## 2 Materials and Methods  
The carbon fiber composite material selected to manufacture the lap shear and end notch flexure (ENF) samples was a unidirectional prepreg material (T800H) from Toray. Following ASTM D5868-01 [17] and ASTM D7905/7905M [18] standards for the manufacturing process, the lap shear specimens had a 12-layer layup process and the end notch flexure specimens had a 10-layer layup process. A polyester peel ply was placed on both sides of the prepreg layups to prepare the surface for bonding. An autoclave from Amer  
Figure 1: Possible sample loading history influences on the output magnetic signal of MEN-doped adhesives. ican Company Co. was used to cure the prepreg layup at a temperature of 177 \({}^{\circ}\)C and a pressure of 30 psi for 1 hour. The lap shear specimens were cut to a size of 25.4 mm by 177.8 mm, with a bonded area of 25.4 mm by 25.4 mm, while ENF specimens were manufactured to be 35 mm by 10 mm. The carbon fiber panels were bonded together using 3M's Scotch-Weld two-part epoxy adhesive EC 2615 B/A. A 2:1 resin-to-hardener ratio was used. For the doped adhesive, MENs, synthesized to consist of a cobalt ferrite (CoFe\({}_{2}\)O\({}_{4}\)) core and barium titanate (BaTiO\({}_{3}\)) shell nanoparticles with a median diameter of \(\sim\)30 nm [19], were hand-mixed into the hardener component of the epoxy at a 1% volume concentration prior to curing. The fabrication and characterization of the MENs used in this study has also been discussed previously [14; 15]. Both ENF and lap shear specimens were placed under vacuum during the adhesive cure in order to minimize void content. Next, the same epoxy adhesive was used to manufacture the tensile-testing dog-bone samples. The lap shear specimens were tested using the ASTM D5868-01 standard [17]. A tensile tester from MTS (Criterion Model 43) was used to test the samples with a loading rate of 13 mm/min. The dog-bone tensile-testing samples were tested at a rate of 5 mm/min using the same MTS instrument using ASTM D638-03 [20]. ENF testing was performed conforming to ASTM D7905/7905M [19] using an MTI Instruments SEM 1000 micro-load frame in a three-point bend configuration. Testing was performed at a fixed displacement rate of 0.5 mm/min. The supporting span was 50 mm, while the sample was 120 mm in length and 3.5 mm in thickness and contained a 25 mm pre-crack. In situ ENF testing was performed within the chamber of a JEOL JIB-4500 SEM/FIB under vacuum at a pressure of 1.4 \(\times\) 10\({}^{-4}\) Pa or below after Au coating the sample for 30 s. Uncertainty measurements were obtained using the law of propagation of uncertainty [21]. To obtain the mode II critical energy release rate, G\({}_{\text{IIC}}\), in kJ/m\({}^{2}\) of the ENF samples, Equation (1) was used as follows [22]:  
\[\text{G}_{\text{II}}=\frac{9a^{2}P\delta}{2\beta(2l^{3}+3a^{3})} \tag{1}\]  
where \(a\) is the pre-crack in meters, \(P\) is the load in kN, \(\delta\) is the displacement of the pre-crack, \(\beta\) is the width of the ENF samples in meters, and \(l\) is the distance between the two bottom points from the three-point bend test fixture, which is fixed at 0.0165 m.  
To study the curing process of the 3M epoxy adhesive, three 8 \(\times\) 8 \(\times\) 4 mm samples were manufactured containing 5 vol% of MENs. This volume percentage was used since the manufacturing process with the resources available was time-consuming, but a higher percentage than the previous 1% used for the lap shear and ENF samples was used to obtain a higher signal using the B-H looper setup. The curing and testing process took place in a laboratory environment at room temperature (\(\sim\)22 \({}^{\circ}\)C). Signal measurements during the curing process were taken every 2 hours using the B-H looper setup, which is described later in this section.