Stresses Due to a Sharp Notch in a Work-Hardening Elastic-Plastic Material Loaded by Longitudinal Shear

1967 ◽  
Vol 34 (2) ◽  
pp. 287-298 ◽  
Author(s):  
J. R. Rice
Keyword(s):  
Applied Stress ◽  
Power Law ◽  
Work Hardening ◽  
Plastic Material ◽  
Longitudinal Shear ◽  
Small Scale ◽  
Sharp Notch ◽  
Initial Yield Stress ◽  
Elastic Plastic ◽  
Deformation Plasticity

A work-hardening elastic-plastic stress analysis is presented for a sharp notch or, as a limiting case, a crack perturbing a remotely applied uniform stress field. Mathematical complexities are reduced through considering the kinematically simple case of antiplane longitudinal shear deformations and by employing a deformation plasticity theory rather than the more appropriate incremental theory. Consequently, a general solution is available valid for any relation between stress and strain in the work-hardening range, so long as the remotely applied stress does not exceed the initial yield stress. When a power law relates stress to a strain in the work-hardening range, the deformation theory solution is also the correct incremental solution at low applied stress levels causing yielding on a scale small compared to notch depth. For cracks, the near crack tip strain field is shown to depend on loads and geometry only through the elastic stress intensity factor when yielding is on a small scale, and the elastic-plastic boundary and lines of constant strain magnitude are circles. Extensive numerical results are tabulated for a crack, 45 deg V-notch, and 90 deg V-notch in power-law-hardening materials, and exhibited graphically for a crack.

A Finite Element Analysis of Mode III Quasi-Static Crack Growth at a Ductile-Brittle Interface

1996 ◽  
Vol 63 (1) ◽  
pp. 204-209 ◽  
Author(s):  
S. Omprakash ◽  
R. Narasimhan
Keyword(s):  
Finite Element ◽  
Crack Growth ◽  
Power Law ◽  
Plastic Material ◽  
Bimaterial Interface ◽  
Mode Iii ◽  
Elastic Substrate ◽  
Elastic Plastic ◽  
Static Crack ◽  
Elastic Plastic Material

Steady-state quasi-static crack growth along a bimaterial interface is analyzed under Mode III, small-scale yielding conditions using a finite element procedure. The interface is formed by an elastic-plastic material and an elastic substrate. The top elastic-plastic material is assumed to obey the J2 incremental theory of plasticity. It undergoes isotropic hardening with either a bilinear uniaxial response or a power-law response. The results obtained from the full-field numerical analysis compare very well with the analytical asymptotic results obtained by Castan˜eda and Mataga (1991), which forms one of the first studies on this subject. The validity of the separable form for the asymptotic solution assumed in their analysis is investigated. The range of dominance of the asymptotic fields is examined. Field variations are obtained for a power-law hardening elastic-plastic material. It is seen that the stresses are lower for a stiffer substrate. The potential of the bimaterial system to sustain slow stable crack growth along the interface is studied. It is found that the above potential is larger if the elastic substrate is more rigid with respect to the elastic-plastic material.

scholarly journals Elastic-plastic analysis of crack on bimaterial interface

2005 ◽  
Vol 32 (3) ◽  
pp. 193-207
Author(s):  
Ruzica Nikolic ◽  
Jelena Veljkovic
Keyword(s):  
Phase Angle ◽  
Plastic Material ◽  
Crack Tip ◽  
Bimaterial Interface ◽  
Small Scale ◽  
Small Scale Yielding ◽  
Elastic Plastic ◽  
Singular Form ◽  
Scale Yielding ◽  
New Phase

In this paper are presented solutions for the stress and dis?placement fields for a crack that lies along the interface of an elastic and elastic - plastic material and for a crack between two different elastic - plastic materials. These solutions are obtained using the J2-deformation theory with the power - law strain hardening. In this paper results are described for a small scale yielding at the crack tip. The near tip fields do not have a separable singular form, of the HRR type fields, as in homogeneous media, they do, however bare interesting similarities to certain mixed -mode HRR fields. Under the small scale yielding the elastic fields are specified by a complex stress intensity factor and phase angle loading, while plastic field is characterized by a new phase angle. The size of plastic zone in plane strain and plane stress and displacement fields at the crack tip for the new phase angle are obtained. The crack tip opens smoothly and the crack opening displacement is scaled by the J-integral. The whole analysis is performed by application of the Mathematica symbolic programming routine.

scholarly journals Effect of Hardening Exponent of Power-Law Hardening Elastic-Plastic Substrate on Contact Behaviors in Coated Asperity Contact

Materials ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 1965 ◽  
Author(s):  
Xiqun Lu ◽  
Hanzhang Xu ◽  
Bin Zhao
Keyword(s):  
Power Law ◽  
Coating Thickness ◽  
Plastic Material ◽  
Contact Load ◽  
Plastic Substrate ◽  
Thickness Variation ◽  
Asperity Contact ◽  
Elastic Plastic ◽  
Specific Contact ◽  
Elastic Plastic Material

The contact between a rigid flat and a coated asperity is studied using the finite element method. The substrate is assumed as the power-law hardening elastic–plastic material. The effect of the hardening exponent of the substrate (n) on the contact behaviors including contact load, area, coating thickness variation and stress in the coating, is investigated. It shows larger hardening exponent results in larger contact loads and larger maximum stresses in the coating at a given interference, and leads to smaller contact area at a specific contact load. The coating thickness becomes smaller monotonically as the interference increases for larger hardening exponents, while it recovers gradually after reaching the minimum value for the smaller n cases. This work will give some universal guidance to improve the contact performance for coatings by adjusting the hardening exponent of the substrate and by optimizing the coatings parameters.

