Analysis of the tilted flat punch in couple-stress elasticity

This paper was accepted for publication in the journal International Journal of Solids and Structures and the definitive published version is available at https://doi.org/10.1016/j.ijsolstr.2016.01.017.In the present paper we explore the response of a half-plane indented by a tilted flat punch with sharp corners in the context of couple-stress elasticity theory. Contact conditions arise in a number of modern engineering applications ranging from structural and geotechnical engineering to micro and nanotechnology. As the contact scales reduce progressively the effects of the microstructure upon the macroscopic material response cannot be ignored. The generalized continuum theory of couple-stress elasticity introduces characteristic material lengths in order to describe the pertinent scale effects that emerge from the underlying material microstructure. The problem under investigation is interesting for three reasons: Firstly, the indentor's geometry is simple so that benchmark results may be extracted. Secondly, important deterioration of the macroscopic results may emerge in the case that a tilting moment is applied on the indentor inadvertently or in the case that the flat punch itself is not self-aligning so that asymmetrical contact pressure distributions arise on the contact faces. Thirdly, the voluntary application of a tilting moment on the flat punch during an experiment gives rise to potential capabilities of the flat punch for the determination of the material microstructural characteristic lengths. The solution methodology is based on singular integral equations which have resulted from a treatment of the mixed boundary value problem via integral transforms and generalized functions. The results show significant departure from the predictions of classical elasticity revealing that valuable information may be deducted from the indentation of a tilted punch of a microstructured solid

Acoustic emission signal processing framework to identify fracture in aluminum alloys

Acoustic emission (AE) is a common nondestructive evaluation tool that has been used to monitor fracture in materials and structures. The direct connection between AE events and their source, however, is difficult because of material, geometry and sensor contributions to the recorded signals. Moreover, the recorded AE activity is affected by several noise sources which further complicate the identification process. This article uses a combination of in situ experiments inside the scanning electron microscope to observe fracture in an aluminum alloy at the time and scale it occurs and a novel AE signal processing framework to identify characteristics that correlate with fracture events. Specifically, a signal processing method is designed to cluster AE activity based on the selection of a subset of features objectively identified by examining their correlation and variance. The identified clusters are then compared to both mechanical and in situ observed microstructural damage. Results from a set of nanoindentation tests as well as a carefully designed computational model are also presented to validate the conclusions drawn from signal processing

Interaction of cracks with dislocations in couple-stress elasticity. Part II: Shear modes

In the second part of this study, the interaction of a finite-length crack with a glide and a screw dislocation is examined within the framework of couple-stress elasticity. The loading from the two defects on the crack results to plane and antiplane shear modes of fracture, respectively. Both problems are attacked using the distributed dislocation technique and the cracks are modeled using distributions of discrete glide or screw dislocations. The antiplane strain case is governed by a single hyper-singular integral equation with a cubic singularity, whereas the plane strain case by a singular integral equation. In both cases, the integral equations are numerically solved using appropriate collocation techniques. The results obtained herein show that a crack under antiplane conditions closes in a smoother way as compared to the classical elasticity result. Further, the evaluation of the energy release rate in the crack-tips reveals an ‘alternating’ behavior between strengthening and weakening effects in the plane strain case, depending on the defect's distance from the crack-tip and the magnitude of the characteristic material length. On the other hand, the energy release rate in the antiplane mode shows a strengthening effect when couple-stresses are considered

Interaction of cracks with dislocations in couple-stress elasticity. Part I: Opening mode

In the present work the interaction of a finite-length crack with a discrete climb dislocation is studied within the framework of the generalized continuum theory of couple-stress elasticity. The climb dislocation is placed on the crack plane resulting in an opening crack mode. For the solution of the crack problem the distributed dislocation technique is employed. Due to the nature of the boundary conditions that arise in couple-stress elasticity, the crack is modeled by a continuous distribution of translational and rotational defects. The distribution of these defects produces both stresses and couple stresses in the body. It is shown that the interaction problem is governed by a system of coupled singular integral equations with both Cauchy and logarithmic kernels which is solved numerically using an appropriate collocation technique. The results for the near-tip fields differ in several respects from the predictions of classical fracture mechanics. It is shown that a cracked couple-stress solid behaves in a more rigid way compared to one governed by classical elasticity. Moreover, the evaluation of the energy release rate in the crack-tips and the associated driving force exerted on the dislocation reveals an interesting ‘alternating’ behavior between strengthening and weakening of the crack, depending on the distance of the crack-tip to the dislocation core as well as on ratio of the material length, introduced by the couple-stress theory, to the length of the crack

Some basic contact problems in couple stress elasticity

Indentation tests have long been a standard method for material characterization due to the fact that they provide an easy, inexpensive, non-destructive and objective method of evaluating basic properties from small volumes of materials. As the contact scales in such experiments reduce progressively (micro to nano-scales) the internal material lengths become important and their effect upon the macroscopic response cannot be ignored. In the present study, we derive general solutions for three basic two-dimensional (2D) plane-strain contact problems within the framework of the generalized continuum theory of couple-stress elasticity. This theory introduces characteristic material lengths in order to describe the pertinent scale effects that emerge from the underlying microstructure and has proved to be very effective for modeling microstructured materials. By using this theory, we initially study the problem of the indentation of a deformable elastic half-plane by a flat punch, then by a cylindrical indentor, and finally by a shallow wedge indentor. Our approach is based on singular integral equations which have resulted from a treatment of the mixed boundary value problems via integral transforms and generalized functions. The results show significant departure from the predictions of classical elasticity revealing that it is inadequate to analyze indentation problems in microstructured materials employing only classical contact mechanics. (C) 2014 Elsevier Ltd. All rights reserved