Recent Results on the Elasticity Theory of Inclusions

1994 ◽  
Vol 47 (1S) ◽  
pp. S10-S17 ◽  
Author(s):  
Jin H. Huang ◽  
T. Mura
Keyword(s):  
Composite Materials ◽  
Work Hardening ◽  
Strain Energy ◽  
Volume Fraction ◽  
Exact Formula ◽  
Stress And Strain ◽  
Inclusion Problems ◽  
Elastic Fields ◽  
Work Hardening Rate ◽  
Minimum Strain Energy

A method drawing from variational method is presented for the purpose of investigating the behavior of inclusions and inhomogeneities embedded in composite materials. The extended Hamilton’s principle is applied to solve many problems pertaining to composite materials such as constitutive equations, fracture mechanics, dislocation theory, overall elastic moduli, work hardening and sliding inclusions. Especially, elastic fields of sliding inclusions and workhardening rate of composite materials are presented in closed forms. For sliding inclusion problems, the sliding is modeled by adding the Somigliana dislocations along a matrix-inclusion interface. Exact formula are exploited for both Burgers vector and the disturbances in stress and strain due to sliding. The resulting expressions are obtained by utilizing the principle of minimum strain energy. Finally, explicit expressions are obtained for work-hardening rate of composite materials. It is verified that the work-hardening rate and yielding stress are independent on the size of inclusions but are dependent on the shape and the volume fraction of inclusions.

Elastic Fields in a Polygon-Shaped Inclusion With Uniform Eigenstrains

1997 ◽  
Vol 64 (3) ◽  
pp. 495-502 ◽  
Author(s):  
H. Nozaki ◽  
M. Taya
Keyword(s):  
Composite Materials ◽  
Closed Form ◽  
Strain Field ◽  
Strain Energy ◽  
Convex Polygon ◽  
Numerical Examples ◽  
Elastic Fields ◽  
Closed Form Solutions ◽  
Arbitrary Convex ◽  
Shaped Inclusion

In this paper the elastic fields in an arbitrary, convex polygon-shaped inclusion with uniform eigenstrains are investigated under the condition of plane strain. Closed-form solutions are obtained for the elastic fields in a polygon-shaped inclusion. The applications to the evaluation of the effective elastic properties of composite materials with polygon-shaped reinforcements are also investigated for both dilute and dense systems. Numerical examples are presented for the strain field, strain energy, and stiffness of the composites with polygon shaped fibers. The results are also compared with some existing solutions.

scholarly journals A Strategy for Dimensionality Reduction and Data Analysis Applied to Microstructure–Property Relationships of Nanoporous Metals

Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 1822
Author(s):  
Norbert Huber
Keyword(s):  
Machine Learning ◽  
Dimensionality Reduction ◽  
Work Hardening ◽  
Large Range ◽  
Scaling Law ◽  
Principal Component ◽  
Underlying Structure ◽  
Structure Property ◽  
Work Hardening Rate ◽  
Nanoporous Metals

Nanoporous metals, with their complex microstructure, represent an ideal candidate for the development of methods that combine physics, data, and machine learning. The preparation of nanporous metals via dealloying allows for tuning of the microstructure and macroscopic mechanical properties within a large design space, dependent on the chosen dealloying conditions. Specifically, it is possible to define the solid fraction, ligament size, and connectivity density within a large range. These microstructural parameters have a large impact on the macroscopic mechanical behavior. This makes this class of materials an ideal science case for the development of strategies for dimensionality reduction, supporting the analysis and visualization of the underlying structure–property relationships. Efficient finite element beam modeling techniques were used to generate ~200 data sets for macroscopic compression and nanoindentation of open pore nanofoams. A strategy consisting of dimensional analysis, principal component analysis, and machine learning allowed for data mining of the microstructure–property relationships. It turned out that the scaling law of the work hardening rate has the same exponent as the Young’s modulus. Simple linear relationships are derived for the normalized work hardening rate and hardness. The hardness to yield stress ratio is not limited to 1, as commonly assumed for foams, but spreads over a large range of values from 0.5 to 3.

scholarly journals Forming Limit Stress Diagram Prediction of Pure Titanium Sheet Based on GTN Model

