A finite element model with slip-oxidation is proposed for solving intergranular stress corrosion cracking (IGSCC) with duplex oxides replicating the cyclic physics of the slip oxidation. The purpose is to investigate the crack growth effect due to different rate, compositions and kinetics of the duplex oxide. The finite element model is based on a coupling between cohesive zone formulation, slip-oxidation model and a diffusion model. The cohesive zone formulation includes a degradation formulation which is linked to the slip-oxidation formulation. The environmental properties in the slip-oxidation were obtained from the diffusion modeled with Fick?s second law in one-dimension. This was then coupled to the structural model by a segregated solution scheme. The mesh of the cohesive zone adapts to the oxide thickness of the duplex oxide during the crack growth. The duplex oxide has the mathematical form of a power law or a logarithmic form. The model showed matching results for all duplex oxide combinations in varying stress, but the inner logarithmical oxide gave higher crack growth rates than the power law. The power law with the thicker inner oxide showed good results for the change of stress intensity factor and gave the best results when the yield stress was varied. Grain misorientation effect was higher for the duplex oxides with thicker outer oxides.

Adaptive oxide thickness was developed in a cohesive element based multi-physics model including a slip-oxidation and diffusion model. The model simulates the intergranular stress corrosion cracking (IGSCC) in boiling water reactors (BWR). The oxide thickness was derived from the slip-oxidation and updated in every structural iteration to fully couple the fracture properties of the cohesive element. The cyclic physics of the slip oxidation model was replicated. In the model, the thickness of the oxide was taken into consideration as the physical length of the cohesive element. The cyclic process was modelled with oxide film growth, oxide rupture, and re-passivation. The model results agreed with experiments in the literature for changes in stress intensity factor, yield stress representing cold work, and environmental factors such as conductivity and corrosion potential.

When assessing nuclear power plant life, stress corrosion cracking (SCC) plays an important role. Stress corrosion cracking in nuclear power plants is well recognized and heavily researched. Still due to its complicated nature it is not completely understood. There are many different damage mechanisms behind SCC. The focus in this thesis is on the slip-oxidation model. In the slip-oxidation model, the aggressive ions are diffused to the crack tip. In the crack tip the aggressive ions act as a catalyst to slow down the repassivation rate of the oxide film. At the crack tip the localized anodic dissolution occurred until an oxide film was produced to repassivate the corrosion process. Due to the constant stresses applied, the oxide film ruptured, and new virgin material was exposed to be dissolved and finally repassivated. This process is consequently repeated.   The first part of the work introduces a new formulation of a cohesive element with extended environmental degradation capability, which is essential to create the later SCC models. The new degradation method was evaluated against a Hydrogen Embrittlement (HE) experiment showing improved agreement with the experiment compared to the literature. The effect of different susceptibility zones at the crack tip was also investigated, showing that a uniform degradation throughout the susceptible zone is more influenced by the χ parameter than a triangular susceptible zone.  In the second part a phenomenological SCC model was created with the purpose to model primary water conditions in pressurized water reactors (PWR). It used the slip-oxidation model for considering SCC in boiling water reactors (BWR) under normal water chemistry (NWC).   The PWR model was implicit, coupled with a segregated solution scheme including a diffusion equation based on Fick’s second law and a cohesive zone description for the fracture mechanics part. The degradation was modelled with an anodic slip-dissolution equation that uses the effective cohesive traction and concentration as the main parameters. The model was evaluated against experiments on the effects of cold work on intergranular stress corrosion cracking (IGSCC). The model showed good agreements for both shifting amount of cold work illustrated by only changing the yield stress in the bulk material and for shifting the stress intensity factor. The model versatility was also shown by simulating IGSCC in Alloy600, also with good agreements.   The BWR model was multi-physical including a slip-oxidation, diffusion model and had adaptive oxide thickness developed into the cohesive element framework. The oxide thickness was derived from the slip-oxidation model and updated in every structural iteration to fully couple the fracture properties of the cohesive element. The cyclic physics of the slip oxidation model was replicated. The model results agreed with experiments in the literature for changes in the stress intensity factor, yield stress representing cold work and environmental factors such as conductivity and corrosion potential. The adaptive model was also expanded into a duplex oxide model with an inner and outer oxide. The model showed agreeing results with literature and the model was used to simulate different oxide growth kinetics

