Thesis (M. Phil.)--University of Hong Kong, 1996. / Includes bibliographical references (leaf 207-212).

This thesis presents a detailed experimental programme on understanding the mechanics of drilling in porous brittle solids. Gypsum was used as a model material for this experimental study, in which the mechanics of drilling was decoupled into equivalent problems of indentation and cutting. A comprehensive understanding of the mechanics of indentation and cutting was gained by performing experiments in 2-D conditions. A camera and microscope assembly was used to capture images at high temporal and spatial resolution to measure the in situ deformation. Particle image velocimetry (PIV) algorithm was used to measure the deformation parameters such as velocity, strain-rate, strain and volume change. In the last part of this research, drilling experiments were performed in 3-D conditions and an attempt was made for understanding the mechanics of drilling by relating the drilling experiment results to that of indentation and cutting. A series of wedge indentation experiments were performed under 2-D plane-strain conditions. Development of a parabolic zone of deformation, surrounding the indenter, was observed, wherein this size of the deformation zone and the strain accumulation in the deformation zone was a function of the geometry of the indenter. The maximum effective strain decreased and the overall strain field was more diffuse with increase in the wedge angle. Significant volume change was also observed in this deformation zone and the amount of volume change increased with increase in the porosity of the material. The zones of high volume change (compaction bands) were stacked in the form of layers oriented perpendicular to the direction of indentation. These compaction bands were more localized for the case of lower angles of wedge indenter. The extent of the compaction bands was also a function of porosity and spread over a larger area for the case of low porosity samples. A change in the material response was also observed with change in porosity and geometry of the indenter. The appearance of the crack was delayed with increase in porosity and reduction of wedge angle. The experimental results were also used to validate an analytical cavity expansion model. A better prediction of indentation pressure and the size of the deformation zone was possible after volume change corrections were incorporated into the cavity expansion formulation. A series of orthogonal cutting experiments were performed in 2-D plane-strain conditions. The e ect of tool geometry and the depth of cut on the mechanics of cutting was studied with the help of image based measurements and cutting force signatures. Different types of cutting mechanisms were observed for the case of positive and negative rake angle tool. A cyclic increase and decrease in the cutting force was observed in case of positive rake angle cutting tool. The decrease in the cutting force corresponded to the initiation of crack from the tip of the tool. The crack traversed towards the surface of the material and resulted in the removal of a material chip. With progress of cutting, the tool scratched the material surface, giving rise to the gradual increase in the cutting force as it again reached local maxima when the tool completely re-engaged with the material. For the case of negative rake angle, apart from cyclic increase and decrease of the cutting force, there was a development of a triangular dead zone at the tip of the cutting tool. The size of the dead zone varied cyclically with the progress of cutting. The length of crack, which resulted in the removal of the chip from the material, was found to be a function of the rake angle and the depth of cut. Drilling experiments were performed on gypsum samples in 3-D conditions. Two types of twist drills with different helix angles were used for this research work. Experiments were performed on the samples with two different porosities. Thrust force and torque signatures were recorded for five values of depth of cut per revolution. Since these experiments were performed in 3-D, image analysis was not performed. However, in order to ascertain a qualitative understanding of the drilling process, few experiments were performed on the edge of the material surface so that a cylindrical groove with semicircular cross section is made and the exposed surface of the material and the drill were imaged. The normalized thrust force and normalized torque were compared with indentation pressure and cutting force signatures and remarkable similarities between them was found. A transition from ductile to brittle type of response was observed with increase in the depth of cut per revolution, which was similar to what was observed in case of indentation. The magnitude of torque was found to be higher for high helix angle drills, which was counter to what was observed in cutting, which was due to the deposition of the material in helix for high helix angle drills, resulting in the reduction of the effective helix angle. An approximate estimate of the effective helix angle was made with the help of analytical solutions as well as from the qualitative analysis of the images.

