Showing papers on "Strain rate published in 1972"

Rheological Equations from Molecular Network Theories

Abstract: Lodge's molecular network theories are quite successful in describing the linear viscoelastic behavior of polymer solutions and melts, but cannot account for the rate‐of‐strain dependence of various material functions By allowing the junction‐creation rate and the probability of loss of junctions to depend on the second invariant of the rate‐of‐strain tensor, more realistic constitutive equations were obtained Two rheological models are proposed by assuming two different mechanisms for the effect of the rate of strain on the kinetics of the network The experimental data on three fluids (representative of eight viscoelastic fluids) are used to test the models in various flow situations For steady simple shearing and small‐amplitude, sinusoidal simple shearing, both model A and model B are capable of fitting the four functions η, −(τ11−τ22), η′, and G′ rather well over many decades of shear rate or frequency For suddenly changing flow experiments model A is inadequate Model B however appears to be the

Steady-State Flow in Marble at 500° to 800°C

Abstract: The stress-strain behavior of Yule marble, both parallel and normal to the foliation, has been determined in a series of constant strain-rate extension tests at 5000 bars confining pressure, at temperatures of 500° to 800° C and at strain rates ranging from 10−3 to 10−7/sec. These data correlate well with earlier results at 25° to 500° C and l0−1 to 10−8/sec. Steady-state flow is dominant at 400° C and rates <10−7/sec, at 500° C < 10−4/sec, and at all strain rates at higher temperatures. Transient flow (work hardening) is prevalent at lower temperatures and higher rates. Transmission and reflection microscopy as well as etch-pit studies reveal that translation gliding on r, f and twinning on e are dominant in the transient region, becoming less prominent in the steady-state region at high temperatures. Polygonization by dislocation climb becomes characteristic in the steady-state flow region, along with intergranular and intra-granular recrystallization. Grain boundary sliding is present, but of minor importance. The effect of temperature and strain rate on the mechanical behavior, as well as on the correlation of subgrain formation and recrystallization with steady-state flow, is consistent with a diffusion-controlled process. Comparison of the data with several models for diffusion-controlled flow show poor correlation with the Eyring equation, e = A exp ( −E/RT) sinh (Bσ), but excellent correlation with the Weertman equation, e = C exp ( −E/RT) <σN. The activation energy E and the stress exponent N are nearly identical for both orientations of this highly anisotropic marble, and thus this material becomes nearly isotropic (mechanically) for steady-state flow. On the basis of the empirical-flow equation, extrapolations to representative natural strain rates of 3 × 10−14/sec predict stresses of 103 bars at 250° C, ranging to about 30 bars at 700° C. Work-hardening can be expected at these rates at temperatures <250° C; in this region, this marble is expected to be mechanically anisotropic. Calculated equivalent viscosities at natural strain rates range from 3 × 1022 poises at 25° to 4 × 1020 poises at 700° C.

The Temperature Dependence of Yield of Polycarbonate in Uniaxial Compression and Tensile Tests

Abstract: The tensile yield stress is compared with the uniaxial compression yield stress for specimens of polycarbonate tested at constant strain rate from −120 to + 120°C. The strain rate dependence of the tensile yield stress is also studied from − 140 to + 20°C.

Creep of Discontinuous Fibre Composites. II. Theory for the Steady-State

Abstract: A simple theory is developed to explain the results of paper I, for the steady-state creep of a fibre composite containing alined discontinuous fibres. Rigid and creeping fibres are considered and also the effect of sliding at the interface. The physical basis of the theory is that due to the presence of the fibres the rate of shearing of the matrix is increased. An assumption is made that this increase is inversely proportional to the fibre separation. It is shown that the assumption is not critical for large values of the exponent relating strain rate and stress of the matrix. The theory accounts for the experimental results in paper I, predicts how the strain rate sensitivity of the composite will depend on those of fibre and matrix and reduces to a known form for a Newtonian fluid.

Sub-grain boundary migration in aluminium

Abstract: Observations on the migration of sub-grain boundaries during high-temperature testing of aluminium are presented. It is shown that the migration contributes significantly to the overall strain rate of the specimen and that the stress dependence and temperature dependence are in accord with the macroscopic strain rate, and are strictly related to the deformation contribution from fine slip. The mobility of the sub-boundaries leads to a new understanding of the dynamic equilibrium of the sub-structure and its stability with respect to recrystallization. It further leads to the possibility of sub-boundaries acting both as effective obstacles to deformation and as sources of internal stress.

