Stress Time History Research Articles

Determination of stress-time histories in axially symmetric impacts with the two-gauge technique

We present an experimental technique for the direct measurement of stress-time histories in axially symmetric dynamic impacts, where the state of strain is not uniaxial. The technique is based on placing two different well-calibrated piezoresistance gauges in the desired location on the symmetry axis. The two measured resistance changes are then substituted in a system of two equations with two unknowns from which one obtains the axial stress and the lateral strain histories. We demonstrate the technique with manganin and constantan gauges which were calibrated both under uniaxial strain and hydrostatic conditions. As an example we bring the results of stress measurements inside thick polymethyl methacrylate targets which were impacted by thick copper discs. The measured stress-time history is then compared to that predicted by a two-dimensional Lagrangian code.

The use of in-material stress gauges for estimating the dynamic yield strength of shock-loaded solids

We present stress-time history measurements, with in-material manganin gauges, from which we obtain the dynamic yield strength of shock-loaded 2024 Al and Ti-6 Al-4 V specimens. This yield strength is inferred from the cusp in the release curve which results from the elastoplastic nature of the release process. We show that while the strength of the aluminum alloy increases with shock amplitude, in the 0–100 kb range, that of the titanium alloy does not.

A study of limiter damage in a magnetic field error region of the ZT-40M experiment

A study has been initiated of material plasma interactions on the ZT-40M, Reversed Field Pinch (RFP) plasma physics confinement experiment at Los Alamos National Laboratory. Observations of the evaporation and cracking of TiC coatings, initially placed on an AXF-5Q Graphite mushroom limiter, installed in a high field error region (e.g. an experimental vacuum vessel/liner port) were investigated. A parametric study was performed of the thermal and stress behavior of the limiter and coating materials undergoing plasma material heat exchange processes, in order to infer the magnitude of heat flux necessary to explain the observed material damage. In addition the vacuum (liner) wall material behavior was studied parametrically using the same heat flux values as the limiter study. A one-dimensional conduction model was used with applied heat and radiation boundary conditions, for predicting temperature distributions in space and time, where the thermal stress was calculated using a restrained in bending only plate model. Wall loadings corresponding to first wall, limiter energy fluxes ranging between 1 × 10 2 W/cm 2 and 1 × 10 5 W/cm 2 were used as parameters with plasma material interaction times (τ QO) between 0.5 ms and 10 ms. Short plasma energy deposition time (τ QO ⩾ 10 ms) spacial and time histories of temperature and stress were calculated for SS-304, Inconel-625, TiC and AXF-5Q Graphite materials. The parametric study indicates that for τ QO ∼ 6 ms a wall loading of ⋍ 1 × 10 4 W/cm 2 results in the melting of Inconel and SS-304 first wall material and a loading of ⩽ 5 × 10 4 W/cm 2 results in the melting of TiC and Graphite. For Inconel, stresses in excess of the tensile strength occur for Q O greater 1 × 10 3 W/cm 2 . The same is true for SS-304. For Graphite AXF-5Q the tensile strength is exceeded for Q O ≳ 1 × 10 4 W/cm 2 . From the observations of damage and the parametric results calculated it can be inferred that an energy flux of 1 × 10 4 W/cm 2 ≲ Q O ≲ 5 × 10 4 W/cm 2 was observed over a time scale of 5 ms ≲ τ QO ≲ 10 ms in the field error region, if the model considered is relevant to the phenomenon in question.

The Use of Manganin Stress Transducers in Impulsively Loaded Long Rod Experiments

The purpose of this Brief Note is to demonstrate the feasibility of using commercial manganin stress gauges in dynamic uniaxial stress experiments. This was demonstrated by measuring the stress-time histories inside long aluminum rods that were impacted by rigid wall impactors. The experimental records are compared with a two-dimensional Lagrangian calculation using a recently developed constitutive model (the Phases Model) to describe material behavior.

