scholarly journals Corrigendum to “Representative Stress-Strain Curve by Spherical Indentation on Elastic-Plastic Materials”

2019 ◽  
Vol 2019 ◽  
pp. 1-1
Author(s):  
Chao Chang ◽  
M. A. Garrido ◽  
J. Ruiz-Hervias ◽  
Zhu Zhang ◽  
Le-le Zhang
Keyword(s):  
Strain Curve ◽  
Spherical Indentation ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Elastic Plastic ◽  
Plastic Materials ◽  
Elastic Plastic Materials

scholarly journals Representative Stress-Strain Curve by Spherical Indentation on Elastic-Plastic Materials

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Chao Chang ◽  
M. A. Garrido ◽  
J. Ruiz-Hervias ◽  
Zhu Zhang ◽  
Le-le Zhang
Keyword(s):  
Strain Curve ◽  
Stress Constraint ◽  
Spherical Indentation ◽  
Stress Strain Curve ◽  
Constraint Factor ◽  
Stress Strain ◽  
Constraint Factors ◽  
Plastic Materials ◽  
Elastic Plastic Materials ◽  
The Relationship

Tensile stress-strain curve of metallic materials can be determined by the representative stress-strain curve from the spherical indentation. Tabor empirically determined the stress constraint factor (stress CF), ψ, and strain constraint factor (strain CF), β, but the choice of value for ψ and β is still under discussion. In this study, a new insight into the relationship between constraint factors of stress and strain is analytically described based on the formation of Tabor’s equation. Experiment tests were performed to evaluate these constraint factors. From the results, representative stress-strain curves using a proposed strain constraint factor can fit better with nominal stress-strain curve than those using Tabor’s constraint factors.

Improving elastic modulus measurements for rock based on geology

2000 ◽  
Vol 6 (4) ◽  
pp. 333-346 ◽  
Author(s):  
Paul M. Santi ◽  
Jason E. Holschen ◽  
Richard W. Stephenson
Keyword(s):  
Elastic Modulus ◽  
Strain Curve ◽  
Elastic Behavior ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Rock Types ◽  
Plastic Materials ◽  
Straight Line ◽  
Elastic Plastic Materials ◽  
Engineering Projects

Abstract Since many engineering projects in rock never mobilize strengths near the uniaxial compressive strength (UCS) of the rock, elastic modulus becomes a critical parameter to describe the rock's behavior under loading. There are a number of methods available for calculating the elastic modulus from laboratory test data, and each method gives a slightly different value. The objective of this study is to evaluate the most repeatable method for each of a number of rock types, and then to develop guidelines to aid the practitioner in selecting the best method as a function of rock behavior. UCS tests were performed on 78 samples of nine rock types, including two basalts, two granites, two limestones, a quartzite, a sandstone, and a gypsum. Elastic moduli were calculated using six different methods reported in the literature or modified for this study. The modified secant and modified secant-at-50-percent-strength moduli (modified by shifting the origin to best intercept the extension of the main straight-line portion of the stress-strain curve) were the most repeatable methods for rocks with elastic and plastic-elastic behavior. Elastic-plastic materials, which have a broad concave-downward stress-strain curve, are best evaluated using the tangent modulus on the upper of two distinct straight-line segments. For materials which show creep or extended plastic deformation with no sharp failure, the secant-at-50-percent-strength modulus and modified secant-at-50-percent-strength modulus are the most repeatable.

