Effects Of Stress Rate Research Articles

Automated procedures for the determination of high temperature viscoplastic damage constitutive equations

Methods have been developed for the determination of the material parameters in the Chaboche viscoplasticity model, and in the evolution equation for cyclic plasticity damage. The matrix of cyclic plasticity tests required for parameter determination consists of nine tests to be carried out for three strain ranges, and for each strain range, three strain rates. A programme of uni-axial cyclic plasticity tests has been carried out on cast copper (nominal composition: 99.99% Cu, 0.005% O 2 , B. S. 1035-1037) at strain ranges ± 0.3%, ± 0.6%, and ± 1.0%, each at strain rates 0.6% s -1 , 0.06% s -1 , and 0.006% s -1 . The matrix of tests has been carried out at each of the following temperatures: 20, 50, 150, 250 and 500 °C. At elevated temperature, strain rate has been found to have a significant effect on specimen lifetime. Low strain rates lead to increased creep damage evolution at high temperature, and hence lead to reduced cycles to failure. Cast copper has been found to be a rate sensitive material at temperatures above 150 °C. No strain rate effect was observed at temperatures below 150 °C. Ratchetting tests have been carried out at 20, 150, 250 and 500 °C. The effect of mean stress and stress rate on ratchet rates and lifetimes has been examined. Mean stresses of the order of 1 % of the applied stress range have been found to lead to significant ratchet rates for this material, resulting in failure by plastic collapse at elevated temperature. The methods presented for the determination of the material parameters and the results of the cyclic plasticity testing programme have enabled the viscoplastic damage model to be developed.

Experimental investigation of the effects of stress rate and stress level on fracture in polystyrene

The effects of stress rate and stress level on fatigue crack propagation in compression-moulded single-edge notched specimens (0.25 mm in thickness) of polystyrene are reported. Values of the stress rate\(\dot \sigma\) are obtained from the formula\(\dot \sigma\) = 2v(σmax − σmax),, wherev is the frequency and σmax, σmin are the maximum and minimum stresses of the fatigue cycle. Different levels of\(\dot \sigma\) are achieved by changing the frequency while keeping σmax, σmin at fixed values. The effect of the stress level is investigated by keeping\(\dot \sigma\) and σmin constant and varying σmax andv. The results show that when the kinetic data are plotted as Δl/Δt against the energy release rateG1, a relatively small effect of the stress rate is observed. If the same data are treated as Δl/ΔN againstG1, a decrease in Δl/ΔN with test frequency is seen. The increase in the level of σmax results in a higher crack speed. The critical crack length is found to be practically the same for all stress-rate experiments. A decrease in the critical crack length is observed with the increase in stress level. Analysis of craze distribution around the crack path shows that the extent of crazing decreases with the increase in stress rate and increases with the increase in stress level. For all experimental conditions, the ratio of the second moment to the square root of the fourth moment of the histograms of craze density along directions normal to the crack path is found to be constant throughout the slow phase of crack propagation. This result supports a self-similarity hypothesis of damage evolution proposed in the crack layer model.

Effect of specimen size and stress rate for the Brazilian test — a statistical analysis. Technical note : Newman, D A; Bennett, D G Rock Mech Rock EngngV23, N2, April–June 1990, P123–134

Effect of specimen size and stress rate for the Brazilian test — a statistical analysis. Technical note : Newman, D A; Bennett, D G Rock Mech Rock EngngV23, N2, April–June 1990, P123–134

A simple model of nonisothermal coextrusion

AbstractA numerical method has been developed that takes the streamline finite difference method for modeling fully developed multilayer polymer flows and adds to it a simple means of accounting for nonisothermal conditions. In industrial practice, temperature control is often used to match material viscosities and, thereby, to avoid flow instabilities. By numerically calculating both viscosity ratios and normal stress difference ratios, the numerical method allows one to judge the relative stability of different flows and to choose an intelligent set of experiments when designing a coextrusion process. The algorithm has been successfully tested for a number of polymer melt constitutive equations in flows where the viscosity jumps no more than two orders of magnitude between fluids. Results for a rheologically well characterized polystyrene low‐density polyethylene system and for an industrially interesting high‐density polyethylene/Ultem system show that the common practice of matching zero‐shear viscosities is overly simplistic when interface shear rate, conduction, normal stress, and flow rate effects are taken into account.

