Distortional Strain Energy Research Articles

Shear band formation in polycarbonate-glass bead composites

The shear band formation at glass beads embedded in a polycarbonate matrix subjected to a uniaxial tension has been investigated by microscopic in situ observation. The degree of interfacial adhesion was varied by different glass surface treatments. To gain insight into the three-dimensional stress field requirement for shear band formation, the distributions of several elastic failure criteria around an isolated adhering glass sphere in a polycarbonate matrix have been computed with the aid of finite element analysis. It was found that the mechanism for shear band formation is fundamentally different for adhering and non-adhering glass beads. In the case of excellent interfacial adhesion, the shear bands form near the surface of the bead in regions of maximum principal shear stress and of maximum distortion strain energy. In the case of poor interfacial adhesion, shear band formation is preceded by dewetting along the interface between bead and matrix.

Continental fault structure and the shallow earthquake source

Plate boundaries in continental crust are generally less sharply defined than in the oceans, with seismicity spread over broad areas. Interplate displacements appear to be largely accommodated by networks of major fault zones. A simple 2-level model for these important structures accounts for the depth distribution of most continental earthquakes, and for the observed range of faulting styles and associated rock deformation textures. The model consists of a seismogenic frictional slip regime overlying quasi-plastic mylonite belts wherein shearing is largely accommodated aseismically, due mainly to the changing response of quartz to deformation with increasing temperature. Shear resistance increases with depth to a peak value in the vicinity of the frictiona1/quasi-plastic transition and then decreases rapidly. The depth to which microseismic activity extends appears inversely related to regional heat flow and can be satisfactorily modelled as the frictional/quasi-plastic transition for different geotherms using laboratory determined flow laws for quartz-bearing rocks. Larger earthquake ruptures ( M > 5.5) tend to nucleate near the base of the seismogenic regime in the region inferred to have the highest shear resistance and concentration of distortional strain energy. Consideration is also given to the depression of isotherms and seismic activity in regions of thrusting, and to the question of the downward continuation of major fault zones through the lithosphere. Decoupling of the upper crust on flat-lying shear zones may accompany higher-level dip-slip (and perhaps in some circumstances, strike-slip) faulting, being favoured by above average continental heat flow and a high quartz content in the middle or deep crust. The average level of deviatoric stress within the seismogenic regime remains an outstanding problem.

Fault zone models, heat flow, and the depth distribution of earthquakes in the continental crust of the United States

abstract Models of fault zones in continental crust, based on the analysis of rock deformation textures, suggest that the depth of seismic activity is controlled by the passage from a pressure-sensitive, dominantly frictional regime to strongly temperature-dependent, quasi-plastic mylonitization at greenschist and higher grades of metamorphism. Sufficient knowledge now exists concerning the frictional and rheological properties of quartz-bearing rocks to construct crude strength-depth curves for different geotherms. In such models, shear resistance peaks sharply at the inferred seismic-aseismic transition. The maximum depth of microseismic activity in various heat flow provinces of the conterminous United States generally correlates well with the frictional to quasi-plastic transition modeled for the different geotherms. Larger earthquakes ( M L > 5.5) also tend to nucleate near the base of the seismogenic zone. This region is postulated to have the highest concentration of distortional strain energy for stress levels at failure, and can be regarded as the prime asperity in crustal fault zones.

Experimental investigations of shear and elongational flow properties of polystyrene melts reinforced with calcium carbonate, titanium dioxide, and carbon black

AbstractShear and elongational flow measurements on polystyrene melts reinforced with small particles were carried out. The influences of loading level, particle size and surface treatment on shear viscosity, principal normal stress difference, and elongational viscosity were discussed. These systems exhibited yield values for both shear and elongational flow. Experimental values for the ratio of the tensile to the shear yield stress give satisfactory agreement with the predictions of the von Mises yield criterion. The yield value appears to increase with decreasing particle size and may be varied with surface treatment. The principal normal stress difference at fixed shear stress decreases with volume loading of particulates. The results are interpreted in terms of a system forming a gel due to interparticle forces, which is disrupted by a critical distortional strain energy.

Mechanical behaviour of polycrystalline BeO, Al2O3 and AlN at high pressure

The mechanical behaviour of various types of BeO, Al2O3, and AlN have been investigated at confining pressures up to 1.25 GPa, at 25° C, and at strain rates of 3 to 7×10−5 sec−1. The stress-strain data taken in uniaxial compressive-stress loading indicate the BeO aggregates undergo a transition from brittle fracture at low pressures to plastic flow at high pressures. Depending on the fabrication process, this transition pressure in BeO occurs at 0.4 to 0.7 GPa. Concurrently, the ultimate compressive strength of BeO increases from 1.0 to 1.9 GPa at 0.1 MPa pressure to over 4.0 GPa at 1.O GPa. Alumina remains brittle at all pressures up to 1.25 GPa; its strength increases from 4.5 GPa at 0.1 MPa pressure to over 6.0 GPa at 1.25 GPa. Aluminium nitride behaves similarly to BeO, having a brittle-ductile transition at 0.55 GPa. Its ultimate strength increases from 3.2 GPa at 0.1 MPa pressure to 4.7 GPa at 0.8 GPa. The distortional strain energy (proportional to the area under the stress-strain curve) absorbed by each material during compression at pressure was calculated and compared to available data from the literature. Alumina shows a degraded energy absorption with pressure, but both BeO and AlN yield a strongly enhanced performance at moderate pressures. Beryllium oxide and AlN thus appear to be promising structural materials for certain applications where high strengths and ductilities are required at moderate pressures.

