Tresca Yield Condition Research Articles

Thermal assembly of an elastic-plastic shrink fit with solid inclusion

The subject of the investigation is the thermal assembly of an elastic-plastic ring and a solid disk. Based on Tresca's yield condition and the flow rule associated with it, the transient stress distribution is discussed and illustrated by numerical results.

Thermal stresses in a heat generating elastic-plastic cylinder with free ends

The exact solution of the distribution of stress and deformation in an elastic-perfectly plastic cylindrical rod with uniform internal heat generation under generalized plane strain condition is presented. The treatment is based on Tresca's yield condition and the associated flow rule. The stress image points of the outer and inner plastic regions lie on two different edges of Tresca prism. With increasing heat generation parameter, the image points of the intermediate regions spread out through two side regimes and meet at another edge regime in the fully plastic state.

The influence of the temperature dependence of the yield stress on the stress distribution in a thermally assembled elastic-plastic shrink fit

The subject of the investigation is the thermal assembly of an elastic-plastic shrink fit with hollow inner component. Based on Tresca's yield condition and the flow rule associated with it, the transient stress distribution is studied. Special attention is paid to the influence of the reduction of the yield stress at elevated temperatures on the interface pressure. However, it turns out that this influence is not significant.

The rotating elastic-plastic shrink fit with solid inclusion after thermal assembly

The behaviour of a thermally assembled shrink fit consisting of an elastic-plastic ring and a solid disk subject to rotation is investigated. Special attention is paid to the evolution of the interface pressure. All the results are based on Tresca's yield condition and the flow rule associated with it.

Thermal stresses in a shrink fit due to an inhomogeneous temperature distribution

Based on Tresca's yield condition and its associated flow rule, a semianalytical method is presented for the calculation of thermal stresses due to steady-state thermal loading in an assembled shrink fit. The calculation is evaluated assuming plane stress conditions, linear elastic-perfectly plastic materials, and linearly temperature dependent yield stresses. Depending on the temperature gradient, different combinations of pure elastic and plastic zones arise in the shaft and in the hub.

Optimization of rigid-plastic shallow spherical shells of piecewise constant thickness

An approximate method developed earlier for the investigation of large plastic deflections of circular and annular plates is accommodated for shallow spherical shells. The material of the shells is assumed to obey Tresca's yield condition and the associated deformation law. The minimum weight problem concerning shells operating in the post-yield range is posed under the conditions that (i) the thickness of the structure is piece-wise constant and (ii) the maximal deflections of the optimized shell and a reference shell of constant thickness, respectively, coincide. Necessary optimality conditions are derived with the aid of the variational methods of the optimal control theory. The set of equations obtained is solved numerically.

On the elastic-plastic rotating shrink fit with linearly hardening hub exhibiting variable thickness in exponential form

The plane state of stress in a rotating shrink fit is investigated. The analysis is based on Tresca's yield condition, its associated flow rule and linear strain hardening. The rotating shrink fit consists of an elastic solid inclusion and a partially plasticized hub with variable thickness in the exponential formh=h 0e−n(r/ro) k, whereh 0, n andk are real constants. It is assumed that the hub is thin and the variation of thickness is radial and symmetric with respect to the midplane. The stresses are obtained in terms of confluent hypergeometric functions.

Limit Analysis of Weak Layers under Embankments

Limit loads on finite layers of weak soil over a rigid base are analyzed using the upper bound approach. The soil is considered cohesive, and the Tresca yield condition is used to describe its strength. Strength increasing with depth is considered, and different strengths of the base interface are accounted for. The analysis is performed having the design of embankments in mind, and it makes it possible to account for the arbitrary horizontal component of the load generated by the horizontal thrust in the embankment. Results are compared to the lower bound solutions of particular cases available in the literature. Even though the upper bound approach was used, the solutions presented fall very close to the lower bound solutions. The advantage of the solutions presented in this paper is in easier calculations of bearing capacity, especially when the soil strength increases with depth, and in accounting for the arbitrary horizontal load transmitted from the embankment to the foundation soil. A proposal for arriving at critical heights of both unreinforced and reinforced embankments is given.

On the stresses in an elastic-plastic annular disk of variable thickness under external pressure

The plane state of stress in an elastic-plastic annular disk of variable thickness subjected to external pressure is studied. The thickness of the annular disk is assumed to vary exponentially with any power of the radius. The analysis is based on Tresca's yield condition, its associated flow rule and linear strain hardening. The stresses are obtained in terms of confluent hypergeometric functions.

Stress distribution in shrink fit with elastic-plastic hub exhibiting variable thickness

The state of plane stress in shrink fit with an elastic-plastic hub exhibiting variable thickness is studied. The thickness of the hub is assumed to vary exponentially with a general power of the radial distance from the inner boundary of the hub. The analysis is based on Tresca's yield condition, its associated flow rule and linear strain-hardening. Closed-form solutions are obtained in terms of confluent hypergeometric functions.

