A New Interaction Integral Method for Mesh-Free Analysis of Cracks in Functionally Graded Materials

This paper presents a Galerkin-based meshless method for calculating stress-intensity factors (SIFs) for a stationary crack in two-dimensional functionally graded materials of arbitrary geometry. The method involves an element-free Galerkin method (EFGM), where the material properties are smooth functions of spatial co-ordinates and two newly developed interaction integrals for mixed-mode fracture analysis. These integrals can also be implemented in conjunction with other numerical methods, such as the finite element method (FEM). Five numerical examples including both mode-I and mixed-mode problems are presented to evaluate the accuracy of SIFs calculated by the proposed EFGM. Comparisons have been made between the SIFs predicted by EFGM and available reference solutions in the literature, generated either analytically or by FEM using various other fracture integrals or analyses. A good agreement is obtained between the results of the proposed meshless method and the reference solutions.

Stochastic Meshless Analysis of Elastic-Plastic Cracked Structures

This paper presents a stochastic mesh-free method for probabilistic fracture-mechanics analysis of nonlinear cracked structures. The method involves enriched element-free Galerkin formulation for calculating the J-integral; statistical models of uncertainties in load, material properties, and crack geometry; and the first-order reliability method (FORM) for predicting probabilistic fracture response and reliability of cracked structures. The sensitivity of fracture parameters with respect to crack size, required for probabilistic analysis, is calculated using a virtual crack extension technique. Numerical examples based on mode-I fracture problems have been presented to illustrate the proposed method. The results from sensitivity analysis indicate that the maximum difference between sensitivity of the J-integral calculated using the proposed method and reference solutions obtained by the finite-difference method is about six percent. The results from reliability analysis show that the probability of fracture initiation using the proposed sensitivity and meshless-based FORM are very accurate when compared with either the finite-element-based Monte Carlo simulation or finite-element-based FORM. Since all gradients are calculated analytically, the reliability analysis of cracks can be performed efficiently using meshless methods.

Crack Opening Areas During High Temperature Operation

This paper presents results from two-dimensional finite element analyses of a centre cracked plate under both plane stress and plane strain conditions. The plate has been loaded in tension and secondary creep conditions have been assumed. The variation of the crack opening area with time has been calculated. It has been shown that the rate of change of the crack opening areas reduces with time up to the redistribution time which approximates the time to achieve steady creep conditions. Thereafter, the rate of change of crack opening area is constant. From curve fits to finite element results, a simplified expression for the rate of change of crack opening area of a stationary crack has been derived in terms of the elastic crack opening area, the creep strain rate, the elastic strain and two characteristic crack lengths (one for a strain field dominated by elastic strains and one for a strain field dominated by creep strains). This expression predicts the rate of change of the crack opening area both during the transient period up to the redistribution time and at all times thereafter.

Large Elastic-Plastic Deformation Analysis of Rectangular Plates

The purpose of this paper is to find a fast and simple solution for the large deformation of rectangular plates considering elastic-plastic behavior. This analysis contains material and geometric nonlinearities. For geometric nonlinearity the concept of load analogy is used. In this method the effect of nonlinear terms of lateral displacement is considered as suitable combination of additional fictitious lateral load, edge moment and in-plane forces acting on the plate. Variable Material Property (V.M.P.) method has been used for analysis of material nonlinearity. In this method, the basic relations maintain the form of stress-strain elastic formula, while material properties are modified to take into account the path-dependency involved in elastic-plastic deformations. Therefore, the solution of a von-Karman plate enduring large elastic-plastic deformations is reduced to that of an equivalent elastic plate undergoing small deformations. The method of solution employed in this study is computationally efficient and can easily be used for various boundary conditions and loadings.

Fatigue Test Plan to Obtain S-N Curves

S-N curves of structural materials are obtained through fatigue tests. These tests are often performed using five different stress levels, with fifteen test specimens for each stress level. This kind of test plan provides estimates that are less precise compared to other experimental plans, for example, the ones called optimum plan or compromise plan. The main reason for this drawback is the use of the same number of specimens for all stress levels. It has been observed that less precise results are obtained for lower stress levels because failure occurs less frequently. That is why more specimens should be used for lower stress levels as compared to higher stress levels. As long as the number of specimens to be tested at low stress levels is increased, the total number of failures will also increase, which allows one to develop a more precise data analysis. The objective of this work is to present an alternative experimental plan to obtain S-N curves, which intends to provide accurate estimators. A practical application is done for planning a fatigue test, in a flex-rotating machine, to obtain the S-N curve of SAE 8620 steel.

