Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 An overview of the virtual crack closure technique is presented. The approach used is discussed, the history summarized, and insight i n to its applications provided. Equations for two-dimensional quadrilateral elements with linear and quadratic shape functions are given. Formulae for applying the technique in conjuction with threedimensional solid elements as well as plate shell elements are also provided. Necessary modi cations for the use of the method with geometrically nonlinear nite element analysis and corrections required for elements at the crack tip with di erent lengths and widths are discussed. The problems associated with cracks or delaminations propagating between di erent materials are mentioned brie y, a s w ell as a strategy to minimize these problems. Due to an increased interest in using a fracture mechanics based approach to assess the damage tolerance of composite structures in the design phase and during certi cation, the engineering problems selected as examples and given as references focus on the application of the technique to components made of composite materials. • TECHNICAL MEMORANDUM. Scientific and technical findings that are preliminary or of specialized interest, e.g., quick release reports, working papers, and bibliographies that contain minimal annotation. Does not contain extensive analysis.• CONTRACTOR REPORT. Scientific and technical findings by NASA-sponsored contractors and grantees.• CONFERENCE PUBLICATIONS. Collected papers from scientific and technical conferences, symposia, seminars, or other meetings sponsored or cosponsored by NASA.• SPECIAL PUBLICATION. Scientific, technical, or historical information from NASA programs, projects, and missions, often concerned with subjects having substantial public interest.• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientific and technical material pertinent to NASA's mission. propagating between different materials are mentioned briefly, as well as a strategy to minimize these problems.Due to an increased interest in using a fracture mechanics based approach to assess the damage tolerance of composite structures in the design phase and during certification, the engineering problems selected as examples and given as references focus on the application of the technique to components made of composite materials.

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A consistent step-wise approach is presented to investigate the damage mechanism in composite bonded skin/stringer constructions under uniaxial and biaxial (in-plane/out-of-plane) loading conditions. The approach uses experiments to detect the failure mechanism, computational stress analysis to determine the location of first matrix cracking and computational fracture mechanics to investigate the potential for delamination growth. In a first step, tests were performed on specimens, which consisted of a tapered composite flange, representing a stringer or frame, bonded onto a composite skin. Tests were performed under monotonic loading conditions in tension, three-point bending, and combined tension/bending to evaluate the debonding mechanisms between the skin and the bonded stringer. For combined tension/bending testing, a unique servohydraulic load frame was used that was capable of applying both in-plane tension and out-ofplane bending loads simultaneously. Specimen edges were examined on the microscope to document the damage occurrence and to identify typical damage patterns. For all three load cases, observed failure initiated in the flange, near the flange tip, causing the flange to almost fully debond from the skin. In a second step, a two-dimensional plane-strain finite element model was developed to analyze the different test cases using a geometrically nonlinear solution. For all three loading conditions, computed principal stresses exceeded the transverse strength of the material in those areas of the flange where the matrix cracks had developed during the tests. In a third step,

The development and application of benchmark examples for the assessment of quasi-static delamination propagation capabilities is demonstrated. The methodology proposed, based on fracture mechanics, is used to develop benchmarks for the double cantilever beam, end-notched flexure, single leg bending as well as mixed-mode bending specimens for 20%, 50% and 80% mode II. The methodology proposed for the development of quasi-static benchmark results is discussed in detail, and will be presented using the double cantilever beam specimen as an example. The practical application of the benchmarks generated is illustrated by using the double cantilever beam and mixed-mode bending (50% mode II) benchmarks to assess the automated procedure implemented in Abaqus/Standard®. This assessment proved to be valuable by highlighting the issues (e.g. overshooting, saw-tooth behavior, non-convergence) associated with choosing the input parameters unique to the Virtual Crack Closure Technique implementation in Abaqus/Standard®. Additional studies should include the assessment of the propagation capabilities in more complex specimens and on a structural level.

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