Showing papers on "Stress concentration published in 1992"

A Course on Damage Mechanics

Abstract: 1 Phenomenological Aspects of Damage.- 1.1 Physical Nature of the Solid State and Damage.- 1.1.1 Atoms, Elasticity and Damage.- 1.1.2 Slips, Plasticity and Irreversible Strains.- 1.1.3 Scale of the Phenomena of Strain and Damage.- 1.1.4 Different Manifestations of Damage.- 1.1.5 Exercise on Micrographic Observations.- 1.2 Mechanical Representation of Damage.- 1.2.1 One-Dimensional Surface Damage Variable.- 1.2.2 Effective Stress Concept.- 1.2.3 Strain Equivalence Principle.- 1.2.4 Coupling Between Strains and Damage Rupture Criterion Damage Threshold.- 1.2.5 Exercise on the Micromechanics of the Effective Damage Area.- 1.3 Measurement of Damage.- 1.3.1 Direct Measurements.- 1.3.2 Variation of the Elasticity Modulus.- 1.3.3 Variation of the Microhardness.- 1.3.4 Other Methods.- 1.3.5 Exercise on Measurement of Damage by the Stress Amplitude Drop.- 2 Thermodynamics and Micromechanics of Damage.- 2.1 Three-Dimensional Analysis of Isotropic Damage.- 2.1.1 Thermodynamical Variables, State Potential.- 2.1.2 Damage Equivalent Stress Criterion.- 2.1.3 Potential of Dissipation.- 2.1.4 Strain-Damage Coupled Constitutive Equations.- 2.1.5 Exercise on the Identification of Material Parameters.- 2.2 Analysis of Anisotropic Damage.- 2.2.1 Geometrical Definition of a Second-Order Damage Tensor.- 2.2.2 Thermodynamical Definition of a Fourth-Order Damage Tensor.- 2.2.3 Energetic Definition of a Double Scalar Variable.- 2.2.4 Exercise on Anisotropic Damage in Proportional Loading.- 2.3 Micromechanics of Damage.- 2.3.1 Brittle Isotropie Damage.- 2.3.2 Ductile Isotropie Damage.- 2.3.3 Anisotropie Damage.- 2.3.4 Microcrack Closure Effect, Unilateral Conditions.- 2.3.5 Damage Localization and Instability.- 2.3.6 Exercise on the Fiber Bundle System.- 3 Kinetic Laws of Damage Evolution.- 3.1 Unified Formulation of Damage Laws.- 3.1.1 General Properties and Formulation.- 3.1.2 Stored Energy Damage Threshold.- 3.1.3 Three-Dimensional Rupture Criterion.- 3.1.4 Case of Elastic-Perfectly Plastic and Damageable Materials.- 3.1.5 Identification of the Material Parameters.- 3.1.6 Exercise on Identification by a Low Cycle Test.- 3.2 Brittle Damage of Metals, Ceramics, Composites and Concrete.- 3.2.1 Pure Brittle Damage.- 3.2.2 Quasi-brittle Damage.- 3.2.3 Exercise on the Influence of the Triaxiality on Rupture.- 3.3 Ductile and Creep Damage of Metals and Polymers.- 3.3.1 Ductile Damage.- 3.3.2 Exercises on the Fracture Limits in Metal Forming.- 3.3.3 Creep Damage.- 3.3.4 Exercise on Isochronous Creep Damage Curves.- 3.4 Fatigue Damage.- 3.4.1 Low Cycle Fatigue.- 3.4.2 Exercise on Creep Fatigue Interaction.- 3.4.3 High Cycle Fatigue.- 3.4.4 Exercise on Damage Accumulation.- 3.5 Damage of Interfaces.- 3.5.1 Continuity of the Stress and Strain Vectors.- 3.5.2 Strain Surface Energy Release Rate.- 3.5.3 Kinetic Law of Debonding Damage Evolution.- 3.5.4 Simplified Model.- 3.5.5 Exercise on a Debonding Criterion for Interfaces.- 3.6 Table of Material Parameters.- 4 Analysis of Crack Initiation in Structures.- 4.1 Stress-Strain Analysis.- 4.1.1 Stress Concentrations.- 4.1.2 Neuter's Method.- 4.1.3 Finite Element Method.- 4.1.4 Exercise on the Stress Concentration Near a Hole.- 4.2 Uncoupled Analysis of Crack Initiation.- 4.2.1 Determination of the Critical Point(s).- 4.2.2 Integration of the Kinetic Damage Law.- 4.2.3 Exercise on Fatigue Crack Initiation Near a Hole.- 4.3 Locally Coupled Analysis.- 4.3.1 Localization of Damage.- 4.3.2 Postprocessing of Damage Growth.- 4.3.3 Description and Listing of the Postprocessor DAMAGE 90.- 4.3.4 Exercises Using the DAMAGE 90 Postprocessor.- 4.4 Fully Coupled Analysis.- 4.4.1 Initial Strain Hardening and Damage.- 4.4.2 Example of a Calculation Using the Finite Element Method.- 4.4.3 Growth of Damaged Zones and Macrocracks.- 4.4.4 Exercise on Damage Zone at a Crack Tip.- 4.5 Statistical Analysis with Microdefects.- 4.5.1 Initial Defects.- 4.5.2 Case of Brittle Materials.- 4.5.3 Case of Quasi Brittle Materials.- 4.5.4 Case of Ductile Materials.- 4.5.5 Volume Effect.- 4.5.6 Effect of Stress Heterogeneity.- 4.5.7 Exercise on Bending Fatigue of a Beam.- History of International Damage Mechanics Conferences.- Authors and Subject Index.

