A Comparison of Constitutive Equations for the Energy-Based Lifing Method

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
John Wertz ◽  
Casey Holycross ◽  
M.-H. Herman Shen ◽  
Onome Scott-Emuakpor ◽  
Tommy George ◽  
...  
Keyword(s):  
Experimental Data ◽  
Dynamic Process ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Endurance Limit ◽  
Predictive Accuracy ◽  
Total Strain Energy ◽  
Constitutive Relationships ◽  
Energy Dissipated ◽  
Quasi Static Process

Alternatives to quasi-static and dynamic constitutive relationships have been investigated with respect to a previously developed energy-based fatigue lifing method for various load profiles, which states: the total strain energy dissipated during both a quasi-static process and a dynamic process are equivalent and a fundamental material property. Specifically, constitutive relationships developed by Ramberg–Osgood and Halford were modified for application to the existing energy-based framework and were compared to the lifing method originally developed by Stowell. Extensive experimentation performed on Titanium 6Al-4V (Ti-64) combined with experimental data generated for Aluminum (Al) 6061-T6 at various temperatures were utilized in support of this investigation. This effort resulted in considerable improvements to the accuracy of the lifing prediction for materials with an endurance limit through application of a modified-Halford approach. Additionally, the relative equality in predictive accuracy between the modified-Stowell approach the modified-Ramberg–Osgood approach was demonstrated.

An Energy-Based Axial Isothermal-Mechanical Fatigue Lifing Method

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
John Wertz ◽  
Todd Letcher ◽  
M.-H. Herman Shen ◽  
Onome Scott-Emuakpor ◽  
Tommy George ◽  
...  
Keyword(s):  
Strain Energy ◽  
Thermal Loading ◽  
Elevated Temperatures ◽  
Testing Procedure ◽  
Mechanical Fatigue ◽  
Full Life ◽  
Energy Dissipated ◽  
Life Predictions ◽  
Quasi Static Process

An energy-based fatigue lifing method for the determination of the full-life and critical-life of in-service structures subjected to axial isothermal-mechanical fatigue (IMF) has been developed. The foundation of this procedure is the energy-based axial room-temperature lifing model, which states: the total strain energy dissipated during both a quasi-static process and a dynamic (fatigue) process is the same material property. The axial IMF lifing framework is composed of the following entities: (1) the development of an axial IMF testing capability; (2) the creation of a testing procedure capable of assessing the strain energy dissipated during both a quasi-static process and a dynamic process at elevated temperatures; and (3) the incorporation of the effect of thermal loading into the axial fatigue lifing model. Both an axial IMF capability and a detailed testing procedure were created. The axial IMF capability was employed to produce full-life and critical-life predictions as functions of temperature, which were shown to have an excellent correlation with experimental fatigue data. For the highest operating temperature, the axial IMF full-life prediction was compared to lifing predictions made by both the universal slopes and the uniform material law prediction and was found to be more accurate at an elevated temperature.

Development of a Fatigue Damage and Lifing Assessment Method for Inconel 625 and Aluminum 6061-T6

2017 ◽  
Author(s):  
Dino Celli ◽  
M.-H. Herman Shen ◽  
Tommy George ◽  
Onome Scott-Emuakpor ◽  
Casey Holycross
Keyword(s):  
Fatigue Damage ◽  
Strain Energy ◽  
Room Temperature ◽  
Assessment Method ◽  
Fatigue Tests ◽  
Inconel 625 ◽  
Total Strain Energy ◽  
Mechanical Fatigue ◽  
Energy Dissipated ◽  
Good Agreement

An energy based fatigue damage and lifing assessment method is developed for a high temperature material, Inconel 625, and Aluminum 6061-T6. A newly developed experimental method is used for interrogating accumulated fatigue damage and evolution for low and high cycle fatigue (LCF/HCF) at continuum scales. The proposed fatigue lifing assessment method is based on assessing the total strain energy dissipated to cause fatigue failure of a material, known as the fatigue toughness. From the fatigue toughness and experimentally determined fatigue lives at two different stress amplitudes, the cyclic parameters of the Ramberg-Osgood constitutive equation that describes the hysteresis stress-strain loop of a cycle are determined. Stress controlled mechanical fatigue tests are performed to construct room temperature stress-life (S-N) curves and to determine damage progression based on accumulated fatigue damage. The predicted fatigue life obtained from the present energy based approach is found in good agreement with experimental data.

