Uniaxial Strain Tests Research Articles

Effect of Laser Welding on Formability of DP980 steel

Limiting dome height (LDH) tests were used to evaluate the formability of laser butt welded blanks of the dual phase 980 steel in comparison with the base metal. Two different lasers were used: diode and Nd:YAG, giving a wide range of welding thermal cycles. A sharp decrease in LDH was observed in the welded specimens due to the formation of a softened zone in the outer heat affected zone. Softened zone characteristics were correlated with the LDH. Larger softened zones led to a larger reduction in the LDH. The welding orientation relative to the rolling direction or to the punch surface did not influence the formability, as the softened zone dominated the formability behavior. It was observed that in both uniaxial and biaxial strain tests, the fracture occurred in the softened zone of the welded samples consistently slightly farther out from the weld centerline than in the location of the minimum hardness.

Mechanical modeling of MX-80–Development of constitutive laws

In a previous paper [Åkesson, M., Hökmark, H., 2007. Mechanical model for unsaturated MX-80. In: Schanz, T. (Ed.), Theoretical and Numerical Unsaturated Soil Mechanics, Springer Proceeding in Physics, vol. 113, pp. 3–10] a new elastoplastic model for unsaturated swelling clay was presented. The model was formulated as two differential equations, for elastic and plastic strains, respectively. Each equation described a relation between the (air-filled) macro void ratio and the two independent variables stress and (water-filled) micro void ratio. The established concept of swelling pressure and its void ratio dependence were incorporated in the model. To do this, the grain-to-grain contact stress and the contact area had to be considered. In its original form the model only handled one-dimensional problems, e.g. compression tests with uniaxial strain and water uptake test at constant volume with assumed isotropic conditions. This paper describes a first attempt to generalize the model to address multidimensional problems with the intention to integrate it into the framework of Code_Bright. This was made through definition of an expression for the retention properties and through variable substitution. In this way, four functions for the kappa moduli were identified: two elastic and two plastic. These functions provide unique values for each given state. In the used framework of the Barcelona Basic Model (BBM), all strains are treated as elastic, and there is thus no explicit treatment of any deviatoric yield condition. The only remaining parameter outside the new model is the Poisson’s ratio.

A yield function for copper powder in compaction

A powder conglomerate, consisting of loose metal particles, yields by shear stress as well as by hydrostatic stress. Strength of the conglomerate in tension is negligible. Thus, the yield surface of such a material can be described as an ellipse in the space defined by J 1 axis and J ′ 2 axis, which is shifted toward the negative direction in the J 1 axis. In the present investigation, the parameters used in the yield function were determined by uniaxial strain and hydrostatic compression tests of Cu powder under the assumption that they are functions of relative density. Flow rules were obtained by imposing the normality condition to the yield function and they were applied to predict pressures required in uniaxial strain, plane strain and hydrostatic compressions. The predictions are in good agreement with the experiments.

The uniaxial strain test - a simple method for the characterization of porous materials

The application of cellular materials in load-carrying and security-relevant structures requires the exact prediction of their mechanical behavior, which necessitates the development of robust simulation models and techniques based on appropriate experimental procedures. The determination of the yield surface requires experiments under multi-axial stress states because the yield behavior is sensitive to the hydrostatic stress and simple uniaxial tests aim only to determine one single point of the yield surface. Therefore, an experimental technique based on a uniaxial strain test for the description of the influence of the hydrostatic stress on the yield condition in the elastic-plastic transition zone at small strains is proposed and numerically investigated. Furthermore, this experimental technique enables the determination of a second elastic constant, e.g., Poisson\'s ratio.

Poroelastic parameters of Meuse/Haute Marne argillites: effect of loading and saturation states

The aim of this paper is to summarize the experimental work carried out by IFP on rock samples taken from the Meuse/Haute Marne underground research laboratory host formation. The behavior of this clayey rock, called “argillite,” has been studied within the framework of Biot's mechanics of fluid saturated porous solids. Drained and undrained oedometric tests (i.e., uniaxial strain tests) have been performed to determine the poroelastic parameters for different stress levels. As the provided samples were not fully water-saturated, particular care has been taken over the definition of a preliminary resaturation phase and the estimation of each sample's final saturation level. Argillites poromechanical behavior appears to depend on the rock saturation state. Samples with a greater initial saturation seem to show a less apparent degree of overconsolidation and a higher compressibility. The obtained results also show the influence of the applied stress on the poroelastic parameters. Biot's coefficient decreases when the axial stress increases, while the drained bulk modulus and the shear modulus increase. The effect of the applied stress on Biot's modulus is more difficult to explain because its measure strongly depends on the saturation level of the sample.

