Quantification of constraint on elastic–plastic 3D crack front by the J–A2 three-term solution

Kim, Y.; Zhu, Xiaomeng; Chao, Yuh J.

doi:10.1016/s0013-7944(00)00134-x

Cited by 54 publications

(48 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…As discussed by Nikishkov et al [18] and Chao and Zhu [19], the J-A 2 three-term solution [13][14][15] is considered as the most effective and theoretically sound asymptotic solution. As a result, the three-term solution has been extensively applied to the following areas: 1) fracture toughness evaluation (Chao and Ji, [20], and Chao and Lam [21]); 2) specimen size requirements in two-parameter fracture testing (Chao and Zhu [19]); 3) non-hardening materials (Zhu and Chao [22]); 4) creeping materials (Chao et al, [23]); 5) three dimensional cracks (Kim et al [24]); and 6) ductile crack growth (Chao and Zhu [16], and Chao et al [17]). Other approaches to quantify the crack tip constraint include the J-T technique proposed by Betegon and Hancock [25], and the J-Q theory by O'Dowd and Shih [26,27].…”

Section: Introductionmentioning

confidence: 99%

Determination of Constraint-Modified J-R Curves for Carbon Steel Storage Tanks

Lam

Chao

Zhu

et al. 2003

Journal of Pressure Vessel Technology

Self Cite

View full text Add to dashboard Cite

Mechanical testing of A285 carbon steel, a storage tank material, was performed to develop fracture properties based on the constraint theory of fracture mechanics. A series of single edge-notched bend (SENB) specimen designs with various levels of crack tip constraint were used. The variation of crack tip constraint was achieved by changing the ratio of the initial crack length to the specimen depth. The test data show that the J-R curves are specimen-design-dependent, which is known as the constraint effect. A twoparameter fracture methodology is adopted to construct a constraint-modified J-R curve, which is a function of the constraint parameter, A 2 , while J remains the loading parameter. This additional fracture parameter is derived from a closed form solution and can be extracted from the finite element analysis for a specific crack configuration. Using this set of SENB test data, a mathematical expression representing a family of the J-R curves for A285 carbon steel can be developed. It is shown that the predicted J-R curves match well with the SENB data over an extensive amount of crack growth. In addition, this expression is used to predict the J-R curve of a compact tension specimen (CT), and good agreement to the actual test data is achieved. To demonstrate its application in a flaw stability evaluation, a generic A285 storage tank with a postulated axial flaw is used. For a flaw length of 10% of the tank height, the predicted J-R curve is found to be similar to that for a SENB specimen with a short notch, which is in a state of low constraint. This implies that the use of a J-R curve from the ASTM (American Society for Testing and Materials) standard designs, which typically are high constraint specimens, may be overly conservative for analysis of fracture resistance of large structures.

show abstract

Section: Introductionmentioning

confidence: 99%

Determination of Constraint-Modified J-R Curves for Carbon Steel Storage Tanks

Lam

Chao

Zhu

et al. 2003

Journal of Pressure Vessel Technology

Self Cite

View full text Add to dashboard Cite

show abstract

“…This parameter is not frequently used to analyze problems related to fracture mechanics. It was described in [20,21], where the authors tried to determine the difference between the distribution of stresses calculated numerically using a finite element method and those calculated according to the HRR solution recommended for the predominantly plane strain conditions. The author of this paper suggests that the use of the parameter Q pso is a good approach because it shows the difference between the actual distribution of stresses responsible for the crack opening and the distribution determined according to a theoretical solution for a case of the dominance of plane strain.…”

Section: Mgrabamentioning

confidence: 99%

“…A year later, Rice and Tracey [18] employed the ratio of the average stresses  m to the effective stresses  eff , calculated according to the Huber-Misses-Hencky (HMH) hypothesis,  m / eff . Some researchers have considered the influence of geometric constraints on the distribution of stresses for three-dimensional cases, analyzing the actual stresses responsible for the crack opening [19], or the differences between the actual description obtained through the FEM analysis and that obtained on the basis of the HRR solution for a case of plane strain [20,21]. It is difficult to discuss all the parameters in one article.…”

Section: Introductionmentioning

confidence: 99%

On The Parameters of Geometric Constraints for Cracked Plates under Tension – Three-Dimensional Problems

Graba

2017

International Journal of Applied Mechanics and Engineering

View full text Add to dashboard Cite

This paper provides a comparative analysis of selected parameters of the geometric constraints for cracked plates subjected to tension. The results of three-dimensional numerical calculations were used to assess the distribution of these parameters around the crack front and their changes along the crack front. The study also involved considering the influence of the external load on the averaged values of the parameters of the geometric constraints as well as the relationship between the material constants and the level of the geometric constraints contributing to the actual fracture toughness for certain geometries.

