Showing papers on "Stress relaxation published in 1981"

Yield and transient effects during the plastic deformation of solid polymers

Abstract: Tensile tests were performed on seven commercial polymers at 22° C and at constant true strain rates of 10−4 to 10−1 sec−1. The constant strain rates were imposed on the minimum section of each sample with the aid of a diametral transducer, an exponential function generator and a closed-loop hydraulic testing machine. The polymers investigated were: high and low density polyethylene, polytetrafluoroethylene, polypropylene. polyvinylchloride and polyamide 6 and 66. True yield drops were observed in the rigid glassy polymers, whereas yielding was more gradual in the semi-crystalline or plasticized polymers. Strain rate change tests were also performed, during which one order of magnitude increases and decreases were imposed on the specimens. “Normal” transients were observed at small strains in the samples containing a rubbery phase, while the transients were of an “inverse” nature in the samples containing a glassy phase. With an increase in the strain at which the change was initiated, the “normal” transients changed in character to “inverse”. Transient tests were also performed in which straining was interrupted to permit a period of stress relaxation or of holding in the unloaded condition prior to the resumption of straining. A quantitative model is proposed, based on the dynamics of plastic waves which accounts for the transition from “normal” to “inverse” transient behaviour with increasing strain, and also explains the opposite effects of stress relaxation and of specimen unloading on the restraining transients.

The glass transition in basalt.

Abstract: The glass transition has been experimentally detected in basalt as (1) an increase in the aggregate linear thermal expansion coefficient αL, (2) an abrupt change in the temperature dependence of Young's modulus dE/dT, and (3) a change in stress relaxation behavior that effectively separates the T> TG and T TG. Collectively, the mechanical results suggest that for Hawaiian olivine tholeiite at 1-atm pressure, the principal material responses are (1) elastic (T ≤ 600°C), (2) reduced creep (600 980°C). Fracture surface morphologies developed during solidification suggest that the presence of the supercooled melt grain boundary phase may participate in the regulation of the thermal cracking process. Well-preserved fracture surfaces formed by incremental crack growth are found to be covered with striations that correspond to the inferred sequential stopping positions of the advancing fracture front. These striae may be rationalized in terms of experimental analogues that have been produced in viscoelastic polymers by cyclic tension-tension loading. The fracture surface morphology, mechanical data, and the controlled crack growth analogues suggest that thermal fracture in solidifying basalt is an incremental and cyclic process, involving three steps: (1) the accumulation of elastic strain energy in cooling rock at temperatures below that required for stress relaxation due to viscous flow in the intercrystalline liquid phase, (2) fracture at a ΔT determined primarily by the aggregate thermal expansion coefficient αυ and Young's modulus E, (3) the penetration by the advancing crack tip, of the thermal horizon capable of relaxing stress due to the creep of intercrystalline supercooled melt, producing the rough surface texture associated with the termination of a striation. Further crack growth must now await the migration of the solidus. The cycle then repeats. Striations measured in deep Hawaiian lava lakes have been compared with the crack advance increments expected in the vicinity of the glass transition, based on two tests: (1) thermal gradients measured in Kilauea Iki, combined with the mechanical properties of olivine tholeiite evaluated near TG, and (2) the crack advance required to match the recorded seismic stopping phases for prexisting cracks of the dimensions expected for Kilauea Iki. The observed versus predicted comparisons are (1) 31 versus 36 cm; and (2) 31 versus 30 cm. We envision this incremental crack growth process as contributing to the control on the downward movement of the thermal cracking front—and its associated hydrothermal circulation zone—in the upper portions of solidifying subaerial and submarine ponded basalt.

Influence of strain rate on dilatancy and strength of Oshima granite under uniaxial compression

Abstract: Uniaxial compression tests have been conducted on Oshima granite under various constant axial strain rates ranging from 10−8 to 10−4. The results showed that the strength and the acoustic emission rate increased exponentially with increasing strain rate. The inelastic volumetric strain rate defined by the differentiation with respect to the stress increased with decreasing strain rate. The redistribution of microcracks due to subcritical crack growth was considered theoretically, and the equations derived from the theory were compared with the experimental results. The agreement between the theoretical and experimental results shows that stress corrosion plays not only a major role in the brittle creep under constant load but also dominates the strain rate effects on strength and dilatancy observed in the constant strain rate loadings.

