Supplementary figures

Height profile of a typical fracture surface. a, Profilometry measurement of the
fracture surface with the zoom-in view on the right. The highlighted dashed lines in the right panel are
where the height profiles are sampled. b, Height profiles of he dashed lines in b) with corresponding
colors. c, The height profiles is separated into low and high frequency part. The low frequency signal
is obtained using linear low pass filter with a cutoff frequency of 1/(2 × 4.28) radians/sec, where
4.28 μm is the z step size for most of the image stacks taken with confocal microscopy.

Comparison of image processing methods. a, Gc vs ̃L for different segmenta-
tion method. The same color represent the same image stack. The images are processed using
either Imaris and Fiji softwares with different parameters for the 3D Gaussian blur and the fractional
intensity levels used to threshold the image stacks, as described in the Materials and Methods. Seg-
mentation carried out with Imaris is indicated by triangle symbols. Combinatorial variation of the
Gaussian blur and threshold parameters is carried out with Fiji over a total of 31 unique parameter
sets each image stack. Segmented volumes are compared with the raw images to ensure correspon-
dence between the post-processes images and the original data. After segmentation, morphological
operations as described in Materials and Methods are used to obtain the final segmented volume
with the python package scikit-image[36]. b, Comparison of the same crack front curves segmented
by three different methods as highlighted in a.

Fitted data for CTOD measurement of crack interacting with rigid particle.
Fitted parabola of cracks a before and b after encountering the rigid inclusion, overlaid on the image
slices. Only the most left CTOD are used in the fitting in order to minimize the influence of the rigid
inclusion. The scale bars are 100 μm.