Showing papers on "Elastic modulus published in 1989"

Bending elasticity and thermal fluctuations of lipid membranes. Theoretical and experimental requirements

Abstract: Thermal fluctuations of giant lipid vesicles have been investigated both theoretically and experimentally. At the theoretical level, the model developed here takes explicitly into account the conservation of vesicle volume and membrane area. Under these conditions, the amplitude of thermal fluctuations depends critically not only on the bending elasticity of the bilayer, but also on the membrane tension and/or hydrostatic pressure difference between the interior and exterior of the vesicle. At the experimental level, the determination of the bending modulus kc first requires the analysis of a large number (several hundred) of vesicle contours to obtain a significant statistics. Secondly, the contribution of the experimental error on the contour coordinates, which results in a white noise on the Fourier amplitudes, must be eliminated, and this can be done by using the angular autocorrelation function of the fluctuations. Finally, the amplitudes of harmonics having short correlation times must be corrected from the effect of the integration time (40 ms) of the video camera, which otherwise leads to an overestimation of kc. All these theoretical and experimental requirements have been considered in the analysis of the thermal fluctuations of 42 giant vesicles composed of egg phosphatidylcholine. The behaviour of this population of vesicles can be accounted for with a bending modulus kc equal to 0.4 - 0.5 x 10-19 J, and extremely low membrane tensions, ranging below 15 × 10-5 mN/m.

Mechanical properties of model polyethylenes: tensile elastic modulus and yield stress

Abstract: Etude sur un polyethylene lineaire et un copolymere ethylene-butene-1, entre 175 o K et 260 o K

A Model for Abrasive-Waterjet (AWJ) Machining

Abstract: Ultrahigh-pressure abrasive-waterjets (AWJs) are being developed as net shape and near-net-shape machining tools for hard-to-machine materials. These tools offer significant advantages over existing techniques, including technical, economical, environmental, and safety concerns. Predicting the cutting results, however, is a difficult task and a major effort in this development process. This paper presents a model for predicting the depth of cut of abrasive-waterjets in different metals. This new model is based on an improved model of erosion by solid particle impact, which is also presented. The erosion model accounts for the physical and geometrical characteristics of the eroding particle and results in a velocity exponent of 2.5, which is in agreement with erosion data in the literature. The erosion model is used with a kinematic jet-solid penetration model to yield expressions for depths of cut according to different modes of erosion along the cutting kerf. This kinematic model was developed previously through visualization of the cutting process. The depth of cut consists of two parts: one due to a cutting wear mode at shallow angles of impact, and the other due to a deformation wear mode at large angles of impact. The predictions of the AWJ cutting model are checked against a large database of cutting results for a wide range of parameters and metal types. Materials are characterized by two properties: the dynamic flow stress, and the threshold particle velocity. The dynamic flow stress used in the erosion model was found to correlate with a typical modulus of elasticity for metals. The threshold particle velocity was determined by best fitting the model to the experimental results. Model predictions agree well with experimental results, with correlation coefficients of over 0.9 for many of the metals considered in this study.

Effects of surface stress on the elastic moduli of thin films and superlattices.

Abstract: A thermodynamic model which predicts a significant sample-size effect on the elastic properties of very thin films and small-period superlattices is presented. Compressive surface stresses cause the in-plane interatomic distances in a thin metal film to decrease as the thickness decreases. For copper films with a thickness of 0.75 nm, a 1% in-plane biaxial compressive strain is obtained which gives rise to a 50% increase in the biaxial modulus. This model also predicts a similar modulus enhancement (supermodulus effect) in multilayered thin films due to strains caused by incoherent interfacial stress.

Elastic moduli for a class of porous materials

Abstract: The effective elastic moduli for a class of porous materials with various distributions of spheroidal voids are given explicitly. The distributions considered include the unidirectionally aligned voids, three-dimensionally and two-dimensionally, randomly oriented voids, and voids with two types of biased orientations. While the 3-d random orientation results in a macroscopically isotropic solid, the porous media associated with the other arrangements are transversely isotropic. The five independent elastic constants for each arrangement, as well as the two for the isotropic case, are derived by means of Mori-Tanaka's mean field theory in conjunction with Eshelby's solution. Specific results for long, cylindrical pores and for thin cracks with the above orientations are also obtained, the latter being expressed in terms of the crack-density parameter. Before we set out the analysis, it is further proven that, in the case of long, circular inclusions, the five effective moduli of a fiber composite derived from the Mori-Tanaka method coincide with Hill's and Hashin's lower bounds if the matrix is the softer phase, and coincide with their upper bounds if the matrix is the harder.