Creep deformation at crack tips in elastic-viscoplastic solids

Abstract: The evaluation of crack growth tests under creep conditions must be based on the stress analysis of a cracked body taking into account elastic, plastic and creep deformation. In addition to the well-known analysis of a cracked body creeping in secondary (steady-state) creep, the stress field at the tip of a stationary crack is calculated for primary (strain-hardening) or tertiary (strain-softening) creep of the whole specimen. For the special hardening creep-law considered, a path-independent integral C ∗ h , can be defined which correlates the near-tip field to the applied load. It is also shown how, after sudden load application, creep strains develop in the initially elastic or, for a higher load level, plastic body. Characteristic times are derived to distinguish between short times when the creep-zones, in which creep strains are concentrated, are still small, and long times when the whole specimen creeps extensively in primary and finally in secondary and tertiary creep. Comparing the creep-zone sizes with the specimen dimensions or comparing the characteristic times with the test duration, one can decide which deformation mechanism prevails in the bulk of the specimen and which load parameter enters into the near-tip stress field and determines crack growth behavior. The governing load parameter is the stress intensity factor K 1 if the bulk of the specimen is predominantly elastic and it is the J -integral in a fully-plastic situation when large creep strains are still confined to a small zone. The C ∗ h -integral applies if the bulk of the specimen deforms in primary or tertiary creep, and C ∗ is the relevant load parameter for predominantly secondary creep of the whole specimen.

Effects of fault interaction on moment, stress drop, and strain energy release

Abstract: Solutions for collinear shear cracks are used to examine quantitatively the effects of fault slip zone interaction on determinations of moment, stress drop, and static energy release. Two models, the barrier model and the asperity model, are considered. In the asperity model, the actual distribution of strengths on a fault plane is idealized as a combination of two limiting cases: areas which slip freely at a uniform value of a residual friction stress and unbroken ligaments or ‘asperities’ across which slip occurs only at the time of a seismic event. In the barrier model, slip zones separated by unbroken ligaments (barriers) are introduced into a uniformly stressed medium to approximate the nonuniform fault propagation proposed by Das and Aki. The strain energy change due to introducing collinear slip zones or due to breaking the asperities between them is shown to be given by the usual formula for an isolated slip zone with the stress drop replaced by the effective stress. Significant interaction between slip zones occurs only if the length of the asperity is less than half the length of the slip zones. For the case of two collinear slip zones, fracture of the asperity between them is shown to cause a large moment primarily because of the additional displacement which is induced on the adjacent slip zones. For example, if the asperity length is 0.05l, where l is the length of each adjacent slip zone, then fracture of the asperity causes a moment almost 1.8 times the moment caused by introducing a slip zone of length l. For two collinear slip zones, the local stress drop due to fracture of the separating asperity is shown to become unbounded as the asperity length goes to zero, but in the same limit the stress drop averaged over the entire fault length is approximately equal to the apparent stress drop inferred for an isolated fault of the same moment and total fault length. This apparent stress drop is approximately equal (within a factor of 2 or 3) to the effective stress and hence can be used in the usual formula to give a good estimate of the strain energy change. For the barrier model, numerical results are given for the ratio of the stress drop calculated on the assumption of an isolated slip zone to the true stress drop. For example, in the case of two collinear slip zones of length l separated by a barrier of length 0.2l, this ratio is 0.5, whereas for a barrier length equal to that of the adjacent slip zones, the ratio is 0.24. Stress drop estimates become worse with increasing number of fault segments.

Tissue mechanics of canine pericardium in different test environments. Evidence for time-dependent accommodation, absence of plasticity, and new roles for collagen and elastin.