Theoretical and experimental results of the plastic and strain-hardening behaviour of En8 at a controlled rate

This investigation contains two theoretical analyses of the plastic behaviour and work-hardening characteristics of medium carbon steel (En8). The first of these analyses employs Perzyna's visco-plastic constitutive law for strain-rate sensitive and work-hardening material behaviour, and the second uses the strain-rate independent theory of Prandtl and Reuss. Both theories gave good agreement with the time histories of the axial stress, the plastic strains and the stress trajectory. However, these theories gave an under-estimate of the shear stress decay versus time. It is also evident from the present study that neither of these theories could account for the lack of coaxiality between the plastic strain-rate and deviatoric stress vectors observed in the experimental results for the present bilinear deformation path. The objective of the present study was to test the ability of these two models to predict the overall response of a real material to biaxial loading at a controlled rate under a deformation path with an abruptly changing direction. A preliminary comparison was made of the strain-hardening response according to the two models for a material without Lüders strain region. Then existing experimental results of a bilinear deformation path of quasi-static twisting at a reference rate of 10 −6 s −1 beyond the initial yield in torsion (to γ = 10γ 0 where the Lüders strain was exhausted), followed by extension at a constant strain-rate with γ held constant, performed earlier by Meguid and Malvern [1], were used for comparison with these models. It is hoped that this information will guide the designer and the user of stress analyses programs towards more realistic material input data.

Laterally converging flow. Part 2. Temporal wall shear stress

Instantaneous measurements of the wall shear stress were made in the laterally converging duct also used for mean measurements in part 1 and were analysed by conditional sampling and by conditional averaging. The sidewalls of the duct were adjusted to provide (i) a straight duct of constant rectangular cross-section and (ii) laterally (spanwise) converging ducts resulting in streamwise acceleration of the flow. The Reynolds number varied from 7600 to 47 200 and the dimensionless acceleration parameter Kv = (ν/V2)dV/dx ranged from 0 to 3·4 × 10−6, yielding a variation of the flow regime from fully turbulent to nearly laminar. The typical burst pattern, or conditionally averaged time history of the wall shear stress, resembled the time history of the streamwise velocity component deduced at y+ = 15 by Blackwelder and Kaplan using the same general technique. For fully developed flows, inner or wall scaling of the bursting frequency was found to be less dependent upon Reynolds number than outer scaling; other characteristics examined varied with both inner and outer scaling. For converging flows measurements of bursting characteristics essentially confirmed the indicated flow regimes deduced in part 1 and showed that the measured characteristic that was most affected by acceleration was the bursting frequency. All characteristics varied with acceleration, but the variation was generally less when normalized by wall variables rather than when normalized by outer variables.

Nonlinear finite element analysis of an autofrettage process

Generally metal forming processes are nonlinear problems. A method is presented to calculate stress and deformation time history and residual states of a mechanically autofrettaged thick walled cylinder. The finite-element-model and the results of the nonlinear analysis are demonstrated.

Residual stresses in a CrMoV-2CrMo pipe weld: Part 2—The heat treated condition

The rate at which the three-dimensional residual stresses in a CrMoV-2CrMo main steam pipe weld decay during stress relieving has been determined by means of a finite element creep analysis. The analysis used a two-material model, weld metal and parent metal, and the creep laws ascribed to these materials were based upon appropriate uniaxial stress relaxation data. The manner in which multiaxial residual stresses decay during stress relief is revealed by examination of the stress-time history of relevant locations. The results of the analysis are shown to have significant implications upon stress relieving practice and upon the allowances made for residual stresses in the assessment of defects in such welds.

Dynamics of the Water-Pipeline-Soil Interaction

A design engineer-oriented approach to determining the pipeline dynamic response to ocean forces accounting for complex environmental and pipeline conditions is presented. The described analysis yields time histories of pipeline motion and steel pipe stresses induced by water motion. Sinusoidal variation of normal water particle motion in time and along the pipeline, waves, flexural rigidity of pipe, damaged concrete coating, among other effects, are accounted for in the mathematical model.