A Promising New Energy-Based Fatigue Life Prediction Framework

2005 ◽  
Author(s):  
Onome Scott-Emuakpor ◽  
M.-H. Herman Shen ◽  
Charles Cross ◽  
Jeffrey Calcaterra ◽  
Tommy George
Keyword(s):  
Fatigue Life ◽  
Strain Energy ◽  
Life Prediction ◽  
Total Strain ◽  
Total Strain Energy ◽  
Bending Fatigue ◽  
New Energy ◽  
Stress Ratios ◽  
Energy Dissipated ◽  
Fatigue Criterion

An energy-based fatigue life prediction framework has been developed for prediction of axial and bending fatigue life at various stress ratios. The framework for the prediction of fatigue life via energy analysis was developed in accordance with the approach in our previous study which states: the total strain energy dissipated during a monotonic fracture process is a material property that can be determined by measuring the area underneath the monotonic true stress-strain curve. The framework consists of the following two elements: (1) Development of a bending fatigue criterion by observing the total strain energy of the effective volume, which is achieved by computing the total plastic strain energy with consideration of the stress gradient influence through the thickness of a specimen, in the fatigue area, during cyclic loading. A comparison between the prediction and the experimental results from 6061-T6 aluminum specimens was conducted and shows that the new energy-based fatigue criterion is capable of predicting accurate fully reversed bending fatigue life. (2) Development of a new life prediction criterion for axial fatigue at various stress ratios. The criterion was constructed by accounting for both the residual energy dissipated, monotonically, due to the mean stress, and the incorporation of the mean stress effect into the total strain energy density dissipated per cycle. The performance of the criterion was demonstrated by experimental results from 6061-T6 aluminum dog-bone specimens subjected to axial stress at various stress ratios. The comparison shows very good agreement, thus validating the capability of producing accurate fatigue life predictions.

scholarly journals A generalized strain approach to anisotropic elasticity

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
M. H. B. M. Shariff
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Single Variable ◽  
Energy Functions ◽  
Anisotropic Strain ◽  
Strain Energy Functions ◽  
Strain Function

AbstractThis work proposes a generalized Lagrangian strain function $$f_\alpha$$ f α (that depends on modified stretches) and a volumetric strain function $$g_\alpha$$ g α (that depends on the determinant of the deformation tensor) to characterize isotropic/anisotropic strain energy functions. With the aid of a spectral approach, the single-variable strain functions enable the development of strain energy functions that are consistent with their infinitesimal counterparts, including the development of a strain energy function for the general anisotropic material that contains the general 4th order classical stiffness tensor. The generality of the single-variable strain functions sets a platform for future development of adequate specific forms of the isotropic/anisotropic strain energy function; future modellers only require to construct specific forms of the functions $$f_\alpha$$ f α and $$g_\alpha$$ g α to model their strain energy functions. The spectral invariants used in the constitutive equation have a clear physical interpretation, which is attractive, in aiding experiment design and the construction of specific forms of the strain energy. Some previous strain energy functions that appeared in the literature can be considered as special cases of the proposed generalized strain energy function. The resulting constitutive equations can be easily converted, to allow the mechanical influence of compressed fibres to be excluded or partial excluded and to model fibre dispersion in collagenous soft tissues. Implementation of the constitutive equations in Finite Element software is discussed. The suggested crude specific strain function forms are able to fit the theory well with experimental data and managed to predict several sets of experimental data.

