Showing papers in "Journal of The Mechanics and Physics of Solids in 1968"
TL;DR: In this paper, a total deformation theory of plasticity, in conjunction with two hardening stress-strain relations, is used to determine the dominant singularity at the tip of a crack in a tension field.
Abstract: D istributions of stress occurring at the tip of a crack in a tension field are presented for both plane stress and plane strain. A total deformation theory of plasticity, in conjunction with two hardening stress-strain relations, is used. For applied stress sufficiently low such that the plastic zone is very small relative to the crack length, the dominant singularity can be completely determined with the aid of a path-independent line integral recently given by rice (1967). The amplitude of the tensile stress singularity ahead of the crack is found to be larger in plane strain than in plane stress.
2,667 citations
TL;DR: In this article, the dominant singularity governing the plastic behavior at a crack tip is analyzed for conditions of plane stress and plane strain for cracks in both far tensile and far shear fields.
Abstract: Further details of the stress and strain fields associated with the dominant singularity governing the plastic behaviour at a crack tip are presented for conditions of plane stress and plane strain for cracks in both far tensile and far shear fields. Results are obtained for a power hardening material. Limiting cases for non-hardening materials are shown to correspond to certain perfect plasticity solutions.
700 citations
TL;DR: In this paper, pragmatic postulates of material behaviour not given by thermodynamics are reviewed critically, and possible improvements to the inequalities are explored, having regard to the available evidence for actual materials.
Abstract: S ome pragmatic postulates of material behaviour, not given by thermodynamics, are reviewed critically. The postulates typically state lower bounds to the work expended on infinitesimal or finite paths of deformation. It is pointed out that such bounds implicitly depend on arbitrary choices of the strain measure. This dependence is investigated in the general context of conjugate stress and strain variables. Possible improvements to the inequalities are explored, having regard to the available evidence for actual materials. Part I is mainly concerned with elastic solids.
459 citations
TL;DR: In this article, a n integral series representation for non-linear viscoelastic response to an arbitrary strain (or stress) history is obtained, where the series has the distinctive property that it terminates at the n th term whenever the strain or stress history is an n-step history.
Abstract: A n integral series representation is obtained for non-linear viscoelastic response to an arbitrary strain (or stress) history. The series is arranged so that experimental data can be incorporated directly. Each of the terms has a definite intrinsic meaning that is independent of the choice of strain measure. The first term is a single integral with a non-linear integrand determined completely by single-step creep or relaxation tests. The n th term is obtained directly by the difference, if any is observed, between the experimental results for n -step tests and the prediction based on ( n −1)-step data. The series has the distinctive property that it terminates at the n th term whenever the strain (or stress) history is an n -step history. p]Previously published experimental data on non-linear viscoelastic behaviour are re-interpreted on the basis of this theory; in most cases they agree very closely with the single integral approximation given by the first term alone. p]The generalization to three-dimensional form and the implications of isotropy are also given.
250 citations
TL;DR: In this paper, the shape of the subsequent yield surface and the correlation between the change of the stress increments and that of the plastic strain increments for a zigzag loading path were discussed with reference to a shape of stress-strain diagram.
Abstract: T he subsequent yield surfaces after prestraining along various loading paths or by cold rolling were determined with cross-shaped specimens of brass plate. The shape of the subsequent yield surface and the correlation between the change of the stress increments and that of the plastic strain increments for a zigzag loading path were discussed with reference to the shape of stress-strain diagram. The experimental values of the yield surfaces of the cold-rolled brass plate were compared with the calculated values by Dorn's theory.
100 citations
TL;DR: In this article, the propagation of discontinuities of the stresses and the temperatures is studied in a one-dimensional medium, in which the displacement and the temperature fields are coupled, and in which transport of heat takes place at a finite velocity.
Abstract: T he propagation of discontinuities of the stresses and the temperatures is studied in a one-dimensional medium, in which the displacement and the temperature fields are coupled, and in which the transport of heat takes place at a finite velocity. It is shown that the application of a thermal or a mechanical disturbance gives rise to two wave fronts, whose speeds are expressed in terms of the material constants. The temperatures at the wave fronts are discontinuous unless Fourier's classical law of heat conduction is valid. The jumps at the wave fronts decay exponentially, and expressions for the exponents in terms of the material constants are presented. All results are obtained through application of the theory of propagating surfaces of discontinuity.
