ABSTRACT:
The application of a shell/3D modeling technique for the simulation of skin/stringer debond in a specimen subjected to tension and three-point bending was studied. The global structure was modeled with shell elements. A local three-dimensional model, extending to about three specimen thicknesses on either side of the delamination front was used to model the details of the damaged section. Computed total strain energy release rates and mixed-mode ratios obtained from shell/3D simulations were in good agreement with results obtained from full solid models. The good correlation of the results demonstrated the effectiveness of the shell/3D modeling technique for the investigation of skin/stiffener separation due to delamination in the adherents.
ABSTRACT:
An approach for assessing the delamination propagation capabilities in commercial finite element codes is presented and demonstrated for one code. For this investigation, the Double Cantilever Beam (DCB) specimen and the Single Leg Bending (SLB) specimen were chosen for full three-dimensional finite element simulations. First, benchmark results were created for both specimens. Second, starting from an initially straight front, the delamination was allowed to propagate. Good agreement between the load-displacement relationship obtained from the propagation analysis results and the benchmark results could be achieved by selecting the appropriate input parameters. Selecting the appropriate input parameters, however, was not straightforward and often required an iterative procedure. Qualitatively, the delamination front computed for the DCB specimen did not take the shape of a curved front as expected. However, the analysis of the SLB specimen yielded a curved front as may be expected from the distribution of the energy release rate and the failure index across the width of the specimen. Overall, the results are encouraging but further assessment on a structural level is required.
ABSTRACT:
A shear loaded, stringer reinforced composite panel is analyzed to evaluate the fidelity of computational fracture mechanics analyses of complex structures. Shear loading causes the panel to buckle. The resulting out-of-plane deformations initiate skin/stringer separation at the location of an embedded defect. The panel and surrounding load fixture were modeled with shell elements. A small section of the stringer foot, web and noodle as well as the panel skin near the delamination front were modeled with a local 3D solid model. Across the width of the stringer foot, the mixed-mode strain energy release rates were calculated using the virtual crack closure technique. A failure index was calculated by correlating the results with a mixed-mode failure criterion of the graphite/epoxy material. The objective was to study the effect of the fidelity of the local 3D finite element model on the computed mixed-mode strain energy release rates and the failure index.
ABSTRACT:
Interlaminar fracture mechanics has proven useful for characterizing the onset of delaminations in composites and has been used successfully primarily to investigate onset in fracture toughness specimens and laboratory size coupon type specimens. Future acceptance of the methodology by industry and certification authorities, however, requires the successful demonstration of the methodology on the structural level. For this purpose, a panel was selected that is reinforced with stiffeners. Shear loading causes the panel to buckle, and the resulting out-of-plane deformations initiate skin/stiffener separation at the location of an embedded defect. A small section of the stiffener foot, web and noodle as well as the panel skin in the vicinity of the delamination front were modeled with a local 3D solid model. Across the width of the stiffener foot, the mixed-mode strain energy release rates were calculated using the virtual crack closure technique. A failure index was calculated by correlating the results with a mixed-mode failure criterion of the graphite/epoxy material. Computed failure indices were compared to corresponding results where the entire web was modeled with shell elements and only a small section of the stiffener foot and panel were modeled locally with solid elements. Including the stiffener web in the local 3D solid model increased the computed failure index. Further including the noodle and transition radius in the local 3D solid model changed the local distribution across the width. The magnitude of the failure index decreased with increasing transition radius and noodle area. For the transition radii modeled, the material properties used for the noodle area had a negligible effect on the results. The results of this study are intended to be used as a guide for conducting finite element and fracture mechanics analyses of delamination and debonding in complex structures such as integrally stiffened panels.
