Stress-strain Rate Relationship Research Articles

211 高速引張試験によるひずみ速度を考慮した材料特性の構築(OS7 オーガナイズドセッション《材料強度と構造設計》)

We provide a modeling method of strain rate dependent material which derived from force-displacement relationships for strain rates measured by high speed tensile tests. The strain dependent material model consists of a stress-strain rate relationship in low strain rate, a stress-strain rate elationship in high strain rate and a stress-strain relationship in large strain. To evaluate the modeling method, high speed tensile tests, the material modeling with test result and simulations of high speed tensile test with the material model were carried out. Then it found that the force-displacement relationships of analysis match to those of tests.

Compression of the Material Characteristics of Steel, Aluminum, Wood and Woven Graphite Epoxy Composites in Response to High Strain Rate Load

The stresses developed in the material by impact load are analyzed experimentally, numerically, and analytically for specimens out of steel, aluminum, wood and woven graphite epoxy composites to investigate the material response to high strain rate stresses for aforementioned materials. The applied strain rates in experiments were set to be within 950 and 3500 s-1. The thin circular shape specimens were examined with high strain rate laboratory tests using the perforation split Hopkinson pressure bar (P-SHPB) with dimensional ratio accepted for One-dimensional stress analysis hypothesis. The article describes analytical solutions for one dimensional in detail to be implemented for numerical analyzing via trapezoid computation. The graphs of the four listed materials with two different thicknesses are compared for the specimen’s energy absorbed, specimen’s strain rate, stress strain rate relationship of the specimen, maximum energy absorbed, and maximum strain in specimen. It turned out that the dependency of deformation on energy absorption follows a power law for the woven composite and is approximated with linear relationships for aluminum and steel. Studying the effect of thickness in energy absorbed shows that doubling the thickness of the specimen reduces the strain of the specimen by 50 percentages for woven graphite epoxy and wood specimens, but the reduction is 25 percentages in the steel and aluminum specimens

A Microstructure-Based Constitutive Model for Superplastic Forming

A constitutive model is proposed for simulations of hot metal forming processes. This model is constructed based on dominant mechanisms that take part in hot forming and includes intergranular deformation, grain boundary sliding, and grain boundary diffusion. A Taylor type polycrystalline model is used to predict intergranular deformation. Previous works on grain boundary sliding and grain boundary diffusion are extended to drive three-dimensional macro stress–strain rate relationships for each mechanism. In these relationships, the effect of grain size is also taken into account. The proposed model is first used to simulate step strain-rate tests and the results are compared with experimental data. It is shown that the model can be used to predict flow stresses for various grain sizes and strain rates. The yield locus is then predicted for multiaxial stress states, and it is observed that it is very close to the von Mises yield criterion. It is also shown that the proposed model can be directly used to simulate hot forming processes. Bulge forming process and gas pressure tray forming are simulated, and the results are compared with experimental data.

Optimization of processing parameters based on high temperature flow behavior and microstructural evolution of a nitrogen enhanced 316L(N) stainless steel

The flow behavior of a high nitrogen grade 316L(0.14N) has been studied in a range of temperatures (1073–1423K) and strain rates (0.001–10s−1). The material exhibits two-slope behavior in the stress–strain rate relationship at ≤1223K. It exhibits local negative strain rate sensitivity (LNSRS) in the regime bounded by 1073–1123K and 0.1–1s−1. In the LNSRS domain, material shows inhomogeneous flow, reduced ductility and cracks under tensile loading. The experimental data has been used to develop processing map and activation energy map. The material exhibits a wide stable domain below 0.1s−1 spanning over 1073–1423K, whereas the domain above 0.1s−1 is demarcated as unsafe for processing. The stable domain consists of four peaks with efficiency of 35%, 45%, 50% and 45%, respectively. The activation energy for these peaks has been found to vary between 100 and 200kJ/mol. The localization of heavily deformed grains and random bimodal distribution of grains have been identified as the signatures of instability. Based on the processing map, activation energy map and microstructural evolution, the optimum window for hot deformation has been identified as 1350–1423K and 0.001–0.05s−1 with peak efficiency of 50% and activation energy of 150kJ/mol.

