Systematic Error in the Measure of Microdamage by Modulus Degradation During Four-Point Bending Fatigue

2007 ◽  
Author(s):  
Matthew D. Landrigan ◽  
Ryan K. Roeder
Keyword(s):  
Fatigue Testing ◽  
Elastic Beam ◽  
Beam Theory ◽  
Maximum Load ◽  
Beam Deflection ◽  
Linear Elastic ◽  
Four Point Bending ◽  
Specimen Width ◽  
Initial Modulus ◽  
Specimen Height

The accumulation of fatigue damage in bovine and human cortical bone is conventionally measured by modulus or stiffness degradation. The initial modulus or stiffness of each specimen is typically measured in order to normalize tissue heterogeneity to a prescribed strain [1,2]. Cyclic preloading at 100 N for 20 cycles has been used for this purpose in both uniaxial tension and four-point bending tests [1–3]. In four-point bending, the specimen modulus is often calculated using linear elastic beam theory as, (1)E=3Fl4bh2ε where F is the applied load, l is the outer support span, b is the specimen width, h is the specimen height, and ε is the maximum strain based on the beam deflection [2]. The maximum load and displacement data from preloading is used to determine the initial specimen modulus. The initial modulus and a prescribed maximum initial strain are then used to determine an appropriate load for fatigue testing under load control.

Revisiting the crevasse-depth calving law in the presence of melt undercutting

2021 ◽  
Author(s):  
Donald Slater ◽  
Doug Benn ◽  
Tom Cowton ◽  
Jeremy Bassis ◽  
Joe Todd
Keyword(s):  
Mass Loss ◽  
Ice Sheet ◽  
Elastic Beam ◽  
Beam Theory ◽  
Principal Mechanism ◽  
Tidewater Glaciers ◽  
Linear Elastic ◽  
Tidewater Glacier ◽  
Elastic Fracture ◽  
The Impact

<p>For tidewater glaciers worldwide, calving is a principal mechanism of mass loss. In turn, undercutting of tidewater glacier termini by submarine melting is understood to be a principal driver of calving. Yet, we currently have no practical and widely-accepted parameterisations that can represent the impact of submarine melting on calving in ice sheet models that are used for sea level projection, reducing confidence in their predictions.</p><p>The ‘crevasse-depth calving law’ that broadly relates depth-mean stress to a crevasse depth has been very widely used in models of tidewater glaciers, but this law does not fully account for the impact of submarine melt undercutting on the near-terminus stress field, which may be the key link between tidewater glaciers and the ocean. As such, we here work to incorporate the full impact of melt undercutting into a revised crevasse-depth calving law.</p><p>We combine elastic beam theory, linear elastic fracture mechanics and Elmer/Ice simulations to study the propagation of surface and basal crevasses near the front of tidewater glaciers in response to melt undercutting. We work to parameterise these results through a simple revision of the existing crevasse-depth calving law. The revised law explicitly accounts for the impact of melt undercutting on crevasses near the terminus, without increasing the computational demand on ice sheet models that might incorporate such a law, representing an important step towards better projection of ice sheet mass loss driven by the ocean.</p>

scholarly journals On Measuring Flexural Properties of Ice Using Cantilever Beams

1983 ◽  
Vol 4 ◽  
pp. 58-65 ◽  
Author(s):  
R. M. W. Frederking ◽  
G. W. Timco
Keyword(s):  
Loading Rate ◽  
Ice Sheets ◽  
Elastic Beam ◽  
Beam Theory ◽  
Beam Width ◽  
Beam Deflection ◽  
Cantilever Beams ◽  
Beam Length ◽  
Fine Grained ◽  
Geometry Dependence

