Stiffness Properties Of Materials Research Articles

Effective elastic moduli and interface effects of nanocrystal-line materials

Many properties of nanocrystalline materials are associated with interface effects. Based on their microstructural features, the influence of interfaces on the effective elastic property of nanocrystalline materials is investigated. First, the Mori-Tanaka method is employed to determine the overall effective elastic moduli by considering a nanocrystalline material as a binary composite solid consisting of a crystal or inclusion phase with regular lattice connected by an amorphous-like interface or matrix phase. The effects of strain gradients are then examined on the effective elastic property by using the strain gradient theory to analyze a representative unit cell. Two interface mechanisms are elucidated that influence the effective stiffness and other mechanical properties of materials. One is the softening effect due to the distorted atomic structures and the increased atomic spacings in interface regions, and the other is the baffling effect due to the existence of boundary layers near interfaces.

Influence of fiber defects on the stiffness properties of flax fibers-epoxy composite materials

Influence of fiber defects on the stiffness properties of flax fibers-epoxy composite materials

NUMERICAL MODELING OF MICROHARDNESS TESTS FOR POLYMER MATERIALS1*

A computational method in conjunction with indentation measurements is presented to determine stiffness properties of different polymeric materials. Experiments were performed using a Vickers-type indenter. Five different polymers were tested: polyethylene naphthalate (PEN), copolymer amorphous polyethylene terephthalate/polyethylene naphthalate (PET/PEN 70/30), copolymer crystalline polyethylene terephthalate/polyethylene naphthalate (PET/PEN 70/30), a random copolyester of polyethylene naphthalate/hydroxybenzoate (PEN/PHB 50/50), and a blend of isotactic polypropylene/ethylene co-propylene rubber (i-PP/EPR 85/15). Elastic properties are determined from the unloading curve of indentation. Identification of plastic properties of polymers are performed from the loading curve of indentation. A novel approach based on experimental design and finite-element analysis is discussed. Yield stress and tangent modulus are obtained by minimizing the deviation between the calculated and the experimental data. Results are verified by the finite-element method. Good agreement between the experimental and numerical load-indentation depth curves is observed. *Dedicated to Prof. Francisco J. Baltá Calleja on the occasion of his 65th birthday.

Multiresolution Analysis of Elastic Degradation in Heterogeneous Materials

In this study we examine the stiffness properties of heterogeneous elastic materials and their degradation at different levels of observations. To this end we explore the opportunities and limitations of multiresolution wavelet analysis, where successive Haar transformations lead to a recursive separation of the stiffness properties and the response into coarse- and fine-scale features. In the limit, this recursive process results in a homogenization parameter which is an average measure of stiffness and strain energy capacity at the coarse scale. The basic concept of multiresolution analysis is illustrated with one- and two-dimensional model problems of a two-phase particulate composite representative of the morphology of concrete materials. The computational studies include the microstructural features of concrete in the form of a bi-material system of aggregate particles which are immersed in a hardened cement paste taking due account of the mismatch of the two elastic constituents.

Control of seismically excited vibration using electrorheological materials and Lyapunov methods

Describes the use of electrorheological (ER) materials in a vibration control system designed to suppress earthquake-excited vibrations. A state-variable model for the ER device is based on micromechanical simulations and rheometric measurements of ER materials. A decentralized bang-bang control law is synthesized using Lyapunov's direct method and is implemented using analog circuitry. The behavior of the closed-loop system is illustrated on a small scale (1:15) building model driven by ground accelerations. The combined effects and relative importance of the controllable stiffness and damping properties of ER materials are examined.

