**3. Results**

#### *3.1. In Situ Testing and Temperature Control*

Temperature readings from the thermocouple attached to the surface of the bone specimens suggested a consistent temperature gradient ( ΔT = 0.4 ◦C) at each exposure period (Figure 2a) corresponding to the opening (rise in temperature) and closing (drop in temperature) of the X-ray shutter. Small fluctuations in the temperature were recorded once the X-ray shutter was open, as they are more evident during tomographic acquisition compared to the steady position. However, those fluctuations were far less important than the temperate gradients recorded between consecutive tomographies. The stress-relaxation curves recorded during in situ testing showed that the X-ray beam significantly influenced the relaxation behaviour of the trabecular bone specimen at room temperature (Figure 2b). A consistent increase in the force was recorded after the start of each tomographic acquisition. This trend was not observed for the compact bone specimen.

**Figure 2.** (**a**) Temperature readings measured using a thermocouple attached to the compact and trabecular bone surface at room temperature. The solid line corresponds to thermocouple readings during ~15 min with the X-ray shutter opened and the thermocouple in the beam path. Dotted lines represent thermocouple readings during tomographic acquisition. The sudden drop and consequent rise in temperature coincide with the closing and opening of the X-ray shutter. (**b**) Force readings in trabecular bone specimen at room temperature during five consecutive tomograms. An increase in the force was observed and corresponded with the opening of the X-ray shutter.

#### *3.2. Compact Bone*

No damage was visually detected in the compact bone specimens after five tomograms, either at room temperature or 0 ◦C. The residual <sup>ε</sup>p<sup>1</sup> distribution (Figure 3) did not show any notable changes in the tissue after the acquisition of two (Figure 3a) and five (Figure 3b) tomograms, with some localised areas of higher residual strain in the specimen imaged at room temperature. The strain histograms (Figure 3c) showed peak values below 1000 με for both specimens, and no clear trends were observed between exposure to SR radiation and peak strain values. However, histograms showed tails with higher strains after five tomograms at room temperature compared to 0 ◦C. Similar findings were observed for the residual <sup>ε</sup>p<sup>3</sup> and γmax (Figure S2), suggesting a strain redistribution between consecutive tomographies, which did not cause important damage overall. Highly strained regions of the specimen tested at room temperature were localised around the Haversian and Volkmann's canals (Figure 4). Residual strain in a region of approximately 20 μm surrounding the canals was compared to the strain in the internal bone matrix volume. Particularly, the cumulative histograms of γmax (Figure 4e) after two and five acquired tomograms showed slightly higher strains around the canals for the same bone volume percentage.

**Figure 3.** Three-dimensional first principal strain (<sup>ε</sup>p1) distribution in compact bone tissue imaged at room temperature (top) and 0 ◦C (bottom) after two (**a**) and five (**b**) acquired tomograms. A representative cube (~1 mm3) in the centre of the analysed VOI is represented. Histograms of the residual strain distribution (**c**) in the tissue are shown for all the acquired tomograms.

**Figure 4.** Maximum shear strain (γmax) distribution in compact bone tissue imaged at room temperature. Cross-sections in 2D are shown after (**a**) two, (**b**) three, (**c**) four and (**d**) five acquired tomograms. Arrows indicate highly strained regions. A cumulative histogram of the residual strain (**e**) in the tissue voxels around the canals (solid lines) and the remaining bone matrix (dotted lines) is shown for after two and five tomograms.

#### *3.3. Trabecular Bone*

A visual inspection of the reconstructed images showed the presence of several microcracks after five tomograms, corresponding to ~80 min of total exposure to SR X-ray radiation, in the trabecular bone specimen at room temperature. However, decreasing the temperature to 0 ◦C facilitated tissue preservation, as microdamage was not observed. Furthermore, the high levels of residual strain measured with DVC correlated well with the microdamage visible from the images. The histograms of residual strain distributions (Figure 5) after each tomogram highlighted the differences between the two trabecular bone specimens. On one hand, the specimen imaged at room temperature showed a consistent increase in residual strain when increasing the exposure to X-ray radiation (Figure 5a–c). This trend was clearly observed in <sup>ε</sup>p<sup>1</sup> (Figure 5a), for which strain peak values increased from ~1500 to ~3000 με after two and five consecutive scans, respectively. <sup>ε</sup>p<sup>3</sup> (Figure 5b) peak values were found to be below −1500 με, whereas peak γmax (Figure 5c) ranged from ~2000 με to ~3500 με after two and five tomograms, respectively. The residual strain accumulation was less evident for the trabecular bone specimen maintained at 0 ◦C (Figure 5d–f). In fact, peak strain values remained below ±1000 με for <sup>ε</sup>p<sup>1</sup> (Figure 5d) and <sup>ε</sup>p<sup>3</sup> (Figure 5 e), respectively, and below 2000 με for γmax (Figure 5f) after five tomograms. The 3D full-field strain distribution in the trabecular bone (Figure 6) was accumulated in the tissue after each tomogram. In particular, for the specimen at room temperature (Figure 6, top), it could be seen that <sup>ε</sup>p<sup>1</sup> was increasing after each tomography, and regions of high residual strains after two full tomographies (Figure 6a, top) were progressively enlarged, reaching strain values of over 4000 με after five tomograms (Figure 6d, top). This strain accumulation was less pronounced in the specimen at 0 ◦C (Figure 6, bottom), although some areas of high strain concentration were observed after each tomogram. Furthermore, some strain redistributions could be seen after three (Figure 6b, bottom) and four (Figure 6c, bottom) full tomographies.

