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Modified spectrometer system with a low-noise preamplifier reduces rate-dependent distortions at high counting rates, 25,000 counts per second. Pole-zero cancellation minimizes pulse undershoots due to multiple time constants, baseline restoration improves resolution and prevents spectral shifts.
In this paper the mode I fracture behavior of graphite/epoxy and graphite/PEEK composites is examined over four decades of crosshead rates (0.25-250 mm/min). Straight-sided double-cantilever-beam specimens consisting of unidirectional laminates were tested at room temperature. For graphite/epoxy the load-deflection response was linear to fracture, and stable slow crack growth initiating at the highest load level was observed for all rates tested. In contrast, mode I crack growth in the graphite/PEEK material was often unstable and showed stick-slip behavior. Subcritical crack growth occurring prior to the onset of fracture was observed at intermediate displacement rates. A mechanism for the fracture behavior of the graphite/PEEK material (based on viscoelastic, plastic, and microcrack coalescence in the process zone) is proposed and related to the observed rate-dependent phenomena.
Strain rate effect on crack growth within subcritical load range, deriving expressions for rate-independent and rate-dependent quasi-brittle solids
A new definition of loading and unloading along the yield surface of Roscoe and Burland is introduced. This is achieved by noting that the strain-hardening parameter in the plastic potential function is deduced from the yield locus equation of Roscoe and Burland. The analytical results are compared with the experimental results for plate-bearing and cone-penetrometer problems and close agreements are demonstrated. The wheel-soil interaction is studied under dynamic loading. The rate-dependent plasticity or viscoelastoplastic behavior is considered. This is accomplished by the internal (hidden) variables associated with time-dependent viscous properties directly superimposed with inelastic behavior governed by the yield criteria of Roscoe and Burland. Effects of inertia and energy dissipation are properly accounted for. Example problems are presented.
An equation governing the prior-to-failure crack propagation is proposed. For a rate-sensitive solid containing a two-dimensional crack and subject to the tensile mode of fracture the differential equations are integrated numerically for loads increasing monotonically in time. The resulting integral curves of load vs crack length and length vs time indicate that the growth of cracks in the subcritical range is strongly rate-dependent. The fatigue growth, viewed as a sequence of slow growth periods, is simulated on an EAI 380 analog computer. The fourth-power law proposed by Paris is confirmed only within certain range of high-cycle fatigue propagation and for a rate-insensitive solid. Otherwise, i.e., for a more pronounced rate dependence induced by viscosity of a solid and/or in the proximity of the final instability point, the growth is markedly enhanced.
Extension of the classical theory of fracture to viscoelastic and elastic-plastic materials in which the plasticity effects are confined to a narrow band encompassing the crack front. It is suggested that the Griffith-Irwin criterion of fracture, which requires that the energy release rate computed for a given boundary value problem equal the critical threshold, ought to be replaced by a differential equation governing the slow growth of a crack prior to the onset of rapid propagation. A new term which enters the equation of motion in the dissipative media is proportional to the energy lost within the end sections of the crack, and thus it reflects the extent of inelastic behavior of a solid. A concept of 'apparent' surface energy is introduced to account for the geometry-dependent and the rate-dependent phenomena which influence toughness of an inelastic solid. Three hypotheses regarding the condition for fracture in the subcritical range of load are compared.
The partitioning of energy and the distribution of the resultant ejecta on the moon is numerically modeled using a Eulerian finite difference grid. The impact of an iron meteoroid at 15 km/sec on a gabbroic anorthosite lunar crust is examined. The high speed impact induced flow is described over the entire hydrodynamic regime from a time where the peak pressures are 6 Mbar until the stresses everywhere in the flow are linearly elastic, and less than 5 kbar. Shock-induced polymorphic phase changes, (plagioclase and pyroxene to hollandite and perovskite), and the subsequent reversion to low pressure phases are demonstrated to enhance shock wave attenuation. A rate-dependent equation of state is used for describing the hysteretic effect of the phase change. Ballistic equations for a spherical planet are then applied to material with net velocity away from the moon.