Tests have been performed on fine-grained, columnar, freshwater ice sheets 40 to 70 mm thick grown in a refrigerated model basin. Cantilever beams of various geometries were tested for lengths ranging from 200 to 2 000 mm and widths of 50 to 250 mm. Analysis of the results in terms of simple elastic beam theory indicated that modulus increased with increasing beam length and decreasing bean width. An analytical model for beam deflection was developed, taking into account the effects of buoyancy, shear, and rotation and deflection at the root. This model satisfactorily explained the observed deflection behaviour and the apparent geometry dependence of the modulus. Flexura! strength was independent of beam length, but decreased with increasing beam width. Flexural strength was independent of loading rate, whereas modulus decreased with increased loading time.

scholarly journals On Measuring Flexural Properties of Ice Using Cantilever Beams

1983 ◽  
Vol 4 ◽  
pp. 58-65 ◽  
Author(s):  
R. M. W. Frederking ◽  
G. W. Timco
Keyword(s):  
Loading Rate ◽  
Ice Sheets ◽  
Elastic Beam ◽  
Beam Theory ◽  
Beam Width ◽  
Beam Deflection ◽  
Cantilever Beams ◽  
Beam Length ◽  
Fine Grained ◽  
Geometry Dependence

Tests have been performed on fine-grained, columnar, freshwater ice sheets 40 to 70 mm thick grown in a refrigerated model basin. Cantilever beams of various geometries were tested for lengths ranging from 200 to 2 000 mm and widths of 50 to 250 mm. Analysis of the results in terms of simple elastic beam theory indicated that modulus increased with increasing beam length and decreasing bean width. An analytical model for beam deflection was developed, taking into account the effects of buoyancy, shear, and rotation and deflection at the root. This model satisfactorily explained the observed deflection behaviour and the apparent geometry dependence of the modulus. Flexura! strength was independent of beam length, but decreased with increasing beam width. Flexural strength was independent of loading rate, whereas modulus decreased with increased loading time.

Capillary Force Induced Elastic Deformation on ZnS Nanobeams

2011 ◽  
Author(s):  
Xinnan Wang ◽  
Xiaodong Li
Keyword(s):  
Electron Microscope ◽  
Surface Energy ◽  
Total Energy ◽  
Elastic Deformation ◽  
Capillary Force ◽  
Elastic Beam ◽  
Small Strain ◽  
Beam Deflection ◽  
Atomic Force ◽  
Transmission Electron

In this study, synthesized Wurtzite-structured ZnS nanobelts was investigated using high resolution transmission electron microscope, atomic force microscope, and scanning electron microscope for structural and morphology analyses. Results show that ZnS nanobelts are tens of microns in length, mostly ∼40×50 nm2 in width and thickness. The nanobelts grow along direction [001] and are dislocation free. The distance spacing for (001) plane is 3.19A˚. The capillary force was found strong enough to deform the ZnS nanobeam down to the substrate. Theoretical analysis on small strain elastic deformation was conducted. It was found that as the maximum beam deflection increases, beam elastic energy increases; in the meantime, the surface energy decreases. The net increase in elastic beam energy is less than the net decrease in the surface energy, resulting in total energy decrease. In addition, as the volume of liquid increases, for a certain maximum beam deflection, the total energy increases, this is result of the increase of the surface energy. Furthermore, for a specific nanobeam to be deflected to the underlying surface, the amount of liquid can be calculated.

scholarly journals Nonlinear ferro-electro-elastic beam theory

2009 ◽  
Vol 46 (11-12) ◽  
pp. 2397-2406 ◽  
Author(s):  
Uri Kushnir ◽  
Oded Rabinovitch
Keyword(s):  
Elastic Beam ◽  
Beam Theory

scholarly journals Analysis of dynamics of a vertical cantilever in rotary coupling to the moving frame with movement limiters

