Michael C. Larson

Limits of crack growth stability in the double cleavage drilled compression specimen

A theoretical investigation of the double cleavage drilled compression specimen was undertaken to define the limits of stable crack growth for a range of geometries and fracture toughnesses typically used in fracture testing of brittle materials. Two-dimensional large displacement solutions for the mode I stress intensity factor were derived using energy methods. Comparisons with finite element results indicate that these models maintain a high level of accuracy well past the onset of unstable crack growth. Crack growth stability was assessed by differentiating the semi-analytical solutions and assembling the results in the form of design curves.

Inverse method of identification for three-dimensional subsurface cracks in a half-space

A procedure is presented which is well suited for three-dimensional subsurface crack identification in a half-space through the inversion of measured surface displacements. The investigation began with the linear, forward problem of generating contour maps of surface deformation produced by a fracture of known geometry and loading which is embedded in a finite medium. The fundamental solutions for tensile and shear multipoles in a half-space provided an efficient mathematical representation of the three-dimensional fracture. The inverse problem of crack identification centers on the development of a hybrid of the Marquardt–Levenberg algorithm. Initial guesses for the constrained set of search variables were determined heuristically from the correspondences between crack geometry and loading and the resulting uplift at the free surface. Physical measurements of surface deformation were taken for a cube of transparent acrylic polyester in which a fracture was hydraulically pressurized. Displacements induced at the surface of the specimen, which were measured by laser interferometry, had a strong correlation with predictions of the computational model (coupled with a finite element discretization). Numerical tests demonstrate the robustness of the inverse methodology even in the presence of the random and systematic errors corresponding to the experimental interferometric measurements.

NONDESTRUCTIVE IDENTIFICATION OF THREE-DIMENSIONAL EMBEDDED CRACKS IN FINITE BODIES BY INVERSION OF SURFACE DISPLACEMENTS

Abstract A combined experimental and numerical investigation demonstrates the effectiveness of a nondestructive method for crack identification based on inversion of surface displacements. Holographic interferometry was used to measure displacements of transparent acrylic cubes containing pressurized cracks. Results compared favorably with those of a three-dimensional hybrid numerical model. A nonlinear inversion code, using Levenberg–Marquardt iterations, was developed in order to search for the fracture geometries which minimized the difference between the theoretical and experimental predictions of surface displacement. The resulting algorithm was able to distinguish clearly the specimen geometries. The requisite level of robustness was achieved by gradually relaxing the constraints on the fracture geometry.

Fracture propagation near a frictionally - constrained fiber interface

Abstract This work provides a three-dimensional numerical fracture mechanics analysis of a crack periphery as it propagates through a brittle matrix and encounters an individual brittle fiber. The surface integral method, based upon a distribution of singular fundamental solutions, is used to represent both the cracks and the coupled interfacial sliding zone. The interfacial frictional tractions are assumed to satisfy a Coulomb relationship and are determined iteratively from the stress induced by the matrix crack, the stress induced by the developing slip, and the initial normal compressive interfacial stress (i.e. from setting or thermal mismatch). Simulations of an initially long straight crack front moving toward and past a fiber for different interfacial frictional characteristics were conducted. The implications for tailoring fiber/matrix interfaces to optimize the global toughening effect are discussed. If the interface between fiber and matrix is cohesive enough (but not too cohesive) then tractions which develop at the interface may effectively retard the local growth of a matrix crack. Raising the friction coefficient (or cohesion) at the interface must, however, be balanced against the potential for fiber failure in the high stress zone near the matrix crack periphery. The implications frictional slippage holds for inhibiting and possibly arresting small matrix cracks are emphasized.

High Cycle Vibration Testing of BGA Packages

The objective of this work is to develop an experimental apparatus, which will facilitate visual monitoring of the solder joint interconnects in a plastic ball grid array (PBGA) package during cyclic testing. The apparatus has been used to determine crack initiation, crack propagation speed, and joint failure. The experiments are complemented by nonlinear finite element modeling and static strain measurements using moire interferometry. A representative test is described and the result compared to two model descriptions found in the literature.Copyright

Experiments of Crack-Fiber Interactions in Composites with Frictional Interfaces

1. ABSTRACT The goal of the research is to provide design insight for enhancing apparent global fracture toughness of composite materials by exploiting friction between fibers and matrix. If the interface between fiber and matrix is cohesive enough then tractions a t the interfaces may impede the development of a matrix crack. However, increases of the interfacial friction must be balanced against the potential for fiber failure. This trade-off is being explored through threedimensional computational modeling using the surface integral method. This paper discusses some important features of the interaction between cracks and frictional interfaces and proceeds with a description of experiments on model systems which are being used to guide and verify the computational models. The numerical simulations are intended to clarify the physics of crack-fiber interaction and to generate guidelines for optimal design. Two experiments are described. The first involves a method for visually tracking the evolution of frictional sliding on an interface in the vicinity of a pseudo crack. The second comprises a method for growing and recording the progress of a three dimensional crack periphery as it encounters a cylindrical inclusion.