Showing papers on "Deformation (engineering) published in 1983"

Linear elastic materials with voids

Abstract: A linear theory of elastic materials with voids is presented. This theory differs significantly from classical linear elasticity in that the volume fraction corresponding to the void volume is taken as an independent kinematical variable. Following a discussion of the basic equations, boundary-value problems are formulated, and uniqueness and weak stability are established for the mixed problem. Then, several applications of the theory are considered, including the response to homogeneous deformations, pure bending of a beam, and small-amplitude acoustic waves. In each of these applications, the change in void volume induced by the deformation is determined. In the final section of the paper, the relationship between the theory presented and the effective moduli approach for porous materials is discussed. In the two year period between the submission of this manuscript and the receipt of the page proof, there have been some extensions of the results reported here. In the context of the theory described, the classical pressure vessel problems and the problem of the stress distribution around a circular hole in a field have uniaxial tension have been solved [19,22]. The solution given in the present paper for the pure bending of a beam when the rate effect of the theory is absent is extended to case when the rate effect is present in [21]. The various implications of the rate effect in the void volume deformation are pursued all the subsequent works [19,20,21,22].

Some surprising features of the plastic deformation of body-centered cubic metals and alloys

Abstract: The metals which have the bcc structure at and below room temperature include iron, refractory metals of Groups VA and VIA, and alkali metals. Experimental and theoretical investigations of deformation behavior carried out in the last twenty years are reviewed. Attention is concentrated mainly on low temperature properties where many anomalous features have been discovered. The phenomena discussed include slip asymmetry, failure of the Schmid law of critical resolved shear stress, the observation of anomalous slip in very pure metals and alloys, solution softening, and the ductile-brittle transition.

Differential stress magnitudes during regional deformation and metamorphism: Upper bound imposed by tensile fracturing

Abstract: Veins occupying tensile fractures are a common feature of metamorphic rocks of all grades. It can be shown in many cases that such veins are synmetamorphic and that they underwent repeated cycles of fracturing and healing throughout deformation and foliation development. Theoretical failure models have predicted that tensile failure is limited to differential stresses less than four times the tensile strength of the material (σ 1 −σ 3 ⩽ 4 T ), and this condition can therefore be used to place an upper bound on differential stress intensities during deformation and foliation development where they are concurrent with vein formation. The tensile strengths of rocks are generally less than 10 MPa, and in the presence of a high temperature metamorphic fluid, a value of 5 MPa may be more reasonable, due to subcritical crack growth. It is thus concluded that differential stress intensities during crustal orogenesis will be less than 40 MPa, and they may be lower than 20 MPa.

Constraints on extension of continental lithosphere

Abstract: The extension of the continental lithosphere is considered in terms of the deformation of a thin viscous sheet with a temperature-dependent rheology which is governed primarily by the strength of the upper mantle. The lithosphere is subjected either to a constant strain rate or to a strain rate decreasing with time, corresponding to the stretching of a region of fixed volume with a constant velocity boundary condition. The progress of the extension is influenced by the decrease in strength of the lithosphere, owing to its attenuation, and by an increase in strength resulting from cooling. The relative importance of these two effects depends on two parameters, a dimensionless strain rate and the total strain. For a given strain rate the extending lithosphere goes through two phases as the strain increases: in the first, the effect of thinning the lithosphere is predominant and the average strength of the lithosphere remains close to, and perhaps slightly below, its original strength; in the second, the effect of cooling of the lithosphere leads to very rapid increase in strength as a function of strain, resulting, presumably, in an effective limit on the degree of stretching that the lithosphere experiences.For the case of strain rate decreasing with time, when the initial strain rates are of order 10−15s−1, this maximum extension is between 100% and 150%; for a strain rate of 10−l4 s−1 the maximum lies around 400% to 500%. At higher strain rates than this, very large extension may occur before cooling significantly affects the strength of the lithosphere. This model accords well with the constraints available from the continental margins of the North Atlantic.

On the role of strain and stress state in ductile failure

Abstract: U sing plane strain and axisymmetric notched tensile specimens in combination with finite deformation stress analysis, the strain to initiate failure in a range of structural steels is shown to be co-related by the state of stress for both axisymmetric and plane states of strain. The implications of this result for ductile failure terminated by flow localisation is discussed in the light of the theoretical work on localised flow.

A technique for the determination of stress in thin films

Abstract: Intrinsic stress, elastic bulk modulus, and yield strength of thin films has been determined by measuring the deformation versus pressure of circular membranes of the materials. Low pressure chemical vapor deposited (LPCVD) silicon‐rich silicon nitride (SiNx) has been extensively characterized and found to have an intrinsic stress of ∼1×109 dyn/cm2 and a bulk modulus of ∼1.9×1012 dyn/cm2. A SiNx membrane 1.0 cm in diameter and 1.0 μm thick has been found to survive a differential pressure of 470 Torr with no measurable plastic deformation. Experimental data for several different types of silicon nitride membranes is given. It is shown that the stress measurement technique can be extended to measure accurately the intrinsic stress of thin films deposited onto SiNx membranes.

