Stress Intensity Factors for Externally and Internally Cracked Pressurized Thick Cylinders with Residual and Thermal Stresses

Andrasic, C.P.; Parker, Anthony P.

doi:10.1007/978-94-009-6914-8_14

Cited by 4 publications

(4 citation statements)

References 9 publications

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“…A variety of numerical methods for the determination of WFs for cracked bodies have been developed, and only some representative ones are noted here. A MMC technique was proposed by Andrasic and Parker, giving accurate WFs of cracked curved beams and hollow cylinders . Sham presented a FE implementation of the variational principle leading to a unified approach in numerical computations of WFs .…”

Section: Numerical Weight Function Methodsmentioning

confidence: 99%

“…Since the pioneering work of Bueckner and Rice, many numerical and analytical methods for the determination of WFs for various crack geometries have been developed in the past several decades. An early numerical WFM was due to Andrasic and Parker using a modified mapping collocation (MMC) technique . Subsequent numerical WFMs mainly include the finite element method (FEM), boundary element method (BEM), boundary collocation method (BCM), and etc.…”

Section: Introductionmentioning

confidence: 99%

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A review and verification of analytical weight function methods in fracture mechanics

2019

Fatigue Fract Eng Mat Struct

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The weight function method is a powerful method for the determination of key parameters of stress intensity factors and crack opening displacements that are fundamental for crack analyses in fracture mechanics. The method has a remarkable computational efficiency without compromising solution accuracy and is especially suited for cracks in real‐world components with complex stress gradients. A critical issue for successful development and reliable application of the weight function method is how to achieve verifiable and high solution accuracy. This paper provides several reflections on the current state of the art in weight function methods, including a brief historical perspective and description of several analytical and numerical weight methods, with main focus on the two‐dimensional (2D) analytical approaches. A variety of typical application examples are presented. A platform for point‐by‐point accuracy assessment by using the Green's functions is established on a completely independent numerical approach with validated accuracy. Rigorous and systematic verification of the accuracy levels of different 2D analytical weight function approaches are conducted using several benchmark crack geometries. The sources of inaccuracy of different analytical weight function methods are analysed. A brief account on weight function methods for analysing three‐dimensional (3D) crack problems with arbitrary univariant and bivariant stress distributions is provided.

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Section: Numerical Weight Function Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A review and verification of analytical weight function methods in fracture mechanics

2019

Fatigue Fract Eng Mat Struct

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“…In this case, unlike in the case considered in [1], pressure was also applied to the crack faces. Andrasis and Parker [3][4][5] improved the method proposed in [1] and solved a linear fracture mechanics problem for a cylinder containing a varied number of identical cracks equidistant from each and subjected to external and internal pressures, and also in the presence of a selfbalanced field of residual stresses. Pu and Hussain [6] solved the same problem using the finite-element method.…”

mentioning

confidence: 99%

“…J-integral versus pressure in the case of an unheated cylinder: curves 1-3 refer to the calculation taking into account elastoplastic deformation for δ/a = 0.05 (1) and 0.1 (2); curve 3 is the calculation result of[8]; curve 4 refers to the calculation taking into account only elastic deformation[3].…”

mentioning

confidence: 99%

Thermoelastoplastic deformation of a thick-walled cylinder with a radial crack

Lavit

Trung

2008

J Appl Mech Tech Phys

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UDC 539.375 I. M. Lavit and Nguyen Viet TrungThe thermoelastoplastic fracture mechanics problem of a thick-walled cylinder subjected to internal pressure and a nonuniform temperature field is solved by the method of elastic solutions combined with the finite-element method. The correctness of the solution is provided by using the Barenblatt crack model, in which the stress and strain fields are regular. The elastoplastic problem of a cracked cylinder subjected to internal pressure and a nonuniform temperature field are solved. The calculation results are compared with available data.Introduction. In strength analysis, structural members used in power and chemical engineering can be treated as thick-walled cylinders subjected to internal pressure and a nonuniform temperature field. Under quasistatic loading, fracture of a cylinder is a results of radial crack propagation from the inner surface. The length of the segment of steady crack growth is comparable to the thickness of the cylinder; therefore, the strength of the cylinder should be analyzed using the fracture mechanics concepts. In addition, it is necessary to take into account the possibility of plastic deformation.The computational scheme of the problem is given in Fig. 1. A cylinder of inner radius R 1 and outer radius R 2 is in a plane strain state. It is assumed that the material of the cylinder is homogeneous, isotropic, and perfectly plastic and that its strain is small. In elastic deformation, the behavior of the material obeys Hooke's law, and in plastic deformation, it obeys the Prandtl-Reuss relations and the Mises yield condition. The yield point σ Y depends on temperature. The cylinder is weakened by a radial crack of length a. The interior of the cylinder and the crack cavity are acted upon by pressure p. The cylinder is heated nonuniformly. By virtue of the quasistatic formulation of the problem, the temperature field can be considered axisymmetric.The problem of elastic deformation of a cracked cylinder was first solved by Bowie and Freese [1] using the Kolosov-Muskhelishvili method with a conformal mapping of a circular ring onto the cross section of the cracked cylinder combined with a collocation method. Only the action of external pressure was considered. Shannon [2] solved the problem of the action of internal pressure using a finite-element method. In this case, unlike in the case considered in [1], pressure was also applied to the crack faces. Andrasis and Parker [3][4][5] improved the method proposed in [1] and solved a linear fracture mechanics problem for a cylinder containing a varied number of identical cracks equidistant from each and subjected to external and internal pressures, and also in the presence of a selfbalanced field of residual stresses. Pu and Hussain [6] solved the same problem using the finite-element method. The elastoplastic deformation of cracked cylinders have also been studied. Sumpter [7] solved an elastoplastic problem for a cylinder subjected to internal pressure using the finite-element method, and Tan an...

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Mode I Stress Intensity Factors for Point-Loaded Cylindrical Test Specimens with One or Two Radial Cracks

Parker

Andrasic

1984

Fracture Mechanics: Fifteenth Symposium

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Weight (or Green's) functions are obtained, using an accurate modified mapping collocation numerical technique, for cylindrical specimens with either one or two internal or external radial cracks. Radii ratios (the ratio of external/internal radius) of 1.25, 1.5, 1.75, 2.0, 2.5, and 3.0 are considered. The weight functions are used to obtain stress intensity (K) factors for radial loading by point forces symmetrically located about the crack line and about an axis at right angles to the crack line, through the center of the specimen. The maximum errors associated with the solutions are estimated at 1%. Notable features of the results obtained include a significant range of crack lengths with near-constant K-values, and configurations in which K changes sign as the crack length is increased. The point force configurations are suited to serve as cylindrical test specimens, either for fracture toughness or fatigue crack growth testing.

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Stress Intensity Factors for Externally and Internally Cracked Pressurized Thick Cylinders with Residual and Thermal Stresses

Cited by 4 publications

References 9 publications

A review and verification of analytical weight function methods in fracture mechanics

A review and verification of analytical weight function methods in fracture mechanics

Thermoelastoplastic deformation of a thick-walled cylinder with a radial crack

Mode I Stress Intensity Factors for Point-Loaded Cylindrical Test Specimens with One or Two Radial Cracks

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