The Dynamic Stress-Strain Behavior in Torsion of 1100-0 Aluminum Subjected to a Sharp Increase in Strain Rate

Abstract: : A modification of the torsional split Hopkinson bar is described which superimposes a high rate of shear strain on a slower 'static' rate. The 'static' rate of 0.00005/sec is increased to 850/sec at a predetermined value of plastic strain by the detonation of small explosive charges; the rise time of the strain rate increment is about 10 microseconds. During deformation at the dynamic rate, direct measurement is made of the excess stress above the maximum static stress attained. Results for 1100-0 aluminum show that the initial response to the strain rate increment is elastic, followed by yielding behavior reminiscent in appearance to an upper yield point. The magnitude of the stress measured at this yield point is always less than the stress obtained at the same strain in a wholly dynamic test; as the stress-strain curve asymptotically. It is concluded that the material behavior is a function of strain, strain rate and strain rate history. (Author)

Temperature effects on the strainrange partitioning approach for creep-fatigue analysis

Abstract: Examination is made of the influence of temperature on the strainrange partitioning approach to creep-fatigue. Results for Cr-Mo steel and Type 316 stainless steel show the four partitioned strainrange-life relationships to be temperature insensitive to within a factor of two on cyclic life. Monotonic creep and tensile ductilities were also found to be temperature insensitive to within a factor of two. The approach provides bounds on cyclic life that can be readily established for any type of inelastic strain cycle. Continuous strain cycling results obtained over a broad range of high temperatures and frequencies are in excellent agreement with bounds provided by the approach. The observed transition from one bound to the other is also in good agreement with the approach.

Biaxial stress relaxation in glassy polymers - Polymethylmethacrylate.

Abstract: Biaxial stress relaxation studies were performed on glassy polymethylmethacrylate in combined torsion-tension strain fields using a specially designed apparatus with exceptionally high stiffness and low cross talk between the torsional and tensile load measuring transducers. It was found that at low strain levels uniaxial tension relaxation is slower than pure torsion relaxation; tensile-component relaxation rates are unaffected by the level of torsional strain; torsional-component relaxation rates decrease as tensile strain is increased; uniaxial tension relaxation rates approach the pure torsion rates at higher strains (about 2%). A phenomenological treatment is presented which shows that relaxation rates can be coupled to the strain fields in which they are observed and yet be consistent with the concepts of linear viscoelasticity and the Boltzmann superposition integral.

The Effects of Phosphorus on the Mechanical Properties of Low-Carbon Iron

Abstract: Fe-P alloys with nominal compositions of 0.05, 0.1, 0.2, and 0.6 wt pet P were deformed in compression at temperatures between 77 and 295 K at strain rates between 2.5 x 10-4 and 3.5 x 10-2 per sec. The effect of grain size on the yield strength was investigated over a range of about ASTM 7 to 3.5. The results show that the yield strength of iron is increased 40 to 50 pet in the 0.05 and 0.1 P alloys at 295 K without affecting the notch impact transition temperature. At temperatures of 200 K and below solid solution softening occurs in all the alloys except for 0.6 pet P. The degree of softening at a given temperature is a function of the strain rate and grain size, being more pronounced at higher strain rates and larger grain sizes.

Plastic flow in binary substitutional alloys of BCC iron-effects of wire drawing and alloy content on work hardening and ductility

Abstract: The strength of cold-drawn, titanium-gettered iron wires can be substantially increased by substitutional solutes. For the elements studied, strengthening is progressively less in the order Si, Pt, Mn, Ni, Cr, and Co. The strengthening effect of the solute increases with strain, but at a greatly diminishing rate for true strains greater than unity. Six at. pct Si reduces the strain necessary to achieve a tensile strength of 200,000 psi (1380 MN/m2) from 7.3 for iron to 3.7. This effect of alloying on strain hardening appears to be related to the strength of the annealed alloy rather than to the specific alloying element used to achieve that strength. Also, the reduction-of-area ductility of the drawn wires is more closely related to the tensile strength of the wire than to its alloy content or degree of cold work. A fibrous cellular substructure is formed in all the alloys, but the formation of these cells is displaced to higher strains, the greater the strengthening effect of the solute. The transition from homogeneously distributed, tangled dislocations to a cellular substructure has no effect on the rate of strain hardening of the alloy-alloying can be used effectively as a substitute for cold work without adversely affecting the resistance of the alloy to ductile failure.

The Effect of Strain History on the Crystallization Behavior of Bulk Poly(ethylene Terephthalate)

Abstract: The crystallization of bulk tensile samples of glassy, amorphous poly(ethylene terephthalate) was studied as a function of various deformation and annealing treatments. Per cent crystallinity, orientation function, crystallite size, and long period spacing were measured to characterize the samples. Crystallization, necking, and orientation occurred during straining when, at a given temperature, the strain rate was sufficient to generate a critical stress level within the material. During subsequent annealing crystallization was nucleated by the crystallites formed during deformation. The observed behavior was consistent with a model proposed by Dismore and Statton for drawn nylon 66 yarns and which was previously discussed by Dumbleton for the case of poly(ethylene terephthalate).

Reinforcement of structural materials by Long Strong Fibres

Abstract: Materials which flow at low stresses such as soft metals or plastics, can be strengthened by incorporation of stronger fibres. The mechanical principles governing this reinforcement are presented in a fashion applicable to discontinuous fibres and to matrices which have flow stresses dependent upon the strain rate. The strengths attainable by composites containing discontinuous fibres are discussed. Compliant matrices of small breaking strain,e.g. cement or plaster, are reinforced with fibres in order to prevent a single crack leading to rupture of the composite. The rules governing the density of cracks, the stress-strain curve of the composite and the cracking strain of the matrix within the composite are discussed and applied. Finally the relationship between fibre reinforcement and dispersion hardening is commented upon and the ways in which fibres interfere with dislocation motion and rearrangement discussed.

