NQR piezospectroscopy: In-situ and nondestructive stress gauge for polymer binders – Piezo NQR

Nuclear Quadrupolar Resonance (NQR) is a RF spectroscopic technique that probes the Electrical Field Gradient (EFG) around quadrupolar nuclei. The EFG reflects the charge distribution in the crystal and is thus modified by a strain of the lattice under the influence of an external source of stress. Indeed, the Copper NQR signal in Cu2O has been used as a pressure gauge within pressurized fluids or compressed polymers. However, the corresponding applications have been limited to hydrostatic stress and the understanding of the underlying EFG-strain-stress coupling remains partial and mostly empirical.
We propose to revisit the stress-induced modification of the EFG at the copper site of Cu2O to gain a full understanding of this dependency through the comparison of first-principle calculations and well-controlled loading of macrocrystals in a specific micro-scale force apparatus fitted with a NQR probe. Thanks to this set-up and the efficiency of the most recent Density Functional Theory codes a complete understanding of the stress-NQR frequency dependency will be obtained,
even in the case of non-hydrostatic stress. From the understanding gained on Cu2O, the rationale for finding new
compounds with piezo-NQR properties will be derived.
Then, we will assemble a dedicated portable NQR set-up for collecting the distribution of NQR frequencies arising from Cu2O filler in a rubber matrix under various mechanical stresses. Building on the formal understanding gained in the first part of the project, we will aim at interpreting this frequency distribution in terms of the stress field within the rubber matrix. Finally, we will assess the practical application of NQR as a stress sensor and even as a stress field imager for the in-situ and nondestructive detection of failure in composites. In other words, in the foreseen industrial research follow-up to this basic research project, the dispersed particles would act as embedded micromechanical gauges.

We have been able to probe the stress field inside a fim of PDMS filled with cuprite. The film was set on a rigid substrate and indented by a ram. To do so, we used a surface spiral inductive antenna that was moved under the film. In that way, the antenna probed different areas at different positions with respect of the contact with the ram. The shift of the NQR frequency with respect to the position of the antenna thus reflects the hydrostatic stress distribution within the contact.
Indeed, in a preliminary experiment, it was established that the NQR frequency of 63Cu within cuprite depends on the hydrostatic component of the stress tensor according to 0.38 kHz.MPa-1.
The value of stress integrated over the sensitive volume of the antenna is reflected in the NQR shift. Experiments show a good agreement between the predictions of an elastic model and actual measured values. It must be understood though that the hypothesis underlying the calculus does not exactly corresponds to the experimental conditions: to reach a level of stress measurable by NQR, the PDMS film had to be compressed well beyond its elastic domain.

- Theoretical understanding and experimental validation on a Cu2O monocrystal of the stress dependence of the Electrical Field Gradient and of the Nuclear Quadrupolar Resonance.
- Validation and optimisation of NQR piezospectroscopy of copper oxyde in polymer matrices such as PDMS, polybutadiene and epoxy.
- Exploration of other compounds with piezo-NQR properties.
- Development of a portable instrument with a RF probe of sufficient penetration to be used in an industrial R&D context.

1. R.DUBOURGETa, A.CHATEAUMINOISa, L. LE POLLES b, R.GAUTIER b, J-C AMELINE c, H.MONTESa, N.LEQUEUXd, G.LANGd, J-B d’ESPINOSE DE LACAILLERIE « Influence de la contrainte sur le signal RQN : modélisation, expériences et applications envisagées comme jauge de contrainte » Groupe d’Etude de Résonance Magnétique, may 2015, Sète.

