Effect of the Type of Stress-Strain Law on the Validity of the Reference Stress Approach in Fracture Mechanics

2014 ◽  
Author(s):  
Philippe Gilles ◽  
Gongchen Zhang ◽  
Komlanvi Madou
Keyword(s):  
Fracture Mechanics ◽  
Power Law ◽  
Plasticity Theory ◽  
Material Behavior ◽  
Stress Strain ◽  
Hardening Law ◽  
Reference Stress ◽  
Deformation Plasticity ◽  
Reference Stress Approach ◽  
J Estimation

In fracture mechanics, several J-estimation schemes are based on the reference stress approach. This approach has been developed initially in the frame of the R5 rule for creep and R6 rule for elasto-plastic fracture assessments. Later other methods, based on the reference stress concept, where derived like the Js method introduced in the French RSE-M code en 1997 and the Enhanced Reference Stress (ERS) method in Korea around 2001. However these developments are based on the J2 deformation plasticity theory and well established for a pure power hardening law. Even in this latter case, the reference stress depends on the hardening exponent. Js and ERS attempt to minimize this dependence and propose some corrections for recorded behavior laws which cannot be fitted by a power law. However their validation has been established mainly on cases where the material behavior is governed by a Ramberg-Osgood (R0) law. The question may be raised, as for the bilinear hardening law case, of the existence of a reference stress for non RO laws.

Improvement of J Estimation Schemes Based on Reference Stress for Linear Hardening Behavior

2018 ◽  
Author(s):  
Philippe Gilles
Keyword(s):  
Plasticity Theory ◽  
Practical Case ◽  
Linear Hardening ◽  
Hardening Behavior ◽  
Hardening Law ◽  
Reference Stress ◽  
Deformation Plasticity ◽  
3D Applications ◽  
Reference Stress Approach ◽  
J Estimation

In Elastic-Plastic Fracture Mechanics, several J-estimation schemes are based on the reference stress approach. This approach has been developed initially for creep analyses and later on for elasto-plastic fracture assessments in 1984, then included in the R6 rule. Much later, other methods, based on the reference stress concept, were derived for 3D applications like the Js method introduced in the French RSE-M code in 1997 and the Enhanced Reference Stress (ERS) method in Korea around 2001. However, these developments are based on the J2 deformation plasticity theory and well established for a pure power hardening law. Js and ERS schemes propose some corrections for recorded behavior laws which cannot be fitted by a power law. Nevertheless, their application to materials governed by a bilinear hardening law has been called into question by several studies. One of these, carried out by M. T. Kirk and R. H. Dodds [1, 2] is of great interest since addressing the practical case of a surface cracked plate.

Residual Stress Analysis of Bimaterial Strips Under Multiple Thermal Loading

1997 ◽  
Vol 119 (4) ◽  
pp. 281-287 ◽  
Author(s):  
J. W. Tierney ◽  
J. W. Eischen
Keyword(s):  
Residual Stress ◽  
Power Law ◽  
Thermal Loading ◽  
Material Behavior ◽  
Algebraic Equations ◽  
Stress Strain ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Nonlinear Stress ◽  
Microelectronics Industry

The residual stress distribution in bimaterial beams induced by multiple thermal loadings has been investigated. Three models for the nonlinear stress-strain material behavior were considered: bilinear elastic-plastic, power law elastic-plastic, and power law purely plastic. The equations governing equilibrium, compatibility of strain, and stress-strain for the bimaterial configuration make up a system of nonlinear algebraic equations which is solved numerically. The elastic-plastic power law model leads to stress discontinuity in the layers. The other two models have been verified with a finite element analysis. Several examples are included using materials common to the microelectronics industry.

Approximate Elastic-Plastic J Estimate of Cylinders With Off-Centered Circumferential Through-Wall Cracks

2003 ◽  
Author(s):  
Do-Jun Shim ◽  
Nam-Su Huh ◽  
Yun-Jae Kim ◽  
Young-Jin Kim
Keyword(s):  
Fracture Mechanics ◽  
Strain Hardening ◽  
Combined Loading ◽  
Influence Functions ◽  
Elastic Plastic ◽  
Crack Geometry ◽  
Reference Stress ◽  
Plastic Influence Functions ◽  
Reference Stress Approach

This paper provides approximate J estimates for off-centred, circumferential through-wall cracks in cylinders under bending and under combined tension and bending. The proposed method is based on the reference stress approach, where the dependence of elastic and plastic influence functions of J on the cylinder/crack geometry, the off-centred angle and strain hardening is minimised through the use of a proper normalising load. Based on published limited FE results for off-centred, circumferential through-wall cracks under bending, such normalising load is found, based on which the reference stress based J estimates are proposed for more general cases, such as for a different cylinder geometry and for combined loading. Comparison of the estimated J with extensive FE J results shows overall good agreements for different crack/cylinder geometries and for combined tension and bending, which provides sufficient confidence in the use of the proposed method to fracture mechanics analyses of off-centred circumferential cracks. Furthermore, the proposed method is simple to use, giving significant merits in practice.

