Elasticity Approach to Load Transfer in Cord-Composite Materials

2009 ◽  
Vol 76 (6) ◽  
Author(s):  
Anthony J. Paris
Keyword(s):  
Composite Materials ◽  
Closed Form ◽  
Axial Force ◽  
Load Transfer ◽  
Axial Loading ◽  
Shear Stresses ◽  
Matrix Interface ◽  
Closed Form Solutions ◽  
Apparent Modulus ◽  
Reinforced Composite

An elasticity approach to the mechanics of load transfer in cord-reinforced composite materials is developed. Finite cords embedded in an elastic matrix and subjected to axial loading is considered, and the extension-twist coupling of the cords is taken into account. Closed form solutions for the axial force and twisting moment in the cord, the shear stresses at the cord-matrix interface in the axial and circumferential directions, the effective axial modulus of the cord, and the apparent modulus of the cord composite are presented. An example of a cord composite typical of what can be found in steel-belted-radial tires is used to illustrate the results. It was found that large shear stresses occur at the cord-matrix interface in both the axial and circumferential directions at the cord ends and that the effective modulus of the cords may be greatly reduced. As a result, the apparent modulus of the composite may be significantly less than that found by a conventional application of the rule-of-mixtures approach.

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.

A Study of the Fiber-Matrix Interface in Composite Materials

1992 ◽  
Vol 59 (2S) ◽  
pp. S163-S165 ◽  
Author(s):  
Jin O. Kim ◽  
Haim H. Bau
Keyword(s):  
Composite Materials ◽  
Experimental Technique ◽  
Stress Waves ◽  
Matrix Interface ◽  
Fiber Reinforced ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite ◽  
The Matrix ◽  
Fiber Matrix Interface ◽  
Dispersion And Attenuation

A novel experimental technique for studying the characteristics of the interface between the fibers and the matrix in both undamaged and damaged fiber-reinforced composite materials is described. The experimental technique involves the transmission of stress waves in one or more fibers of the composite. The characteristics of the stress waves, such as speed, dispersion, and attenuation, are measured. These measured variables can be correlated with the characteristics of the bonding between the fiber and the matrix.

The role of interface in improving fracture toughness of shaped steel fiber-reinforced composites

2017 ◽  
Vol 52 (7) ◽  
pp. 981-987
Author(s):  
MS Ghoraishi ◽  
JE Hawk ◽  
M Ghoreishi ◽  
A Zadhoush
Keyword(s):  
Composite Materials ◽  
Load Transfer ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Fiber Pullout ◽  
Sulfuric Acid Treatment ◽  
Atomic Force ◽  
Reinforced Composite ◽  
Fiber Matrix

Mechanical properties of composite materials and their final performance are strongly influenced by the structure and properties of the fiber–matrix interface. A balance between sufficient load transfer and fiber pullout properties helps improve the performance of the composite materials. In this research, we employed sulfuric acid treatment to enhance fiber pullout and debonding through decreasing the fiber–matrix interlock. Atomic force microscope and scanning electron microscopy were employed to investigate the surface morphology of both treated and untreated steel fibers. Our results indicate that surface treatment improves the fiber roughness and therefore hinders brittle failures of the epoxy fiber-reinforced composite materials.

scholarly journals The eigenbuckling analysis of hexagonal lattices: closed-form solutions

2021 ◽  
Vol 477 (2251) ◽  
pp. 20210244
Author(s):  
S. Adhikari
Keyword(s):  
Closed Form ◽  
Elastic Properties ◽  
Axial Force ◽  
Hexagonal Lattice ◽  
Force Parameter ◽  
Closed Form Solutions ◽  
Analysis And Design ◽  
Lattice Materials ◽  
Design Calculations ◽  
Analytical Expressions

Elastic instability such as the buckling of cellular materials plays a pivotal role in their analysis and design. Despite extensive research, the quantifi- cation of critical stresses leading to elastic instabi- lities remains challenging due to the inherent nonlinearities. We develop an analytical approach considering the spectral decomposition of the elasticity matrix of two-dimensional hexagonal lattice materials. The necessary and sufficient condition for the buckling is established through the zeros of the eigenvalues of the elasticity matrix. Through the analytical solution of the eigenvalues, the conditions involving equivalent elastic properties of the lattice were directly connected to the mathematical requirement of buckling. The equivalent elastic properties are expressed in closed form using geometric properties of the lattice and trigonometric functions of a non-dimensional axial force parameter. The axial force parameter was identified for four different stress cases, namely, compressive stress in the longitudinal and transverse directions separately and together and torsional stress. By solving the resulting nonlinear equations, we derive exact analytical expressions of critical eigenbuckling stresses for these four cases. Crucial parameter combinations leading to minimum buckling stresses are derived analytically. The exact closed-form analytical expressions derived in the paper can be used for quick engineering design calculations and benchmarking related experimental and numerical studies.