Seismic stability of the Revelstoke earthfill dam

The foundation soil beneath the earthfill section of the proposed Revelstoke dam comprises, in part, a deep silt-clay layer that contains pockets of loose to compact saturated sands. Removal of this material beneath the core of the dam was required for seepage and erosion control. Analyses were performed to determine if considerations of earthquake stability would also require removal of this material beneath the shells.A factor of safety against the occurrence of a liquefaction failure beneath the shells was determined by comparing the dynamic resistance obtained from cyclic triaxial tests on undisturbed samples with the time history of dynamic stresses caused by the design earthquakes. Preliminary analyses clearly indicated that the silt-clay beneath the upstream shell should be removed. Beneath the downstream shell, the computations indicated factors of safety at the lower range of acceptable values and a portion of the silt-clay beneath the downstream shell was removed so that only minor damage would occur even in the unlikely event of liquefaction of the material left in place.

A rational theory for predicting soil liquefaction

In this paper the authors propose a theory and equations that predict pore-pressure buildup and hence soil liquefaction potential under a given earthquake stress time history. A procedure is outlined for easy determination of the soil parameters that are used in the above prediction equations. Experimental data are presented that indicate good agreement between pore pressures predicted by the above theory and those observed in the laboratory.

Plastic flow of mild steel (En8) at different strain-rates under abruptly-changing deformation paths

Strain-gauged thin-walled tubular specimens of annealed medium carbon steel (En8) were tested at room temperature in combined twisting and extension using a closed-loop, servo-controlled, electro-hydraulic biaxial testing machine. Bilinear deformation paths of twisting at a constant rate followed by extension at three different rates were investigated. Precise measurements of the resulting torque and load, together with the controlled deformation parameters, were recorded as functions of time. This study extends earlier work ( Meguid, Malvern and Campbell, 1979, J. Engng Mater. Technol. 101, 248) in which a notable feature of this particular type of bilinear testing was reported: namely, that it was possible to obtain almost the entire positive quadrant of the initial yield locus from a single run without unloading or reloading (neutral loading). Here, particular attention has been given to the effect of the axial strain-rate on the shape of these “initial” yield loci. Attention has also been given to the effect of the sudden change of direction in the deformation path upon the deviatoric stress and the plastic strain-rate vectors. The results indicate that there exist appreciable differences between the Mises equivalent stress and equivalent plastic strain curves (up to strains of order 2%) for the three axial strain-rates investigated. These differences are attributed to the rate-sensitivity of the material. The results also show a much slower alignment of the deviatoric stress vector direction to the direction of the plastic strain-rate vector than had been expected. Comparisons with two theoretical analyses of a bilinear deformation path of quasistatic twisting followed by extension at a constant strain-rate are made, one using Perzyna's (1966) viscoplastic constitutive law for rate-sensitive (but non-strainhardening) material and the other using a rate-independent theory. Refinements in the test procedures now reveal that significant differences exist between calculated and measured axial and shear stresses. In contrast, both theories gave reasonably good agreement with the time history of the equivalent stress and the stress trajectory, in agreement with the earlier work.

Reflection characteristics of torsional waves in a semi-infinite cylindrical rod connected to an elastic half-space—II

Using the Pochhammer-Chree equation and applying Laplace transformations with respect to time and numerical inverse Laplace transformations, reflection characteristics of torsional waves in a semi-infinite rod connected to an elastic half-space are analyzed under a condition where the incident stress pulse varies proportionally with the distance from the rod axis. Time histories of surface torsional stress and circumferential displacement, and cross-sectional torsional stress and circumferential displacement distributions of the semi-infinite rod at an arbitrary point are shown. When the shear modulus ratio G R/G and the velocity ratio K are small, i.e. The half-space is hard and the rod is soft, time histories of surface stress and displacement obtained from the Pochhammer-Chree equation coincide with those obtained from the elementary equation which is derived from the assumption that each cross-section of the rod undergoes a pure rotation about the rod axis. However, when G r/G and K are not small, the curves obtained from the Pochhamer-Chree equation differ from those obtained from the elementary equation, and the difference in stress increases as the observed point approaches the interface between the rod and the half-space.

