Strain Rate Relationship Research Articles

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

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

Design of a New Rheometer for Concrete

Abstract A new concrete rheometer has been presented including its concept, actual design, working principle, calibration, and repeatability. Resistance offered by vertical wall of cylindrical container to concrete has been taken into consideration to represent actual flow condition of concrete during shearing. An expression for total shear stress has been derived whereby shear stress versus torque and overall shear strain rate versus rotational frequency relationships have been established for the given geometry of the rheometer. A magneto-rheological fluid has been tested with the present rheometer and the results have been compared with the test results obtained by HAAKE RS1 rheometer to validate the present analytical approach. Repeatability tests were conducted with different concrete mixes and results were found to be reasonable.

Effects of water and iron content on the rheological contrast between garnet and olivine

The effects of water and iron content on the relative creep strengths of garnet and olivine were investigated by shear deformation experiments. Garnet and olivine samples were sandwiched together between alumina pistons in a simple shear geometry and were deformed at P = 1–2 GPa, T = 1473 K and strain rates ranging from 10 −5 to 10 −3 s −1 using a Griggs-type solid-medium apparatus. The stress- and strain-rate relation, as well as the deformation microstructures including lattice-preferred orientation and dynamic recrystallization, indicates that the deformation by dislocation creep. The creep tests show that the Fe-rich garnet (Alm 67Prp 29Grs 3) was slightly weaker than olivine (Fo90), whereas the Mg-rich garnet (Alm 19Prp 68Grs 12) was significantly stronger than olivine under dry conditions. The wet experiments show that the creep rate of the Mg-rich garnet is more sensitive to water than olivine; the water fugacity exponent on strain rate was estimated to be ∼2.4 for garnet and ∼1.2 for olivine, and the Mg-rich garnet becomes weaker than olivine in a water-rich environment. The experimental results show that the rheological contrast between garnet and olivine depends strongly on water content and to a lesser degree on Fe content. Consequently, the geodynamic behavior of geochemical reservoirs can be sensitive to their chemical environments in the upper mantle.

Mesoscale calculations of the dynamic behavior of a granular ceramic

Mesoscale calculations have been conducted in order to gain further insight into the dynamic compaction characteristics of granular ceramics. The primary goals of this work are to numerically determine the shock response of granular tungsten carbide and to assess the feasibility of using these results to construct the bulk material Hugoniot. Secondary goals include describing the averaged compaction wave behavior as well as characterizing wave front behavior such as the strain rate versus stress relationship and statistically describing the laterally induced velocity distribution. The mesoscale calculations were able to accurately reproduce the experimentally determined Hugoniot slope but under predicted the zero pressure shock speed by 12%. The averaged compaction wave demonstrated an initial transient stress followed by asymptotic behavior as a function of grain bed distance. The wave front dynamics demonstrate non-Gaussian compaction dynamics in the lateral velocity distribution and a power-law strain rate–stress relationship.

On the indentation contact area of a creeping solid during constant-strain-rate loading by a sharp indenter

Poly(methyl methacrylate) was contacted by a Berkovich indenter at a range of constant loading strain rates. This particular loading scheme was used to maintain the strain-rate-dependent elastic modulus and indentation hardness of the creeping solid constant throughout loading. A loading curve analysis method identical to that of Malzbender and de With but based on the elastic-perfectly plastic contact model of Hochstetter et al. [Tribol. Int.36, 973–985, 2003] was used to process the load-displacement curves. Using the analysis method together with the strain-rate-dependent elastic modulus of the creeping solid known a priori, the strain-rate-dependent hardness could then be predicted. The predicted hardness versus strain-rate relationship was compared with that evaluated from the observed topographic images of the residual impressions due to heavier indentations at three constant loading strain rates. Based on this comparison, the elastic-perfectly plastic contact model was shown to be applicable to the creeping solid only when deformation takes place at a quasi-static strain rate.