Structure and deformation properties of red blood cells: concepts and quantitative methods.

Abstract: The lamellar configuration of the red cell membrane includes a (liquid) superficial bilayer of amphiphilic molecules supported by a (rigid) subsurface protein meshwork. Because of this composite structure, the red cell membrane exhibits very large resistance to changes in surface density or area with very low resistance to in-plane extension and bending deformations. The primary extrinsic factor in cell deformability is the surface area-to-volume ratio which establishes the minimum-caliber vessel into which a cell can deform (without rupture). Within the restriction provided by surface area and volume, the intrinsic properties of the membrane and cytoplasm determine the deformability characteristics of the red cell. Since the cytoplasm is liquid, the static rigidity of the cell is determined by membrane elastic constants. These include an elastic modulus for area compressibility in the range of 300-600 dyn/cm, an elastic modulus for in-plane extension or shear (at constant area) of 5-7 X 10(-3) dyn/cm, and a curvature or bending elastic modulus on the order of 10(-12) dyn.cm. Even though small, the surface rigidity of the cell membrane is sufficient to return the membrane capsule to a discoid shape after deformation by external forces. Viscous dissipation in the peripheral protein structure (cytoskeleton) dominates the dynamic response of the cell to extensional forces. Based on a time constant for recovery after extensional deformation on the order of 0.1 sec, the coefficient of surface viscosity is on the order of 10(-3) dyn.sec/cm. On the other hand, the dynamic resistance to folding of the cell appears to be limited by viscous dissipation in the cytoplasmic and external fluid phases. Dynamic rigidities for both extensional and folding deformations are important factors in the distribution of flow in the small microvessels. Although the red cell membrane normally behaves as a resilient viscoelastic shell, which recovers its conformation after deformation, structural relaxation and failure lead to break-up and fragmentation of the red cell. The levels of membrane extensional force which is two orders of magnitude less than the level of tension necessary to lyse vesicles by rapid area dilation. Each of the material properties ascribed to the red cell membrane plays an important role in the deformability and survivability of the red cell in the circulation over its several-month life span.

Stress transfer in single-fibre composites: effect of adhesion, elastic modulus of fibre and matrix, and polymer chain mobility

Abstract: The stress transfer in single-fibre composites is studied experimentally by determining the critical fibre length to diameter ratio,I c/d, in carbon fibre-epoxy resin or poly (ethylene vinyl acetate) systems. Our results and a great number of others available in the literature are compared with the predictions given, on the one hand, by the analytical approach by Cox and, on the other hand, by the theoretical study using finite element technique by Termonia. First, the influence of the fibre-matrix adhesion is analysed and it is observed, in agreement with Termonia, thatI c/d strongly decreases when the bonding efficiency between the two components is increased. Secondly, assuming a perfect fibre-matrix adhesion, it is shown that the critical fibre aspect ratio is proportional to the square root of the ratio of fibre to matrix elastic modulus, as predicted by Cox. However, two linear relationships are established: the first corresponds to the thermosetting and thermoplastic matrices, while the second corresponds to the elastomeric matrices. The difference between these two kinds of materials is attributed to the great difference in polymer chain mobility as shown by a study of the temperature dependence ofI c/d, particularly in the glass transition temperature zone of the matrices. However, in the case of elastomeric materials, the existence of an interphase layer between the fibre and the matrix, having an elastic modulus close to that of the elastomer in its glassy state, can also explain this particular behaviour.

Elasticity of grossular and spessartite garnets by Brillouin spectroscopy

Abstract: The single-crystal elastic moduli of natural samples of grossular (99.0 mol % Ca3Al2Si3O12) and spessartite (94.8 mol % Mn3Al2Si3O12) have been measured by Brillouin spectroscopy under ambient conditions. From these results the adiabatic bulk moduli Ks and shear moduli μ are calculated to be Ks = 168.4 ± 0.7, μ = 108.9 ± 0.4 for grossular, and Ks = 178.8 ± 0.8, μ = 96.3 ± 0.5 for spessartite (all in units of gigapascals). A calibration of our spectrometer by determination of the elastic properties of MgO indicates that these modulus values are accurate to within twice the stated rms error. Of the major rock-forming silicate garnets, spessartite has the largest bulk modulus, and grossular has the largest shear modulus, with the possible exception of majorite (a high-pressure form of pyroxene). Approximate values for the bulk and shear moduli of common aluminosilicate garnet solid solutions can be obtained with an estimated uncertainty of less than 3% from a linear molar average of the end-member properties. The elastic properties of pure almandite garnet (Fe3Al2Si3O12), which have thus far not been measured, are estimated as Ks = 177 ± 3 and μ = 97 ± 1 GPa by a linear regression analysis of extant measurements on garnet solid solutions and end-members. These same data imply, however, that a linear modulus-composition relationship may not be appropriate for all silicate garnet compositions.