Free vibrations of delaminated beams

Abstract: Free vibration of laminated composite beams is studied. The effect of interply delaminations on natural frequencies and mode shapes is evaluated both analytically and experimentally. The equation of motion and associated boundary conditions are derived for the free vibration of a composite beam with a delamination of arbitrary size and location. A generalized variational principle is used to formulate the equation of motion, taking into account the interlaminar stress concentration at the crack-tips. This is accomplished by introducing a 'crack function' into the beam's compatibility relations. This function has its maximum value at the crack tip and decays exponentially in the longitudinal direction. The rate of exponential decay is determined by a least-square fit with the experimental results. The effect of coupling between longitudinal vibration and bending vibration is considered in the present study. This coupling effect is found to significantly affect the natural frequencies and mode shapes of the delaminated beam.

Cyclic Plasticity and Low Cycle Fatigue Life of Metals

Abstract: 1 Introduction 2 Stress and Strain in Cyclic Loading Monotonic stress-strain curve Stress-strain relationship in cyclic loading Hysteresis loop Cyclic hardening/softening curves Cyclic stress-strain curve 3 Cyclic Plasticity and Microstructure Metals and simple alloys with fcc structure Metals and single phase alloys with bcc structure Other metals and single phase alloys Multiphase materials 4 Dislocation Mechanisms in Cyclic Plastic Straining Athermal mechanisms in fcc metals Thermally activated cyclic straining Dislocation mechanisms in particle strengthened metals 5 Statistical Description of Cyclic Stress-Strain Response Internal and effective stress in an elementary volume Statistical approach 6 Experimental Investigation of the Dynamics of Cyclic Plastic Straining Stress-dip method Stress and strain relaxation Strain rate changes Analysis of hysteresis loop shape Evaluation of results using individual methods 7 Cyclic Creep Relevant experimental investigations Dislocation arrangements Mechanisms and models 8 Fatigue Crack Initiation Observation of surface relief evolution Models of surface relief evolution Mechanisms of crack initiation Role of grain boundaries Role of inclusions 9 Growth of Fatigue Cracks Fracture mechanics approach to fatigue crack growth Crack growth under small scale yielding General yield fatigue crack growth Short crack growth 10 Fatigue Life of Smooth Bodies Strain controlled cycling Plastic strain controlled cycling Stress controlled cycling Energy criterion Evaluation of fatigue life of a smooth body using the fatigue process model 11 Fatigue Life of Notched Bodies Stress and strain concentration in a notched body Fatigue life evaluation 12 Variable Amplitude Loading Phenomenological description Analysis of load history Sudden changes of strain amplitude Cyclic plasticity in repeated block loading Hypothesis of cumulative damage Fatigue life prediction 13 Effect of Depressed Temperature Cyclic plasticity Fatigue life 14 High Temperature Low Cycle Fatigue Cyclic plasticity at elevated temperatures Fatigue life and its evaluation Damage mechanisms Fatigue life prediction 15 Thermal and Thermomechanical Fatigue The effect of temperature changes under constraint Reversed plasticity and thermal cracking Thermal ratchetting 16 Multiaxial Loading Multiaxial stress and strain Cyclic stress-strain response Fatigue life 17 Computer Controlled Fatigue Testing Role of the digital computer Low cycle fatigue test Crack growth test Variable amplitude test Other tests 18 Characterisation of Low Cycle Fatigue Resistance of Metallic Materials Basic characteristics Review of materials properties References Subject Index