92 citations
TL;DR: In this article, the influence of the indenter on the slipline field for the standard Charpy-Izod test specimen was studied and the constraint factor, but not the stress-state around the notch, was found to be sensitive to indenter conditions assumed.
Abstract: Standard plane-strain solutions for the bending of notched rigid/plastic bars apply only if the notch is sufficiently deep ( Gpreen 1956). Following Green, critical notch depths are calculated for a range of V-notches with circular roots, under pure bending. In particular, the conventional deep-notch soluton does not apply to the pure bending of the standard Charpy-Izod test specimen. The influence of the indenter on the slipline field for the Charpy test is also studied. The constraint factor, but not the stress-state around the notch, is found to be sensitive to the indenter conditions assumed. Detailed calculations are presented.
76 citations
TL;DR: In this article, a slip line field was constructed for the deformation of a rigid perfectly-plastic wedge compressed by a flat rigid die and subsequently sheared by a force acting tangentially to the face of the die.
Abstract: A slip-line field has been constructed for the deformation of a rigid perfectly-plastic wedge compressed by a flat rigid die and subsequently sheared by a force acting tangentially to the face of the die. An associated velocity field is suggested. Consistency between the slip-line field, the velocity field and the changing profile of the wedge as deformation proceeds is closely, though not exactly, preserved. The progressive deformation has been found, using these fields, by an incremental graphical construction. The deformation and the growth of the area of contact between the wedge and the die face under the action of a constant normal force and increasing tangential force are found to agree well with experiment. The theoretical contact area growth supports Tabor's empirical expression for ‘junction growth’ in the build-up of static friction between metallic surfaces.
48 citations
TL;DR: In this article, a phenomenological analysis of the mechanism of creep in a fiber composite is made using virtual displacements to demonstrate the usefulness of such an approach and the implications of the combined effect of these processes on the mode of rupture of the composite are briefly examined.
Abstract: A phenomenological analysis is made of the mechanism of creep in a fibre composite. This is done using virtual displacements to demonstrate the usefulness of such an approach. The creep of the composite is found to be governed by the following three processes. (i) Relaxation of shear stresses at fibre ends causing load re-distribution. (ii) Stress relaxation of the matrix causing load transfer to the fibres. (iii) Creep of the fibres. The implications of the combined effect of these processes on the mode of rupture of the composite are briefly examined. Finally, hypothetical composites are analysed to illustrate the application of the theory. Reported observations of the creep behaviour of conventional fibre-reinforced composites are explained by the theory proposed.
45 citations
TL;DR: In this article, it is shown that unless passive constraints are acting, only a bending mode of instability is possible for the title problem with slenderness ratios exceeding 6. This leads one to question the interpretation given by beatty and hook to some recent experimental work of their.
Abstract: The title problem is studied by means of the stability criterion due to hill (1957). The stationary principle associated with Hill's criterion provides precise stability bounds for the problem which are compared with the critical loads predicted by the classical Euler formula. It is found, if one uses the slenderness ratio defined in engineering practice, that the Euler formula gives excellent estimates of the critical stress for slenderness ratios exceeding 35. Furthermore, if the results are plotted in terms of the dimensions of the underformed body and the ‘ nominal stress,’ then the Euler formula gives conservative estimates of the critical stress for slenderness ratios exceeding 6. It is proved, unless passive constraints are acting, that only a ‘bending’ mode of instability is possible. This leads one to question the interpretation given by beatty and hook (1968) to some recent experimental work of theirs.
43 citations
TL;DR: In this paper, a steady state dynamic solution for a Dugdale crack propagating at a constant speed is obtained with the Sneddon-Radok formulation of the dynamic plane elasticity equations.
Abstract: A steady state dynamic solution for a Dugdale crack propagating at a constant speed is obtained with the Sneddon-Radok formulation of the dynamic plane elasticity equations. The dynamic stress distribution and the Tresca yield condition are used to determine the limiting ductile crack propagation speed. It is shown that the limiting brittle crack speed criteria of Yoffe and of Craggs are satisfied as well. A simple relation between the flow stress and the crack speed based on observations of ductile crack propagation in steel foil is utilized in order to express the limiting speed in terms of the applied load and material properties. Calculated values of the limiting speed in steel and aluminium sheets are found to be not strongly dependent on the applied load and are about 0-1C 2 and 0-3C 2 , respectively.