Materials ◽  
2019 ◽  
Vol 12 (11) ◽  
pp. 1783 ◽  
Author(s):  
Tao Huang ◽  
Mei Zhan ◽  
Kun Wang ◽  
Fuxiao Chen ◽  
Junqing Guo ◽  
...  
Keyword(s):  
Volume Fraction ◽  
Pure Titanium ◽  
Void Volume Fraction ◽  
Void Volume ◽  
Forming Limit ◽  
Stress And Strain ◽  
Gtn Model ◽  
Stress Diagram ◽  
Limit Stress ◽  
Hemispherical Punch

In this paper, the initial values of damage parameters in the Gurson–Tvergaard–Needleman (GTN) model are determined by a microscopic test combined with empirical formulas, and the final accurate values are determined by finite element reverse calibration. The original void volume fraction (f0), the volume fraction of potential nucleated voids (fN), the critical void volume fraction (fc), the void volume fraction at the final failure (fF) of material are assigned as 0.006, 0.001, 0.03, 0.06 according to the simulation results, respectively. The hemispherical punch stretching test of commercially pure titanium (TA1) sheet is simulated by a plastic constitutive formula derived from the GTN model. The stress and strain are obtained at the last loading step before crack. The forming limit diagram (FLD) and the forming limit stress diagram (FLSD) of the TA1 sheet under plastic forming conditions are plotted, which are in good agreement with the FLD obtained by the hemispherical punch stretching test and the FLSD obtained by the conversion between stress and strain during the sheet forming process. The results show that the GTN model determined by the finite element reverse calibration method can be used to predict the forming limit of the TA1 sheet metal.

Crack Driving Force in Anisotropic Media due to Non-Elastic Deformation

2004 ◽  
Vol 261-263 ◽  
pp. 75-80
Author(s):  
G.H. Nie ◽  
H. Xu
Keyword(s):  
Elastic Deformation ◽  
Driving Force ◽  
Strain Energy ◽  
Elastic Stress ◽  
Complex Function ◽  
Crack Driving Force ◽  
Special Cases ◽  
Degree Of Anisotropy ◽  
Minimum Strain Energy ◽  
Orthotropic Media

In this paper elastic stress field in an elliptic inhomogeneity embedded in orthotropic media due to non-elastic deformation is determined by the complex function method and the principle of minimum strain energy. Two complex parameters are expressed in a general form, which covers all characterizations of the degree of anisotropy for any ideal orthotropic elastic body. The stress acting on the long side of ellipse can be considered as a crack driving force and applied in failure and fatigue analysis of composites. For some special cases, the resulting solutions will reduce to the known results.

Mechanical characterization of a woven multi-layered hyperelastic composite laminate under uniaxial loading

2021 ◽  
pp. 002199832110115
Author(s):  
Shaikbepari Mohmmed Khajamoinuddin ◽  
Aritra Chatterjee ◽  
MR Bhat ◽  
Dineshkumar Harursampath ◽  
Namrata Gundiah
Keyword(s):  
Composite Materials ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Mechanical Tests ◽  
Stress Strain ◽  
Aerospace Applications ◽  
Envelope Material ◽  
The Individual ◽  
High Dielectric

We characterize the material properties of a woven, multi-layered, hyperelastic composite that is useful as an envelope material for high-altitude stratospheric airships and in the design of other large structures. The composite was fabricated by sandwiching a polyaramid Nomex® core, with good tensile strength, between polyimide Kapton® films with high dielectric constant, and cured with epoxy using a vacuum bagging technique. Uniaxial mechanical tests were used to stretch the individual materials and the composite to failure in the longitudinal and transverse directions respectively. The experimental data for Kapton® were fit to a five-parameter Yeoh form of nonlinear, hyperelastic and isotropic constitutive model. Image analysis of the Nomex® sheets, obtained using scanning electron microscopy, demonstrate two families of symmetrically oriented fibers at 69.3°± 7.4° and 129°± 5.3°. Stress-strain results for Nomex® were fit to a nonlinear and orthotropic Holzapfel-Gasser-Ogden (HGO) hyperelastic model with two fiber families. We used a linear decomposition of the strain energy function for the composite, based on the individual strain energy functions for Kapton® and Nomex®, obtained using experimental results. A rule of mixtures approach, using volume fractions of individual constituents present in the composite during specimen fabrication, was used to formulate the strain energy function for the composite. Model results for the composite were in good agreement with experimental stress-strain data. Constitutive properties for woven composite materials, combining nonlinear elastic properties within a composite materials framework, are required in the design of laminated pretensioned structures for civil engineering and in aerospace applications.