Strength and fracture of glass and ceramics

Abstract: 1. Strength and Fracture of Glass and Ceramics. Structure. Glass. Ceramics. Glass-ceramics. Mechanical properties. Elasticity. Non-elastic phenomena. The strength of glass and ceramics. Glass. Ceramics. Theoretical strength of brittle materials. The causes of low strength in glass and ceramics. Glass. Ceramics. Conditions for crack growth. Fracture behaviour with time. Subcritical crack growth, influence of the environment. Maximum fracture velocity. Crack trajectory. Failure due to various types of load. Concentrated load. Impact loading. Thermal stresses. Statistical aspects of strength and fracture. 2. The Principles of Fracture Mechanics. Stresses in a body with cracks. Basic terms, stress intensity factor. Determination of the stress intensity factor. The criterion for crack growth. The Irwin criterion for brittle fracture. The Griffith criterion for brittle fracture. The energy release rate. Practical use of fracture criteria. Fracture toughness of glass and ceramics. Velocity of crack growth. Glass. Ceramics. Determination of strength and lifetime of a body with a crack. Materials without subcritical crack growth. Materials with subcritical crack growth. Materials at high temperatures. Methods for ensuring service safety and lifetime. Non-destructive testing. Statistical methods. Proof tests. 3. Determination of Mechanical Properties. Determination of elastic constants. Young's modulus. Shear modulus. Determination of inelastic properties. Hardness. Viscosity. Creep. Strength tests. Tensile strength. Compressive strength. Bending strength. Shear strength. Strength under multiaxial stress. Inert and impact strength. Determination of fracture mechanics parameters. Test specimens. Determination of fracture toughness. Determination of the relationship v(K1). Determination of constants A, N. Other kinds of tests. Tests of resistance to sudden changes of temperature. Tests of impact resistance. Tests of resistance to pressure. Proof tests. Non-destructive tests, acoustic emission. Wear tests. Statistical methods. Introduction. Principal types of probability distribution. Determination of failure probability and allowable stress. The influence of body size. Errors due to scatter of measured values. 4. Fracture Analysis. Fracture pattern. General features. Practical examples. Morphology of fracture surfaces. General features. Fracture: origin, mirror, drawing. Rough surface. Shell-like fracture. General principles of fracture analysis. 5. Strengthening of Glass and Ceramics. General methods of increasing failure resistance. Strengthening of glass. Protection against surface defect generation. Surface treatment to remove or reduce surface flaws. Formation of a compressive prestress in surface layer. Controlled crystallization. Combination with other materials. Increasing the strength of ceramics. Reducing the size of critical flaws. Reducing unfavourable inner stresses.

Analysis of mammalian connective tissue: relationship between hierarchical structures and mechanical properties.