Spänningskorrosion (SCC) har stor inverkan vid bedömningen av kärnkraftverkens livslängd. Spänningskorrosionssprickor i kärnkraftverk är ett välkänt fenomen och är intensivt undersökta, men än i dag är den grundläggande orsaken inte helt förstådd pga. dess komplicerade natur. Det finns många olika skademekanismer bakom SCC. Fokus i denna avhandling ligger på slip-oxidation modellen. I slip-oxidation modellen diffunderar de aggressiva jonerna till sprickspetsen, de fungerar där som en katalysator för att bromsa återväxt av oxidfilmen. Vid sprickspetsen inträffar den lokaliserade anodiska upplösningen ända tills en oxidfilm byggts upp och passiverat korrosionsprocessen. En yttre last skapar konstanta spänningar, vilka i sin tur leder till att oxidfilmen spricker efter att ha växt ett tag. Detta skapar tillväxt av ny oxid och processen upprepas cykliskt.   I den första delen av arbetet introduceras en ny formulering av ett kohesivt element med utökad förmåga at simulera olika miljöförhållanden. Vilket ingår i de senare SCCmodellerna. Den nya degraderingsmetoden utvärderades mot ett väteförsprödningsexperiment (HE). Resultaten av simuleringarna med den nya modellen för degradering överensstämde bättre med experimentet än tidigare simuleringar i litteraturen.  I den andra delen skapades en fenomenologisk SCC-modell som är baserad på slipoxidation modellen. Den simulerar vattenkemin i primärkretsen hos tryckvattenreaktorer (PWR) och i kokvattenreaktorer (BWR) under normal vattenkemi (NWC).   PWR-modellen var implicit, med ett segregerad lösningsschema inklusive en diffusionsekvation baserad på Ficks andra lag och en kohesiv brottzonsbeskrivning för sprickmekanismen. Degraderingen simuleras med en anodisk slip-oxidation modell som använder den effektiva kohesiva normalkraften och koncentrationen av de aggressiva jonerna som huvudparametrar. Modellen utvärderades mot experiment som visar effekten av kallbearbetning på intergranulär spänningskorrosion (IGSCC). Modellen överensstämmer för skiftande mängd kallbearbetning, vilket illustrerades genom att endast ändra flytspänningen i bulkmaterialet. Modellen överensstämde även för olika spänningsintensitetsfaktorer. Mångsidigheten av modellen illustrerades genom att simulera IGSCC i Alloy600, även det med bra överenstämmelse.  BWR-modellen är en multifysikmodell som bygger på en slip-oxidation modell, diffusionsmodell och en adaptiv oxidtjocklek som utvecklats i det kohesiva elementet. Oxidtjockleken utgick från slip-oxidationsmodellen och uppdaterades i varje strukturell iteration för att helt koppla samman det kohesiva elementets sprickegenskaper. Den cykliska fysiken i slip-oxidationsmodellen replikerades. Modellresultaten överensstämde med experiment i litteraturen för förändringar i stressintensitetsfaktor, flytspänning som representerar kallbearbetning och miljöfaktorer som konduktivitet och korrosionspotentialen. Den adaptiva oxidmodellen utvecklades också till en duplex modell där två oxider simulerades. Den totala oxiden delades upp i en inre oxid med både logaritmisk och exponentiell tillväxtlag och en yttre oxid som styrdes av slip-oxidationsmodellens totala oxidation.

A multi-physics model was developed to simulate intergranular stress corrosion cracking (IGSCC) in austenitic stainless steel. The model is implicit, coupled with a segregated solution scheme including a diffusion equation based on Fick's second law and a cohesive zone description for the fracture mechanics part. The degradation is modelled with an anodic slip-dissolution equation that uses the effective cohesive traction and concentration as the main parameters. The diffusivity in Fick's second law creates a moving boundary. The cohesive zone is modelled using the PPR model with extended degradation properties using the degradation parameter chi. The model was evaluated against experiments on the effects of cold work on IGSCC. The model showed good agreements for both shifting amount of cold work, illustrated by only changing the yield stress in the bulk material and for shifting the stress intensity factor. The model versatility was also shown by simulating IGSCC in Alloy 600, also with good agreements. The change in the bulk material made crack propagation more disadvantageous for the lower yield stress where the crack blunts, creates more plastic strain and lowers the cohesive traction. The model predicts that cold work of the bulk material creates a faster crack growth velocity due to lower amount of plastic deformation in the bulk and higher cohesive traction. The higher crack growth rate is a coupled effect of both fracture and oxidation properties.