Simulation of Hot Sheet Metal Forming Processes Based on a Micro-Structural Constitutive Model

A constitutive model is proposed for simulations of hot forming processes. Dominant mechanisms in hot forming including inter-granular deformation, grain boundary sliding and grain boundary diffusion are considered in the constitutive model. A Taylor type polycrystalline model is used to predict inter-granular deformation. Previous works on grain boundary sliding and grain boundary diffusion are extended to drive three dimensional macro stress-strain rate relationships for each mechanism. In these relationships, the effect of grain size is also taken into account. It is shown that for grain boundary diffusion, stress-strain rate relationship obeys the Prandtl-Reuss flow rule. The proposed model is used to simulate step strain rate tests and the results are compared with experimental data. It is concluded that the model can be used to predict flow stress for various grain sizes and strain rates. The proposed model can be directly used in simulation of hot forming processes and as an example the bulge forming process is simulated and the results are compared with experimental data.

Simulation of Super-Plastic Forming Based on a Micro-Structural Constitutive Model and Considering Grain Growth

Constitutive models based on dominant mechanisms in hot forming are proposed. These models consider inter-granular deformation, grain boundary sliding, grain boundary diffusion and grain growth. New stress-strain rate relationships are proposed to predict deformation due to grain boundary sliding and grain boundary diffusion. Beside a Taylor type polycrystalline constitutive model, a visco-plastic relation in conjunction with a yield function is used to predict inter-granular deformation with much less computational costs. The proposed models are calibrated with tensile test data of AA5083 at . The calibrated models closely fit simple tension experimental data for various strain rates and strains. Then as an example the models are used to simulate a tray forming experiment. Dome heights and tray thicknesses at various positions during forming time can well predict experimental observations.

Direct numerical simulation of two-phase flow: Effective rheology and flow patterns of particle suspensions

We analyze the mechanical behavior of a two-phase system consisting of rigid grains and an interconnected pore fluid. For this purpose we use 2D direct numerical simulations on the spatial scale of individual grains for Newtonian and non-Newtonian fluid rheology. By using the stress–strain rate relation we derive scaling laws for effective viscosity of two-phase particle suspensions. We demonstrate that the effective rheology of the assemblage is non-Newtonian only if the fluid has a non-Newtonian rheology. At small fluid fraction, inter-granular strain rates are up to 3 orders of magnitude higher than the applied background strain rate. We suggest that this effect explains the experimentally observed change at higher strain rates in rheology, from Newtonian to non-Newtonian aggregate rheology. To establish the conditions at which the fluid–solid aggregate deforms coherently as a consequence of Rayleigh–Taylor instabilities we studied flow patterns of particle suspensions and characterized them as a function of fluid fraction, viscosity, density, shape and size of the grains. From initial conditions with homogeneously distributed grains and interstitial fluid above a layer of pure fluid, our results show that the Rayleigh–Taylor instability dominates for moderate to large fluid fractions. At large fluid fractions, we observed a transition to a Stokes suspension mode, in which grains do not interact but sink independently. An analytical expression is derived that predicts the transition from Rayleigh–Taylor instability to Stokes suspension mode. The transition is a function of fluid fraction, radius of the grains, height of the interface and initial amplitude. Systematic numerical simulations are in good agreement with the analytical predictions.

Strain Rate Sensitivity and Cavitation in Superplastic Deformation of a Commercial AL-5083 Alloy

In this paper the superplastic properties of a commercial 5083 aluminum alloy is studied. The aims are to achieve a proper temperature and strain rate to obtain maximum elongation and to investigate the strain rate sensitivity and cavitation in this alloy. The material is thermo-mechanically processed to produce fine recrystallized grain size. Then hot tensile test is carried out at various temperatures and strain rates. Velocity jump tests are performed to determine stress-strain rate relation and strain rate sensitivity coefficient (m) at various temperatures and strains. The microstructures are studied by optical and electron microscopy (SEM). The area fraction of cavities is determined by analyzing the micrographs from the surface of tensile specimens at various strains. It is found that maximum elongation about 300% is obtained at 520 oC and strain rate of 10-3 s-1. Maximum strain rate sensitivity coefficient (m) about 0.6 is achieved at strain 0.5. With increasing strain the peak m value decreases and shifts to lower strain rates. The failure surface is wide and failure occurs by cavitation.