TL;DR: In this article, the authors present an application of the dislocation theory of intersections to the experimental results obtained at changed strain rates under conditions of pure shear for polycrystalline aluminium.
Abstract: T his work presents an application of the dislocation theory of intersections to the experimental results obtained at changed strain rates under conditions of pure shear for polycrystalline aluminium. Simultaneously, strain-rate history effects have been shown, and discussed in terms of dislocation behaviour.
TL;DR: In this paper, the effect of the prestraining path on the shape of the yield surfaces of an aluminium alloy was investigated. But the results were limited to the case where the initial sectors of the loading path had different initial sectors and a common final sector.
Abstract: Experimental results for fifty-six specimens of an aluminium alloy are presented in a study of the effect of the prestraining path on the shape of the yield surfaces. A special experimental technique has been applied, consisting of cutting out flat specimens from the prestrained sheet material. Experimental results show that if two various loading paths have different initial sectors and a common final sector, the influence of these initial sectors on the yield surface is the smaller the longer is the final common sector. A theoretical analysis of that problem on the basis of the kinematic workhardening rule is also presented.
TL;DR: In this article, a solution of the basic equations for notches and cracks in shear strained prisms is derived in closed form, valid for the same form of boundary for all possible nonlinear stress-strain-laws and all loading intensities.
Abstract: I n order to investigate the mechanism of physically nonlinear stress concentration and crack propagation, a solution of the basic equations for notches and cracks in shear strained prisms is derived in closed form, valid for the same form of boundary for all possible nonlinear stress-strain-laws and all loading intensities. The boundary consists of two parallel straight flanks and a cycloid.
TL;DR: In this paper, classic thermodynamic considerations are employed to derive the condition for bifurcation of a crack situated within a brittle solid deforming in an antiplane strain mode.
Abstract: Classic thermodynamic considerations are employed to derive the condition for bifurcation of a crack situated within a brittle solid deforming in an anti-plane strain mode. Criteria are determined for bifurcation along circular segments at right angles to the initial crack, and also along planar segments inclined at an arbitrary angle with respect to the original crack, the results being used in a brief discussion of physical situations where bifurcation occurs.
TL;DR: In this article, the shape of the initial disturbance and the visco-elastic properties of the medium were used to predict the surface waves produced by the impact of steel balls.
Abstract: Experiments have been carried out to observe the surface waves produced on large blocks of polyethylene and polymethylmethacrylate (p.m.m.) when specimens of these materials have been subjected to surface impacts of steel balls or when small lead azide charges have been detonated on the free surfaces. It has been shown that if Poisson's ratio, v , is taken to be a real constant the shapes of surface waves can be calculated if the shape of the initial disturbance and the visco-elastic properties of the medium are known. It has further been shown that the complex nature of v results in only second-order effects for the materials used. It has consequently been found possible to forecast the shape of surface waves produced by the impact of steel balls. The agreement with experimentally observed shapes was found to be excellent for the p.m.m. specimen. The theoretical predictions were less accurate for the polyethylene specimen, but the predictions here agreed reasonably well with the experiments. It was not found possible to predict the surface waves produced by the explosive charges chiefly because of uncertainty of the shape of the initial disturbance. The experimental results did, however, show two distinct groups of waves, one travelling with the dilatational velocity and the other with a velocity close to that of the shear velocity. At short distances of travel these two groups overlapped.
TL;DR: In this article, a perturbation method is used to investigate the plane strain problem in which plastic deformation of the plane surface of a semi-infinite rigid/ideally-plastic body is produced by the rolling contact with a rigid, circular cylinder.
Abstract: A perturbation method is used to investigate the plane strain problem in which plastic deformation of the plane surface of a semi-infinite rigid/ideally-plastic body is produced by the rolling contact with a rigid, circular cylinder. Calculations are made of the rolling resistance and permanent surface displacement, and a typical slip-line field is constructed.
TL;DR: The most common form of damage in this material appears to be the formation of sharp grain boundary cracks and a model has recently been proposed for the gradual growth of one of these cracks to infinite size as mentioned in this paper.
