Edwin Nagy

Microstructure and fracture in three dimensions

Abstract A high resolution three dimensional (3D) scanning technique called X-ray microtomography was used to measure internal crack growth in small mortar cylinders under compressive loading. Tomographic scans were made at different load increments in the same specimen. 3D image analysis was used to measure internal crack growth during each load increment. Load–deformation curves were used to measure the corresponding work of the external load on the specimen. Fracture energy was calculated using a linear elastic fracture mechanics approach using the measured surface area of the internal cracks created. The measured fracture energy was of the same magnitude that is typically measured in concrete tensile fracture. A nominally bilinear incremental fracture energy curve was measured. Separate components for crack formation energy and secondary toughening mechanisms are proposed. The secondary toughening mechanisms were found to be about three times the initial crack formation energy.

Three-dimensional work of fracture for mortar in compression

Abstract A high resolution three-dimensional scanning technique called X-ray microtomography was used to measure internal crack growth in small mortar cylinders loaded in uniaxial compression. Tomographic scans were made at different load increments in the same specimen. Three-dimensional image analysis was used to measure internal crack growth during each load increment. Load–deformation curves were used to measure the corresponding work of the external load on the specimen. Fracture energy was calculated using a linear elastic fracture mechanics approach, but using the actual surface area of internal cracks created. Preliminary results indicate fracture energies in the same range as those measured using traditional techniques.

Volume and Surface Area Distributions of Cracks in Concrete

Volumetric images of small mortar samples under load are acquired by X-ray microtomography. The images are binarized at many different threshold values, and over a million connected components are extracted at each threshold with a new, space and time efficient program. The rapid increase in the volume and surface area of the foreground components (cracks and air holes) is explained in terms of a simple model of digitization. Analysis of the data indicates that the foreground consists of thin, convoluted manifolds with a complex network topology, and that the crack surface area, whose increase with strain must correspond to the external work, is higher than expected.

Morphological lattice models for the simulation of softwood failure and fracture

Abstract This paper details the development of morphological lattice models to simulate fracture and failure in softwood. The lattice models rationally incorporate growth-ring geometry, differences in strength and stiffness between earlywood and latewood, and variations observed in the grain direction of clear wood (grain perturbation). Details regarding the implementation of these features are presented. Grain perturbation is shown to be a significant contributor to strength and stiffness variability. Simulations demonstrate that the inclusion of growth-ring geometry and incorporation of differences in the mechanical properties of earlywood and latewood are necessary for the lattice models to predict realistic fracture paths. Results are presented for laboratory tests on small red spruce specimens loaded in parallel-to-grain tension and shear. The lattice models give good predictions of mean specimen stiffness and strength, and reasonable predictions of strength variability. The fracture paths predicted by the lattice models are in excellent agreement with the experimental observations.

Acoustic emission measurements and lattice simulations of microfracture events in spruce.

Abstract A statistical lattice model was developed to investigate the energy associated with damage and failure of wood. The model incorporates several important morphological aspects of wood such as grain direction, early wood percentage and grain geometry. The model was developed to investigate progressive damage under enforced boundary displacements and has been adapted to predict fracture energy related phenomena. In this particular study, notched specimens were loaded in uniaxial tension while monitored by a passive acoustic emission (AE) measurement system. The energy associated with the mechanical damage was measured by the AE instruments and compared with the energy released by ruptured elements in the lattice model. Cumulative energy release was tracked as a function of specimen load and deformation in both model and experiment. A ratio was established between the cumulative AE energy released at the first drop in load and the cumulative fracture energy released when the model load-deformation relationship becomes significantly non-linear. An additional ratio was established between the total fracture energy measured prior to 50% of peak strain and the total fracture energy measured prior to peak strain. The magnitudes of these energy release ratios vary owing to a change in failure modes between the short model and the larger specimens; however, the shape of the AE energy release curve up to failure coincides well with that predicted by the model simulations.

Coupling AE Monitoring with Discrete Element Fracture Models

The monitoring and analysis of acoustic emissions related to fracture can be a trade-off between the simplistic yet practical empirical relationships and the more tedious yet fundamental relationships. In an intermediate area between these extremes, we are using acoustic emissions to monitor progressive fracture energy of small specimens of clear-grained wood. The wood specimens were modeled using a statistically variable lattice to represent material heterogeneity and disorder. The central hypothesis of the work is that a microfracture event captured by AE should correspond to the fracture of lattice elements in the simulation. Furthermore, the energy of the AE event should correspond to the local fracture energy released in the lattice simulation. By coupling lattice simulations with laboratory tests, we were able to establish a ratio between the cumulative fracture energy released in the simulation with the relative energy monitored by the AE system up to peak load. The magnitude of this ratio varies with failure mode, but in all cases, the shape of the cumulative AE energy captured mirrors the shape of the cumulative lattice fracture energy released. The results allow us to better match lattice element properties with the physical microstructure that the lattice elements are meant to represent.

Analysis of X-Ray Microtomographic Images to Measure Work of Fracture in Concrete

The fracture problem in concrete has been studied in great depth over the past thirty years. There have been many experimental and analytical attempts to calculate a work of fracture and to gain an understanding of the complex mechanisms of concrete fracture. An emerging theme is the intrinsic three-dimensional nature of the damage that occurs in loaded concrete. This has led to an increase in the amount of interior studies conducted. The insides of concrete have been exposed over the years by, among others, acoustic emission techniques, ultrasonics, dye penetration and radiography [1]. Most recently, x-ray microtomography has been used in order to see into the heart of concrete failure [2].