scholarly journals Loading-Rate Dependency of Young’s Modulus for Class I and Class II Rocks

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Hailong Zhang ◽  
Seisuke Okubo ◽  
Cancan Chen ◽  
Yang Tang ◽  
Jiang Xu
Keyword(s):  
Young’S Modulus ◽  
Loading Rate ◽  
Young's Modulus ◽  
Underlying Mechanism ◽  
Time Dependent ◽  
Rate Dependency ◽  
Underground Structures ◽  
Dependent Behavior ◽  
Rate Of Increase ◽  
Variable Compliance

Understanding the time-dependent behavior of rocks is important for ensuring the long-term stability of underground structures. Aspects of such a time-dependent behavior include the loading-rate dependency of Young’s modulus, strength, creep, and relaxation. In particular, the loading-rate dependency of Young’s modulus of rocks has not been fully clarified. In this study, four different types of rocks were tested, and the results were used to analyze the loading-rate dependency of Young’s modulus and explain the underlying mechanism. For all four rocks, Young’s modulus increased linearly with a tenfold increase in the loading rate. The rocks showed the same loading-rate dependency of Young’s modulus. A variable-compliance constitutive equation was proposed for the loading-rate dependency of Young’s modulus, and the calculated results agreed well with measured values. Irrecoverable and recoverable strains were separated by loading-unloading-reloading tests at preset stress levels. The constitutive equations showed that the rate of increase in Young’s modulus increased with the irrecoverable strain and decreased with increasing stress. The increase in the irrecoverable strain was delayed at high loading rates, which was concluded to be the main reason for the increase in Young’s modulus with an increasing loading rate.

scholarly journals Loading Rate Dependency of Young's Modulus of Rock.

2001 ◽  
Vol 117 (1) ◽  
pp. 29-35 ◽  
Author(s):  
Seisuke OKUBO ◽  
Katsunori FUKUI ◽  
Xu JIANG
Keyword(s):  
Young’S Modulus ◽  
Loading Rate ◽  
Young's Modulus ◽  
Rate Dependency

An Analysis of the “Durometer” Indentation

1993 ◽  
Vol 66 (5) ◽  
pp. 827-836 ◽  
Author(s):  
Brian J. Briscoe ◽  
K. Savio Sebastian
Keyword(s):  
Elastic Modulus ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Theory Of Elasticity ◽  
Time Dependent ◽  
Shore Hardness ◽  
Hardness Tester ◽  
Hardness Number

Abstract The mechanics of the indentation of elastomers by the “Durometer” (Shore A) hardness tester is analysed using the theory of elasticity to derive an interrelation between the Shore hardness number and the Young's modulus. Experimental compliance curves, for different elastomers, are provided to support the theory. The theoretical interrelationships between the International Rubber Hardness and the Shore A Hardness and the corresponding elastic modulus are also compared. The effects of the time dependent deformations are examined. Finally, the error introduced by computing the Young's modulus using an equivalent punch solution is examined and a means of improving the predictions is provided.

Basic Biomechanics for Craniofacial Surgeons: The Responses of Alloplastic Materials and Living Tissues to Mechanical Forces

FACE ◽  
2021 ◽  
pp. 273250162110602
Author(s):  
Jack C. Yu ◽  
Steven R. Buchman ◽  
Arun K. Gosain ◽  
Robert J. Havlik ◽  
Tien-Hsiang Wang ◽  
...  
Keyword(s):  
Young’S Modulus ◽  
Soft Tissues ◽  
Environmental Changes ◽  
Young's Modulus ◽  
Time Dependent ◽  
External Fixators ◽  
Craniofacial Skeleton ◽  
Stress Strain ◽  
Viscoelastic Composite ◽  
Alloplastic Materials