Effect of Contact Force Models on Granular Flow Dynamics

The contact force model consisting of a linear spring dashpot with a frictional glider has been widely adapted to simulate granular flows. Real contact mechanics between two solid bodies is very complicated. Extensive theoretical and experimental studies exist for binary contacts. Very little work has been reported that addresses the effect of contact mechanics on the bulk behavior of granular materials. We first briefly summarize the difference of binary contacts between a linear spring–dashpot model and the Hertzian nonlinear spring with two nonlinear dashpot models. We then compare the constitutive behaviors of a granular material using a linear and a nonlinear model. The stress- and strain-rate relation in simple shear flow and the resulting coordination number are calculated using the discrete element method. It is found that although at the grain level binary contact between two particles depends on whether a linear or a nonlinear model is used, the bulk behavior of granular materials is qualitative...

Effects of molecular characteristics and processing conditions on melt‐drawing behavior of ultrahigh molecular weight polyethylene

AbstractThe effects of molecular characteristics and processing conditions on melt‐drawing behavior of ultrahigh molecular weight polyethylene (UHMW‐PE) are discussed, based on a combination of in situ X‐ray measurement and stress–strain behavior. The sample films of metallocene‐ and Ziegler‐catalyzed UHMW‐PEs with a similar viscosity average MW of ∼107 were prepared by compression molding at 180 °C. Stress profiles recorded at 160 °C above the melting temperature of 135 °C exhibited a plateau stress region for both films. The relative change in the intensities of the amorphous scattering recorded on the equator and on the meridian indicated the orientation of amorphous chains along the draw axis with increasing strain. However, there was a substantial difference in the subsequent crystallization into the hexagonal phase, reflecting the molecular characteristics, that is, MW distribution of each sample film. Rapid crystallization into the hexagonal phase occurred at the beginning point of the plateau stress region in melt‐drawing for metallocene‐catalyzed UHMW‐PE film. In contrast, gradual crystallization into the hexagonal phase occurred at the middle point of the plateau stress region for the Ziegler‐catalyzed film, suggesting an ease of chain slippage during drawing. These results demonstrate that the difference in the MW distribution due to the polymerization catalyst system dominates the phase development mechanism during melt‐drawing. The effect of the processing conditions, that is, the including strain rate and drawing temperature, on the melt‐drawing behavior is also discussed. The obtained results indicate that the traditional temperature–strain rate relationship is effective for transient crystallization in to the hexagonal phase during melt‐drawing, as well as for typically oriented crystallization during ultradrawing in the solid state. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2455–2467, 2006

Characteristics of temporalspatial parameters in quasisolid-fluid phase transition of granular materials

The quasi-solid-fluid phase transition of granular materials is closely related to the shear rate and solid concentration in addition to their intrinsic properties. The contact duration and the coordination number are two important temporal-spatial parameters to describe the granular interaction in phase transition. In this study, characteristics of the contact duration and the coordination number associated with the transition processes are determined using a 3D discrete element model under different shear rates and concentrations. The resulting macroscopic stress and strain-rate relations are discussed. The temporal and spatial parameters provide a linkage between the macroscopic constitutive law and interparticle micromechanics.

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

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

Uniform principle on stress, strain and yield locus for analysing metal forming processes: the contribution of Prof. Z.R. Wang

A new theory concerning a consistent relationship between stress and strain components and associated studies are reviewed. This theory was contributed by Prof. Z.R. Wang. Discussion focuses on the applications of qualitative analyses with respect to metal forming processes. From an application point of view, this theory extends the fundamental concept of plastic stress and strain-rate relations, and then leads to a proposal for the relation between stress and total strain components. Emphasis is given to the theory by which engineering problems can be solved and the simplicity of practical use, such as the relations between stress, strain and yield locus with respect to a metal forming process. Determinations of the locations of typical metal forming processes in plane-stress, or in a three-dimensional stress state are presented.

