ЧИСЛЕННО-АНАЛИТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ПРОЦЕССОВ НАКОПЛЕНИЯ ПОВРЕЖДЕНИЙ И ЭВОЛЮЦИИ НАПРЯЖЕННО-ДЕФОРМИРОВАННОГО СОСТОЯНИЯ У ВЕРШИНЫ ТРЕЩИНЫ В РЕЖИМЕ ПОЛЗУЧЕСТИ

The paper analyzes a series of computer experiments aimed at identifying the self-similar behavior of stresses and continuity (damage) near the crack tip in a steady-state creep mode in a damaged medium. Finite element computations of crack-tip fields under creep regime were carried out using the interdisciplinary, universal finite element platform SIMULIA Abaqus FEA using the UMAT utility, which integrates the process of damage augmentation into the FEM computational scenario. The paper implements computational simulations of uniaxial stretching of a plate weakened by a central horizontal crack in the steady-state creep mode, which includes damage growth that evolves over time according to the mathematical model of damage growth by Kachanov Rabotnov (KR) according to a power law for various values of exponents of the kinetic equation and the power constitutive equations. The study and analysis of the FE for the crack-tip stress and continuity (integrity) fields for a number of material constants clearly reveal a self-similar behavior of stress and damage fields near the front tip. The structure of the solution is revealed and the values of the exponents in the self-similar variable and the self-similar representation of the solution are found, which can be interpreted as an intermediate self-similar solution of the second type according to the classification of G.I. Barenblatt. It is elucidated that the revealed property of self-similarity of the solution can be interpreted as the intermediate asymptotes of the far field of damage and stress. The obtained figures also clearly show the asymptotes of the near-field stress, characterized by the absence of a singularity in the immediate vicinity of the crack.

Delayed Hydride Cracking (DHC) in Zr-2.5 Nb alloy material is of interest to the CANDU (Canada Deuterium Uranium) industry in the context of the potential to initiate DHC at a blunt flaw in a CANDU reactor pressure tube. The material is susceptible to DHC when there is diffusion of hydrogen atoms to the flaw, precipitation of hydride platelets, and development of a hydrided region at the flaw tip. The hydrided region can then fracture to the extent that a crack forms, and is able to grow by the DHC crack growth mechanism. An engineering process-zone model for evaluation of DHC initiation at a blunt flaw that takes into account flaw geometry has been developed. The model is based on representing the stress relaxation due to hydride formation, and crack initiation, by an infinitesimally thin process zone. Application of the engineering process-zone model requires calculation of the stress intensity factor, and the crack-mouth opening displacement, for a fictitious crack at the tip of a blunt flaw. In the current model, calculation of these quantities is based on a cubic polynomial fit to represent the stress distribution ahead of the blunt flaw tip, where the stress distribution is generally calculated by finite element analysis. However, the cubic polynomial is not always an optimum fit to the stress distribution for very small root radius flaws, due to the large stress gradients near the flaw tip. Application of the weight function method will enable a more accurate representation of the flaw-tip stress distribution for the calculation of the stress intensity factor and the crack-mouth opening displacement. Weight functions for a crack at the tip of a blunt flaw in a thin wall cylinder have been developed for implementation into the engineering process-zone model. These weight functions are applicable to a wide range of blunt flaw depths and root radii, as well as a wide range of flaw-tip crack depths. The development and verification of the weight functions is described in this paper. The verification calculations are in reasonable agreement with alternate solutions, and have confirmed that the weight functions have reasonable accuracy for engineering applications of the process-zone methodology.

Finite Element study of fracture initiation in flaws subject to internal fluid pressure and vertical stress

Crack-fiber interaction and interfacial failure models in fiber-reinforced ceramics

Limit load solutions have been applied to estimate the collapse load of a component made of ductile material. Worldwide maintenance codes for power plants, such as ASME Boiler and Pressure Vessels Code, Section XI, and JSME fitness-for-service code, describe limit load solutions under the assumption of a single flaw. Detected flaws are, however, not always a single flaw, and adjacent flaws due to stress corrosion cracking have been detected in power plants. Thus, development of a limit load solution to estimate the collapse load in the case of multiple flaws remains an issue of structural integrity evaluation. Under the aim of developing a method for evaluating the effect of multiple flaws on collapse load as a part of a limit load solution, fracture tests of flat plates and pipes with multiple flaws were conducted. Although experimental approaches have been attempted to establish the evaluation method, further efforts are required to incorporate the evaluation procedure into a code rule. Effective parameters for considering reduction of collapse load on the basis of test results for specimens with multiple flaws were identified. Test results clearly show a correlation between collapse load and ratios of net-section areas. This correlation leads to the conclusion that distance parameters and flaw length of a smaller flaw determine the existence of an effect on the collapse load by multiple flaws. To investigate the physical sense of the correlation, finite element analysis (FEA) was performed. The FEA results show that strain distributions at the flaw tip under several conditions correspond at the time of maximum load of the fracture tests regardless of the effect of multiple flaws. Also according to the FEA results, the extent of the strain field is linearly proportional to flaw length. These FEA results are consistent with the correlation obtained by the test results.

