Plane Waves Due to Combined Compressive and Shear Stresses in a Half Space

1969 ◽  
Vol 36 (2) ◽  
pp. 189-197 ◽  
Author(s):  
T. C. T. Ting ◽  
Ning Nan
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Half Space ◽  
Plastic Material ◽  
Plane Waves ◽  
Shear Stresses ◽  
Elastic Plastic ◽  
Elastic Plastic Material ◽  
Plane Wave Propagation

The plane wave propagation in a half space due to a uniformly distributed step load of pressure and shear on the surface was first studied by Bleich and Nelson. The material in the half space was assumed to be elastic-ideally plastic. In this paper, we study the same problem for a general elastic-plastic material. The half space can be initially prestressed. The results can be extended to the case in which the loads on the surface are not necessarily step loads, but with a restricting relation between the pressure and the shear stresses.

Plane Waves in an Elastic-Plastic Half-Space Due to Combined Surface Pressure and Shear

1966 ◽  
Vol 33 (1) ◽  
pp. 149-158 ◽  
Author(s):  
H. H. Bleich ◽  
Ivan Nelson
Keyword(s):  
Wave Propagation ◽  
Differential Equations ◽  
Half Space ◽  
Nonlinear Differential Equations ◽  
Plane Waves ◽  
Yield Condition ◽  
Shear Stresses ◽  
Von Mises ◽  
Plane Wave Propagation ◽  
Normal And Shear Stresses

The most general case of plane wave propagation, when normal and shear stresses occur simultaneously, is considered in a material obeying the von Mises yield condition. The resulting nonlinear differential equations have not been solved previously for any boundary-value problem, except for special situations where the differential equations degenerate into linear ones. In the present paper, the stresses in a half-space, due to a uniformly distributed step load of pressure and shear on the surface, are obtained in closed form.

Influence of Materials Hardenability Parameters on the Machine Parts Characteristics after Unloading

2016 ◽  
Vol 723 ◽  
pp. 369-375 ◽  
Author(s):  
P.M. Ogar ◽  
D.B. Gorokhov
Keyword(s):  
Rough Surface ◽  
Half Space ◽  
Plastic Material ◽  
Practical Importance ◽  
Pressure Vessels ◽  
Design Stage ◽  
Real Surface ◽  
Height Distribution ◽  
Elastic Plastic ◽  
Elastic Plastic Material

This paper studies the problem of the relative area changing on a decrease of the load applied to the joint of roughness surfaces. The penetration of a rigid rough sphere (indenter) into the elastic hardenable half-space is initially considered, then the elastic crater restoring by unloading is considered. To defining elastic-plastic material, Hollomon’s power law is used. To describe a contact of a rigid rough surface with an elastic plastic half-space, the discrete model of a rough surface is used. Microasperities are represented as a set of identical spherical segments, the height distribution of which corresponds to the bearing profile curve of the real surface. The dependence the dimensionless force elastic-geometric parameter Fq on a relative amount of indentation ε at loading and the dependence of analogous parameter Fqe on amount of ε-Dε at unloading are obtained. The relations of relative contact areas h and he on dimensionless loading Fq and Fqe at loading and unloading for different values of a hardening exponent n and parameter are given. The obtained results are of practical importance for the performance prediction of fixed machine elements’ joints at the design stage, in particular for tightness supply of flange couplings and high pressure vessels seals.

scholarly journals Plane wave propagation in a 3D anisotropic half-space under Green-Naghdi theory II

2016 ◽  
Vol 2 (2) ◽  
pp. 114-134 ◽  
Author(s):  
N. Sarkar ◽  
S. Chakraborty ◽  
S. C. Mandal ◽  
A. K. Das ◽  
A. Lahiri
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Half Space ◽  
Plane Wave Propagation

Transient analytic point‐source response of a layered acoustic medium: Part I

Geophysics ◽  
1985 ◽  
Vol 50 (9) ◽  
pp. 1466-1477 ◽  
Author(s):  
Martin Tygel ◽  
Peter Hubral
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Point Source ◽  
Time Domain ◽  
Plane Waves ◽  
Natural Extension ◽  
Acoustic Medium ◽  
Angle Of Incidence ◽  
The Time Domain ◽  
Plane Wave Propagation

