Anna Dollar

Load transfer in composites with a Coulomb friction interface

Abstract The transfer of load across a frictional interface between elastic solids is investigated. We formulate a model two-dimensional problem in which a fiber is extracted from or pressed into a half-plane to which it is connected via Coulomb friction. With a continuous distribution of dislocations to represent the slip, this problem can be reduced to solving a singular integral equation. Results of interest are the extent of the slip zone, the transfer of load from the fiber to the matrix, and the amount by which the fiber is extracted or depressed, all of which depend on the load in a non-linear fashion. Attention is focused on contrasting the results of the present analysis with approximate treatments generally incorporated into micro-mechanical models of composite materials.

A Tension Crack Impinging Upon Frictional Interfaces

A crack impinging normally upon a frictional interface is studied theoretically. We employ a solution technique which superposes the solution of a crack in a perfectly-bonded elastic medium with a continuous distribution of dislocations which represent slippage at the frictional interface. This procedure reduces the problem to a singular integral equation which is solved numerically. Specifically, we consider the problem of an infinite sheet subjected to uniaxial tension containing a finite crack which lies normal to the tension axis and has both crack tips impinging normally on frictional interfaces. The limiting problem of a semi-infinite crack impinging on a frictional interface is considered as well. Posed as model problems for cracking in weakly bonded fiber composites, these studies reveal the effective blunting that can result when a weak interface serves to deflect a propagating crack.

Results from a Statics Concept Inventory and their Relationship to other Measures of Performance in Statics

Concept inventories have been proposed for an increasing number of subjects in engineering and other fields. Such an assessment tool has been developed for Engineering Statics. An assessment instrument like a concept inventory is of value, however, only if performance on it is an indicator of performance in the subject more generally. The relation between class examinations and inventory performance were reported recently for students at the home institution of inventory developer (Steif). In the present paper, the relation between class examinations and inventory performance for additional schools was analyzed. The inventory is found to be predictive of student performance at other institutions, and is relevant to a wider range of problems than earlier suspected

Longitudinal Shearing of a Weakly Bonded Fiber Composite

The longitudinal shearing of a unidirectional fiber composite which sustains slippage at the fiber-matrix interface is studied theoretically. An expression for the effective shear modulus of the composite, assuming a dilute concentration of fibers, is derived. The necessary quantities are found from the solution to the problem of a single slipping fiber in an infinite matrix. A singular integral equation governing this problem is derived and solved numerically. Results for the progression of slip and for the effective shear modulus are presented.

Analyses of the fiber push-out test

Abstract A two-dimensional model of the fiber push-out test is considered. Two distinct methods of analysis are independently employed in solving the problem, and their accuracy is indicated by the virtual coincidence of the results. Interfacial debonding is assumed to be characterized by a cohesive zone model, and subsequent slippage obeys a Coulomb friction law. We have found that the results depart from those of the more commonly employed fracture-mechanics approach, if the cohesive zone size is of the order of the fiber diameter. The accuracy of various approximate analyses is discussed.

Enhancing traditional classroom instruction with web-based Statics course

A web-based Statics course is being developed by the authors as part of the Open Learning Initiative (OLI) at Carnegie Mellon University. OLI seeks to create and sustain freely available, cognitively informed learning tools designed to provide a substantial amount of instruction through the digital learning environment. This paper highlights the potential opportunities of online learning materials to enhance a traditional lecture-based course. We also identify the challenges that online materials face in promoting learning in an engineering course in which problem solving is intimately tied with drawing, and with writing and solving equations. Examples that illustrate the potential benefits of online materials, and that address the challenges associated with learning engineering courses, are presented. Finally, user studies and initial experience in blending these materials into an ongoing Statics course are summarized.

Stresses in fibers spanning an infinite matrix crack

Abstract The stresses in a unidirectional fiber composite subjected to tension parallel to the fibers, which has a single matrix crack bridged by fibers, are analyzed. Of interest is whether the enhanced load sustained by the fibers causes them to fail. In particular, we attempt to gain insight into the effect of the fiber-matrix interface on the stresses experienced by the fibers. As a preliminary approach to this issue, the analogous two-dimensional problem is studied. To simulate the influence of a real interface, we allow for interfacial slippage governed by a Coulomb friction law. Results for the dependence of the fiber stress on the fiber volume fraction, the interface parameters, and the load are presented.

Collaborative, goal-oriented manipulation of artifacts by students during statics lecture

To apply statics effectively, students must link the concepts and symbols of statics to the mechanical paraphernalia of engineering. Forming these links is challenging, however, because the interactions between inanimate objects are difficult to perceive. We have consequently revamped statics instruction so as to introduce the major concepts of statics-forces, moments, couples, static equivalency, free body diagrams and equilibrium - using simple objects on which students can exert forces and couples with their own hands. Small groups of students manipulate objects in lecture. To guide student interactions with the objects, to lay bare key concepts, and to acclimate students to the representations which are common in mechanics, we have devised multiple choice concept questions implemented through powerpoint presentations. Concept questions involve little or no calculation and focus on understanding of concepts. Moreover, insight into the concept questions can be obtained through manipulation of the objects and peer-to-peer discussions.

Interface Blunting of Matrix Cracks in Fiber-Reinforced Ceramics

A crack impinging upon an interface that can debond and then offer frictional resistance is studied theoretically. The central question at issue is the level of the remote load at which the crack penetrates the interface, whether or not some debonding of the interface occurs first. To answer this question, we compute the stress enhancement experienced by the impinged material—averaged over a microstructural length such as the fiber diameter—as a function of interface parameters. The solution to this elasticity problem is arrived at by means of distributed dislocations to represent relative motion at the interface. Special care needs to be taken to account properly for the contact problem at the interface. Not unexpectedly, it is found that higher debond energies and greater frictional resistances lead to higher stress concentrations and, hence, to lower remote failure loads.

Work in Progress: An Interactive Cognitively-Informed On-Line Statics Course

Progress in developing an highly-interactive online statics course is reported This course is part of Carnegie Mellons Open Learning Initiative (OLI), which is supported by the William and Flora Hewlett Foundation and seeks to create and sustain cognitively-informed online courses, to be available in various forms for individuals and institutions. To provide an effective learning environment this course both incorporates knowledge about typical difficulties faced by students in Statics and segments the subject into modules with clearly defined learning objectives that enable concurrent finegrained assessment. Such assessment allows individual students to track their learning; instructors are empowered to administer targeted remedial instruction to individuals and to discern larger patterns of challenges faced by the class. The power of computer medium is harnessed in providing, for example, discovery-learning that integrates questions with simulations, demonstrations of procedures, and opportunities for learners to practice skills while receiving hints and feedback