Experimental and computational investigations on strain rate sensitivity and deformation behavior of bulk materials made of epoxy resin structural adhesive

The deformation behavior and strain rate sensitivity of an epoxy resin structural adhesive and a CTBN (carboxyl-terminated butadiene-acrylonitrile)-modified epoxy resin adhesive are experimentally investigated using an INSTRON-type material testing machine and a split Hopkinson pressure bar apparatus. The experimental results show some fundamental features of a typical compressive stress–strain behavior of amorphous glassy polymers with linear elastic and nonlinear inelastic deformation stages. In the inelastic deformation, a peak stress and a strain-softening stage after the peak can be observed in the entire range of strain rate from 10 - 4 to 10 3 s - 1 . In addition, it can be found that the relationship between the peak stress and strain rate on a semi-logarithmic plot is linear in the range of low strain rate. However, the slope of the curve changes at a high strain rate, and the nonlinear behavior of the peak stress can be obtained against the strain rate. In order to describe such a nonlinear peak stress–strain rate relationship and the deformation behavior of the structural adhesives in a wide range of strain rate on the basis of the experimental results, a plastic shear strain rate is formulated. Then, a three-dimensional constitutive model is derived based on a four-elements model with an elastic series element by considering the adhesive to be a glassy polymer. The plastic deformation rate tensor is expressed by the effective stress, which is the difference between the total stress and back stress, and the plastic shear strain rate proposed here. The stress tensor can be obtained by solving nonlinear simultaneous equation. The formulated constitutive model is implemented into the commercial FE code, ABAQUS/Explicit, and then a computational simulation is performed. As a result, the validity of the proposed model is shown by comparing the experimental result.

The stress relaxation and creep behaviour of a manganese-stabilized austenitic stainless steel

The stress relaxation behaviour of 21–4N, a manganese-stabilized austenitic stainless steel, is investigated in terms of the metallurgical state, the application of multiple strain levels during ‘stepped’ stress relaxation testing at 700 °C, the strain level during isostrain stress relaxation tests at 538 °C and 700 °C, and the correspondence with results from constant-load creep tests. The results indicate that for isostrain stress relaxation tests the stress relaxation rate is similar for strains that span both elastic and plastic strain levels. A transition in the stress relaxation behaviour occurs at a stress level approximately equivalent to the tensile stress–strain proportional limit; below this transition the stress–strain rate relationship, or the time predicted for 1 per cent creep strain, obeys a creep power law type of equation. Stress relaxation testing successfully delineates the difference between the creep resistances of two different metallurgical conditions with similar tensile properties using fewer specimens and requiring less time. The time to 1 per cent creep strain determined from the analysis of stress relaxation results is always less than the actual time to 1 per cent creep strain during constant-load creep tests.

Load relaxation behavior of a Zr 41.2Ti 13.8Cu 12.5Ni 10 Be 22.5 bulk metallic glass

The load relaxation behavior within the supercooled liquid region of Zr 41.2Ti 13.8Cu 12.5Ni 10Be 22.5 bulk metallic glass has been investigated. To explain the relationship between normalized stress and relaxation time, two different stress relaxation modes such as a Kohlrausch–Williams–Watts (KWW) behavior and a simple power law were applied to the short and long relaxation time regimes, respectively. The apparent activation energy for stress relaxation is 126 ± 10 kJ/mol. Flow curves were obtained by converting load–displacement data into a flow stress–strain rate relation, resulting in three different deformation characteristics through a wide strain rate region interpreted in terms of strain rate sensitivity. A prediction of hot workability has also been attempted by constructing a power dissipation map based on a dynamic materials model.