ABSTRACT:
Strain energy release rates were computed along straight delamination fronts of Double Cantilever Beam, End-Notched Flexure and Single Leg Bending specimens using the Virtual Crack Closure Technique (VCCT). The results were based on finite element analyses using ABAQUS&trade and ANSYS&trade and were calculated from the finite element results using the same post-processing routine to assure a consistent procedure. Mixed-mode strain energy release rates obtained from post-processing finite element results were in good agreement for all element types used and all specimens modeled. Compared to previous studies, the models made of solid twenty-node hexahedral elements and solid eight-node incompatible mode elements yielded excellent results. For both codes, models made of standard brick elements and elements with reduced integration did not correctly capture the distribution of the energy release rate across the width of the specimens for the models chosen. The results suggested that element types with similar formulation yield matching results independent of the finite element software used. For comparison, mixed-mode strain energy release rates were also calculated within ABAQUS&trade/Standard using the VCCT for ABAQUS&trade add on. For all specimens modeled, mixed-mode strain energy release rates obtained from ABAQUS&trade finite element results using post-processing were almost identical to results calculated using the VCCT for ABAQUS&trade add on.
ABSTRACT:
The influence of compression and shear loads on the strength of composite laminates with z-pins is evaluated parametrically using a 2D Finite Element Code (FLASH) based on Cosserat couple stress theory. Meshes were generated for three unique combinations of z-pin diameter and density. A laminated plate theory analysis was performed on several layups to determine the bi-axial stresses in the zero degree plies. These stresses, in turn, were used to determine the magnitude of the relative load steps prescribed in the FLASH analyses. Results indicated that increasing pin density was more detrimental to in-plane compression strength than increasing pin diameter. Compression strengths of lamina without z-pins agreed well with a closed form expression derived by Budiansky and Fleck. FLASH results for lamina with z-pins were consistent with the closed form results, and FLASH results without z-pins, if the initial fiber waviness due to z-pin insertion was added to the fiber waviness in the material to yield a total misalignment. Addition of 10% shear to the compression loading significantly reduced the lamina strength compared to pure compression loading. Addition of 50% shear to the compression indicated shear yielding rather than kink band formation as the likely failure mode. Two different stiffener reinforced skin configurations with z-pins, one quai-isotropic and one orthotropic, were also analyzed. Six unique loading cases ranging from pure compression to compression plus 50% shear were analyzed assuming material fiber waviness misalignment angles of 0, 1, and 2 degrees. Compression strength decreased with increased shear loading for both configurations, with the quasi-isotropic configuration yielding lower strengths than the orthotropic configuration.
ABSTRACT:
Interlaminar fracture mechanics has proven useful for characterizing the onset of delaminations in composites. It has been used primarily to investigate delamination onset in fracture toughness specimens and laboratory-size coupon type specimens. Future acceptance of the methodology by industry and certification authorities however, requires the successful demonstration of the methodology on a structural level. For this purpose, a panel was selected that is reinforced with stringers. Shear loading causes the panel to buckle, and the resulting out-of-plane deformations initiate skin/stringer separation at the location of an embedded defect. For finite element analysis, the panel and surrounding load fixture were modeled with shell elements. A small section of the stringer foot and the panel in the vicinity of the embedded defect were modeled with a local 3D solid model. A failure index was calculated by correlating computed mixed-mode strain energy release rates with the mixed-mode failure criterion of the graphite/epoxy material. Computed failure indices were in good agreement with results from models where the entire delaminated section of the stiffener foot had been modeled with solid elements. The shell-to-solid connection influenced the computed failure indices, and local refinement of the shell model across the stringer foot and web was required to improve the results. The study confirmed that the local 3D solid model did not have to include the entire delaminated section. The use of a smaller local 3D solid model reduced model size without compromising the computed failure indices.
ABSTRACT:
A series of finite element analyses of double cantilever beam (DCB) specimens
reinforced with z-pins were conducted. The z-pins were modeled using spring
elements located in the position of the z-pins. A traction law was assigned to each
spring element for simulating z-pin failure as delamination proceeds through the
DCB specimen. Contact surfaces were used at the delamination to prevent model
interpenetration during analysis. The computed contact pressures were used to
estimate the delamination front location at the end of every increment of an
analysis. The analysis was used to predict the progression of delamination growth
through the z-pin field. The results were compared with data from an existing
analysis based on beam theory. Comparison between the two methods was
moderate to good, ranging from 20 to 6% error. The agreement between the finite
element and beam theory analyses was dramatically improved (less than 2% error)
by the inclusion of decohesion elements into the finite element model. However,
inclusion of the decohesion elements increased the solution time by a factor of 10.