Analogie zwischen elastischem und plastischem Potential anisotroper Stoffe / Analogy between the Elastic and Plastic Potential of Anisotropic Materials

Abstract The elastic strain energy of distortion and its complementary energy of incompressible materials can be represented formally by linear combinations of partial plastic potentials of the forms Fρ = (1/ρ)Dijkl...qr σ′ij′σkl ... σqr. Likewise, it is possible to describe the elastic strain energy of deformation and its complementary energy of compressible materials formally by plastic potentials of the forms Fρ = (1/ρ)Dijkl...qr σijσkl ... σqr. In a linear theory, for example, we have F2= ½Dijkl σ′ij σ′kl for incompressible materials and F2 =½Dijkl σ′ij σ′kl for compressible materials. It is necessary to notice, that only a formal analogy exsists between the elastic and plastic po­tential, because the physical interpretation of these potentials is quite different.

Zur physikalischen Deutung der Hill-Bedingung / About the Physical Interpretation of the Hill-Condition

In this paper it is shown, that the Hill-Condition can be identified with the elastic strain energy of distortion for incompressible materials. The Mises-Potential for anisotropic materials can be identified with the elastic strain energy

Stability analysis of an experimentally deformed single layer of Indiana limestone using finite elements

Experimentally deformed single layers of Indiana limestone provide stress-strain curves and buckled fold shapes as guidelines for incremental analyses based on the finite element method. It is assumed that if computer simulations can approximate these stress-strain curves and fold shapes, then the stress, moment, and energy histories of the simulation are indicative of the behavior of the single layer of limestone during deformation. A simulation with a Young's modulus of 0.075 Mbar, a Poisson's ratio ν of 0.25, an initial sine wave perturbation of 0.2 cm, and hinged end conditions is the best fit to experimental data. A stress and moment analysis suggests that the bottom part of the layer carries the load, provides the driving bending moment, and governs the buckling instability during deformation. Maximum principal stresses change from compressional to extensional as buckling begins near the top center of the layer. In the experimental situation the top part of the layer undergoes microfracture during this extension. The simulation suggests that this behavior is due to a ‘roll over’ of stresses, a decrease of the superposed axial and bending stress as the bending stress becomes a large negative value, and a decrease in distortional strain energy prior to fracture. Distortional strain energy provides the mechanism of deformation, whereas dilatational strain energy is controlled by shortening of the limestone layer. Geometric change of shape is interpreted to be the major factor influencing buckling instability, volume and material property changes occupying a subordinate role.

Plastic strains and energy density in cracked plates

A technique is presented which allows separation of the principal plastic strains within an enclave at a crack tip in relatively thin plates. For plates with a number of crack lengths, several degrees of tensile loading are applied to five ductile materials with widely varying mechanical properties. Principal plastic strain distributions, plastic distortional strain energy density and total plastic energy are determined within the resulting plastic encalves. It is shown that the degree of loading and strain hardening greatly affect the principal plastic strain and energy density distributions and that this is reflected in the amount of strain energy that can be plastically absorbed at a crack tip.

Tidal dissipation in the Moon

Dissipation of tidal energy in the moon was calculated under the assumption that it can be represented as due to imperfect elasticity. If the factor 1/Q for dissipation per cycle is assumed to be 1/100 for distortional strain energy and 1/1000 for dilatational strain energy, the heat now being generated in the moon by tides is less than 0.010 erg/g/yr.; i.e., negligible compared to radioactive heating by a chondritic composition. Tidal heating would be comparable to radioactive heating, however, if the semimajor axis of the moon's orbit was one-third as great, so the mechanism does limit the possible history of the moon's orbit. Also, appreciable tidal dissipation would cause thermal stresses and be conducive to convection, since it is much greater in the center than near the surface of the moon, and has a non-uniform distribution in latitude (and longitude as well, if rotation is synchronous with revolution).

On the Stress Distribution at the Base of a Stationary Crack

Abstract In an earlier paper it was suggested that a knowledge of the elastic-stress variation in the neighborhood of an angular corner of an infinite plate would perhaps be of value in analyzing the stress distribution at the base of a V-notch. As a part of a more general study, the specific case of a zero-angle notch, or crack, was carried out to supplement results obtained by other investigators. This paper includes remarks upon the antisymmetric, as well as symmetric, stress distribution, and the circumferential distribution of distortion strain-energy density. For the case of a symmetrical loading about the crack, it is shown that the energy density is not a maximum along the direction of the crack but is one third higher at an angle ± cos−1 (1/3); i.e., approximately ±70 deg. It is shown that at the base of the crack in the direction of its prolongation, the principal stresses are equal, thus tending toward a state of (two-dimensional) hydrostatic tension. As the distance from the point of the crack increases, the distortion strain energy increases, suggesting the possibility of yielding ahead of the crack as well as ±70 deg to the sides. The maximum principal tension stress occurs on ±60 deg rays. For the antisymmetrical stress distribution the distortion strain energy is a relative maximum along the crack and 60 per cent lower ± 85 deg to the sides.

Some Cases of the Axially Symmetrical Flow of Perfectly Plastic Materials

This paper deals theoretically with one of the three-dimensional isostatical problems in the theory of plasticity. Fundamental equations for plastic states of stress in a solid of revolution are established under the assumptions that the circumferential principal stress is equal to one of the other two lying in the meridian section and that materials obey the theory of constant elastic, strain energy of distortion. The author discusses the method of solving these equations for the case when the equations for slip-lines are known and two plastic states of stress having slip-lines of logarithmic spirals and straight lines. are considered in details as practical examples of applying his method of solution.