Modeling of Oxygen Diffusion Along Grain Boundaries in a Nickel-Based Superalloy

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
L. G. Zhao
Keyword(s):  
Finite Element ◽  
Oxygen Diffusion ◽  
Bulk Material ◽  
Hydrostatic Stress ◽  
High Stress ◽  
Great Influence ◽  
Crack Tip ◽  
Oxygen Diffusivity ◽  
Nickel Based Superalloy ◽  
Pressure Factor

Finite element analyses of oxygen diffusion at the grain level have been carried out for a polycrystalline nickel-based superalloy, aiming to quantify the oxidation damage under surface oxidation conditions at high temperature. Grain microstructures were considered explicitly in the finite element model where the grain boundary was taken as the primary path for oxygen diffusion. The model has been used to simulate natural diffusion of oxygen at temperatures between 650∘C and 800∘C, which are controlled by the parabolic oxidation rate and oxygen diffusivity. To study the effects of mechanical stress on oxygen diffusion, a sequentially coupled deformation-diffusion analysis was carried out for a generic specimen geometry under creep loading condition using a submodeling technique. The material constitutive behavior was described by a crystal plasticity model at the grain level and a unified viscoplasticity model at the global level, respectively. The stress-assisted oxygen diffusion was driven by the gradient of hydrostatic stress in terms of pressure factor. Heterogeneous deformation presented at the grain level imposes a great influence on oxygen diffusion at 750∘C and above, leading to further penetration of oxygen into the bulk material. Increased load level and temperature enhance oxygen concentration and penetration within the material. At 700∘C and below, mechanical loading seems to have negligible influence on the oxygen penetration because of the extremely low values of oxygen diffusivity and pressure factor. In the case of an existing surface microcrack, oxygen tends to accumulate around the crack tip due to the high stress level presented near the crack tip, leading to localized material embrittlement and promotion of rapid crack propagation.

The Influence of Loading Position in A Priori High Stress Detection using Mode Superposition

2020 ◽  
Vol 1 (1) ◽  
pp. 93-102
Author(s):  
Carsten Strzalka ◽  
◽  
Manfred Zehn ◽  
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
A Priori ◽  
High Stress ◽  
Von Mises Stress ◽  
Detailed Knowledge ◽  
Variable Loading ◽  
Numerical Effort ◽  
Von Mises

For the analysis of structural components, the finite element method (FEM) has become the most widely applied tool for numerical stress- and subsequent durability analyses. In industrial application advanced FE-models result in high numbers of degrees of freedom, making dynamic analyses time-consuming and expensive. As detailed finite element models are necessary for accurate stress results, the resulting data and connected numerical effort from dynamic stress analysis can be high. For the reduction of that effort, sophisticated methods have been developed to limit numerical calculations and processing of data to only small fractions of the global model. Therefore, detailed knowledge of the position of a component’s highly stressed areas is of great advantage for any present or subsequent analysis steps. In this paper an efficient method for the a priori detection of highly stressed areas of force-excited components is presented, based on modal stress superposition. As the component’s dynamic response and corresponding stress is always a function of its excitation, special attention is paid to the influence of the loading position. Based on the frequency domain solution of the modally decoupled equations of motion, a coefficient for a priori weighted superposition of modal von Mises stress fields is developed and validated on a simply supported cantilever beam structure with variable loading positions. The proposed approach is then applied to a simplified industrial model of a twist beam rear axle.

scholarly journals Size Effects in Finite Element Modelling of 3D Printed Bone Scaffolds Using Hydroxyapatite PEOT/PBT Composites

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1746
Author(s):  
Iñigo Calderon-Uriszar-Aldaca ◽  
Sergio Perez ◽  
Ravi Sinha ◽  
Maria Camara-Torres ◽  
Sara Villanueva ◽  
...  
Keyword(s):  
Finite Element ◽  
Additive Manufacturing ◽  
Tissue Regeneration ◽  
Finite Element Modelling ◽  
Bulk Material ◽  
Bone Tissue Regeneration ◽  
Patient Specific ◽  
Design Factor ◽  
Element Modelling ◽  
Uncertainty Sources

Additive manufacturing (AM) of scaffolds enables the fabrication of customized patient-specific implants for tissue regeneration. Scaffold customization does not involve only the macroscale shape of the final implant, but also their microscopic pore geometry and material properties, which are dependent on optimizable topology. A good match between the experimental data of AM scaffolds and the models is obtained when there is just a few millimetres at least in one direction. Here, we describe a methodology to perform finite element modelling on AM scaffolds for bone tissue regeneration with clinically relevant dimensions (i.e., volume > 1 cm3). The simulation used an equivalent cubic eight node finite elements mesh, and the materials properties were derived both empirically and numerically, from bulk material direct testing and simulated tests on scaffolds. The experimental validation was performed using poly(ethylene oxide terephthalate)-poly(butylene terephthalate) (PEOT/PBT) copolymers and 45 wt% nano hydroxyapatite fillers composites. By applying this methodology on three separate scaffold architectures with volumes larger than 1 cm3, the simulations overestimated the scaffold performance, resulting in 150–290% stiffer than average values obtained in the validation tests. The results mismatch highlighted the relevance of the lack of printing accuracy that is characteristic of the additive manufacturing process. Accordingly, a sensitivity analysis was performed on nine detected uncertainty sources, studying their influence. After the definition of acceptable execution tolerances and reliability levels, a design factor was defined to calibrate the methodology under expectable and conservative scenarios.