The results indicated that spring elements are suitable for modeling z-pins bridging
delaminations that are subjected to mode I-dominated loading. Application of the
spring elements as z-pins was extended to a finite element analysis of a postbuckled
skin/stringer panel containing a delamination at a stiffener/skin interface.
Preliminary results indicated that a small density of z-pins will cause a significant
reduction in the driving force for delamination growth.
ABSTRACT:
Interlaminar fracture mechanics has proven useful for characterizing the onset of delaminations in composites and has been used with limited success primarily to investigate onset in fracture toughness specimens and laboratory size coupon type specimens. Future acceptance of the methodology by industry and certification authorities however, requires the successful demonstration of the methodology on structural level. For this purpose a panel was selected that is reinforced with stringers. Shear loading causes the panel to buckle and the resulting out-of-plane deformations initiate skin/stringer separation at the location of an embedded defect. For finite element analysis, the panel and surrounding load fixture were modeled with shell elements. A small section of the stringer foot and the panel in the vicinity of the embedded defect were modeled with a local 3D solid model. A failure index was calculated by correlating computed mixed-mode strain energy release rates with the mixed-mode failure criterion of the graphite/epoxy material. Computed failure indices were in good agreement with results from models where the entire delaminated section of the stiffener foot had been modeled with solid elements. The shell-to-solid connection influenced the computed failure indices and local refinement of the shell model across the stringer foot and web was required to improve the results. The study confirmed that the section modeled locally did not have to include the entire delaminated section. The use of a smaller local inserts reduced model size without compromising the computed failure indices.
ABSTRACT:
Interlaminar fracture mechanics has proven useful for characterizing the onset of delaminations in composites and has been used with limited success primarily to investigate onset in fracture toughness specimens and laboratory size coupon type specimens. Future acceptance of the methodology by industry and certification authorities however, requires the successful demonstration of the methodology on the structural level. In this paper, the state-of-the-art in fracture toughness characterization, and interlaminar fracture mechanics analysis tools are described. To demonstrate the application on the structural level, a panel was selected which is reinforced with stringers. Full implementation of interlaminar fracture mechanics in design however remains a challenge and requires a continuing development effort of codes to calculate energy release rates and advancements in delamination onset and growth criteria under mixed mode conditions.
ABSTRACT:
The influence of compression and shear loads on the strength of composite laminates with z-pins is evaluated parametrically using a 2D Finite Element Code (FLASH) based on Cosserat couple stress theory. Meshes were generated for three unique combinations of z-pin diameter and density. A laminated plate theory analysis was performed on several layups to determine the bi-axial stresses in the zero degree plies. These stresses, in turn, were used to determine the magnitude of the relative load steps prescribed in the FLASH analyses. Results indicated that increasing pin density was more detrimental to in-plane compression strength than increasing pin diameter. Compression strengths of lamina without z-pins agreed well with a closed form expression derived by Budiansky and Fleck. FLASH results for lamina with z-pins were consistent with the closed form results, and FLASH results without z-pins, if the initial fiber waviness due to z-pin insertion was added to the fiber waviness in the material to yield a total misalignment. Addition of 10% shear to the compression loading significantly reduced the lamina strength compared to pure compression loading. Addition of 50% shear to the compression indicated shear yielding rather than kink band formation as the likely failure mode. Two different stiffener reinforced skin configurations with z-pins, one quai-isotropic and one orthotropic, were also analyzed. Six unique loading cases ranging from pure compression to compression plus 50% shear were analyzed assuming material fiber waviness misalignment angles of 0, 1, and 2 degrees. Compression strength decreased with increased shear loading for both configurations, with the quasi-isotropic configuration yielding lower strengths than the orthotropic configuration.
