Deformation Versus Modified J-Integral Resistance Curves for Ductile Materials

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Xian-Kui Zhu ◽  
Poh-Sang Lam
Keyword(s):  
Deformation Theory ◽  
Size Dependence ◽  
Fracture Property ◽  
J Integral ◽  
Resistance Curve ◽  
Structural Components ◽  
Ductile Materials ◽  
Size Dependent ◽  
Resistance Curves ◽  
Better Than

The J-integral resistance curve (or J-R curve) is an important fracture property of materials and has gained broad applications in assessing the fracture behavior of structural components. Because the J-integral concept was proposed based on the deformation theory of plasticity, the J-R curve is a deformation-based result. It has been known that the J-R curves of a material depend on specimen size and geometry; therefore, a modified J-integral or Jm was proposed to minimize the size dependence. Extensive experiments have shown that the Jm-R curves might remain size-dependent and could not behave better than the traditional deformation J-R curves. To date, however, it is noticed that the Jm-R curves were still used as “size-independent” results in some fracture mechanics analyses. It is necessary to revisit this topic for further clarification. This paper presents a brief review on the development of deformation and modified J-integral testing, and obtains a simple incremental Jm-integral equation. It is followed by typical experimental results with discussions on the issues of constraint or size dependence of J-R and Jm-R curves for different steels and specimens. Finally, a recommendation is made on properly selecting a resistance curve in the fracture analysis.

Deformation Versus Modified J-Integral Resistance Curves for Ductile Materials

2012 ◽  
Author(s):  
Xian-Kui Zhu ◽  
Poh-Sang Lam
Keyword(s):  
Fracture Mechanics ◽  
Size Dependence ◽  
Structural Integrity ◽  
Experimental Results ◽  
Integral Parameter ◽  
Fracture Toughness Test ◽  
J Integral ◽  
Resistance Curve ◽  
Integrity Assessment ◽  
Resistance Curves

The J-integral resistance curve (or J-R curve) has been widely used as material property in fracture mechanics methods for structural integrity assessment. ASTM E1820 provides the standard fracture toughness test methods to measure JIc and J-R curves. The conventional J-R curve utilizes the J-integral parameter proposed by Rice [1] based on the deformation theory of plasticity. Due to crack-tip constraint effect, J-R curves of a material depend on specimen size, geometry type and crack length. In order to obtain size-independent resistance curves, Ernst [11] introduced a modified J-integral or Jm to minimize the size dependence and to characterize the resistance curve for large crack extensions beyond the limitation of deformation J-R curves. In the late 1980s and in the early 1990s, different experimental results showed the modified Jm-R curves were still size-dependent and may even behave worse than the deformation J-R curves. However, to date, the Jm-R curves are still regarded as “size-independent” in fracture mechanics analysis. To clarify this, the present paper gives a brief historical review of ductile resistance curves in terms of deformation J-integral and the modified Jm-integral, and evaluates the size dependence using experimental results for various steels and specimens, including A285 carbon steel and SENB specimens. A suggestion how to use the resistance curves is made accordingly.

Path-dependent J-integral evaluations around an elliptical hole for large deformation theory

2016 ◽  
Vol 25 (3-4) ◽  
pp. 77-81
Author(s):  
David J. Unger
Keyword(s):  
Work Hardening ◽  
Deformation Theory ◽  
Elliptical Hole ◽  
Exact Expression ◽  
J Integral ◽  
Resistance Curve ◽  
Hardening Material ◽  
Initial Stage ◽  
Path Dependent ◽  
Crack Tip Blunting

AbstractAn exact expression is obtained for a path-dependent J-integral for finite strains of an elliptical hole subject to remote tensile tractions under the Tresca deformation theory for a thin plate composed of non-work hardening material. Possible applications include an analytical resistance curve for the initial stage of crack propagation due to crack tip blunting.

Comparison of J Resistance Curves From Toughness Testing Specimens With Those From Various Cracked Pipe Tests

2013 ◽  
Author(s):  
Jong-Hyun Kim ◽  
Jae-Jun Han ◽  
Yun-Jae Kim ◽  
Do-Jun Shim
Keyword(s):  
Damage Model ◽  
Fe Analysis ◽  
Contour Integral ◽  
Damage Analysis ◽  
Resistance Curve ◽  
Size Dependent ◽  
Element Size ◽  
Toughness Testing ◽  
Resistance Curves ◽  
J Estimation

J contour integral still has great importance to predict fracture of both small specimen and full-scaled pipes. However, it is difficult to obtain experimental J resistance curve of full-scaled pipes due to the differences of defect shape and complexity of loads. Due to the recent development of the FE damage analysis to predict fracture of full-scaled pipes, it is also possible to predict J resistance of full-scaled pipes. To use this FE damage model for fracture estimation, it is necessary to verify the validity of this model by compared with toughness testing specimens. In this paper, J resistance curves of full-scaled pipes using FE damage analysis were compared with various toughness testing specimens from Pipe Fracture Encyclopedia performed by Battelle. And the J contour integral were calculated from FE analysis using the element-size-dependent damage model recently proposed by the authors. Compared results showed that J calculation using FE damage analysis could be used for J-estimation of full-scaled pipes by compared with fracture toughness testing specimens.