Abstract: Mechanisms for creep damage and fracture are analyzed and compared with phenomenological creep rupture theories for an austenitic stainless steel The most common form of damage in this material appears to be the formation of sharp grain boundary cracks A model has recently been proposed for the gradual growth of one of these cracks to infinite size The size of this crack should represent the extent of damage in the material when widespread crack coalescence does not take place It is shown that the model is consistent with the Kachanov-Odqvist theory for creep rupture and, under certain conditions, with the Robinson life-fraction rule for the summation of creep periods of different stress levels Ductile creep theories appear to be applicable only in rare cases for these materials
TL;DR: In this paper, the rigid/plastic plane strain constraint factor for V-notched bars with circular roots in simple tension was investigated and the results showed that as long as yielding spreads to the bar sides, without being confined to the notch neighborhood, the yieldpoint load is fairly insensitive to enlarging, without deepening, the notch.
Abstract: Close bounds are found to the rigid/plastic plane strain constraint factor for V-notched bars with circular roots in simple tension. This extends previous work ( Ewing and Hill 1967) on sharply-notched bars. The end results are expressed as simple functions of the geometrical parameters, with an error within 0.2 per cent. As long as yielding spreads to the bar sides, without being confined to the notch neighbourhood, the yieldpoint load is found to be fairly insensitive to enlarging, without deepening, the notch. The minimum length of bar needed for these solutions to apply is discussed briefly. Comparisons are made with existing elastic/plastic numerical calculations. In particular, the constraint factor for a semicircularly notched bar, of net width twice its core width, is here found to be 1.386, in contrast to the value 1.22 found by Allen and Southwell (1950) using relaxation methods.
TL;DR: In this article, the authors proposed a method for the direct determination of the short-time portion of creep and relaxation functions of linear viscoelastic materials, which can yield accurate results for very early times, the range in which it is usually difficult to assess the mechanical properties of VMs.
Abstract: The analytical bases are given for the design of some experiments for the direct determination of the short-time portion of creep and relaxation functions of linear viscoelastic materials. These procedures, which emanate from a study of the manner in which waves propagate in viscoelastic media, should yield accurate results for very early times—the range in which it is usually difficult to assess the mechanical properties of viscoelastic materials. Some of the proposed methods utilize expansions valid for short times, while others are based primarily on convolutional operations. They require the measurement of the same response quantity at two different locations in the medium, or measurements of two different response quantities at the same location.
TL;DR: In this paper, the operational method of analysing slip-line fields developed by Collins (1968) is applied to the extrusion problem and a new technique is introduced involving artificial deformation modes.
Abstract: Pimple relations between various lengths occurring in some slip-line field solutions are rigorously established. The problems are compression of rigid/plastic material between smooth dies and extrusion through smooth square dies with medium reduction. The operational method of analysing slip-line fields developed by Collins (1968) is applied to the extrusion problem. In addition a new technique is introduced involving ‘ artificial deformation modes’. This is used to establish the remaining formulae previously suggested for these two problems.
TL;DR: In this paper, a general procedure for predicting the way in which transient pulses propagate through an arbitrary, linearly viscoelastic, medium characterized by creep or stress relaxation functions is developed.
Abstract: A general procedure is developed for predicting the way in which transient pulses propagate through an arbitrary, linearly viscoelastic, medium characterized by creep or stress relaxation functions. By use of the Laplace transform, differential operations in transform space, and some asymptotic methods, the boundary-value problem in question is reformulated in terms of a Volterra integral equation, with the space variable playing the role of a parameter. This equation is readily resolved numerically, and results obtained by this procedure compare very well with solutions available in the literature.
TL;DR: In this paper, the authors define a mode de definition de l'etat thermodynamique based on the relations of Coleman liant les contraintes and l'entropie aux derivees partielles of l'energie libre par rapport aux deformations and a la temperature.
Abstract: Les relations de Coleman liant les contraintes et l'entropie aux derivees partielles de l'energie libre par rapport aux deformations et a la temperature ne s'appliquent qu'aux corps viscoelastiques doues d'une elasticite instantanee complete (6 degres de liberte). On etablit ici des relations analogues] mais valables pour tous les milieux, pourvu qu'il n'y ait pas de deformations instantanees irreversibles. Pour obtenir ce resultat, il est necessaire de substituer les contraintes aux deformations comme variables independantes. Ce mode de definition de l'etat thermodynamique est compare au mode classique, notamment dans le cas des fluides. Les relations obtenues permettent d'etudier en toute generalite les proprietes des ondes de discontinuite ordinaires dans un milieu viscoelastique et en particulier de preciser le nombre des ondes possibles pour une meme direction de normale.