Abstract: We have tested the mechanical properties of isolated canine pericardium at 37°C in Hanks' solution, and compared those results with similar tests on tissue at room temperature, both in Hanks' solution and merely kept moist with saline. Pericardium, which is nearly isotropic due to the layers of collagen aligned in different directions, is a composite material made up of collagen and elastin fibers in a viscous ground substance matrix. Rapidly applied loads result in a stress-strain response similar to the previous in vivo pressure-volume curves. Slowly applied loads produce an accommodatioii effect as fiber geometry rearranges through the viscous ground substance. Plasticity of the pericardium, long accepted as fact, is not present An accommodation effect is produced instead by shifts in the stress-strain curve due to cyclic loading, stress relaxation, and creep. The slow time course of the accommodation effect is responsible for the differences in hemodynamic effect between an acute and a chronic pericardial effusion. The mechanical properties of the pericardium are due primarily to collagen, which establishes the high ultimate tensile strength and high final slope of the stress-strain curves. The initial extensible portion of the stress-strain curve probably is due to initial rearrangement of collagen fiber weave under stress. Temperature dependence and previous digestion studies indicate a major role for elastin in determining the stress-strain response and limits to stress relaxation and creep. Thixotropy of the ground substance matrix may produce rate Independence In rapid filling of the pericardial sac Circ Res 49: 633-544, 1981

Ideal elastic, anelastic and viscoelastic deformation of a metallic glass

Abstract: The elastic, viscoelastic and anelastic components of the homogeneous strain response of the metallic glass Pd82Si18 to an applied stress have been examined. The elastic response is fully reversible, instantaneous and linear. The measured elastic modulus, E, and temperature dependence, d(ln E)/dT, are 84±8 GPa and (−3.2±0.6) × 10−4 C−1, respectively. The viscoelastic flow is non-recoverable and, if the configuration remains constant, is characterized by a constant strain rate. This strain rate varies linearly with the stress, gtr, in the low stress regime (τ < 300 MPa), becoming non-linear for higher stresses. For isoconfigurational flow, the strain rate has an Arrhenius-type temperature dependence with an activation energy of - 200 ± 15 kJ mol−1, independent of stress and thermal history. The magnitude of the strain rate is strongly dependent on the degree of structural relaxation and therefore on thermal history. During isothermal annealing the viscoelastic strain rate varies inversely with time. The anelastic response is a transient that, at 500 K, contributes to the flow for approximately fifty hours after a stress increase and is fully recovered upon stress reduction. A spectrum of exponential decays is required to model this flow component. The anelastic strain, τA, varies linearly with the magnitude of the stress change, Δτ, over the entire stress range tested: γA/gDAτ=(8.0±0.8)× 10−6 MPa−1.

Sub‐sub Tg structural relaxation in glassy polymers

Abstract: Structural relaxation in a temperature range from 32 to 62° K glass transition has been investigated, for the first time, for a nearly monodisperse polystyrene using a differential scanning calorimeter and a thermal mechanical analyzer. Low temperature anneals in the vicinity of 320 K stabilize the glassy structure and lead to volume contraction. Upon heating, the annealed samples show an excess endothermic peak and exhibit a gradual expansion associated with structural recovery above the annealing temperature. Significantly, the samples recover the initial heat content and volume without reheating through the glass transition temperature. This sub‐Tg structural relaxation behavior is in many respects distinct from that commonly observed near the glass transition. Kinetics of relaxation processes are also discussed.

Mechanical and structural correlates of canine pericardium.

Abstract: We have assessed viscoelastic properties of pericardium within the physiological range of stresses and related mechanical behavior to fiber direction as defined by scanning electron microscopy. Stiffness, stress relaxation, and creep were measured in samples taken from the anterior surface of 14 canine pericardia. Stress-strain relations generally were not exponential; stiffness at a stress of 1 g/mm2 ranged from 12.9 to 239 g/mm2 during stretch and varied both from pericardium to pericardium and with the orientation of the strip within the sample (anisotropy). The strips exhibited hysteretic behavior which was not promotional to rate of strain. Following a rapid increase in stress, creep averaged less than 1% and stress relaxation, 34% in a 30-minute test period. The orientation of the strip with the greatest stiffness was consistent from pericardium to pericardium, and correlated with a layer of collagen fibers oriented along the major axis of te strip.

