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.

Neuber prediction of elastic-plastic strain concentration in notched tensile specimens under large-scale yielding

2003 ◽  
Vol 38 (1) ◽  
pp. 79-94 ◽  
Author(s):  
G Härkegård ◽  
T Mann
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Large Scale ◽  
Plastic Material ◽  
Elastic Plastic ◽  
Notch Stress ◽  
Scale Yielding ◽  
Elastic Plastic Material ◽  
Neuber's Rule

A general version of Neuber's rule, applicable to large-scale yielding, is presented. It is applied to a variety of notched tensile specimens made of power-hardening elastic-plastic material. Neuber's rule predictions of notch stress and strain are compared with finite element results. The best agreement is obtained for shallow mild notches. Models of more limited applicability, based on the invariance of the total strain energy density and the strain energy density at the root of the notch, have been applied to some of the specimens.

On the Crack Quasi-Static Growth

2019 ◽  
Vol 827 ◽  
pp. 312-317
Author(s):  
Vitalijs Pavelko
Keyword(s):  
Fracture Toughness ◽  
Crack Growth ◽  
Plastic Material ◽  
Small Scale ◽  
Invariant Equation ◽  
Practical Applications ◽  
Wide Range ◽  
Scale Yielding ◽  
Elastic Plastic Material ◽  
Principal Assumption

The theoretical model of quasi-static crack growth in the elastic-plastic material under load variation in a wide range. Small-scale yielding is principal assumption and main restriction of proposed theory. The model of crack growth provides for continues and interrelated both the crack propagation and plastic deformation development. The nonlinear first-order differential equation describes the quasi-static process of crack growth. In dimensionless form this equation invariant in respect to geometrical configuration and material. The critical size of the plastic zone is proposed as the characteristics of material resistance which is directly connected with the fracture toughness, but more convenient in practical applications of invariant equation. The demonstration of solution is performed for the double cantilever beam that widely used as the standard (DCB) sample for measurement of the mode-I interlaminar fracture toughness. he short analysis of some properties of solution of the invariant equation and its application is done.

Two Parameter J-A Estimation for Weld Centerline Cracks in Welded Single-Edge Cracked Plate Under Tensile Loading

2019 ◽  
Author(s):  
Chuanjie Duan ◽  
Shuhua Zhang
Keyword(s):  
Large Scale ◽  
Tensile Loading ◽  
Small Scale ◽  
Material Strength ◽  
Single Edge ◽  
Weld Width ◽  
Elastic Plastic ◽  
Cracked Plate ◽  
Scale Yielding ◽  
Two Parameter

Abstract This work examines the J–A two-parameter characterization of elastic–plastic crack front fields for weld centerline cracks under tensile loading. Extensive finite element analyses (FEA) have been conducted to obtain solutions of constraint parameter A, which is the second parameter in a three-term elastic-plastic asymptotic expansion for the stress field near the tip of mode-I crack, for modified boundary layer (MBL) model and welded single-edge cracked plate (SECP). Solutions of the constraint parameter A were obtained for the material following the Ramberg-Osgood power law. The crack geometries analyzed include shallow and deep cracks, and remote tension loading levels cover from small-scale to large-scale yielding conditions. The effects of weld material mismatch and weld width on crack tip constraint were considered in the FEA. A constraint parameter AM, only caused by material strength mismatch, is defined and its parametric equation was obtained. The total constraint in the bi-material weldment can be predicted by adding together AM and A in the homogeneous material. Good agreements were achieved for welded SECP specimen with different crack size and weld width from small-scale to large-scale yielding conditions. This methodology would be useful for performing constraint-based elastic-plastic fracture analyses of other welded test specimens.

A Note on the Path-Dependence of the J-Integral Near a Stationary Crack in an Elastic-Plastic Material With Finite Deformation

2012 ◽  
Vol 79 (4) ◽  
Author(s):  
Dorinamaria Carka ◽  
Robert M. McMeeking ◽  
Chad M. Landis
Keyword(s):  
Finite Deformation ◽  
Path Dependence ◽  
Plastic Material ◽  
Crack Tip ◽  
J Integral ◽  
Stationary Crack ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Elastic Plastic Material ◽  
Elastic Perfectly Plastic

In this technical brief, we compute the J-integral near a crack-tip in an elastic-perfectly-plastic material. Finite deformation is accounted for, and the apparent discrepancies between the prior results of the authors are resolved.