Experimental Evaluation of the M-Integral in an Elastic-Plastic Material Containing Multiple Defects

2012 ◽  
Vol 80 (1) ◽  
Author(s):  
N. Y. Yu ◽  
Q. Li ◽  
Y. H. Chen
Keyword(s):  
Path Dependence ◽  
Large Scale ◽  
Plastic Material ◽  
Image Correlation ◽  
Small Scale ◽  
Elastic Plastic ◽  
Multiple Defects ◽  
Scale Yielding ◽  
Elastic Plastic Material ◽  
M Integral

An experimental technique for evaluation of the M-integral in an elastic-plastic material containing multiple defects is proposed by using digital image correlation (DIC). This technique makes direct use of the definition of M by experimentally evaluating the integrand of M at various points along a square contour and determining the integral by numerical integration. The nonlinear Ramberg–Osgood model is used to capture the elastic-plastic behavior such as the elastic-plastic stress and the total strain energy density in terms of the measured displacements by DIC used in an ARAMIS 4M instrument. Compared with the previous experimental method proposed by King and Herrmann (King and Herrmann, 1981, “Nondestructive Evaluation of the J and M Integrals,” ASME J. Appl. Mech., 48, pp. 83–87), the present technique could be suitable to measure the M-integral for the various complicated damages, specimen geometries, loading conditions, and material behaviors. The path-independence or path-dependence of the M-integral is investigated under small-scale and large-scale yielding conditions, respectively. It is found that the values of M are path independent when the contours entirely enclose the nonlinear plastic region near the multiple defects. In contrast, the path-dependence is concluded for an elastic-plastic solid under large-scale yielding condition when the contours have to pass through the plastic zone. This interesting path-dependence of the M-integral is consistent with numerical prediction via the finite element method and theoretical analysis developed in this paper.

scholarly journals Computational Geometry-Based Surface Reconstruction for Volume Estimation: A Case Study on Magnitude-Frequency Relations for a LiDAR-Derived Rockfall Inventory

2021 ◽  
Vol 10 (3) ◽  
pp. 157
Author(s):  
Paul-Mark DiFrancesco ◽  
David A. Bonneau ◽  
D. Jean Hutchinson
Keyword(s):  
Computational Geometry ◽  
Surface Reconstruction ◽  
Power Law ◽  
Point Cloud ◽  
Point Clouds ◽  
Volume Estimation ◽  
Estimation Methods ◽  
Small Scale ◽  
Reconstruction Methods ◽  
3D Volume

Key to the quantification of rockfall hazard is an understanding of its magnitude-frequency behaviour. Remote sensing has allowed for the accurate observation of rockfall activity, with methods being developed for digitally assembling the monitored occurrences into a rockfall database. A prevalent challenge is the quantification of rockfall volume, whilst fully considering the 3D information stored in each of the extracted rockfall point clouds. Surface reconstruction is utilized to construct a 3D digital surface representation, allowing for an estimation of the volume of space that a point cloud occupies. Given various point cloud imperfections, it is difficult for methods to generate digital surface representations of rockfall with detailed geometry and correct topology. In this study, we tested four different computational geometry-based surface reconstruction methods on a database comprised of 3668 rockfalls. The database was derived from a 5-year LiDAR monitoring campaign of an active rock slope in interior British Columbia, Canada. Each method resulted in a different magnitude-frequency distribution of rockfall. The implications of 3D volume estimation were demonstrated utilizing surface mesh visualization, cumulative magnitude-frequency plots, power-law fitting, and projected annual frequencies of rockfall occurrence. The 3D volume estimation methods caused a notable shift in the magnitude-frequency relations, while the power-law scaling parameters remained relatively similar. We determined that the optimal 3D volume calculation approach is a hybrid methodology comprised of the Power Crust reconstruction and the Alpha Solid reconstruction. The Alpha Solid approach is to be used on small-scale point clouds, characterized with high curvatures relative to their sampling density, which challenge the Power Crust sampling assumptions.

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.

Singular stresses at the tip of a sharp notch in power-law-hardening materials under antisymmetric loading

1996 ◽  
Vol 31 (6) ◽  
pp. 693-701 ◽  
Author(s):  
N. V. Kouzniak ◽  
H. P. Rossmanith ◽  
M. P. Savruk
Keyword(s):  
Power Law ◽  
Sharp Notch ◽  
Antisymmetric Loading
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