Revisiting classical concepts of Linear Elastic Fracture Mechanics - Part I: The closing ‘mathematical’ crack in an infinite plate and the respective Stress Intensity Factors

This is the first part of a short three-paper series, aiming to revisit some classical concepts of Linear Elastic Fracture Mechanics. The motive of this first paper is to highlight some controversial issues, related to the un­natu­ral overlapping of the lips of a ‘mathematical’ crack in an in­fin­­­ite plate load­ed by specific combinations of principal stresses at in­finity (predicted by the clas­si­c­al solu­tion of the respective first fundamental problem), and the closely as­so­ciated issue of negative mode-I Stress Intensity Factor. The problem is con­­­front­ed by superimposing to the first funda­mental problem of Lin­ear Elastic Frac­ture Mechanics for an in­fin­ite cracked plate (with stress-free crack lips) an ‘in­­verse’ mixed fund­amental problem. This superposition provides naturally ac­­­­­­­­ceptable stress and displacement fields, prohibiting overlapping of the lips (by means of contact stresses generated along the crack lips, which force the over­lapped lips back to naturally accepted position) and, also, non-negative mode-I Stress Intensity Factors. The solu­tions of this first paper form the basis for the next two papers of the series, dealing with the respective prob­lems in fi­­n­ite do­­mains (recall, for example, the cracked Brazil­ian disc con­fig­u­ra­tion) weak­­ened by artificial notches (rather than ‘math­e­mat­ical’ cracks), by far more interesting for practical engineer­ing ap­pli­­ca­tions

Fracture precursor phenomena in marble specimens under uniaxial compression by means of Acoustic Emission data

Marble specimens are subjected to a specially designed stepwise load­­ing protocol, in an attempt to detect fracture precursor phenomena taking advantage of Acoustic Emission (AE) data. The analysis is carried out in terms of the number of acoustic hits recorded and the time evolution of the improved b-value (Ib-value), the cumulative energy of the acoustic signals and the F-fun­c­tion. During the stage of in­creasing load, intense acoustic activity is detected as the cor­responding stress reaches the transitional phase from the linear to the nonlinear mechanical re­sponse of the material. When the stress is stabilized at levels exceeding 95% of the material’s compressive strength, the acous­tic activ­ity is drastically reduced. During the first seconds of the stress stabil­iz­ation stage the reduction follows an exponential law. Special attention is paid to the phases, where the occurrence of AE hits shows a strong increase. During these phases acoustic signals of low frequency and high RA are re­corded, in­di­cating that the micro-cracking process is of shear rather than of opening mode

Numerical simulation of bone screw induced pretension: The cases of under-tapping and conical profile

Even though screw induced pretension impacts the holding strength of bone screws, its implementation into the numerical simulation of the pullout phenomenon remains a problem with no apparent solution. The present study aims at developing a new methodology to simulate screw induced pretension for the cases of: a) cylindrical screws inserted with under-tapping and b) conical screws. For this purpose pullout was studied experimentally using synthetic bone and then simulated numerically. Synthetic bone failure was simulated using a bilinear cohesive zone material model. Pretension generation was simulated by allowing the screw to expand inside a hole with smaller dimensions or different shape than the screw itself. The finite element models developed here were validated against experimental results and then utilized to investigate the impact of under-tapping and conical angle. The results indicated that pretension can indeed increase a screw's pullout force but only up to a certain degree. Under-tapping increased cylindrical screws' pullout force up to 12%, 15% and 17% for synthetic bones of density equal to 0.08 g/cc, 0.16 g/cc and 0.28 g/cc respectively. Inserting a conical screw into a cylindrical hole increased pullout force up to 11%. In any case an optimum level of screw induced pretension exists

Revisiting classical concepts of Linear Elastic Fracture Mechanics - Part I: The closing ‘mathematical’ crack in an infinite plate and the respective Stress Intensity Factors