Tertiary Creep in Nickel-base Single-Crystal Superalloys: a Case of Geometric Effect

The tertiary creep in nickel-base single-crystal superalloys observed in conventional constant-load tests, for conditions where rafting of γ´ precipitates does not play a dominant role, represents a dynamic steady-state condition. The accelerating strain rate corresponds primarily to the increasing stress with decreasing cross-sectional area as the strain increases. Experiments on [001]-oriented CMSX-10 at 900 °C for the initially applied stresses of 500–700 MPa revealed this geometrically induced effect for the most part of the creep life. A power-law describes the stress dependence of creep rate. It is shown that one creep rupture test provides a stress-strain rate relationship for dislocation creep over a stress range of about 100 MPa. Consequently, this suggests an economical, time-saving experimental scheme for determining stress exponent n from one test for a short stress range or the variations in n over a larger stress range using only a few specimens. A simple nonlinear elasto-viscous creep mod...

Crystallization during Superplastic Deformation in a Zr<sub>65</sub>Al<sub>10</sub>Ni<sub>10</sub>Cu<sub>15</sub> Glass Metallic Alloy

Superplastic behavior of the Zr65Al10Ni10Cu15 glass metallic alloy produced by powdermetallurgy method was examined in the supercooled liquid region. Stress-strain and stress-strain rate relationships showed that Newtonian viscous flow governed the plastic flow until strain hardening took place. The large strain hardening was proved to a result of occurrence of crystallization during deformation.

Simulation of semi-solid thixoforging using a micro-macro constitutive equation

The constitutive equation of the isothermal steady-state behaviour of semi-solid materials is described with a micro-macro modelling. It is based on the application of the micromechanics concept of “coated inclusion” to semi-solid behaviour and the introduction of an evolving bimodal distribution of the liquid and solid phases. The micro-macro modelling is implemented in the FE code Forge2. The influence of the normal and abnormal namely softening stress–strain rate relationship on thixoforging is analyzed using compression and extrusion tests simulations.

Evidence of power-law flow in the Mojave desert mantle.

Studies of the Earth's response to large earthquakes can be viewed as large rock deformation experiments in which sudden stress changes induce viscous flow in the lower crust and upper mantle that lead to observable postseismic surface deformation. Laboratory experiments suggest that viscous flow of deforming hot lithospheric rocks is characterized by a power law in which strain rate is proportional to stress raised to a power, n (refs 2, 3). Most geodynamic models of flow in the lower crust and upper mantle, however, resort to newtonian (linear) stress-strain rate relations. Here we show that a power-law model of viscous flow in the mantle with n = 3.5 successfully explains the spatial and temporal evolution of transient surface deformation following the 1992 Landers and 1999 Hector Mine earthquakes in southern California. A power-law rheology implies that viscosity varies spatially with stress causing localization of strain, and varies temporally as stress evolves, rendering newtonian models untenable. Our findings are consistent with laboratory-derived flow law parameters for hot and wet olivine--the most abundant mineral in the upper mantle--and support the contention that, at least beneath the Mojave desert, the upper mantle is weaker than the lower crust.