Abstract: It is widely accepted that the mechanical properties of implants must match those of the surrounding connective tissue to prevent stress concentration and premature failure. The purpose of this paper is to review the structure-mechanical property relationships that exist for connective tissue. The mechanical properties of connective tissue depend on the content of collagen, elastic tissue, and proteoglycans, as well as the geometric arrangement of the fibrous components, age, and location of the specimen. To a first approximation the geometry and loading pattern of the collagen networks in these tissues dominate the mechanical response at high strains. The behavior of the elastic fiber networks dominate the low-strain mechanical response in tissues where energy and shape recovery are critical. Proteoglycans are involved in resisting tissue compressive forces. Since the stiffness of connective tissue increases with age, it is necessary to attempt to match this property by designing implants that have similar behaviors to insure that stress concentration does not occur at the interface between the implant and host.

Fatigue crack growth in metals and alloys: mechanisms and micromechanics

Abstract: Fatigue crack growth has been studied using several new experimental tools in the past ten years. The observation of fatigue cracks during growth under high resolution conditions has shown that crack advance is an intermittent process. These results, when combined with measurements of crack opening, displacements, crack closure, crack tip strains, fractography, and other information, leads to a reasonable understanding of many intrinsic aspects of fatigue crack growth at ambient temperature in a number of metallic alloys. Models of fatigue crack growth are reviewed from the perspective of this understanding. No model has achieved the capability of predicting fatigue crack growth from a description of microstructural and mechanical properties. The factors limiting a deeper understanding of fatigue crack growth are also more clearly defined, which gives some direction for future research. This paper is a critical review of crack growth mechanisms, mainly for large fatigue cracks subject to constant ...

Tensile properties of polypropylene/kaolin composites

Abstract: Tensile properties of isotactic polypropylene filled with particulate kaolin fillers were evaluated in the composition range 0–60 wt % kaolin. Tensile modulus increased with filler concentration while breaking elongation and tensile strength decreased. The modulus increase was attributed to the restriction on the molecular mobility of the polymer imposed by kaolin particles. The decrease in elongation was also an effect of this restriction coupled with interference to stress transfer by the filler particles. Generation of discontinuity in the composite structure through formation of stress concentration points accounted for the tensile strength decrease. Morphology studies by SEM also indicated the introduction of stress concentration points by the presence of bare and nonadherent kaolin particles and their agglomerates with sharp edges in these composites.

Mode-III cracks in piezoelectric materials

Abstract: The stress and electric fields around a mode‐III crack containing a dielectric medium are formulated. Mechanical equilibrium requires that the crack surfaces be traction free. Previous solutions have used the electrical boundary condition that the electric displacement component perpendicular to the crack surfaces should be zero. However, cracks that are filled with a dielectric medium, such as vacuum or air, require that the electric displacement be continuous across the crack faces. Using the boundary condition appropriate for an insulating crack, the stress, strain, and electric‐field strength are found to exhibit r−1/2 singularities while the electric displacement does not. The singularity in the electric‐field strength arises from piezoelectricity. The driving force for crack growth is only related to the effective level of applied stress. Under constant displacement, the applied field may increase or decrease the effective applied stress depending on its direction. As a result the electric field may...