Microstructure, tensile deformation, and fracture in aged ti 10V-2Fe-3Al

Abstract: In the /3-Ti alloy Ti-10V-2Fe-3Al a variety ofα-andω-aged microstructures with different yield stresses was established by combinations of forging and heat treatment. Tensile tests have shown that plastic deformation and fracture are strongly influenced by the morphology, size, and volume fraction of the different types of a-phase (primary a, secondaryα, grain boundaryα), as well as by the-phase. A detailed microscopical study revealed several deformation and fracture modes. It appears that at several sites stress and strain concentrations and subsequent void nucleation can occur and that the quantitative combinations of the differentα-types determine which sites are active. The dominant deformation mode for the (α +gb) solution treated andα-aged conditions was a strain localization in theα-aged matrix leading to voids at the interface between aged matrix and primary a-phase. In case of theβ-solution treated andα-aged microstructures the grain boundaryα leads to a strain localization in the softα-film and to void nucleation at grain boundary triple points at low macroscopic strains. Based on the above mechanisms it is discussed in detail how varying size, volume fraction, and morphology of theα-phase affect the ductility. The embrittling effect ofω-particles can be largely reduced by a grain refinement.

Controlled Flaws in Ceramics: A Comparison of Knoop and Vickers Indentation

Abstract: Application of indentation fracture analysis to Knoop and Vickers indentation is examined, with particular emphasis on determining the limitations of the point force representation for the residual stress field. Deviation from the point force approximation is insignificant for crack-size/plastic-zone-size ratios 1.3. The Vickers deformation/fracture configuration in brittle materials invariably conforms to this requirement, whereas the Knoop configuration does not (except at very high indentation loads). However, stable crack growth during a failure test extends the crack sufficiently that the strength degradation for both types of indentation is well described by the point force approximation.

The effect of grain size on deformation twinning in a textured zinc alloy

Abstract: The incidence of deformation twinning in samples of a commercial rolled zinc-0.1% aluminium-0.05 wt % magnesium alloy has been measured at room temperature as a function of strain, grain size and direction of loading relative to the rolling direction. The volume fraction of twinned material has been measured at the surface and in the bulk. It is shown that this volume fraction is a linear function of both strain and grain size in most cases. Bands of heavily twinned grains are found to form inhomogeneously across the gauge length of tensile specimens, by an autocatalytic mechanism. Several examples are given of the interaction of twins and slip bands at grain boundaries which illustrate the formation and the accommodation of twins. The smaller volume fraction of twins found at the surface compared with the bulk reflects a relaxation of Von Mises criterion.

Mechanisms of Deformation and Fracture

Abstract: Publisher Summary This chapter provides an overview of mechanisms of deformation and fracture. Crystalline solids deform plastically by a number of alternative (and often competing) mechanisms: Low-temperature plasticity, twinning, power-law creep, diffusional flow, and so forth. Each has certain characteristics: A rate that depends strongly on temperature, for instance, or on grain size, or which is influenced by a dispersion of a second phase. These characteristics are summarized by the constitutive law for that mechanism and each has a characteristic regime of dominance, that is, a range of stresses, temperatures, and strain rates over which it is the primary mechanism. Fracture, too, can occur by any one of a number of alternative micromechanisms: Cleavage, ductile fracture, rupture intergranular creep fracture, and so forth. Each has certain characteristics: Negligible ductility, for instance, or a ductility that depends on inclusion density or grain size; and, for given stress states-simple tension, for example—each has a characteristic regime of dominance, that is, a range of stresses and temperatures over which it is the primary mechanism. This chapter describes the mechanisms of plasticity and fracture and develops ways of displaying their ranges of dominance and certain of their characteristics.