This is the first part of a short three-paper series, aiming to revisit some classical concepts of Linear Elastic Fracture Mechanics. The motive of this first paper is to highlight some controversial issues, related to the un­natu­ral overlapping of the lips of a ‘mathematical’ crack in an in­fin­­­ite plate load­ed by specific combinations of principal stresses at in­finity (predicted by the clas­si­c­al solu­tion of the respective first fundamental problem), and the closely as­so­ciated issue of negative mode-I Stress Intensity Factor. The problem is con­­­front­ed by superimposing to the first funda­mental problem of Lin­ear Elastic Frac­ture Mechanics for an in­fin­ite cracked plate (with stress-free crack lips) an ‘in­­verse’ mixed fund­amental problem. This superposition provides naturally ac­­­­­­­­ceptable stress and displacement fields, prohibiting overlapping of the lips (by means of contact stresses generated along the crack lips, which force the over­lapped lips back to naturally accepted position) and, also, non-negative mode-I Stress Intensity Factors. The solu­tions of this first paper form the basis for the next two papers of the series, dealing with the respective prob­lems in fi­­n­ite do­­mains (recall, for example, the cracked Brazil­ian disc con­fig­u­ra­tion) weak­­ened by artificial notches (rather than ‘math­e­mat­ical’ cracks), by far more interesting for practical engineer­ing ap­pli­­ca­tions

Damage evolution in marble under uniaxial compression monitored by Pressure Stimulated Currents and Acoustic Emissions

The spatiotemporal evolution of damage in marble speci­mens under uniaxial compression is monitored using Pressure Stimulated Currents (PSCs) and Acoustic Emissions (AEs). The novelty of the study is the use of an integrated grid of sensors (instead of a single pair of electrodes) to detect the weak electrical signals, emitted during loading. The use of such a grid of sensors does indeed enhance the capabilities of the PSC technique providing valuable information about the initiation and propagation of micro-fracturing at the interior of the specimens. The experimental results indicate that both the im­proved b-value of the AE hits and the energy of the PSCs offer information about the proximity of the applied stress to that causing fracture. It is thus con­­cluded that both quantities could be considered as pre-failure indicators

Pre-failure indicators detected by Acoustic Emission: Alfas stone, cement-mortar and cement-paste specimens under 3-point bending

Acoustic Emission (AE) is the technique most widely used nowadays for Structural Health Monitoring (SHM). Application of this technique for continuous SHM of restored elements of stone monuments is a challenging task. The co-existence of different materials creates interfaces rendering “identification” of the signals recorded very complicated. To overcome this difficulty one should have a clear overview of the nature of AE signals recorded when each one of the constituent materials is loaded mechanically. In this direction, an attempt is here described to enlighten the signals recorded, in case a series of structural materials (natural and artificial), extensively used for restoration projects of classic monuments in Greece, are subjected to 3-point bending. It is hoped that obtaining a clear understanding of the nature of AE signals recorded during these elementary tests will provide a valuable tool permitting “identification” and “classification” of signals emitted in case of structural tests. The results appear encouraging. In addition, it is concluded that for all materials tested (in spite their differences in microstructure and composition) clear prefailure indicators are detected, in good accordance to similar indicators provided by other techniques like the Pressure Stimulated Currents (PSC) one

Parametric study of the deformation of transversely isotropic discs under diametral compression

The displacement field in a circular disc made of a transversely isotropic material is explored in a parametric manner. The disc is assumed to be loaded by a parabolic distribution of compressive radial stresses along two finite arcs of its periphery in the absence of any tangential (frictional) stresses. Advantage is here taken of a recently introduced closed-form analytic solution for the displacement field developed in an orthotropic disc under diametral compression which was achieved adopting the complex potentials technique for rectilinear anisotropic materials as it was formulated in the pioneering work of S.G. Lekhnitskii. The analytic nature of this solution permits thorough, indepth exploration of the influence of some crucial parameters on the qualitative and quantitative characteristics of the deformation of transversely isotropic circular discs compressed between the jaws of the devise suggested by the International Society for Rock Mechanics for the standardized implementation of the Brazilian-disc test. The parameters considered include the anisotropy ratio (i.e., the ratio of the two elastic moduli characterizing the disc material), the angle between the loading axis and the planes of transverse isotropy and the length of the loaded arcs. Strongly non-linear relationships between these parameters and the components of the displacement field are revealed

