Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Correlating toughness and roughness in ductile fracture   Three dimensional calculations of ductile crack growth under mode I plane
strain, small scale yielding conditions are carried out using an
elastic-viscoplastic constitutive relation for a progres- sively cavitating
plastic solid with two populations of void nucleating second phase particles.
Full field solutions are obtained for three dimensional material
microstructures characterized by ran- dom distributions of void nucleating
particles. Crack growth resistance curves and fracture surface roughness
statistics are calculated using standard procedures. The range of void
nucleating particle volume fractions considered give rise to values of
toughness, JIC, that vary by a factor of four. For all volume fractions
considered, the computed fracture surfaces are self-affine over a size range of
about two orders of magnitude with a roughness exponent of 0.54 $\pm$ 0.03. For
small void nucleating particle volume fractions, the mean large particle
spacing serves as a single dominant length scale. In this regime, the
correlation length of the fracture surface corresponding to the cut-off of the
self-affine behavior is found to be linearly related to JIC thus quantitatively
correlating toughness and fracture surface roughness.

23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex