Showing papers on "Creep published in 1999"

The yield stress—a review or ‘παντα ρει’—everything flows?

Abstract: An account is given of the development of the idea of a yield stress for solids, soft solids and structured liquids from the beginning of this century to the present time. Originally, it was accepted that the yield stress of a solid was essentially the point at which, when the applied stress was increased, the deforming solid first began to show liquid-like behaviour, i.e. continual deformation. In the same way, the yield stress of a structured liquid was originally seen as the point at which, when decreasing the applied stress, solid-like behaviour was first noticed, i.e. no continual deformation. However as time went on, and experimental capabilities increased, it became clear, first for solids and lately for soft solids and structured liquids, that although there is usually a small range of stress over which the mechanical properties change dramatically (an apparent yield stress), these materials nevertheless show slow but continual steady deformation when stressed for a long time below this level, having shown an initial linear elastic response to the applied stress. At the lowest stresses, this creep behaviour for solids, soft solids and structured liquids can be described by a Newtonian-plateau viscosity. As the stress is increased the flow behaviour usually changes into a power-law dependence of steady-state shear rate on shear stress. For structured liquids and soft solids, this behaviour generally gives way to Newtonian behaviour at the highest stresses. For structured liquids this transition from very high (creep) viscosity (>106 Pa.s) to mobile liquid (

Ceramics: Mechanical Properties, Failure Behaviour, Materials Selection

Abstract: 1 Overview and Basic Properties.- 1.1 General Behaviour.- 1.2 Overview of Ceramic Materials.- 1.3 Fields of Application.- 2 Physical Properties.- 2.1 Thermal Expansion Coefficient.- 2.2 Thermal Conductivity.- 2.3 Electrical Conductivity.- 2.4 Specific Heat.- 2.5 Density.- 2.6 Elastic Constants.- 3 Fracture Mechanics.- 3.1 Fundamentals.- 3.1.1 Linear-Elastic Fracture Mechanics.- 3.1.2 Rising Crack Growth Resistance.- 3.2 Experimental Methods for the Determination of the Mode-I Fracture Toughness KIc.- 3.2.1 The Edge-Cracked Bending Bar.- 3.2.2 Specimens with Chevron Notches.- 3.2.3 Specimen with Knoop Indentation Crack.- 3.2.4 Vickers Indentation Cracks.- 3.2.5 Comparison of Different Specimen Types.- 3.3 Experimental Methods for the Determination of Mode-II and Mixed-Mode Fracture Toughness.- 3.3.1 Bending Test with Bars Containing Oblique Notches.- 3.3.2 Three-Point Bending Test with an Eccentric Notch.- 3.3.3 The Asymmetric Four-Point Bending Test.- 3.3.4 Diametral Compression Test.- 3.3.5 Surface Haws in Mixed-Mode Loading.- 3.4 Mixed-Mode Criteria and Experimental Results.- 4 R-Curve Behaviour.- 4.1 Experimental Observation.- 4.1.1 Results for Different Materials.- 4.1.2 Effect of Geometry and Loading Conditions.- 4.1.3 Work-of-Fracture.- 4.1.4 Comparison of Macro- and Microcracks.- 4.2 Determination of R-Curves.- 4.2.1 Specimens with Macrocracks.- 4.2.2 Specimens with Vickers Indentations.- 4.3 Reasons for R-Curve Behaviour.- 4.4 Influence of R-Curves on Strength.- 4.5 Computation of R-Curves.- 4.5.1 Fracture Mechanical Treatment of Bridging Stresses.- 4.5.2 Phase-Transformation Zone and Shielding Stress Intensity Factor.- 4.6 Determination of Bridging Stresses from Crack Profiles.- 5 Subcritical Crack Growth.- 5.1 Basic Relations.- 5.2 Computation of Lifetimes.- 5.2.1 Lifetimes Under Arbitrary Loading History.- 5.2.2 Lifetimes Under Static Load.- 5.2.3 Lifetimes Under Cyclic Load.- 5.3 Methods of Determining Subcritical Crack Growth.- 5.3.1 Double-Torsion Test.- 5.3.2 The Double-Cantilever-Beam Specimen.- 5.3.3 Crack Growth Data from Dynamic Bending Tests.- 5.3.4 Crack Growth Data from Static Bending Tests.- 5.3.5 Lifetime Prediction.- 5.4 Influence of R-Curve Behaviour on Subcritical Crack Growth.- 5.4.1 General Influence.- 5.4.2 Tests with Macroscopic Cracks.- 5.4.3 R-Curves for Subcritical Crack Extension.- 5.4.4 Lifetimes for Natural Cracks.- 5.5 Some Theoretical Considerations on Subcritical Crack Growth.- 6 Cyclic Fatigue.- 6.1 Representation of Cyclic Fatigue Results.- 6.2 Proof of a Cyclic Effect.- 6.3 Methods for the Determination of da/dN-?K Curves.- 6.4 Effect of R-Ratio.- 6.5 Theoretical Considerations.- 6.5.1 Effect of Crack Surface Interactions.- 6.5.2 Effect of Glass Phase Content.- 6.5.3 Effect of Phase Transformation Zones.- 6.6 Differences Between Micro- and Macrocracks.- 7 Determination of Strength.- 7.1 Measurement of Tensile Strength.- 7.1.1 The Tensile Test.- 7.1.2 The Bending Test.- 7.1.3 Test of Pipe Sections.- 7.2 Measurement of Compressive Strength.- 7.2.1 Compression Tests with Cylindrical Specimens.- 7.2.2 Compression Test on Hollow Cylinders.- 7.2.3 Results of Compression Tests.- 8 Scatter of Mechanical Properties.- 8.1 Principal Behaviour.- 8.2 Determination of Weibull Parameters.- 8.3 The Size Effect.- 8.4 Scatter of Lifetimes.- 8.5 Some Specific Problems.- 8.5.1 Three-Parameter Weibull Distribution.- 8.5.2 Multiple Flaw Population.- 8.5.3 Influence of the R-Curve.- 9 Proof Test Procedure.- 9.1 Proof Test Without Subcritical Crack Growth.- 9.2 Proof Test Including Subcritical Crack Growth.- 9.3 Problems in Proof Tests.- 9.3.1 Subcritical Crack Growth During the Proof Test.- 9.3.2 Different Flaw Population at High Temperatures.- 9.3.3 Simulation of the Service Conditions.- 10 Multiaxial Failure Criteria.- 10.1 Representation in Multiaxiality Diagrams.- 10.2 Global Multiaxiality Criteria.- 10.3 Defect Models.- 10.3.1 Cylindrical Pore.- 10.3.2 Spherical Pore.- 10.3.3 Ellipsoidal Pore.- 10.3.4 Circular Cracks.- 10.3.5 Conclusions from Defect Models.- 10.3.6 Statistical Treatment.- 10.3.7 Lifetime.- 10.4 Experimental Methods.- 10.4.1 The Ring-on-Ring Test.- 10.4.2 Ball-on-Ring Test.- 10.4.3 Brazilian-Disk Test.- 10.4.4 Tests with Tubes.- 10.4.5 Triaxial Stress States.- 10.5 Experimental Results.- 11 Thermal Shock Behaviour.- 11.1 Thermal Stresses.- 11.2 Measurement of Thermal Shock Sensitivity.- 11.3 Fracture Mechanical Treatment of Thermal Shock.- 11.4 Thermal Shock Parameters.- 11.5 Size Effect in Thermal Shock.- 11.6 Thermal Fatigue.- 12 High-Temperature Behaviour.- 12.1 Creep Deformation.- 12.1.1 Creep Relations for Tensile Tests.- 12.1.2 Differences in Tensile and Compression Creep.- 12.1.3 Creep Under Variable Stresses.- 12.1.4 Creep Under Bending Load.- 12.2 Failure in the Creep Range.- 12.2.1 Creep Fracture.- 12.2.2 Failure Maps.- 12.3 Creep Crack Growth.- 12.3.1 The C* Integral.- 12.3.2 Experimental Determination of C*.- 13 Plasticity.- 13.1 Plasticity During Contact Loading.- 13.2 Plasticity During Surface Grinding.- 13.3 Plasticity by Phase Transformation in Zirconia.- 13.4 Plasticity by Domain Switching in Piezoelectric Ceramics.- 13.5 Measurement of Plastic Deformations in Bending Tests.- 13.6 Time-Dependent Plasticity Effects.- A.1 Rectangular Bar.- A.2 Comact-Tension (CT) Specimen.- A.3 Round Compact Tension (RCT) Specimen.- A.4 Double-Cantilever-Beam Specimen (DCB).- A.5 Weight Function for Chevron-Notched Bending Bars.- A.6 Specimens for Mixed-Mode Tests.

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Abstract: Ceramic matrix composites (CMC) are potentially designed for use in the high temperature environment because of their high strength and noncatastrophic failure characteristics. For ceramics at elevated temperature, the materials exhibit time-dependent deformation. The phenomenon is further accelerated by an increase in the stress or the temperature. Reinforcement by incorporating high-strength fibers is one of the several approaches to significantly improving the creep fracture resistance of the CMC. Experimental studies in mechanical behavior of CMC [1-4] have shown that failure is preceded by matrix cracking at high temperatures. Further, the creeping matrix causes stress transfer from the matrix to the fiber. However, there is a lack of any investigation in understanding of the relation between the matrix cracking at the micro level and the overall mechanical behavior of CMC at elevated temperature. In this research effort, the crack tip fields for a matrix crack are considered. Using generalized expansions at the crack tip in each region and matching the stresses and displacements across the interface in an asymptotic sense, a series asymptotic solution is constructed for the stresses and strain rates near the crack tip. It is found that the stress singularities, to the leading order, are the same in each material, oscillatory higher-order terms exist in both regions, and stress higher-order term with the order of

Indentation power-law creep of high-purity indium

Abstract: Using a variety of depth-sensing indentation techniques, the creep response of high-purity indium, from room temperature to 75 °C, was measured. The dependence of the hardness on the variables of indentation strain rate (stress exponent for creep (n)) and temperature (apparent activation energy for creep (Q)) and the existence of a steady-state behavior in an indentation test with a Berkovich indenter were investigated. It was shown for the first time that the indentation strain rate (-este-/h) could be held constant during an experiment using a Berkovich indenter, by maintaining the loading rate divided by the load (-este-/P) constant. The apparent activation energy for indentation creep was found to be 78 kJ/mol, in accord with the activation energy for self-diffusion in the material. Finally, by performing -este-/P change experiments, it was shown that a steady-state path independent of hardness could be reached in an indentation test with a geometrically similar indenter.

Rupture Time Under Creep Conditions

Abstract: The problem of long time strength (evaluation of time to rupture) is of obvious relevance for various machine parts working under high temperature conditions. The existing data on specimens tested under uniaxial tension are insufficient for general loading conditions and inhomogeneous stress states: intensive experimental investigations are being conducted in this direction. Theoretical modelling of long time strength in the framework of continuum mechanics appears to be important. In recently published work of Hoff (1953), the moment of failure of a rod under tension is defined as the one at which the cross-sectional area becomes zero as a result of quasiviscous flow. His result is in satisfactory agreement with experimental data. A similar concept was used by Katz (1957) and by Rosenblum (1957) in their studies of times to rupture of thick-walled pipes and of a rotating disk with a hole. We note, however, that the experimental data points typically lie below the theoretical predictions and that rupture occurs at elongations not exceeding several tens per cent. The concept of Hoff has certain limitations. It predicts, for example, that creep under torsion does not result in rupture, contrary to observations. Also, his scheme does not explain fractures at small strains (‘brittle’ ruptures) and the change of character of rupture (from ‘viscous’ to ‘brittle’) if the material is not sufficiently stable. Here, we suggest a theoretical model for the time to rupture with the account of embrittlement. We emphasize that the physics of such phenomena is very complex and has not been studied sufficiently. Although we discuss microcracking, the results can be interpreted in a more general way, in terms of development of damage.

Structural Modeling and Experimental Techniques

Abstract: Introduction to Physical Modeling in Structural Engineering Introduction Structural Models - Definitions and Classifications A Brief Historical Perspective on Modeling Structural Models and Codes of Practice Physical Modeling and the New Engineering Curriculum Choice of Geometric Scale The Modeling Process Advantages and Limitations of Model Analysis Accuracy of Structural Models Model Laboratories Modeling Case Studies The Theory of Structural Models Introduction Dimensions and Dimensional Homogeneity Dimensional Analysis Structural Models Similitude Requirements Elastic Models - Materials and Techniques Introduction Materials for Elastic Models Plastics Time Effects in Plastics - Evaluation and Compensation Effects of Loading Rate, Temperature, and the Environment Special Problems Related to Plastic Models Other Common Elastic Model Materials Balsa Wood, Structural Wood, and Paper Elastic Models - Design and Research Applications Determination of Influence Lines and Influence Surfaces Using Indirect Models - Muller-Breslau Principle Inelastic Models: Materials for Concrete and Masonry Structures Prototype and Model Concretes Engineering Properties of Concrete Unconfined Compressive Strength and Stress-Strain Relationship Tensile Strength of Concrete Flexural Behavior of Prototype and Model Concrete Behavior in Indirect Tension and Shear Design Mixes for Model Concrete Summary of Model Concrete Mixes Used by Various Investigators Gypsum Mortars Modeling of Concrete Masonry Structures Strength of Model Block Masonry Assemblages Inelastic Models: Structural Steel and Reinforcing Bars Introduction Steel Structural Steel Models Reinforcement for Small-Scale Concrete Models Model Prestressing Reinforcement FRP Reinforcement for Concrete Models Bond Characteristics of Model Steel Bond Similitude Cracking Similitude and General Deformation Similitude in Reinforced Concrete Elements Model Fabrication Techniques Introduction Basic Cutting, Shaping and Machining Operations Basic Fastening and Gluing Techniques Construction of Structural Steel Models Construction of Plastic Models Construction of Wood and Paper Models Fabrication of Concrete Models Fabrication of Concrete Masonry Materials Instrumentation Principles and Applications General Quantities to Be Measured Strain Measurements Displacement Measurements Full-Field Strain Measurements and Crack Detection Methods Stress and Force Measurement Temperature Measurements Creep and Shrinkage Characteristics and Moisture Measurements Data Acquisition and Reduction Fiber Optics and Smart Structures Loading Systems and Laboratory Techniques Introduction Types of Loads and Loading Systems Discrete vs. Distributed Loads Loading for Shell and Other Models Loading Techniques for Buckling Studies and for Structures Subject to Sway Miscellaneous Loading Devices Size Effects, Accuracy and Reliability in Materials System and Models General What Is a Size Effect? Factors Influencing Size Effects Theoretical Studies in Size Effects Experimental Work in Plain Concrete Size Effects in Reinforced and Prestressed Concrete Size Effects in Metal and Other Materials Size Effects in Masonry Mortars Size Effects and Design Codes Errors in Model Studies Types of Errors Statistics of Measurements Propagation of Random Errors Accuracies in (Concrete) Models Overall Reliability of Model Results Influence of Cost and Time on Accuracy of Models Model Applications and Case Studies Introduction Modeling Applications Case Studies Structural Models for Wind, Blast, Impact and Earthquake Loads Introduction Similitude Requirements Materials for Dynamic Models Loading Systems for Dynamic Model Testing Examples of Dynamic Models Case Studies Educational Models for Civil and Architectural Engineering Introduction Historical Perspective Linearly Elastic Structural Behavior Nonlinear and Inelastic Structural Behavior Structural Dynamics Concepts Experimentation and the New Engineering Curriculum Case Studies and Student Projects

Thermo-chemo-mechanical model for concrete. I: hydration and aging

Abstract: In this work a coupled thermo-chemo-mechanical model for the behavior of concrete at early ages is proposed. The model allows simulation of the observed phenomena of hydration, aging, damage, and creep. It is formulated within an appropriate thermodynamic framework, from which the state equations are derived. In this first part, the formulation and assessment of the thermochemical aspects of the model are presented. It is based on the reactive porous media theory, and it can accurately predict the evolution in time of the hydration degree and the hydration heat production. The evolution of the compressive and tensile strengths and elastic moduli is related to the aging degree, a concept introduced to account for the effect of the curing temperature in the evolution of the mechanical properties. The short- and long-term mechanical behavior is modeled by means of a viscoelastic damage model that accounts for the aging effects. The formulation and assessment of the mechanical part of the model are relegated to a companion paper.