Shock-induced structural transitions and dynamic strength of solids

Shock tests of series of materials under uniaxial strain conditions including constructional and armor steels, aluminum alloy, copper and beryllium, show that spall-strength sensitively depends on the structural instability of material under compression at the front of compressive pulse. This instability is shown to be a shock-induced structural transition which results in irreversible mesostructure formation in solid. It is also shown that value of structural instability threshold under dynamic compression measured in uniaxial strain tests determines a strength-component of resistance of material to high-velocity penetration in Alekseevskii–Tate model.

Effect of shock-induced mesoscopic processes on dynamic strength of solids

Dynamic deformation and fracture behavior of a series of metals under uniaxial strain conditions are studied by using light gas gun facility and velocity interferometer. In the majority of tests the thickness of target and impactor were adjusted to provide spallation. Spall-strength is found to be sensitively depended on the plastic instability of a material under compression. It is considered to be important strength-characteristic of material. Specifically, for all the tested material the value of instability threshold determined in uniaxial strain tests coincides with the strength-component of resistance to high-velocity penetration in Aleksmvskii-Tate model.

A novel approach to measure local strains in polymer matrix systems using polarised Raman microscopy

A novel approach to measure local strains in amorphous polymers is described. The method is based on the identification of changes in the molecular orientation with strain. Molecular orientation is quantified through a series expansion of Legendre functions where the coefficients of the series are determined from the Raman scattering intensities by varying the polarizations of incident and scattered light. The relations between the elements of the strain tensor and the coefficients of the Legendre functions are obtained from a set of simple uniaxial strain tests. The experimental technique is applied to measure the thermal strain field in the matrix around an embedded fibre in a single fibre model composite. The experimental results indicate that local shear yielding takes place within the matrix. This conclusion was supported by measurements of strain distribution in the fibre.

On the stability of rate-dependent solids with application to the uniaxial plane strain test

The linear stability criterion, proposed for structural models in an earlier paper, is now extended for a general class of elastic–viscoplastic continua. The time-dependent trajectories, whose stability is under investigation, are functions of two characteristic times: the relaxation time of the viscous solid and the rate of the applied loading, with their ratio denoted by T. It is assumed that the loading conditions of the trajectory are not modified by the perturbation. The criterion predicts that a solid is initially unstable if there exists a unit norm perturbation in the velocity field whose time derivative is positive. This condition is equivalent to finding a positive eigenvalue in the self-adjoint part of the operator relating the initial first and second rate of the displacement perturbations. If the dominant eigenvalue is obtained from the non self-adjoint operator, the change in sign of its real part is a sufficient condition for instability. For solids with an associated flow rule, it is shown that the exclusion of instability in a trajectory, in the limit of vanishing T, coincides with stability of the corresponding rate-independent solid in the sense of Hill. The theory is applied to the analysis of a finitely strained rectangular block under uniaxial tension and compression, for different elastic–viscoplastic solids of the von Mises and Drucker–Prager type.

Experimental characterization of quasi static and shock wave behavior of porous aluminum

Experiments of quasi static hydrostatic and uniaxial strain compression, and of shock wave propagation performed on 9% and 17% porous aluminum are presented, analyzed, and compared. Quasi static experiments show the influence of coupling between void collapse and plasticity induced in the matrix on the material macroscopic behavior. The amount of pore compaction appears to be enhanced by the deviatoric stress component present in the uniaxial strain tests and not in the hydrostatic ones. The originality of the plate impact setup and its associated metrology [velocity interferometer system for any reflector (VISAR) interferometry and polyvinylidene fluoride (PVDF) piezoelectric gages] exhibits also the influence of these local physical mechanisms on shock wave propagation in porous aluminum. More, the variations observed between the rise times of shocks seem to point out a preponderance of the dynamic effects (inertia or strain rate) over the material behavior. We observe indeed that the higher the stress in the material, the shorter the shock rise time. This point is confirmed by comparing quasi static and dynamic responses of porous aluminum. Comparison of these experimental results to numerical simulations should be interesting to prove or not this hypothesis.

