scholarly journals Study of Frictional Effects of Granite Subjected to Quasi-Static Contact Loading

Lubricants ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 106
Author(s):  
Hossein Shariati ◽  
Mahdi Saadati ◽  
Kenneth Weddfelt ◽  
Per-Lennart Larsson ◽  
Francois Hild
Keyword(s):  
Stress State ◽  
Frictional Contact ◽  
Frictional Coefficient ◽  
Constitutive Law ◽  
Spherical Indentation ◽  
Plasticity Model ◽  
Frictionless Contact ◽  
Weibull Parameters ◽  
Static Contact ◽  
Frictional Effects

The rock fragmentation response to drilling, in particular percussive drilling, is important in order to improve the efficiency of such an operation. The resulting problem includes spherical contact between the drill bit and the material and therefore, a numerical analysis of frictional effects in quasi-static spherical indentation of Bohus granite is presented. The frictional coefficient between the indenter and the granite surface is accounted for in numerical simulations. A previously determined constitutive law is used for the purpose of numerical analyses. The latter consists of a Drucker-Prager plasticity model with variable dilation angle coupled with an anisotropic damage model. Since the tensile strength is random, Weibull statistics was considered. Using a frictionless contact model, the stress state of Bohus granite corresponding to the first material failure occurrence, observed in indentation experiments, was numerically determined. However, the frictional effects, which are of interest in this study, may lead to changes in the numerically established stress state and consequently the Weibull parameters should be recalibrated. The so-called Weibull stress decreases from 120 MPa for a frictionless contact to 75 MPa for frictional contact, and the Weibull modulus from 24 to 12. It is numerically observed that the predicted force-penetration response, using the new set of Weibull parameters, is not influenced by friction. Conversely, the predicted fracture pattern, in the case of frictional contact, is similar to the case of frictionless contact, but its size is somewhat larger. Last, a parametric study analyzing the dependence of the friction coefficient is carried out and no significant changes are detected. The novelty of the present findings concerns the fact that both an advanced damage description in combination with an advanced plasticity model, both implemented for finite element analyses, is used to analyze frictional effects at granite indentation.

scholarly journals Fault model of the 2012 doublet earthquake, near the up-dip end of the 2011 Tohoku-Oki earthquake, based on a near-field tsunami: implications for intraplate stress state

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Tatsuya Kubota ◽  
Ryota Hino ◽  
Daisuke Inazu ◽  
Syuichi Suzuki
Keyword(s):  
Stress State ◽  
Frictional Coefficient ◽  
Fault Model ◽  
Japan Trench ◽  
Time Interval ◽  
Depth Range ◽  
Seismic Zone ◽  
Bending Stress ◽  
Normal Faulting ◽  
Brittle Strength

AbstractOn December 7, 2012, an earthquake occurred within the Pacific Plate near the Japan Trench, which was composed of deep reverse- and shallow normal-faulting subevents (Mw 7.2 and 7.1, respectively) with a time interval of ~10 s. It had been known that the stress state within the plate was characterized by shallow tensile and deep horizontal compressional stresses due to the bending of the plate (bending stress). This study estimates the fault model of the doublet earthquake utilizing tsunami, teleseismic, and aftershock data and discusses the stress state within the incoming plate and spatiotemporal changes seen in it after the 2011 Tohoku-Oki earthquake. We obtained the vertical extents of the fault planes of deep and shallow subevents as ~45–70 km and ~5 (the seafloor)–35 km, respectively. The down-dip edge of the shallow normal-faulting seismic zone (~30–35 km) deepened significantly compared to what it was in 2007 (~25 km). However, a quantitative comparison of the brittle strength and bending stress suggested that the change in stress after the Tohoku-Oki earthquake was too small to deepen the down-dip end of the seismicity by ~10 km. To explain the seismicity that occurred at a depth of ~30–35 km, the frictional coefficient in the normal-faulting depth range required would have had to be ~0.07 ≤ μ ≤ ~0.2, which is significantly smaller than the typical friction coefficient. This suggests the infiltration of pore fluid along the bending faults, down to ~30–35 km. It is considered that the plate had already yielded to a depth of ~35 km before 2011 and that the seismicity of the area was reactivated by the increase in stress from the Tohoku-Oki earthquake.

Dynamic contact problem with thermal effect

2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Justyna Ogorzaly
Keyword(s):  
Thermal Effect ◽  
Frictional Contact ◽  
Dynamic Contact ◽  
The Body ◽  
Constitutive Law ◽  
Hemivariational Inequalities ◽  
Banach Fixed Point Theorem ◽  
Dynamic Contact Problem ◽  
System Of Inequalities ◽  
Evolution Hemivariational Inequalities

AbstractWe consider a model of a dynamic frictional contact between the body and the foundation. In this model the contact is bilateral. The behaviour of the material is described by the elastic-viscoplastic constitutive law with thermal effect. The variational formulation of this model leads to a system of two evolution hemivariational inequalities. The aim of this paper is to prove that this system of inequalities has a unique solution. The proof is based on the Banach fixed point theorem and some results for hemivariational inequalities.

