Prediction of Elastic Properties in Discontinuous Composite Materials

2005 ◽  
Vol 297-300 ◽  
pp. 1265-1269
Author(s):  
Hong Gun Kim
Keyword(s):  
Stress Transfer ◽  
Shear Stresses ◽  
Shear Lag ◽  
Analysis Model ◽  
Concentration Effects ◽  
Element Analysis ◽  
Fiber Aspect Ratio ◽  
The Matrix ◽  
Elastic Loading ◽  
Shear Lag Theory

The shortcoming of conventional SLT (Shear Lag Theory) is due to the neglect of stress transfer across the fiber ends, which results in the inaccurate stress variation for the fiber when the fiber aspect ratio is small in elastic loading. Thus a new model called NSLT (New Shear Lag Theory) is developed considering the stress concentration effects that exists in the matrix regions near fiber ends. In this paper the prediction of elastic composite modulus is presented to evaluate the stress transfer mechanism using NSLT. A micromechanical FEA (Finite Element Analysis) model with axisymmetry is implemented to verify the results of fiber stresses and interfacial shear stresses. It is found that the proposed model gives a reasonable prediction compared with the results based on other models.

Modification of the Shear Lag Analysis for Determination of Elastic Modulus of Short-Fiber (or Whisker) Reinforced Metal Matrix Composites

1992 ◽  
Vol 59 (2S) ◽  
pp. S176-S182 ◽  
Author(s):  
S. V. Nair ◽  
H. G. Kim
Keyword(s):  
Aspect Ratio ◽  
Stress Transfer ◽  
Local Stress ◽  
Short Fiber ◽  
Correct Prediction ◽  
Shear Stresses ◽  
Shear Lag ◽  
Stress Concentrations ◽  
End Effects ◽  
The Matrix

A major shortcoming of the original shear lag analysis is its inability to provide sufficiently accurate strengthening predictions when the fiber aspect ratio is small. This is due to its neglect of stress transfer across fiber ends and the stress concentrations that exist in the matrix regions near fiber ends. In this paper, a straightforward, yet rigorous, modification of the original shear lag analysis is presented by taking fiber end effects into account and to result in fully closed-form solutions. It is demonstrated that the modification not only results in a correct prediction of the modulus increases in the small aspect ratio regime when compared to finite element results, but is also able to correctly predict the values of interfaciat shear stresses and local stress variations in the matrix and fiber.

scholarly journals Stress Transfer from Axially Loaded Fiber to Matrix in a Microcomposite

1994 ◽  
Vol 365 ◽  
Author(s):  
Chun-Hway Hsueh
Keyword(s):  
Analytical Solutions ◽  
Volume Fraction ◽  
Axial Stress ◽  
Stress Transfer ◽  
Radial Dependence ◽  
Shear Lag ◽  
Shear Lag Model ◽  
The Matrix ◽  
Lag Model ◽  
Loaded Fiber

ABSTRACTThe shear lag model has been used extensively to analyze the stress transfer in a singe fiberreinforced composite (i.e., a microcomposite). To achieve analytical solutions, various simplifications have been adopted in the stress analysis. Questions regarding the adequacy of those simplifications are discussed in the present study for the following two cases: bonded interfaces and frictional interfaces. Specifically, simplifications regarding (1) Poisson's effect, and (2) the radial dependences of axial stresses in the fiber and the matrix are addressed. For bonded interfaces, the former can be ignored, and the latter can generally be ignored. However, when the volume fraction of the fiber is high, the radial dependence of the axial stress in the fiber should be considered. For frictional interfaces, the latter can be ignored, but the former should be considered; however, it can be considered in an average sense to simplify the analysis. Comparisons among results obtained from analyses with various simplifications are made.

Theoretical Assessment of Stress Analysis in Short Fiber Composites

2004 ◽  
Vol 261-263 ◽  
pp. 1421-1426
Author(s):  
Hong Gun Kim ◽  
Sung Mo Yang ◽  
Hong Gil Noh ◽  
Dong Joo Lee
Keyword(s):  
Stress Concentration ◽  
Aspect Ratio ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Stress Transfer ◽  
Shear Lag ◽  
Modulus Ratio ◽  
Fiber Aspect Ratio ◽  
Shear Lag Model ◽  
Lag Model

An investigation of composite mechanics to investigate stress transfer mechanism accurately, a modification of the conventional shear lag model was attempted by taking fiber end effects into account in discontinuous composite materials. It was found that the major shortcoming of conventional shear lag theory is not being able to provide sufficiently accurate strengthening predictions in elastic regime when the fiber aspect ratio is very small. The reason is due to its neglect of stress transfer across the fiber ends and the stress concentrations that exist in the matrix regions near the fiber ends. To overcome this shortcoming, a more simplified shear lag model introducing the stress concentration factor which is a function of several variables, such as the modulus ratio, the fiber volume fraction, the fiber aspect ratio, is proposed. It is found that the modulus ratio is the most essential parameter among them. Thus, the stress concentration factor is expressed as a function of modulus ratio in the derivation. It is also found that the proposed model gives a good agreement with finite element results and has the capability to correctly predict the variations of the internal quanitities.