The exact transient responses (e.g., reflection or transmission responses) of a transient point source above a stack of parallel acoustic homogeneous layers between two half‐spaces can be analytically obtained in the form of a finite integral strictly in the time domain. (The theory is presented in part II of this paper, this issue.) The transient acoustic potential of the point source is decomposed into transient plane waves, which are propagated through the layers at any angle of incidence as well in the time domain; finally, they are superposed to obtain the total point‐source response. The theory dealing with transient analytic plane wave propagation is described here. It constitutes an essential part of computing the synthetic seismogram by the new transient method proposed in part II. The plane‐wave propagation is achieved by an exact discrete recursion that automatically handles the conversion of homogeneous waves into inhomogeneous transient plane waves at layer boundaries. A particularly efficient algorithm is presented, that can be viewed as a natural extension of the popular normal‐incidence Goupillaud (1961)-type algorithm to the nonnormal incidence case.

Plane waves in anisotropic elastic–plastic material with voids

2020 ◽  
pp. 107754632097771
Author(s):  
Suraj Kumar ◽  
Sushil Kumar Tomar
Keyword(s):  
Dispersion Equation ◽  
Plastic Material ◽  
Plane Waves ◽  
Transversely Isotropic ◽  
Specific Model ◽  
Elastic Plastic ◽  
Anisotropic Elastic ◽  
Elastic Plastic Material ◽  
The One ◽  
Elastic Plastic Materials

Dispersion equation is derived for the propagation of one-dimensional plane waves in a general linear anisotropic isothermal elastic–plastic material with voids. The plasticity of the considered material is defined through the dislocation of a single slip plane and direction. The derived dispersion equation is then reduced for the relevant wave propagation in particular media, namely, monoclinic, orthotropic, transversely isotropic, and isotropic elastic–plastic material with voids. In general, it is found that there exist four basic waves traveling with distinct speeds in these specific anisotropic elastic–plastic materials with voids. A new wave is found to appear because of the presence of plasticity in the material. Out of the four basic waves traveling in an orthotropic/transversely isotropic material with voids, a wave travels independent of plasticity and void parameters, whereas the remaining three waves depend on plasticity as well as on the presence of voids. The one which is traveling independent of plasticity and voids is nondispersive and nonattenuating, whereas the other waves are dispersive in nature. The speeds of all the existing waves are computed numerically for a specific model, displayed graphically, and discussed.

Structural Integrity Research for Reactor Pressure Vessel Under In-Vessel Retention of a Core Melt

2016 ◽  
Author(s):  
Yongjian Gao ◽  
Yinbiao He ◽  
Ming Cao ◽  
Yuebing Li ◽  
Shiyi Bao ◽  
...  
Keyword(s):  
Pressure Vessel ◽  
Material Properties ◽  
Power Plants ◽  
Structural Integrity ◽  
Plastic Material ◽  
Plastic Region ◽  
Reactor Pressure Vessel ◽  
Elastic Plastic ◽  
Elastic Plastic Material ◽  
Reactor Pressure

In-Vessel Retention (IVR) is one of the most important severe accident mitigation strategies of the third generation passive Nuclear Power Plants (NPP). It is intended to demonstrate that in the case of a core melt, the structural integrity of the Reactor Pressure Vessel (RPV) is assured such that there is no leakage of radioactive debris from the RPV. This paper studied the IVR issue using Finite Element Analyses (FEA). Firstly, the tension and creep testing for the SA-508 Gr.3 Cl.1 material in the temperature range of 25°C to 1000°C were performed. Secondly, a FEA model of the RPV lower head was built. Based on the assumption of ideally elastic-plastic material properties derived from the tension testing data, limit analyses were performed under both the thermal and the thermal plus pressure loading conditions where the load bearing capacity was investigated by tracking the propagation of plastic region as a function of pressure increment. Finally, the ideal elastic-plastic material properties incorporating the creep effect are developed from the 100hr isochronous stress-strain curves, limit analyses are carried out as the second step above. The allowable pressures at 0 hr and 100 hr are obtained. This research provides an alternative approach for the structural integrity evaluation for RPV under IVR condition.

Sign in / Sign up

Export Citation Format

Share Document