The effect of specimen size and stress rate for the Brazilian test?A statistical analysis

The Brazilian test is a widely accepted method for the determination of the tensile strength of intact rock. Specifications for the Brazilian tensile strength test have been established by the American Society for Testing and Materials (ASTM), ASTM D 3967-86 and a suggested approach is provided by the International Society for Rock Mechanics (ISRM). The ASTM and ISRM allow a relatively wide range of values for specimen geometry defined in terms of length to diameter ratio and loading rates defined as either time to failure or stress rate.

Stress rate, grain size and material constant dependence of dynamic stress intensity factor by dynamical piling-up of dislocations.

A computer simulation concerning the dynamic stress intensity factor, Kd(t), was carried out for various material constants. The constitutive equation of Kd(t) was formulated as a function of stress rate, grain size and material constants. This theory corresponds to the effect of stress rate on experimental results of the yield stress and the fracture toughness under room temperature. Furthermore, the mechanical characteristics of the dimensional value of the dislocation-free zone for free expansion were analyzed for various materials, and Kd(t) was estimated by the dislocation-free zone.

Studies on binary and ternary blends of polypropylene with ABS and LDPE. I. Melt rheological behavior

AbstractStudies are presented on melt rheological properties of binary blend of polypropylene (PP) and acrylonitrile–butadiene–styrene terpolymer (ABS), and ternary blend of PP, ABS, and low‐den‐sity polyethylene (LDPE). Data obtained in capillary rheometer are presented to describe the effect of blending ratio, shear stress, and shear rate on flow properties, melt viscosity, and melt elasticity. At a blend composition corresponding to 10 wt % ABS content, both binary and ternary blends show maximum in melt viscosity accompanied by minimum in melt elasticity. Pseudoplasticity of the melt decreases with increasing ABS content. In ternary blends, LDPE facilitates the flow at low LDPE contents and obstructs the flow at high LDPE contents. Scanning electron microscopic studies are also presented to illustrate the state of dispersion and its variation with blend composition.

Factors Affecting the Stress Corrosion Cracking Susceptibility of Zirconium in 90% Nitric Acid

Abstract U-bend, C-ring, and slow strain rate tests were performed to evaluate the effects of texture, stress, surface condition, heat treatment, electrochemical potential, and strain rate on stres...

Chemical disintegration of coal in triaxial stress fields

This paper studies the effects of stress and flow rate on comminution rates of a coal sample. Chemical disintegration of coal involves introducing a solvent or comminution reagent into a coal seam and converting the monolithic coal into a particulate slurry of coal particles. A 2.5 molar solution of methanol and sodium hydroxide solution at 55 °C was used as the chemical reagent and its comminution ability was studied under different applied stress and solvent flow rates. The comminution rates ranged from 19.5 to 1.2 mg/(cm 2·h) as the overburden stress was increased from 0 to 17 MPa. The results showed a substantial increase in the comminution rate at stresses higher than 10 MPa and the disintegrated particles demonstrated a high degree of angularity, indicative of physical breakage. It was also shown that the fracturing rates increased with a rise in the solvent flow rate.

Stress Rate and Proof‐Testing of Silicon Wafers

Fracture mechanics test methods were applied to evaluate the proof‐test characteristics of single‐crystal silicon wafers. The results indicate that the strength distribution of silicon wafers is truncated by proof‐testing. No subcritical crack growth occurred during proof‐loading, as inferred from the lack of a stress‐rate effect on strength. Mechanical proof‐testing appears to be an effective method for eliminating weak samples before cell processing.

Molecular kinetic theory of the glass transition

AbstractAn overview of a new molecular kinetic theory of glass‐transition phenomena is presented and experimental comparisons of its prediction for a variety of thermal and stress histories reviewed. The theory, which was developed in accordance with the balance of nonequilibrium statistical entropy, is shown to provide a unified interpretation of some recent models. The volume‐relaxation process in amorphous polymers over the glass‐transition region is regarded as the result of the collapse of a series of free volumes having different levels of energies of hole formation. An applied stress is shown to contribute to the variation of the entropy. An activation volume is introduced as a new tensorial extensive variable. The theory is applied to the phenomenon of physical aging in polymer glasses and shown to provide good quantitative agreement with the results of a well‐known experiment on volume recovery of poly(vinyl acetate). This supports the underlying postulate of a fundamental link between the apparent relaxation time and the mean energy of hole formation, the distribution of relaxation times and the free‐volume fractions. In contrast to the prevalent thinking toward free volume theories, an explicit expression between Tg and stress is presented and reveals that Tg does not continue to increase at all pressures but levels off to a semi universal asymptote at very high pressure. The calculated effect of stress rate is found to be in good agreement with dynamic viscoelastic measurements.