An Energy-Based Axial Isothermal-Mechanical Fatigue Lifing Method

2012 ◽  
Author(s):  
John Wertz ◽  
Todd Letcher ◽  
M.-H. Herman Shen ◽  
Onome Scott-Emuakpor ◽  
Tommy George ◽  
...  
Keyword(s):  
Strain Energy ◽  
Thermal Loading ◽  
Elevated Temperatures ◽  
Testing Procedure ◽  
Mechanical Fatigue ◽  
Full Life ◽  
Energy Dissipated ◽  
Life Predictions ◽  
Quasi Static Process

An energy-based fatigue lifing method for the determination of the full-life and critical-life of in-service structures subjected to axial isothermal-mechanical fatigue (IMF) has been developed. The foundation of this procedure is the energy-based axial room-temperature lifing model, which states: the total strain energy dissipated during both a quasi-static process and a dynamic (fatigue) process is the same material property. The axial IMF lifing framework is composed of the following entities: (1) the development of an axial IMF testing capability; (2) the creation of a testing procedure capable of assessing the strain energy dissipated during both a quasi-static process and a dynamic process at elevated temperatures; and (3), the incorporation of the effect of thermal loading into the axial fatigue lifing model. Both an axial IMF capability and a detailed testing procedure were created. The axial IMF capability was employed to produce full-life and critical-life predictions as functions of temperature, which were shown to have excellent correlation with experimental fatigue data. For the highest operating temperature, the axial IMF full-life prediction was compared to lifing predictions made by both the Universal Slopes and the Uniform Material Law prediction and was found to be more accurate at elevated temperature.

A Generalized Strain Approach to Anisotropic Elasticity

2021 ◽  
Author(s):  
M.H.B.M. Shariff
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Single Variable ◽  
Energy Functions ◽  
Anisotropic Strain ◽  
Strain Energy Functions ◽  
Strain Function

Abstract This work proposes a generalized Lagrangian strain function fα (that depends on modified stretches) and a volumetric strain function gα (that depends on the determinant of the deformation tensor) to characterize isotropic/anisotropic strain energy functions. With the aid of a spectral approach, the single-variable strain functions enable the development of strain energy functions that are consistent with their infinitesimal counterparts, including the development of a strain energy function for the general anisotropic material that contains the general 4th order classical stiffness tensor. The generality of the single-variable strain functions sets a platform for future development of adequate specific forms of the isotropic/anisotropic strain energy function; future modellers only require to construct specific forms of the functions fα and gα to model their strain energy functions. The spectral invariants used in the constitutive equation have a clear physical interpretation, which is attractive, in aiding experiment design and the construction of specific forms of the strain energy. Some previous strain energy functions that appeared in the literature can be considered as special cases of the proposed generalized strain energy function. The resulting constitutive equations can be easily converted, to allow the mechanical influence of compressed fibres to be excluded or partial excluded and to model fibre dispersion in collagenous soft tissues. Implementation of the constitutive equations in Finite Element software is discussed. The suggested crude specific strain function forms are able to fit the theory well with experimental data and managed to predict several sets of experimental data.

Local material symmetry group for first- and second-order strain gradient fluids

2021 ◽  
pp. 108128652110216
Author(s):  
Victor A. Eremeyev
Keyword(s):  
Symmetry Group ◽  
Strain Gradient ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Mass Density ◽  
Material Model ◽  
Second Order ◽  
Material Symmetry ◽  
Local Material ◽  
Current Mass

Using an unified approach based on the local material symmetry group introduced for general first- and second-order strain gradient elastic media, we analyze the constitutive equations of strain gradient fluids. For the strain gradient medium there exists a strain energy density dependent on first- and higher-order gradients of placement vector, whereas for fluids a strain energy depends on a current mass density and its gradients. Both models found applications to modeling of materials with complex inner structure such as beam-lattice metamaterials and fluids at small scales. The local material symmetry group is formed through such transformations of a reference placement which cannot be experimentally detected within the considered material model. We show that considering maximal symmetry group, i.e. material with strain energy that is independent of the choice of a reference placement, one comes to the constitutive equations of gradient fluids introduced independently on general strain gradient continua.

