PSI - Issue 13

Leonardo Giangiulio Ferreira de Andrade et al. / Procedia Structural Integrity 13 (2018) 1908–1914 Leonardo G. F. Andrade and Gustavo H. B. Donato / Structural Integrity Procedia 00 (2018) 000–000

1909

2

Nomenclature Latin a :

Crack depth ( mm ) a/W : Relative crack depth ( mm/mm ) a/W eq : Equivalent relative crack depth ( mm/mm ) B : Thickness ( mm ) C : Compliance ( mm/N ) C DELTA : Compliance variation ( % ) CMOD : Crack mouth opening displacement ( mm ) C(T) : Compact under tension specimen da/dN : Fatigue crack growth rate E : Elastic modulus ( GPa ) H : SE(T) daylight length ( mm ) J :

J integral. Non-linear energy release rate ( J/mm 2 )

K : n : P : T : V : W :

Stress intensity factor ( MPa.m 0.5 )

Hardening exponent

Load ( N )

Tunneling level ( mm )

T/B :

Relative tunneling level ( mm/mm ) Crack mouth opening displacement ( mm )

Width ( mm )

Greek β :

Weights for the points of measurement used for deter-mining the equivalent crack front

ν :

Poisson’s ratio

σ ys : ε ys :

Yield stress, 0.2% offset ( MPa ) Yield strain, 0.2% offset

1. Introduction The increasing demand for high strength and high toughness materials applicable to high responsibility components call the attention for the determination of accurate fracture mechanics properties to ensure safety. In special, J-R curves and da/dN vs. Δ K evolutions are usually of great relevance to support structural integrity assessments. However, such mechanical properties demand accurate real-time crack size measurements during tests, which, among other techniques, can be performed based on Elastic Unload Compliance ( EUC ), which is the correlation of the crack size ( a ) with specimen compliance ( C=V/P ) ( ASTM E1820 , 2018). Several phenomena may affect EUC accuracy, including stress triaxiality, side-grooves, specimen rotation, closure, crack tip plasticity and crack tip tunneling, and those can cause errors above 10% in compliance prediction. Additionally, spurious effects such as negative crack growth can be predicted with this technique, which is unrealistic and demand investigation. As a step to further improve the EUC technique, this paper investigates the effects of tunneling and plasticity on the EUC technique applied to SE(B) specimens of varying thicknesses and geometrical proportions. Tunneling is an effect that originates from the variation of stress states found in the center and on the edges of a specimen. In the central portion a more severe condition with high triaxiality can be detected, whereas on the edges a plane stress condition prevails. That difference in stress condition can cause the crack to grow deeper in the center and shallower in the edges, forming a crack front shape that resembles a semi-ellipse (Anderson, 2005). Studies addressing tunneling in Single-Edge notched under Bending - SE(B) - specimens can be found in the literature, being Steenkamp (1988) one of the first researchers to investigate this phenomenon. More recently, Yan and Zhou (2014) also conducted a similar investigation with modern simulation tools. Both studies concluded that compliance changes within ASTM limits were negligible and compliance would decrease as crack curvature increases for the same ASTM equivalent straight crack. However, a systematic study and correction proposals are open issues. The calculation of the ASTM equivalent straight crack follows instructions found on the ASTM E1820 standard (2018). A post-mortem analysis of the specimen is done, and crack depth is measured on nine equidistant points. An