A MICROSTRUCTURE-BASED PROBABILISTIC MODEL FOR CLEAVAGE IN RPV STEELS

Abstract

ABSTRACT In both simple ferrite-carbide materials, and more complex ferritic steels, cleavage is mediated by the fracture of the particles they contain. If particle cracking is easy, then extension of the resulting particle-sized microcracks into the ferrite matrix, can become the critical step in inducing fracture. Under these circumstances, brittle fracture is essentially stress-controlled, and several models use this as a basis for failure prediction. Fracture toughness data from a series of MnMoNi steels are presented, together with observations of fracture initiation sites, and calculations of the stresses and strains pertaining to these locations at failure, to show that there are circumstances under which particle cracking is not easy. A strain criterion is found to describe the probability of particle cracking effectively. A previouslypublished, stress-based model is generalised to include the strain criterion. The more general model correlates initiation site properties with K, and predicts a marked temperaturedependence of K (i.e. a ductile-to-brittle transition), even though the only temperature-dependent input parameters are the flow properties. Other input parameters for the model are linked explicitly to the microstructure. The relative dominance of particle cracking and microcrack extension in cleavage depends most strongly on initiating particle type, and final quench severity. Keywords Cleavage, reactor pressure vessel steel, model Nomenclature A * Critical area over which σ * must be exceeded in RKR model DBT ductile-to-brittle transition DBTT ductile to brittle transition temperature E Young's modulus of matrix F Fraction of particles taking part in fracture K Facture toughness n work hardening exponent N particles number density P(c ) probability that a particle in a volume element has cracked P f probability of failure P(r 0 ) probability that r>r 0 P(r max >r≥r 0 ) probability that r is between r max and r 0 P(ε particle ≥ε min ) probability that the strain in the particle is greater than ε min P(µe) probability of microcrack extension r size of particle / microcrack r 0 size of microcrack which will extend under locallyapplied stresses r max maximum size of particle remaining uncracked after quenching T temperature T ∞ temperature at which cleavage becomes impossible X distance ahead of precrack tip X c distance between precrack tip and fracture initiation site X p location of peak in tensile stress field X(r=r max )location at which r=r ma