Stress-dependent permeability measurement using the oscillating pulse technique

Permeability of Indiana Limestone samples undergoing deformation in a triaxial cell along several stress paths such as triaxial compression, hydrostatic compression and uniaxial strain was measured using the oscillating pulse technique. This technique consists of applying a sinusoidal pressure wave at the upstream end of the sample and recording the pressure—time behavior at the downstream end. The solution to the general one-dimensional diffusivity equation can be obtained by applying the appropriate boundary conditions to give a method of evaluating diffusivity and permeability in a relatively short time. The process of sending a pulse to evaluate permeability has been programmed in Visual Basic which can be incorporated into any regular triaxial testing automated routines to measure permeability at different stages of loading until failure. Stored waveforms of the upstream and downstream pressure responses with time are analyzed to evaluate the attenuation and phase shift in the waveform. For comparison purposes, permeability was also measured using steady-state methods for samples subjected to a hydrostatic compression stress path and good correlations were observed. During triaxial compression failure tests, in most tests the permeability decreased continuously until the end of the test. Permeability also decreased with increasing confining pressure, while under uniaxial strain (i.e. one-dimensional compaction ( k 0) tests), there was a sudden reduction of permeability at a particular stress level.

Creep related subsidence caused by oil and gas extraction : G. Eiksund, G. Svano & N. B. Nagel, in: Land subsidence. Proc. international symposium, The Hague, 1995, ed. F.B.J. Barends & others, (IAHS; Publication, 234), 1995, pp 277–285

The paper presents results from a project in which the contribution from creep on compaction of the Ekofisk oil and gas reservoir is studied. Creep parameters are derived from long-term uniaxial strain tests on the formation rock for specific porosity classes. The accumulated thickness within each porosity class is used to establish a one-dimensional model of the reservoir. Laboratory tests with sea water injections (SWI) are used to model the effect of SWI on creep. The pore pressure depletion history for the reservoir in combination with arching effects, is used to estimate the effective stress history in the reservoir. The role of creep to date is addressed and future compaction predictions for different pore pressure scenarios are presented.

Parallel Elastoplastic Models of Inelastic Material Behavior

Parallel mathematical models are presented and analyzed as a basis for representing the mechanical behavior of inelastic materials. These models are developed within the framework of incremental elastoplasticity theory. The models are shown to simply represent strain hardening through the adjustment of internal stresses within internal elements of the model, to capture Bauschinger's effect during stress reversal, and to provide hysteretic loops in closed stress cycles. The models are shown to provide stable, nonassociated plastic flow for frictional materials such as geologic materials, i.e., to obey Drucker's stability postulate. A simple parallel model for rock is presented that gives the same response as a conventional elastoplastic material model when used to fit idealized uniaxial strain and triaxial compression test data. However, the two models give much different results in triaxial extension after initial hardening occurred on the compression side first. It is believed that this modeling concept holds significant promise for improving mathematical models of the inelastic mechanical behavior of a variety of engineering materials.

Fiber-reinforced-superconductors for a 15 T-class high-field pulsed magnet and their conceptual design

The authors are developing a novel type of Nb/sub 3/Sn superconductor with high elastic modulus fibers for application to high field pulsed superconducting magnets, called the fiber-reinforced superconductor (FRS). They describe the conceptual design of a conductor for a pulsed magnet using FRSs and present superconducting characteristics for monofilamentary FRS samples. Each monofilamentary FRS supports hoop stress under operation of the magnet. Short lengths of monofilamentary FRSs using tungsten fiber were prepared by RF-magnetron sputtering. Critical current measurement up to 15 T and a uniaxial strain test at 10 T have been carried out. The data support the conceptual design of the 15-T-class pulsed superconducting magnet using FRSs.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

One‐Dimensional Loading‐Rate Effects

It has long been recognized that the one‐dimensional or uniaxial strain response of most soils subjected to high‐intensity transient loads (i.e., blast pulses) differs from the response measured under quasi‐static loading rates. Recent research has suggested that for submillisecond rise times, increases up to 10‐fold in the loading constrained modulus occur for some remolded partially saturated granular soils under undrained conditions. Parallel research has shown that, in contrast, loading‐rate effects can be ignored for a similar granular material tested under nearly identical boundary conditions. Stress‐strain curves from 60 uniaxial strain tests are summarized and presented herein depicting the behavior of three soils (two clean sands and a silty clay) to a variety of loading rates. Loadings are typically carried to 10,000 psi (69 MPa) with times to peak ranging from a few tenths of a millisecond to several minutes. These laboratory test results show that a dramatic increase in the loading constrained...

