In recent years there has been much engineering effort channeled toward obtaining higher strength, lower weight and cost product designs. In pursuit of this goal some carefully designed and tested parts have catastrophically failed after a long history of repeated successful service, even though the load at the time of failure was no higher than the part had repeatedly carried previously. These mechanical failures are commonly classified as fatigue failures.

A project report submitted to the Faculty of Engineering, University of the Witwatersrand, Johannesburg, in partial fulfillment of the requirements for the degree of Master of Science in Engineering. / The project report deals with the relationship between the undrained shear strength and the moisture content of Red Berea sand tailings. The tailings were obtained from the Red Berea sand dunes near Richards Bay, Kwa-Zulu Natal, South Africa. The geology of the area consists of Miocene deposits of red clayey sand, classified as Berea Formation. A method for determining stability of a tailings dam for Red Berea sand tailings, was investigated. The general method of using the degree of saturation of the tailings to specify the rate of rise, is not applicable to this type of tailings. It was found that a relationship exists between the undrained shear strength of the tailings, and the moisture content. The moisture content can easily be measured and the undrained shear strength can then be calculated. The calculated undrained shear strength can be used in a total stress analysis to determine a factor of safety against failure. This project report consists of a discussion of the literature, which was used as the basis for the assumptions made, as well as a description of the tests performed to prove the above-mentioned relationship. Test results are given, interpreted and used in an illustrative example of a stability analysis. / Andrew Chakane 2020

Results of an experimental study of the failure and crippling of thin-walled open section prismatic compression members are presented. Twenty-four specimens were tested, 13 of which were channel sections and the other 11 were zee sections. Three specimens were made of 2024-T3 aluminum. The remaining 21 specimens were made of AS4-3502 graphite-epoxy. All specimens were tested to failure. Seventeen specimens exhibited local buckling of flanges and webs prior to failure, four exhibited global column buckling prior to failure, two exhibited material short column failure, and one exhibited unstable postbuckling behavior prior to failure. The buckling loads for each specimen were also calculated by a computer code and compared to experimental buckling loads. Good correlation was achieved for specimens that did not buckle as columns. The graphite-epoxy specimens which buckled locally had significant postbuckling response prior to failure at a maximum load (crippling). Differences in the crippling failure and compressive strength failure are discussed for the graphite-epoxy specimens. / Master of Science

Micromechanical models are presented which can be used to evaluate: stress concentrations in the vicinity of single and multiple fiber fractures in unidirectional composites under axial loading; the tensile strength of unidirectional composites; fiber coatings that can be used to maximize the transverse strain-to-failure and longitudinal shear strain-to-failure of composites; and the compression strength of composite materials containing embedded cylindrically shaped sensors or actuators. In each case, with the exception of the longitudinal shear model, the micromechanical predictions are compared with the experimental results. In the cases of the fiber fracture model and the transverse strain-to-failure model, these experimental results are obtained by employing a macro-model composite. It is demonstrated that the constituents of the macromodel composite can be systematically altered in order to study physical parameters such as fiber volume fraction and fiber coatings. / Master of Science

A simple expression using a critical fillet hoop stress (CFHS) model was derived to predict the capacity of a simply supported wood beam with a notch on the tension face between the supports. The derivation used the hypothesis that cracking initiates when the hoop stress tangent to the free surface of a round-cornered notch exceeds a critical value. This critical value is characteristic to the material. Finite element modeling was used to explore the effects of a broad range of notch geometries, notch locations, beam sizes, loading configurations, and material elastic properties on fillet hoop stress. The analyses assumed homogeneous, orthotropic, linear elastic behavior, and used a hybrid element to provide accurate results in the region of high stress gradients. Simplified, closed form expressions to predict maximum hoop stress were developed from the numerical results. Notched beam tests included nine wood materials, encompassing hardwoods and softwoods in both green and kiln-dried conditions. A broad array of notch geometries was tested. A theoretical framework related the experimental failure loads with the calculated maximum fillet hoop stress values. The dependence of failure loads on notch geometry, location, and loading condition was described well by the predictive expression derived from the finite element modeling. The CFHS model can be applied to sharp-cornered notches when an appropriate effective fillet radius is substituted into the strength equation. Preliminary test results showed the effective fillet radius to be material dependent; theoretical analysis suggested a beam depth dependence as well. The notched beam strength equation utilizes a single material constant which can be experimentally determined from tests of beams with a single notch geometry. The notched beam strength parameter, κ, was found to be strongly related to specific gravity and cross-grain tensile strength. The regression equation from this work can be used to estimate κ for solid wood materials outside of this study. CFHS results compared favorably with those of earlier models shown to be accurate over a more limited set of cases. In addition to its broad applicability, the CFHS method benefits from its reliance on only one, easily determined, material parameter and avoids the need for directional fracture toughness and elastic parameter data which are very difficult to obtain. / Ph. D.