Effect of roughness on the stress state of bodies in frictional contact

1978 ◽  
Vol 14 (9) ◽  
pp. 950-955 ◽  
Author(s):  
E. A. Kuznetsov ◽  
G. A. Gorokhovskii
Keyword(s):  
Stress State ◽  
Frictional Contact

Analysis of a piezoelectric contact problem with subdifferential boundary condition

2014 ◽  
Vol 144 (5) ◽  
pp. 1007-1025 ◽  
Author(s):  
Stanisław Migórski ◽  
Anna Ochal ◽  
Mircea Sofonea
Keyword(s):  
Boundary Condition ◽  
Variational Formulation ◽  
Contact Process ◽  
Constitutive Law ◽  
Time Dependent ◽  
Hemivariational Inequalities ◽  
Material Behaviour ◽  
Nonlinear Integral Equations ◽  
Frictionless Contact ◽  
System Coupling

We consider a mathematical model which describes the frictionless contact between a piezoelectric body and a foundation. The contact process is quasi-static and the foundation is assumed to be insulated. The novelty of the model consists in the fact that the material behaviour is described with an electro-elastic–visco-plastic constitutive law and the contact is modelled with a subdifferential boundary condition. We derive a variational formulation of the problem which is in the form of a system coupling two nonlinear integral equations with a history-dependent hemivariational inequality and a time-dependent linear equation. We prove the existence of a weak solution to the problem and, under additional assumptions, its uniqueness. The proof is based on a recent result on history-dependent hemivariational inequalities obtained by Migórski, Ochal and Sofonea in 2011.

An Energy Model for Bifurcation Analysis of a Double-Notched Concrete Panel: Continuum Model

2003 ◽  
Vol 6 (1) ◽  
pp. 45-51 ◽  
Author(s):  
G. Chen ◽  
G. Baker
Keyword(s):  
Continuum Model ◽  
Peak Load ◽  
Companion Paper ◽  
Constitutive Law ◽  
Simplified Model ◽  
Plasticity Model ◽  
Notch Depth ◽  
Axial Tension ◽  
Order Energy ◽  
Energy Computation

In this paper, the uni-axial tension of double-notched concrete specimens is analyzed by using a continuum plasticity model. As in a companion paper, the concept of minimization of the second-order energy is used as the criterion for judging a bifurcation. The energy computation is formulated in standard continuum plasticity. The analysis confirms that the unsymmetrical crack propagation (i.e. strains localizing on one side of the specimen) may occur either before or after the peak load. Influences on bifurcation of three factors, the notch depth to panel width, the local constitutive law, and the ratio of the panel width to panel length are investigated. A larger ratio of the notch depth to panel width, a steeper softening constitutive law, and a smaller ratio of the panel width to panel length, leads to an earlier bifurcation. These conclusions are consistent with those obtained from a simplified model.

Optimal aspect ratio of interference fits for maximum load transfer capacity

2005 ◽  
Vol 40 (2) ◽  
pp. 177-184 ◽  
Author(s):  
D Castagnetti ◽  
E Dragoni
Keyword(s):  
Stress State ◽  
Aspect Ratio ◽  
Load Transfer ◽  
Load Capacity ◽  
Frictional Coefficient ◽  
Axial Loading ◽  
Maximum Load ◽  
Material Response ◽  
Optimal Ratio ◽  
Joint Design

The stress state in frictional interference fits under torsional and axial loading is examined. The optimal ratio between the inside and outside diameters of the hub is calculated, which maximizes the load transmitted by the joint. Design formulae and charts are provided, giving the most efficient aspect ratio of the hub for all practical situations. It is found that the maximum load capacity is achieved for an aspect ratio in the range from 0.5 to 0.7, regardless of the frictional coefficient (up to 1), of the kind of loading (torsional or axial), and of the material response (brittle or ductile).

Weak solvability of a piezoelectric contact problem

2009 ◽  
Vol 20 (2) ◽  
pp. 145-167 ◽  
Author(s):  
STANISŁAW MIGÓRSKI ◽  
ANNA OCHAL ◽  
MIRCEA SOFONEA
Keyword(s):  
Mathematical Model ◽  
Variational Formulation ◽  
Frictional Contact ◽  
Constitutive Law ◽  
Potential Fields ◽  
Material Behaviour ◽  
Abstract Result ◽  
Electrically Conductive ◽  
Piezoelectric Body ◽  
Weak Solvability

We consider a mathematical model which describes the frictional contact between a piezoelectric body and a foundation. The material behaviour is modelled with a non-linear electro-elastic constitutive law, the contact is bilateral, the process is static and the foundation is assumed to be electrically conductive. Both the friction law and the electrical conductivity condition on the contact surface are described with subdifferential boundary conditions. We derive a variational formulation of the problem which is of the form of a system of two coupled hemi-variational inequalities for the displacement and the electric potential fields, respectively. Then we prove the existence of a weak solution to the model and, under additional assumptions, its uniqueness. The proof is based on an abstract result on operator inclusions in Banach spaces.

Sign in / Sign up

Export Citation Format

Share Document