Showing papers in "Journal of The Mechanics and Physics of Solids in 1960"
TL;DR: In this article, a relation between extent of plastic yielding and external load applied was investigated, and panels containing internal and edge slits were loaded in tension and lengths of plastic zones were measured.
Abstract: Y ielding at the end of a slit in a sheet is investigated, and a relation is obtained between extent of plastic yielding and external load applied. To verify this relation, panels containing internal and edge slits were loaded in tension and lengths of plastic zones were measured.
6,830 citations
TL;DR: In this article, the equations of motion of cracks in tensile and cleavage samples have been derived, assuming that the deformation of the sample is maintained constant after the critical condition for fracture has been attained.
Abstract: The equations of motion of cracks in tensile and cleavage samples have been derived, assuming that the deformation of the sample is maintained constant after the critical condition for fracture has been attained. It is shown that the behaviour of cracks in tensile samples depends on their initial size and that large cracks are, in one sense, more stable than small cracks. The behaviour of cracks of all sizes in cleavage samples is shown to resemble that of large cracks in tensile samples.
225 citations
TL;DR: In this paper, the Giffith theory of brittle cracking is extended to a dynamic problem, in which a semi-infinite craek in an infinite medium is extended by finite forces.
Abstract: T he G riffith theory of brittle cracking is extended to a dynamic problem, in which a semiinfinite craek in an infinite medium is extended by finite forces. The conclusion is drawn that the force required to maintain a steady rate of extension of the craek decreases as the rate increases. It is also observed that various criteria which may be assumed for crack division lead to limiting velocities of propagation of a single crack.
210 citations
TL;DR: In this paper, the authors investigated the penetration of a viscoelastic half-space by a rigid spherical indenter in a quasi-static approximation, and the analysis was used to estimate the duration of contact and coefficient of restitution for the Hertzian impact of a spherical impact on a Maxwell solid.
Abstract: The penetration of a viscoelastic half-space by a rigid spherical indenter is investigated in a quasi static approximation. Solutions to the problem are obtained for monotonic contact radius and also when the radius possesses a single maximum. The analysis is used to estimate the duration of contact and coefficient of restitution for the Hertzian impact of a spherical indenter on a Maxwell solid.
207 citations
77 citations
TL;DR: In this article, the authors investigated some of the phenomena resulting from the incidence of plane thermoelastic waves on a plane, traction-free, thermally radiating boundary.
Abstract: I nvestigated are some of the phenomena, resulting from the incidence of plane thermoelastic waves on a plane, traction-free, thermally radiating boundary.
56 citations
54 citations
TL;DR: In this article, the authors derived the solution for a partially closed excavation of infinite length in an infinite medium, and from this solution were derived those for an unclosed and a completely closed panel.
Abstract: So Long as the excavation is comparatively deep the seam thickness may be considered infinitesimal and the convergence of opposing points in roof and floor may be treated as a discontinuity in displacement at a single point A result in plane elasticity can then be used to find the solution for a partially closed excavation of infinite length in an infinite medium, and from this solution are derived those for an unclosed and a completely closed panel The corresponding results for a semi-infinite medium are found only approximately for the unclosed and partially closed panels but exactly for complete closure In the last case the expression for the displacement at the plane boundary is independent of the elastic constants and forms an unequivocal limit with which actual subsidence profiles may be compared In British coalfields the magnitude of maximum subsidence is almost always greater than that given by the bounding expression, and the discrepancy cannot be explained on grounds of minor departures from the basic assumptions It follows that these assumptions must be drastically modified before agreement may be expected
52 citations
TL;DR: In this paper, the authors investigated the influence of shear stiffening on the mode of deflection in inelastic columns and derived an analytic approximate solution and an exact solution when in addition the unloading modulus is infinite.
Abstract: B ifurcation phenomena in inelastic columns, examined by the authors in two earlier papers (1960), are here investigated more extensively, especially in the range of loads between the tangent modulus and reduced modulus values. The novelty of the approach lies in its generality (arbitrary section geometry and very wide material properties) and in the comparative rigour and reliance on variation principles. Equations incorporating the influence of shear stiffening on the mode of deflection are first formulated. When the shear effect is negligible an analytic approximate solution is obtained, and an exact solution when in addition the unloading modulus is infinite. For illustration numerical results are presented for a rectangular section with arbitrary moduli.
32 citations
TL;DR: In this paper, the authors extended the solution for the stress field around the tip of a crack subjected to longitudinal shear and travelling with a constant velocity in an elastic medium, as given by Bilby and Bullough (1954), to a configuration analogous to the tensile case studied by Craggs (1960).
Abstract: The solution for the stress field around the tip of a crack subjected to longitudinal shear (antiplane strain) and travelling with a constant velocity in an elastic medium, as given by Bilby and Bullough (1954), has been extended to a configuration analogous to the tensile case studied by Craggs (1960). As in the case of tensile cracks, the applied stress required for constant velocity is lower for higher crack velocity and there is a critical velocity approximately 0.6 times that of the shear wave velocity above which the crack will branch. Similar stress levels are found using two different fracture criteria : the Griffith energy criterion and the criterion of critical shear strain averaged over a critical area.