ABSTRACT:
Interlaminar fracture mechanics has proven useful for characterizing the onset of delaminations in composites and has been used with limited success primarily to investigate onset in fracture toughness specimens and laboratory size coupon type specimens. Future acceptance of the methodology by industry and certification authorities however, requires the successful demonstration of the methodology on structural level for which a panel was selected which is reinforced with stringers. Shear loading causes the panel to buckle and the resulting out-of-plane deformations initiate skin/stringer separation at the location of an embedded defect. For finite element analysis, the panel and surrounding load fixture were modeled with shell elements. A small section of the stringer foot and the panel in the vicinity of the embedded defect were modeled with a local 3D solid model. Across the width of the stringer foot the mixed-mode strain energy release rates were calculated using the virtual crack closure technique. A failure index was calculated by correlating the results with the mixed-mode failure criterion of the graphite/epoxy material.
For small applied loads the failure index is well below one across the entire width. With increasing load the failure index approaches one first near one edge of the stringer foot from which delamination is expected to grow. With increasing delamination lengths the buckling pattern of the panel changes and the failure index increases which suggests that rapid delamination progress is to be expected once the delamination starts to grow from the initial defect.
ABSTRACT:
Interlaminar fracture mechanics has proven useful for characterizing the onset of
delaminations in composites and has been used with limited success primarily to
investigate onset in fracture toughness specimens and laboratory size coupon type
specimens. Future acceptance of the methodology by industry and certification
authorities however, requires the successful demonstration of the methodology on
structural level. For this purpose a panel was selected that is reinforced with stringers.
Shear loading causes the panel to buckle and the resulting out-of-plane deformations
initiate skin/stringer separation at the location of an embedded defect. For finite element
analysis, the panel and surrounding load fixture were modeled with shell elements. A
small section of the stringer foot and the panel in the vicinity of the embedded defect
were modeled with a local 3D solid model. Across the width of the stringer foot the
mixed-mode strain energy release rates were calculated using the virtual crack closure
technique. A failure index was calculated by correlating the results with the mixed-mode
failure criterion of the graphite/epoxy material. For small applied loads the failure index
is well below one across the entire width. With increasing load the failure index
approaches one first near the edge of the stringer foot from which delamination is
expected to grow. With increasing delamination lengths the buckling pattern of the panel
changes and the failure index increases which suggests that rapid delamination growth from the initial defect is to be expected.
ABSTRACT:
The influence of compression and shear loads on the strength of
composite laminates with z-pins is evaluated parametrically using a 2D
Finite Element Code (FLASH) based on Cosserat couple stress theory.
Meshes were generated for three unique combinations of z-pin diameter and
density. A laminated plate theory analysis was performed on several layups
to determine the bi-axial stresses in the zero degree plies. These stresses, in
turn, were used to determine the magnitude of the relative load steps
prescribed in the FLASH analyses. Results indicated that increasing pin
density was more detrimental to in-plane compression strength than
increasing pin diameter. Compression strengths of lamina without z-pins
agreed well with a closed form expression derived by Budiansky and Fleck.
FLASH results for lamina with z-pins were consistent with the closed form
results, and FLASH results without z-pins, if the initial fiber waviness due to
z-pin insertion was added to the fiber waviness in the material to yield a total
misalignment. Addition of 10% shear to the compression loading
significantly reduced the lamina strength compared to pure compression
loading. Addition of 50% shear to the compression indicated shear yielding
rather than kink band formation as the likely failure mode. Two different
stiffener reinforced skin configurations with z-pins, one quasi-isotropic and
one orthotropic, were also analyzed. Six unique loading cases ranging from
pure compression to compression plus 50% shear were analyzed assuming
material fiber waviness misalignment angles of 0, 1, and 2 degrees.
Compression strength decreased with increased shear loading for both
configurations, with the quasi-isotropic configuration yielding lower
strengths than the orthotropic configuration.
