eprintid: 1969
rev_number: 7
eprint_status: archive
userid: 56
dir: disk0/00/00/19/69
datestamp: 2013-11-29 11:48:33
lastmod: 2014-10-09 09:20:25
status_changed: 2013-11-29 11:48:33
type: article
metadata_visibility: show
creators_name: Ciavarella, Michele
creators_name: Paggi, Marco
creators_name: Carpinteri, Alberto
creators_id: 
creators_id: marco.paggi@imtlucca.it
creators_id: 
title: One, no one, and one hundred thousand crack propagation laws: a generalized Barenblatt and Botvina dimensional analysis approach to fatigue crack growth 
ispublished: pub
subjects: TJ
divisions: CSA
full_text_status: none
keywords: Fatigue crack growth; Paris’ law parameters; Dimensional analysis; Complete and incomplete self-similarity; Size-scale effects
abstract: Barenblatt and Botvina with elegant dimensional analysis arguments have elucidated that Paris’ power-law is a weak form of scaling, so that the Paris’ parameters C and m should not be taken as material constants. On the contrary, they are expected to depend on all the dimensionless parameters of the problem, and are really “constants” only within some specific ranges of all these. In the present paper, the dimensional analysis approach by Barenblatt and Botvina is generalized to explore the functional dependencies of m and C on more dimensionless parameters than the original Barenblatt and Botvina, and experimental results are interpreted for a wider range of materials including both metals and concrete. In particular, we find that the size-scale dependencies of m and C and the resulting correlation between C and m are quite different for metals and for quasi-brittle materials, as it is already suggested from the fact the fatigue crack propagation processes lead to m = 2 – 5 in metals and m = 10 – 50 in quasi-brittle materials. Therefore, according to the concepts of complete and incomplete self-similarities, the experimentally observed breakdowns of the classical Paris’ law are discussed and interpreted within a unified theoretical framework. Finally, we show that most attempts to address the deviations from the Paris’ law or the empirical correlations between the constants can be explained with this approach. We also suggest that “incomplete similarity” corresponds to the difficulties encountered so far by the “damage tolerant” approach which, after nearly 50 years since the introduction of Paris’ law, is still not a reliable calculation of damage, as Paris himself admits in a recent review. 
date: 2008
date_type: published
publication: Journal of the Mechanics and Physics of Solids
volume: 56
number: 12
publisher: Elsevier
pagerange: 3416 - 3432
id_number: 10.1016/j.jmps.2008.09.002
refereed: TRUE
issn: 0022-5096
official_url: http://www.sciencedirect.com/science/article/pii/S002250960800149X
citation:   Ciavarella, Michele and Paggi, Marco and Carpinteri, Alberto  One, no one, and one hundred thousand crack propagation laws: a generalized Barenblatt and Botvina dimensional analysis approach to fatigue crack growth.  Journal of the Mechanics and Physics of Solids, 56 (12).  3416 - 3432.  ISSN 0022-5096      (2008)