Rock Mechanics of the Ekofisk Reservoir in the Evaluation of Subsidence

Mechanical properties have been determined for Ekofisk reservoir rock for use in subsidence simulation. Tests were to describe the mechanical properties of the Ekofisk chalk for reservoir conditions. The mechanisms and time dependence of chalk compaction and the effect of waterflooding on chalk strength were also examined.

Rock Compressibility, Compaction, and Subsidence in a High-Porosity Chalk Reservoir: A Case Study of Valhall Field

Etude de l'utilisation des essais de compaction realises en laboratoire sur des carottes du champ Valhall (Mer du Nord) afin de mieux prevoir les pressions du reservoir et la subsidence superficielle entrainee par l'epuisement du champ

Formation and evolution of strike‐slip faults, rifts, and basins during the India‐Asia Collision: An experimental approach

The processes which have governed the formation and evolution of large Tertiary strike‐slip faults during the penetration of India into eastern Asia are investigated by means of plane strain indentation experiments on layered plasticine models. The steady state deformation of plasticine obeys a power creep flow law . The stress exponent (n) is between 6 and 9 at 25°C. Uniaxial plane strain tests on cubic specimens show that the growth of faults in layered plasticine results from strain softening, a process observed for strain rates ranging from 3.5×10−5 to 3.6×10−3 s−1. Fault or shear zones form after only 7–10 % bulk strain. Subsequent deformation is controlled by the geometry of the fault pattern rather than the physical properties of the plasticine. A series of nine plane strain indentation experiments shows the influence of boundary conditions, as well as that of the internal structure of the plasticine model on the faulting sequence. The ubiquity of strain softening in experimental deformation of a variety of rocks, as well as the widespread occurrence of shear zones in nature suggest that long‐term deformation of the continental lithosphere may also be primarily influenced by the geometry of large faults which rapidly develop with increasing strain. The deformation and faulting sequence observed in the plasticine indentation experiments may thus be compared to collision‐induced strikeslip faulting in Asia, particularly to total offsets and rates of movements on the faults. The experiments simulate the evolution of the western ends of the strike‐slip faults, which have probably been analogous to trench‐fault‐fault triple junctions. The experiments also illustrate mechanisms for the formation of extensional basins, such as the South China Sea, North China Basin, and Andaman Sea, near active continental margins. The basins, which appear to absorb terminal offsets along major strike‐slip faults near such margins may result from mismatch between the sharply angular shape of the deformed continental edge and the more regularly curved trench along which the smoothly flexed oceanic lithosphere subducts. The existence of distinct phases of strike‐slip extrusion corroborates the idea that the discontinuities in time which typify intracontinental tectonics and orogenic cycles may often result from strain localization and the ensuing discontinuous, non‐steady state deformation of the continental lithosphere.

A microstatistical model for ductile fracture with rate effects

A micromechanical ductile fracture model was used in a parametric study of void-induced softening. The model describes rate-dependent nucleation and growth of microscopic void size distributions. The Gurson yield surface is used as the threshold condition for viscous void growth. The relative amounts of shear stress and mean stress relaxations due to void nucleation and growth in a material element are found to be strongly dependent on both the material viscosity and the path taken by the material element in stress space. Material elements subjected to uniaxial stress load paths show much less shear strength softening than those subjected to uniaxial strain load paths. Shear strength softening is enhanced by loading rates high enough to activate viscous response. Computational simulations of uniaxial stress and strain tests over a range of strain rate show a complicated interplay of the above factors.

The determination of the normal interaction term in the Tsai-Wu tensor polynomial strength criterion

The determination of the normal interaction term, F 12, in the Tsai-Wu polynomial strength criterion, using a single uniaxial strain test is proposed. The appropriate formulae are derived and it is explicitly shown how F 12 depends on the elastic constants of the maternal. Two other simple geometries are also considered. Numerical estimates from existing experimental data are provided for two graphite/epoxy composites and some comments are made on the viability of the proposed tests.