Statistical entropy model for relaxation in stressed polymer glasses

AbstractThe molecular kinetic theory near the glass transition, bused on the existence of free volume distribution, is extended to incorporate the effects of stress and stress rate. The fundamental equations for the volume relaxation and recovery in stressed amorphous polymers are derived in accordance with the balance of nonequilibrium statistical entropy. Using these kinetic equations, an earlier nonequilibrium criterion for the glass transition temperature, Tg, is generalized to include the effects of stress and stress rate. In contrast to the prevalent thinking toward free volume theories, an explicit expression between Tg and stress is developed and reveals that Tg does not continue to increase at all pressures but levels off to a “universal” asymptote at very high pressure (>10 K bars). The expression is applicable to any tension and compression stress conditions. A comparison between theory and experiment under constant stresses determines the activation volume tensor which reveals the molecular mechanism relating Tg and the plastic yield of glassy polymers.

Rotations, stress rates and strain measures in homogeneous deformation processes

The article draws the distinction between homogeneous and pure homogeneous deformation. In the latter mode, an orthogonal triad can be identified (the principal axes), which remain orthogonal throughout the deformation. An appropriate strain measure in such processes is that of logarithmic strain. Furthermore, its material derivative equals the rate of deformation tensor. In homogeneous processes, the deformation gradient tensor is unsymmetric, and there is no triad which remains orthogonal throughout. This often leads to a description of the actual deformation by means of the polar decomposition theorem. The material derivative of the tensor logorithm is no longer simply related to the rate of deformation tensor, and this is exemplified herein. As a result of material rotation the stress components will vary, and constitutive equations which involve stress rate must be formulated to compensate for the rotation. A number of objective stress rates are examined herein, and employed in a constitutive equation describing a hypoelastic solid. The effect of stress rate on the evolution of stresses in the deforming solid is demonstrated for the case when the body undergoes simple (rectilinear) shear.

Flow properties of epoxide prepolymers

AbstractThe following characterstics of four molten epoxide prepolymers are described: flow curvepeculiarities, shift factor and temperature‐independent flow activation energy, shear stress and shear rate effects, and their graphical and analytical descriptions.

確率過程理論に基づいたコンクリートの破壊理論 Part I

The fracture mechanism of concrete may be considered as a series of crack-propagation processes within the cement paste phase. From such a viewpoint, this paper presents a stochastic theory for concrete fracture under simple loading, in which, not only the stochastic characteristic of the process, but also the statistical stress distpibution due to material defects, is taken into consideration. The adequancy of this theory has been ascertained by comparison with the results of previous experimental investigations. The effect of environmental temperature on fracture strength is described as follows : lnΛ_<temp>=C・(λ_T-1) where Λ_<temp>=strength ratio : (σ/σ_0), C=const., λ_T=absolute temperature ratio : (T/T_0) The stress rate effect on fracture strength is shown as follows : Λ_<atr>=σ^^-/σ^^-_0=(σ^^・/σ^^・_0)^ζ

硬化過程におけるコンクリートの圧縮強度・変形に及ぼす載荷速度の影響

It is well known that the strength and the modulus of elasticity of some materials are greater for rapid application of load than for slow loading. The theoretical interpretation of this fact has been given in the past based on the linear viscoelastic theory. The present experimental study was carried out to investigate the effects of strain or stress rate the compressive ultimate strength, the modulus of elasticity and the deformation characteristics of cement mortar and concrete at age of 1 to 28 days. The test variables were: the mean rate of stress, σ=0.01 to 35 (kgf/cm2·sec), the mean rate of strain, ε=0.15 to 450 (×10-6/sec); the test age of 1, 3, 7, and 28 days; the water-cement ratio W/C=0.45 to 0.75. 10φ×20cm size cylindrical specimens were used for all tests.The test results were summarized as follows. The dependence of the ultimate strength on strain rate for concrete was more remarkable at an early-age than at the age of 28 days. On the contrary, this dependence for cement mortar was remarkable at the age of 28 days. The strain at the ultimate strength of concrete at an early-age was influenced by strain rate, but it was not influenced at 28 days. The coefficient of viscosity of concrete λ is expressed by the equation as λ=aε-b, and the relationship between stress rate and strain rate is given by σ=αεβ. The variation of concrete strength σu, which is brought by various rates of loading, can be expressed by the following equation based on the rheological theory, where σu, s is the statical ultimate strength.σu=σu, s+λε(t)

