Fracture mechanics

This thesis presents the experimental and analytical investigation of fiber (steel and Kevlar) reinforced concrete (FRC) to determine its fracture mechanic properties especially the J-integral. The freeze-thaw durability of fiber reinforced and air-entrained concrete is also investigated. The fiber reinforced concretes were found to have a much greater flexural strength and toughness compared to plain concrete. The compressive strength was found to decrease with the addition of fibers and air-entrainment. In all cases the addition of 1.0% or more fibers prevented catastrophic failures. The mixing and setting of FRC requires a rigorous procedure which must be followed to achieve a homogeneous matrix.

Fracture toughness of a large range of PVC foam cores was determined using the single edge notch bend (SENB) specimen. Debond fracture toughness for sandwich specimens with the same foam cores was characterized using the TSD specimen. Examination of the crack propagation path in specimens with adequate face/core adhesion revealed that the debonding process occurred by crack propagation in the core, near the face/core interface. It was observed that the debond toughness and core toughness are of similar magnitude although the debond toughness exceeds the core toughness, especially for the higher density cores. Possible reasons for the elevation of the debond toughness over the core toughness such as plastic zone enlargement, mode mixity, core thickness, and gradient of properties of the core are examined. It was found that the plastic zone enlargement is a major factor for increase in debond toughness over the other factors examined.

This study presents the experimental and theoretical studies on debond of carbon fiber laminates bonded to concrete, which aids in understanding the mechanics of the repaired damaged prestressed concrete girders with externally bonded carbon plates. The bond strength of carbon plate specimens bonded to concrete is determined experimentally by the debond test. The initial crack is introduced in the specimens at one location, namely the plate/adhesive interface. The fracture toughness for debonding is evaluated and expressed as the critical strain energy release rate. A finite element analysis was performed to evaluate the compliance and stress distribution in the debond test specimens.

A new test specimen, named tilted sandwich debond specimen (TSD), has been Introduced to promote face/core debonding over crack kinking and enable characterization of an important failure mode of sandwich structures. An experimental compliance calibration procedure was developed for evaluation of debond fracture toughness in a straight-forward manner. The specimen has been evaluated through kinematics analysis, elastic foundation model, finite element analysis and a comprehensive experimental investigation. An elastic foundation model of the TSD specimen was developed to obtain analytical expressions for specimen compliance and strain energy release rate. A design equation for the maximum tolerable crack length was derived. Finite element analysis of various configurations of the TSD specimen was conducted to obtain the mixed mode stress intensity factors, crack kinking angle, specimen compliance and strain energy release rate. The results revealed that the bimaterial character of the TSD specimen influences the mode mixity for the specimen and that crack kinking was more likely for thick and low density cores. The presence of the interphase layer only slightly influenced the mode mixity and kinking angle. The debonding characteristics of several sandwiches consisting of glass/vinylester face sheets and PVC foam cores of various densities were examined using the TSD specimen. Crack propagation from the beelcore precrack involved "micro-kinking" or kinking deeply in the core for all specimens at the first crack propagation increment(s). Crack kinking in the intermediate density core could be suppressed by selecting a certain range of tilt angles. After kinking, crack returned to a path parallel and close to the interface in agreement with the analysis of sub-interface cracks. Cracks propagated in a stick/slip manner. Measurements of the debond fracture toughness, Gc, using the TSD specimen revealed that Gc is fairly independent of crack length and increases with increasing core density. The debond toughness was of similar order as the mode I toughness of the core.

In the present investigation, the boundary/finite element alternating methods are used to evaluate the stress intensity factors and weight functions for surface crack problems. For two dimensional problems, Westergaard stress functions are used to find the analytical solutions for an infinite plate with an embedded crack, subjected to crack face tractions, and the boundary element method for the numerical solution. The stress intensity factors and weight functions for an arbitrary plate with an edge crack subjected to mixed mode loads are obtained by the alternating technique. For three dimensional problems, an elliptical coordinate system and the gravity potential functions are used to derive the three dimensional analytical solutions for an infinite solid with an embedded crack. The analytical solutions are derived for the cases of shear tractions and normal tractions, separately, by assuming that the tractions are symmetric about both the major and minor axes. Superposition gives the general solutions. The analytical solutions and the finite element method, in conjunction with alternating technique, are used to evaluate the stress intensity factors for a solid with a semi-elliptical surface crack, subjected to arbitrary loads. A general approach to evaluate the weight functions for a two dimensional plate with a three dimensional semi-elliptical surface crack is formulated. Numerical examples are evaluated using the formulation developed in the present investigation. The results show good agreement with those from classical solutions. The convergence characteristics of the alternating methods are also discussed. Finally, the formulation is applied to welded plate T-joints with edge/semi-elliptical surface cracks, subjected to three point bending, to obtain stress intensity factors.