Effects of sic content on fatigue crack growth in

Abstract: An experimental study has been conducted with the purpose of examining the fatigue crack growth characteristics of cast aluminum alloy matrix composites reinforced with different vol- ume fractions of silicon carbide particles. Particular attention has been paid to developing com- posite microstructures with similar matrix aging condition, precipitation, matrix strength, reinforcement particle size distribution, and interfacial characteristics but with different con- trolled amounts of reinforcement particles. Fatigue crack growth experiments have been con- ducted using constant stress amplitude methods with a fixed load ratio as well as constant Kmax control involving a varying load ratio. The development of crack closure and the microscopic path of the crack through the composite microstructure are monitored optically and using the electron microscope in an attempt to examine the mechanisms of fatigue fracture. The results indicate that an increase in SiC content results in the suppression of striation formation in the ductile matrix. Although ductile matrix failure involving the formation of striations in the low SiC content composite or of void growth in the high SiC content composite is evident, the results also show that fracture of the reinforcement particles plays a significant role in dictating the rates of fatigue crack growth. Detailed quantitative analyses of the extent of particle fracture as a function of the reinforcement content have been performed to elucidate the mechanistic origins of fatigue resistance. The propensity of particle fracture increases with particle size and with the imposed value of stress intensity factor range. While discontinuously reinforced metal- matrix composites with predominantly matrix cracking are known to exhibit superior fatigue crack growth resistance as compared to the unreinforced matrix alloy, the tendency for particle fracture in the present set of experiments appears to engender fatigue fracture characteristics in the composite which are inferior to those seen in the unreinforced matrix material. Particle fracture also results in noticeable differences in the microscopic fracture path and causes a reduction in crack closure in the composites as compared to that in the matrix alloy. The results of this work are discussed in light of other related studies available in the literature in an attempt to develop a mechanistic perspective on fatigue crack growth resistance in metal-matrix composites.

The yield strength of particulate reinforced thermoplastic composites

Abstract: The effects of the filler volume fraction and strength of adhesion on the mode of tensile failure of a particulate reinforced polypropylene (PP) are investigated using finite element simulation (FES). When there is perfect adhesion between con- stituents, an upper bound for tensile yield strength is found to be 1.33 times the matrix yield strength above a critical volume of particulate concentration. Utilizing Sjoerdsma's model for interacting stress concentration fields, one can determine the concentration dependence of the yield strength below the critical filler volume fraction

An Evaluation of the Iosipescu Specimen for Composite Materials Shear Property Measurement

Abstract: A detailed evaluation of the suitability of the Iosipescu specimen tested in the modified Wyoming fixture is presented. An experimental investigation using conventional strain gage instrumentation and moire interferometry is performed. A finite element analysis of the Iosipescu shear test for unidirectional and cross-ply composites is used to assess the uniformity of the shear stress field in the vicinity of the notch, and demonstrate the effect of the nonuniform stress field upon the strain gage measurements used for the determination of composite shear moduli. From the test results for graphite-epoxy laminates, it is shown that the proximity of the load introduction point to the test section greatly influences the individual gage readings for certain fiber orientations but the effect upon shear modulus measurement is relatively unimportant. A numerical study of the load contact effect shows the sensitivity of some fiber configurations to the specimen/fixture contact mechanism and may account for the variations in the measured shear moduli. A comparison of the strain gage readings from one surface of a specimen with corresponding data from moire interferometry on the opposite face documented an extreme sensitivity of some fiber orientations to eccentric loading which induced twisting and yielded spurious shear stress-strain curves. In the numerical analysis, it is shown that the Iosipescu specimens for different fiber orientations have to be modeled differently in order to closely approximate the true loading conditions. Correction factors are needed to allow for the nonuniformity of the strain field and the use of the average shear stress in the shear modulus evaluation. The correction factors, which are determined for the region occupied by the strain gage rosette, are found to be dependent upon the material orthotropic ratio and the finite element models. Based upon the experimental and numerical results, recommendations for improving the reliability and accuracy of the shear modulus values are made, and the implications for shear strength measurement discussed. Further application of the Iosipescu shear test to woven fabric composites is presented. The limitations of the traditional strain gage instrumentation on the satin weave and high tow plain weave fabrics is discussed. Test results of a epoxy based aluminum particulate composite is also presented. A modification of the Iosipescu specimen is proposed and investigated experimentally and numerically. It is shown that the proposed new specimen design provides a more uniform shear stress field in the test section and greatly reduces the normal and shear stress concentrations in the vicinity of the notches. While the fabrication and the material cost of the proposed specimen is tremendously reduced, it is shown the accuracy of the shear modulus measurement is not sacrificed.