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Guest Editorial

Strains and displacements in the Mam Tor landslip, Derbyshire, England

The spectacular Mam Tor landslip, near Castleton, Derbyshire, formed over 3000 years ago on an oversteepened slope left after the last ice age. A section of the Namurian Edale mudstones and overlying Mam Tor sandstones has collapsed, leaving an 80 m high scar on the eastern side of Mam Tor. The slip is about 750 m long and nearly 300 m wide and has the old main road from Manchester to Sheffield built across it. The slipped mass is in a state of year-on-year creep motion, which over the 190 years since the construction of the highway has led to extensive damage to the road, culminating in its closure in 1979. Since 1996 we have carried out annual monitoring by electronic distance measurement of the movement of a network of some 30 stations on the slipped mass. The average movement rate of the whole mass is about 10 cm a −1 , with the central region moving significantly faster, at almost 50 cm a −1 . Thus substantial readjustments of mass are taking place within the landslip. Local vertical displacements are systematically related to horizontal offsets, and the ratio of the two allows inference of the local attitude of the basal slip surface. The development of surface morphological features (pressure ridges and irregular topography, shear offsets on the highway, bulging of the road surface) reflects the lateral variations in displacement rate. Comparison of our survey of the present-day road position with that recorded in the topographical survey of 1880 shows a total 40 m downhill displacement of the highway over 122 years. This is consistent with extrapolation of our measured displacement rates back to 1880. Displacement rates within this period are, however, clearly higher than during the past 3000 years. There is a fairly clear correlation between vertical and horizontal displacement rates and annual variations in rainfall, with accelerated displacements following winter rainfall above a critical threshold level. Using survey points to define nodal points of a network of triangles, we have analysed the distribution of strain within the slipped mass. This revealed a pattern of continuous strain variations comparable with that found in flowing glaciers. In the lower part of the slip, horizontal strains are contractional and triangle areas are decreasing, causing some uplift of the ground relative to the general downhill flow on the basal slip surface. In the uphill part, strains are extensional and triangle areas are increasing. The new data allow an estimate of the time-dependent rheological behaviour of the sheared mudstone in the basal shear zone. The shear stress vs. shear strain rate relationship is very non-linear, with significant shear strain rates occurring only at shear stress levels within 10% of that required for rapid (catastrophic) shearing.

Process Modeling in Composites Manufacturing

9R13. Process Modeling in Composites Manufacturing. - SG Advani (Univ of Delaware, Newark DE) and EM Sozer (Koc Univ, Istanbul, Turkey). Marcel Dekker, New York. 2003. 436 pp. ISBN 0-8247-0860-1. $175.00.Reviewed by L Mishnaevsky Jr (MPA, Univ of Stuttgart, Pfaffenwaldring 32, Stuttgart, D-70569, Germany).This textbook introduces the reader to the concepts and methods of the modeling of polymer composite manufacturing processes on the basis of the fundamental principles of fluid mechanics, heat transfer, theory, and the analysis of the physics of the process. The authors are successful in their aim to create a self-contained text, which systematically demonstrates “how one would go about modeling a composite manufacturing process.”The book is logically divided into three major parts: introduction to the polymer composite materials and manufacturing processes (Ch 1 and 2), theoretical tools and approaches needed to model the processes (Ch 3–5), and the applications of the models to several manufacturing technologies (Chapters 6–8).The microstructures and classifications of polymer matrix composites, properties of polymer matrices (thermoplastic and thermoset resines), and fibers, are discussed in the Introduction.In Chapter 2, Overview of Manufacturing Process, different composites manufacturing techniques are outlined. The manufacturing methods are classified according to the dominant flow processes: short fiber suspension manufacturing methods (processes which involve the transport of fibers and resin as a suspension into a mold or through a die to form a composite; examples: injection and compression molding, extrusion), squeeze flow manufacturing methods (in which the fibers and resin deform together to form a composite shape), and porous media manufacturing methods (in which the resin impregnate and displace the air in a continuous fiber network).In Chapter 3, Transport Equations for Composite Processing, the basics of fluid mechanics and heat transfer are reviewed. The conservation equations of mass, momentum and energy, stress-strain rate relationships, and their application to modeling the resin flow in the presence of fibers are discussed. Many examples with solutions are included in this chapter.In Chapter 4, Constitutive Law and Their Characterization, constitutive equations of resins for different cases are discussed. Physical meaning, mechanisms, and temperature dependence of the viscosity of resins, as well as the effect of bundles of aligned fibers and the short fibers on the mechanical behavior of resin are explained. Modeling of the curing of the resin (kinetics of the reaction of forming 3D network from mono- or oligomers), techniques to monitor cure at macro- and microlevel, and the effect of reinforcement on the curing are described. Then, the authors discuss the mechanisms and the effects of the kinetics of crystallization of thermoplastics during solidification. The permeability concept, which serves as a basis for the analysis of the flow behavior of resin as it impregnates the preform, is described in this chapter as well.Chapter 5, Model Simplifications and Solutions, deals with the techniques of modeling the manufacturing processes on the basis of the physical laws and concepts described in the previous chapter. Several techniques and approaches, which can be useful in formulation of a model and finding a solution, are described: dimensional analysis, commonly accepted assumptions for polymer composites processing (like quasi-steady state assumption, lubrication approximation, this shell approximation), possible simplifications of boundary conditions and geometry, some mathematical techniques (like coordinate transformations, superposition of solutions, decoupling of equations).In Chapters 6 (Short Fiber Composites), 7 (Advanced Thermoplastic Composite Manufacturing Processes), and 8 (Processing Advanced Thermoset Fiber Composites), models of technological processes of the composite manufacturing, based on the ideas and principles given in Chapters 3–5 and grouped according to the classification from Chapter 2, are presented and discussed. Models of flow and heat transfer in the compression molding, a method of screw design in the extrusion process and a model of filling stage in injection molding (Ch 6), a model for consolidation and void reduction during the processing of thermoplastic composites, which is based on the consideration of a squeeze flow of a compressible viscous fluid (Ch 7), and the processes of autoclave molding, liquid composite molding and filament molding (Ch 8) are covered.The book is addressed to seniors and first-year graduate students in materials science and engineering, industrial, mechanical, and chemical engineering, and can also be very useful to specialists in composite manufacturing and modeling, working both in industry and in academia. The book is well structured, and all of the concepts, ideas, and solutions are explained clearly and with many examples and illustrations. Each chapter contains questions and example problems, fill-in-blanks sections, and original figures. The layout of the book is pleasant, and a subject index is available.Process Modeling in Composites Manufacturing is a very good and useful book, and can be highly recommended to students, scientists, and specialists in modeling and manufacturing of composites and to libraries.