This paper discusses nonlinear stress-wave propagation in a perfectly flexible string obeying a quasilinear (rate-dependent) constitutive equation. Wave speeds and compatibility relations valid along various families of characteristics were determined. It was shown that the compatibility relations associated with the transverse as well as the longitudinal waves readily yield a physical interpretation when they are expressed in suitable variables and in vector form. Coding based on the present information was completed for the machine solution of a class of mixed initial- and boundary-value problems of practical interest. Computer simulation of the stress-wave interaction in the 40-foot lanyard in the Arcas 'Rocoz' system during deployment was carried out using a stress-strain relation for nylon at the strain rate of 30/second. A method for estimating the maximum tension and strain in a string during the initial loading phase is proposed.
The results of a series of tensile tests on some graphite/epoxy laminates, at rates varying from 0.002 to 2 in./min are examined. The loads were applied at various angles to the fiber directions in each case. The rate-dependent behavior of the stress-strain response is assessed. Evidence is presented to indicate that failure first occurs on inner plies, and that, in some cases, moduli increase with increasing stress (or strain) level. Lamination theory is used to predict the moduli, and comparisons with experiment are given. This theory is also used in conjunction with three failure theories to predict ultimate strengths (with varying degrees of success). Further, two approaches to ply unloading after first-ply failure are used and discussed. One is a standard method found in the literature while the other is a proposed 'strength-of-materials' type of technique which is computationally much simpler.
Equilibrium and controlled cooling rate experiments on a synthetic analog of Apollo 15 quartz normative basalt 15597 are reported. While the partitioning of the major elements Ca, Mg, and Fe between pyroxene and liquid is rate independent, the K sub D parameter for Fe/Mg, which is calculated for low-Ca pyroxene, is temperature dependent. It is suggested that chemical trends observed in lunar pyroxenes are a consequence of three rate processes. The processes are (1) rate-dependent suppression of crystallization of other phases until lower temperature alters liquid composition and, therefore, the composition of the pyroxene that crystallizes; (2) the efficiency of fractional crystallization and the extent of crystal zoning are rate dependent; and (3) the partitioning of Al2O3, TiO2, and Cr2O3 between pyroxene and liquid depends on cooling rate.
The scope of any aerodynamic formulation proposing to embrace a range of possible maneuvers is shown to be determined principally by the extent to which the aerodynamic indicial response is allowed to depend on the past motion. Starting from the linearized formulation, in which the indicial response is independent of the past motion, two successively more comprehensive statements about the dependence on the past motion are assigned to the indicial response (1) dependence only on the recent past and (2) dependence additionally on a characteristic feature of the distant past. The first enables the rational introduction of nonlinear effects and accommodates a description of the rate-dependent aerodynamic phenomena characteristic of airfoils in low-speed dynamic stall; the second permits a description of the double-valued aerodynamic behavior characteristic of certain kinds of aircraft stall. An aerodynamic formulation based on the second statement, automatically embracing the first, may be sufficiently comprehensive to include a large part of the aircraft's possible maneuvers. The results suggest a favorable conclusion regarding the role of dynamic stability experiments in flight dynamics studies.
Secular resonances in the early solar system are investigated with the aim of establishing constraints on the time scale and method of solar nebula dispersal. Simplified nebula models and dispersal routines are used to approximate changes in an assumed axisymmetric nebula potential. These changes drive an evolutionary sequence of Laplace-Lagrange solutions for the secular variations of the solar system. These sequences are characterized by a sweep of one or more giant planet resonances through the inner solar system. Their effect is rate-dependent; characteristic dispersal times of not greater than 10,000 to 100,000 years are required to avoid the generation of terrestrial eccentricities and inclinations in excess of observed values.
Among the topics discussed are developments in structural engineering hardware and software, computation for fracture mechanics, trends in numerical analysis and parallel algorithms, mechanics of materials, advances in finite element methods, composite materials and structures, determinations of random motion and dynamic response, optimization theory, automotive tire modeling methods and contact problems, the damping and control of aircraft structures, and advanced structural applications. Specific topics covered include structural design expert systems, the evaluation of finite element system architectures, systolic arrays for finite element analyses, nonlinear finite element computations, hierarchical boundary elements, adaptive substructuring techniques in elastoplastic finite element analyses, automatic tracking of crack propagation, a theory of rate-dependent plasticity, the torsional stability of nonlinear eccentric structures, a computation method for fluid-structure interaction, the seismic analysis of three-dimensional soil-structure interaction, a stress analysis for a composite sandwich panel, toughness criterion identification for unidirectional composite laminates, the modeling of submerged cable dynamics, and damping synthesis for flexible spacecraft structures.