R. Krueger.
Modeling of Unit-Cells with Z-Pins Using FLASH: Pre-Processing and Post-Processing.
NIA Report No. 2005-01, NASA/CR-2005-213905, 2005.
ABSTRACT:
Although the toughening properties of stitches, z-pins and similar structures have been studied extensively, investigations on the effect of z-pins on the in-plane properties of laminates are limited. A brief summary on the effect of z-pins on the in-plane tensile and compressive properties of composite laminates is presented together with a concise introduction into the finite element code FLASH. The remainder of the report illustrates the modeling aspect of unit cells with z-pins in FLASH and focuses on input and output data as well as post-processing of results.
ABSTRACT:
The application of a shell/3D modeling technique for the simulation of skin/stringer debond in a specimen subjected to tension
and three-point bending was studied. The global structure was modeled with shell elements. A local three-dimensional model,
extending to about three specimen thicknesses on either side of the delamination front was used to model the details of the damaged
section. Computed total strain energy release rates and mixed-mode ratios obtained from shell/3D simulations were in good agreement
with results obtained from full solid models. The good correlation of the results demonstrated the effectiveness of the
shell/3D modeling technique for the investigation of skin/stiffener separation due to delamination in the adherents. In addition,
the application of the submodeling technique for the simulation of skin/stringer debond was also studied. Global models made of
shell elements and solid elements were studied. Solid elements were used for local submodels, which extended between three and six
specimen thicknesses on either side of the delamination front to model the details of the damaged section. Computed total strain
energy release rates and mixed-mode ratios obtained from the simulations using the submodeling technique were not in agreement with
results obtained from full solid models.
ABSTRACT:
An overview of the virtual crack closure technique (VCCT) is presented. The approach used is discussed, the history summarized,
and insight into its applications provided. Equations for two-dimensional quadrilateral finite elements with linear and quadratic
shape functions are given. Formulae for applying the technique in conjuction with three-dimensional solid elements as well as
plate/shell elements are also provided. Necessary modifications for the use of the method with geometrically nonlinear finite
element analysis and corrections required for elements at the crack tip with different lengths and widths are discussed.
The problems associated with cracks or delaminations 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.
ABSTRACT:
The difference in delamination onset predictions based on the type and location of the assumed initial damage are compared
in a specimen consisting of a tapered flange laminate bonded to a skin laminate. From previous experimental work, the
damage was identified to consist of a matrix crack in the top skin layer followed by a delamination between the top and second
skin layer (+45/45 interface). Two-dimensional finite elements analyses were performed for three different assumed
flaws and the results show a considerable reduction in critical load if an initial delamination is assumed to be present,
both under tension and bending loads. For a crack length corresponding to the peak in the strain energy release rate, the
delamination onset load for an assumed initial flaw in the bondline is slightly higher than the critical load for delamination
onset from an assumed skin matrix crack, both under tension and bending loads. As a result, assuming an initial flaw in
the bondline is simpler while providing a critical load relatively close to the real case. For the configuration studied, a small
delamination might form at a lower tension load than the critical load calculated
for a 12.7 mm (0.5 in) delamination, but it would grow in a stable manner. For the bending case, assuming an initial
flaw of 12.7 mm (0.5 in) is conservative, but the crack would grow unstably.
ABSTRACT:
The state-of-the-art in the areas of delamination characterization, interlaminar fracture mechanics analysis tools and
experimental verification of life predictions is demonstrated using skin/stringer debonding failure as an engineering problem
to describe the overall methodology.
ABSTRACT:
Finite element (FE) analyses were performed on 3-point and 4-point bending test configurations of glass-epoxy and carbon-epoxy unidirectional
tape beams tested at ninety degrees to the fiber direction to identify deviations from beam theory predictions. Both linear and geometric non-linear
analyses were performed using the ABAQUS&trade finite element code. The 3-point and 4-point bending specimens were first modeled with two-dimensional elements.
