Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “strain rate”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13

The viscoplastic behavior of Hastelloy-X single crystal

A viscoplastic constitutive model for simulating the behavior of Hastelloy-X single crystal material was derived based on crystallographic slip theory. To determine the appropriate constitutive model constants and to test the predictions of the model, tests on Hastelloy-X crystals were carried out, including the rate sensitivity, cyclic hardening, nonproportional hardening, relaxation, and strain rate dip tests. It was found necessary to include cube slip in the model in order to correlate the uniaxial behavior of the single crystal, to incorporate the interaction effects in both the hardening and the dynamic recovery evolution equations for the drag stress, and to successfully capture correct strain rate sensitivity under biaxial tension-torsion loading conditions.

Jordan, Eric H.↗

Optimal measurement of ice-sheet deformation from surface-marker arrays

Surface strain rate is best observed by fitting a strain-rate ellipsoid to the measured movement of a stake network or other collection of surface features, using a least squares procedure. Error of the resulting fit varies as 1/(L delta t square root of N), where L is the stake separation, delta is the time period between initial and final stake survey, and n is the number of stakes in the network. This relation suggests that if n is sufficiently high, the traditional practice of revisiting stake-network sites on successive field seasons may be replaced by a less costly single year operation. A demonstration using Ross Ice Shelf data shows that reasonably accurate measurements are obtained from 12 stakes after only 4 days of deformation. It is possible for the least squares procedure to aid airborne photogrammetric surveys because reducing the time interval between survey and re-survey permits better surface feature recognition.

Macayeal, D. R.↗

Optimal measurement of ice-sheet deformation from surface-marker arrays

Surface strain rate is best observed by fitting a strain-rate ellipsoid to the measured movement of a stake network or other collection of surface features, using a least squares procedure. Error of the resulting fit varies as 1/(L delta t square root of N), where L is the stake separation, delta is the time period between initial and final stake survey, and n is the number of stakes in the network. This relation suggests that if n is sufficiently high, the traditional practice of revisiting stake-network sites on successive field seasons may be replaced by a less costly single year operation. A demonstration using Ross Ice Shelf data shows that reasonably accurate measurements are obtained from 12 stakes after only 4 days of deformation. It is possible for the least squares procedure to aid airborne photogrammetric surveys because reducing the time interval between survey and re-survey permits better surface feature recognition.

Macayeal, D. R.↗

Determining damping mechanisms in a composite beam by experimental modal analysis

A method of estimating the distributed damping parameters of a beam based on measured modal parameters (frequency and damping ratios) is derived. Three different mathematical models were used to model the damping mechanism of a quasi-isotropic pultruded cantilevered beam. These three models were (1) viscous (air) damping, (2) strain-rate damping, and (3) both viscous and strain-rate damping. Values were obtained for each of the damping models as well as the modulus of elasticity of the beam. It is found that the two-parameter damping model provides the best fit to measure modal data. However, the two-parameter damping model can only reproduce the measured damping ratios to within 85 percent.

Cudney, H. H.↗

1300 K compressive properties of a reaction milled NiAl-AlN composites

When B2 crystal-structure nickel aluminide is subjected to high-intensity mechanical ball milling in a liquid nitrogen bath, or 'cryomilling', an NiAl composite is obtained which contains about 10 vol pct AlN particles. This composition arises from the incorporation of N during cryomilling; during subsequent thermomechanical processing, the N reacts with Al. While compressive testing of extruded or isostatically pressed specimens at 1300 K indicated that strength at relatively fast strain rates is slightly dependent on consolidation method, slower strain rates indicate no clear dependency on densification technique: four different consolidation methods were found to yield similar creep strengths. The creep properties of NiAl-AlN are similar to those of the single-crystal Ni-base superalloy NASAIR 100.