Finite Element Modeling of Damage Formation in Rubber-Toughened Polymer

2005 ◽  
Vol 297-300 ◽  
pp. 1019-1024
Author(s):  
Mitsugu Todo ◽  
Yoshihiro Fukuya ◽  
Seiya Hagihara ◽  
Kazuo Arakawa
Keyword(s):  
Finite Element ◽  
Damage Zone ◽  
Damage Model ◽  
Crack Tip ◽  
Optical Microscope ◽  
Toughening Mechanism ◽  
Element Analysis ◽  
Zone Formation ◽  
Macro Scale ◽  
Rubber Toughened

Microscopic studies on the toughening mechanism of rubber-toughened PMMA (RTPMMA) were carried out using a polarizing optical microscope (POM) and a transmission electron microscope (TEM). POM result showed that in a typical RT-PMMA, a damage zone was developed in the vicinity of crack-tip, and therefore, it was considered that energy dissipation due to the damage zone development was the primary toughening mechanism. TEM result exhibited that the damage zone was a crowd of micro-crazes generated around rubber particles in the vicinity of notch-tip. Finite element analysis was then performed to simulate such damage formations in crack-tip region. Macro-scale and micro-scale models were developed to simulate damage zone formation and micro-crazing, respectively, with use of a damage model. It was shown that the damage model introduced was successfully applied to predict such kind of macro-damage and micro-craze formations.

Investigation on Stress and Strain Singularity in LEFM

2006 ◽  
Vol 306-308 ◽  
pp. 31-36
Author(s):  
Zheng Yang ◽  
Wanlin Guo ◽  
Quan Liang Liu
Keyword(s):  
High Stress ◽  
Crack Tip ◽  
Plane Stress State ◽  
Stress And Strain ◽  
Linear Elastic ◽  
Geometrical Nonlinear ◽  
Maximum Crack ◽  
Elastic Fracture ◽  
Plain Strain ◽  
Strain Singularity

Stress and strain singularity at crack-tip is the characteristic of Linear Elastic Fracture Mechanics (LEFM). However, the stress, strain and strain energy at crack-tip may be infinite promoting conflicts with linear elastic hypothesis. It is indicated that the geometrical nonlinear near the crack-tip should not be neglected for linear elastic materials. In fact, the crack-tip blunts under high stress and strain, and the singularity vanishes due to the deformation of crack surface when loading. The stress at crack-tip may still be very high even though the singularity vanishes. The low bound of maximum crack-tip stress is the modulus of elastic in plane stress state, while in plain strain state, it is greater than the modulus of elastic, and will increase with the Poisson’s ratio.

Finite Element Simulation of Stable Fatigue Crack Growth Using Critical CTOD Determined by Preliminary Finite Element Analysis

2014 ◽  
Vol 891-892 ◽  
pp. 1675-1680
Author(s):  
Seok Jae Chu ◽  
Cong Hao Liu
Keyword(s):  
Finite Element ◽  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Finite Element Simulation ◽  
Crack Growth ◽  
Crack Tip ◽  
Stress Intensity Factor Range ◽  
Crack Tip Opening Displacement ◽  
Element Analysis ◽  
Element Simulation

Finite element simulation of stable fatigue crack growth using critical crack tip opening displacement (CTOD) was done. In the preliminary finite element simulation without crack growth, the critical CTOD was determined by monitoring the ratio between the displacement increments at the nodes above the crack tip and behind the crack tip in the neighborhood of the crack tip. The critical CTOD was determined as the vertical displacement at the node on the crack surface just behind the crack tip at the maximum ratio. In the main finite element simulation with crack growth, the crack growth rate with respect to the effective stress intensity factor range considering crack closure yielded more consistent result. The exponents m in the Paris law were determined.

Atomistic Study of Cleavage and Dislocation Emission in NiAl

1994 ◽  
Vol 364 ◽  
Author(s):  
M. Ludwig ◽  
P. Gumbsch
Keyword(s):  
Finite Element ◽  
Mixed Mode ◽  
Crack Tip ◽  
Mode I ◽  
Crack Plane ◽  
Dislocation Emission ◽  
Dislocation Generation ◽  
Embedded Atom ◽  
Atomistic Study ◽  
Eam Potential

AbstractThe atomistic processes during fracture of NiAl are studied using a new embedded atom (EAM) potential to describe the region near the crack tip. To provide the atomistically modeled crack tip region with realistic boundary conditions, a coupled finite element - atomistic (FEAt) technique [1] is employed. In agreement with experimental observations, perfectly brittle cleavage is observed for the (110) crack plane. In contrast, cracks on the (100) plane either follow a zig-zag path on (110) planes, or emit dislocations. Dislocation generation is studied in more detail under mixed mode I/II loading conditions.

