scholarly journals Stress-Strain Response of Cylindrical Rubber Fender under Monotonic and Cyclic Compression

Materials ◽  
2019 ◽  
Vol 12 (2) ◽  
pp. 282 ◽  
Author(s):  
Chia-Chin Wu ◽  
Yung-Chuan Chiou
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Polynomial Function ◽  
Compressive Strain ◽  
Strain Curve ◽  
Strain Range ◽  
Compression Tests ◽  
Cyclic Compression ◽  
The Relationship

The study was devoted to the observation and modeling the mechanical behaviors of a hybrid SBR/NR (Styrene-Butadiene/Natural Rubber) hybrid vulcanized rubber fender under monotonic/cyclic compression. In experimental observations of the monotonic compression tests, it was found that lateral deformation occurred on the tested fender and was more significant with increasing the extent of the compressive strain. The relationship between the transmission stress S c and the compressive strain e c was nonlinear and the absorbed strain-energy-density was increased monotonically with the increment of the compressive strain. Among all cyclic compression tests with strain controlled, the reductions in both the stress range and the absorbed strain-energy-density up to the ten-thousandth cycle were found and then both of the cyclic properties remain approximately constant in the following compression cycles. Two new properties, the softening factor and the energy reduction factor, were introduced to quantify the effect of the strain range on the extent of the reduction in stress range and that on the absorbed strain-energy-density, respectively. It was found that both of the calculated values of the new properties increase with the increment of strain range. In mathematical modeling of the relationship between the transmission stress and the compressive strain, a new approach based on energy-polynomial-function E s ( e c ) was presented and was successfully used to simulate the monotonic curve and the stable hysteresis loop curves of the tested rubber fender in compression. Essentially, the energy-polynomial-function E s ( e c ) was obtained by performing a polynomial regression on a large amount of ( e c , E s ) data. Moreover, the least-square approach was applied to determine the corresponding regression coefficients in E s ( e c ) . Clearly, the stress-polynomial-function in modeling the S c − e c curve could be obtained from the differentiation of the energy-polynomial-function with respect to the compressive strain. In addition, to provide an adequate estimation of the mechanical properties of the cylindrical rubber fender under compression, the named cyclic stress-strain curve and cyclic energy-strain curve were developed and also modeled in this study.

Fatigue Life Law Based on Inelastic Strain Energy Density of Solder Alloys and its Simple Prediction Method

2020 ◽  
Author(s):  
Tomoya Fumikura ◽  
Mitsuaki Kato ◽  
Takahiro Omori
Keyword(s):  
Fatigue Life ◽  
Energy Density ◽  
Fatigue Test ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Prediction Method ◽  
Strain Range ◽  
Inelastic Strain ◽  
Stress Strain ◽  
Wide Range

Abstract In recent years, a fatigue life law based on inelastic strain energy density as proposed by Morrow has been applied to solder materials. In this study, the effectiveness of the fatigue life law based on inelastic strain energy density was compared with the conventional law based on inelastic strain range. First, the fatigue properties of Sn-Ag-Cu solder alloy were investigated by a torsional fatigue test with strain control. It was found that the stress–strain hysteresis loop arising from inelastic deformation occurred even under a low strain load with a fatigue life of about 1 million cycles. Therefore, as an extension of the low-cycle fatigue test, evaluation was performed using inelastic strain range and inelastic strain energy density. Experimental results show that when fatigue life was evaluated using inelastic strain energy density, a single power law was found over a wide range from the low-cycle region to the high-cycle region, and the validity of the fatigue life law based on inelastic strain energy density was confirmed. Next, a simple prediction method for the fatigue life law based on inelastic strain energy density was examined, taking the physical background into account. Two material constants of the fatigue life law based on the inelastic strain energy density were estimated from the stress–strain curve for a monotonic load and shown to be close to the actual fatigue test results.

scholarly journals Strain Energy Density as Failure Criterion for Quasi-Static Uni-axial Tensile Loading

2021 ◽  
Vol 15 (57) ◽  
pp. 331-349
Author(s):  
Andrea Kusch ◽  
Simone Salamina ◽  
Daniele Crivelli ◽  
Filippo Berto
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Notch Root ◽  
Tensile Load ◽  
Strain Curve ◽  
Material Behavior ◽  
Uniaxial Tensile ◽  
Notched Specimens ◽  
Nonlinear Stress

Strain energy density is successfully used as criterion for failure assessment of brittle and quasi-brittle material behavior. This work investigates the possibility to use this method to predict the strength of V-notched specimens made of PMMA under static uniaxial tensile load. Samples are characterized by a variability of notch root radii and notch opening angles. Notched specimens fail with a quasi-brittle behavior, albeit PMMA has a nonlinear stress strain curve at room temperature. The notch root radius has most influence on the strength of the specimen, whereas the angle is less relevant. The value of the strain energy density is computed by means of finite element analysis, the material is considered as linear elastic. Failure prediction, based on the critical value of the strain energy density in a well-defined volume surrounding the notch tip, show very good agreement (error <15%) with experimental data.