C*estimation for cracks in mismatched welds and finite element validation

A C* integral estimation method is proposed for a crack located in the weld with a mismatch in mechanical properties from the surrounding base material. The method involves the definition of an equivalent stress-creep strain rate (ESCSR) relationship based on the mechanical properties of both the weld and base materials and the geometrical dimension of welding seam. The value of creep fracture mechanics parameter C*, for the mismatched weldment, is then estimated using the proposed ESCSR in conjunction with the reference stress (RS) method where the reference stress is defined based on the plastic limit load and the GE/EPRI estimation scheme. Referring to the equivalent stress-plastic strain (ESPS) curve in R6 and SINTAP procedures, an approximate solution for the ESCSR relationship has been obtained. Detailed formulae for the compact tension (CT) specimens have been derived on the basis of limit load solutions. Nonlinear finite element analysis of 48 cases with various degrees of mismatch in creep behaviour and different dimension of welding seam has been performed for CT specimens. Overall good agreement between the ESCSR method and the FE results provides confidence in the use of the proposed method in practice.

Guest Editorial

Guest Editorial

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

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

Ice flow at low deviatoric stress

AbstractThe effective viscosity of ice depends upon many factors, including temperature, deviatoric stress, crystal orientation and impurities. A flow law that includes these factors and is simple to implement is a requirement for numerically efficient ice-flow models. The dominant microscale flow mechanism changes as temperature, deviatoric stress or grain-size changes. For both anisotropic and isotropic constitutive relations, this shift in dominant flow mechanism is expressed as a change in the stress exponent. We study the effects of this shift in stress exponent on ice flow using a two-term flow law for isotropic ice. Our stress–strain-rate relationship does not explicitly describe the microscale processes of ice deformation; however, it encompasses a range of deformation behaviors with a simple law. In terrestrial ice, a flow-mechanism shift may occur in low-deviatoric-stress regions near ice divides, resulting in a near-linear constitutive relationship for ice flow. Compared to a non-linear (Glen) divide, a divide dominated by a near-linear flow mechanism has vertical-velocity profiles that are similar at divide and flank sites, internal layers that do not develop a Raymond bump, and a steady-state surface profile that is more rounded near the divide.

FE simulation of rectangular box forming using material characteristics from the multi-dome forming test

The finite element (FE) simulation of superplastic rectangular box forming process was conducted to examine the validity of the material characteristics, stress–strain rate relationship, strain rate sensitivity, m, and strength coefficient, K, which have been obtained by utilising a multi-dome test. The simulation results were then compared with those obtained with material characteristics from the tensile jump test. The material characteristics m and K were included as variable parameters and a function of the strain rate in a special subroutine. The subroutine was linked to the FE simulation in order to investigate the correctness of the superplastic material characteristics. The influence of die shape factor (length-to-width-to-depth ratio) and die friction on the deformation behaviour and on the final thickness distribution was also demonstrated. The results of rectangular box forming simulation revealed that the multi-dome test can be used not only in simple processes (such as free bulge-forming) but also in more complex situations such as rectangular box forming process and with consideration of the friction between the sheet metal and the die surface.

Dynamic tensile deformation and fracture of metal cylinders at high strain rates

An experimental study has been presented on the radial deformation of aluminium and copper cylinders of internal diameter 52 mm and wall thickness 1–7 mm, internally loaded with high explosives. High speed photography and flash radiography have been employed to record the distance–time ( x– t) history of the cylinder wall, which has been found to expand under strain rates of 10 4–10 5 s −1. The rupture of the cylinder is identified by the leakage of detonation gases, through the cracks in the cylinder wall. Rupture strains of 70–160% have been found for commercially pure aluminium. For a fixed wall thickness, the rupture strain increases with the strain rate. However, when the cylinder wall thickness is changed, a maximum is observed in a graph showing the strain and strain rate relationship. Aluminium appears to follow the Ivanov rupture criteria. From the experimental data the macroscopic viscosity coefficient for aluminium has been found to be 0.55–0.87×10 3 Pa s. In the deformation of a copper cylinder the cracks initiate at strains of 30–60%, followed by rupture at very high strains up to 300%. The crack propagation velocity through the copper cylinder wall has been found to be 250–300 m/s. Recovered fragments show wall thinning by 50–60% and also exhibit shear fracture which dominates the radial fracture in high velocity deformation of the metal cylinder.