A FRACTAL MODEL FOR PREDICTING OXYGEN EFFECTIVE DIFFUSIVITY OF POROUS MEDIA WITH ROUGH SURFACES UNDER DRY AND WET CONDITIONS

Fractals ◽  
2021 ◽  
pp. 2150076
Author(s):  
BOQI XIAO ◽  
QIWEN HUANG ◽  
BOMING YU ◽  
GONGBO LONG ◽  
HANXIN CHEN
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Oxygen Diffusion ◽  
Water Saturation ◽  
Rough Surfaces ◽  
Effective Diffusivity ◽  
Fractal Model ◽  
Relative Roughness ◽  
Oxygen Diffusivity ◽  
Dry And Wet Conditions

Oxygen diffusion in porous media (ODPM) with rough surfaces (RS) under dry and wet conditions is of great interest. In this work, a novel fractal model for the oxygen effective diffusivity of porous media with RS under dry and wet conditions is proposed. The proposed fractal model is expressed in terms of relative roughness, the water saturation, fractal dimension for tortuosity of tortuous capillaries, fractal dimension for pores, and porosity. It is observed that the normalized oxygen diffusivity decreases with increasing relative roughness and fractal dimension for capillary tortuosity. It is found that the normalized oxygen diffusivity increases with porosity and fractal dimension for pore area. Besides, it is seen that that the normalized oxygen diffusivity under wet condition decreases with increasing water saturation. The determined normalized oxygen diffusivity is in good agreement with experimental data and existing models reported in the literature. With the proposed analytical fractal model, the physical mechanisms of oxygen diffusion through porous media with RS under dry and wet conditions are better elucidated. Every parameter in the proposed fractal model has clear physical meaning, with no empirical constant.

Features Testing of Stud Material Under Low Constraint Ductile Tearing

2017 ◽  
Author(s):  
P. James ◽  
M. Jackson ◽  
P. Birkett ◽  
C. Madew
Keyword(s):  
Structural Integrity ◽  
High Stress ◽  
Crack Tip ◽  
Pressure Vessels ◽  
Materials Testing ◽  
Screw Thread ◽  
Surface Point ◽  
Defect Tolerance ◽  
Material Response ◽  
Crack Tip Constraint

Defect tolerance assessments are carried out to support the demonstration of structural integrity for high integrity components such as nuclear reactor pressure vessels. These assessments often consider surface-breaking defects and assess Stress Intensity Factors (SIFs) at both the surface and deepest points. This can be problematic when there is a high stress at the surface, for example due to the stress concentration at the root of a screw thread. In the past this has led to the development of complex and costly 3D finite element analyses to calculate more accurate SIFs, and still resulting in small apparent limiting defect sizes based on initiation at the surface point. Analysis has been carried out along with supporting materials testing, to demonstrate that the increased SIF at the surface point is offset by a reduction in crack-tip constraint, such that the material exhibits a higher apparent fracture toughness. This enables a more simplistic assessment which reduces the effective SIF at the surface such that only the SIF at the deepest point needs to be considered. This then leads to larger calculated limiting defect sizes. This in turn leads to a more robust demonstration of structural integrity, as the limiting defect sizes are consistent with the capability of non-destructive examination techniques. The high SIF at the surface location, and the concomitant reduction in crack-tip constraint, meant that it was not possible to demonstrate the material response with conventional tests, such as those using shallow-notched bend specimens. Instead it was necessary to develop modified specimens in which semielliptical defects were introduced into a geometry which replicated the notch acuity at the root of a screw thread. These feature tests were used to demonstrate the principle, prior to testing with more conventional specimens to fit more accurately the parameters required to represent the material response in a defect tolerance assessment. Margins in defect tolerance assessments are usually measured against the initiation of tearing, even though the final failure for the material may occur at a higher load following stable crack extension. This work measured and assessed the benefit of reduced crack-tip constraint on both the point of initiation and on the development of the tearing resistance curve. This demonstrated that the effect of constraint was valid with tearing for this material and that there was additional margin available beyond the onset of tearing. The feature test geometry also provided evidence of the tearing behaviour at the surface and deepest points of a surrogate component under representative loading. This paper provides an overview of the range of tests performed and the post-test interpretation performed in order to provide the R6 α and k constraint parameters.

A Novel Singular Finite Element on Mixed-Mode Dugdale Model Based Crack

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
W. A. Yao ◽  
X. F. Hu
Keyword(s):  
Finite Element ◽  
Analytical Solutions ◽  
Mixed Mode ◽  
Crack Tip ◽  
Dugdale Model ◽  
Dual Approach ◽  
Singular Finite Element ◽  
Crack Tip Opening ◽  
Method Show ◽  
Dugdale Crack

The symplectic dual approach is employed to obtain the analytical solutions of displacements and stresses around the mixed-mode Dugdale crack tip. Based on the analytical solutions, a novel singular finite element is developed to study the problem. The singular finite element can be applied to determine the sizes of crack tip opening/sliding displacement of a mixed-mode Dugdale model. Numerical results obtained by the present method show excellent agreement with the existing analytical solutions.

Sign in / Sign up

Export Citation Format

Share Document