This study focuses on a finite element analysis of stress, strain, and damage fields near the tip of a central crack in a plate subjected to a tensile load under creep conditions, taking into account the damage accumulation effect. The simulation was performed in Simulia ABAQUS using the UMAT (User Material) procedure, which implements the Bailey-Norton power law constitutive relation and the Kachanov-Rabotnov damage kinetics equation. The results of calculations without damage confirmed compliance with the known Hutchinson-Rice-Rosengren analytical asymptotics for the creep zone and the asymptotics of linear fracture mechanics in the elastic region. It was established that the presence of damage significantly affects the asymptotic behavior in the creep zone near the defect tip. Numerical calculations showed that the continuity parameter exhibits asymptotic behavior. Power-law asymptotics were found for both the stress tensor components and the damage parameter. The result of the study is also the identification of a self-similar structure of the fields of mechanical quantities in the vicinity of the crack tip.

Fractures of low-k materials in a RF package with integrated passive device based on TGV

Surface scratches and flaws encountered in CANDU nuclear pressure tubes must be evaluated to ensure that a cracking mechanism, called delayed hydride cracking (DHC), is not initiated. The stress concentration due to a flaw can cause diffusion of hydrogen and precipitation of zirconium hydride at the flaw tip. The presence of a hydride results in reduced fracture resistance in a local region where high stress prevails. In many cases, flaws exist for an extended period of time before the hydrogen content in the base material is sufficient to form a hydride. In this situation high stress creep can significantly relax the local stress at the flaw tip. The assessment of flaws on the basis of local stress distribution not considering creep is expected to be overly conservative, and may result in unnecessary remedial action in reactor operation and maintenance procedures. An experimental program has been developed to isolate and quantify the effect of creep on DHC in irradiated Zr-2.5%Nb pressure tube material. As part of this program, the thermal and load histories relevant to reactor operating conditions have been considered, and initial experimental results indicate that the action of creep increases the threshold load for crack initiation. Finite element analysis of creep relaxation around a hydride also supports the experimental results, and a fracture initiation model is applied to the experimental conditions in order to establish an analytical trend for the effect of creep. The quantitative effect predicted by the model is in reasonable agreement with the experimental results, and an improved, less conservative assessment procedure that accounts for creep is deemed to be practical.

The bending problem of an anisotropic finite plate with smooth boundary containing defects like nonintersecting through thickness curvilinear cracks and rigid inclusions is considered. The problem is solved by the Lekhnitskii method of complex potentials written in the form of Cauchy-type integrals along the defect contours with unknown integrand density function which has the root type singularity on the defect tips. The boundary-value problem is reduced to a system of singular integral equations subject to the conditions for the displacements to be single-valued upon circulating the closed contours around the cuts and equilibrium conditions for rigid inclusions. To illustrate the efficiency of the method proposed, some specific plate bending problems are solved. The stress distribution in the vicinity of the defect tips are studied for various plate configurations and orientation of defects. For isotropic plates, the solutions are obtained by setting appropriate numerical values of the anisotropic constants.

This paper presents a formulation of the problem of deformation of variable thickness shells reinforced by fibers of constant cross-section. All components of these metal-composite shells operate under steady-state creep conditions. The system of resolution equations together with the appropriate boundary conditions is analyzed. A method for the solution of the problem formulated here is developed. The way to get the approximate solution to the problem at the first stage of unsteady-state creep is proposed. Calculations performed for cylindrical shells indicate that the compliance of such structures under steady-state creep conditions depends strongly on the reinforcement structure.

