A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks

1968 ◽  
Vol 35 (2) ◽  
pp. 379-386 ◽  
Author(s):  
J. R. Rice
Keyword(s):  
Plastic Material ◽  
Crack Tip ◽  
Plastic Zone Size ◽  
Crack Model ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Direct Evaluation ◽  
Strain Concentration ◽  
Hydrostatic Tension ◽  
Elastic Plastic

A line integral is exhibited which has the same value for all paths surrounding the tip of a notch in the two-dimensional strain field of an elastic or deformation-type elastic-plastic material. Appropriate integration path choices serve both to relate the integral to the near tip deformations and, in many cases, to permit its direct evaluation. This averaged measure of the near tip field leads to approximate solutions for several strain-concentration problems. Contained perfectly plastic deformation near a crack tip is analyzed for the plane-strain case with the aid of the slip-line theory. Near tip stresses are shown to be significantly elevated by hydrostatic tension, and a strain singularity results varying inversely with distance from the tip in centered fan regions above and below the tip. Approximate estimates are given for the strain intensity, plastic zone size, and crack tip opening displacement, and the important role of large geometry changes in crack blunting is noted. Another application leads to a general solution for crack tip separations in the Barenblatt-Dugdale crack model. A proof follows on the equivalence of the Griffith energy balance and cohesive force theories of elastic brittle fracture, and hardening behavior is included in a model for plane-stress yielding. A final application leads to approximate estimates of strain concentrations at smooth-ended notch tips in elastic and elastic-plastic materials.

scholarly journals A Numerical Analysis of Selected Elastic-Plastic Fracture Parameters for DEN(T) Plates under Plane Strain Conditions

2017 ◽  
Vol 22 (1) ◽  
pp. 49-80 ◽  
Author(s):  
M. Graba
Keyword(s):  
Numerical Analysis ◽  
Fracture Mechanics ◽  
Plane Strain ◽  
Plastic Material ◽  
Crack Tip ◽  
Limit Load ◽  
Material Model ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Elastic Plastic

Abstract This paper provides a numerical analysis of selected parameters of fracture mechanics for double-edge notched specimens in tension, DEN(T), under plane strain conditions. The analysis was performed using the elastic-plastic material model. The study involved determining the stress distribution near the crack tip for both small and large deformations. The limit load solution was verified. The J-integral, the crack tip opening displacement, and the load line displacement were determined using the numerical method to propose the new hybrid solutions for calculating these parameters. The investigations also aimed to identify the influence of the plate geometry and the material characteristics on the parameters under consideration. This paper is a continuation of the author’s previous studies and simulations in the field of elastic-plastic fracture mechanics [4, 6, 16, 17, 31].

The Inelastic Line-Spring: Estimates of Elastic-Plastic Fracture Mechanics Parameters for Surface-Cracked Plates and Shells

1981 ◽  
Vol 103 (3) ◽  
pp. 246-254 ◽  
Author(s):  
D. M. Parks
Keyword(s):  
Fracture Mechanics ◽  
Crack Growth ◽  
Computing Time ◽  
Crack Tip ◽  
J Integral ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Elastic Plastic ◽  
Plates And Shells ◽  
Crack Tip Opening

Recent studies of the mechanics of elastic-plastic and fully plastic crack growth suggest that such parameters as the J-integral and the crack tip opening displacement can, under certain conditions, be used to correlate the initiation and early increments of the ductile tearing mode of crack growth. To date, elastic-plastic fracture mechanics has been applied mainly to test specimen geometries, but there is a clear need for developing practical analysis capabilities in structures. In principle, three-dimensional elastic-plastic finite element analysis could be performed, but, in fact, such analyses would be prohibitively expensive for routine application. In the present work, the line-spring model of Rice and Levy [1-3] is extended to estimate the J-integral and crack tip opening displacement for some surface crack geometries in plates and shells. Good agreement with related solutions is obtained while using orders of magnitude less computing time.