Structural integrity assessment of nuclear components assessed using the R6 Failure Assessment Diagram approach requires an understanding of the limiting condition in terms of both fracture and plastic collapse. For ductile materials, such as stainless steels used for nuclear components, including the primary pipe-work of a Pressurised Water Reactor (PWR), the limiting condition defined by plastic collapse is likely to occur prior to the initiation of fracture. This is due to the relatively low yield stress of the material and the high fracture toughness. If this is the case, structural integrity may be solely assessed on plastic collapse criteria, with little or no reference to fracture toughness; thus considerably simplifying the assessment procedure, whilst maintaining the integrity of the plant. Nevertheless, an in-depth understanding of fracture under plastic collapse conditions is required to make a robust case for single parameter assessments based on a plastic collapse criterion alone. The challenge in this project lay in understanding and predicting ductile fracture initiation under large-scale yielding conditions, i.e. outside the normal validity limits of conventional elastic-plastic fracture mechanics as plastic collapse conditions are achieved. The approach developed in this research has explored three fracture assessment methods: (a) two parameter fracture mechanics based on the J-integral and a refined Q-parameter calculated closer to the crack-tip under widespread plasticity than is conventionally the case, (b) two local approach methods based on critical void growth ratio defined by Rice and Tracey, and (c) a local approach method based on the critical work of fracture. All three methodologies were found to adequately describe failure across a range of constraint conditions. The fracture toughness constraint dependence of 304(L) stainless steel was studied experimentally and analytically. Significant constraint loss was shown to occur in nominally high constraint fracture toughness specimens due to extensive plastic deformation at fracture initiation. Furthermore, significant fracture toughness constraint dependence was observed experimentally. An analytical method using local approach criteria was developed to predict high constraint fracture toughness, required for structural integrity assessments, and to quantify the constraint dependence fracture toughness as a function of two parameter fracture mechanics based on the J-integral and the refined Q-parameter. The influence of constraint on the prediction of failure in a stainless steel pipe containing a fully circumferential crack of various depths was investigated analytically for a range of loading conditions. A refined constraint independent failure assessment methodology was developed using local approach analyses. Using this methodology, the pipe component was shown to consistently fail by plastic collapse irrespective of the crack depth or loading condition. The conservatism of the conventional structural integrity assessment was quantified and shown to vary with crack depth and with loading conditions. This research has suggested that failure in a 304(L) stainless steel pipe will be by plastic collapse prior to ductile initiation for a limited range of defects and loading conditions. Further analytical studies and experimental work will be required to demonstrate whether this observation is general for a wider range of defects and loading conditions.

The investigation of failure in brittle materials, subjected to dynamic transient loading conditions, represents one of the ongoing challenges in the mechanics community. Progresses on this front are required to support the design of engineering components which are employed in applications involving extreme operational regimes. To this purpose, this thesis is devoted to the development of a framework which provides the capabilities to model how crack patterns form and evolve in brittle materials and how they affect the quantitative description of failure. The proposed model is developed within the context of diffusive interfaces which are at the basis of a new class of theories named phase field models. In this work, a set of additional features is proposed to expand their domain of applicability to the modelling of (i) rate and (ii) pressure dependent effects. The path towards the achievement of the first goal has been traced on the desire to account for micro-inertia effects associated with high rates of loading. Pressure dependency has been addressed by postulating a mode-of-failure transition law whose scaling depends upon the local material triaxiality. The governing equations have been derived within a thermodynamically-consistent framework supplemented by the employment of a micro-forces balance approach. The numerical implementation has been carried out within an updated lagrangian finite element scheme with explicit time integration. A series of benchmarks will be provided to appraise the model capabilities in predicting rate-pressure-dependent crack initiation and propagation. Results will be compared against experimental evidences which closely resemble the boundary value problems examined in this work. Concurrently, the design and optimization of a complimentary, improved, experimental characterization platform, based on the split Hopkinson pressure bar, will be presented as a mean for further validation and calibration.