Enhanced superplasticity and strength in modified Ti-6AI-4V alloys

Abstract: Although Ti-6A1-4V displays extensive superplasticity at 1200 K, lower superplastic forming temperatures are desirable. A study was conducted with the goal of modifying the composition of the Ti-6A1-4V alloy to lower the optimum superplastic forming temperature. Computer modeling results and previous experimental data suggested that additions to Ti-6A1-4V of beta-stabilizing elements which have high diffusivity in the beta-phase would permit lower superplastic forming temperatures. A series of modified alloys with 2 wt pct additions of Fe, Co, and Ni was prepared for experimental evaluation. The modified alloys achieved desirable microstructures for superplasticity at 1088 K,i.e., the grain size was approximately 5 µm and roughly equal volume fractions of the alpha- and beta-phases were present at the deformation temperature. The superplastic properties of the modified alloys were measured at 1088 K and 1144 K. The modified alloys produced values of flow stress, strain rate sensitivity, and total elongation at 1088 K approaching those of the base Ti-6A1-4V alloy at its standard superplastic forming temperature of 1200 K. In addition to lowering the superplastic forming temperature, the β-stabilizing additions also increased room temperature strength levels above those normally found for Ti-6A1-4V. Based on the room temperature and elevated temperature tensile properties, addition of selected beta-stabilizing elements to Ti-6A1-4V simultaneously raises resistance to deformation at room temperature and lowers resistance to deformation at elevated temperatures. This reversal in behavior is explained by considering the effect of beta-stabilizer additions on the deformation mechanisms at room temperature and at elevated temperatures.

The role of Terzaghi effective stress in linearly elastic deformation

Abstract: It has been shown that the overall strain of a fluid-filled porous elastic solid is not governed by the Terzaghi effective stress law. The authors show, in the context of anisotropic linear elasticity, that the overall strain may be resolved into a component which is the average strain of the solid matrix and a component due to change in relative pore geometry, and that the latter is determined by the Terzaghi effective stress. This leads to a simple form of the response laws and, in particular, to effective stress laws for overall strain (obtained previously) and for strain of the pore space.

Tensile properties of CaCO3‐filled polyethylenes

Abstract: Tensile stress–strain behavior and dilatation behavior of CaCO3-filled linear polyethylenes with differing molecular weight was found to be dependent upon filler content, polymer filler interface, and polymer molecular weight. Electron microscopy of samples undergoing deformation revealed the presence of craze type deformation.

Strain dependent attenuation: Observations and a proposed mechanism

Abstract: The measured attenuation (Q−1) of a rock is a function of a number of parameters, one of those being the applied strain amplitude. It is important to understand the effect that strain amplitude has on Q−1 for several reasons: different measurement techniques use differing strain amplitudes and may measure a dissimilar Q−1, near source (large strain) wave propagation may behave highly non-linearly, and the strain amplitude dependence can provide insight into the attenuation mechanism. A physical model based on the contact friction between crack surfaces in the rock has been developed to describe rock deformation and dissipation under large applied strain. The three-dimensional crack surfaces are characterized by a statistical distribution of asperity heights. The sliding contact of these spherically-tipped asperities dissipates frictional energy. Hertzian theory is applied to the average asperity contact and predicts that the large strain attenuation is given by Q−1 = kζe/P4/3, where k is a constant consisting of the matrix elastic parameters, ζ is the crack density, e is the strain amplitude, and P is the confining pressure. The total attenuation measured appears to be the sum of this strain dependent term and a strain independent term. The results of ultrasonic pulse transmission experiments are compared with the model's prediction. Both P and S waves with strain amplitudes from 10−8 to 10−5 were employed. Frequencies from 0.4 to 1.5 MHz were used in conjunction with rock confining pressures of 2 to 580 bars on dry Berea sandstone and lucite samples. The spectral ratio method and rise time technique were applied to deduce the Q−1 values. The observed data and other observations from the literature compare well with the model's prediction for the dependence of Q−1 on large strain amplitude, crack density, and pressure.

An investigation on the creep and fracture behavior of cast nickel-base superalloy IN738LC

Abstract: The creep-rupture properties of cast nickel-base superalloy IN738LC were studied over the temperature range 750 to 950 °C. Our results show that primary and steady-state creep should not be regarded as distinct stages and that they have basically the same deformation mechanism. The dependence of the steady-state creep rate,es, on stress,δ, and on temperature,T, for this superalloy can be described ases = Aδ nexp(−Qc/RT).n = 8.3 - 9.8 andQc = 570 - 730 kJ mol−1 at high stress levels, whereasn = 4.1 - 4.9 andQc = 370 - 420 kJ mol−1 at low stress levels. The observations of dislocation structures during steady-state creep confirm that the creep mechanism is different in the high and low stress regimes. The observations of the microstructure show that the initial acceleration in creep rate during the tertiary stage is connected with changes in the size and distribution ofγ′ particles during creep. Rupture occurs by the propagation of oxidized intergranular cracks which initiate at the specimen surface, and the rate of crack propagation is controlled by the deformation behavior of the superalloy.

Plastic Deformation of Partially Stabilized Zirconia

Abstract: The results of room-temperature compression experiments conducted on poly-crystalline Mg partially stabilized zirconia are described. It is shown that, in addition to prefuilure axial microfracture, the material exhibits significant plasticity. This plasticity arises from deformation bands formed by cooperative martensitic transformation of melastable tetragonal precipitates; the deformation bands lead to significant surface rumpling. It is suggested that both stress- and strain-induced martensitic transformations may be involved in the deformation process.