The Double Cantilever Beam (DCB) and the End Notched Flexure (ENF) specimens are employed to characterize MODE I and MODE II interlaminar fracture resistance of graphite/epoxy (CYCOM 982) and graphite/PEEK (APC2) composites. Sizing of test specimen geometries to achieve crack growth in the linear elastic regime is presented. Data reduction schemes based upon beam theory are derived for the ENF specimen and include the effects of shear deformation and friction between crack surfaces on compliance, C, and strain energy release rate, G sub II. Finite element (FE) analyses of the ENF geometry including the contact problem with friction are presented to assess the accuracy of beam theory expressions for C and G sub II. Virtual crack closure techniques verify that the ENF specimen is a pure Mode II test. Beam theory expressions are shown to be conservative by 20 to 40 percent for typical unidirectional test specimen geometries. A FE parametric study investigating the influence of delamination length and depth, span, thickness and material properties on G sub II is presented. Mode I and II interlaminar fracture test results are presented. Important experimental parameters are isolated, such as precracking techniques, rate effects, and nonlinear load-deflection response. It is found that subcritical crack growth and inelastic materials behavior, responsible for the observed nonlinearities, are highly rate-dependent phenomena with high rates generally leading to linear elastic response.
In developing the constitutive equations an interdisciplinary approach is being pursued. Specifically, both metallurgical and continuum mechanics considerations are recognized in the formulation. Experiments will be utilized to both explore general qualitative features of the material behavior that needs to be modeled and to provide a means of assessing the validity of the equations being developed. The model under development explicitly recognizes crystallographic slip on the individual slip systems. This makes possible direct representation of specific slip system phenomena. The present constitutive formulation takes the anisotropic creep theory and incorporates two state variables into the model to account for the effect of prior inelastic deformation history on the current rate-dependent response of the material.
Mechanical properties and morphology of poly(etheretherketone) (PEEK) were studied for samples having different thermal histories. Isothermal and rate-dependent crystallization were studied to ascertain the relationship between crystallinity/morphology and processing condition. Degree of crystallinity and microstructure were controlled by cooling the melt at different rates, ranging from quenching to slowly cooling, and by annealing amorphous material above the glass transition temperature Tg. It is found that degree of crystallinity was not as important as processing history in determining the room temperature mechanical properties. Samples with the same degree of crystallinity had very different tensile properties, depending on rate of cooling from the melt. All samples yielded by shear band formation and necked down. Quenched films had the largest breaking strains, drawing to 270 percent. Slowly cooled films exhibited ductile failure at relatively low strains. Best combined mechanical properties were obtained from semicrystalline films cooled at intermediate rates from the melt.
The purpose of this research is to develop a tool for the mechanical analysis of nickel-base single-crystal superalloys, specifically Rene N4, used in gas turbine engine components. This objective is achieved by developing a rate-dependent anisotropic constitutive model and implementing it in a nonlinear three-dimensional finite-element code. The constitutive model is developed from metallurgical concepts utilizing a crystallographic approach. An extension of Schmid's law is combined with the Bodner-Partom equations to model the inelastic tension/compression asymmetry and orientation-dependence in octahedral slip. Schmid's law is used to approximate the inelastic response of the material in cube slip. The constitutive equations model the tensile behavior, creep response and strain-rate sensitivity of the single-crystal superalloys. Methods for deriving the material constants from standard tests are also discussed. The model is implemented in a finite-element code, and the computed and experimental results are compared for several orientations and loading conditions.
Selected results of cardiocirculatory measurements in healthy volunteers who breathed 100 percent O2 continuously at 3.0 ATA for up to 3.5 hr, at 2.5 ATA for up to 6.0 hr, at 2.0 ATA for up to 11.9 hr, and at 1.5 ATA for up to 19.0 hr are reported. The results indicate that resting hemodynamic responses to prolonged hyperbaric oxygen breathing in man usually consist of small deviations from normal sea-level responses. Rapid onset of bradycardia occurred at all four oxygen pressures investigated. This effect was accompanied by a rate-dependent reduction in cardiac output and a degree of systematic vasoconstriction which were small in magnitude and appeared to be functionally unimportant.