Whittenberger, J. Daniel↗

Microstructure and Mechanical Properties of Extruded Gamma Met PX

A gamma TiAl alloy with a high Nb content is being assessed as a compressor blade material. The microstructure and mechanical properties of extruded Ti-45Al-X(Nb,B,C) (at %) were evaluated in both an as-extruded condition and after a lamellar heat treatment. Tensile behavior of both as-extruded and lamellar heat treated specimens was studied in the temperature range of RT to 926 C. In general, the yield stress and ultimate tensile strength reached relatively high values at room temperature and decreased with increasing deformation temperature. The fatigue strength of both microstructures was characterized at 650 C and compared to a baseline TiAl alloy and to a Ni-base superalloy. Tensile and fatigue specimens were also exposed to 800 C for 200 h in air to evaluate the alloy's environmental resistance. A decrease in ductility was observed at room temperature due to the 800 C exposure but the 650 C fatigue properties were unaffected. Compressive and tensile creep testing between 727 and 1027 C revealed that the creep deformation was reproducible and predictable. Creep strengths reached superalloy-like levels at fast strain rates and lower temperatures but deformation at slower strain rates and/or higher temperature indicated significant weakening for the as-extruded condition. At high temperatures and low stresses, the lamellar microstructure had improved creep properties when compared to the as-extruded material. Microstructural evolution during heat treatment, identification of various phases, and the effect of microstructure on the tensile, fatigue, and creep behaviors is discussed.

Draper, S. L.↗

Microstructure and Mechanical Properties of Extruded Gamma Microstructure Met PX

A gamma TiAl alloy with a high Nb content is being assessed as a compressor blade material. The microstructure and mechanical properties of extruded Ti-45Al-X(Nb,B,C) (at.%) were evaluated in both an as-extruded condition and after a lamellar heat treatment. Tensile behavior of both as-extruded and lamellar heat treated specimens was studied in the temperature range of RT to 926 C. In general, the yield stress and ultimate tensile strength reached relatively high values at room temperature and decreased with increasing deformation temperature. The fatigue strength of both microstructures was characterized at 650 C and compared to a baseline TiAl alloy and to a Ni-base superalloy. Tensile and fatigue specimens were also exposed to 800 C for 200 h in air to evaluate the alloy's environmental resistance. A decrease in ductility was observed at room temperature due to the 800 C. exposure but the 650 C fatigue properties were unaffected. Compressive and tensile creep testing between 727 and 1027 C revealed that the creep deformation was reproducible and predictable. Creep strengths reached superalloy-like levels at fast strain rates and lower temperatures but deformation at slower strain rates and/or higher temperature indicated significant weakening for the as-extruded condition. At high temperatures and low stresses, the lamellar microstructure had improved creep properties when compared to the as-extruded material. Microstructural evolution during heat treatment, identification of various phases, and the effect of microstructure on the tensile, fatigue, and creep behaviors is discussed.

Draper, S. L.↗

Detailed Studies on the Structure and Dynamics of Reacting Dusty Flows at Normal and Microgravity

Dusty reacting flows are of particular interest for a wide range of applications. Inert particles can alter the flammability and extinction limits of a combustible mixture. Reacting particles can release substantial amount of heat and can be used either for power generation or propulsion. Accumulation of combustible particles in air can result in explosions which, for example, can occur in grain elevators, during lumber milling and in mine galleries. Furthermore, inert particles are used as flow velocity markers in reacting flows, and their velocity is measured by non-intrusive laser diagnostic techniques. Despite their importance, dusty reacting flows have been less studied and understood compared to gas phase as well as sprays. The addition of solid particles in a flowing gas stream can lead to strong couplings between the two phases, which can be of dynamic, thermal, and chemical nature. The dynamic coupling between the two phases is caused by the inertia that causes the phases to move with different velocities. Furthermore, gravitational, thermophoretic, photophoretic, electrophoretic, diffusiophoretic, centrifugal, and magnetic forces can be exerted on the particles. In general, magnetic, electrophoretic, centrifugal, photophoretic, and diffusiophoretic can be neglected. On the other hand, thermophoretic forces, caused by steep temperature gradients, can be important. The gravitational forces are almost always present and can affect the dynamic response of large particles. Understanding and quantifying the chemical coupling between two phases is a challenging task. However, all reacting particles begin this process as inert particles, and they must be heated before they participate in the combustion process. Thus, one must first understand the interactions of inert particles in a combustion environment. The in-detail understanding of the dynamics and structure of dusty flows can be only advanced by considering simple flow geometries such as the opposed-jet, stagnation-type. In such configurations the imposed strain rate is well characterized, and the in-depth understanding of the details of the physico-chemical processes can be systematically obtained. A number of computational and experimental studies on spray and particle flows have been conducted in stagnation-type configurations. Numerically, the need for a hybrid Eulerian-Lagrangian approach has been identified by Continillo and Sirignano, and the use of such approach has allowed for the prediction of the phenomenon of droplet flow reversal. Gomez and Rosner have conducted a detailed study on the particle response in the opposed-jet configuration, and the particle thermophoretic diffusivities were determined experimentally. Sung, Law and co-workers have conducted numerical studies on the effect of strain rate and temperature gradients on the dynamics of inert particles, as a way of understanding potential errors in experimental LDV data that may arise from thermophoretic forces. This investigation is a combined experimental and numerical study on the details of reacting dusty flows. The specific tasks are: (1) Experimental determination of laminar flame speeds, and extinction strain rates of dusty flows at normal- and micro-gravity as functions of the particle type, particle initial diameter, particle initial number density, and gas phase chemical composition; (2) Detailed numerical simulation of the experiments. Results are compared with experiments and the adequacy of theoretical models is assessed; and (3) Provision of enhanced insight into the thermo-chemical coupling between the two phases.