Supplementary Medial Locking Plate Fixation Of Ludloff Osteotomy versus Sole Lag Screw Fixation: A Biomechanical evaluation

Background: The Ludloff oblique osteotomy is inherently unstable, which might lead to delayed union and loss of correction. Supplementary fixation to two lag screw fixation has been proposed. The hypothesis is that the osteotomy fixation constructs supplemented by a mini locking plate provide greater resistance to osteotomy gaping and loss of angular correction in response to cyclic loading. Methods: Twenty fourth generation composite 1st metatarsals were used and underwent a Ludloff osteotomy. They were divided in two fixation groups: two lag screws (Group A), and with a supplementary mini locking plate (Group B). Specimens were subjected to either monotonic loading up to failure or to fatigue (cyclic) tests and tracked using an optical system for 3D Digital Image Correlation. Findings: The osteotomy gap increased in size under maximum loading and was significantly greater in Group A throughout the test. This increase was observed very early in the loading process (within the first 1000 cycles). The most important finding though, was that with the specimens completely unloaded the residual gap increase was significantly greater in Group A after only 5000 cycles of loading up to the completion of the test. The lateral angle change under maximum loading was also significantly greater in Group A throughout the test, with that increase observed early in the loading process (5000 cycles). With the specimens completely unloaded the residual lateral angle change was also significantly greater in Group A at the completion of the test. Interpretation: Supplementary fixation with a mini locking plate of the Ludloff osteotomy provided greater resistance to osteotomy gaping and loss of angular correction compared to sole lag screws, in response to cyclic loading

The critical influence of some “tiny” geometrical details on the stress field in a Brazilian Disc with a central notch of finite width and length

The role of some geometrical characteristics of the notches ma­chined in circular discs, in order to determine the mode-I fracture tough­ness of brittle materials, is discussed. The study is implemented both analyti­cally and numerically. For the analytic study advantage is taken of a recently intro­duced solution for the stress- and displacement-fields developed in a finite disc with a central notch of finite width and length and rounded corners. The vari­ation of the stresses along strategic loci and the deformation of the peri­me­ter of the notch obtained analytically are used for the calibration/validation of a flexible nu­mer­ical model, which is then used for a parametric investiga­tion of the role of geometrical features of the notched disc (thickness of the disc, length and width of the notch, radius of the rounded corners of the notch). It is con­cluded that the role of the width of the notch is of critical im­port­ance. Both the ana­lytic and the numerical studies indicate definitely that ignoring the ac­curate geo­metric shape of the notch leads to erroneous results concerning the actual stress field around the crown of the notch. Therefore, it is possible that misleading values of the fracture toughness of the material of the disc may be obtained

A biomechanical study of the role of sitagliptin on the bone characteristics of diabetic rats

An experimental protocol is described aiming to explore the in­fluence of Type 2 Diabetes Mellitus on the biomechanical response of the bone tissue and, also, to quantify the potential beneficial role of a pharma­ceutical treatment, based on sitagliptin, a diabetes drug that increases the levels of natural substances called incretins. Twenty eight male, 10-week old Wistar rats were used, divided into three groups, i.e., the control one, the group including the diabetic rats and, finally, the group including the diabetic rats which were treated using sitagliptin. The biomechanical study was based on a series of three-point bending tests of the femora of the sacrificed rats and the analysis of the experimental data was implemented in terms of the actual geometry of the fractured cross-section. It was concluded that diabetic bones undertake larger forces despite the fact that the “diameter” of their cross-section was some­­how smaller. On the contrary, the slope of the load-deflection curve (cor­responding to a measure of the stiffness) of diabetic bones is slightly lower compared to the control bones. Finally, it seems that treating diabetic animals with sita­gliptin only partly reverses the effect of Type 2 Diabetes Mellitus on their bone tissue, at least concerning its strength and stiffness