Characterization of Fatigue Crack Growth in Intermediate and Large Scale Yielding

1991 ◽  
Vol 113 (1) ◽  
pp. 15-22 ◽  
Author(s):  
R. C. McClung ◽  
H. Sehitoglu
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Crack Closure ◽  
Large Scale ◽  
Small Scale ◽  
Parameter Estimates ◽  
Growth Data ◽  
Elastic Plastic ◽  
Scale Yielding

Parameters previously proposed for the correlation of elastic-plastic fatigue crack growth data are critically reviewed and compared from a pragmatic engineering standpoint. Commonly employed estimates for the four most common parameters are shown to have essentially the same structure and to be numerically similar, despite their widely differing theoretical backgrounds. The significance of fatigue crack closure for crack growth under these conditions is considered. Elastic-plastic finite element analyses of crack closure are presented and compared with experimental data and simple analytical models. Normalized crack opening stresses are shown to change significantly between small scale and large scale yielding conditions, especially for R= − 1 loading. Different schemes for incorporating closure information into the crack growth parameters are examined, and the consequences of closure for the numerical structure of the parameter estimates are demonstrated. Experimental crack growth data from 1026 and 1070 steels are correlated with estimates of ΔK and ΔJ, both considering and neglecting the effects of crack closure. The data comprise wide ranges of maximum stress, plastic strain amplitude, and crack length, including conditions of small, intermediate, and large scale yielding. Correlations which include an explicit correction for crack closure are shown to be superior.

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.

Description of the M-integral in an elastic plastic material

2017 ◽  
Author(s):  
Huiyu Tao ◽  
Cheng Gao ◽  
Jinyong Xu ◽  
Yan Tang ◽  
Dayong Cai ◽  
...  
Keyword(s):  
Plastic Material ◽  
Elastic Plastic ◽  
Elastic Plastic Material ◽  
M Integral

scholarly journals Evaluation of SSY boundary using DIC results

2021 ◽  
Author(s):  
Antunes FV ◽  
Jose Vasco-Olmo ◽  
Francisco Diaz ◽  
Diogo Neto ◽  
Sérgio ERA ◽  
...  
Keyword(s):  
Aluminium Alloys ◽  
Large Scale ◽  
Pure Titanium ◽  
Image Correlation ◽  
Small Scale ◽  
Commercially Pure Titanium ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Numerical Work ◽  
Scale Yielding

In this work the boundaries of small-scale yielding (SSY) and large-scale yielding (LSY) have been experimentally evaluated from the analysis of crack tip opening displacement (CTOD) measured by Digital Image Correlation (DIC). The approach published in a previous numerical work [18] has been used to define the boundaries of SSY and LSY. According to this approach, CTOD must be resolved into its elastic and plastic components, analysing the ratio between the elastic CTOD range and the total CTOD range ( Δδ/ Δδ) to define the boundary where SSY conditions can be established. Three materials have been studied, commercially pure titanium and 2024-T3 and 7050-T6 aluminium alloys, tested at different stress ratio values (0.1 and 0.6 for titanium, and 0.1, 0.3 and 0.5 for the aluminium alloys). SSY conditions are shown to dominate when Δδ/ Δδ≥79% and ≥78% for titanium and the two aluminium alloys, respectively. In addition, LSY can be established when Δδ/ Δδ≤66.3% and ≤67.2% for titanium and for 2024-T3 and 7050-T6 aluminum alloys, respectively. Transition or LSY conditions are more probable in fatigue tests conducted at low R-ratio than in tests at high R-ratio. In addition, crack lengths above 40% with respect to the width of the specimen promote transition or LSY conditions. The results obtained in this work can assist to a better understanding of the mechanisms driving fatigue crack growth.

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.

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