The flexural vibration of two incomplete circular rings, approximately 360º, fixed at one end and free at the other, is investigated. One ring lies in the thin ring range. The other ring lies in the borderline range between a thick and thin ring. A theoretical approach is used in an attempt to approximate the first three natural frequencies of the rings. These theoretical results are then compared with the results obtained from an experimental investigation. In an attempt to simplify the general equation of motion of the ring an assumption was made that the tangential inertia term had a negligible effect on the natural frequencies of a thin ring. The frequencies obtained from the resulting frequency equation were found to be poor approximations for the system. Good approximations were obtained for the first two frequencies of the thin ring, using the method of Rayleigh -Ritz. / Master of Science

The objective of this study was to investigate the out-of-plane tensile strength of graphite/epoxy laminates as a function of porosity. An experimental test program was designed to apply tension to the faces of circular graphite/epoxy specimens in a direction perpendicular to the laminate mid-plane. The specimens were removed from the webs of angle sections fabricated by Lockheed Georgia Company using (AS4/1806 and AS4/3501-6 graphite/epoxy material systems with a stacking sequence of (±45/90₂/ ±45/0₂)_S or (±45/0₂/ +̅ 45/90₂)_S. The specimen porosities were the result of four distinct processing methods: a baseline hand lay-up, low pressure cure-cycle, a solvent wipe of pre-preg to remove resin, and the addition of water between pre-pregs. The experimental results have shown a significant reduction in the out-of-plane tensile strength as a function of increasing void content. The volume fraction of pores, pore geometry, size, and orientation were determined for a representative number of specimens by metallography and optical analysis methods. This data was combined with the out-of-plane tensile data and used in the theoretical model, prepared by Brown et al, to predict the out-of-plane strength as a function of porosity. The predicted strength values compared very well with the experimental data when the pores were found to be uniformly distributed throughout the laminate. / Master of Science

It is important in structural analysis and design, whether deterministic or reliability-based, to know the level of uncertainty for the methods of strength prediction. The uncertainty associated with strength prediction is the result of ambiguity and vagueness in the system. This study addresses the ambiguity component of uncertainty; this includes uncertainty due to randomness in the basic strength parameters (random uncertainty) and systematic errors and scatter in the prediction of strength (modeling uncertainty). The vagueness component is briefly discussed. A methodology for quantifying modeling and random uncertainty is presented for structural failure modes with a well defined limit state. A methodology is also presented for determining the relative importance of the basic strength parameters in terms of their importance to the total random uncertainty. These methodologies are applied to the compressive failure of longitudinally stiffened panels. The strength prediction model used in this analysis was developed in the UK and is widely used in analysis and design. Several experimental sample sets are used in the analysis. Mean values and coefficients of variation are reported for the random and modeling uncertainties. A comparison with results from other studies with several strength prediction algorithms is undertaken for the modeling uncertainty. All of these studies involve longitudinally stiffened panels which fail in axially compressive collapse. Ranges for the mean and coefficient of variation of the modeling uncertainty are presented. / Master of Science

The strength of notched and impact damaged laminates was studied. The solution for a plate containing an elliptic opening and inclusion was used as given by Lekhnitskii. The solution for the infinite plate, combined with laminate analysis to determine the ply stresses, and the average stress criterion proposed by Whitney and Nuismer were used to predict the notched strength. However, unlike Whitney and Nuismer, the average stress criterion was used at the ply level. The strength of off-axis unidirectional laminates was predicted by using a matrix oriented failure criterion applied at a critical point on the boundary of the hole. A good agreement between the experimental and predicted data was obtained. On the other hand, an attempt made to predict the notched strength of angle-ply laminates was not as successful. This is believed to be due to the different failure modes existing among different [± 𝛉]_s laminates. The controversy on whether the characteristic dimension is a material or geometric property, together with the belief that the physics of fracture of composites is better represented at the ply level, have motivated the author to seek an invariant equation which describes the dependence of the characteristic dimension, D₀. A quantitative approach to determine the characteristic dimension in the average stress criterion was proposed. A good agreement between experimental and predicted data was found. It was also found that contrary to prior claims, the value of D₀ does not depend on the diameter of the hole, when used at the ply level. Moreover, the strength of quasi-isotropic laminates loaded at an angle ϕ with respect to the material x-axis was also studied. Again, excellent agreement between experiment and predictions was shown. The tensile strength after impact (TSAI) was investigated. An approach based on modeling the delaminated area as an elliptic inclusion was used. The difference between the compliances of the plate and the inclusion was assumed to be proportional to the ratio of the delaminated areas. At low impact energy, a reference area was used. The results obtained using this approach gave good agreement with the experimental data. / Ph. D.

This study developed a general methodology for probabilistic service life prediction of a composite viscoelastic cylindrical structure under random outdoor environment. The analysis emphasized both the statistical variations of environmental thermal loads and of material properties. The daily probability of failure was calculated considering failures due to both the excessive stress and strain. The probabilistic service life was then obtained via the evaluation of cumulative hazard function. Models for the deterministic and random variations of environmental thermal loads- ambient temperature, sky radiation, wind convection, and solar radiation, were developed and were considered in obtaining the structure's surface temperature. The statistical characteristics such as the mean and variance of the induced stresses and-strains were calculated via the uses of complex frequency response functions. Methods for statistical characterization of time and temperature dependent viscoelastic material properties were presented. Five statistical distributions- Normal, Log-Normal, Beta, Gamma, and Weibull, were considered for the goodness of fit. Two forms of material deterioration- time and temperature dependent aging and cumulative damage due to loading were also recognized. Three statistical distributions- Normal, Log-Normal, and Weibull, were used to represent the variations of induced daily maximum stress and strain. The daily probabilities of failure due to the maximum stress and strain were calculated based on the concept of load and resistance interference. The effects of these failure modes were then combined to define daily probability of failure of the structure. / Doctor of Philosophy