31 citations
TL;DR: In this paper, the elastic-plastic deformation of a solid cylinder in the presence of a distributed heat source and subjected to a lateral pressure p and an axial fource F is considered in detail using Tresca's yield function, its associated flow law, and a linear workhardening law.
Abstract: T he elastic-plastic deformation of a solid cylinder in the presence of a distributed heat source and subjected to a lateral pressure p and an axial fource F is considered in detail using Tresca's yield function, its associated flow law, and a linear workhardening law. Particular attention is given to the class of problems in which the radial stress, and not the axial stress, is the intermediate principal stress. The general results are applied to the cylindrical nuclear reactor fuel element in the state of plane strain with a radially distributed Gaussian heat source, acting in its fissionable interior. The solution is expressed in closed form in terms of the exponential integral and the incomplete gamma function and is found to exhibit three stages of plastic deformation. In stage I the plastic domain consists of two concentric and adjacent zones with different stress fields and different rates of propagation which expand outward from the centre of the cylinder; in stage II the elastic domain vanishes, while the inner plastic zone continues to propagate; and in stage III a third plastic zone is formed at the outer radius which propagates inward. Throughout the deformation the states of stress are found to exhibit regular progression. A numerical example is included.
TL;DR: In this article, an impact indentation test is described for investigating the behavior of metals and alloys subjected to stress cycles of a few milliseconds duration, which consists of the normal impact of a conically tipped tungsten carbide indenter on a plane surface of the specimen at impact velocities in the range 2-30 cm sec.
Abstract: An impact indentation test is described for investigating the behaviour of metals and alloys subjected to stress cycles of a few milliseconds duration. The test consists of the normal impact of a conically tipped tungsten carbide indenter on a plane surface of the specimen at impact velocities in the range 2–30 cm sec. An analysis of impact indentation is made, using a quasi-stationary approach; relations between impression dimensions, contact duration and impact velocity are obtained and verified experimentally. Comparison of the impact test results with those derived from hardness measurements, using the same indenter, affords an assessment of the strain rate sensitivity of the material. Results are reported for a wide range of materials, including copper, aluminium, iron, various steels and non-ferrous alloys.
TL;DR: In this article, a numerical solution of the second order non-linear differential equation derived by H andelman for a Levy-Mises material was obtained for a triangular beam section.
Abstract: T he paper deals with the plastic flexure and torsion of prismatic beams loaded by terminal bending and twisting moments which, acting together, cause full plastic flow. The material is assumed to behave according to the Tresca-Levy-Mises hypotheses, and in nonhardening and rigid plastic. The results were obtained by numerical solution of the second order non-linear differential equation derived by H andelman for a Levy-Mises material, and the beam sections investigated were circular, square and triangular. The relationships obtained were found to give points lying virtually on a single interaction curve plotted with non-dimensional coordinates. The results are consistent with the two cases considered by S teele , who first reported a numerical solution for a square section. The interaction curve obtained is compared with the lower bound curve given by H ill and S iebel .
TL;DR: In this article, the motion under plane strain conditions of an ideal plastic rigid solid, where the inertial forces are not negligible, is studied and a perturbation method of solving the equations is described.
Abstract: This paper is concerned with the motion under plane strain conditions of an ideal plastic rigid solid, wlicn the inertial forces are not negligible. It is shown that the equations for such a motion can be expressed in a particularly simple form when referred to a system of moving curvilinear coordinates which is a generalization of the system defined by the slip-line field in quasistatic plane plasticity. A perturbation method of solving the equations is described ; in this, approximate solutions to dynamic problems are obtained as perturbations of a known (usually quasistatic) solution. The method is illustrated by application to problems of indentation of a plastic rigid half-space by stationary and moving loads.
TL;DR: In this article, it was shown that when the load is constant, yielding can take place after some time in creep, and when a constant rate of strain is applied, the yield stress increases with the rate of stress.
Abstract: By means of the application of a yield criterion, according to which yielding takes place when that part of the stress-work which is conserved reaches a definite maximum value, it is shown that from the constitutive equation of anelasticity two phenomena follow. On one hand, when the load is constant, yielding can take place after some time in creep. On the other hand, when a constant rate of strain is applied, the yield stress increases with the rate of strain.
TL;DR: In this article, an electrical analogue for solving the biharmonic equation was used to determine the elastic stresses near a hole or crack in a flat rectangular plate subjected to uniaxial tension.
Abstract: An electrical analogue for solving the biharmonic equation was used to determine the elastic stresses near a hole or crack in a flat rectangular plate subjected to uniaxial tension. Problems concerning both simply and multiply connected regions were solved by the method and, where a comparison between the experimental results and existing analytical solutions was possible, the agreement was good. The advantages and limitations of the method are discussed and the desirability of extending the method for the determination of the stresses after plastic yielding has occurred, is emphasized.
TL;DR: In this article, a model of a crack is developed in which the surface energy in the Griffith treatment is taken to depend on the temperature and strain rate, and it is shown that such a crack shows a transition from brittle to ductile behaviour as the temperature is raised.
