We present an a-posteriori method for computing rigorous upper and lower bounds of the J-integral in two dimensional linear elasticity. The J-integral, which is typically expressed as a contour integral, is recast as a surface integral which yields a quadratic continuous functional of the displacement. By expanding the quadratic output about an approximate finite element solution, the output is expressed as a known computable quantity plus linear and quadratic functionals of the solution error. The quadratic component is bounded by the energy norm of the error scaled by a continuity constant, which is determined explicitly. The linear component is expressed as an inner product of the errors in the displacement and in a computed adjoint solution, and bounded using standard a-posteriori error estimation techniques. The method is illustrated with two fracture problems in plane strain elasticity. / Singapore-MIT Alliance (SMA)

Abstract The interface crack of an IC package is easily existed under vibration, high temperature or collision. Its reliability will be reduced significantly for the existence of the crack. This study, therefore, is to investigate the fracture mechanism of the underfill/substrate interface with different crack length. In this study, mixed mode fracture of the underfill/substrate interface, was investigated by single lap tension test. Based on the load-displacement curve, J integral, energy release rate and stress intensity factor were calculated. Moreover, the relationships among the stress intensity facto KI, KII and phase angle were also derived.

The rate dependence of several aluminum alloys (6061, 7075, 5083) was examined through the means of quasi-static tension tests, dynamic tension tests, and split pressure Hopkinson bar tests. The macroscopic strains of the quasi-static and dynamic tension tests were measured after failure within the uniform region and the necked region using high-resolution images and edge detection. The study continued with an exploration into the plane-stress ductile fracture of Al 6061 in the T6 and O condition. Digital image correlation (DIC) was used to find the displacement and strain fields, and a numerical method for calculating the stress fields for a power law hardening material was developed. The J-integral was then calculated locally. The effect of strain hardening on the type of fracture (slant or flat) was also investigated. Macroscopic and microscopic observations of the fracture were made with DIC and by dissecting, polishing and/or etching the broken fracture specimens. Local failure strain measurements were made on the grain level and compared with those found through traditional failure strain measurements. / text

Premature failures of vital gas turbine components, such as blades and vanes, have been the result of increasing demands of power generation facilities. As power needs fluctuate throughout the day, operators are quickly firing up gas turbines as a means of providing instant power. Traditionally, these engines run at constant operating conditions; however, contemporary operating conditions call for these engines to be applied on an “as necessary” basis. The result of the cyclic startup and shutdown of gas turbines has led to a phenomenon known as creep-fatigue (CF). A coupling of two primary failure mechanisms in gas turbines, CF conditions exacerbate the mechanisms of creep and fatigue, ultimately leading to a premature failure of components. Traditionally, independent creep and fatigue analyses are conducted to determine the limiting life factor of gas turbines. Recently, fracture mechanics approaches have been successfully used in extending the traditional analyses to include fatigue- and creep-crack growth analyses. Founded on existing approaches to creep-fatigue crack growth analyses, including experimental elastic and plastic fracture mechanics approaches, a coupled creep-fatigue crack initiation and propagation model is developed. To bring these models to fruition, the current study utilizes the development of an experimental setup capable of subjecting a modified fracture specimen to creep-fatigue conditions. With two test temperatures key to turbine components, a blunt notch compact tension specimen was subjected to trapezoidal load waveforms with various lengths of holds at maximum load. A developed direct current potential drop (DCPD) system was used to monitor crack initiation and crack lengths throughout the duration of tests. Numerical simulations on a representative specimen were conducted, to correlate and predict key fracture mechanics parameters used in the development of creep-fatigue crack initiation and propagation models. iv Metallurgical analysis of specimens was conducted, implementing both optical and scanning electron microscopy. From the experimental and numerical studies, a model for both the initiation and propagation of cracks on a single specimen is furnished. Through the use of elastic-plastic fracture mechanics parameters, the proposed models are observed to predict crack initiation and replicate crack propagation rates based on the experimental conditions. Assisting in the implementation of the proposed models, intended uses and applications for the models are provided, simplifying the life prediction analyses for components expected to fail due to creepfatigue service conditions.

No description available.