Crenulation Cleavage and Faulting in an Artificial Salt-Mica Schist

Abstract: A synthetic foliated material made of mica flakes and NaCl has been compressed normal to the foliation, in plane strain, with and without interstitial brine, at room temperature. The experiments have employed confining pressures to 2,070 bars, and strain rates from $$10^{-4}sec^{-1} to 10^{-6}sec^{-1}$$. Specimens deformed with brine are weak and ductile compared with specimens deformed dry. A specimen run with kerosine shows intermediate strength. The deformed specimens are traversed by conjugate sets of planar discontinuities, the character of which is sensitive to strain rate, confining pressure, and nature of the pore fluid. In wet specimens deformed at medium strain rate typical discontinuities are morphologically identical with natural crenulation cleavage. In comparable specimens run dry or with kerosine, typical discontinuities are more faultlike. A transition from faulting toward cleavage development is effected in dry specimens by increasing confining pressure and can be obtained in wet specimen...

A study of the relationships between time, strength, deformation and fracture of plain concrete

Abstract: Synopsis A review of previous work shows that the relationship between compressive strength and rate of strain for concrete is dependent upon curing conditions, strength and age. Tests are reported in which for strain rates slower than 2·5 7times; 10−4/s the strength of concrete was independent of strain rate. The applicability to concrete of a criterion recently established for a sandstone is examined. This criterion is based upon the incremental Poisson's ratio and defines the critical stress of concrete. The use of cored and sawn concrete cylinders produced uniform fracturing of test specimens and facilitated the study of fracture patterns resulting from varying strain rates and load histories.

Dislocation motion in pure NaCl at low temperatures

Abstract: In annealed NaCl crystals of high purity, dislocation displacements under stress pulses at various temperatures obey Poisson type distributions which spread out toward larger distances with increasing time at constant stress. The calculated thermally-penetrable obstacle density of 105 cm−2 corresponds to that of the grown-in forest dislocations. The measurements suggest that the forest dislocations are flexible and are plucked by the glide dislocations at intersection, resulting in a displacement of the mechanical threshold stress to higher levels, and in an unusually small activation distance. The increase in the calculated activation distances with temperature suggests a split core. The stress dependence of the strain rate at yielding is compatible with the velocity-stress measurements for individual dislocations when account is taken of the stress dependence of the mobile dislocation density and of a temperature-dependent internal stress which results from multiplication of screw dislocations ...

The propagation and growth of acceleration waves in heat-conducting elastic materials

Abstract: In the thermo-mechanical theory of continua an acceleration wave may be defined as a propagating singular surface on which the strain, velocity, temperature and entropy are continuous and on which discontinuities in acceleration, strain rate and strain gradient occur. We study here basic properties of such waves in homogeneous heat-conducting elastic bodies, placing no restriction on the symmetry of the material. In a paper which has strongly influenced the course of recent research in the theory of non-linear elastic waves TRUESDELL [1961] has discussed the propagation of acceleration waves through a finitely strained material according to the purely mechanical theory of elasticity. The central result in this analysis is the FRESNEL-HADAMARD theorem, requiring the acceleration amplitude of a wave travelling in a given direction to be a right proper vector of a certain tensor, called the acoustical tensor, which depends upon the direction of propagation and the state of deformation at the location of the wave. The wave speed is determined by the proper number of the acoustical tensor associated with the acceleration amplitude, and thus in a given direction there are up to three speeds with which an acceleration wave can propagate, different speeds corresponding to distinct amplitudes. The FRES~,mL-HADAMARO theorem determines the direction of the acceleration amplitude but places no restriction on its magnitude. For plane acceleration waves propagating through a homogeneously deformed isotropic elastic material GREEN [1964, 1965] has shown that the magnitude of the acceleration amplitude either increases without bound over a finite interval of the time t, decays towards zero as t ~ ~ , or remains constant. These results have been extended to acceleration waves of arbitrary form by CHEN [1968, 1, 2] and JtrNEJA & NARiBOLI [1970], and to general elastic materials by CrrEN [1970, 1, 2] (in respect of longitudinal and transverse waves*) and CHADWICK & OGDEN [1971, 1]. An analysis of the growth of acceleration waves in hyperelastic materials embracing both of these generalizations has been given by SUI-IVBI [1970], and BOWEN & WANG [1970] have studied.

Triaxial stress behavior of Solenhofen limestone and westerly granite at high strain rates

Abstract: Constant strain rate tests were conducted on solid cylinders and thin-walled hollow cylinders of Solenhofen limestone and Westerly granite. Loads and axial and transverse strains were measured to provide the stress-strain response and to define the brittle failure or ductile yield locus. Tests were conducted at confining pressures to 3 kb and strain rates to 103/sec. The strength of the rocks is strain rate sensitive; i.e., somewhat increased strength with strain rate is shown. Stiffness and compressibility are stress state dependent and for Westerly granite, also strain rate dependent at low confining pressures.