Extensile Cracking in Porous Rock Under Differential Compressive Stress

Abstract: Under differential compressive stress rocks exhibit nonlinear deformation that includes initial compaction, near-linear elastic behavior, and strain-hardening followed by strain-softening and dilation (or compaction in clastic rocks) and localization. This behavior derives largely from changes in the microstructure of the rocks. Much of it has been attributed to the growth of extensile microcracks. The stress-induced microstructural changes brought about by successively more complicated states of stress produced by uniaxial and triaxial compression of circular cylinders, axisymmetric stresses in hollow cylinders, and indentation by hemispheres in Indiana limestone and Berea sandstone have been preserved using Wood`s metal porosimetry. In this technique molten Wood`s metal at about 100{degrees}C is used as a pore fluid at a pressure of about 10 MPa, and the experiments are conducted using the concepts of effective stress. At the deformation state of interest, the temperature is lowered to solidify the metal, thereby preserving the microstructure as it exists under load and facilitating subsequent preparation of the specimen for microscopic study. Mode I microcrack growth is observed to occur by a variety of mechanisms such as bending, point loading and sliding cracks. The effects of this are analyzed using an elastic continuum within which Mode II displacement acrossmore » microcracks and Mode I microcrack growth results from heterogeneous stress concentrations that produce local tensile stresses. While the continuum model replicates many of the observations, it fails to account for localization by en echelon arrays of extensile microcracks that precede macroscopic shear faulting. Using a {open_quotes}zero order{close_quotes} continuum approximation, the spatially stochastic distribution of grains in clastic rocks is shown to be important in the formation of the en echelon arrays of microcracks that form shear bands. 63 refs., 26 figs., 1 tab.« less

Crack-tip stress in gels

Abstract: Calculations of drying stresses have previously been presented in terms of the total stress, which is the sum of the stresses in the liquid and solid phases. However, the criterion for fracture involves the stress on the solid phase. In this note, the stress on the network at the crack tip is given explicitly. It is shown that the stress at the tip of a flaw can be tensile, even though the solid network is in compression elsewhere.

An analysis of stress concentrations caused by shot peening and its application in predicting fatigue strength

Abstract: — In order to calculate the stress concentration caused by shot-peening dents, three simplified models, namely a one-pit model, a seven-pit model and a pit-loop model, are proposed in this paper. By using a finite element program for automatic dynamic incremental non-linear analysis, the stress concentration coefficients based on these models are calculated for different pit parameters and different stress fields. When considering the stress concentration and residual stress field produced by shot peening, a modified Goodman formula is proposed and used for forecasting the fatigue strength of peened specimens having the fatigue sources at the surface. The forecasted results were verified by peening followed by fatigue tests on 40Cr steel.

The structure of the near-tip field during transient elastodynamic crack growth

Abstract: T he process of dynamic crack growth in a nominally elastic malerial under conditions of plane strain or plane stress is considered. Of particular concern is the influence of the transient nature of the process on the stress field in the immediate vicinity of the crack tip during nonsteady growth. Asymptotically, the crack tip stress field is square root singular at the crack tip, with the angular variation of the singular field depending weakly on the instantaneous crack tip speed and with the instantaneous stress intensity factor being a scalar multiplier of the singular field. However, for a material particle at a small distance from the moving crack, the local stress field depends not only on instantaneous values of crack speed and stress intensity factor, but also on the past history of these lime-dependent quantities. A representation of the crack tip field is obtained in the form of an expansion about the crack up in powers of radial coordinate, with the coefficients depending on the time rates of change of crack tip speed and stress intensity factor. This representation is used to interpret some experimental observations, with the conclusion that the higher-order expansion provides an accurate description of crack tip fields under fairly severe transient conditions. In addition, some estimates are made of the practical limits of using a stress intensity factor field alone to characterize the local fields.