2. R. DUBOURGET, J.-C. AMELINE, A. CHATEAUMINOIS, R. GAUTIER, G. LANG, L. LE POLLES, C. ROILAND, J.-B. d’ESPINOSE DE LACAILLERIE ”Influence of Stress on the Nuclear Quadrupole Resonance Signal: Modeling, Experiments and Potential Applications as a Strain Gauge” International Conference on Advanced Materials Modelling (ICAMM), Rennes (France), september 2016

3. R. DUBOURGET, J.-C. AMELINE, A. CHATEAUMINOIS, R. GAUTIER, H. MONTES, G. LANG, L. LE POLLES, N. LEQUEUX, C. ROILAND, J.-B. d’ESPINOSE DE LACAILLERIE ”Influence of Stress on the Nuclear Quadrupole Resonance Signal: Modeling, Experiments and Potential Applications as a Strain Gauge” 5th Annual Practical Applications of NMR in Industry Conference (PANIC), Hilton Head, South Carolina (USA), february 2017

4. R. DUBOURGET, J.-C. AMELINE, A. CHATEAUMINOIS, R. GAUTIER, H. MONTES, G. LANG, L. LE POLLES, N. LEQUEUX, C. ROILAND, J.-B. d’ESPINOSE DE LACAILLERIE “Stress influence on Nuclear Quadrupole Resonance: Experiments, Modeling and Application as a Strain Gauge” 59th Experimental Nuclear Magnetic Resonance Conference, Asilomar, California (USA), march 2017

The determination of strain and stress distributions is a key issue for assessing a material’s behavior in terms of strength, fatigue and durability. In many applications, the combination of complex geometries with multiaxial loading results in highly heterogeneous strain and stress fields within mechanical parts. Of particular concern is the occurrence of stress concentration which can potentially induce crack nucleation and propagation. Charged elastomers and more generally composite materials, are highly heterogeneous materials. As such, their stress fields can rarely be efficiently modeled by numerical means. Experimental methods to determine stress distribution within composites are thus much needed either as an on-site monitoring tool or as a laboratory tool to validate and calibrate numerical models.
However, experimental means to measure nondestructively spatially-resolved strain/stress fields within materials and structures remain scarce. Mechanical stress/strain measurements are traditionally based on the use of electrical or optical gauges which necessitates the deployment of an extensive array of gauges and wires. Moreover, the spatial resolution of these gauges remains poor.
The photoelastic properties of polymers and the fluorescence piezospectroscopy of ruby provide a way to map the stress field efficiently at a small scale. In Digital Image Correlation Technique (DIC), the surface displacement field is determined from a comparison of the grey intensity changes of the object surface before and after deformation. The limitation of these methods is evident. As the signal is in the optical range, the penetration depth is small, and one can only provide surface images in the case of optically non-transparent materials.
Hence, it appears desirable to develop other piezospectroscopic methods but in a wavelengths range allowing for a better penetration of matter, such as the radio-frequency (RF) range. Nuclear Quadrupolar Resonance (NQR) is a RF spectroscopic technique that probes the Electrical Field Gradient (EFG) around quadrupolar nuclei in insulating or poorly conducting bulk materials. The EFG reflects the charge distribution in the crystal and is thus modified by a strain of the lattice under the influence of an external source of stress. Indeed, the Copper NQR signal in Cu2O has been used as a pressure gauge within pressurized fluids or compressed polymers. However, the corresponding applications have been limited to hydrostatic stress and the understanding of the underlying EFG-strain-stress coupling remains partial and mostly empirical.
We propose to revisit the stress-induced modification of the EFG at the copper site of Cu2O to gain a full understanding of this dependency through the comparison of first-principle calculations and well-controlled loading of macrocrystals in a specific micro-scale force apparatus fitted with a NQR probe. Thanks to this set-up and the efficiency of the most recent Density Functional Theory codes a complete understanding of the stress-NQR frequency dependency will be obtained, even in the case of non-hydrostatic stress. From the understanding gained on Cu2O, the rationale for finding new compounds with piezo-NQR properties will be derived.
In a second step, we will assemble a dedicated portable NQR set-up for collecting the distribution of NQR frequencies arising from Cu2O filler in a rubber matrix under various mechanical stresses. Building on the formal understanding gained in the first part of the project, we will aim at interpreting this frequency distribution in terms of the stress field within the rubber matrix. Finally, when successful, we will assess the practical application of NQR as a stress sensor and even as a stress field imager for the in-situ and nondestructive detection of failure in composites. In other words, in the foreseen industrial research follow-up to this basic research project, the dispersed particles would act as embedded micromechanical gauges.