Finite deformation analysis of crack-tip opening in elastic-plastic materials and implications for fracture

McMeeking, Robert M.

doi:10.1016/0022-5096(77)90003-5

Cited by 845 publications

(375 citation statements)

References 26 publications

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“…The mean stress (σ m = (σ 11 + σ 22 + σ 33 )/3) at a fixed distance equal to 0.1%R p and θ = 0 o ( [15]) is plotted in Fig. 2 as function of the material length scales ( 1 = 2 = 3 = ) for various strain hardening exponents, n. Three distinct regions can be identified: a) for small length scale, , the solutions converge to conventional plasticity predictions which strongly depend on the strain hardening exponent [30], b) for large the solutions approach the elastic solution which of course is independent of n and c) in between these two regions is the area where strain gradient plasticity has a profound effect (approximately for 10 −3 ≤ /R p ≤ 1, depending on n) in elevating the mean stress. The same trend has been shown for σ θθ , (θ = 0 o ) by [16].…”

Section: Mode Imentioning

confidence: 87%

Mode I and mixed mode crack-tip fields in strain gradient plasticity

Goutianos

2011

International Journal of Non-Linear Mechanics

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To cite this version:Stergios Goutianos.Mode I and mixed mode crack-tip fields in strain gradient plasticity.International Journal of Non-Linear Mechanics, Elsevier, 2011, 46 (9) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractStrain gradients develop near the crack-tip of Mode I or mixed-mode cracks.A finite strain version of the phenomenological strain gradient plasticity theory of Fleck-Hutchinson (2001) is used here to quantify the effect of the material length scales on the crack-tip stress field for a sharp stationary crack under Mode I and mixed-mode loading. It is found that for material length scales much smaller than the scale of the deformation gradients, the predictions converge to conventional elastic-plastic solutions. For length scales sufficiently large, the predictions converge to elastic solutions. Thus, the range of length scales over which a strain gradient plasticity model is necessary is identified. The role of each of the three material length scales, incorporated in the multiple length scale theory, in altering the near-tip stress field is systematically studied in order to quantify their effect.

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Section: Mode Imentioning

confidence: 87%

Mode I and mixed mode crack-tip fields in strain gradient plasticity

Goutianos

2011

International Journal of Non-Linear Mechanics

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“…The Green-Naghdi rate may be written alternatively as the rate of unrotated Cauchy stress, i, expressed on the fixed, Cartesian axes (20) Transformation of the spatial deformation rate D in this expression to the unrotated deformation rate d yields (21) Constitutive computations, equivalent to the Green-Naghdi rate in eqn (19b), therefore can be performed using stress-strain rates defined on the unrotated configuration. Updated values of t are rotated via R to obtain the updated Cauchy stress at the end of a load increment.…”

Section: Selection Of Strain-stress Ratementioning

confidence: 99%

“…Rice and Tracey [26] and McMeeking [20,21] developed a boundary-layer approximation for the infinite body model that is suitable for finite-element analysis. The SSY model consists of an annular region containing either a sharp or smoothly blunt crack tip which is subjected to increasing displacements of the elastic (Mode I) singular field on the outer circular boundary.…”

Section: Crack-tip Blunting In Small-scale Yieldingmentioning

confidence: 99%

A large strain plasticity model for implicit finite element analyses

Healy

Dodds

1992

Computational Mechanics

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Annual:11-1-89 to 12-31-90 14.The theoretical basis and numerical implementation of a plasticity model suitable for finite strains and rotations are described. The constitutive equations governing J2 flow the0!y' are formulated using strainsstresses and their rates defined on the unrotated frame of reference. Unhke models based on the classical J aumann (or corotational) stress rate, the present model predicts physically acceptable responses for homogeneous deformations of exceedingly large magnitude. The associated numerical algorithms accommodate the large strain increments that arise in finite-element formulations employing an implicit solution of the global equilibrium equations. The resulting computational framework divorces the finite rotation effects on . Consequently, all of the numerical refinements developed previously for small-strain plasticity (radial return with subincrementation, plane stress modifications, kinematic hardening, consistent tangent operators) are utilized without modificatIOn. Details of the numerical algorithms are provided including the necessary transformation matrices and additional techniques re9.uired for finite deformations in plane stress. Several numerical examples are presented to illustrate the realIstic responses predicted by the model and the robustness of the numerical procedures. ABSTRACTThe theoretical basis and numerical implementation of a plasticity model suitable for finite strains and rotations are described. The constitutive equations governing J2 flow theory are formulated using strains-stresses and their rates defined on the unrotated frame of reference. Unlike models based on the classical Jaumann (or corotational) stress rate, the present model predicts physically acceptable responses for homogeneous deformations of exceedingly large magnitude. The associated numerical algorithms accommodate the large strain increments that arise in finite-element formulations employing an implicit solution of the global equilibrium equations. The resulting computational framework divorces the finite rotation effects on strain-stress rates from integration of the rates to update the material response over a load (time) step. Consequently, all of the numerical refinements developed previously for small-strain plasticity (radial return with subincrementation, plane stress modifications, kinematic hardening, consistent tangent operators) are utilized without modification. Details of the numerical algorithms are provided including the necessary transformation matrices and additional techniques required for finite deformations in plane stress. Several numerical examples are presented to illustrate the realistic responses predicted by the model and the robustness of the numerical procedures.-ii - ACKNOWLEDGMENTS

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“…While this high triaxiality field is only one of many possible states that can exist under fully yielded conditions, it is the only field that has received careful study until recently. When the high triaxiality field (Hutchinson (2], Rice and Rosengren [3), Rice and Johnson [4], McMeeking [5)) prevails over distances comparable to several crack tip openings, J alone sets the near-tip stress level and the size scale of the zone of high stresses and deformations. Considerable efforts have been directed to establishing, for different crack geometries, the remote deformation levels which ensure that the near-tip behavior is uniquely measured by J (McMeeking and Parks [6], Shih and German [7]).…”

Section: Introductionmentioning

confidence: 99%

Two-Parameter Fracture Mechanics: Theory and Applications

O'Dowd

Shih

1994

Fracture Mechanics: Twenty-Fourth Volume

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z Approved for public release; distribution is unlimited. ABSTRACT A family of self-similar fields provides the two parameters required to characterize the full range of high-and low-triaxiality crack tip states. The two parameters, J and Q, have distinct roles: J sets the size scale of the process zone over which large stresses and strains develop, while Q scales the near-tip stress distribution relative to a high triaxiality reference stress state. An immediate consequence of the theory is this: it is the toughness values over a range of crack tip constraint that fully characterize the material's fracture resistance. It is shown that Q provides a common scale for interpreting cleavage fracture and ductile tearing data thus allowing both failure modes to be incorporated in a single toughness locus.The evolution of Q, as plasticity progresses from small scale yielding to fully yielded conditions, has been quantified for several crack geometries and for a wide range of material strain hardening properties. An indicator of the robustness of the J-Q fields is introduced;Q as a field parameter and as a pointwise measure of stress level is discussed.1Wx~ QUALITY INSPEMTD 3

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Finite deformation analysis of crack-tip opening in elastic-plastic materials and implications for fracture

Cited by 845 publications

References 26 publications

Mode I and mixed mode crack-tip fields in strain gradient plasticity

Mode I and mixed mode crack-tip fields in strain gradient plasticity

A large strain plasticity model for implicit finite element analyses

Two-Parameter Fracture Mechanics: Theory and Applications

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