Guist and marble revisited—On the natural knuckle radius in tube inversion

An attempt has been made to resolve an apparent anomaly between theoretical predictions and experimental observations on the natural knuckle radius during external inversion of tubes. A rigid, linear strain-hardening material model is used. The Tresca yield condition and associated flow rules along with a kinematic hardening law are employed. Analytical results show good agreement between predicted and experimentally observed values of the critical knuckle radius. It is found that the strain-hardening parameter which provides the best agreement with the experimental data depends on the magnitude of the strain and hence the geometry of the tube. The calculated inversion loads are seen to agree better with the observed values than those from an earlier analysis.

Optimal design of rigid-plastic annular plates with piecewise constant thickness

Rigid-plastic stepped annular plates under uniform pressure load are considered. Both plate edges are supported. Four types of boundary conditions are studied. Tresca's yield condition is used. Such plate dimensions are sought for which the plate of constant volume has the maximal load carrying capacity.

Elastic-plastic stresses in a rotating annular disk of variable thickness and variable density

The influence of a radial density gradient on elastic-plastic stresses and radial displacement in a rotating disk with variable thickness is investigated for a linear strain-hardening material. The analysis is based on Tresca's yield condition, its associated flow rule and linear strain-hardening. Closed-form solutions for stresses and radial displacement are obtained. Some numerical results are provided showing the influence of density gradient on the stresses and the relation between angular velocity and elastic-plastic interface radius. It is shown that the density gradient influences the radial stresses, the critical angular velocities and the elastic-plastic interface radius significantly.

The rotating shrink fit with elastic-plastic hub exhibiting variable thickness

Based on Tresca's yield condition, the associated flow rule and linear strain hardening, the stress distribution in the hub of a rotating shrink Pit is studied. The rotating shrink fit consists of an elastic solid disk with uniform thickness and partially plasticized hub with variable thickness. It is assumed that the assembly is thin and that the variation of thickness is radial. The problem is solved in closed form.

Elastic-plastic stress distribution in the rotating annular disk with variable thickness

The plane state of stress in a rotating annular disk with variable thickness is studied. The analysis is based on Tresca's yield condition, its associated flow rule and linear strain hardening.

The shrink fit with elastic-plastic hub exhibiting variable thickness

An analytical solution for a shrink fit consisting of an elastic disk with constant thickness and partially plasticized hub with variable thickness is presented. The analysis is based on Tresca's yield condition, its associated flow rule and linear strain hardening.

Elastic-plastic deformation of a centrally heated cylinder

Subject of the investigation is the deformation of a perfectly plastic cylinder with uniform temperature inside its cylindrical core and zero surface temperature. The calculation is based on Tresca's yield condition and the flow rule associated to it. For small radii of the hot core, a plastic region appears at the center expands towards the surface of the cylinder with increasing core temperature. The other possibility is that, depending on the core radius, two plastic regions form one after the other or simultaneously, in the core and at the surface and join in the fully plastic state. The image points of the cylinder lie on different edges and sides of the Tresca-prism in stress space.

KINEMATICALLY DETERMINED AXIALLY-SYMMETRIC PLASTIC FLOWS OF METALS AND GRANULAR MATERIALS

In certain plastic regimes for axially symmetric flows of rigid-perfectly plastic solids obeying Tresca's yield condition and associated flow rule, the velocity equations uncouple from the stress equations and are kinematically determined. Moreover, the same equations apply for axially-symmetric deformations of an incompressible granular material which deforms according to the Coulomb-Mohr yield condition and the so-called ‘double-shearing theory’. Here we derive a new family of exact solutions of these equations and the underlying first-order ordinary differential equation is shown to be exactly integrable. When the integration constant B is set to zero, two simple families of exact solutions are obtained; one is well known while the other appears not to have been given previously. Moreover, we note that these two simple families of exact solutions can be combined to present an additional exact solution which is continuous across the join z = 0. When the constant B is non-zero, the solution involves the roots of a quartic equation and there appears to be no simple expressions for the associated velocity field. For the new solution arising from B = 0, a partial analysis of the corresponding stress field is presented assuming Tresca's yield condition, and some simple closed expressions, which incorporate gravity, are obtained. The stress-field calculations assuming a oulomb-Mohr yield criterion are far more elaborate and are not attempted here. Stream paths for both the previously known exact solution and the new solution are displayed.

Rotating elastic-plastic tube with free ends

Based on Tresca's yield condition and the associated flow rule, the distribution of stress, strain and displacement in a rotating hollow cylinder of elastic-plastic material under generalized plane strain is discussed.

Some generalized similarity solutions for plastic flow

In kinematically determined regimes, the velocity equations for axially symmetric flow of a perfectly plastic solid which obeys Tresca's yield condition and associated flow rule possess many symmetries. These equations apply also to the flow of granular materials according to the ‘double-shearing’ theory of Spencer [1], [2]. Using Lie group methods, five classes of generalized self-similar solutions are identified. Special cases are the two types of solution due to Lippmann [3] [4] and the flow past a cone found by Spencer [5]. For each class of solution, determination of the stream function requires the solution of a second-order ordinary differential equation, which can in each case be reduced to the analysis of a first-order equation. Examples of the flow fields and corresponding streamlines for three of the four newly determined cases are computed numerically.