Recent developments in microstructure/property relationships of beta titanium alloys

Abstract: There has been significant progress in regard to the effect of stability and grain size of the beta phase on deformation modes and mechanical properties of beta titanium alloys. For example, it has been shown recently, that an increase in the stability of the beta phase reduces the formation of stress-induced plates thereby decreasing the ambient temperature creep strain. Increase in the stability appears to favor deformation by slip. The grain size of the beta phase has also been shown to effect the deformation modes in tensile deformation and the extent of ambient temperature creep strain. In this paper the interrelationships between stability, microstructure, deformation modes and mechanical properties of beta titanium alloys will be critically reviewed.

Boron-doped molybdenum silicides for structural applications

Abstract: The addition of as little as 1 wt.% (=3 at.%) boron improved the oxidation resistance of Mo5Si3 by as much as five orders of magnitude over a temperature range of 800–1500°C. The mechanism of oxidation protection is the formation of a borosilicate glass scale that flows to form a passivating layer over the base intermetallic. The compositional homogeneity range for T1 (Mo5Si3Bx) phase was determined to be much smaller than that reported previously by Nowotny. Compressive creep measurements show that materials based on the phase assemblage of T1-T2 (Mo5SiB2)–Mo3Si have high creep strengths similar to single phase Mo5Si3. Electrical resistivity of selected compositions was also measured and varied from ≈0.06 mΩ-cm at room temperature to 0.14 mΩ-cm at 1500°C. Temperature coefficient of resistivity (TCR) was estimated to be on the order of 1×10−4 C−1 for most compositions.

Physical Aging of Polycarbonate: Enthalpy Relaxation, Creep Response, and Yielding Behavior

Abstract: The effect of annealing polycarbonate at 125 °C (≈Tg − 20 K) for aging times up to almost 2000 h has been investigated by differential scanning calorimetry, and the kinetics of the enthalpy relaxation process are compared with the effects of aging at the same temperature on the creep response and on the yield behavior. The enthalpy relaxation is analyzed by the peak shift method, and the following kinetic parameters are obtained: nonlinearity parameter x = 0.46 ± 0.02; apparent activation energy Δh* = 1160 kJ mol-1; nonexponentiality parameter β is in the range 0.456 < β < 0.6. The similarities and/or differences between these results and others quoted in the literature are discussed. The creep response is analyzed by the commonly accepted procedure of horizontal and vertical shifting of deflection vs log(creep time) curves, and a shift rate of μ = 0.87 is obtained, with an excellent master curve. It is shown that a similar shift rate for enthalpy relaxation can be defined, and a value of μH = 0.49 is fo...

The viscoplastic compaction of composite powders

Abstract: A model for the densification of spherical powders is developed for the early stages of cold and hot compaction under general loading. General viscoplastic properties are adopted which reduce to strain hardening plasticity at ambient temperature and to power law creep at elevated temperature. A large strain analysis is carried out to determine the macroscopic compaction behaviour, based on the affine motion of particles with viscoplastic dissipation occurring at the contacts between particles. Random packing is assumed and the model includes the increase in the number of contacts per particle with densification. A general prescription is given for computing the macroscopic stress as a function of strain rate and accumulated strain. Detailed results are presented for yield surfaces and creep dissipation surfaces after isostatic and closed die compaction. A scalar constraint factor is derived for a random mixture of two populations of particles with different sizes and strengths. The predictions include the limiting case of deformable spheres reinforced with rigid spheres of different size.

A simple parameterization of strain localization in the ductile regime due to grain size reduction: A case study for olivine

Abstract: We propose a simple parameterization of the transition between dislocation creep and grain-size-sensitive creep under conditions characteristic of the lithospheric mantle and derived from the results of laboratory experiments on olivine-rich rocks. Through numerical modeling and linear stability analysis, we determine the conditions under which this transition takes place and potentially leads to strain localization. We pay particular attention to the effect of cooling rate and strain rate which are likely to be dominant parameters in actively deforming tectonic areas. We conclude that at constant temperature, strain localization can only take place if the rheology of the material is nonlinearly related to grain size; that strain localization is facilitated by syndeformation cooling; that there is only a narrow region in the strain rate versus cooling rate parameter space where localization is likely to take place; and that grain growth inhibits strain localization at fast cooling rates but may lead to “grain growth localization” at low cooling rates. We draw attention to the potential consequences of our analysis of strain localization for the style of plate motions at the Earth's surface.

