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REVIEW ARTICLES

Virtual crack closure technique: History, approach, and applications

[+] Author and Article Information
Ronald Krueger

National Institute of Aerospace, Hampton, Virginia 23666rkrueger@nianet.org

Appl. Mech. Rev 57(2), 109-143 (Apr 26, 2004) (35 pages) doi:10.1115/1.1595677 History: Online April 26, 2004
Copyright © 2004 by ASME
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Figures

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Mixed-mode delamination criterion for IM7/8552
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Crack closure method (two-step method). a) First step—crack closed and b) second step—crack extended.
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Modified crack closure method (one-step VCCT)
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Crack modeled as one-dimensional discontinuity. a) Initially modeled, undeformed finite element mesh and b) deformed finite element mesh.
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Kinematic compatible crack opening/closure. a) Nodewise crack opening for four-noded element and b) crack opening for eight-noded element.
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Virtual crack closure technique for 2D solid elements. a) Virtual crack closure technique for four-noded element (lower surface forces are omitted for clarity) and b) virtual crack closure technique for eight-noded element (lower surface forces are omitted for clarity).
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Singularity elements with quarter-point nodes at crack tip. a) Quadtrilateral elements with quarter-point nodes and b) collapsed quarter-point element.
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Delaminations modeled as two-dimensional discontinuity. a) Delamination modeled with bilinear 3D solid elements and b) delamination modeled with bilinear plate/shell type elements.
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Virtual crack closure technique for four-noded plate/shell and eight-noded solid elements. a) 3D view (lower surface forces are omitted for clarity) and b) top view of upper surface (lower surface terms are omitted for clarity).
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Virtual crack closure technique for corner nodes in eight-noded plate/shell and twenty-noded solid-elements. a) 3D view (lower surface forces are omitted for clarity) and b) top view of upper surface (lower surface terms are omitted for clarity).
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Virtual crack closure technique for midside nodes in eight-noded plate/shell and twenty-noded solid elements. a) 3D view (lower surface forces are omitted for clarity) and b) top view of upper surface (lower surface terms are omitted for clarity).
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Virtual crack closure technique (element method) for eight-noded plate/shell and twenty-noded solid elements. a) 3D view (lower surface forces are omitted for clarity) and b) top view of upper surface (lower surface terms are omitted for clarity).
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Virtual crack closure technique (element method) for twenty-noded quarter point elements. a) 3D view (lower surface forces are omitted for clarity) and b) top view of upper surface (lower surface terms are omitted for clarity).
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Collapsed twenty-noded solid singularity elements with quarter point nodes at crack tip
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Virtual crack closure technique for four-noded plate/shell elements. a) 3D view (lower surface forces are omitted for clarity) and b) top view of upper surface (lower surface terms are omitted for clarity).
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Virtual crack closure technique for nine-noded plate/shell elements. a) 3D view (lower surface forces are omitted for clarity) and b) top view of upper surface (lower surface terms are omitted for clarity).
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Virtual crack closure technique for geometrically nonlinear analysis. a) Definition of local crack tip coordinate system and b) forces and displacements in local coordinate system (lower surface forces are omitted for clarity).
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Correction for elements with different lengths in front and behind the crack tip
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Correction for elements with different lengths in front and behind the crack tip. a) Shorter elements in front of the crack tip and b) longer elements in front of the crack tip.
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Virtual crack closure technique for eight-noded solid elements with different widths
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Virtual crack closure technique for arbitrarily shaped front
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Definition of mode separation at sharp corners. a) Undefined mode separation at corner nodal point and b) well-defined mode separation at rounded corner.
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Detail of a finite element mesh with modeled square insert
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Bimaterial interface. a) Bimaterial interface, b) dependence of computed energy release rate on element size at crack tip and c) upper and lower bounds for element size at crack tip.
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Three-dimensional finite element model of SLB specimen
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Influence of the number of elements in refined section on computed mode I strain energy release rate distribution across the width of a SLB specimen
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Influence of the number of elements in refined section on computed mode II strain energy release rate distribution across the width of a SLB specimen
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Influence of the number of elements in refined section on computed mode III strain energy release rate distribution across the width of a SLB specimen
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Influence of the number of elements in refined section on mode ratio distribution across the width of a SLB specimen
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Skin/flange debonding specimen. a) Specimen configuration and b) finite element model of skin/flange specimen.
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Computed total strain energy release rate for delamination between top 45°/−45° skin plies
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Computed mixed mode ratio for delamination between top 45°/−45° skin plies
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Delamination buckling specimen. a) Delamination buckling specimen and section modeled with three-dimensional solid elements and b) x ray showing the initial circular delamination and detected growth after 200 000 load cycles.
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Computed mixed-mode energy release rate along detected delamination front after 200 000 load cycles
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Crack modeled as one-dimensional discontinuity. a) Intact region in front of the crack modeled with single nodes and b) intact region in front of the crack modeled with double nodes tied by multipoint constraints.
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Flow chart of routine extract.f to calculate strain energy release rates

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