Validation on the Relationship Between J Integral and CTOD for Offshore Structural Steel Weldments by Experimental and Numerical Analyses

2014 ◽  
Author(s):  
Dong Hyun Moon ◽  
Jeong Soo Lee ◽  
Jae Myung Lee ◽  
Myung Hyun Kim
Keyword(s):  
Plastic Deformation ◽  
Crack Tip ◽  
J Integral ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Constraint Factor ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Plastic Constraint ◽  
The Relationship

Elastic plastic fracture mechanics (EPFM) is the domain of fracture analysis which considers extensive plastic deformation at crack tip prior to fracture. J integral and crack tip opening displacement (CTOD) have been commonly used as parameters for EPFM analysis. The relationship between these parameters has been extensively studied by industry and academia. The plastic constraint factor can serve as a parameter to characterize constraint effects in fracture involving plastic deformation. Therefore, the characteristics of plastic constraint factor are important in EPFM analysis. In this study, the relationship between J Integral and CTOD was investigated by conducting fracture toughness tests using single edge notched bend (SENB) specimens. Also, plastic constraint factor was investigated by using finite element analysis. Numerical analysis was carried out using ABAQUS elastic-plastic analysis mode.

Elastic-Plastic Finite Element Analysis of the Effect of the Compressive Loading on Fatigue Crack Tip Parameters

2008 ◽  
Vol 392-394 ◽  
pp. 980-984 ◽  
Author(s):  
Y. Sha ◽  
Hui Tang ◽  
Jia Zhen Zhang
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Compressive Stress ◽  
Kinematic Hardening ◽  
Compressive Loading ◽  
Crack Tip ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Element Analysis ◽  
Elastic Plastic

In this paper, a detailed elastic-plastic finite element analysis of the effect of the compressive loading on crack tip plasticity is studied based on the material’s kinematic hardening model. Five centre-cracked panel specimens with different crack lengths are analyzed. The analysis shows that in a tension-compression loading the maximum spread of the crack tip reverse plastic zone increases with the increase of the compressive stress and the near crack tip opening displacement decreases with the increase of the compressive stress at the same nominal stress intensity factor. The applied compressive stress is the main factor controlling the near crack tip parameters.

The interaction problem of two Zener–Stroh cracks with a nearby inhomogeneity

2017 ◽  
Vol 24 (3) ◽  
pp. 542-558
Author(s):  
M Fan ◽  
ZM Xiao ◽  
YM Zhang
Keyword(s):  
Plastic Zone ◽  
Influence Factors ◽  
Crack Tip ◽  
Singular Integral Equations ◽  
Plastic Zone Size ◽  
Circular Inclusion ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Crack Tips ◽  
Crack Tip Opening

In this paper, the interaction among two Zener–Stroh cracks (with plastic zone correction) and a nearby circular inclusion are investigated. To evaluate the plastic zone sizes at crack tips in the current physical problem is a great challenge. As the first attempt to explore the multiple defects’ interaction effect on the yielding behavior of a crack, we focused on the analysis of one target crack, while the other crack and the circular inhomogeneity are treated as influence factors. With the help of coordinate transformation and superposition procedure, the formulated singular integral equations can be solved numerically. The influence of material properties, crack–crack positions and other parameters, such as crack length and Burgers vector of the Zener–Stroh crack, on the target crack tip stress intensity factor, plastic zone size and crack tip opening displacement are examined. It is found that the effects of the aforesaid parameters on the cracks are all inter-related and dependent on each other. This observation reveals the complexity of fracture analysis and the necessity to have a deep research on interacting defects in composite materials.

A Nonlinear Analysis of an Equilibrium Craze: Part II—Simulations of Craze and Crack Growth

1988 ◽  
Vol 55 (1) ◽  
pp. 52-58 ◽  
Author(s):  
T. Ungsuwarungsri ◽  
W. G. Knauss
Keyword(s):  
Crack Growth ◽  
Crack Tip ◽  
Energy Dissipation Rate ◽  
Crack Model ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Critical Crack ◽  
Dugdale Model ◽  
Nonlinear Force ◽  
Crack Tip Opening

In this study we investigate the effects of nonlinear fibril behavior on the mechanics of craze and crack growth. The effect of strain-softening cohesive material on crack stability is of particular interest and is examined via a craze and crack model developed in the first part of this work where the formulation and solution of the problem are discussed.1 In this second part, quasi-static growth of a craze with a central crack is analyzed for different nonlinear force-displacement (p-v) relations for the craze fibrils. A “critical crack tip opening displacement” (CTOD), or more precisely, “critical fibril extension” is employed as the criterion for fracture. The p-v relation is further assumed to be invariant with respect to the craze and crack lengths. The results are compared with the Dugdale model; the craze zone size and the energy dissipation rate approach asymptotic values in the limit of long cracks. The problem of craze growth from a precut crack under increasing far-field loading is then studied. In the case where the p-v relation is monotonically softening, the crack can start to grow in an unstable manner before the crack tip opening displacement reaches its critical value.

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