Transient shear flow behavior of polymeric fluids according to the Leonov model

Abstract: The viscoelastic behavior of polymeric systems based upon the Leonov model has been examined for (i) stress growth and relaxation with intermittent shear flow, (ii) stress relaxation after a step in the shear strain and (iii) elastic recovery after shear flow. A large number of modes have been conveniently incorporated through the determination of the model parameters from conventional rheological data by using an effective least-square procedure. With a sufficient number of modes, the predictions are in very good agreement with corresponding experiments in literature, including the recent data for cases (i) and (ii) obtained by optical methods.

The Rate (Time)-Dependent Behavior of Ti-7Al-2Cb-1Ta Titanium Alloy at Room Temperature Under Quasi-Static Monotonic and Cyclic Loading

Abstract: : Uniaxial tests using a servocontrolled testing machine and strain measurement at the gage length were performed on a high-strength, low-ductility, Titanium Alloy Tests involved monotonic and cyclic loadings with strain rates between 2 x 10 to the minus 8th power to 10 to the minus 3rd power s to the minus 1st power, stress rates from 10 to the minus 1st power to 100 MPa s to the minus 1st power and short-term relaxation and creep tests The inelastic behavior is strongly rate-dependent Ratchetting is shown to increase as the stress rate decreases No strain-rate history effect was found A unique stress-strain curve is ultimately reached for a given strain rate irrespective of prior history as long as only positive stresses are imposed In the plastic range the relaxation drop in a given time period depends only on the strain rate preceding the test and is independent of the actual stress and strain The results are qualitatively in accordance with the viscoplasticity theory based on total strain and overstress (Author)

Creep Theory of Anisotropic Solids

Abstract: In this paper the secondary creep stage of anisotropic solids in a state of multiaxial stress is considered. The theory is based on the assumption of the existence of a creep potential, which can depend only on invariants of the stress tensor or its deviator, if the material is isotropic. The anisotropic behavior is described by using a mapped stress tensor instead of the actual stress tensor in the isotropic creep potential. Assuming a linear transformation, the anisotropic behavior is expressed by a material tensor of rank four. The theory of the creep potential is based upon the principle of maximum dissipation rate, from which, following Lagrange's method in connection with a creep condition, one obtains the flow rule of anisotropic materials. This flow rule leads to the constitutive equations formulated in this paper. The material constants involved in these equations are related to experimental data. For example, the orthotropic case is considered, and the Poynting‐effect is accounted for. Furthermo...

Internal friction caused by diffusion around a second-phase particle Al-Si alloy

Abstract: The stress relaxation caused by diffusion round a second-phase particle has been measured by internal friction in Al-Si alloys. Reproducible clear internal-friction peaks were found at ∼420 K at a frequency of ∼ 1 Hz. These were unambiguously assigned to the presence of Si particles in Al. In accordance with a theory of the relaxation caused by diffusion along the matrix—particle interface, the relaxation time is proportional to the third power of the particle size. The activation energy and the pre-exponential factor of this diffusion are ∼ 0·92 eV and ∼ 3·9 × 10−5 m2/s, respectively. The magnitude of the relaxation strength agrees with the theory.

Plastic relaxation of the transformation strain energy of a misfitting spherical precipitate: linear and power-law strain hardening

Abstract: Complete solutions to the displacement, stress and strain fields, plastic zone size and misfit energy are calculated for an isotropic misfitting spherical precipitate under the assumptions of von Mises’ yield criterion and incremental plasticity. Analytical solutions are obtained for the case of linear strain hardening while a numerical technique is necessary for the case of power-law hardening. Large changes in the stress field in the regions surrounding the precipitate are observed when contrasted with the elastic state. The energy of the relaxed state is found to be a strong function of the strain-hardening parameter as is the plastic work done during the relaxation process. The plastic zone size, however, is not strongly dependent upon the strain-hardening parameter and for a homogeneous precipitate is independent of it.