A cohesive element with extended environmental degradation capability was developed and implemented into an Abaqus user element. The element uses a virgin and a fully degraded Traction Separation Law (TLS) as input. The use of the potential based PPR model enables flexibility in the softening shapes for both TSL. When the element is degraded, the TSL gradually goes from the shape of the virgin material to the fully degraded TSL shape. This transition was made with a new parameter. that can govern a more ductile or brittle crack growth behaviour at degradation. The effect on the plastic zone due to changing the softening shape is shown, where the convex shaped softening TSL gives higher plastic dissipation and larger plastic zones than the concave and more brittle TSL. The new degradation method was evaluated against a Hydrogen Embrittlement (HE) experiment showing improved agreement with the experiment compared to the literature. The effect of different susceptibility zones at the crack tip was also investigated, showing that a uniform degradation throughout the susceptible zone is more influenced by the. parameter than a triangular susceptible zone.

A model has been developed to predict crack growth velocities at IGSCC for varied stress and ion concentration. The model is a coupling between Fick's second law and a newly developed cohesive element with degradation of damage resisting properties, implemented into a user element in ABAQUS. High stresses at the crack tip are assumed to drive the corrosion process and change the diffusivity. The stress and ion concentrations are varied which shows that higher stresses or higher ion concentrations gives different oxide thicknesses and higher crack propagation velocities.

A fracture mechanic and diffusion model was coupled to simulate the behavior of Intergranular Stress Corrosion Cracking (IG-SCC). To ensure correct physical behavior some assumptions were made, the ion travel, the non-reversible adsorption, the oxide growth dependencies and the diffusion dependency on damage. The model was implemented in a user subroutine in ABAQUS using a cohesive element formulation and an extra adsorption term in Fick’s second law. The coupling was achieved by assuming proportionality between the total adsorption and fracture energy. The physical assumtion were verified on a DCB model.

A finite element model with slip-oxidation is proposed for solving intergranular stress corrosion cracking (IGSCC) with duplex oxides. The purpose is to investigate the crack growth effect due to different rate, compositions and kinetics of the duplex oxide. The finite element model is based on a coupling between cohesive zone formulation, slip-oxidation model and a diffusion model. The cohesive zone formulation includes a degradation formulation which is linked to the slip-oxidation formulation. The environmental properties in the slip-oxidation were obtained from the diffusion modeled with Fick’s second law in onedimension. This was then coupled to the structural model by a segregated solution scheme. The mesh of the cohesive zone adapts to the oxide thickness of the duplex oxide during the crack growth. The duplex oxide has the mathematical form of a power law or a logarithmic form. The model showed matching results for all duplex oxide combinations in varying stress, but the inner logarithmical oxide gave higher crack growth rates than the power law. The power law with the thicker inner oxide showed good results for the change of stress intensity factor and gave the best results when the yield stress was varied. Grain misorientation effect was higher for the duplex oxides with thicker outer oxides

A finite element framework with mesh adaptivity was developed to simulate the oxide growth of the intergranular stress corrosion cracking (IGSCC). In particular, the environment of boiling water reactors (BWR) in combination with austenitic stainless steel and constant stress was studied. The model is interdisciplinary, it is a combination of a cohesive element fracture model, electrochemical slip-oxidation model and Fick’s second law as the diffusion model. The cyclic physics of the slip oxidation model was replicated. In the model, the thickness of the oxide was taken into consideration as the physical length of the cohesive element. The cyclic process was modelled with oxide film growth. Oxide rupture occurred due to degradation of the fracture energy. The degradation is a result of both external traction and diffusion of aggressive ions. The rate of degradation is defined by a variety of parameters as material properties, electrochemical properties and diffusivity. Next, the re-passivation will be initiated by the mesh adaptivity framework. The model was solved with a staggered solution scheme and the mesh adaptivity was set every Newton-Raphson trial. The model results agreed with experiments in the literature for changes in stress intensity factor, yield stress representing cold work and environmental factors such as conductivity and corrosion potential. The model also shows cost effective predicting, which is useful for larger simulation or optimization situations.