Unresolved Issues With Regard to Creep and Creep Fatigue Life Prediction

This paper studies intergranular creep failure of high temperature service material under a stress-controlled unbalanced cyclic loading condition. The grain boundary rupture process was numerically analyzed using Tvergaard’s axisymetric model. The present numerical model incorporated the experimentally verified Murakami-Ohno cyclic strain hardening creep law and Norton’s creep law. The numerical results show that void growth accelerates under cyclic loading condition. Also, analysis shows that a steady state creep law is not sufficient to analyze damage evolution under cyclic loading conditions.

The Influence of Thermophysical Properties on a Numerical Model of Solidification

Solidification and cooling of a (con)casting, with the simultaneous heating of the mold, is a case of transient spatial heat and mass transfer. This paper introduces an original and universal numerical model of solidification, cooling and heating, of a one-to-three-dimensional stationary and transient temperature field in a system comprising the casting, the mold and its surroundings. This model simulates both traditional as well as non-traditional technologies of casting conducted in foundries, metallurgical plants, forging operations, heat-treatment processes, etc. The casting process is influenced not only by the thermophysical properties (i.e. heat conductivity, the specific heat capacity and density in the solid and liquid states) of the metallic and non-metallic materials, but also by the precision with which the numerical simulation is conducted. Determining these properties is often more demanding than the actual calculation of the temperature field of the solidifying object. Since the influence of individual properties should be neither under- nor over-estimated, it is necessary to investigate them via a parametric study. It is also necessary to determine the order of these properties in terms of their importance.

A Sensitivity Study of Creep Crack Growth in Pipes

Failure of pressure vessels and piping systems that operate at high temperatures can occur by net section rupture, creep crack growth or a combination of both processes. Several design and assessment procedures are available for dealing with this situation. These include the ASME Pressure Vessel and Piping, French RCC-MR (Appendix 16) and British R5 and BS7910 codes. Each of these procedures uses a combination of continuum mechanics and fracture mechanics concepts to make an assessment. Although the procedures adopt the same basic principles, often different formulae are employed to make an assessment. The main parameters that are used are reference stress, σref, stress intensity factor, K, and the creep fracture mechanics term C*. In this paper, an analysis is performed to estimate the sensitivity of the predictions of creep crack growth in a pressurised pipe to the choice of formulae used and materials properties employed. It is shown that most sensitivity is obtained to choice of expression employed for calculating σref and to whether batch specific or more generic materials properties data are selected.

Evaluation of Coalescence Criteria for Parallel Cracks

When multiple cracks approach one another, the stress intensity factor (SIF) is likely to change due to the interaction of the stress field. Since the change in the SIF is not always conservative in structural reliability evaluations, this interaction between multiple cracks must be taken into account. Section XI of the ASME Boiler and Pressure Vessel Code (Sec. XI) provides a flaw characterization method for considering multiple crack interactions. In Sec. XI, adjacent cracks are replaced by a coalesced single combined crack if they are located within a certain distance. However, no systematic analysis of the SIF for interacting parallel surface cracks is provided. Furthermore, the background of the coalescence criterion prescribed in Sec. XI is not clear. In this study, the SIF of interacting parallel cracks was calculated using the finite element method. A coalescence criterion for parallel cracks was then proposed based on the calculation results. A simplified mesh generation method was adopted in order to improve the complexity of the mesh generating procedure, which uses a transitional mesh, referred to as a “Tie Block.”

Local Failure Modes of a Nuclear Reactor Pressure Vessel Nozzle Under Severe Accident Conditions

Most past studies for the creep rupture of a nuclear reactor pressure vessel (RPV) lower head under severe accident conditions, have focused on global deformation and rupture modes. Limited efforts were made on local failure modes associated with penetration nozzles as a part of TMI-2 Vessel Investigation Project (TMI-2 VIP) in 1990’s. However, it was based on an excessively simplified shear deformation model. In the present study, the mode of nozzle failures is investigated using data and nozzle materials from Sandia National Laboratory’s Lower Head Failure Experiment (SNL-LHF). Crack-like separations were revealed at the nozzle weld metal to RPV interfaces indicating the importance of normal stress component rather than the shear stress in the creep rupture. Creep rupture tests were conducted for nozzle and weld metal materials, respectively, at various temperature and stress levels. Stress distribution in the nozzle region is calculated using elastic-viscoplastic finite element analysis (FEA) using the measured properties. Calculation results are compared with earlier results based on the pure shear model of TMI-2 VIE It has been concluded from both LHF-4 nozzle examination and FEA that normal stress at the nozzle/lower head interface is the dominant driving force for the local failure with its likelihood significantly greater than previously assumed.