Comparative study of a high-strain-rate superplastic Al-4.4Cu-1.5Mg/21SiCW sheet under uniaxial and equibiaxial tension

In this paper, the strain rate sensitivity exponent and the cavitation behavior of a high-strain-rate superplastic Al-4.4Cu-1.5Mg/21SiCW sheet were examined under uniaxial and equibiaxial tension at the optimal temperature of 793 K. A maximum elongation of about 335% was obtained at the initial strain rate of 0.17 s−1. It was found that the strain rate sensitivity of the composite under uniaxial and equibiaxial tension was 0.34 and 0.36, respectively. The reasons for a large discrepancy between uniaxial and equibiaxial stress versus strain rate curves were analyzed. It was concluded that the flow stress–strain rate relationship determined from uniaxial tension could be used for forming processes subject to complex stress states after proper adjustment. The amount of cavity was found to increase with increasing strain and the amount of cavity obtained under equibiaxial tension was slightly larger than that under uniaxial tension at the same effective strain rate. A slightly higher cavity growth rate parameter was also observed under equibiaxial tension. The experimental results revealed that the cavity growth was essentially plastic-controlled. It was suggested that the presence of liquid phase was beneficial to nucleation at the interfaces and limited the cavity growth rate.

Diffusional Creep: Stresses and Strain Rates in Thin Films and Multilayers

AbstractIn this article, we discuss creep deformation as it relates to thin films and multilayer foils. We begin by reviewing experimental techniques for studying creep deformation in thin-film geometries, listing the pros and cons of each; then we discuss the use of deformation-mechanism maps for recording and understanding observed creep behavior. We include a number of cautionary remarks regarding the impact of microstructural stability, zero-creep stresses, and transient-creep strains on stress–strain rate relationships, and we finish by reviewing the current state of knowledge for creep deformation in thin films. This includes both thin films that are heated on substrates as well as multilayer films that are tested as freestanding foils.

Modeling of ice flow and internal layers along a flowline through Swiss Camp, West Greenland

AbstractAn anisotropic-ice flowline model is applied to a flowline through Swiss Camp (69.57° N, 49.28° W), West Greenland, to estimate the dates of internal layers detected by radio-echo sounding measurements. The effect of an anisotropic-ice fabric on ice flow is incorporated into the steady-state flowline model. The stress–strain-rate relationship for anisotropic ice is characterized by an enhancement factor based on the laboratory observations of ice deformation under combined compression and shear stresses. By using present-day data of accumulation rate, surface temperature, surface elevation and ice thickness along the flowline as model inputs, a very close agreement is found between the isochrones generated from the model and the observed internal layers with confirmed dates. The results indicate that this part of the Greenland ice sheet is primarily in steady state.

Modeling the viscoplastic behaviour of clays during consolidation: application to Berthierville clay in both laboratory and field conditions

To analyze the effects of strain rate and viscoplastic strain on consolidation of natural clay, this paper presents a nonlinear viscoplastic model in which viscoplastic behaviour is modeled by a unique effective stress (σ'v) – viscous strain (εv) – viscous strain rate (ε·v) relationship. The proposed model can consider the effects of strain rate and viscoplastic strain on consolidation, to take into account the difference in strain rate between laboratory and field conditions, and the combined processes of generation and dissipation of pore pressure during consolidation. This model can also predict the behaviour of clay during stepwise loading, constant rate of strain, and relaxation of effective stress. The predicted values using numerical analysis are compared with measured values in laboratory tests and in situ, under an embankment built on soft clay at Berthierville, Quebec. It is possible to estimate the consolidation behaviour of natural clay with reasonable accuracy using the proposed nonlinear viscoplastic model.Key words: consolidation, soft clay, strain rate, viscoplastic, relaxation.