Inversion of ultrasonic, plane-wave transmission data in composite plates to infer viscoelastic material properties

Stiffness and damping properties of viscoelastic materials are given by the real and imaginary components, respectively, of the material constants. A new technique is proposed to experimentally measure the real and imaginary components of anisotropic (and isotropic) viscoelastic plates. Main advantage of this technique is that material properties of thin plates can be measured where many other techniques fail. Material properties are obtained by numerically inverting the transmitted ultrasonic fields, obtained for different incident angles. Simplex inversion algorithm is applied to initial estimates of plate thickness and plate properties. By this iterative technique the values of the unknown parameters (material properties and plate thickness) are continuously modified to give better agreement between the experimental and theoretical transmitted fields. After a certain number of iterations the speed of convergence of the Simplex scheme is significantly reduced. To improve the accuracy of convergence the Newton–Raphson inversion technique is adopted at that point. By this technique material properties of different types of plates are measured. These is a glass plate (isotropic plate with no damping), a polymer plate (isotropic plate with damping), and glass fiber reinforced epoxy plates with different fiber orientations (anisotropic plates with damping). Both real and imaginary components are successfully measured for all these plates. In a relative scale the measurement error for the imaginary components is higher. Reliability of the measured material constants of fiber reinforced epoxy plates is verified by the method of invariance. All experiments are carried out in the frequency range that is appropriate for satisfying two conditions—the specimen homogeneity and the plane wave conditions.

Direct imaging of traveling Lamb waves in plates using photorefractive dynamic holography

Anisotropic stiffness properties of sheet materials can be determined by measuring the propagation of Lamb waves in different directions, but this typically requires multiple positioning of a suitable transducer at several points or scanning over the area of the sample plate. A laser imaging approach is presented that utilizes the adaptive property of photorefractive materials to produce a real-time measurement of the antisymmetric Lamb traveling wave displacement and phase in all planar directions simultaneously without scanning. Continuous excitation and lock-in methodology is employed, enabling the data to be recorded and displayed by a video camera. Analysis of the image produces a direct quantitative determination of the phase velocity in all directions showing plate stiffness anisotropy in the plane. The method is applicable to materials that scatter light diffusely and provides quantitative imaging of the dynamic surface motion exhibited by traveling elastic waves. A description is given of this imaging process and, for the first time, its ability to perform lock-in measurement of elastic wave displacement amplitude and phase.

Application of genetic algorithms for the identification of elastic constants of composite materials from dynamic tests

This work has been placed within the framework of the identification of stiffness properties of composite materials from dynamic tests. More precisely, the used approach has been inserted in the general context of model updating. The genetic algorithms method has been used as a complementary technique allowing a first estimation of the elastic coefficients. In other words, the initial finite element model is estimated. The refinement of solutions can thus be made by a classical updating method, such as the sensitivity method. The procedure allows the simultaneous estimation of several properties from a single test. Properties of extension, bending, twisting and transverse shear effects can be identified. Results obtained by numerical simulation show the efficiency and robustness of the genetic algorithms. Copyright © 1999 John Wiley & Sons, Ltd.

Application of genetic algorithms for the identification of elastic constants of composite materials from dynamic tests

This work has been placed within the framework of the identification of stiffness properties of composite materials from dynamic tests. More precisely, the used approach has been inserted in the general context of model updating. The genetic algorithms method has been used as a complementary technique allowing a first estimation of the elastic coefficients. In other words, the initial finite element model is estimated. The refinement of solutions can thus be made by a classical updating method, such as the sensitivity method. The procedure allows the simultaneous estimation of several properties from a single test. Properties of extension, bending, twisting and transverse shear effects can be identified. Results obtained by numerical simulation show the efficiency and robustness of the genetic algorithms. Copyright © 1999 John Wiley & Sons, Ltd.

Application of model updating techniques in dynamics for the identification of elastic constants of composite materials

This work consists of the identification of the stiffness properties of composite materials from dynamic tests. Unknown coefficients are identified by a technique of model updating. The formulation used (modal approach) is based on the minimization of the eigensolution residuals (sensitivity method). This technique allows the simultaneous identification of several properties from a single test. Stiffness properties of extension, bending, twisting and transverse shear have been identified. A discussion of the different identification approaches of elastic constants of composite materials from dynamic tests has been presented. Important points of the model updating in dynamics have been addressed: generalized mass errors, placement of sensors and approximate reanalysis of eigensolutions. Results obtained by numerical simulations show the efficiency of the proposed methodology.