Creep deformation and rupture experiments are conducted on samples of the Ni-base superalloy directionally solidified GTD-111 tested at temperatures between 649°C and 982°C and two orientations (longitudinally and transversely oriented). The secondary creep constants are analytically determined from creep deformation experiments. The classical Kachanov–Rabotnov model for tertiary creep damage is implemented in a general-purpose finite element analysis (FEA) software. The simulated annealing optimization routine is utilized in conjunction with the FEA implementation to determine the creep damage constants. A comparison of FEA and creep deformation data demonstrates high accuracy. Using regression analysis, the creep constants are characterized for temperature dependence. A rupture prediction model derived from creep damage evolution is compared with rupture experiments.

The creep deformation and damage evolution of nickel base superalloy (Waspaloy) at 700 °C are studied using the classic Kachanov–Rabotnov (KR) and a recently developed Sin-hyperbolic (Sinh) model. Uniaxial creep deformation and Bridgman rupture data collected from literature are used to determine the model constants and to compare the KR and the Sinh solutions. Finite-element (FE) simulations on a single eight-node element are conducted to validate the accuracy of the FE code. It is observed that KR cannot predict the creep deformation, damage, and rupture life of nickel base superalloys accurately using one set of constants for all the stress levels. The Sinh model exhibits a superior ability to predict the creep behavior using one set of constants for all the stress levels. Finite-element analysis (FEA) on 3D Bridgman notched Waspaloy specimen using the Sinh model is conducted. The results show that the Sinh model when combined with a representative stress equation and calibrated with experimental data can accurately predict the “notch effect” observed in the rupture life of notched specimen. Contour plots of damage evolution and stress redistribution are presented. It is demonstrated that the Sinh model is less stress sensitive, produces unconditional critical damage equal to unity at rupture, exhibits a more realistic damage distribution around the crack tip, and offers better crack growth analysis than KR.

The need to evaluate the significance of flaws in welded pipelines for gas transportation requires the knowledge of the material resistance to ductile tearing. In particular, the fracture resistance of pipe girth welds should be evaluated since they may potentially be critical for structural integrity. Standard toughness Three Point Bending tests (SENB) are too conservative since they are more constrained than actual pipeline. In this case, the adoption of a reduced notch depth, which is considered to reproduce well actual stress-strain conditions at the crack tip of a weld flaw, increases critical toughness values when compared to standard specimen configuration. Alternative solutions may be applied, even if not yet included in toughness standards. In particular, the Single Edge Notch Tensile (SENT) test is a possible solution reducing conservatism. A matter of concern for toughness characterization of weld joint is also represented by the notch orientation, since the weld microstructure is inhomogeneous in nature. The L–R oriented specimen (notch at the pipe inner surface) typically shows CTOD values strongly lower than the ones of L–T oriented specimens (through thickness notch) for both weld metal and heat affected zone. All these issues are discussed within this paper, while an advanced approach is presented to determine the resistance curve by using a single SENT specimen with the compliance method for crack growth evaluation. A relationship between the specimen elastic compliance and actual crack growth was determined through Finite Element Analysis and a Fracture Mechanics model. Such a relationship is presented and compared to other solutions available in scientific literature.

In this study, crack growth under steady state creep conditions is analysed. A theoretical framework is introduced in which the constitutive behaviour of the bulk material is described by power-law creep. A new class of damage zone models is proposed to model the fracture process ahead of a crack tip, such that the constitutive relation is described by a traction-separation rate law. In particular, simple critical displacement, empirical Kachanov type damage and micromechanical based interface models are used. Using the path independency property of the C^*-integral and dimensional analysis, analytical models are developed for pure mode-I steady-state crack growth in a double cantilever beam specimen (DCB) subjected to constant pure bending moment. A computational framework is then implemented using the Finite Element method. The analytical models are calibrated against detailed Finite Element models. The theoretical framework gives the fundamental form of the model and only a single quantity hat{C}_k needs to be determined from the Finite Element analysis in terms of a dimensionless quantity phi _0, which is the ratio of geometric and material length scales. Further, the validity of the framework is examined by investigating the crack growth response in the limits of small and large phi _0, for which analytical expression can be obtained. We also demonstrate how parameters within the models can be obtained from creep deformation, creep rupture and crack growth experiments.

The notched strengthening effect during creep of P92 steel has been studied by finite element analysis and experimental research. It was found that there was a transforming tendency from ductile to brittle at the root of the notch and the extent of the transforming intensified with the increment of the nominal stress. It was the transforming tendency that increased the value of creep life enhancement factor. With the help of finite element software, Kachanov–Rabotnov creep damage constitutive model was embedded into the interface program and the notched specimens creep was simulated. The result has shown the Kachanov–Rabotnov model can be used to simulate the notched strengthening effect of P92 steel accurately when the material constant α = 0·73.