On Constitutive Relations and Failure Criteria of an Austenitic Steel under Cyclic Loading at Elevated Temperature

Abstract: The paper records and interprets a series of tests on 316 stainless steel at 600°C which seek to investigate the interaction of short term plastic deformation and subsequent creep deformation. Strain controlled tests have been used to determine the influence of strain range, the number of cycles and the dwell period. The implications for structural behaviour and the prediction of stress relaxation are discussed.

Effect of physical aging on stress relaxation of poly(methyl methacrylate)

Abstract: A study was made on the stress relaxation behavior at 25 C of poly(methyl methacrylate) in uniaxial tension as a function of physical aging at both room temperature and 60 C. Test specimens were compression molded at 165 C, then quenched to room temperature and allowed to age for up to 30 days prior to testing. Stress relaxation curves measured after different aging times could be superposed to a single master curve for each aging temperature. Superposition was achieved by applying vertical and horizontal shifts. Hence, the shape of the response curves was not changed by aging. This is in accordance with observations made by Struik for tensile creep curves. Volume changes as a function of physical aging were also determined. Simple exponential relationships were observed between volume and both horizontal and vertical shifts. The horizontal shift implies a shift in the effective time scale caused by a change in free volume. The vertical shifts could be correlated with changes in Young's modulus caused by a change in density. For the range of aging studied, the response time scale varied over nearly two decades of log-time. For the same conditions modulus varied by 30 percent.

Viscoelastic properties of sulfonated styrene ionomers

Abstract: The solid-state viscoelastic properties of polystyrene containing randomly distributed groups of styrene-p-sodium sulfonate are studied and compared with the corresponding properties of copolymers of styrene and sodium methacrylate (S-NaMA). The viscoelastic behavior in the primary transition region of these two ionomers is very similar. As for the S-NaMA copolymers, it is proposed that sulfonated polystyrene is composed of ion-rich regions (clusters) immersed in a matrix of low ion concentration. Two peaks are observed in the plot of mechanical loss tangent versus temperature for the sulfonated material. The lower peak is assigned to the glass transition of the ion-poor matrix and the upper to the glass transition of the clustered regions. As for some other ionomers, the presence of ions is found to slow down the stress relaxation rate, giving a broad distribution of relaxation times. Above a certain ion concentration, the sulfonated polystyrenes are thermorheologically complex owing to the onset of a secondary relaxation mechanism associated with the ion-rich regions.

State of stress in the oceanic lithosphere in response to loading

Abstract: Summary. Flexure studies of the oceanic lithosphere constrained by bathymetry and gravity data suggest that the lithosphere behaves elastically over geological time-scales. For loads to be supported, however, large bending stresses (approaching 10 kb in some cases) are required at the top and bottom of the elastic plate. These stress-differences can be significantly reduced by introducing more complex rheologies: we propose a model of layered lithosphere, consisting of a purely elastic upper layer, a transition zone with viscosity varying with depth and a perfectly plastic lower layer. The transition layer is grossly centred at the bottom of the elastic plate. Such a model results in a noticeable reduction of stress differences; reaching 60 per cent for flow laws representing creep mechanisms in olivine. When applied to a number of seamount loads, this model leads to maximum stress-differences which do not exceed 1–2kb. The approach used in this study allows us to follow stress relaxation over time. Taking account of the thermal cooling of the lithosphere, we show that the elastic thickness of the lithosphere is stabilized after a given time, while the time required for stabilization is found to be of the order 5—6 per cent of the age of the lithosphere at the date of loading.

Energy‐related failure criteria of thermoplastics

Abstract: Three aspects of the failure of thermoplastics, having a special importance in engineering, are investigated. They are: (a) Transition from linear to nonlinear viscoelasticity; (b) Crazing; (c) Fracture. Energy related criteria, developed from the Reiner-Weissenberg thermodynamical theory of strength, are used for the characterization and prediction of failure under its different forms, for simple uniaxial loading histories such as creep, stress relaxation and constant rate of strain. The computation of the stored and dissipated parts of the specific stress energy becomes possible in a relatively simple way, if the relaxation modulus and the creep compliance are approximated by Prony-Dirichlet-type series with a finite number of terms. Published experimental data, as well as experiments carried out by the author on different thermoplastics are in very good agreement with theoretical results. Further, based on experimental data, the equations obtained can be reduced to very simple and useful relations. The influence of elevated temperatures (below the glassy-transition point) on failure is also considered.