Determining engineering stress–strain curve directly from the load–depth curve of spherical indentation test

2010 ◽  
Vol 25 (12) ◽  
pp. 2297-2307 ◽  
Author(s):  
Baoxing Xu ◽  
Xi Chen
Keyword(s):  
Indentation Test ◽  
Strain Curve ◽  
Spherical Indentation ◽  
Displacement Curve ◽  
Large Set ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Constraint Factors ◽  
Engineering Stress ◽  
Depth Curve

The engineering stress–strain curve is one of the most convenient characterizations of the constitutive behavior of materials that can be obtained directly from uniaxial experiments. We propose that the engineering stress–strain curve may also be directly converted from the load–depth curve of a deep spherical indentation test via new phenomenological formulations of the effective indentation strain and stress. From extensive forward analyses, explicit relationships are established between the indentation constraint factors and material elastoplastic parameters, and verified numerically by a large set of engineering materials as well as experimentally by parallel laboratory tests and data available in the literature. An iterative reverse analysis procedure is proposed such that the uniaxial engineering stress–strain curve of an unknown material (assuming that its elastic modulus is obtained in advance via a separate shallow spherical indentation test or other established methods) can be deduced phenomenologically and approximately from the load–displacement curve of a deep spherical indentation test.

Nanoindentation by Multiple Loads Methodology: A Pile Up Correction Procedure

2007 ◽  
Vol 345-346 ◽  
pp. 805-808 ◽  
Author(s):  
Miguel Angel Garrido ◽  
Jesus Rodríguez
Keyword(s):  
Element Model ◽  
Spherical Indentation ◽  
Correction Procedure ◽  
Elastic Plastic ◽  
Multiple Loads ◽  
Plastic Materials ◽  
Wide Range ◽  
Pile Up ◽  
Elastic Plastic Materials

Young’s modulus and hardness data obtained from nanoindentation are commonly affected by phenomena like pile up or sink in, when elastic-plastic materials are tested. In this work, a finite element model was used to evaluate the pile up effect on the determination of mechanical properties from spherical indentation in a wide range of elastic-plastic materials. A new procedure, based on a combination of results obtained from tests performed at multiple maximum loads, is suggested.

201 Stress-strain curve estimation of anisotropic plastic materials using indentation method

2010 ◽  
Vol 2010.85 (0) ◽  
pp. _2-1_
Author(s):  
Keishi YONEDA ◽  
Akio YONEZU ◽  
Masayuki SAKIHARA ◽  
Hiroyuki HIRAKATA ◽  
Koji MINOSHIMA
Keyword(s):  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Indentation Method ◽  
Curve Estimation ◽  
Plastic Materials ◽  
Anisotropic Plastic

Non-linear delamination fracture analysis by using power-law hardening

2016 ◽  
Vol 12 (1) ◽  
pp. 80-92 ◽  
Author(s):  
Victor Iliev Rizov
Keyword(s):  
Power Law ◽  
Strain Curve ◽  
Fracture Analysis ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Content Type ◽  
Elastic Plastic ◽  
Linear Fracture ◽  
Delamination Fracture ◽  
Non Linear

Purpose – The purpose of this paper is to perform a theoretical analysis of non-linear delamination fracture in cantilever beam opened notch (CBON) configuration. It is assumed that the non-linear mechanical behavior of the CBON can be described by using a stress-strain curve with power-law hardening. Design/methodology/approach – The fracture analysis is carried-out by applying the integration contour independent J-integral. For this purpose, a model based on the technical beam theory is used. Equation is derived for determination of the CBON specimen curvature in elastic-plastic stage of deformation. The equation is solved by using the MatLab program system. Solutions of the J-integral are obtained at linear-elastic as well as elastic-plastic behavior of the CBON. The influence of the power-law exponent on the non-linear fracture is evaluated. Findings – The analysis reveals that the J-integral value increases when the exponent of the power-law increases. The solution obtained here is very useful for parametric analyses of the non-linear fracture behavior, since the simple formulas derived capture the essentials of the fracture response. Practical implications – Beside for parametric investigations, the solution obtained here can also be applied for calculating the critical J-integral value at non-linear behavior using experimentally determined critical fracture load at the onset of crack growth from the initial crack tip position in the CBON configuration. Originality/value – An analysis is performed of the non-linear fracture in the CBON configuration by applying the J-integral approach, assuming that the mechanical response can be modeled using a stress-strain curve with power-law hardening.

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