2018 ◽  
Vol 241 ◽  
pp. 01021
Author(s):  
Piotr Wolszczak ◽  
Grzegorz Litak ◽  
Krystian Lygas
Keyword(s):  
Mechanical Energy ◽  
Elastic Beam ◽  
Beam Deflection ◽  
Moving Frame ◽  
Nonlinear Phenomena ◽  
Horizontal Distance ◽  
Energy Effect ◽  
Cross Sectional ◽  
Excitation Beam ◽  
Analysis Of Dynamics

The efficiency of the mechanical energy harvesting with the use of vibrating elements can be improved by synchronizing stimulation vibrations and own linear frequencies of systems as well as super or sub harmonics induced by non-linear phenomena. The article presents numerical cross-sectional study of the mechanical system. The system consists of an elastic beam set vertically, which the lower end is fixed in the rotary support, and is stimulated to move in the horizontal axis. The upper end of the beam is free but below its level there are bumpers limiting the free rotation of the beam. Numerical studies took into account the variability of the frequency and amplitude of the excitation beam movement, and horizontal distance between bumpers. Beam deflection was observed, on the basis of which the amount of energy generated by the piezo element was estimated. Nonlinear phenomena and analysis of frequency synchronization of vibrations improving the energy effect of an energy generator are presented.

scholarly journals On controllability of a linear elastic beam with memory under longitudinal load

2014 ◽  
Vol 3 (2) ◽  
pp. 231-245 ◽  
Author(s):  
Sergei A. Avdonin ◽  
◽  
Boris P. Belinskiy ◽  
Keyword(s):  
Elastic Beam ◽  
Linear Elastic ◽  
Longitudinal Load ◽  
With Memory

Design of High Frequency Fatigue Testing Machine Driven by Piezoelectric Vibrator

2012 ◽  
Vol 220-223 ◽  
pp. 543-548
Author(s):  
Meng Jie ◽  
Hai Feng Xie ◽  
Yan Liu ◽  
Zhi Gang Yang
Keyword(s):  
High Frequency ◽  
Fatigue Testing ◽  
Testing Machine ◽  
Fatigue Property ◽  
Maximum Load ◽  
Load Level ◽  
Piezoelectric Resonance ◽  
Piezoelectric Vibrator ◽  
Plate Spring ◽  
Working Principle

In order to measure the fatigue property of the small and hard brittle components working under conditions of the little amplitude, high frequency force, a novel kind of resonant high frequency fatigue testing machine which is driven by the piezoelectric vibrator (PZT、PLZT or PMN) has been proposed. Firstly, the working principle of the piezoelectric resonance high frequency fatigue testing machine is analyzed, and the dynamic model of the fatigue testing machine is established to get the systemic dynamic characteristics. Then a prototype is designed and produced. Finally, the maximum load on the sample is measured by the test with the machine. The results indicate that the maximum load on the sample is 23.4N-98.1N when changing the voltage (100V-250V) and the thickness of the plate spring (1.1mm-0.6mm). The prototype made in this paper is suitable for the tensile and fatigue testing with the load level mentioned above under the condition of little amplitude and high frequency force.

scholarly journals Comparison of 1D and 2D solutions for a beam under transverse impact

2018 ◽  
Vol 148 ◽  
pp. 05005 ◽  
Author(s):  
Vítězslav Adámek
Keyword(s):  
Analytical Solution ◽  
Timoshenko Beam ◽  
Elastic Beam ◽  
Beam Theory ◽  
Two Dimensional ◽  
Transverse Impact ◽  
Dimensional Theory ◽  
Beam Geometry ◽  
Stationary Vibration ◽  
Main Factors

The problem of non-stationary vibration of an elastic beam caused by a transverse impact loading is studied in this work. In particular, two different approaches to the derivation of analytical solution of the problem are compared. The first one is based on the Timoshenko beam theory, the latter one follows the exact two-dimensional theory. Both mentioned methods are used for finding the response of an infinite homogeneous isotropic beam. The obtained analytical results are then compared and their agreement is discussed in relation to main factors, i.e. the beam geometry, the character of loading and times and points at which the beams responses are studied.

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