This study considers a symmetrical finite strip with a length of 2L and a width of 2h containing two collinear edge cracks located at the center of the strip. Each edge crack has a width h&amp / #8211 / a. Two ends of the finite strip are bonded to two rigid plates through which uniformly distributed axial tensile loads of intensity p0 are applied. The finite strip is assumed to be made of a linearly elastic and isotropic material. For the solution of the finite strip problem, an infinite strip of width 2h containing two internal cracks of width b&amp / #8211 / a at y=0 and two rigid inclusions of width 2c at y=&plusmn / L is considered. When the width of rigid inclusions approach the width of the strip, the portion of the infinite strip between the inclusions becomes identical with the finite strip problem. When the outer edges of the internal cracks approach the edge of the strip, they become edge cracks (notches). Governing equations are solved by using Fourier transform technique and these equations are reduced to a system of three singular integral equations. By using Gauss-Lobatto and Gauss-Jacobi integration formulas, these three singular integral equations are converted to a system of linear algebraic equations which is solved numerically.

An axisymmetric finite cylinder with rigid ends and a circumferential edge crack is considered in this study. The finite cylinder is under the action of uniformly distributed loads at two rigid ends. Material of the finite cylinder is assumed to be linearly elastic and isotropic. This finite cylinder problem is solved by considering an infinite cylinder containing an internal ring-shaped crack located at z=0 plane and two penny-shaped rigid inclusions located at z=&plusmn / L planes. General expressions of the infinite cylinder problem are obtained by solving Navier equations with Fourier and Hankel transforms. This infinite cylinder problem is then converted to the target problem by letting the radius of the rigid inclusions approach the radius of the cylinder and letting the outer edge of the crack approach the surface of the cylinder. Consequently, these rigid inclusions form the rigid ends and internal crack form the circumferential edge crack resulting in the problem of a finite cylinder with rigid ends having an edge crack. The problem is reduced to a set of three singular integral equations. These singular integral equations are converted to a system of linear algebraic equations with the aid of Gauss-Lobatto and Gauss-Jacobi integration formulas and are solved numerically.

<p>Advanced high strength steels (AHSS) exhibit significant higher springback and different fracture modes in forming processes and these problems cannot be accurately predicted using conventional simulation methods in many cases. In this thesis, new simulation technologies have been developed to improve the predictability for AHSS forming. The technologies integrated various aspects of simulation techniques, including development of material models and local formability criteria, calibration of the models with experimental data, and simulation method and parameter optimisations. Both laboratory and full scale parts were used to validate the simulation technologies developed. These technologies are originally applied to solve AHSS forming problems.</p> <p>The springback predictions have been significantly improved using the newly developed simulation technology. The technologies include the implementation of the smooth contact to reduce contact errors, modification of mass scaling to reduce dynamic effect, implementation of isotropic/kinematic hardening model and optimization of simulation parameters. Shear fracture (a stretch bending fracture on a small radius) have been successful predicted using Modified Mohr Coulomb (MMC) fracture criterion. Both laboratory experiments and full scale parts have been used to validate the predictions. Shearing and pre-forming effects on hole expansion and edge stretching have been investigated. A new approach was introduced to evaluate AHSS sheared edge deformation and quality by measuring material flow line angle change on a shearing edge. Shearing processes were simulated using MMC failure criterion and the sheared edge deformation has been integrated to hole expansion simulation to produce a more accurate prediction. The pre-forming effect on edge cracking has been investigated through both experiments and simulations. The limit strains have been measured by experiments. Simulation technology was also developed to predict surface strains of pre-form and subsequent stretching. Formulation of plane stress characteristics considering normal anisotropy have been developed and applied to analyze the flange deformations and optimum blanks for cup drawing. The method of plane strain characteristics has been used to predict earing throughout the entire cup drawing process.</p> / Doctor of Philosophy (PhD)

In this thesis, transverse vibration of a cracked beam on an elastic foundation and the effect of crack and foundation parameters on transverse vibration natural frequencies are studied. Analytical formulations are derived for a beam with rectangular cross section. The crack is an open type edge crack placed in the medium of the beam and it is uniform along the width of the beam. The cracked beam rests on an elastic foundation. The beam is modeled by two different beam theories, which are Euler-Bernoulli beam theory and Timoshenko beam theory. The effect of the crack is considered by representing the crack by rotational springs. The compliance of the spring that represents the crack is obtained by using fracture mechanics theories. Different foundation models are discussed / these models are Winkler Foundation, Pasternak Foundation, and generalized foundation. The equations of motion are derived by applying Newton&#039 / s 2nd law on an infinitesimal beam element. Non-dimensional parameters are introduced into equations of motion. The beam is separated into pieces at the crack location. By applying the compatibility conditions at the crack location and boundary conditions, characteristic equation whose roots give the non-dimensional natural frequencies is obtained. Numerical solutions are done for a beam with square cross sectional area. The effects of crack ratio, crack location and foundation parameters on transverse vibration natural frequencies are presented. It is observed that existence of crack reduces the natural frequencies. Also the elastic foundation increases the stiffness of the system thus the natural frequencies. The natural frequencies are also affected by the location of the crack.

The AASHTO LRFD design specifications and the AASHTO manual for bridge evaluation are consistently revised using knowledge of previous bridge failures. Although modern steel structures are designed to resist fatigue cracking from service loads, cracks in the tension flanges of steel bridge girders have been observed as a result of stress concentrations, design errors, welding quality control, and vehicular impacts. Cracks can grow in size with time and active cyclic live loads and may result in a member fracture. Fracture is a dangerous limit state which occurs with little to no warning. One method to quantify the stress field in the vicinity of a crack tip is by calculating the Stress Intensity Factor (SIF) around the crack tip. Finding SIFs for a cracked geometry may help an engineer to determine the fracture potential based on crack dimensions found during the inspection. Rolled I-beam and steel plate girders are extensively used as bridge superstructure members to efficiently carry live loads. This research was focused on determining Stress Intensity Factors (SIFs) of partially cracked I-sections using Finite Element Analysis. Two different tension flange crack profiles were studied: edge cracks, and full-width cracks. The SIF solutions were further used to study the fracture behavior and stress redistribution in the partially cracked flexural I-shaped members. / Master of Science / Steel is one of the fundamental materials used in the construction of bridge structures, and steel girder bridges are one of the most common types of bridge structures seen in the United States. Past bridge failures have helped engineers to understand shortcomings in design specifications, and AASHTO codes have been developed and revised over the years to reflect an improved understanding and evolution of engineering behavior. Engineers must make sure that a design is robust enough for functional use of the component during its service life. It is also equally important to understand the potential chances of failure and make the structure strong enough to overcome any failure mechanisms. Fracture is one structural failure mode which occurs with little to no warning and hence is very dangerous. One efficient way to quantify the stress field in the vicinity of a crack tip is by calculating the Stress Intensity Factor (SIF) around a crack tip. Fracture literature is available which describes different methods of determining SIFs for cracked members. However, there are no solutions available to find a SIF of a partially cracked flexural I-shaped members. This research was focused on determining Stress Intensity Factors and studying the fracture behavior of partially cracked I-sections using Finite Element Analysis. The resulting SIF solutions were further used to study the fracture behavior and stress redistribution in partially cracked flexural I-shaped members.