Stress-Strain Rate Relations in Ultrahigh Carbon Steels Deformed in the Ferrite Range of Temperature

The stress-strain rate relations in ultrahigh carbon steels (UHCSs) have been analyzed at high temperatures in the ferrite range where dislocation slip is the principal deformation mechanism. Specifically, the present investigation centers on the factors influencing the strength of UHCS in the ferrite range of 500 to 700 C and in the strain rate range of 10{sup -3} to 10{sup 3} s{sup -1}. These steels contain iron carbide as a second phase either in the form of spheroidite or pearlite and vary in the grain size according to the processing history. The new variables that need to be taken into account are the effect of ferromagnetism and its change with temperature on the creep strength of the ferritic UHCSs. Recent studies have shown that ferromagnetism strongly influences the lattice and dislocation pipe diffusion coefficient and the elastic modulus of iron in the ferrite range of temperature. These variables are shown to influence the creep strength of ferrite-base steels and explain the high activation energies that are observed in many of the ferritic UHCSs.

Deformation behavior during hot torsion of an ultrahigh carbon steel containing 1.3 wt.% C

Abstract The torsion behavior of an ultrahigh carbon steel containing 1.3 wt.% C has been studied at high strain rates (2–26 s–1) and high temperatures (900–1200 °C). Adiabatic heating strongly affects the shape of the stress–strain curves. Grain size measurements at strains of e = 2 and e = 5 reveal that the austenite grain size does not change between these two strains and is finer than the initial austenite grain size. This is an indication that a recrystallization process took place in the interval of strains between epeak and e = 2 and that the deformation state associated to the strains of e = 2 and e = 5 can be considered as steady state. Stress–strain rate relations have been analysed for epeak, e = 2 and e = 5. It has been found that data obtained at epeak correlate well with a lattice diffusion-controlled dislocation creep process. On the other hand, analysis of the stress–strain rate relations found at the steady state indicated that the deformation occurs by the contribution of two independent...