Determination of J Resistance Curves From CWP Specimens

2012 ◽  
Author(s):  
Fan Zhang ◽  
Honggang Zhou ◽  
Yong-Yi Wang ◽  
Ming Liu ◽  
Yaxin Song
Keyword(s):  
Fracture Toughness ◽  
Crack Growth ◽  
J Integral ◽  
Resistance Curve ◽  
Constraint Condition ◽  
Longitudinal Loading ◽  
Resistance Curves ◽  
Unloading Compliance ◽  
Girth Welds

A crack is highly constrained in traditional toughness tests, e.g., CVN and SE(B). However, a crack in the girth welds of pipelines under longitudinal loading is low constrained. Curved wide plate (CWP) test provides similar constraint condition as that of pipeline girth weld. CWP tests are being used recently for strain-based design. One of the desirable outcomes from those tests is fracture toughness resistance curves. The resistance curve consists of two components, the crack growth and the toughness measure, such as J-integral or CTOD. The paper describes the development of procedures for the determination of those two components. A normalized equation was developed to estimate the crack growth from the experimentally measured unloading compliance. The equation was verified by multiple FEA simulations with different pipe geometries and materials. The second set of equations was developed to evaluate the J-integral through an incremental frame based on the instantaneous crack growth and the load-CMOD record. The application of the resistance curve procedures was demonstrated through CWP tests of X80 and X100 welds.

J-Integral Analysis of the Compact Tension Specimen

1989 ◽  
Vol 111 (2) ◽  
pp. 138-144 ◽  
Author(s):  
A. Zahoor
Keyword(s):  
Limit Load ◽  
Compact Tension ◽  
Compact Tension Specimen ◽  
J Integral ◽  
Resistance Curve ◽  
Tension Specimen ◽  
Specimen Width ◽  
Present Solution ◽  
Resistance Curves ◽  
Η Factor

A J-integral solution is presented for the compact tension specimen. The solution allows analysis for crack lengths greater than 20 percent of the specimen width. Unlike previous solutions that were based on the assumptions of full ligament yielding, deeply cracked specimen, or limit load, this paper derives a J solution that does not require such assumptions. Solutions are presented for both the deformation theory J and modified J, JM. These solutions are suitable for J-resistance curve development. A relationship between the plastic and the elastic η factor is presented. A comparison of the present solution with earlier solutions indicates that the J for those solutions is underestimated for a/W below 0.5. Numerical results show that Jd and JM resistance curves are closer than previously obtained. A criterion for extrapolating J-resistance curve is proposed. A relationship for scaling load-displacement curves suitable for key curve analysis is also presented.

Limit Strains of X70 Pipes With a Semi-Elliptical Crack Based on Initiation and Ductile Tearing Criteria

2018 ◽  
Author(s):  
Ju-Yeon Kang ◽  
Youn-Young Jang ◽  
Nam-Su Huh ◽  
Ki-Seok Kim ◽  
Woo-Yeon Cho
Keyword(s):  
Crack Initiation ◽  
Crack Resistance ◽  
Crack Growth ◽  
Driving Force ◽  
J Integral ◽  
Resistance Curve ◽  
Crack Driving Force ◽  
Ductile Tearing ◽  
Resistance Curves ◽  
Crack Resistance Curves

Crack-tip opening displacement (CTOD) and J-integral have been used for elastic-plastic fracture parameters as a crack driving force (CDF) and crack resistance curve to evaluate tensile strain capacity (TSC) of cracked pipelines based on strain-based design (SBD). The TSC can be determined by using two kinds of failure criteria. One is based on the limit state corresponding to an onset of stable crack growth and the other is tangency approach which determines an onset of unstable crack growth by comparing crack driving force and resistance curve. For this reason, the accurate calculation of crack driving force and crack resistance curve is highly required to determine TSC. In the present study, the TSCs for X70 pipelines with a circumferential semi-elliptical surface crack were estimated based on both crack initiation and ductile tearing criteria using crack driving force diagram (CDFD) method. The CDF curves of cracked pipelines were calculated through the detailed elastic-plastic finite element (FE) analyses. Crack resistance curves were obtained from experimental data of single edged notch tension (SENT) specimens. Both the CDF and crack resistance curves were represented using CTOD and J-integral, respectively. As for loading conditions, axial strain and internal pressure were considered. The TSCs based on CTOD were compared with those based on J-integral to investigate the effect of choice of the fracture parameters on TSC. From the FE results, the TSCs based on ductile tearing allowed higher TSCs than those based on crack initiation. Although there were some differences between the TSCs using CTOD and J-integral, the effect of choice of fracture parameter on TSC with internal pressure was not significant.

