiffness in instrumented indentation for creep effects, before using it in the OliverPharr method for elastic modulus calculation. The rate-jump method is more general than the Oliver-Pharr method and includes the latter as a trivial special case when there is no creep in the specimen during unloading.

The rate-jump method has been adapted into nanomechanical test platforms including nanoindentation^6-8, atomic-force microscope^9,10, and optical tweezers¹¹. As of today, the rate-jump method has also been used by more than 130 SCI publications by peer researchers other than the author’s group. It has also been developed into a Chinese National Standard GB/T 43112-2023 for instrumented indentation for metallic materials, with implementation starting in April 2024.

The Awardee is from the Department of Mechanical Engineering of The University of Hong Kong.

References

1. Ngan A H W, Wang H T, Tang B, and Sze K Y (2005). ‘Correcting powerlaw viscoelastic effects in elastic modulus measurement using depthsensing indentation’. International Journal of Solids and Structures, 42/5-6, pp.1831-1846. doi: https://doi.org/10.1016/j.ijsolstr.2004.07.018.

2. Ngan A H W and Tang B (2009). ‘Response of power-law-viscoelastic and time-dependent materials to rate jumps’. Journal of Materials Research, 24, pp.853-862. doi: https://doi.org/10.1557/jmr.2009.0111.

3. Oliver W C and Pharr G M (1992). ‘An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments’. Journal of Materials Research, 7, p.1564-1583. doi: https://doi.org/10.1557/JMR.1992.1564.

4. Sun X X, Zhou Z L, Man C H, Leung A Y H, and Ngan A H W (2017). ‘Cell-structure specific necrosis by optical-trap induced intracellular nuclear oscillation’. Journal of the Mechanical Behavior of Biomedical Materials, 66, pp.58-67. Doi: https://doi.org/10.1016/j.jmbbm.2016.10.020.

5. Siu K W and Ngan A H W (2013). ‘The continuous stiffness measurement technique in nanoindentation intrinsically modifies the strength of the sample’. Philosophical Magazine, A93, pp.449-467. doi: https://doi.org/10.1080/14786435.2012.722234.

6. Feng G and Ngan A H W (2002). ‘Effects of Creep and Thermal Drift on Modulus Measurement Using Depth-sensing Indentation’. Journal of Materials Research, 17, pp.660-668. doi: https://doi.org/10.1557/JMR.2002.0094.

7. Ngan A H W and Tang B (2002). ‘Viscoelastic effects during unloading in depth-sensing indentation’. Journal of Materials Research, 17, pp.2604-2610. doi: https://doi.org/10.1557/JMR.2002.0377.

8. Tang B and Ngan A H W (2003). ‘Accurate measurement of tip-sample contact size during nanoindentation of viscoelastic materials’. Journal of Materials Research, 18, pp.1141-1148. doi: https://doi.org/10.1557/JMR.2003.0156.

9. Tang B, Ngan A H W, and Pethica J B (2008). ‘A method to quantitatively measure the elastic modulus of materials in nanometer scale using atomic force microscope’. Nanotechnology, 19, 495713. Doi: https://doi.org/10.1088/0957-4484/19/49/495713.

10. Tang B and Ngan A H W (2012). ‘A rate-jump method for characterization of soft tissues using indentation techniques’. Soft Matter, 8, pp.5974-5979. doi: https://doi.org/10.1039/C2SM25227A.

11. Zhou Z L, Hui T H, B. Tang, A.H.W. Ngan (2014). ‘Accurate measurement of stiffness of leukemia cells and leukocytes using optical trap by rate-jump method’. RSC Advances, 4, 8453-8460. doi: https://doi.org/10.1039/C3RA45835K.