Many terms such as twist, compress, bend, and stretch, describe how materials behave when subjected to mechanical stresses. Subjective adjectives to describe the property of materials such as hard or brittle are imprecise and impedes proper understanding of important principles needed in planning and performing surgical treatments. The viability of tissue and time dependent variables effect healing and compound the issue. Some parameters are time dependent (strain rate), while others are nearly independent of time (Young’s modulus). The craniofacial skeleton and enveloping soft tissues are viscoelastic composite materials which undergo time-dependent changes upon loading. The ability to remodel and respond to environmental changes makes them “smart,” reenforcing where needed and removing where not required based on a set of predetermined upper and lower thresholds. This mini review has 7 sections on engineering principles that underpin craniofacial surgery: (1) The general concept of mechanics: load, force, stress, strain, compression, tension, shear, stress-strain curves and values derived from them such as Young’s modulus, fatigue damage, and load- shearing. (2) Material properties of bone and suture and structural engineering of the craniofacial skeleton in normal and pathological conditions. (3) Fixation using wires, screws, and plates: anatomy and function of screws and plates, locking plates, lag screws, internal and external fixators. (4) Biomechanics of distraction osteogenesis and the effects of radiation. (5) Finite element analysis and other computational biomechanical tools. (6) Virtual surgical planning, cutting guides, and intra-operative navigation. (7) Tissue engineering: design goals, criteria, and constraints. An appreciation and understanding of these biomechanical principles will help craniofacial surgeons to facilitate intrinsic optimization and better treat complex morphological problems, helping one achieve the most favorable and durable results. The biological responses to mechanical stress are extremely important as well, but due to space constraints, they will be the subject of a separate dedicated review.

Modeling the Effect of Strain Rate on the Mechanical Properties of HDPE/Clay Nanocomposite Foams

2008 ◽  
Vol 16 (8) ◽  
pp. 561-575
Author(s):  
Choonghee Jo ◽  
Hani E. Naguib
Keyword(s):  
Mechanical Properties ◽  
Electron Microscope ◽  
Constitutive Model ◽  
Strain Rate ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Favorable Effect ◽  
Logarithmic Scale ◽  
Nanocomposite Foams ◽  
Rate Of Increase

A constitutive model considering the effect of strain rate on the mechanical properties of semicrystalline polymer/clay nanocomposite foams was studied. Also, the influence of crystallinity on the effect of strain rate was incorporated in the model. High density polyethylene (HDPE)/clay nanocomposite foam was manufactured by a batch foaming process. Intercalated clay structures in the nanocomposite were investigated by means of transmission electron microscope (TEM), and the crystallinity of the material was measured using differential scanning calorimeter (DSC). Also, foam morphologies were studied by using scanning electron microscope (SEM). The favorable effect of nanoclay on the foaming was increased as crystallinity decreases. Also, the influence of crystallinity on the foaming decreased at high clay contents. The tensile strength of the foams increased linearly to the logarithmic scale of strain rate. The Young's modulus of the foams was reinforced by increasing the crystallinity. However, the rate of increase in the modulus was blunted as strain rate increases. Also, the Young's modulus increased gradually with increasing the strain rate, but the rate of increase diminished as crystallinity increases. This combining effect of strain rate and crystallinity on the Young's modulus was modeled and a viscoelastic stress-strain behavior of the foam was also proposed. The proposed constitutive model was validated by experiments.

scholarly journals Generalized Relaxation Behavior of Rock Under Various Loading Conditions Using a Constant Linear Combination of Stress and Strain

2021 ◽  
Vol 9 ◽  
Author(s):  
Hailong Zhang ◽  
Yang Tang ◽  
Seisuke Okubo ◽  
Shoujian Peng ◽  
Cancan Chen
Keyword(s):  
Linear Combination ◽  
Control Method ◽  
Relaxation Behavior ◽  
Time Dependent ◽  
Feedback Signal ◽  
Failure Behavior ◽  
Stress And Strain ◽  
Loading Conditions ◽  
Underground Structures ◽  
Dependent Behavior