Effects of deposition temperature and thermal cycling on residual stress state in zirconia-based thermal barrier coatings

Abstract: Advanced ceramic multilayered coatings are commonly used as protective coatings for engine metal components to improve performance, e.g. thermal barrier coatings (TBCs). Zirconia-based TBCs were produced by plasma spraying process and characterized in terms of microstructure, porosity, elastic modulus, adherence and residual stresses. In this contribution the residual stresses in multilayered coatings applied on Ni based superalloys for use as thermal barrier coatings were studied both by numerical modelling and experimental stress measurement. The thermal residual stresses generated during the spraying process of duplex TBCs were simulated by using an heat transfer finite element program and an elasto-plastic biaxial stress model. The TBC system was subjected to different thermal cycling conditions (maximum temperature, heating up and cooling down rates, dwell time at maximum temperature, etc.). The stress distribution within the TBC was also modelled after thermal cycling. The stress state in the as-deposited and in thermally cycled coatings was verified using an X-ray diffraction technique. The measurements were in good agreement with the residual stress modelled calculations. It was observed that the residual stresses were dependent on the thermal history of the TBC (as-deposited and thermally cycled). It is proposed that thermal cycling allowed the stresses to relax by microcracking and creep mechanisms at high temperature such that on cooling down to room temperature, an in-plane biaxial compressive stress will arise on the zirconia top coating due to the difference on the coefficients of thermal expansion between the metallic substrate and ceramic coating material.

High Temperature Behavior of a Gel-Derived SiOC Glass: Elasticity and Viscosity

Abstract: The high temperature behavior of a sol-gel derived silicon oxycarbide glass containing 12 at.% carbon has been characterized by means of creep and in-situ ultrasonic echography measurements. Temperature induced changes include structural relaxation and densification from 1000 to 1200°C, and crystallization to form a fine and homogeneous β-SiC/glass-matrix nanocomposite with 2.5 nm large crystals above 1200°C. Young's modulus measurements clearly reveal a consolidation of the material upon annealing below 1200°C. Crystallization is almost complete after few hours at 1300°C and results in a significant increase in Young's modulus. The viscosity of the oxycarbide glass is much higher than that of fused silica, with two orders of magnitude difference at 1200°C, and the glass transition temperature ranges from 1320 to 1370°C.

Interconversion between relaxation modulus and creep compliance for viscoelastic solids

Abstract: Methods of interconversion between relaxation modulus and creep compliance for linear viscoelastic materials are discussed and illustrated using data from asphalt concrete Existing methods of approximate interconversion are reviewed and compared for their approximating schemes A new approximate interconversion scheme that uses the local log-log slope of the source function is introduced The new scheme is based on the concept of equivalent time determined by rescaling the physical time The rescaling factor, which can be interpreted as a shift factor on a logarithmic time axis, is dictated by the local slope of the source function on log-log scales The unknown target function at a given time is obtained by taking the reciprocal of the source function evaluated at an equivalent time Although the method is developed using a mathematical relationship based on the power-law representations of relaxation modulus and creep compliance, the method is not limited to material functions characterized by power-laws but can be applied to general, non-power-law material functions as long as the relevant material behaviors are broadband and smooth on logarithmic scales The new method renders good results especially when the log-log slope of the source function varies smoothly with logarithmic time

Effect of W on recovery of lath structure during creep of high chromium martensitic steels

Abstract: Effect of W on creep strength of martensitic steels was investigated paying special attention to microstructural degradation during creep. Though tempered martensitic lath structure is stable at the elevated temperatures without stress, its recovery takes place substantially during creep. After the recovery, lath width and dislocation density in lath interior reached the stationary values determined by creep stress. There was no difference in the stationary values between the two steels with (TAF650 steel) and without (Mod.9Cr–1Mo steel) W. However, recovery processes of the lath structure are significantly different between the two steels. The growth of lath width and the annihilation of dislocations in lath interior are slower in W containing TAF650 steel than those in Mod.9Cr–1Mo steel. Accumulation of creep strain is suppressed in TAF650 steel because of the slow recovery of its lath structure. The retardation of the recovery of lath structure results in the lower creep rate and the higher creep rupture strength of the W containing steel. The slow recovery of lath structure in the W containing steel is ascribed to pinning effect of M23C6 and Laves phase (Fe2W) precipitated on lath boundaries.