Andac, M. Gurhan↗

Rate and time dependent failure of structural adhesives

Studies on two adhesives (Metlbond 1113 and 1113-2) identified as having important applications in the bonding of composite materials are presented. A testing program to ascertain stress-strain, strain-rate, time, yield, and/or failure behavior of these materials in bulk form using uniaxial tensile constant strain-rate, creep, and relaxation tests is described. The stress-strain behavior of each material is shown to be significantly rate dependent. A rate dependent stress whitening (crazing) phenomenon occurs prior to either yield or fracture. A region of linear elasticity, a region of viscoelasticity, and the onset of yielding are identified in the stress-strain behavior. The linear elastic limit and the yield point are shown to be rate dependent and agree well with an empirical equation proposed by Ludwik. A creep to failure phenomenon is shown to exist and is correlated with a delayed yield equation proposed by Crochet. Analytical predictions based on a modified Bingham model are shown to agree well with experimental stress-strain strain-rate data. Analytical predictions based on a modified Ramberg-Osgood equation are also shown for comparison purposes.

Brinson, H. F.↗

The gabbro-eclogite phase transition and the elevation of mountain belts on Venus

The hypothesis is explored that the crust-mantle boundary of Venus is not in phase equilibrium but rather is rate-limited by the temperature-dependent volume diffusion of the slowest ionic species. The 1D thermal evolution problem is solved assuming that the mountains formed by uniform horizontal shortening of the crust and the lithospheric mantle at a constant rate. The time-dependent density structure and surface elevation are calculated by assuming a temperature-dependent reaction rate and local Airy isostatic compensation. For a horizontal strain rate of 10 exp -15/s or greater, the temperature increase at the base of the crust during mountain formation is modest to negligible, the deepening lower crust is metastable, and the surface elevation increases as the crust thickens. For strain rates less than 10 exp -16/s, crustal temperature increases with time because of internal heat production and the lower crust is more readily transformed to the dense eclogite assemblage. For such models, a maximum elevation is reached during crustal shortening.

