A micromechanics approach to assess effects of constraint on cleavage fracture toughness: a weibull stress model

Claudio Ruggieri Claudio Ruggieri University of São Paulo Dept. of Naval Arch. and Ocean Engineering PNV – EPUSP 05508-030 São Paulo, SP, Brazil A Micromechanics Approach to Assess Effects of Constraint on Cleavage Fracture Toughness: a Weibull Stress Model This work describes an engineering methodology incorporating the statistics of microcracks and a probability distribution of the (local) fracture stress to assess the effects of constraint loss and weld strength mismatch on crack-tip driving forces. One purpose of this investigation is to establish a definite fracture assessment framework capable of providing robust correlations between toughness data measured using small, laboratory specimens to large, complex structural components with varying crack configurations and loading modes (tension vs. bending). Another purpose is to verify the effectiveness of the proposed methodology building upon a local fracture parameter, here characterized by the Weibull stress, in structural integrity assessments of cracked components including steel weldments. Overall, the exploratory applications conducted here lend strong support to use Weibull stress based procedures in defect assessments of cracked structures. Keywords: cleavage fracture, local approach, Weibull stress, constraint effect, weld strength mismatch Introduction 1 The fundamental importance of cleavage fracture behavior in structural integrity assessments has stimulated a rapidly increasing amount of research on predictive methodologies for quantifying the impact of defects in load-bearing materials such as, for example, cracks in critical weldments of high pressure vessels. Such methodologies play a key role in repair decisions and life-extension programs for in-service structures (e.g., aerospace, nuclear and offshore structures) while, at the same time, ensuring acceptable safety levels during normal operation. For ferritic materials at temperatures in the ductile-to-brittle transition (DBT) region, fracture by transgranular cleavage along well defined, low index crystallographic planes (see, e.g., Averbach, 1965 and Tetelman and McEvily, 1967) is the dominant operative micromechanism. This failure mode potentially limits the load bearing capacity of the structure as local crack-tip instability may trigger catastrophic failure at low applied stresses with little plastic deformation. Conventional methods of fracture mechanics analysis employ a one-parameter characterization of loading and toughness, most commonly the J-integral or the corresponding value of the Crack Tip Opening Displacement (CTOD, δ). The approach correlates unstable crack propagation in different cracked bodies based on the similarity of their respective near-tip stress and strain fields provided small scale yielding (SSY) conditions prevail. Under these conditions, near-tip plastic deformation is well-contained with plastic zones vanishingly small compared to the relevant physical dimensions in fracture specimens and structural components such as crack length, remaining ligament, etc. (see, e.g., the review by Hutchinson, 1983). However, the stress histories that develop in the near-tip region of a macroscopic crack in engineering structures containing shallow cracks are more often of different character than those for the high constraint SSY condition. At increasing levels of loading and deformation, large scale yielding conditions (LSY) gradually develop at the crack tip region, which relax the near-tip stress fields below the SSY levels, particularly for moderate-to-low hardening materials. The decreased level of crack-tip constraint and the strong interaction of remote loading with near-tip plasticity potentially cause significant elevations (factors exceeding 3~5) in the elastic-plastic fracture toughness for shallow crack configurations of ferritic steels tested in the transition region, where transgranular cleavage triggers macroscopic fracture. The enormous practical implications of this apparent increased toughness of common ferritic steels in low-constraint conditions, particularly in defect assessment and repair decisions of in-service structures, have spurred a flurry of new analytical, computational and experimental research over the past years. More recent efforts within the framework of continuum fracture mechanics have focused on the development of two-parameter fracture methodologies to describe the full range of Mode I, elasticplastic crack-tip fields with varying near-tip stress triaxiality. Within these methodologies, J sets the size scale over which large stresses and strains develop, while the second parameter, such as the T stress (Al-Ani and Hancock, 1991; Betegon and Hancock, 1991; Du and Hancock, 1991; Parks, 1992) or the nondimensional Q parameter (O'Dowd and Shih, 1991, 1992), scales the near-tip stress distribution. The approach also enables the introduction of a toughness locus for a specific material and temperature in connection with a J-Q driving force trajectory for each crack geometry; here, the toughness locus for the material is constructed upon determining the Q-value at fracture which corresponds to each measured J c -value (O'Dowd and Shih, 1991, 1992). However, the large number of fracture specimens and different temperatures needed to construct the J-Q toughness locus greatly complicate direct implementation of this approach to fracture assessments as does the application of the method (which derives from a 2-D framework) to fully 3-D crack geometries. Moreover, such models do not address the strong sensitivity of cleavage fracture to material characteristics at the microlevel nor do they provide a means to predict the effects of constraint and prior ductile tearing on toughness. In particular, the random inhomogeneity in local features of the material causes large scatter in experimentally measured values of fracture toughness ( J c , δ c or CTOD). Such features do assessments of structural integrity using laboratory testing of standard specimens and simplified crack configurations to a complex task: what is the “actual" material toughness and how is the scatter in measured values of fracture toughness incorporated in defect assessment procedures? Paper accepted June, 2010. Technical Editor: Nestor A. Zouain Pereira. J. of the Braz. Soc. of Mech. Sci. & Eng. Copyright © 2010 by ABCM October-December 2010, Vol. XXXII, No. 4 / 475 Claudio Ruggieri The above arguments that continuum fracture mechanics approaches do not suffice to characterize the fracture behavior of fully yielded crack geometries motivated the development of micromechanics models based upon a probabilistic interpretation of the fracture process (most often referred to as local approaches). Attention has been primarily focused on probabilistic models incorporating weakest link statistics to describe material failure caused by transgranular cleavage. In the context of probabilistic fracture mechanics, a limiting distribution (...truncated)