The Stress Field Surrounding the Tip of a Crack Propagating in a Finite Body

The goal of this dissertation was to establish the relationship between a parameter descriptive of the trajectory of a smoothly curving crack, such as the curvature of the crack path, and the local stress state in the close vicinity of the crack tip. The behavior of fast -running cracks propagating along straight and smoothly curving paths in fracture specimens of various geometries was examined using dynamic photoelasticity and representations of the running crack stress field we redeveloped in terms of the coefficients of a set of infinite series, for both opening and shear mode loading conditions. Analysis of the isochromatic patterns, using local collocation methods based on this stress field representation, allowed the stress state in the neighborhood of the propagating crack-tip to be modelled with a high degree of accuracy and results were obtained for the variations with crack tip position of both the singular and leading non- singular stress field coefficients of interest. The results obtained for quasi-static and rapid crack propagation under opening mode conditions in a ring segment revealed the importance of retaining terms of order (at a minimum) r^1/2 even when only the singular term was to be determined accurately. Furthermore, it was found that the non-singular stress field coefficients varied similarly in both static and dynamic situations, with some variations in magnitude that could be attributed to crack speed. The results from the curved crack experiments also showed systematic variation of the non-singular terms, but more importantly, it was found that the instantaneous curvature of the crack path was related to the magnitude of the lowest order non-singular stress component (the coefficient of the r^1/2 term) associated with the local shear mode of deformation in the vicinity of the tip of the running crack. Furthermore, the results established that the only singularity associated with a crack propagating along a smoothly curving path in a brittle, isotropic material was that associated with the opening mode stress intensity factor, K1, and that the shear mode singularity, KII, was identically equal to zero

Asymptotic stress fields for thermomechanically loaded cracks in FGMs

The problem of a stationary crack in functionally graded materials (FGM), subjected to a combination of thermal and mechanical loading is considered. An asymptotic analysis coupled with Westergaard\u27s stress function approach is used to characterize the stress field around the crack tip. Thermal and mechanical properties (e.g., elastic modulus, coefficient of thermal expansion, and thermal conductivity) are assumed to vary exponentially. The crack is assumed to be inclined to the direction of the property gradation. The thermal loading is taken to be a uniform heat flow in a direction inclined to the crack. The principal of superposition from linear elasticity is used to solve the problem, whereby the problem is divided into a number of subproblems. The first four terms in the expansion of the stress field are derived to explicitly bring out the influence of nonhomogeneity on the structure of the stress field. It is observed that the presence of heat flow produced no additional singularity and hence the classical inverse square root singularity still prevails around the crack tip. Using these stress field contours of constant maximum shear stress are generated and the effect of thermal loading on the crack-tip stress field is discussed. Copyright © 2006 by ASTM International

Effect of Two-Dimensional Grading on the Thermomechanical Response of the Panel

Some of the advantages of functionally graded materials (FGM) are related to their ability to provide a better thermal protection and reduce delamination tendencies present in layered composites. In particular, in ceramic-metal systems these goals can be achieved by increasing the concentration of ceramic particles in the region adjacent to the heated surface using a heterogeneous single layered structure. The unfortunate by-products of such design are asymmetry about the middle surface of the structure and bending-stretching coupling. As a result, displacements and stresses increase as compared to the symmetric counterpart, while the buckling loads and natural frequencies decrease. One of the possible solutions to the problem compensating for a reduced stiffness of FGM structures is based on the replacement of one-dimensional grading with a two-dimensional grading, including the regions with enhanced stiffness. The paper illustrates the formulation of the problem and peculiarities introduced in the solution by two-dimensional grading on the example of a large aspect ratio panel subject to thermomechanical loading. ©2008 American Institute of Physic

Response of Spatially Tailored Structures to Thermal Loading

The paper presents the formulation and analysis of composite plates serving as STATs, i.e., spatially tailored advanced thermal structures where the distribution of the constituent phases varies throughout the surface as well as through the thickness. This is an extension of the well-known concept of functionally graded materials (FGM) and structures with the constituent phases varying only in the latter direction. As a result of two- or three-dimensional grading it is possible to optimize the response and properties of the structure providing multitask and multi-scale optimization. The response of plates with two- or three-dimensional grading to an arbitrary thermal loading is elucidated, including the conditions that result in thermal bending versus thermal instability

Dynamic response of pre-loaded structures subjected to combined extreme environments

A series of experiments was performed on Hastelloy X plates which were subjected to a combination of extreme temperatures, in-plane tensile loading, and transverse shock loading. To achieve these conditions a shock tube apparatus was used in conjunction with a novel hydraulic pre-loading fixture and propane flame torches. In order to understand the effects of shock load magnitude on the deformation behavior of the plates, two series of experiments were carried out at peak shock pressures of 1.7 MPa and 3.1 MPa, respectively. Both series of experiments were conducted over a range of temperatures from room temperature to 900 °C. High speed photography and Digital Image Correlation (DIC) were used to obtain three-dimensional, full-field deformation information. Side view images were also captured to validate the DIC results. The addition of a tensile pre-load reduced the maximum deflection for all temperatures. However, a higher magnitude of the tensile pre-load did not further reduce the maximum out-of-plane deflection of the plate for temperatures higher than 400 °C. The specimen deformation increased with increasing temperature until 800 °C. However, at 900 °C, due to anomaly in material constitutive behavior, the specimen deflection was observed to be lower than at 800 °C. An indentation mode of deformation was observed in some instances of the 3.1 MPa peak shock pressure experiments, particularly at higher temperatures