Namiki, Noriyuki↗

Large Primtive Asteroids: Thermal and Dynamical Context

Primitiveasteroids, most of which are located in the outer belt and Jupiter’s Trojan clouds, provide information related to the origin and evolution of the solar system and the conditions in which the solar nebula was formed. These asteroids are widely thought to be the origin of the least-altered car-bonaceous chondrite that allow us to put crucial con-straints on the current dynamical and thermal theories of the formation and evolution of the early solar sys-tem. The nature of surface composition of large and low-albedo asteroids, like (1) Ceres, (10) Hygiea and (52) Europa, is still under intense debate and different interpretations have beenput forth to explain the ab-sorption features in these objects (e.g.,[1, 2, 3,4,5,6]). Laboratory and spectroscopic experiments on me-teorites that represent all nine carbonaceous chondrite types also found no spectral matches for these large asteroids (e.g.,[7]). Previous studies of asteroid Ceres (the largest primitive asteroid in the solar system) have been conducted to constrain and estimate its surface composition (e.g., [2, 5]). Using linear mixing,[2]found hydroxide brucite, serpentines, and carbonates, to be consistent with Ceres’ ground-based spectra.[5]estimated the surface composition of Ceres and found evidence of widespread NH3-phyllosilicates across its surface using best-fit solutions to Dawn’s NIR spectra. The presence of NH3-phyllosilicates implies that mate-rial from the outer solar system was incorporated into large primitive asteroids, either during their formation at great heliocentric distance or by incorporation of material transported into the Main Belt region. Here we presentnew largeand primitive asteroidsthat share the same spectral similaritieswith the largest asteroid in the solar system, Ceres.We also present the context of these new observations in terms oftheirthermal and dynamicalevolution.Large Primitive Asteroids: Dynamical and Thermal Context:Orbital Distribution of LargePrimitiveAsteroids: Constraining the mineralogy and surface composition of large primitive asteroids will place crucial con-straints on existing dynamical and thermal theories of the formation of the early solar system. We identified several additional asteroids in the Europa-like group in addition to asteroids Europa, Euphrosyne, and Patien-tia, that wereidentified in [8]using NASA IRTFtele-scope (e.g.,Figure 1). These new asteroids along with the already-observed Ceres-and Europa-like group members are localized in the 2.8 < a < 3.4 AU region and characterized by larger sizes, showing an interest-ing orbital distribution (Figure 2). Ceres-likeand Eu-ropa-like groups, which include the largest asteroids in the solar system, show an interesting orbital distribu-tion. These groups are located in the 2.6 < a < 3.6 AU region that contains the snow-line. The snow-line’s location may have been driftedinwards due to the disk’s cooling and evolution[9,10]. Recent dynamical models[11,12]suggested that a substantial fraction of primitive asteroids originated between or beyond the giant planets (a > 5 AU), where water ice would have been stable, and then implanted in the outer Main Belt region because of the giant planets’ growth.Figure 1. Two asteroids, 94 Aurora and 423 Diotima, showing spectra similar to asteroids (1)Ceres and (52)Europa.Thermal modeling and evolution of primitive aster-oids:Primitive water-rich asteroids are thought to be originally composed of mixtures of anhydrous materi-als and water ice that waslater melted by heating sources such as the decay of 26Al, reacting with anhy-drous materials to form H2O/OH-rich minerals. Calcu-lations of the evolution of the temperature and struc-ture of icy planetesimals were performedusing a 1D finite differences thermal evolution model[13, 14] for 26Al-heated planetesimals. In particular, thermally activated compaction due to hot pressing of bodies with an initially unconsolidated porous structure is included. An ice-rich initial composition that leads to a material dominated by phyllosilicates upon aqueous alteration (with 25 vol% H2O and a rock fraction that contains 85 vol% phyllosilicates and 15 vol% olivine upon aque-ous alteration, similar to CIand CM chondrites) was assumed. Atypical initial porosity of 40%[15] is re-duced following the change of the strain rate that is calculated as Voigt approximation from the strain rates of components[16]. Material properties (thermal con-ductivity, density, heat capacity, etc.) correspond to the composition assumed and are adjusted with tempera-ture and porosity. Melting of the water ice as well as water-rock separation are included[14]. Both short-and long-lived radionuclides are consideredas heat sources. Figure 3 shows the maximum temperature calculated as a function of radius and accretion time. A variety of internal structures is obtained, ranging from primordial (no melting of water ice) over partially melted or partially differentiated (melting of water ice, hydration, formation of a rocky core and water ocean below an undifferentiated layer) to completely differ-entiated ones (rocky core, water mantle, Enceladus-like case). The heating and differentiation of planetesi-mals is determined by the availability of 26Al, i.e., by the accretion time t0 relative to the formation of the calcium-aluminum-rich inclusions (CAIs), such that maximum temperatures and structures vary stronglyfor t0< 6 Myr rel. to CAIs. However, for a later accre-tion only the size of the body determines its maximum tempera-ture and structure due to the nearly constant heating by long-lived radionuclides. Average densities of Ceres-and Europa-like group membersimply high-ly porous interiors and, consequently, relatively late accretion at t0> 3 Myr rel. to CAIs with a maximum temperature of < 600 K (Figure3)

D Takir↗

Hot forming of silicon sheet, silicon sheet growth development for the large area silicon sheet task of the low cost silicon solar array project

The hot workability of polycrystalline silicon was studied. Uniaxail stress-strain curves are given for strain rates in the range of .0001 to .1/sec and temperatures from 1100 to 1380 C. At the highest strain rates at 1380 C axial strains in excess of 20% were easily obtainable without cracking. After deformations of 36%, recrystallization was completed within 0.1 hr at 1380 C. When the recrystallization was complete, there was still a small volume fraction of unrecyrstallized material which appeared very stable and may degrade the electronic properties of the bulk materials. Texture measurements showed that the as-produced vapor deposited polycrystalline rods have a 110 fiber texture with the 110 direction parallel to the growth direction and no preferred orientation about this axis. Upon axial compression perpendicular to the growth direction, the former 110 fiber axis changed to 111 and the compression axis became 110 . Recrystallization changed the texture to 110 along the former fiber axis and to 100 along the compression axis.