The effects of various nonuniform stress fields on the stress intensity factors for the semi-elliptic surface crack (three-dimensional problem) in a finite plate are determined using the weight function approach. The formulation satisfies the linear elastic fracture mechanics criteria and the principle of conservation of energy. Based on the knowledge of stress intensity solutions for the reference load/stress system, the expression for the crack opening displacement function for the surface crack is derived. Using the crack opening displacement function and the reference stress intensity factor, the three-dimensional weight functions and subsequently the stress intensity solutions for the surface crack subjected to nonuniform stress fields are derived. The formulation is then applied to determine the effects of linear, quadratic, cubic, and pure bending stress fields on the stress intensity factor for the surface crack in a finite plate. In the initial stage of the study a two-dimensional problem of an edge-crack emanating from the weld-toe in a T-joint is considered. The effect of parameters such as plate thickness, weld-toe radius, and weld-flank angle on the stress intensity factor for an edge-crack is studied. Finite element analyses of the welded T-joints are performed to study the effects of plate thickness, weld-toe radius and the weld-flank angle on the local stress distribution. The ratio of plate thickness to weld-toe radius ranging from 13.09 to 153.93, and the weld-flank angles of 30, 45, and 60 degrees are considered in the analyses. Based on the results from FEM analyses, a parametric equation for the local stress concentration factor and a polynomial expression for the local stress distribution across the plate thickness are derived using the method of least squares and the polynomial curve-fitting technique.

The local buckling failure mechanism and subsequent debond propagation in sandwich columns and panels with composite face sheets containing a face-to-core debond is experimentally, analytically, and numerically analyzed. The experimental investigation is based on a comprehensive test program to examine local buckling failure and fracture toughness of sandwich specimens consisting of glass/epoxy face sheets over various density PVC foams and a balsa wood core. Elastic foundation and finite element models are developed for prediction of the local buckling load of sandwich columns and panels containing an implanted debond at the face/core interface. Nonlinear finite element analysis was conducted to investigate debond propagation in the post-buckling region. Overall, model predictions were in agreement with experimental results. The buckling load was found to decrease with reduced face sheet stiffness, reduced core modulus, and increased debond length. Sandwich panels with circular debonds were more resistant to local buckling than those with square debonds of the same characteristic size. Circular debonds of 50 mm diameter and square debonds of 45 mm side length established the threshold for local buckling failure. Nonlinear finite element analysis of debonded sandwich columns and panels showed that the major crack displacement is opening (mode I). The tendency of the crack tip to first open and then close after buckling of the face sheet is believed to be due to the formation of an eccentric load path at the onset of buckling. The fracture mechanics analysis of debonded sandwich panels showed that the energy release rate is much higher in the direction perpendicular to the applied load than along the loading direction, and exceeds the measured toughness value in the transverse direction. This explains the experimental observation that a debond embedded in a sandwich panel tends to propagate in the transverse direction.

This thesis deals with corrosion problems of underwater turbines in marine environment. The effect of a tensile stress on the uniform corrosion rate of a metal bar is studied, and an analytical model predicting the time of service of a bar under a tensile load in a corrosive environment is proposed. Stress corrosion relationships are provided for different type of alloys, and different types of relationships. Dolinskii's and Gutman's models are studied and extended to a general order polynomial, along with a Least Square and Spline Interpolation of the experimental data. In a second part, the effect of the passive film, delaying the initiation of the corrosion process, is studied. Finally, an algorithm predicting the time of service of a cracked bar is provided, using the stress corrosion assumption, along with a validation using experimental data.

In this thesis multiple controllers are developed which command a small boat with twin tied outboard motors to hold a desired position. In the process of developing a controller to hold a position, controllers were first developed which follow a desired heading or path over ground with the motors outputting constant thrust. These heading and path following controllers were tuned and tested in a numerical simulation, then validated on the R/V Lee and Ocean Power vessels through sea trials in the Atlantic Ocean. After successful path following trials were performed, station keeping algorithms were developed and tuned in the numerical simulation, now with heading and thrust of the vessel both being variables to be controlled. After tuning in the numerical simulation, the Ocean power vessel was outfitted with systems for controlling throttle and steering with sea trials conducted in the Atlantic Ocean for station keeping.

This manuscript predicts the behavior of a doubly reinforced concrete beam with a circular opening at its midspan by closely analyzing traditional beam theory and design. It then confirms these predictions with finite element modeling software while providing design suggestions. The analysis is limited to the tensile and compressive stresses and cracking behavior. The objectives are to determine the stress distribution around a circular opening that agrees with conventional beam theory. The beam behavior is examined from zero load to failure load. ANSYS is utilized in lieu of real world testing, and the appendix includes the finite element results for a beam including design recommendations. The results lay the foundation for a possible new design procedure of concrete beams with single or multiple circular openings. This research offers useful information that was unavailable previously. More research can be conducted to help designers to design lighter, more efficient concrete beams.