scholarly journals Modelling the Inflation and Elastic Instabilities of Rubber-Like Spherical and Cylindrical Shells Using a New Generalised Neo-Hookean Strain Energy Function

2021 ◽  
Author(s):  
Afshin Anssari-Benam ◽  
Andrea Bucchi ◽  
Giuseppe Saccomandi
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Limit Point ◽  
Strain Energy ◽  
Cylindrical Shells ◽  
Strain Energy Function ◽  
Model Parameters ◽  
Wide Range ◽  
Cylindrical Tubes ◽  
Gent Model

AbstractThe application of a newly proposed generalised neo-Hookean strain energy function to the inflation of incompressible rubber-like spherical and cylindrical shells is demonstrated in this paper. The pressure ($P$ P ) – inflation ($\lambda $ λ or $v$ v ) relationships are derived and presented for four shells: thin- and thick-walled spherical balloons, and thin- and thick-walled cylindrical tubes. Characteristics of the inflation curves predicted by the model for the four considered shells are analysed and the critical values of the model parameters for exhibiting the limit-point instability are established. The application of the model to extant experimental datasets procured from studies across 19th to 21st century will be demonstrated, showing favourable agreement between the model and the experimental data. The capability of the model to capture the two characteristic instability phenomena in the inflation of rubber-like materials, namely the limit-point and inflation-jump instabilities, will be made evident from both the theoretical analysis and curve-fitting approaches presented in this study. A comparison with the predictions of the Gent model for the considered data is also demonstrated and is shown that our presented model provides improved fits. Given the simplicity of the model, its ability to fit a wide range of experimental data and capture both limit-point and inflation-jump instabilities, we propose the application of our model to the inflation of rubber-like materials.

Three-Dimensional Stress Distribution in Arteries

1983 ◽  
Vol 105 (3) ◽  
pp. 268-274 ◽  
Author(s):  
C. J. Chuong ◽  
Y. C. Fung
Keyword(s):  
Experimental Data ◽  
Stress Distribution ◽  
Vessel Wall ◽  
Strain Energy ◽  
Arterial Wall ◽  
Three Dimensional ◽  
Strain Energy Function ◽  
Exponential Form ◽  
Strain Relationship ◽  
Longitudinal Stretch

A three-dimensional stress-strain relationship derived from a strain energy function of the exponential form is proposed for the arterial wall. The material constants are identified from experimental data on rabbit arteries subjected to inflation and longitudinal stretch in the physiological range. The objectives are: 1) to show that such a procedure is feasible and practical, and 2) to call attention to the very large variations in stresses and strains across the vessel wall under the assumptions that the tissue is incompressible and stress-free when all external load is removed.

scholarly journals Ut vis sic tensio

2018 ◽  
Vol 45 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Giuseppe Saccomandi
Keyword(s):  
Experimental Data ◽  
Mechanical Properties ◽  
Elastic Strain ◽  
Strain Energy ◽  
Nonlinear Response ◽  
Solid Mechanics ◽  
Functional Form ◽  
Elastic Strain Energy ◽  
Strongly Nonlinear ◽  
Long Time

The mechanical properties of rubber-like materials have been offering an outstanding challenge to the solid mechanics community for a long time. The behaviour of such materials is quite difficult to predict because rubber self-organizes into mesoscopic physical structures that play a prominent role in determining their complex, history-dependent and strongly nonlinear response. In this framework one of the main problems is to find a functional form of the elastic strain-energy that best describes the experimental data in a mathematical feasible way. The aim of this paper is to give a survey of recent advances aimed at solving such a problem.

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