Numerical methods in dynamic fracture mechanics

European Union

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Industrial research and development

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• Sciences et techniques

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• Publié par: EUROPEAN-UNION
• Nombre de lectures: 54
• Langue: English
• Poids de l'ouvrage: 2 Mo

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Commission of the European Communities
nuclear science and technology
NUMERICAL METHODS
IN DYNAMIC FRACTURE MECHANICS
Report
EUR 11300 EN
Blow-up from microti" ;£ original Commission of the European Communities
nuclear science and technology
NUMERICAL METHODS
IN DYNAMIC FRACTURE MECHANICS
D.E. BESKOS
(Visiting Scientist)
Commission of the European Communities
Joint Research Centre
1-21020 ISPRA (VARESE)
PARL EUROP. Tibficth.
Directorate-General Science, Research and Development
Joint Research Centre N.C./E
£
1987 ctUR 11300 EN Published by tht
COMMISSION OF THE EUROPEAN COMMUNITIES
Directorate-General
Telecommunications, Information Industries and Innovation
Bailment Jean Monnet
LUXEMBOURG
LEGAL NOTICE
Neither the Commission of the European Communities nor any person acting on behalf
of then is responsible for the use which might be made of the following
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ECSC—EEC—EAEC Brussels - Luxembourg, 1988 Ill
ABSTRACT
A review of numerical methods for the solution of dynamic problems
of fracture mechanics is presented. Finite difference, finite element
and boundary element methods as applied to linear elastic or visco-
elastic and non-linear elastoplastic or elastoviscoplastic dynamic
fracture mechanics problems are described and critically evaluated.
Both cases of stationary cracks and rapidly propagating cracks of
simple I, II, III or mixed modes are considered. Harmonically varying
with time or general transient dynamic disturbances in the form of
external loading or incident waves are taken into account. Determina­
tion of the dynamic stress intensity factor for stationary cracks or
moving cracks with known velocity history as well as determination of
the crack-tip propagation history for given dynamic fracture toughness
versus crack velocity relation are described and illustrated by means
of certain representative examples. Finally, a brief assessment of the
present state of knowledge is made and research needs are identified. CONTENTS
Page
1. INTRODUCTION 1
2. SOLID MECHANICS FUNDAMENTALS 6
3. BASIC ASPECTS OP DYNAMIC FRACTURE MECHANICS 16
4. NUMERICAL FORMULATIONS AND SOLUTIONS 23
5. FINITE DIFFERENCE METHODS 38
6. FINITE ELEMENT METHODS 4
7. BOUNDARY ELEMENT METHODS 54
8. NUMERICAL EXAMPLES AND APPLICATIONS
9. CONCLUSIONS AND RECOMMENDATIONS 63
ACKNOWLEDGEMENTS 65
REFERENCES7
FIGURES 81. INTRODUCTION
Dynamic fracture mechanics is a relatively new branch of fracture
mechanics which deals with the analysis of cracked solids and structures
that takes into account the effects of inertia forces. In general, any
dynamic boundary value problem involving rapid crack initiation, pro­
pagation, branching and/or arrest belongs to the realm of dynamic
fracture mechanics. More specifically, dynamic fracture mechanics
concerns itself with a) the study of bodies with stationary cracks sub­
jected to dynamic loading and the initiation of crack propagation, and
b) the study of bodies with rapidly propagating cracks subjected to
quasi-static or dynamic loading and the crack growth process and crack
arrest.
The importance of the subject for nuclear pressure vessels and piping,
ship hulls, gas transmission pipelines and other structures subjected
to agressive dynamic environments is well established (e.g. Francois,
1979; Kanninen, 1985; Kanninen & Popelar, 1985). The importance of
inertia effects in crack initiation and propagation has also been
demonstrated (e.g. Hahn et al , 1973; Achenbach, 1974; Kanninen, 1980;
Kalthoff, 1985). A number of analytical solutions of dynamic fracture
problems, which have been obtained during the last twenty years,
certainly help to understand the mechanics of the phenomena (e.g.
Achenbach, 1974,1977; Freund, 1976a & b, Rose, 1976). They are limited,
however, to simple loadings, simple material constitution and to plane
bodies with geometries of infinite extent in at least one direction.
Dynamic analysis of finite cracked solids of complex material beha­
viour and subjected to general types of loading can only be accomplished with the aid of numerical methods, which have seen extensive application
in the last ten years or so. Numerical methods are also frequently used
in a combined experimental-numerical fashion for the determination of
various material constants of the dynamic fracture phenomena.
The purpose of this work is basically to present a comprehensive
review of the various numerical methods that have been developed for
the dynamic analysis of cracked solids and structures, provide a criti­
cal appraisal of these methods with repsect to their accuracy, efficiency
and range of applicability and identify areas where further developments
are needed. The finite difference method (FDM), the finite element
method (FEM) and the boundary element method (BEM) are all treated in
this work. The need for such an undertaking is apparent in view of the
fact that information on the subject is either scattered in various
places or more often outdated or incomplete. Indeed, the first compre­
hensive review on the subject by Kanninen (1978) is almost ten years
old, while the more recent excellent reviews of Nilsson and Brickstad
(1983), Kobayashi (1984) and Atluri and Nishioka (1985) are generally
incomplete with respect to dynamic fracture by numerical methods.
Nilsson and Brickstad (1983) treat not only numerical methods but
analytical ones, as well as physical aspects of dynamic fracture, while
the work of Atluri and Nishioka (1985) is restricted to crack propa­
gation by the FEM only. Kobayashi's (1984) article represents a general
review on numerical methods for fracture analysis with some key re­
ferences on dynamic fracture by the FEM and the FDM.
Information about the FEM and the FDM as applied to dynamic frac­
ture mechanics problems can also be found, e.g., in the recent excellent