Fully Developed Sliding of Rough Surfaces

1989 ◽  
Vol 111 (3) ◽  
pp. 445-451 ◽  
Author(s):  
C. Liu ◽  
B. Paul
Keyword(s):  
Closed Form ◽  
Contact Region ◽  
Tangential Force ◽  
Normal Pressure ◽  
Shear Stresses ◽  
Closed Form Solutions ◽  
Pressure Distributions ◽  
The Coefficient Of Friction ◽  
Force Components ◽  
Instantaneous Center

Given the contact region between two bodies, the normal pressure distribution over the contact region, and the coefficient of friction, we seek to find all combinations of tangential forces and twisting moment (about the normal to the contact surface) for which fully developed sliding impends. As part of the solution we must determine the distribution of the surface tractions (shear stresses) and the location of the instantaneous center (IC) of the impending motion. New closed form solutions of the stated problem are found for circular contact patches with pressure distributions corresponding to (a): a flat stamp; and (b): elastic spheroids with Hertzian pressure distributions. For contact regions other than circular, no closed form solutions are known. We have developed numerical procedures to solve for arbitrary contact patches, with arbitrary distributions of normal pressure, and present carpet plots of tangential force components (Fx, Fy) and IC coordinates for the following cases: flat ellipsoidal stamps; ellipsoidal indenters (Hertzian pressure); and a non-Hertzian, nonelliptical contact of a rail and wheel. Level curves of twisting moment Mz versus tangential force components are provided. Given any two of the three quantities (Fx, Fy, Mz), the algorithms and the plots in this paper make it possible and convenient to find the remaining force or moment which will cause gross sliding to impend, for virtually arbitrary contact regions and arbitrary pressure distributions.

scholarly journals Analytical Model and Back-Analysis for Pile-Soil System Behavior under Axial Loading

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Hong-Fa Xu ◽  
Ji-Xiang Zhang ◽  
Xin Liu ◽  
Han-Sheng Geng ◽  
Ke-Liang Li ◽  
...  
Keyword(s):  
Transfer Function ◽  
Analytical Model ◽  
Axial Force ◽  
Load Transfer ◽  
Back Analysis ◽  
Axial Loading ◽  
Distribution Functions ◽  
Soil System ◽  
Relationship Model ◽  
Load Transfer Function

The interaction mechanism between piles and soils is very complicated. The load transfer function is generally nonlinear and is affected by factors such as pile side roughness, soil characteristics, section depth, and displacement. Therefore, it is difficult to solve the pile-soil system based on load transfer function. This paper presents a new method to study the soil-pile interaction problem with respect to axial loads. First, the shapes of the axial force-displacement curves at different depths and the displacement distribution curves along pile axis at different pile-top displacements were analyzed. A simple exponential function was taken as relationship model to express the relationship curves between two distribution functions of axial force and displacement along pile shaft obtained by using the geometric drawing method. Second, a new analytical model of the pile-soil system was established based on the basic differential equations for pile-soil load transfer theory and the relationship model and was used to derive the mathematical expressions on the distribution functions of the axial force, the lateral friction, and the displacement along pile shaft and the load transfer function of pile-side. We wrote the MATLAB program for the analytical model to analyze the influence laws of the parameters u and m on the pile-soil system characteristics. Third, the back-analysis method and steps of the pile-soil system characteristics were proposed according to the analytical model. The back-analysis results were in good agreement with the experimental results for the examples. The analysis model provides an effective way for the accurate design of piles under axial loading.

scholarly journals Closed-Form Solutions for a Mode-III Moving Interface Crack at the Interface of Two Bonded Dissimilar Orthotropic Elastic Layers

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
B. M. Singh ◽  
J. Rokne ◽  
R. S. Dhaliwal
Keyword(s):  
Closed Form ◽  
Integral Transform ◽  
Practical Importance ◽  
Leading Edge ◽  
Shear Stresses ◽  
Mode Iii ◽  
Closed Form Solutions ◽  
Moving Interface ◽  
Elastic Layers ◽  
Physical Quantities

An integral transform technique is used to solve the elastodynamic problem of a crack of fixed length propagating at a constant speed at the interface of two bonded dissimilar orthotropic layers of equal thickness. Two cases of practical importance are investigated. Firstly, the lateral boundaries of the layers are clamped and displaced in equal and opposite directions to produce antiplane shear resulting in a tearing motion along the leading edge of the crack, and secondly, the lateral boundaries of the layers are subjected to shear stresses. The analytic solution for a semi-infinite crack at the interface of two bonded dissimilar orthotropic layers has been derived. Closed-form expressions are obtained for stressing the intensity factor and other physical quantities in all cases.

scholarly journals Thermoelastic Closed-Form Solutions of FGM Plates Subjected to Temperature Change in Axial and Thickness Directions

2020 ◽  
Author(s):  
Yen-Ling Chung
Keyword(s):  
Closed Form ◽  
Temperature Change ◽  
Axial Force ◽  
Maximum Stress ◽  
Closed Form Solution ◽  
Bending Moment ◽  
Bottom Surface ◽  
Thermal Loads ◽  
Element Analysis ◽  
Closed Form Solutions

Abstract An analytical solution of simply supported FGM plates under thermal loads is developed based on medium-thick plate assumption. Further to assume constant Poisson’s ratio and thermal expansion coefficient, the closed-form solutions of the FGM plates with through-the-thickness Young’s modulus under temperature change in x - and z -directions are evaluated, expressed in terms of the thermal axial force and thermal bending moment. The closed-form solutions confirmed by finite element analysis give a complete insight into the thermal-mechanical behavior of FGM plates. Hence, the deflection, strain, stress, axial force, and bending moment of the FGM plate under thermal loads in axial and thickness directions are discussed. Results show that the use of FGM makes the maximum stress from the top or bottom surface move to the inner portion of the FGM plate, and significantly reduces the maximum stress of the plates. Moreover, although the FGM plate is subjected to thermal load in the thickness direction, the deflection of the FGM plate can be zero by properly choosing the steep material gradation, directly derived from the obtained closed-form solution.

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