Effects of cellulose fibers in polypropylene composites

Abstract: A systematic study of the effect of surface pretreatment of cellulosic fibers and the processing time and temperature on the mechanical properties of the cellulose-containing polypropylene was undertaken. Using non-treated fibers, the elastic modulus increased gradually with the cellulose content, typically doubling its value at 30 phr fiber content. Treatment of fibers with coupling agent improves significantly the interfacial adhesion and therefore the mechanical properties of composite. Scanning electron micrographs reveal that the shear stress is sufficiently high to break and delaminate the cellulosic fibers. Addition of maleic anhydride modified polypropylene also improves the properties of resulting composites.

Applicability of the classical curvature-stress relation for thin films on plate substrates

Abstract: The applicability in various circumstances of the classical equation relating substrate curvature to film stress for the case of a thin film on a plate substrate is examined. Theoretical treatments, based on elementary plate‐bending theory and general elasticity theory, are given of the effects of gravity, substrate shape, film nonuniformity, and substrate crystallinity on substrate curvature. Formulas describing the effect of gravity and of film nonuniformity are confirmed experimentally using a laser‐beam reflection technique. It is shown that gravity effects can cause significant errors in stress calculations based on the classical curvature versus stress equation, but these effects are largely avoidable or subtractable. Within limits, curvature is independent of substrate shape. For a film of nonuniform thickness, the classical equation does not apply, but in certain cases a simple analog does. Appropriate interpretation of elastic moduli appearing in the classical equation allows the equation to apply when the substrate is elastically anisotropic (e.g., a single crystal) with third‐order or higher symmetry about its z axis. These studies augment thin‐film stress measurement experimental technique.

Ginzburg-Landau Approach to Elastic Effects in the Phase Separation of Solids

Abstract: We introduce a Ginzburg-Landau model for solid solutions to examine elastic effects near the phase separation. As a first application the spinodal curve is calculated when the elastic moduli depend on the concentration and an external stress is applied. The instability is triggered by fluctuations with wave vectors in particular directions. This indicates the morphology of emerging domains,

A simple development of the shear lag theory appropriate for composites with a relatively small modulus mismatch

Abstract: The standard shear lag analysis is known to give unreliable predictions for composite stiffness and other properties when applied to systems with a relatively small ratio between the elastic moduli of the two constituents, such as metal matrix composites. This has long been thought to be at least partly due to neglect of the transfer of normal stresses across the fibre end jaces. In this paper, a simple postulate is made that this stress will approximate to the mean between the peak value in the fibre and the average value in the matrix remote from the interface. On this basis, simple analytical expressions are derived for composite stiffness and applied stress at the onset of yielding. It is shown by comparison with the Eshelby predictions and experimental data that the analysis appears reliable over the complete range of fibre aspect ratios and volume fractions when applied to metal matrix composites.

Mechanical properties of BIS-GMA resin short glass fiber composites.

Abstract: The use of short glass fibers as a filler for dental restorations or cement resins have not been examined extensively. The mechanical properties and untreated glass fibers (5 microns dia x 25 microns) in Bis-phenol A glycidyl methacrylate (BIS-GMA) diluted with triethylene-glycol dimethacrylate (TEGDMA) resin were investigated for possible use as a restorative dental composite or bone cement. Compression, uniaxial tension and fracture toughness tests were conducted for each filler composite mixtures of 40, 50, 60 and 70%. Set time and maximum temperature of polymerization were determined. The results show that the elastic modulus, tensile strength and compressive strength are dependent on the percent of filler content. Elastic modulus and compressive yield (0.2%) strength of silane treated glass fibers filled composite increased from 2.26 to 4.59 GPa and 43.3 to 66.6 MPa, respectively, wtih increasing the filler content while the tensile strength decreased from 26.7 to 18.6 MPa. The elastic modulus of the untreated composite was less than that of the silane treated fiber composite. The tensile strength and compressive strengths were 20 to 50% lower than those of silane treated composites. The fracture toughness of the silane treated glass fiber additions were not significantly different from the untreated additions. The highest fracture toughness was obtained at 50% filler content with 1.65 MPa m.5. Set time increased from 3.5 to 7.7 minutes with increased filler content and peak temperature dropped from 68.3 to 34 degrees C. The results of this study indicate that the addition of silane coated glass fiber to BIS-GMA resin increased the elastic modulus, tensile and compressive strengths compared with non-treated fibers. The addition of either treated or non-treated fibers increased the set time of the material and decreased the maximum temperature.