TL;DR: In this article, the authors investigated the plastic yielding of truncated solid cones under quasistatic and dynamic axial loads at strain rates of 10 −5 sec −1 and 10 2 sec t1, respectively.
Abstract: The plastic yielding of truncated solid cones has been investigated experimentally under quasistatic and dynamic axial loads at strain rates of 10 −5 sec −1 and 10 2 sec t1 , respectively. The quasistatic experiments were performed both with and without friction at the interface between the truncated end of the cone and the ‘ rigid ’ wall. Both the dynamic and the quasi-static yield stresses increase linearly with an increase in conical angle, and the dynamic values are about 20–80 per cent higher than the frictional quasi-static results. A part of this increase is due to Coulomb friction. The quasi-static experimental results are compared with lower bound axisymmetric plasticity solutions, with favourable agreement. The coefficient of friction is determined by comparing the theoretical results with the experimental results. The condition for sticking at the interface is also given. The velocity fields associated with the stress fields were considered and it was found that the Haar-von Karman hypothesis is violated in limited regions for a certain range of conical angles.
TL;DR: In this article, the convexity conditions of strain energy and complementary energy of classical elasticity were derived for history-dependent time independent materials, and energy theorems, which provide generalizations of the elastic theorem, were discussed.
Abstract: G lobal convexity conditions, corresponding to the convexity of strain energy and complementary energy of classical elasticity, are derived for history dependent time independent materials. Energy theorems, which provide generalizations of the elastic theorems, are discussed.
TL;DR: In this article, the surface wave produced by the Hertzian impact was calculated by considering the variation of the normal stress and the area of contact with respect to time, and the predicted pulse shapes at four different distances from the centre of the contact area were found to be in reasonable agreement with those determined experimentally.
Abstract: The surface waves produced by Hertzian impact were calculated by considering the variation of the normal stress and the area of contact with respect to time. The predicted pulse shapes at four different distances from the centre of the contact area were found to be in reasonable agreement with those determined experimentally.
TL;DR: In this article, a complete analytical solution was developed for the problem of finite expansion of a circular hole of zero (pin-hole) or finite initial radius, using Tresca's yield condition and the associated flow rule together with an isotropic strain-hardening law.
Abstract: An infinite disk with an initial thickness h0=αr0n, where α and n are constants, is considered. A complete analytical solution is developed for the problem of finite expansion of a circular hole of zero (pin-hole) or finite initial radius, using Tresca's yield condition and the associated flow rule together with an isotropic strain-hardening law. Results of previous investigations are obtained as special cases of the present more general closed-form solution.
TL;DR: In this paper, diffraction grating measurements of finite strain nonlinear wave fronts are described for elastic-plastic interface experiments, and a correlation with theory under these varied conditions is shown.
Abstract: T he diffraction grating measurements of finite strain nonlinear wave fronts are described for elastic-plastic interface experiments. Close agreement with theoretical prediction on both sides of the interface is shown to exist when the non-viscous finite deformation parabolic stress-strain runction for annealed polycrystalline aluminium is introduced into the finite amplitude wave theory of Taylor, von Karman and Rakhmatulin, and into the nonlinear unloading wave theory of Lee. Dynamic studies of interface lubrication, of Pochhammer-Chree oscillations in the hard bar, and of variations in the mode of unloading are included providing detailed experimental correlation with theory under these varied conditions. Diffraction grating surface-angle measurements in the elastic-plastic interface experiment are shown to provide a detailed demonstration that the nonlinear finite amplitude wave fronts are one-dimensional extending across the entire specimen diameter. These measurements also have demonstrated experimentally that finite amplitude wave propagation in dynamic plasticity is an incompressible distortional deformation.
TL;DR: In this article, the effect of tensile prestrain rate and compressive strain rate on metal behavior during reversed loading was investigated and the results of an exploratory study of the impact of strain rates on metal behaviour during reverse loading were presented.
Abstract: Results of an exploratory study of the effect of strain rate on metal behaviour during reversed loading are presented. All test specimens were made from commercially pure aluminium; these specimens were prestrained in tension and then strained in compression at several strain rates. The effect of tensile prestrain rate and compressive strain rate is shown. Also, the compressive strain rate dependence of aluminium with a tensile prestrain is compared to the strain rate dependence of aluminium with no prestrain.