J-Integral Analysis of Three-Point Bend Specimen

1989 ◽  
Vol 111 (2) ◽  
pp. 132-137 ◽  
Author(s):  
A. Zahoor
Keyword(s):  
Deformation Theory ◽  
Displacement Curve ◽  
J Integral ◽  
Hardening Material ◽  
Resistance Curves ◽  
Point Bend ◽  
Special Case ◽  
Η Factor ◽  
Uncracked Ligament ◽  
Require Data

A J-integral solution is derived for the three-point bend [SE(B)] specimen. The solution allows analysis for a/W greater than 0.2. The solution is based on an approach that does not require an assumption of net-section yielding in the remaining uncracked ligament. Solutions are presented for both the deformation theory J and modified J. These solutions are suitable for J-resistance curve analysis and require data from only one specimen. Solution for a special case of power law hardening material is presented. Consequences of the separability assumption between load-point displacement and crack length on the resulting J solution are discussed. This work indicates that the plastic η factor from previous solutions is significantly underestimated for a/W less than 0.6. Numerical results show that Jd and JM resistance curves are closer than those obtained from previous solutions. A solution for normalizing the load-displacement curve is also presented.

SIZE-DEPENDENT EFFECTS IN ATOMIC CLUSTERS

2020 ◽  
Author(s):  
A. S. Sharipov ◽  
◽  
B. I. Loukhovitski ◽  
Keyword(s):  
Binding Energy ◽  
Physical Properties ◽  
Size Dependence ◽  
Atomic Clusters ◽  
Energy Collision ◽  
Size Dependent

The size-dependence of different physical properties of atomic clusters (by the example of binding energy, collision diameter, and static isotropic polarizability) is discussed.

Quantification of the Complex Crack Geometry Effect On Fracture Resistance Using Strain Based FE Damage Analysis

2021 ◽  
Author(s):  
Seung-Jae Kim ◽  
Ho-Wan Ryu ◽  
Jin Weon Kim ◽  
Young-Jin Oh ◽  
Yun-Jae Kim
Keyword(s):  
Crack Length ◽  
Surface Crack ◽  
Crack Depth ◽  
Damage Model ◽  
Simulation Method ◽  
Resistance Curve ◽  
Crack Geometry ◽  
Model And Simulation ◽  
Resistance Curves ◽  
Complex Crack

Abstract This paper examines the effect of complex crack geometry on the J-resistance curves obtained by strain-based ductile tearing simulation of complex cracked tension (CC(T)) specimens. The damage model is determined by analyzing the results of a smooth bar tensile test and a C(T) specimen toughness test on an SA508 Gr.1a low-alloy steel at 316 ?. The validity of the damage model and simulation method is checked by comparing the fracture test data for two CC(T) specimen tests. To investigate the effect of the complex crack geometry on the crack growth profiles and J-resistance curves, two geometric parameters (namely, the through-wall crack length and the surface crack depth) are systematically varied. It is found that the J-resistance curves for the CC(T) specimens with various through-wall crack lengths and surface crack depths are consistently lower than the corresponding 1T C(T) J-resistance curves. The effect of the through-wall crack length upon the J-resistance curve is found to be less significant than that of the surface crack depth. Moreover, the J-resistance curve decreases continuously with increasing surface crack depth.

scholarly journals Energetic analysis of succinic acid in water droplets: insight into the size-dependent solubility of atmospheric nanoparticles

2021 ◽  
Author(s):  
Chuchu Chen ◽  
Xiaoxiang Wang ◽  
Kurt Binder ◽  
Mohammad Mehdi Ghahremanpour ◽  
David van der Spoel ◽  
...  
Keyword(s):  
Succinic Acid ◽  
Size Dependence ◽  
Volume Ratio ◽  
Size Dependent ◽  
Bulk Volume ◽  
Energetic Analysis ◽  
Entropic Effect ◽  
Dynamics Simulations ◽  
Enhanced Surface ◽  
Potential Of Mean Forces

Abstract. Size-dependent solubility is prevalent in atmospheric nanoparticles, but a molecular level understanding is still insufficient, especially for organic compounds. Here, we performed molecular dynamics simulations to investigate the size dependence of succinic acid solvation on the scale of ~1–4 nm with the potential of mean forces method. Our analyses reveal that the surface preference of succinic acid is stronger for a droplet than the slab of the same size, and the surface propensity is enhanced due to the curvature effect as the droplet becomes smaller. Energetic analyses show that such surface preference is primarily an enthalpic effect in both systems, while the entropic effect further enhances the surface propensity in droplets. On the other hand, with decreasing droplet size, the solubility of succinic acid in the internal bulk volume may decrease, imposing an opposite effect on the size dependence of solubility as compared with the enhanced surface propensity. Meanwhile, structural analyses, however, show that the surface to internal bulk volume ratio increases drastically, especially when considering the surface in respect to succinic acid, e.g., for droplet with radius of 1 nm, the internal bulk volume would be already close to zero for the succinic acid molecule.

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