Mechanical behavior of plant tissues as inferred from the theory of pressurized cellular solids

Abstract: The mechanical behavior of plant tissues and its dependency on tissue geometry and turgor pressure are analytically dealt with in terms of the theory of cellular solids. A cellular solid is any material whose matter is distributed in the form of beamlike struts or complete "cell" walls. Therefore, its relative density is less than one and typically less than 0.3. Relative density is the ratio of the density of the cellular solid to the density of its constitutive ("cell wall") material. Relative density depends upon cell shape and the density of cell wall material. It largely influences the mechanical behavior of cellular solids. Additional important parameters to mechanical behavior are the elastic modulus of "cell walls" and the magnitude of internal "cell" pressure. Analyses indicate that two "stiffening" agents operate in natural cellular solids (plant tissues): 1) cell wall infrastructure and 2) the hydrostatic influence of the protoplasm within each cellular compartment. The elastic modulus measured from a living tissue sample is the consequence of both agents. Therefore, the mechanical properties of living tissues are dependent upon the magnitude of turgor pressure. High turgor pressure places cell walls into axial tension, reduces the magnitude of cell wall deformations under an applied stress, and hence increases the apparent elastic modulus of the tissue. In the absence of turgid protoplasts or in the case of dead tissues, the cell wall infrastructure will respond as a linear elastic, nonlinear elastic, or "densifying" material (under compression) dependent upon the magnitude of externally applied stress. Accordingly, it is proposed that no single tangent (elastic) modulus from a stress-strain curve of a plant tissue is sufficient to characterize the material properties of a sample. It is also suggested that when a modulus is calculated that it be referred to as the tissue composite modulus to distinguish it from the elastic modulus of a noncellular solid material. THE MECHANICAL BEHAVIOR of plant tissues varies as a function of turgor pressure and the geometry of their constituent cells. Studies indicate that the elastic modulus of pith parenchyma increases monotonically as turgor pressure increases (Falk, Hertz, and Virgin, 1958; Lin and Pitt, 1986). (The elastic modulus is measured from the slope of the linear portion of a material's stress-strain curve. It measures a specimen's material properties.) A similar relationship has been reported for more anatomically complex structures, such as the leaves of Dubautia and Allium (Robichaux, Holsinger, and Morse, 1986; Niklas and O'Rourke, 1987). In addition to the influence of water content, the elastic modulus of a tissue increases as the ratio of cell wall to protoplasm increases (Niklas, 1989a), while the maximum elastic modulus of algal and higher plant cells decreases as cell size decreases but the cell wall fraction remains relatively constant (Steudle, Zimmermann, and Luttge, 1977; Robichaux I Received for publication 31 May 1988; revision accepted 7 February 1989. et al., 1986). Cell wall composition is another factor that can influence the mechanical properties of tissues. However, data relating to this issue are limited (see Mark, 1967). The influence of turgor pressure and the ratio of cell wall thickness to cell radius on the elastic modulus of pith parenchyma has been modelled by various authors (Nilsson, Hertz, and Falk, 1958; Pitt, 1982, 1984; Gatesetal., 1986; Lin and Pitt, 1986). In all cases, cells are approximated as thin-walled spheres, for which simple shell theory yields the relationship at = Pr/2, where a is the circumferential stress on a cell with a wall-thickness t, radius r, and a turgor pressure of P (see Lin and Pitt, 1986, p. 306). This relationship conforms well to empirical data from pith tissues, since t << r. An underlying assumption to these models is that tissue stiffness increases as the number of cells in a tissue sample increases because increasing cell numbers decrease the capacity for cell-tocell displacements, particularly as turgor pressure increases. This has been experimentally verified (Niklas, 1988). However, for plant tissues other than parenchyma, the assumptions of simple shell theory are violated (cell walls