A combination of fractography, microstructural analysis and finite element modelling was used to investigate several topics relating to the fatigue of nuclear grades of austenitic stainless steel operating in both air and simulated PWR water environments. The work is broadly separated into four main categories. The first two involved analysing specimens from standard fatigue endurance tests using a wide range of microscopic techniques. The relevance and uses of a modern laser scanning confocal microscope are presented and the benefits of using such a technique are discussed. Methods for the automation of both striation counting procedures and hysteresis data analysis are described and the results are demonstrated. Finite element analyses were performed in order to develop the understanding of fatigue crack growth within standard cylindrical endurance specimens. A variety of different crack tip parameters were used in order to develop expressions for crack growth rates in terms of the strain intensity factor and the J-integral. The derived expressions were compared to the results of striation spacing measurements from multiple endurance specimens that were tested in both air and water environments. The expressions were used to perform back-fitting calculations on standard endurance curves in order to produce alternative curves representing the number of loading cycles to cause the initiation of short cracks with depths in the range of 0.25-0.5 mm. The effects of hold-times on the fatigue life of stainless steel endurance specimens were explored as part of the international AdFaM research programme. Results from the programme partners are presented which demonstrate the beneficial effects of static hold-times on extending the fatigue lifetime of specimens. A range of microstructural analyses were performed on test specimens and results are presented. No significant effects of hold-times on microstructure, crack growth rates or material hardness were found. Analysis of hysteresis data demonstrated an increase in the cyclic hardening and a decrease in the plastic strain range after a hold. From an analysis of the fatigue test results, it was concluded that hold-times affect the earliest stages of fatigue (nucleation and initiation), most likely due to the effects of strain ageing. Several possible explanations for the observed phenomenon of specimen shrinkage during static holds are presented and discussed, however no conclusive explanation was identified. Further work is identified that could lead to future improvements in the understanding of all areas of investigation that have been reported. Overall, the work reported here has helped to develop the understanding of fatigue behaviour and mechanisms in the materials of interest. This was done through investigations using a synergistic combination of microscopy and numerical modelling techniques.

No description available.

This paper describes the analytical work done by modelling and evaluating a thermal shock in a WWER-440 reactor pressure vessel due to an emergency case. An axial oriented semielliptical underclad/surface crack is assumed to be located in the core weld line. Threedimensional finite element models are used to compute the global transient temperature and stress-strain fields. By using a three-dimensional submodel, which includes the crack, the local crack stress-strain field is obtained. With a subsequent postprocessing using the j-integral technique the stress intensity factors KI along the crack front are obtained. The results for the underclad and surface crack are provided and compared, together with a critical discussion of the VERLIFE code.

Abstract Ferroelectric/ferroelastic ceramics are used in a range of smart structure applications, such as actuators and sensors due to their electromechanical coupling properties. However, their inherent brittleness makes them susceptible to cracking and understanding their fracture is of prominent importance. A numerical study for a stationary, plane strain crack in a ferroelastic material is performed as part of this work. The stress and strain fields are analyzed using a constitutive law that accounts for the strain saturation, asymmetry in tension versus compression, Bauschinger effects, reverse switching, and remanent strain reorientation that can occur in these materials due to the non-proportional loading that arises near a crack tip. The far-field K-loading is applied using a numerical method developed for two-dimensional cracks allowing for the true infinite boundary conditions to be enforced. The J -integral is computed on various integration paths around the tip and the results are discussed in relation to energy release rate results for growing cracks and for stationary cracks in standard elastic–plastic materials. In addition to the fracture studies, we examine the far field electromechanical loading conditions that favor the formation, existence and evolution of stable needle domain array patterns, using a phase-field modeling approach. Such needle arrays are often seen in experimental imaging of ferroelectric single crystals, where periodic arrays of needle-shaped domains of a compatible polarization variant coexist with a homogeneous single domain parent variant. The infinite arrays of needles are modeled via a representative unit cell and the appropriate electrical and mechanical periodic boundary conditions. A theoretical investigation of the generalized loading conditions is carried out to determine the sets of averaged loading states that lead to stationary needle tip locations. The resulting boundary value problems are solved using a non-linear finite element method to determine the details of the needle shape as well as the field distributions around the needle tips. / text

Abstract Ferroelectric/ferroelastic ceramics are used in a range of smart structure applications, such as actuators and sensors due to their electromechanical coupling properties. However, their inherent brittleness makes them susceptible to cracking and understanding their fracture is of prominent importance. A numerical study for a stationary, plane strain crack in a ferroelastic material is performed as part of this work. The stress and strain fields are analyzed using a constitutive law that accounts for the strain saturation, asymmetry in tension versus compression, Bauschinger effects, reverse switching, and remanent strain reorientation that can occur in these materials due to the non-proportional loading that arises near a crack tip. The far-field K-loading is applied using a numerical method developed for two-dimensional cracks allowing for the true infinite boundary conditions to be enforced. The J -integral is computed on various integration paths around the tip and the results are discussed in relation to energy release rate results for growing cracks and for stationary cracks in standard elastic–plastic materials. In addition to the fracture studies, we examine the far field electromechanical loading conditions that favor the formation, existence and evolution of stable needle domain array patterns, using a phase-field modeling approach. Such needle arrays are often seen in experimental imaging of ferroelectric single crystals, where periodic arrays of needle-shaped domains of a compatible polarization variant coexist with a homogeneous single domain parent variant. The infinite arrays of needles are modeled via a representative unit cell and the appropriate electrical and mechanical periodic boundary conditions. A theoretical investigation of the generalized loading conditions is carried out to determine the sets of averaged loading states that lead to stationary needle tip locations. The resulting boundary value problems are solved using a non-linear finite element method to determine the details of the needle shape as well as the field distributions around the needle tips. / text