Graham, C. D., Jr.↗

The relationship between plate velocity and trench viscosity in Newtonian and power-law subduction calculations

The relationship between oceanic trench viscosity and oceanic plate velocity is studied using a Newtonian rheology by varying the viscosity at the trench. The plate velocity is a function of the trench viscosity for fixed Rayleigh number and plate/slab viscosity. Slab velocities for non-Newtonian rheology calculations are significantly different from slab velocities from Newtonian rheology calculations at the same effective Rayleigh number. Both models give reasonable strain rates for the slab when compared with estimates of seismic strain rate. Non-Newtonian rheology eliminates the need for imposed weak zones and provides a self-consistent fluid dynamical mechanism for subduction in numerical convection models.

King, Scott D.↗

An Evaluation of Some Current Practices for Short-Time Elevated-Temperature Tensile Tests of Metals

The effect of different testing practices on the short-time elevated-temperature tensile properties was determined for 2024-T3 aluminum-alloy, HM21A-T8 and HK31A-H24 magnesium-alloy, and 12 MoV stainless-steel sheet. Tests were made under single strain-rate and single head-speed conditions. A dual strain-rate test was also included. An evaluation of the effects of these practices is given for the tensile and yield strengths, the elongation in 2 inches, and the uniform elongation. The need for a uniform testing practice is demonstrated. Recommended practices suggested by different organizations are included.

Manning, Charles R., Jr.↗

Dynamic Weakening (Extinction) of Simple Hydrocarbon-air Counterflow Diffusion Flames by Oscillatory Inflows

This study of laminar non-premixed HC-air flames used an Oscillatory-input Opposed Jet Burner (OOJB) system developed from a previously well-characterized 7.2-mm Pyrex-nozzle OJB system. Over 600 dynamic Flame Strength (FS) measurements were obtained on unanchored (free-floating) laminar Counterflow Diffusion Flames (CFDF's). Flames were stabilized using plug inflows having steady-plus-sinusoidal axial velocities of varied magnitude, frequency, f, up to 1600 Hz, and phase angle from 0 (most data) to 360 degrees. Dynamic FS is defined as the maximum average air input velocity (U(sub air), at nozzle exit) a CFDF can sustain before strain-induced extinction occurs due to prescribed oscillatory peak-to-peak velocity inputs superimposed on steady inputs. Initially, dynamic flame extinction data were obtained at low f, and were supported by 25-120 Hz Hot-Wire cold-flow velocity data at nozzle exits. Later, expanded extinction data were supported by 4-1600 Hz Probe Microphone (PM) pk/pk P data at nozzle exits. The PM data were first obtained without flows, and later with cold stagnating flows, which better represent speaker-diaphragm dynamics during runs. The PM approach enabled characterizations of Dynamic Flame Weakening (DFW) of CFDF's from 8 to 1600 Hz. DFW was defined as % decrease in FS per Pascal of pk/pk P oscillation, namely, DFW = - 100 d(U(sub air) / U(sub air),0Hz) / d(pkpk P). The linear normalization with respect to acoustic pressure magnitude (and steady state (SS) FS) led to a DFW unaffected by strong internal resonances. For the C2H4/N2-air system, from 8 to 20 Hz, DFW is constant at 8.52 plus or minus 0.20 (% weakening)/Pa. This reflects a quasi-steady flame response to an acoustically induced dU(sub air)/dP. Also, it is surprisingly independent of C2H4/N2 mole fraction due to normalization by SS FS. From 20 to approximately 150 Hz, the C2H4/N2 air-flames weakened progressively less, with an inflection at approximately 70 Hz, and became asymptotically insensitive (DFW approximately 0) at approximately 300 Hz, which continued to 1600 Hz. The DFW of CH4-air flames followed a similar pattern, but showed much greater weakening than C2H4/N2-air flames; i.e., the quasi-steady DFW (8 to approximately 15 Hz) was 44.3 %/Pa, or approximately 5x larger, even though the 0 Hz (SS) FS was only 3.0 x smaller. The quasi-steady DFW's of C3H8-air and C2H6-air were intermediate at 34.8 and 20.9 %Pa, respectively. The DFW profiles of all four fuels, at various frequencies, correlated well but non-linearly with respective SS FS's. Notably, the DFW profile for C3H8 air fell more rapidly in the range greater than 15 to 60 Hz, compared with the 1- and 2-carbon fuels. This may indicate a shift in chemical kinetics, and/or O2 transport to a flame that moved closer to the fuel-side. In conclusion, Dynamic Flame Weakening limits appear significant and unique for each fuel, and correlate closely, but non-linearly, with Steady-State Flame Strengths at any given frequency. For reasons unknown, the dynamic flames didn't weaken more at intermediate frequencies (e.g., at 20-50 Hz) than they did at low frequencies (less than 15 Hz), where quasi-steady weakening appears to dominate. Quasi-steady flame weakening ostensibly represents a transient input strain rate maximum that just exceeds the steady-state strain-rate-limited extinction limit for a few cycles. Clearly, further detailed mechanistic understanding is needed in the fall-off region.