A Modified Closed Form Energy Based Framework for Fatigue Life Assessment for Aluminum 6061-T6—Damaging Energy Approach

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
M.-H. Herman Shen ◽  
Sajedur R. Akanda
Keyword(s):  
Fatigue Life ◽  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Strain Range ◽  
Life Assessment ◽  
Cycle Fatigue ◽  
Average Strain ◽  
Plastic Strain Range ◽  
Fatigue Life Assessment

A previously developed energy based high cycle fatigue (HCF) life assessment framework is modified to predict the low cycle fatigue (LCF) life of aluminum 6061-T6. The fatigue life assessment model of this modified framework is formulated in a closed form expression by incorporating the Ramberg–Osgood constitutive relationship. The modified framework is composed of the following entities: (1) assessment of the average strain energy density and the average plastic strain range developed in aluminum 6061-T6 during a fatigue test conducting at the ideal frequency for optimum energy calculation, and (2) determination of the Ramberg–Osgood cyclic parameters for aluminum 6061-T6 from the average strain energy density and the average plastic strain range. By this framework, the applied stress range is related to the fatigue life by a power law whose parameters are functions of the fatigue toughness and the cyclic parameters. The predicted fatigue lives are found to be in a good agreement with the experimental data.

An Investigation of the Mechanics of Tactile Sense Using Two-Dimensional Models of the Primate Fingertip

1996 ◽  
Vol 118 (1) ◽  
pp. 48-55 ◽  
Author(s):  
M. A. Srinivasan ◽  
K. Dandekar
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Load Distribution ◽  
Strain Energy ◽  
Compressive Strain ◽  
Surface Load ◽  
Type I ◽  
Tactile Information ◽  
Pass Filter ◽  
Low Pass Filter

Tactile information about an object in contact with the skin surface is contained in the spatiotemporal load distribution on the skin, the corresponding stresses and strains at mechanosensitive receptor locations within the skin, and the associated pattern of electrical impulses produced by the receptor population. At present, although the responses of the receptors to known stimuli can be recorded, no experimental techniques exist to observe either the load distribution on the skin or the corresponding stress-state at the receptor locations. In this paper, the role of mechanics in the neural coding of tactile information is investigated using simple models of the primate fingertip. Four models that range in geometry from a semi-infinite medium to a cylindrical finger with a rigid bone, and composed of linear elastic media, are analyzed under plane strain conditions using the finite element method. The results show that the model geometry has a significant influence on the surface load distribution as well as the subsurface stress and strain fields for a given mechanical stimulus. The elastic medium acts like a spatial low pass filter with the property that deeper the receptor location, the more blurred the tactile information. None of the models predicted the experimentally observed surface deflection profiles under line loads as closely as a simple heterogeneous waterbed model that treated the fingerpad as a membrane enclosing an incompressible fluid (Srinivasan, 1989). This waterbed model, however, predicted a uniform state of stress inside the fingertip and thus failed to explain the spatial variations observed in the neural response. For the cylindrical model indented by rectangular gratings, the maximum compressive strain and strain energy density at typical receptor locations emerged as the two strain measures that were directly related to the electrophysiologically recorded response rate of slowly adapting type I (SAI) mechanoreceptors. Strain energy density is a better candidate to be the relevant stimulus for SAIs, since it is a scalar that is invariant with respect to receptor orientations and is a direct measure of the distortion of the receptor caused by the loads imposed on the skin.

scholarly journals Microstructure-sensitive critical plastic strain energy density criterion for fatigue life prediction across various loading regimes

2020 ◽  
Vol 476 (2236) ◽  
pp. 20190766 ◽  
Author(s):  
Ritwik Bandyopadhyay ◽  
Veerappan Prithivirajan ◽  
Alonso D. Peralta ◽  
Michael D. Sangid
Keyword(s):  
Fatigue Life ◽  
Energy Density ◽  
Plastic Strain ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Hysteresis Loops ◽  
Strain Range ◽  
Strain Ratio ◽  
Material Point ◽  
Plastic Strain Energy

In the present work, we postulate that a critical value of the stored plastic strain energy density (SPSED) is associated with fatigue failure in metals and is independent of the applied load. Unlike the classical approach of estimating the (homogenized) SPSED as the cumulative area enclosed within the macroscopic stress–strain hysteresis loops, we use crystal plasticity finite element simulations to compute the (local) SPSED at each material point within polycrystalline aggregates of a nickel-based superalloy. A Bayesian inference method is used to calibrate the critical SPSED, which is subsequently used to predict fatigue lives at nine different strain ranges, including strain ratios of 0.05 and −1, using nine statistically equivalent microstructures. For each strain range, the predicted lives from all simulated microstructures follow a lognormal distribution. Moreover, for a given strain ratio, the predicted scatter is seen to be increasing with decreasing strain amplitude; this is indicative of the scatter observed in the fatigue experiments. Finally, the lognormal mean lives at each strain range are in good agreement with the experimental evidence. Since the critical SPSED captures the experimental data with reasonable accuracy across various loading regimes, it is hypothesized to be a material property and sufficient to predict the fatigue life.

scholarly journals Volume free strain energy density method for applications to blunt V-notches

2020 ◽  
Vol 28 ◽  
pp. 734-742
Author(s):  
Pietro Foti ◽  
Seyed Mohammad Javad Razavi ◽  
Liviu Marsavina ◽  
Filippo Berto
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Density Method ◽  
Free Strain

scholarly journals On the application of the volume free strain energy density method to blunt V-notches under mixed mode condition

2021 ◽  
Vol 230 ◽  
pp. 111716
Author(s):  
Pietro Foti ◽  
Seyed Mohammad Javad Razavi ◽  
Majid Reza Ayatollahi ◽  
Liviu Marsavina ◽  
Filippo Berto
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Mixed Mode ◽  
Strain Energy ◽  
Density Method ◽  
Free Strain

scholarly journals Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Mircea Bîrsan
Keyword(s):  
Energy Density ◽  
Constitutive Model ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Shell Theory ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Classical Shell Theory ◽  
Three Dimensional Elasticity ◽  
General Method

AbstractIn this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

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