On Relevant Ramberg-Osgood Fit to Engineering Nonlinear Fracture Mechanics Analysis

2004 ◽  
Vol 126 (3) ◽  
pp. 277-283 ◽  
Author(s):  
Yun-Jae Kim ◽  
Nam-Su Huh ◽  
Young-Jin Kim ◽  
Young-Hwan Choi ◽  
Jun-Seok Yang
Keyword(s):  
Fracture Mechanics ◽  
Three Dimensional ◽  
Ferritic Steels ◽  
Stress Strain ◽  
Nonlinear Fracture Mechanics ◽  
Practical Applications ◽  
Nonlinear Fracture ◽  
Mechanics Analysis ◽  
Strain Data ◽  
Deformation Plasticity

The present paper proposes a robust method for the Ramberg-Osgood (R-O) fit to accurately estimate elastic-plastic J from the engineering fracture mechanics analysis based on deformation plasticity. The proposal is based on engineering stress-strain data to determine the R-O parameters, instead of true stress-strain data. Moreover, for practical applications, the method is given not only for the case when full stress-strain data are available but also for the case when only yield and tensile strengths are available. The reliability of the proposed method for the R-O fit is validated against detailed three-dimensional FE analyses for through-wall cracked pipes under global bending using five different materials, three stainless steels and two ferritic steels. Taking the FE J results based on incremental plasticity using actual stress-strain data as the reference, the FE J results based on deformation plasticity using various R-O fits are compared with reference J values. Comparisons show that the proposed R-O fit provides more accurate J values for all cases, compared to existing methods for the R-O fit. Advantages of the proposed R-O fit in practical applications are discussed, together with its accuracy.

Elastic-Plastic Fracture Mechanics Method for Poor Penetration Crack in Welded Piping Branch Junction

2008 ◽  
Author(s):  
Yong-Qiang Bai ◽  
Tong Wang ◽  
Lianghai Lv ◽  
Liang Sun ◽  
Jian Shuai
Keyword(s):  
Fracture Mechanics ◽  
Crack Front ◽  
Crack Depth ◽  
Influence Functions ◽  
Stress Strain ◽  
Elastic Plastic ◽  
Inner Radius ◽  
Plastic Influence Functions ◽  
Remote Stress ◽  
J Estimation

This paper provides two types of engineering J estimation equations for welded piping branch junctions with poor penetration crack under internal pressure. The first type is the so-called GE/EPRI type J estimation equation based on Ramberg-Osgood (R-O) materials. Based on detailed 3-D FE results using deformation plasticity, plastic influence functions for fully plastic J components are tabulated for practical ranges of the inner radius of brace to the inner radius of chord ratio, the thickness of brace to the thickness of chord, the thickness of chord to the inner radius of chord ratio, the crack depth to the thickness of chord ratio, the strain hardening index for the R-O material, and the location along the poor penetration crack front. Based on tabulated plastic influence functions, the GE/EPRI-type J estimation equation along the crack front is proposed. For more general application, the effective remote stress method based on GE/EPRI-type solutions is provided. This method provides a simpler equation for J, which could be used for any stress-strain relationship material, including Ramborg-Osgood (R-O) material and non-R-O materials under monotonic increasing loading. The proposed effective remote stress based J estimation equation is compared with elastic-plastic 3-D FE results using actual stress–strain data for a Type 304 strainless steel. Good agreement between the FE results and the proposed reference stress based J estimation provides confidence in the use of the proposed method for elastic-plastic fracture mechanics of pressurized welded piping branch junction.

Semi-inverse method for predicting stress–strain relationship from cone indentations

2003 ◽  
Vol 18 (9) ◽  
pp. 2068-2078 ◽  
Author(s):  
A. DiCarlo ◽  
H. T. Y. Yang ◽  
S. Chandrasekar
Keyword(s):  
A Priori ◽  
Model Material ◽  
Material Behavior ◽  
The Finite Element Method ◽  
Stress Strain ◽  
Indentation Tests ◽  
Strain Relationship ◽  
Initial Force ◽  
Relationship Of ◽  
Force Displacement

A method for determining the stress–strain relationship of a material from hardness values H obtained from cone indentation tests with various apical angles is presented. The materials studied were assumed to exhibit power-law hardening. As a result, the properties of importance are the Young's modulus E, yield strength Y, and the work-hardening exponent n. Previous work [W.C. Oliver and G.M. Pharr, J. Mater. Res. 7, 1564 (1992)] showed that E can be determined from initial force–displacement data collected while unloading the indenter from the material. Consequently, the properties that need to be determined are Y and n. Dimensional analysis was used to generalize H/E so that it was a function of Y/E and n [Y-T. Cheng and C-M. Cheng, J. Appl. Phys. 84, 1284 (1999); Philos. Mag. Lett. 77, 39 (1998)]. A parametric study of Y/E and n was conducted using the finite element method to model material behavior. Regression analysis was used to correlate the H/E findings from the simulations to Y/E and n. With the a priori knowledge of E, this correlation was used to estimate Y and n.

Numerical Modeling of Macroscopic Behavior of Particulate Composite with Crosslinked Polymer Matrix

2011 ◽  
Vol 465 ◽  
pp. 129-132
Author(s):  
Luboš Náhlík ◽  
Bohuslav Máša ◽  
Pavel Hutař
Keyword(s):  
Young’S Modulus ◽  
Polymer Matrix ◽  
Young's Modulus ◽  
Numerical Models ◽  
Strain Curve ◽  
Particulate Composite ◽  
Material Behavior ◽  
Particulate Composites ◽  
Stress Strain ◽  
Crosslinked Polymer

Particulate composites with crosslinked polymer matrix and solid fillers are one of important classes of materials such as construction materials, high-performance engineering materials, sealants, protective organic coatings, dental materials, or solid explosives. The main focus of a present paper is an estimation of the macroscopic Young’s modulus and stress-strain behavior of a particulate composite with polymer matrix. The particulate composite with a crosslinked polymer matrix in a rubbery state filled by an alumina-based mineral filler is investigated by means of the finite element method. A hyperelastic material behavior of the matrix was modeled by the Mooney-Rivlin material model. Numerical models on the base of unit cell were developed. The numerical results obtained were compared with experimental stress-strain curve and value of initial Young’s modulus. The paper can contribute to a better understanding of the behavior and failure of particulate composites with a crosslinked polymer matrix.

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