Pellett, G.↗

The Influence of C and Si on the Flow Behavior of NiAl Single Crystals

Alloys based on the intermetallic compound NiAl are considered potential replacements for Ni and Co-based superalloys in high temperature structural applications due to their excellent oxidation resistance, low densities, high thermal conductivities, and increased melting points. Unfortunately, NiAl exhibits low tensile ductility at room temperature and low strengths at elevated temperatures which have combined to hinder its development. Recent efforts, have revealed that NiAl in the presence of sufficient solute levels, is subject to the phenomenon of strain aging which manifests itself as: sharp yield points, abnormally low strain rate sensitivities (SRS), plateaus or peaks in yield stress and work hardening rate as a function of temperature, flow stress transients upon an upward change in strain rate, reduced tensile elongations at elevated temperatures, and serrated stress-strain curves. Though recent efforts via either alloying or the removal of interstitial impurities, have resulted in consistent room-temperature tensile elongations exceeding 5% and the elimination of serrated flow, the effects of particular substitutional and interstitial elements and the mechanisms by which they might enhance or hinder the mechanical properties remain unknown. Consequently, the purpose of the present paper is to provide a preliminary assessment of the influence of common substitutional and interstitial impurities on the deformation behavior of NiAl. To accomplish this goal a series of NiAl single crystal alloys containing various interstitial solutes were prepared and their mechanical properties were evaluated between 77 and 1100 K. Because Si is a common impurity in conventional purity single crystals grown by the Bridgman method, Si concentrations were also varied in order to determine the influence of this element.

Weaver, M. L.↗

Geodetic Measurement of Deformation East of the San Andreas Fault in Central California

Triangulation and trilateration data from two geodetic networks located between the western edge of the Great Valley and the San Andreas fault have been used to calculate shear strain rates in the Diablo Range and to estimate the slip rate along the Calaveras and Paicines faults in Central California. Within the Diablo Range the average shear strain rate was determined for the time period between 1962 and 1982 to be 0.15 + or - 0.08 microrad/yr, with the orientation of the most compressive strain at N 16 deg E + or - 14 deg. The orientation of the principal compressive strain predicted from the azimuth of the major structures in the region is N 25 deg E. It is inferred that the measured strain is due to compression across the folds of this area: the average shear straining corresponds to a relative shortening rate of 4.5 + or - 2.4 mm/yr. From an examination of wellbore breakout orientations and the azimuths of P-axes from earthquake focal mechanisms the inferred orientation of maximum compressive stress was found to be similar to the direction of maximum compressive strain implied by the trend of local fold structures. Results do not support the hypothesis of uniform fault-normal compression within the Coast Ranges. From trilateration measurements made between 1972 and 1987 on lines that are within 10 km of the San Andreas fault, a slip rate of 10 to 12 mm/yr was calculated for the Calaveras-Paicines fault south of Hollister. The slip rate of the Paicines fault decreases to 4 mm/yr near Bitter.

Sauber, Jeanne M.↗

Thermoelastic constitutive equations for chemically hardening materials

Thermoelastic constitutive equations are derived for a material undergoing solidification or hardening as the result of a chemical reaction. The derivation is based upon a two component model whose composition is determined by the degree of hardening, and makes use of strain-energy considerations. Constitutive equations take the form of stress rate-strain rate relations, in which the coefficients are time-dependent functions of the composition. Specific results are developed for the case of a material of constant bulk modulus which undergoes a transition from an initial liquidlike state into an isotropic elastic solid. Potential applications are discussed.

Shaffer, B. W.↗