**Figure 5.** Histograms of the residual strain distribution in trabecular bone tissue imaged at room temperature (top) and 0 ◦C (bottom). (**<sup>a</sup>**,**d**) First principal strains (<sup>ε</sup>p1), (**b**,**<sup>e</sup>**) third principal strains (<sup>ε</sup>p3) and (**<sup>c</sup>**,**f**) maximum shear strains (γmax) after each acquired tomogram are shown.

**Figure 6.** Three-dimensional full-field first principal strain (<sup>ε</sup>p1) distribution in trabecular bone tissue imaged at room temperature (top) and 0 ◦C (bottom) after the acquisition of (**a**) two, (**b**) three, (**c**) four and (**d**) five consecutive tomograms. A representative cube (~1 mm3) in the centre of the analysed VOI is represented.

#### *3.4. Tracking of Crack Formation*

Microcracks were clearly visible in the trabecular bone specimen imaged at room temperature after five tomograms (Figure 7a,b). A region inside a trabecula (Figure 7b) was tracked during the in situ test to couple the residual strain accumulation with the crack formation. The displacement field around the damaged region (Figure 7c–f) suggested a relative motion between regions at both sides of the cracks since the earliest stages, before cracking was visible (Figure 7c–e). In fact, low displacements were found on one side, and those were mainly directed toward the positive z-direction, whereas, in the neighbouring side, displacements were progressively increased and reoriented toward the negative z-direction. After cracking (Figure 7f), displacements further increased around the crack, and a pronounced reorientation of their direction was observed. A deeper look at the displacement in the orthogonal planes (Figure 8), before and after crack formation, evidenced the discontinuities in the displacement field in proximity to the crack. Particularly, before crack formation (Figure 8a), displacement showed a high misorientation in the XY and XZ planes. After cracking (Figure 8b), the displacement field at one end of the crack was found perpendicular to the crack direction (XY plane), whereas it seemed aligned with the crack on the other end, which may indicate the further propagation direction. Both <sup>ε</sup>p<sup>1</sup> and γmax showed a progressive increase in the microcracked region, reaching values above 4000 με for <sup>ε</sup>p<sup>1</sup> (Figure 9b) and approximately 5000 με for γmax (Figure 10b) in the damaged area. In general, tensile strains were the most correlated to microdamage detection. In fact, the directions of <sup>ε</sup>p<sup>1</sup> (Figure 9) suggested a combination of tensile and shear modes of crack formation. In addition, the principal directions before cracking seemed to be highly disordered throughout the analysed volume. In particular, the highlighted vectors before cracking (Figure 9a) exhibited a very abrupt change in orientation, whereas the same areas after cracking (Figure 9b) were considerably aligned with the microcrack. γmax (Figure 10) increased after crack formation, and discontinuities at both sides of the crack were observed (Figure 10b). Moreover, higher shear strain levels were found at one side of the crack (XY plane), which also corresponded to principal strains and displacements perpendicular to the crack, thus possibly suggesting the direction of crack propagation.

**Figure 7.** Microcrack tracking in trabecular bone tissue imaged at room temperature. (**a**) Representative orthoslices and (**b**) 3D representation of the trabecular bone region tracked over time. Arrows indicate the microcracks visible in the tissue. (**<sup>c</sup>**–**f**) Digital volume correlation (DVC)-computed displacement field (V) in each subvolume on the analysed region of interest around a microcrack at different time points corresponding to the acquisition of (**c**) two, (**d**) three, (**e**) four and (**f**) five tomograms. Vector lengths are identical, and the colour code refers to the V magnitude in micrometres.

**Figure 8.** DVC-computed displacement field through the region of interest analysed around the microcracked area (**a**) before (fourth tomogram) and (**b**) after cracking was visible (fifth tomogram). Oval regions highlight damaged areas of bone tissue. Vector lengths are identical, and the colour code refers to the displacement vector length (V) in micrometres.

**Figure 9.** DVC-computed first principal strain (<sup>ε</sup>p1) through the region of interest analysed around the microcracked area (**a**) before (fourth tomogram) and (**b**) after cracking was visible (fifth tomogram). Vectors indicate first principal strain directions in each subvolume. Oval regions highlight damaged areas of bone tissue, which correspond to high orientation changes in the principal strain direction before and after cracking. Vector lengths are identical, and the colour code refer to the εp1 magnitude.

**Figure 10.** DVC-computed maximum shear strain (γmax) through the region of interest analysed around the microcracked area (**a**) before (fourth tomogram) and (**b**) after cracking was visible (fifth tomogram). Oval regions highlight damaged areas of bone tissue, which correspond to an increase in shear strain values before and after cracking. High discontinuities in shear strains were identified in the damage region (**b**), which may sugges<sup>t</sup> the direction of crack propagation.