Effect of Ferrite Volume Fraction on Mechanical Properties of X80 Pipeline Steel

2014 ◽  
Vol 989-994 ◽  
pp. 212-215
Author(s):  
J. Liu ◽  
G. Zhu ◽  
W. Mao
Keyword(s):  
Mechanical Properties ◽  
Heat Treatment ◽  
Work Hardening ◽  
Single Phase ◽  
Volume Fraction ◽  
Pipeline Steel ◽  
X80 Pipeline Steel ◽  
Hardening Behavior ◽  
Two Phases ◽  
Better Than

The effect of volume fraction of ferrite on the mechanical properties including strength, plasticity and wok hardening was systematically investigated in X80 pipeline steel in order to improve the plasticity. The microstructures with different volume fraction of ferrite and bainite were obtained by heat-treatment processing and the mechanical properties were tested. The work hardening behavior was analyzed by C-J method. The results show that the small amount of ferrite could effectively improve the plasticity. The work hardening ability and the ratio of yield/tensile strength with two phases of ferrite/bainite would be obviously better than that with single phase of bainite. The improvement of plasticity could be attributed to the ferrite in which more plastic deformation was afforded.

Modeling The Microwave Frequency Dielectric Properties of Thermoplastic Composite Materials

1992 ◽  
Vol 269 ◽  
Author(s):  
Mitchell L. Jackson ◽  
Curtis H. Stern
Keyword(s):  
Composite Materials ◽  
Dielectric Properties ◽  
Volume Fraction ◽  
Perturbation Technique ◽  
Resonant Cavity ◽  
Microwave Frequency ◽  
Thermoplastic Composite ◽  
Fiber Volume ◽  
Thermoplastic Matrix ◽  
Rotation Procedure

ABSTRACTMixture models were studied in an effort to predict the microwave frequency permittivities of unidirectional-fiber-reinforced thermoplastic-matrix composite materials as a function of fiber volume fraction, fiber orientation relative to the electric field, and temperature. The permittivities of the constituent fiber and plastic materials were measured using a resonant cavity perturbation technique at 9.4 GHz and at 2.45 GHz. The permittivities of the composite specimens were measured using a reflection cavity technique at 9.4 GHz and at 2.45 GHz. Simple “rule-of-mixtures” models that use the fiber and plastic permittivities have been found to approximate the complex dielectric properties of the composite for varied fiber volume fractions. The permittivities of oriented composites were modeled using a tensor rotation procedure. Composite permittivities were modeled with temperature up to the glass transition temperature of the thermoplastic matrix.

The Estimation of Thermal Conductivity for Alumina-Epoxy Composite Material with High Filling Volume Fraction

2014 ◽  
Vol 918 ◽  
pp. 21-26
Author(s):  
Chen Kang Huang ◽  
Yun Ching Leong
Keyword(s):  
Thermal Conductivity ◽  
Composite Material ◽  
Composite Materials ◽  
Physical Model ◽  
Electron Scattering ◽  
Volume Fraction ◽  
Epoxy Composite ◽  
The Matrix ◽  
Transport Theorem ◽  
Good Agreement

In this study, the transport theorem of phonons and electrons is utilized to create a model to predict the thermal conductivity of composite materials. By observing or assuming the dopant displacement in the matrix, a physical model between dopant and matrix can be built, and the composite material can be divided into several regions. In each region, the phonon or electron scattering caused by boundaries, impurities, or U-processes was taken into account to calculate the thermal conductivity. The model is then used to predict the composite thermal conductivity for several composite materials. It shows a pretty good agreement with previous studies in literatures. Based on the model, some discussions about dopant size and volume fraction are also made.

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