Effects of hydrogen on the plastic properties of medium-Carbon steels

The effect of hydrogen on the plastic deformation of pearlitic and spheroidized 1045 steels is examined. We find that hyrogen in the dissolved state invariably hardens 1045 steel. Luders band formation and propagation require greater applied stress, the slope of the stress-strain curve is increased, and the amount of plastic deformation over a given stress-time history is decreased by dissolved hydrogen. We find, however, that microvoids, the population of which at a given degree of strain is increased by hydrogen of themselves are a softening influence. Furthermore, because hydrogen at very high input activity has the additional effect of generating very large gas pressures within the microvoids, such hydrogen produces an apparent softening effect. Some prior results in the literature are considered, and a reasonably consistent rationalization is given of the results in terms of the effects here described. An attempt is made to relate the hardening and softening effects to dislocation behavior. It is argued that the increase by hydrogen of the number of microcavities by decohesion, the reduction of the Peierls barrier to dislocation motion observable only in iron of very high purity, and the reduction of cross slip of screw dislocations are all manifestations of the reduction by hydrogen of the cohesive force between metal atoms.

Reflection characteristics of torsional waves in a semi-infinite cylindrical rod connected to an elastic half-space

Reflection characteristics of torsional waves in a semi-infinite rod connected to an elastic half-space are analyzed under two specific incident pulse loads, applying Laplace transformations with respect to time and numerical inverse Laplace transformations. The time histories of the torsional stress and rotation of the semi-infinite rod at an arbitrary point are shown. The advantage of this method, i.e., applying the numerical inverse Laplace transformations, is that it is simpler than using Fourier analysis and synthesis, and applicable to any incident pulse load except where the rise time interval of the incident pulse load is too short. In the case of a step pulse load, the stress curves approach that of the fixed boundary condition and the rotation curves approach asymptotically the static rotation value of each given shear modulus ratio GR/G and velocity ratio K. In the case of a half-sine pulse load, the reflected stress peak values decrease and those of the rotation increase with an increase in GR/G and K. A cross−over effect occurs when GR/G≳1 and K≳1; it becomes pronounced as GR/G and K increase.

Estimation of fatigue life of railway bridges under traffic loads

Random modelling of railway bridge loading enables fatigue damage to be calculated on the basis of the cumulative damage theory of Palmgren-Miner and the classification of the stress-time history by means of the “rain-flow” counting method. The results of calculations are the mean value of the damage and the standard deviation of the stresses, and thus an estimation of the bridge fatigue life. Accordingly the bridge life is dependent on the number of stress cycles and their distribution, the standard deviation of stresses, and on the shape of the Wöhler curve. Bridge life increasing span and decreases with an increasing traffic load. Results are presented as obtained in a detailed study of the effects on the bridge life of different parameters (vehicle speed, damping of bridge vibrations, variability in length and time of the moving load and its magnitude, number of stress cycles and their distribution). The equivalent damage method (the λ T -method) in the integral form enables one to compare the effects of the traffic loads with those of the standard loading.

On the Statistical Distribution of the Maxima of Non-Linear Stress Induced on the Ship Hull in Sea Waves

The useful method is proposed for calculation of the statistical distribution of the maxima of non-linear stress such as the von Mises' equivalent stress induced on the longitudinal member of a ship hull in sea waves. This method is based upon an assumption that the wave normal stress and the wave shearing stress which produce the equivalent stress would be regarded as completely dependent variables and upon another assumption that those stresses would be regarded as completely independent variables.The application of this method is made for a gigantic oil tanker in a short-term seaway and the calculated results of the statistical distribution of the maxima of equivalent stress induced on the longitudinal member have been examined in comparison with the histograms obtained from the numerically simulated time histories of equivalent stress. Satisfactory agreement is found between both results and the validity of the proposed method is recognized.