Abstract: A model of a crack is developed in which the surface energy in the Griffith treatment is taken to depend on the temperature and strain rate. It is shown that such a crack shows a transition from brittle to ductile behaviour as the temperature is raised.
TL;DR: In this article, an annular plate made of a perfectly plastic material is subjected to a uniform normal load over its surface and a constant tensile load around its outer edge, and close bounds on the interaction curve are found for all values of the inner radius under various support conditions at the inner edge.
Abstract: An annular plate made of a perfectly plastic material is subjected to a uniform normal load over its surface and a constant tensile load around its outer edge. Close bounds on the interaction curve are found for all values of the inner radius under various support conditions at the inner edge.
TL;DR: In this paper, an expression for the change in velocity of a light wave propagated along the optic axis due to stresses acting in the plane normal to this axis is derived, and this result offers an explanation of phenomena observed by earlier workers.
Abstract: T he interpretation of the photoelastic stress patterns of vibrating bodies is discussed, with particular reference to quartz crystals. An expression is derived for the change in velocity of a light wave propagated along the optic axis due to stresses acting in the plane normal to this axis. Such stresses should cause an increase in the effective rotary power and this is verified by experiment. This result offers an explanation of phenomena observed by earlier workers.
TL;DR: In this article, the authors apply complex variable analysis to obtain solutions for the Saint-Venant torsion problem corresponding to certain sections with regular curvilinear boundaries, where the area of the cross-section is conformally mapped on the unit circle by a transformation involving some parameters.
Abstract: This paper is concerned with the application of complex variable analysis to obtain solutions for the Saint-Venant torsion problem corresponding to certain sections with regular curvilinear boundaries. The area of the cross-section is conformally mapped on the unit circle by a transformation involving some parameters. By varying these parameters various shapes having several axes of symmetry are obtained. Sections bounded by n (> 2) equal and very approximately circular arcs are included as particular cases. Closed and exact expressions are derived for the complex torsion function, the torsional rigidity, and the shearing stresses at any point of the section. The distribution of shearing stress on the boundary is investigated in the general case and graphs showing its variation in four particular examples are plotted.
TL;DR: In this article, the problem of a thin-wall polyerystalline cylinder subjected to a torsional strain following a plastic tensile strain according to an extension of T aylor's theoretical model has been investigated.
Abstract: T he problem of a thin-wall polyerystalline cylinder subjected to a torsional strain following a plastic tensile strain according to an extension of T aylor 's theoretical model has been investigated. Some agreement with experimental results has been obtained.
TL;DR: In this article, a n approach is presented to the problem of correlating the macroscopic fatigue strength of steels with microscopic explanations of present dislocation theory, in which the stress concentration or notch effect due to the obstacle itself against which the dislocations pile up is taken into account.
Abstract: A n approach is presented to the problem of correlating the macroscopic fatigue strength of steels with microscopic explanations of present dislocation theory. The stress concentration or notch effect due to the obstacle itself against which the dislocations pile up is taken into account in addition to assuming that stress concentration at the piled-up dislocations plays an important role in fatigue fracture of steels. The agreement with the characteristic features in stress criterion tor fatigue fracture of steels is good.
TL;DR: In this paper, the steady-state creep rates of commercial tin were investigated at temperatures between 180 and 230°C and it was shown that the steady state creep process is governed by a single activation energy of 22,500 cal/mole.
Abstract: The steady-state creep rates of commercial tin were investigated at temperatures between 180 and 230°C. Torsional creep equipment was developed for this purpose. At temperatures below 215°C results indicate that the steady-state creep process is one governed by a single activation energy of 22,500 cal/mole. At higher temperatures, however, the simple Arrhenius-type equation cannot properly express the creep behaviour.
TL;DR: In this article, the complex potentials and deflexion of a thin circular annular plate of constant thickness under any system of concentrated forces or concentrated couples in equilibrium, the edges of the annulus being free, are investigated and exact solutions in closed forms are deduced.
Abstract: S eries solutions are presented for the complex potentials and deflexion of a thin circular annular plate of constant thickness under any system of concentrated forces or concentrated couples in equilibrium, the edges of the annulus being free. The limiting cases when the radius of the inner edge tends to zero or the radius of the outer edge tends to infinity are investigated and exact solutions in closed forms are deduced. Worked out in detail are three particular problems; namely, those of circular ring plates subjected, respectively, to two bending couples, to two twisting couples, both applied at the ends of a diameter of a concentric circle, and to four forces applied at the ends of two perpendicular diameters of a concentric circle. The method of images is used to obtain the deflexion of a sectorial plate bounded by two free arcs of concentric circles and two radii when the plate is acted upon by a concentrated load at an arbitrary point and is simply supported along the straight edges.
TL;DR: In this article, the multiple scabbing phenomenon of materials due to tensile reflexion from a free boundary is analyzed and presented graphically, and general rules governing the structure of the characteristics field are obtained.
Abstract: C ontour-plotting methods are applied to non-linear materials with a two-straight-line stress-strain relation, such as certain types of rubber or foam plastic. The multiple scabbing phenomenon of materials due to tensile reflexion from a free boundary is analysed and presented graphically. General rules governing the structure of the characteristics field are obtained.