Time Dependent Probabilistic Failure Model for the Strength of Fiber Reinforced Plastics

The fracture strength of GRP (Glassfiber Reinforced Plastics), which depends on the applied time of stress and the stress rate, was analyzed by using a time dependent probabilistic failure model. The fracture process was assumed to be a 1-step stochastic process and the transition probability of failure to be γSδf(t) where S and t represent stress and time, respectively and γ and δare constants. The evaluation of the damage in the case when the stress varied was done by "the reduced time method" proposed in this paper. When f(t)=tγ and S=at (γ, a; constants), the fracture stress Sc was calculated as follows. [numerical formula] where Dc is a constant. The constant a is stress rate and so the effect of stress rate on the fracture stress could be clearly presented. Static fatigue strength was also analyzed. The analytical results showed a good agreement with experimental results For glass plates and glassfiber composites, the constants γ and δ were found to be about -0.7 and 6.26, respectively. therefore, the traditional time independent probabilistic theory overestimates the effect of strain rate on the strength of materials.

Analysis of stick-slip and earthquake mechanism

A mathematical model of a sliding system that contains a frictional surface embedded in an elastic specimen and machine is proposed to analyze the frictional behavior observed in laboratory and field. It is shown that stick-slip occurs if the slope of the velocity-stress relation on the sliding surface exceeds a critical value at a certain point between static and kinetic frictions. This condition, coupled with Amontons' law and other subsidiary relations, predicts the effects of normal stress, gouge thickness, temperature, and loading rate etc. on the stick-slip instability, consistent with known experimental evidence. The elastic-wave radiation associated with stick-slip is governed by Brune's source time function, in which rise time and effective stress are proportional to fault dimension and stress drop, respectively.

Yield point effects in α-titanium during interrupted tensile tests at 300–496°K

The effects of strain, aging stress, aging time and strain rate on strain - aging yield points in commercial purity α-titanium were investigated in the temperature range of 300° – 496°K. The magnitude of the relative yield point ( Δσ/ σ f) obtained after aging at zero stress was almost independent of time and temperature over the entire temperature range studied; whereas, the relative yield point obtained after aging at the flow stress could be considered to be athermal only up to 423°K. It is proposed that the mechanism responsible for the zero stress yield points is similar to that suggested to explain the Haasen - Kelly effect in f.c.c. metals. Flow stress yield points in the temperature range of 300° – 423°K are explained on the basis of dislocation rearrangements occurring during stress relaxation. Above 423°K, oxygen atoms also seem to play a direct role in the production of yield points; however, it is suggested that dislocation rearrangements are still playing an important role. The variation of the relative yield point with strain at different temperatures is consistent with the effect of temperature and strain on the dislocation substructure.

Frictional characteristics of typical rocks.

Detailed laboratory experiments have been performed on the frictional characteristics of various rocks. Frictional behavior greatly depends not only upon rock type, but upon such surface condition as roughness. The behavior of soft rock is more influenced by roughness than that of hard rock. Frictional behavior is classified into the four types: (1) the behavior characterized by both the predominant force drop at initial sliding and stable sliding subsequent to the predominant force drop, (2) the behavior characterized by both the predominant force drop at initial sliding and a series of sticks and slips, (3) frictional sliding occurring stably without any sudden slip, and (4) the behavior characterized only by a series of sticks and slips. The intermediate behavior between type 3 and type 4 is also observed: stable sliding precedes stick-slip. Frictional force increases with displacement (displacement hardening). This is attributed to the development of adhesive or abrasive wear (gouge) particles on sliding surfaces with increasing displacement at an applied constant normal force, The scatter of the measured values of friction on nominally identical specimens under nominally identical conditions is related to the difference in the amount of wear particles developed on sliding surfaces between runs. The experimental relation between friction and the amount of gouge particles is analyzed from a theoretical viewpoint. It is found that stick-slip occurs only when the amount of wear particles is small, and that frictional sliding takes place stably when the gouge is developed abundantly over the whole of the sliding surfaces. The controlling mechanism of friction for uniform soft rocks, such as limestone and marble, is distinctly different from that for such rocks as granite and monzonite which contain various minerals of different hardness. The effects of normal stress and loading rate on friction are also investigated.