Neural Network Modeling of Anisotropic Aggregate Behavior from Repeated Load Triaxial Tests

Determining horizontal specimen response in a repeated load triaxial test is essential to properly characterize the directional dependency of unbound aggregate resilient behavior under anisotropic loading conditions. Recent research has applied artificial neural networks (ANNs) for predicting, in the absence of lateral deformation data, the anisotropic stiffness properties of granular materials from standard AASHTO tests. Feed-forward backpropagation-type neural networks were successfully trained with two triaxial stresses (confining pressure and applied deviator stress), measured vertical deformation, and two aggregate properties (compacted dry density and crushed particle percentage) used as input variables. The output variables were the horizontal and shear moduli for which the actual (target) values were derived and computed from test results. The ANN models predicted the two moduli, with mean errors of less than 3 percent compared with those computed by using experimental stresses and strains. Both the applied stress state and the aggregate properties were found to affect the generalization and thus the prediction ability of the ANN models.

Inversion of composite material elastic constants from ultrasonic bulk wave phase velocity data using genetic algorithms

In this paper, efforts on the reconstruction of material stiffness properties of unidirectional fiber-reinforced composites from obliquely incident ultrasonic bulk wave data, employing an inverse technique based on genetic algorithms, is described. Computer-generated ultrasonic phase velocity data, as a function of the angle of refraction in both symmetry and nonsymmetry through the thickness planes of unidirectional composites were used as the input to the genetic algorithm. A simple genetic algorithm, with optimal parameters chosen from the literature and numerical analysis (reported here), was implemented for the reconstruction. The inversion using this novel technique was found to be extremely promising in the characterization of the material stiffness properties. Stability to noise in the input phase velocity data set was also investigated. Advantages and disadvantages of the genetic reconstruction technique over conventional methods are also discussed.

Residual Stiffness and Actuation Properties of Piezoelectric Composites: Theory and Experiment

This work attempts to characterize and model the effective stiffness and actuation properties of active composite materials under high uniaxial tensile loads. The motivations for this undertaking are to obtain effective material properties as damage accumulates in the active element and to identify the mechanisms affecting stiffness and actuation to improve the material. A unified model with predictive capability for overall laminate effective material properties was developed. Key model assumptions include a constant linear elastic fiber recovery length and a Weibull form for fiber strength. A one dimensional shear lag model was employed to characterize the load transfer between the composite's layers. In order to validate this model several experiments were conducted on interdigitated electrode piezoelectric fiber composites embedded in E-glass laminae. Actuation data were obtained by performing active tests: specimens were subjected to increasing tensile loads and measurements of actuation under load were taken at selected strain levels. Stiffness data was collected during actuation tests. Very good correlation was demonstrated in most cases between predicted behavior and experimental results.

Non-contact measurement of local grammage and mechanical material properties

A new method that provides a measure of local grammage and makes it possible to study local mechanical stiffness properties of sheet materials is presented. The measurement is achieved without any mechanical contact with the material and the spatial resolution can be chosen in the interval 1 - 100 . The method is based on the use of a high-power pulsed KrF excimer laser which generates a pressure pulse and thus creates a local deformation of the sheet. An optical interferometer is used to detect the deformation of the material over time. From the time-resolved interferometer signal, the desired output values for the grammage and mechanical stiffness can be extracted. The method is applicable to sheet materials such as paper and plastic films. Experimental results obtained from measurements on Mylar polyester films show that it is possible to attain a high reproducibility when measuring the grammage and that it is possible to resolve a small relative change in the elastic modulus.

Modeling Foam Damping Materials in Automotive Structures

Foam damping materials judiciously placed in automotive structures efficiently reduce the vibration amplitudes of large, relatively flat exterior body panels such as the hood, roof, deck lid (trunk) and door skin. These polymer foams (typically epoxy or vinyl) have mechanical properties that depend on the foam homogeneity, degree of expansion, temperature and frequency of excitation. Standard methods for determining true bulk mechanical properties, such as Young’s modulus, shear modulus and damping terms, are discussed along with methods for determining engineering estimates of the properties “as used” in automotive applications. Characterizing these foam damping materials in a component or full body finite element structural model as discrete springs and dashpots provides an accurate and economical means to include these features. Example analyses of the free vibrations and forced response of a hood are presented accompanied by test data that demonstrate the accuracy of the structural model. A parametric study investigates the effect of foam material stiffness and damping properties on hood vibration amplitudes under dynamic air loading. A methodology is discussed to reduce the hood vibration level under cross-wind conditions to an acceptable level with the use of foam materials.