A Self-Consistent Scheme for the Relaxation Behavior of Metals

Abstract: We identify in this paper that stress relaxation in metals is a "strain-free" process. The corresponding self-consistent relations between the strain, and stress variations of a grain and of its aggregate are derived from Eshelby's solution of an ellipsoidal inclusion. It is shown that, under such a process, the strain in a more favorably oriented grain continues to rise and that its stress decreases more drastically than that of the aggregate; conversely, for a less favorably oriented grain, its strain decreases and its stress relaxes less. The self-consistent relations are supplemented with a temperature-dependent, physically consistent constitutive equation for the slip system. Such an equation enables us to determine the single crystal constants at one temperature from the polycrystal data at another temperature; it also makes the self-consistent scheme applicable to the varying-temperature environment. The established theory was finally applied to predict the relaxation behavior of an RR-59 aluminum alloy under combined stress; the results showed reasonably good agreement with the experimental data.

The use of large transient deformations to evaluate rheological models for molten polymers

Abstract: The prediction of models proposed by Acierno et al. (ALMRT) and by Phan-Thien and Tanner (PTT) are compared with data for a low density polyethylene film resin and a high density blow molding resin. The deformations involved are interrupted shear, reduction in shear rate, large amplitude oscillatory shear and uniaxial extension. Both models predict characteristic times for ”reentanglement“ that are significantly larger than stress relaxation times, but that are still much smaller than observed values. The origin of this effect is shown to be quite different in the two models. The ALMRT model fails to predict the observed nonlinearity in the response to large amplitude oscillatory shear. The PTT model predicts nonlinearity and gives the correct value of the maximum stress, but the predicted shape of the stress curve is incorrect. Extensional stress growth data were not in agreement with the predictions of the ALMRT model except in the linear region. It was not possible to fit the PTT model to these data.

Stress relaxation of polybutadiene at large deformation. Measurements of stress and birefringence in shear and elongation

Abstract: The rheological behavior of an uncrosslinked polybutadiene on sudden application of finite strain was examined. The shear stress σ, two components of birefringence, and the extinction angle were measured in shear (magnitude of shear γ ≤ 3.5) and tensile stress and the birefringence were measured in uniaxial elongation (elongation ratio λ ≤ 3.8). Measurements were performed at 30°C with a tensile tester equipped with appropriate sample holders. The stress-optical coefficient was 3.01 × 10−9Pa−1. The first and second normal-stress differences v1 and v2 were separately evaluated with the use of stress-optical law. The Lodge—Meissner relation v1 = γσ held good. The ratio v2/v1 was independent of time and varied from about −0.3 to −0.2 with increasing γ in the range of measurements. Each of the stress components was factored into a function of strain and one of time, and the latter was common to all the stress components. Simple formulas were proposed to represent stress components in step deformations.

Mechanical properties of chemical vapor deposited coatings for fusion reactor application

Abstract: Chemical vapor deposited coatings of TiB2, TiC and boron on graphite substrates are being developed for application as limiter materials in magnetic confinement fusion reactors. In this application severe thermal shock conditions exist and to do effective thermo‐mechanical modelling of the material response it is necessary to acquire elastic moduli, fracture strength, and strain to fracture data for the coatings. Four point flexure tests have been conducted from room temperature to 2000 °C on TiB2 and boron coated graphite with coatings in tension and compression and the mechanical properties extracted from the load‐deflection data. In addition, stress relaxation tests from 500 ° to 1150 °C were performed on TiB2 and TiC coated graphite beams to assess the low levels of plastic deformation which occur in these coatings. Significant differences have been observed between the effective mechanical properties of the coatings and literature values of the bulk properties.