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.

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.

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.

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.

The Determination of the J-Integral on Precracked Charpy Specimens by Instrumented Impact Testing and Slow-Bend Testing

1978 ◽  
Vol 100 (3) ◽  
pp. 253-257 ◽  
Author(s):  
P. Nguyen-Duy ◽  
G. Phelippeau ◽  
R. Simoneau ◽  
G. Begin
Keyword(s):  
Fracture Criterion ◽  
Impact Testing ◽  
Plastic Behavior ◽  
Displacement Curve ◽  
Maximum Point ◽  
J Integral ◽  
Lateral Deformation ◽  
Absorbed Energy ◽  
Point Bend

The fracture criterion JIC is determined on SA-516-70 steel using precracked CVN specimens. The addition of an appropriate side-groove results in a better plane-strain condition at the crack tip and removes a major part of the absorbed energy due to lateral deformation. The value of JIC static is calculated from a single three-point-bend experiment. The displacement of the cracked front is followed by the measurement of the electrical resistance. We have shown that a single specimen is sufficient for determining JIC. Experiments on an instrumented Charpy machine were used for the calculation of the value of JICD. We assumed, for elasto-plastic behavior, that the maximum point of the load-displacement curve corresponds to the instability threshold of the crack. The values of JIC and JICD obtained by these two methods are compared and discussed.

scholarly journals The elastic-plastic delamination analysis of layered beam configurations

2019 ◽  
Vol 39 (2) ◽  
pp. 165-173
Author(s):  
Victor Rizov
Keyword(s):  
Analytical Solutions ◽  
Strain Energy Release ◽  
Integral Approach ◽  
J Integral ◽  
Elastic Plastic ◽  
Crack Location ◽  
Layered Beams ◽  
Delamination Fracture ◽  
Non Linear ◽  
Point Bend

The elastic-plastic delamination fracture in layered beams was studied theoretically. Two Four Point Bend (FPB) beam configurations (the Double Leg Four Point Bend (DLFPB) and the Single Leg Four Point Bend (SLFPB)) were analyzed. An elastic-plastic constitutive model with power law hardening was used in the analysis. Fracture behavior was studied by applying the J-integral approach. The analytical solutions of the J-integral were obtained at characteristic levels of the external load. The solutions obtained were verified by analyzing the strain energy release rate with taking into account the material non-linearity. The variation of J-integral value in a function of crack location along the beam dept was investigated. The effect of material non-linearity on the fracture was evaluated. The analysis revealed that the J-integral value decreased with increasing the lower crack arm thickness. It was also found that the material non-linearity has to be taken into account in fracture mechanics based safety design of structural members and components made of layered materials. The analytical solutions obtained are very useful for non-linear investigations, since the simple formulae derived capture the essentials of non-linear fracture in the layered beams under consideration.

Fracture energy characterisation of a structured interface by means of a novel J-Integral procedure

2019 ◽  
Vol 54 (7-8) ◽  
pp. 364-378
Author(s):  
Lorenzo García-Guzmán ◽  
Luis Távara ◽  
José Reinoso ◽  
Federico París
Keyword(s):  
Finite Element ◽  
Fracture Energy ◽  
Cohesive Zone Model ◽  
Integral Formulation ◽  
Evaluation Procedure ◽  
Crack Advance ◽  
Energy Calculation ◽  
Zone Model ◽  
Displacement Curve ◽  
J Integral

In the present investigation, a J-Integral formulation for non-flat crack paths, in the framework of the cohesive zone model, is developed. The formulation allows fracture energy properties in a direction that is not necessarily coplanar with the global crack advance to be analysed. Specifically, the effective fracture energy, [Formula: see text], has been examined based on the horizontal projection of the crack advance, [Formula: see text] (also called effective crack length). The use of [Formula: see text] is convenient in several situations as the case of patterned interfaces in adhesive joints. Finite-element analysis of double cantilever beam specimens including a trapezoidal patterned interface were employed to check the accuracy of this new definition of the contour integral. Post-process of the finite-element model, including those variables involved in the fracture energy calculation, is discussed together with some considerations that distinguish the energy evaluation procedure for flat profiles from structured designs. Finally, [Formula: see text] values obtained using the modified J-Integral formulation are compared with [Formula: see text] values obtained from the load–displacement curve method for comparison purposes.

C-Specimen Fracture Toughness Testing: Effect of Side Grooves and η Factor

2003 ◽  
Author(s):  
Y. Kim ◽  
Y. J. Chao ◽  
M. J. Pechersky ◽  
M. J. Morgan
Keyword(s):  
Fracture Toughness ◽  
Plane Strain ◽  
Crack Front ◽  
Testing Effect ◽  
Three Dimensional ◽  
Strain Analysis ◽  
Compact Tension ◽  
Compact Tension Specimen ◽  
J Integral ◽  
Η Factor

Elastic-plastic crack front fields in arc-shaped tension specimens (C-specimens) were analyzed by a three-dimensional finite element method. The effect of side grooves on the ductile fracture behavior was investigated by studying the J-integral distribution, plane-strain constraint parameter, and development of plastic zones and comparing to experimental data. The applicability of the η factor (derived for use with compact tension specimens) for the calculation of J-integral values for the C-specimen was also investigated. The results show that side grooves promote and establish near plane strain conditions at the crack front in sub-size specimens. It was also found that a two-dimensional plane-strain analysis in conjunction with the standard American Society for Testing and Materials (ASTM) tests was sufficient to determine the fracture toughness values from side-grooved C-specimen. The results indicate the η factor for compact tension specimen as specified in the ASTM standards appears to produce reliable results for the calculation of J of C-specimens.

Determination of J-Integral Using the Load-COD Record for Circumferential Through-Wall Cracked Pipes

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Nam-Su Huh ◽  
Yun-Jae Kim
Keyword(s):  
Crack Opening ◽  
Estimation Method ◽  
J Integral ◽  
Opening Displacement ◽  
Element Analysis ◽  
Load Line ◽  
Load Line Displacement ◽  
Η Factor ◽  
J Estimation

The present paper provides experimental J estimation equation based on the load-crack opening displacement (COD) record for testing the circumferential through-wall cracked pipe under combined tension and bending. Based on the limit analysis and the kinematically admissible rigid-body rotation field, the plastic η-factor for the load-COD record is derived and is compared with that for the load-load line displacement record. Comparison with the J results from detailed elastic-plastic finite element analysis shows that the proposed method based on the load-COD record provides reliable J estimates even for shallow cracks (small crack angle), whereas the conventional approach based on the load-load line displacement record gives erroneous results for shallow cracks. Thus, the proposed J estimation method could be recommended for testing the circumferential through-wall cracked pipe, particularly with shallow cracks.

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