Fracture Mechanics Parameters for Small Fatigue Cracks

Abstract: This paper presents a review of some common small-crack test specimens, the underlying causes of the small-crack effect, and the fracture-mechanics parameters that have been used to correlate or predict their growth behavior. This review concentrates on continuum mechanics concepts and on the nonlinear behavior of small cracks. The paper reviews some stress-intensity factor solutions for small-crack test specimens and develops some simple elastic-plastic J integral and cyclic J integral expressions that include the influence of crack-closure. These parameters were applied to small-crack growth data on two aluminum alloys, and a fatigue life prediction methodology is demonstrated. For these materials, the crack-closure transient from the plastic wake was found to be the major factor in causing the small-crack effect.

Short Fatigue Cracks

Abstract: For more than a century, metal fatigue research has been associated with producing S-N endurance curves from experiments on plain and notched specimens. Recently a detailed interpretation of S-N curves generated from smooth specimen tests has become possible because of our increased understanding of the behaviour of very small cracks ie cracks growing to about 500 pm in depth, which can involve a high proportion of the fatigue lifetime at high endurances. This recent knowledge has been due to the development of elastic-plastic fracture mechanics of crack growth, new techniques to monitor the growth of small surface cracks, and not least, from commercial pressures to use advanced materials.

Surface patterns on single-crystal films under uniaxial stress: Experimental evidence for the Grinfeld instability.

Abstract: We study the stress relaxation in single-crystal films of polymerized polydiacetylene, in epitaxy with their monomer substrate. Polymerization induces a uniaxial stress. Two types of surface patterns are observed and studied by atomic force microscopy: films thicker than 175 nm exhibit quasiperiodic cracks perpendicular to the polymer chains; thinner ones exhibit regular wrinkles with the same orientation. The wrinkle surface deformation is stress relaxing and plastic. We show that all experimental results, in particular, the order of magnitude of the pattern spacings, are compatible with the following interpretation: as polymerization proceeds, the uniaxial stress generates a Grinfeld instability (Dok. Akad. Nauk SSSR 290, 1358 (1986) [Sov. Phys. Dokl. 31, 831 (1986)]) fed by surface diffusion. The crack pattern is a secondary instability, initiated at the sites of stress concentration provided by the wrinkles.

Theoretical study on the static performance of piezoelectric ceramic- polymer composites with 1-3 connectivity

Abstract: Inhomogeneous displacement profiles have been derived for a single‐rod composite and a single‐tube 1‐3 ceramic‐polymer composite under both uniaxial and hydrostatic stress. The effective piezoelectric constants for the composites have been derived in terms of the ceramic content, the piezoelectric and elastic constants of each component, and the aspect ratio of the ceramic rod. The stress concentration inside both phases is derived from the calculated inhomogeneous displacement profiles. It is found that only a finite portion of the polymer in the vicinity of the ceramic‐polymer interface actually contributes to the stress transfer, and the induced additional stress on the ceramic also has a higher magnitude near the interface. The theoretical results quantitatively predict the performance of a given 1‐3 structure, and can be used to optimize the design parameters, such as ceramic content, aspect ratio of the ceramic rods, rod geometry and rod arrangement, resin hardness, etc., for 1‐3 structures designed for specific purposes.

The Hertzian stress field and formation of cone cracks—I. Theoretical approach

Abstract: A complete three-dimensional solution has been derived for the Hertzian stress field. The solution was used to define an expression for the largest tensile stress under a spherical indenter. A numerical method was developed to solve the fracture mechanics equation related to cone crack formation, leading to a simple expression for fracture toughness. Examination of the relation between load, cone crack size and stress intensity showed that the critical stress intensity factor is independent of load and crack size. This suggests a new method to determine fracture toughness of brittle materials using Hertzian indentation.

An Evaluation of the Neuber and Glinka Relations for Monotonic Loading

Abstract: The abilities of six models of notch root behavior are evaluated by comparing them with experimental results over a range of constraints. The models studied are the Neuber model, the Walker modified Neuber model, the Glinka models for plane strain and for plane stress, and two modifications of the Glinka models. Comparisons are made with strains measured at the roots of notches by resistance gages or by laser-based interferometry.