scholarly journals Indentation and residual stress in the axially symmetric elastoplastic contact problem

2012 ◽  
Vol 7 (10) ◽  
pp. 887-898
Author(s):  
Tian-hu Hao
Keyword(s):  
Residual Stress ◽  
Contact Problem ◽  
Axially Symmetric ◽  
Elastoplastic Contact

Preferred orientation in Debye–Scherrer geometry: interpretation of the March coefficient

2000 ◽  
Vol 33 (6) ◽  
pp. 1434-1435 ◽  
Author(s):  
C. J. Howard ◽  
E. H. Kisi
Keyword(s):  
Residual Stress ◽  
Flat Plate ◽  
Density Profile ◽  
Preferred Orientation ◽  
Correction Function ◽  
Pole Density ◽  
Axially Symmetric ◽  
Powder Specimen ◽  
Residual Stress Analysis ◽  
Plate Geometry

The March function is a widely used preferred-orientation correction function that, in flat-plate geometry, often closely approximates the pole-density profile of axially symmetric textures. It is shown that in Debye–Scherrer geometry, the assumption that the pole-density profile of a powder specimen can be described by a March function with coefficientR, leads to an intensity correction factor that can be approximated quite well by another March function, with coefficientR−1/2. This result validates the use of the March function correction in Debye–Scherrer geometry, facilitates the comparison of results obtained in the different geometries and should prove useful in some studies of axially symmetric textures and in residual-stress analysis.

Rough Contacts Modeled by Nonlinear Coatings

2007 ◽  
Author(s):  
I. I. Kudish
Keyword(s):  
Contact Problem ◽  
Numerical Solutions ◽  
Asymptotic Methods ◽  
Experimental Studies ◽  
Nonlinear Function ◽  
Normal Displacement ◽  
Experimental Fact ◽  
Axially Symmetric ◽  
Elastic Solids ◽  
Local Pressure

A number of experimental studies [1–3] revealed that the normal displacement in a contact of rough surfaces due to asperities presence is a nonlinear function of local pressure and it can be approximated by a power function of pressure. Originally, a linear mathematical model accounting for surface roughness of elastic solids in contact was introduced by I. Shtaerman [4]. He assumed that the effect of asperities present in a contact of elastic solids can be essentially replaced by the presence of a thin coating simulated by an additional normal displacement of solids’ surfaces proportional to a local pressure. Later, a similar but nonlinear problem formulation that accounted for the above mentioned experimental fact was proposed by L. Galin. In a series of papers this problem was studied by numerical and asymptotic methods [5–9]. The present paper has a dual purpose: to analyze the problem analytically and to provide some asymptotic and numerical solutions. The results presented below provide an overview of the results obtained on the topic and published by the author earlier in the journals hardly accessible to the international tribological community (such as Russian and mathematical journals) and, therefore, mostly unknown by tribologists. A number of recent publications on contacts of rough elastic solids supports the view that these results are still of value to the specialists involved in nanotribology. The existence and uniqueness of a solution of a contact problem for elastic bodies with rough (coated) surfaces is established based on the variational inequalities approach. Four different equivalent formulations of the problem including three variational ones were considered. A comparative analysis of solutions of the contact problem for different values of initial parameters (such as the indenter shape, parameters characterizing roughness, elastic parameters of the substrate material) is done with the help of calculus of variations and the Zaremba-Giraud principle of maximum for harmonic functions [10,11]. The results include the relations between the pressure and displacement distributions for rough and smooth solids as well as the relationships for solutions of the problems for rough solids with fixed and free contact boundaries. For plane and axially symmetric cases some asymptotic and numerical solutions are presented.

A Numerical Solution for an Axially Symmetric Contact Problem

1967 ◽  
Vol 34 (2) ◽  
pp. 283-286 ◽  
Author(s):  
Yih-O Tu
Keyword(s):  
Stress Distribution ◽  
Contact Problem ◽  
Contact Stress ◽  
Plate Thickness ◽  
Contact Radius ◽  
Axially Symmetric ◽  
Pressure Distributions ◽  
Linear Algebraic Equations ◽  
Axially Symmetric Contact ◽  
Contact Stress Distribution

A numerical scheme for the axially symmetric contact problem of a plate pressed between two identical spheres is given. The axially symmetric contact stress distribution is represented by a finite set of pressure distributions linearly varying with the radius between values defined in a set of concentric circles. The normal displacements of the bodies in contact resulting from these pressure distributions are matched at every radius of the discrete set of radii of these circles. The integral equation for the unkown contact stress distribution is thus approximated by a set of linear algebraic equations whose solution yields the unknown pressure values of the approximate distribution. The contact radius, relative approach, and the maximum contact stress are then computed numerically from this solution and are presented in terms of the total load, the radius of the sphere, and the plate thickness.

Effect of Geometric and Welding Conditions on Through-Thickness Residual Stress

2006 ◽  
Author(s):  
Masahito Mochizuki ◽  
Jinya Katsuyama ◽  
Masao Toyoda
Keyword(s):  
Residual Stress ◽  
Finite Element Analysis ◽  
Stainless Steel ◽  
Three Dimensional ◽  
Axially Symmetric ◽  
Welding Zone ◽  
Element Analysis ◽  
Butt Welding ◽  
Inner Surface ◽  
Welding Joints

Recently, stress corrosion cracking (SCC) of core internals and/or recirculation pipes of austenite stainless steel (SUS316L) has been observed. SCC is considered to occur and progress at near the inner surface of the welding zone in butt-welded pipes, because of the tensile residual stress introduced by welding. In present work, three-dimensional and axisymmetric thermo-elastic-plastic finite element analysis have been carried out, in order to clarify the effect of geometric and welding conditions in circumferential welding zone on the residual stress. In particular, butt-welding joints of SUS316L-pipes have been examined. The residual stress was simulated by three-dimensional and axially symmetric models and the results were compared and discussed in detail.

Periodic elastoplastic contact problem for a half-plane

1981 ◽  
Vol 17 (5) ◽  
pp. 475-480
Author(s):  
D. V. Grilitskii ◽  
V. V. Matus ◽  
A. M. Rigin
Keyword(s):  
Contact Problem ◽  
Half Plane ◽  
Elastoplastic Contact
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