Fracture Stress Concentrators

FORSCHUNGSZENTRUM KARLSRUHE
Technik und Umwelt Wissenschaftliche Berichte

FZKA 6025

Stress intensity factors and weight functions for special crack problems

T. Fett

Institut für Materialforschung

Forschungszentrum Karlsruhe GmbH, Karlsruhe 1998

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Stress intensity factors and weight functions for special crack problems
Abstract:
The failure of cracked components isgoverned by the stresses in the vicinity of the crack tip. The singular stress contribution is characterised by the stress intensity factor K. Stress intensity factors depend on the geometry of the component and on the special loading conditions (tension, bending, thermal stresses,...). A procedure for their determination is the weight function technique where the weight functions are only dependent onthe crack geometry. Stress intensity factors and weight functions are reported for many practical problems in handbooks. In this report new solutions for stress intensity factors and weight functions are compiled in form of tables or approximate relations.

Spannungsintensitätsfaktoren und Gewichtsfunktionen für spezielle Rißprobleme
Kurzfassung:
Das Versagen von Bauteilen mit Rissen wird durchdie unmittelbar an der Rißspitze auftretenden Spannungen verursacht. Der singuläre Anteil diese Spannungen wird durch den Spannungsintensitätsfaktor K charakterisiert. Spannungsintensitätsfaktoren hängen von der Riß- und Bauteilgeometrie sowie von der speziellen Belastung (Zug, Biegung, Thermospannungen,...) ab. Eine Methode zur Bestimmung von Spannungsintensitätsfaktoren ist die Methode derGewichtsfunktionen. Diese sind nur von den Geometriedaten abhängig. Lösungen für Spannungsintensitätsfaktoren und Gewichtsfunktionen werden für viele praktisch relevante Fälle in Handbüchern angegeben. Im vorliegenden Bericht werden neue Ergebnisse in Form von Tabellen und Näherungsformeln mitgeteilt.

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Contents
1 Introduction
1.1 Stress intensity factor 1.2 Weight function 1 1 2 3 36 8 15 19 22 25 29 29 31 32 35 36

2 Cracks in rectangular plates or bars
2.1 The rectangular plate with an edge crack 2.2 Rectangular plate with an internal crack 2.3 Three-point bending test with eccentric load 2.4 The asymmetric 4-point bend test 2.5 Crack in the neighbourhood of opposite concentrated forces 2.6 Partially loaded rectangular plate with edge crack 2.7 Double-edge-crackedplate

3 Internally cracked circular disk
3.1 Mode-I loading 3.2 Mode-II loading 3.3 Mixed-mode loading (Brazilian disk test)

4 Double-edge-cracked circular disk 5 References

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1 Introduction
The fracture behaviour of cracked structures is dominated by the near-tip stress field. In fracture mechanics most interest is focussed on stress intensity factors, which describe the singularstress field ahead of a crack tip and govern fracture of a specimen when a critical stress intensity factor is reached. While stress intensity factor solutions are reported in handbooks [1-4] for many crack geometries and loading cases, weight functions are seldomly available [5-7]. In [7] a large number of stress intensity factor solutions were given, methods for the determination of weight functionswere reported and numerical results for a number of crack geometries were compiled. In the meantime, further crack problems have been evaluated which will be addressed in this report. For the published results the reference is given. All other data are unpublished results. Section 2 deals with cracks in rectangular plates and Section 3 provides data for circular disks.

1.1 Stress intensityfactor
For the determination of stress intensity factors the Boundary Collocation Method (BCM) was used and for the determination of the weight function the direct adjustment method [7] was applied. The stress intensity factor K is a measure for the singular stress term occurring near the tip of a crack and defined by K σ ij = f ij (ϕ ) 2πa where r and ϕ are polar coordinates with the origin at...