Sebastian Lindqvist
Abstract
Ageing nuclear power plants (NPP) require more accurate methods to assess the structural integrity of pipes. The accuracy of structural assessment methods of pipes can be increased by improving the accuracy of fracture toughness measurements of welds. In these measurements Ș-factor plays a crucial role. The Ș-factor is a parameter that relates the measured load-displacement data to the plastic strain energy. Currently, welds are assessed with Ș-factors developed for homogeneous specimens. Plastic Ș- factors developed specially for welds increase the accuracy of the fracture toughness measurements and the structural safety assessment methods. In this literature survey recently developed Ș-factors for similar metal welds are reviewed. The influence of different parameters, e.g. strength mismatch, on Ș-factor is considered.
1 Introduction
Integrity of pipes in nuclear power plants (NPP) is determined with leak-before-break (LBB) analysis. LBB is important for the design, safety and management of NPP piping. The LBB analysis requires knowledge of the weakest location in the pipe and the fracture toughness of this location.
The weakest location is normally in the weld region. Current safety standards consider the weakest locations to be in the HAZ and close to the fusion line. The reason for determining fracture toughness of HAZ is that brittle microstructures or zones with lower toughness are likely to occur close to the fusion line thereby obtaining lower resistance against crack extension (Donato et al. 2009). However, cracks can develop anywhere in the weldment, even in the weld metal.
The fracture toughness of the weakest location in a weld is determined with fracture toughness measurements (BS7448, ASTM 1290, ASTM 1820). In ASTM E1820 fracture resistance (J) of stationary cracks consists of an elastic component𝐽 , and a plastic component,𝐽 , (equation (1)). Equation (1) is derived for cracked specimens under Mode I deformation. The other standards follow the same principles as ASTM E1820.
𝐽 = 𝐽 + 𝐽 (1)
where
In equation (2) K is the elastic stress intensity factor for the cracked specimen, E is elastic modulus and𝛎 is Poisson’s ratio.
𝐾 = 𝑓( ) (3)
The plastic contribution to the strain energy is given in equation (4).
𝐽 = (4)
In equation 4𝐴 is the plastic area under the load-displacement curve (figure 1), 𝐵 is the net specimen thickness for a specimen with side grooves and b is the remaining ligament. Plastic Ș-factor is a dimensionless constant that relates the plastic contribution𝐴 to 𝐽 . The factor is assumed to be a function of the a/W ratio and independent of loading (Cravero & Ruggieri 2007).𝐴 can be defined in terms of load-load line displacement (LLD) data or load-crack mouth opening displacement (CMOD) data. Depending on the route the Ș-factor is either expressed as𝜂 or 𝜂 (Leonardo et al. 2013). The Ș values based on LLD have different character than Ș based on CMOD.
Figure 1. a) The plastic area under the load-displacement curve. (Leonardo et al. 2013)
ASTM E1820 and similar standards are developed for homogeneous specimens. The fracture toughness estimation equations in these fracture toughness standards are not necessary applicable to assess accurately fracture toughness of heterogeneous materials like welds. The problem of using the current fracture toughness standards results from the difference in deformation behaviour of homogeneous materials and welds. In homogeneous materials the plastic zone in front of the crack is symmetrical and of certain shape. In over- and undermatched welds the plastic zone can be discontinuous, unsymmetrical or forced into a smaller material volume (figure 2).
Figure 2. Heterogeneous fracture toughness specimens like welds have different regions (base metal, weld metal, HAZ) with varying material properties. The strength difference of the base metal and weld metal affects the measured fracture resistance. The ratio of the yield strength of the base metal,𝜎 , and the weld metal, 𝜎 , is known as strength mismatch (𝑀 ). The weld is said to be strength overmatched when 𝑀 >1 and strength undermatched when 𝑀 <1. (Koçak 2010)
For centerline cracked overmatched welds plastic deformation can occur in the base metal. In centreline cracked undermatched welds the plasticity is constrained to the weld. Unsymmetrical deformation zones are generated for cracks at the interface as seen in figure 2.
The deformation behaviour of over- and undermatched welds (figure 2) affects the measured CMOD in a way that is not characteristic for homogeneous materials. The measured CMOD can be suppressed or magnified by strength mismatch (Mw) condition in the heterogeneous specimen. This suppression or magnification of CMOD leads to under- or overestimations of the area under the load–displacement curve,𝐴 (figure 1). If the current fracture toughness standards are used to calculate Jpl from the measured Apl, then the results are inevitably inaccurate.
To calculate fracture toughness accurately from𝐴 for a weld Ș-factors developed for heterogeneous specimens are required. Heterogeneous Ș-factors can be derived from finite element (FE) analyses. Plastic Ș-factors derived for heterogeneous welds show in which cases it is absolutely necessary to apply heterogeneous solutions and in which cases homogeneous Ș-factors give a good approximation of the fracture toughness. (Paredes & Ruggieri 2012)
Accurate Ș-factors derived for welds are a function of strength mismatch, Mw (Xuan et al. 2005). As the properties of the weld metal are close to base metal properties, Ș- factors developed for homogeneous specimens can be used. The Ș-factors for welds with relatively high Mware expected to differ from the once derived for homogeneous specimens. Additionally, the Ș-factor can be affected by other parameters than Mw, like the weld width and configuration, crack location, strain hardening rate and the model used in FE calculations (Ruggieri 2012). To derive precise Ș-factors all of these parameters need to be taken into account. Precisely defined Ș-factors increase the accuracy of fracture toughness measurements of welds.
In this literature survey the main focus is on reviewing recently derived Ș-factors developed for similar metal welds where the weld metal has different properties than the base metal. The effect of different mechanical parameters, weld dimensions and finite element analysis routes on Ș-factor is considered.