show abstract

“…Ejemplos tí-picos de este estado son una grieta que atraviesa de lado a lado una placa -donde el espesor de la placa es del mismo orden de magnitud que la longitud característica de la grieta-o grietas situadas en las esquinas. En estas situaciones, la triaxialidad que aparece en los campos de tensiones en los puntos cercanos al frente de grieta, tiene gran influencia sobre los resultados obtenidos en los estudios de mecánica de la fractura [33,[55][56][57][58][59][60].…”

Section: Situaciones Triaxiales Estudio Del Efecto De La Constricciónunclassified

“…1-6, 8, 10, 14, 37, 38, 45, 46, 51, 57, 58, 64, 67, 119, 139 xfem Método de los elementos finitos extendidos, del inglés Extended Finite Element Method . [2][3][4]14,39,40,[44][45][46][47][48]50,52,53,58,62,67,68,70,72,73,79,88,93,118,120,127,[130][131][132][133]135,[140][141][142][143][144][145][146][147] 7,9,11,14,18,23,31,57,58,[60][61]…”

mentioning

confidence: 99%

Estudio de las singularidades de frente de grieta y de esquina en grietas tridimensionales mediante el método de los elementos finitos extendido

Albuixech¹,

Francisco²

View full text Add to dashboard Cite

ResumenEn esta tesis se aborda primeramente el estudio de las grietas tridimensionales partiendo de las premisas de la Mecánica de la Fractura Elástica Lineal -mfely considerando la importancia de los términos de segundo orden del desarrollo de Williams para la correcta descripción del campo de tensiones en problemas tridimensionales. El estudio de las grietas tridimensionales se realiza mediante una extensión de los resultados bidimensionales en los que se suponen conceptos que en un estado tridimensional no pueden ser admitidos directamente. En la tesis se hace un análi-sis del efecto de la triaxialidad sobre estos resultados, poniéndose de manifiesto que no basta con aceptar los términos singulares, sino que al menos se deben incluir los términos constantes del desarrollo de Williams.El segundo punto lo constituye una introducción al método de los elementos finitos extendido -xfem, del inglés Extended Finite Element Method -para grietas tridimensionales, incluyendo algunos de los avances desarrollados en los últimos años. A continuación se aborda el cálculo de los Factor de Intensidad de Tensiones -fiten grietas genéricas tridimensionales con curvatura. Para ello se proponen mejoras en la formulación de las integrales de dominio y se realizan verificaciones numéricas y estudios de convergencia. El cálculo de los fit en grietas que presentan curvatura es el objetivo principal de la tesis. La formulación de la integral de interacción ha sido modificada para mejorar su eficacia. Además se ha introducido el efecto de la curvatura en los gradientes, para lo cual se han usado conceptos de geometría diferencial aprovechando la formulación mediante la función distancia o de nivel -ls, del inglés Level Set-. Esta propuesta mejora apreciablemente los resultados obtenidos mediante las integrales de dominio.El último punto es el estudio y propuesta de un enriquecimiento para mejorar la descripción del estado existente en las cercanías de la singularidad de esquina -o de borde libre-. Además de una revisión bibliográfica del problema de esta singularidad, se ha introducido parte del efecto local de esta singularidad en la formulación de xfem mediante una propuesta de enriquecimiento basado en armónicos esféricos. Este enriquecimiento utiliza las funciones armónicos esféricos que constituyen una base para la descripción de fenómenos con simetría esférica, justificada en grietas tridimensionales debido al comportamiento esférico de esta singularidad.i AbstractThe first objective of the thesis is the review of the analysis of three-dimensional cracks starting from the premises of the Linear Elastic Fracture Mechanics (lefm). The importance of second-order terms of the Williams' series expansion is considered for the correct description of the stress field in three-dimensional problems. The study of three-dimensional cracks is usually performed using an extension of two-dimensional concepts that cannot be done in a straightforward manner. An analyisis of the effect of triaxiality is done in this thesis, concluding that singul...

show abstract

Quantification of constraint on elastic–plastic 3D crack front by the J–A2 three-term solution

Cited by 54 publications

References 33 publications

Determination of Constraint-Modified J-R Curves for Carbon Steel Storage Tanks

Determination of Constraint-Modified J-R Curves for Carbon Steel Storage Tanks

On The Parameters of Geometric Constraints for Cracked Plates under Tension – Three-Dimensional Problems

Estudio de las singularidades de frente de grieta y de esquina en grietas tridimensionales mediante el método de los elementos finitos extendido

Contact Info

Product

Resources

About