Time-dependent behavior has been demonstrated to be an essential factor in determining the long-term stability of underground structures. Creep and relaxation experiments are commonly used to investigate time-dependent behavior by subjecting rock to constant stress and strain. However, both stress and strain of in-situ rock masses are likely to change with time, a phenomenon known as generalized relaxation that has not been thoroughly investigated. In this study, a newly proposed control method with a constant linear combination of stress and strain as a feedback signal is used in compression and tension tests to investigate generalized relaxation behaviors of rocks. The results showed that the stress and strain of generalized relaxation are dependent on values of α, which represented generalized relaxation direction. The isochronous curves are enclosed within stress–strain curves of different loading conditions. The variation of stress (∆σ) and strain (∆ε) increases with increasing stress level and decreases with increasing confining pressure. Also, ∆σ and ∆ε in region II are smaller than in regions I and III. Furthermore, by performing brittle rock tests, complete generalized relaxation curves are obtained; three stages are observed, which are similar to conventional creep and relaxation behavior. Finally, the time and generalized relaxation failure behavior of Class I and Class II rock are discussed. The study is a valuable resource for gaining a comprehensive understanding of the time-dependent behavior of rocks and improving the stability and safety of underground structures.

Applying digital image correlation to wood strands: Influence of loading rate and specimen thickness

Holzforschung ◽  
2010 ◽  
Vol 64 (6) ◽  
Author(s):  
Gi Young Jeong ◽  
Audrey Zink-Sharp ◽  
Daniel P. Hindman
Keyword(s):  
Digital Image Correlation ◽  
Young’S Modulus ◽  
Digital Image ◽  
Poisson’S Ratio ◽  
Loading Rate ◽  
Young's Modulus ◽  
Image Correlation ◽  
Poisson's Ratio ◽  
Specimen Thickness ◽  
Loading Rates

Abstract Previous studies were devoted to various applications of digital image correlation (DIC) to wood and wood-based composites. However, the focus of these studies was qualitative strain distribution. Overall, there is a lack of testing protocols of DIC for quantifying the elastic properties of woody materials. The objective of this study was to investigate the effects of different specimen thicknesses and loading rates on measurement of Young's modulus and Poisson's ratio by DIC. Young's modulus from DIC decreased as thickness increased at a loading rate of 0.254 mm min-1. Comparing the different loading rates at a thickness of 0.794 mm, Young's modulus from DIC was not in agreement with the value obtained by means of the extensometer regardless of loading rate. However, Young's modulus from DIC at a thickness of 0.381 mm and a loading rate of 0.254 mm min-1 was in good agreement with the corresponding Young's modulus obtained by an extensometer. Poisson's ratio measured from different loading rates and specimen thicknesses was not significantly different between the two measurement systems. From the testing arrangement applied for this study, it is recommended that DIC should be applied at a loading rate of 0.254 mm min-1 or slower for strands with a thickness of 0.381 mm or less.

Young's modulus

AccessScience ◽  
2015 ◽  
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus

CHANGE OF YOUNG'S MODULUS DURING STRUCTURAL RELAXATION IN AMORPHOUS FeB, FeNiB, FeNiP AND FeNiPB

1985 ◽  
Vol 46 (C8) ◽  
pp. C8-561-C8-565
Author(s):  
E. Huizer ◽  
A. van den Beukel
Keyword(s):  
Young’S Modulus ◽  
Structural Relaxation ◽  
Young's Modulus

Mechanical properties of FeAlSi powders prepared by mechanical alloying from different initial feedstock materials

2019 ◽  
Vol 107 (2) ◽  
pp. 207 ◽  
Author(s):  
Jaroslav Čech ◽  
Petr Haušild ◽  
Miroslav Karlík ◽  
Veronika Kadlecová ◽  
Jiří Čapek ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Mechanical Alloying ◽  
Young’S Modulus ◽  
Milling Time ◽  
Young's Modulus ◽  
Element Model ◽  
X Ray Diffraction ◽  
X Ray ◽  
Powder Particles ◽  
Complete Homogenization

FeAl20Si20 (wt.%) powders prepared by mechanical alloying from different initial feedstock materials (Fe, Al, Si, FeAl27) were investigated in this study. Scanning electron microscopy, X-ray diffraction and nanoindentation techniques were used to analyze microstructure, phase composition and mechanical properties (hardness and Young’s modulus). Finite element model was developed to account for the decrease in measured values of mechanical properties of powder particles with increasing penetration depth caused by surrounding soft resin used for embedding powder particles. Progressive homogenization of the powders’ microstructure and an increase of hardness and Young’s modulus with milling time were observed and the time for complete homogenization was estimated.

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