Time evolution of stress under an artificial lake and its implication for induced seismicity

The time history of stress beneath a realistic artificial lake with a realistic loading history on a permeable lithosphere can be calculated by solving the consolidation equations for a uniform permeable medium. The evolution of stress conditions towards or away from a Mohr–Coulomb failure envelope illustrates that highest risk of induced seismicity exists at initial loading and in some cases after a down-draw of the lake. The calculated histories depend crucially on hydrologic and geologic conditions which are very poorly known at many artificial lakes. If the formation strengths are constant in the area of the lake, consolidation theory indicates that failure is most likely under the lake in strike-slip or normal fault regimes. If failure occurs due to loading on a thrust fault regime it will occur at an offset from the lake.

Probabilistic Fatigue Analysis of Fixed Offshore Structures

This paper describes the application of probabilistic techniques to a detailed fatigue analysis of offshore structures. The structural properties are characterized by stress transfer functions in the properties are characterized by stress transfer functions in the frequency domain. Long-term statistics follow by accumulation and fatigue damage is computed using Miner's law. Spectral analysis is used to evaluate short-term stress statistics for each sea state in the wave climate. Introduction General Description of Fatigue in Offshore Structures Failure caused by fatigue in welded structures is related to the variable loads experienced by the structure during its life. Fatigue under random loading conditions, as experienced offshore, is a complex subject. The present state of the art for welded steel structures generally accepts the following as trueWelded connections are most susceptible to the development of fatigue cracks.Small, sharp defects inevitably exist in welds and can cause cracks.Fatigue in offshore structures is predominantly a matter of crack propagation as a result of these defectsIn as-welded connections, stress of yield-strength magnitude in tension exist because of residual stresses.Therefore, stress fluctuations range from tension yield downward and this range of the fluctuation alone is the governing parameter.Consequently, fully tensile stress cycles and partially or wholly compressive stress cycles are equally partially or wholly compressive stress cycles are equally damaging in welded structures.The fatigue strength of welded connections is independent of the yield strength of presently used structural steels.Crack propagation and consequent fatigue damage in an offshore environment will continue at some rate, no matter how small the stress range - that is, no endurance limit is found such as in constant-amplitude, cyclic loading above 2 x 10(6) cycles.Shear stresses may be neglected in fatigue life calculations. Stress fluctuations normally result predominantly from wave loads. These wave-induced stresses are of variable magnitude and occur in random order. The true time history of the local stresses almost invariably is simplified because it can be described adequately in statistical terms by a reasonable number of stress blocks. Each stress block is composed of a number of cycles of constant stress. Thus, the sequence of variations in the true stress history is lost. The cumulative effect of all stress blocks representing the stress history is estimated by Miner's rule of linear accumulation of damage: nb ni Fd = -----, ni i=1 where Fd = damage ratio and nb = number of stress blocks considered A fatigue failure is assumed to occur when the damage ratio, Fd, reaches unity. In fatigue analysis, this criterion is considered the definition of a local fatigue failure. This does not necessarily imply an actual failure nor a partial or complete collapse of the structure. JPT P. 657

Fatigue Analysis of Mechanically Fastened Joints Utilizing PSI) Loads

Multicomponent wing load and corresponding derived internal stress time histories are evaluated considering load transfer through mechanically fastened joints. These time histories are from both analytically derived and dynamic response test measured data considering flights through continuous turbulence of a heavy logistics aircraft. This evaluation is used as a basis to develop a rational fastener load transfer fatigue analysis methodology that includes gust loads in the power spectral density form. The technique developed includes the establishment of a matrix of axial-shear stress phasing relationships based on variations in operational flight parameters. The results of a durability assessment, utilizing the developed procedure, of specific structural joints subjected to two different load spectra are presented. Significant elements of this procedure are the aforementioned stress phasing relationships, joint geometric configuration data, fastener characteristics, and built-up S-N data. The results are compared to a fatigue assessment based on a uniaxial-stress fatigue analysis procedure. The potential applications of the developed load transfer analysis technique include structural joint design optimization and the durability evaluations of structural joints that have operating loads different from their design loads.