A Three-Phase Shear-Lag Model for Longitudinal Cracking of a Ceramic Matrix Composite Ply With Thick Fiber Coatings

2015 ◽  
Vol 83 (1) ◽  
Author(s):  
Lucas R. Hansen ◽  
Anthony M. Waas
Keyword(s):  
Ceramic Matrix Composite ◽  
Stress Transfer ◽  
Ceramic Matrix Composites ◽  
Ceramic Matrix ◽  
Matrix Cracking ◽  
Material System ◽  
Shear Lag ◽  
Thick Fiber ◽  
The Matrix ◽  
Lag Model

During progressive cracking of cross-ply ceramic matrix composites (CMCs), load is transferred from the fiber to the matrix in the longitudinal (0 deg) ply via shear through a compliant interphase layer, also referred to as the coating. In the material system of interest, this coating has significant thickness relative to the fiber diameter. The damage process in the cross-ply CMC is observed to be as follows: (1) elastic deformation, (2) cracking of the transverse plies, (3) matrix cracking within the longitudinal plies, (4) failure of longitudinal fibers, and (5) pullout of the cracked fibers from the matrix. In this paper, the focus is on the longitudinal (0 deg) ply. Existing shear-lag models do not fully represent either the stress transfer through the coating or the true accumulations of shear and normal stresses in the matrix. In the current study, a model is developed that takes into account both of these factors to provide a more accurate, analytical representation of the stress distribution and progressive damage accumulation in a longitudinal CMC ply.

A Transversely Isotropic Viscoelastic Constitutive Equation for Brainstem Undergoing Finite Deformation

2006 ◽  
Vol 128 (6) ◽  
pp. 925-933 ◽  
Author(s):  
Xinguo Ning ◽  
Qiliang Zhu ◽  
Yoram Lanir ◽  
Susan S. Margulies
Keyword(s):  
Shear Deformation ◽  
Transversely Isotropic ◽  
Material Model ◽  
Model Parameters ◽  
Shear Stresses ◽  
Element Analysis ◽  
Cross Sectional ◽  
Implementation Model ◽  
Finite Shear ◽  
The Matrix

The objective of this study was to define the constitutive response of brainstem undergoing finite shear deformation. Brainstem was characterized as a transversely isotropic viscoelastic material and the material model was formulated for numerical implementation. Model parameters were fit to shear data obtained in porcine brainstem specimens undergoing finite shear deformation in three directions: parallel, perpendicular, and cross sectional to axonal fiber orientation and determined using a combined approach of finite element analysis (FEA) and a genetic algorithm (GA) optimizing method. The average initial shear modulus of brainstem matrix of 4-week old pigs was 12.7Pa, and therefore the brainstem offers little resistance to large shear deformations in the parallel or perpendicular directions, due to the dominant contribution of the matrix in these directions. The fiber reinforcement stiffness was 121.2Pa, indicating that brainstem is anisotropic and that axonal fibers have an important role in the cross-sectional direction. The first two leading relative shear relaxation moduli were 0.8973 and 0.0741, respectively, with corresponding characteristic times of 0.0047 and 1.4538s, respectively, implying rapid relaxation of shear stresses. The developed material model and parameter estimation technique are likely to find broad applications in neural and orthopaedic tissues.

The Effect of Interphase Modulus and Thickness on Stress Transfer of Short-Fiber-Reinforced Composites

2011 ◽  
Vol 55-57 ◽  
pp. 303-307 ◽  
Author(s):  
Bin Zhang ◽  
Bo Qin Gu
Keyword(s):  
Stress Distribution ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Stress Transfer ◽  
Short Fiber ◽  
Fiber Reinforced Composites ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
The Matrix

In this paper, the stress distribution of short-fiber-reinforced composites (SFRC) using representative volume element (RVE) approach based on the finite element analysis (FEA) was presented. A three-phase model was built, in which loads were applied to the matrix. The influences of interphase parameters like Young’s modulus and thickness were studied. The FEA confirms that interphase Young’s modulus and thickness control stress distribution in SFRC. The stress concentration at the fiber interface becomes greater with high interphase Young’s modulus and thin interphase thickness. The FEA results were also compared with those obtained by analytic method.

scholarly journals Estimate of theoretical shear strength of C60 single crystal by nanoindentation

2021 ◽  
Vol 56 (18) ◽  
pp. 10905-10914
Author(s):  
Sergey N. Dub ◽  
Cetin Haftaoglu ◽  
Vitaliy M. Kindrachuk
Keyword(s):  
Shear Strength ◽  
Single Crystal ◽  
Shear Stresses ◽  
Slip Systems ◽  
Berkovich Indenter ◽  
Element Analysis ◽  
Theoretical Shear Strength ◽  
Elastic Loading ◽  
Octahedral Slip ◽  
Realistic Geometry