Ultrasonic Determination of Stiffness Properties of an Orthotropic Viscoelastic Material

Ultrasonic velocity measurements were used to populate the real portion of the stiffness matrix of an orthotropic viscoelastic material, as a function of frequency. The orthotropy originated from short cellulose reinforcing fibers cast into the polypropylene matrix. The results were consistent with a Zener relaxation model for the material, with a time constant of the order of a few microseconds. It was found that the shape of the dispersion curve varied markedly with orientation: The frequency dependence of the phase velocity was at a minimum along the primary axis of the reinforcing fibers; the fibers were shown to inhibit viscoelastic behavior in this direction. The attenuation coefficient was measured along one primary axis of the material, and found to be consistent with the dispersion curves and localized form of the Kramers-Kronig relationships linking the real and imaginary components of the stiffness matrix.

Reliability analysis of pole-type transmission structures

The unguyed single-pole transmission structure is widely used in the U.S. to support transmission lines of up to 345 kV capacity. Most poles are naturally grown wood, but some poles of prestressed concrete and some of steel are used, especially in high decay or high load situations. The resistance of each structure is a random variable which can be significantly influenced by time and location. Material strength and stiffness properties, especially of wood, vary from structure to structure, even for nominally identical poles. The life expectancy of poles varies with geographical location with poles in hot, humid climates having lower life times than those in hot, dry areas. The individual load causing phenomena of dead weight, wind velocity, and accretion of ice and snow on the structure are also random variables. Additionally, wind velocity, terrain conditions, temperature and structure shape interact to affect ice and snow accretion. Design of a structure to provide a known level of reliability requires that a reliability-based design methodology be established. To accomplish this the variable nature of the resistances and load causing phenomena must first be defined. Next, a correct method of analysis which properly considers all important response characteristics such as the highly nonlinear behavior of pole structures must be developed. The function of the analysis is to convert loads to load effects directly comparable to resistance. Finally, a procedure which allows the designer to size structures so they will provide the desired level of reliability must be created. A major part of producing such a practical design procedure is developing a method for performing the reliability analysis of transmission structures. As part of an eight-year effort to develop reliability-based design methods for transmission structures, several methods for performing reliability analyses of single-pole transmission structures were established. Implemented in program POLDAR (POLe Design, Analysis and Reliability), these procedures enable the user to perform a reliability assessment of unguyed planar single-pole structures of any material and configuration for the major loads normally considered in design. It is shown that the load and resistance factor design (LRFD) method developed based on reliability analysis results obtained with POLDAR produces structures having reliability levels very close to the target levels assumed by the designer. Thus a reliability-based design method is now available for use in the design of new structures and the assessment and upgrading of existing structures. Since over 130,000,000 wood poles are now in place, and several million additional poles are put into service each year at an in-place cost of $1000 to $2000 each, it is expected that improved design procedures will have a significant financial impact.

Collapse Pressure of Thermoplastic Water Well Casings

ABSTRACTBecause of the relatively low stiffness properties of thermoplastic materials, casings made from these materials may be more susceptible to collapse. For many applications, when a surrounding material tends to support the casing, the casing resistance to collapse should be significantly increased. The Morley equations of equilibrium for two radial collapse pressure loading conditions were modified to include the support of the surrounding medium and were solved using the Galerkin method. Parametric studies were conducted for typical water well casings and restraint values. Simple collapse prediction formulas are proposed for predicting collapse for the two loading conditions considered. Collapse pressures predicted by the proposed formulas for uniform collapse pressure are approximately 25% lower than those values predicted by the current ASTM formula. Collapse pressures for linearly varying pressure were found to be 12% higher than the corresponding values for uniform pressure. When the radial stiffness of the surrounding medium is included in the analysis, the collapse pressure resistance of the casing was found to be significantly increased over the collapse resistance of an unsupported casing.

Stiffness of fibre composite materials

Methods of analysis of the elastic stiffness properties of fibre composite materials are reviewed. The use of these properties in the analysis of structural composites is outlined. Typical results are presented for composite material properties, for laminate properties and for plate problems in which material stiffness is a significant design criterion. The influence of material design upon structural design is illustrated.