Multimodulus pressure sensor

Abstract: A pressure sensor (10, 49, 140) utilizes the effect of different elastic moduli between layers (20, 21; 36, 38; 53, 54; 123, 124; 146, 147) or sections of different material that are bonded together to form a body (17, 35, 52, 122, 145), so that when the bonded material unit (17, 35, 52, 122, 145) is subjected to a uniform hydrostatic external pressure, the differences in the elastic moduli of each of the materials will cause the materials to deflect in a predictable manner proportional to pressure The amount of warpage or deflection of the body (17, 35, 52, 122, 145) of material can be measured as a function of pressure Specifically, two layers of materials (20, 21; 36, 38; 53, 54; 123, 124; 146, 147), such as silicon (20, 38, 54, 123-146) and borosilicate glass (21, 36, 53, 124, 147), which have substantially different elastic moduli can be bonded across an interface surface (40, 55) to form an assembly (17, 35, 52, 122, 145) and when subjected to a substantially uniform pressure on the exterior surfaces the asembly (17, 35, 52, 122, 145) will deflect for indicating applied pressure at relatively high pressure ranges The bonded material assembly (17, 35, 52, 122, 145) is placed in a fluid to provide a substantially uniform applied hydrostatic pressure on all exposed surfaces of the bonded material assembly (17, 35, 52, 122, 145)

Influence of stress-dependent elastic moduli on stresses and strains around axisymmetric boreholes

Abstract: Porous or clastic rocks often have elastic moduli which are not constant but increase with increasing minor principal stress. The use of classical constant modulus linear elasticity in these cases can lead to erroneous predictions of the deformations and of the initiation and extent of failure around underground excavations. To illustrate these effects, solutions are developed for axisymmetric excavations in infinite media having power law and exponential variations of elastic modulus with minor principal stress. The maximum stress concentrations do not occur at the excavation boundaries and are less than the constant value of 2.0 given by constant modulus elasticity. When modified slightly to allow for test boundary conditions, the theory gives predictions that are consistent with aspects of the results obtained in hydrostatic compression tests on thick walled cylinders of three sedimentary rocks.

The effects of cross-linking on the equation of state of a polymer solution

Abstract: Measurements of the swelling pressure ω and shear modulus Gs in a set of poly(vinyl acetate) networks swollen to different degrees in toluene and in acetone are reported, using solutions of the uncross‐linked polymer to obtain deswelling under known conditions of osmotic pressure. The swelling pressure can be completely described by the difference between two terms, each of which is a simple power law in the polymer volume fraction φ. Identification of the subtractive term with that related to the elastic free energy of the network gives the volume elastic modulus Gv. The shear modulus Gs, obtained from mechanical measurements at constant volume, and Gv are found to coincide for these samples, and neither deviates measurably from a one‐third power law dependence on φ, up to values of φ in excess of 0.4. The remaining term in the swelling pressure of the networks behaves like the mixing term in a polymer solution, obeying good solvent scaling predictions as a function of concentration in both diluents. It...

Fatigue Properties of Acrylic Denture Base Resins

Abstract: Observations were made of fractured surfaces caused by flexural and tensile fatigue tests made in polymethyl methacrylate denture base resins (PMMA). In addition, the changes in dynamic viscoelastic and tensile properties of the materials along with fatigue propagation were investigated.In the tensile and flexural fatigue tests, both the fractured surfaces, which had striations on their surfaces and cracks near the fractured section, closely resembled each other in appearance. On the other hand, all of the tensile properties, such as elastic modulus, toughness and tensile strength, decreased with the increase of the number of stress cycles in the fatigue test. The storage modulus (E') of the material decreased gradually along with fatigue propagation over the whole range of temperatures tested. The loss modulus (E") and mechanical loss tangent (tanδ) increased slightly.The fatigue limit of four commercial denture base resins varied widely from one product to another.

Tangent Modulus of Piles Determined from Strain Data

Abstract: When evaluating measurements of strain or telltale shortening of a pile subjected to loading test, precise knowledge of the 'elastic' modulus is necessary. By means of plotting and analyzing the increment of load (or stress) over the increment of strain versus the strain, i.e., the tangent or chord modulus of the stress-strain curve, the modulus can be determined. The paper provides the mathematical background to the analysis and presents examples of the method.

Dynamic Young's Modulus Measurements in Metallic Materials: Results of an Interlaboratory Testing Program

Abstract: The results of a round-robin testing study are presented for measurements of dynamic Young's modulus in two nickel-based alloys. The Interlaboratory Testing Program involved six types of apparatus, six different organizations, and specimens from a well-documented source. All the techniques yielded values of dynamic Young's modulus that agreed within 1.6% of each other. For Inconel alloy 600 the dynamic modulus was 213.5 GPa with a standard deviation of 3.6 GPa; for Incoloy alloy 907 the corresponding values were 158.6 and 2.2 GPa, respectively. No significant effect of frequency over the range 780 Hz to 15 MHz was found.