AbstractThe onset of plasticity in a single crystal C60 fullerite was investigated by nanoindentation on the (111) crystallographic plane. The transition from elastic to plastic deformation in a contact was observed as pop-in events on loading curves. The respective resolved shear stresses were computed for the octahedral slip systems $$\langle{01}\overline{1}\rangle\left\{ {{111}} \right\}$$ ⟨ 01 1 ¯ ⟩ 111 , supposing that their activation resulted in the onset of plasticity. A finite element analysis was applied, which reproduced the elastic loading until the first pop-in, using a realistic geometry of the Berkovich indenter blunt tip. The obtained estimate of the C60 theoretical shear strength was about $${1}/{11}$$ 1 / 11 of the shear modulus on {111} planes. Graphical abstract

Time-Dependent Lateral Transmission of Force in Skeletal Muscle

2009 ◽  
Author(s):  
Yingxin Gao ◽  
Alan S. Wineman ◽  
Anthony M. Waas
Keyword(s):  
Skeletal Muscle ◽  
Muscle Fibers ◽  
Essential Element ◽  
Stress Transfer ◽  
Time Dependent ◽  
Shear Stresses ◽  
Shear Lag ◽  
Shear Lag Model ◽  
Lag Model ◽  
Whole Muscle

The composite structure of skeletal muscle is composed of muscle fibers and an extracellular matrix (ECM) framework. This framework is associated with different levels of structure: (a) epimysium, that ensheaths the whole muscle; (b) perimysium, that binds a group of muscle fibers into bundles and (c) endomysium that surrounds the individual muscle fibers. The properties of ECM components and their interaction with muscle fibers determine the overall mechanical properties of the whole muscle. Previous studies have experimentally demonstrated that stress could be laterally transmitted through the ECM [1]. The ECM is thus an essential element in mechanical function of the muscle [2]. The most widely used model describing load transfer between a discontinuous fiber and matrix is the shear lag model, originally proposed by Cox [3]]. This model centers on the transfer of tensile stress between fibers by means of interfacial shear stresses and shear deformation of the matrix. In this paper, a modified shear lag model is developed to investigate the time-dependent mechanics of stress transfer between activated muscle fibers and the surrounding strained ECM.

Assessment of Fiber Stress Based on Elastoplastic Analysis in Discontinuous Composite Materials

2006 ◽  
Vol 306-308 ◽  
pp. 829-834
Author(s):  
Hong Gun Kim
Keyword(s):  
Cell Model ◽  
Stress Transfer ◽  
Short Fiber ◽  
Concentration Effects ◽  
Elastoplastic Behavior ◽  
Elastoplastic Matrix ◽  
The Matrix ◽  
Matrix Region ◽  
Discontinuous Composite ◽  
Reasonable Prediction

An elastopalstic analysis of the micromechanical approach is performed to investigate the stress transfer mechanism in a short fiber reinforced composites. The model is based on the New Shear Lag Theory (NSLT) which was developed by considering the stress concentration effects that exist in the matrix region near fiber ends. The unit cell model is selected as the Representative Volume Element (RVE) for the investigation of longitudinal elastoplastic behavior in discontinuous composites. Thus far, it is focused on the detailed description to predict fiber stresses in case of the behavior of elastoplastic matrix as well as elastic matrix. Slip mechanisms between fiber and matrix which normally take place at the interface are considered for the accurate prediction of fiber stresses. Consequently, onset of Slip points is determined analytically and it showed a moving direction to the fiber center region from the fiber tip as the applied load increases. It is found that the proposed model gives the more reasonable prediction compared with the results of the conventional model (SLT).

Finite Element Analysis of Tire/Rim Interface Forces Under Braking and Cornering Loads

1992 ◽  
Vol 20 (2) ◽  
pp. 83-105 ◽  
Author(s):  
J. P. Jeusette ◽  
M. Theves
Keyword(s):  
Finite Element ◽  
Shear Stress ◽  
Contact Pressure ◽  
Element Model ◽  
Shear Stresses ◽  
Detailed Knowledge ◽  
Stress Distributions ◽  
Element Analysis ◽  
Plane Shear ◽  
Normal Contact

Abstract During vehicle braking and cornering, the tire's footprint region may see high normal contact pressures and in-plane shear stresses. The corresponding resultant forces and moments are transferred to the wheel. The optimal design of the tire bead area and the wheel requires a detailed knowledge of the contact pressure and shear stress distributions at the tire/rim interface. In this study, the forces and moments obtained from the simulation of a vehicle in stationary braking/cornering conditions are applied to a quasi-static braking/cornering tire finite element model. Detailed contact pressure and shear stress distributions at the tire/rim interface are computed for heavy braking and cornering maneuvers.

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