Three-dimensional finite element models were then performed for selected 4-point bending configurations to study the stress distribution across the width
of the specimens. For 3-point bend test configurations, both the linear and geometric non-linear 2D plane-strain and plane-stress analyses yielded similar
results. The maximum tensile stresses under the center load nose calculated from the FE analysis were slightly lower than stresses predicted by beam theory.
The difference (maximum of 4%) was greatest for the shortest span analyzed. For 4-point bend test configurations, both the plane-stress and plane-strain 2D
linear analysis results agreed closely with beam theory except right below the load points. However, 2D geometric non-linear analyses deviated slightly from
beam theory throughout the inner span as well as below the load points. Plane-stress results deviated from beam theory more than plane-strain results.
The maximum tensile stresses between the inner span load points were slightly greater than the beam theory result. This difference was greatest
(maximum of 4%) for configurations with the shortest spans between inner and outer load points. A contact analysis was also performed in order to investigate
the influence of modeling the roller versus modeling the support as a simple boundary condition at one nodal point. The discrepancy between the FE and beam
theory results became smaller (max. 2Ð3%) when the rollers were modeled in conjunction with contact analysis. Hence, the beam theory yields a reasonably
accurate value for the maximum tensile stress in bending compared to 2D FE analysis. The FE results are primarily for guidance in the choice of beam thickness,
width, and configuration. For the 3-point bend configuration, longer spans are preferred to minimize the error in beam theory data reduction. Similarly,
for the 4-point bend configurations, a longer span between the inner and outer load noses, at least equal to the span between the inner load noses, results
in less error compared to beam theory. In addition, these FE results indicate that the span between the inner load noses should not be too long to avoid
obtaining a non-uniform maximum stress between the inner load noses. Finally, the 3D analysis indicates that specimens should be sufficiently wide to achieve
a fully constrained state of plane-strain at the center of the specimen width.
R. Krueger and P. J. Minguet.
Analysis of Composite Skin-stiffener
Debond Specimens Using Volume Elements and a Shell/3D Modeling Technique.
NASA/CR-2002-211947, ICASE Report No. 2002-38, October 2002.
ABSTRACT:
The debonding of a skin/stringer specimen subjected to tension was studied using threedimensional
volume element modeling and computational fracture mechanics. Mixed mode strain energy release
rates were calculated from finite element results using the virtual crack closure technique. The simulations revealed
an increase in total energy release rate in the immediate vicinity of the free edges of the specimen. Correlation of the
computed mixed-mode strain energy release rates along the delamination front contour with a two-dimensional
mixed-mode interlaminar fracture criterion suggested that in spite of peak total energy release rates at the free edge
the delamination would not advance at the edges first. The qualitative prediction of the shape of the delamination
front was confirmed by X-ray photographs of a specimen taken during testing. The good correlation between
prediction based on analysis and experiment demonstrated the efficiency of a mixed-mode failure analysis for the
investigation of skin/stiffener separation due to delamination in the adherents.
The application of a shell/3D modeling technique for the simulation of skin/stringer debond in a specimen
subjected to three-point bending is also demonstrated. The global structure was modeled with shell elements. A
local three-dimensional model, extending to about three specimen thicknesses on either side of the delamination
front was used to capture the details of the damaged section. Computed total strain energy release rates and mixedmode
ratios obtained from shell/3D simulations were in good agreement with results obtained from full solid
models. The good correlations of the results demonstrated the effectiveness of the shell/3D modeling technique for
the investigation of skin/stiffener separation due to delamination in the adherents.
R. Krueger, I. L. Paris, T. K. O'Brien, and P. J. Minguet.
Comparison of 2D Finite Element Modeling Assumptions
with Results from 3D Analysis for Composite Skin-Stiffener Debonding.
Composite Structures, vol. 57, pp. 161-168, 2002.
ABSTRACT:
The infuence of two-dimensional fnite element modeling assumptions on the debonding prediction for skin-stiffener specimens
was investigated. Geometrically nonlinear fnite element analyses using two-dimensional plane-stress and plane-strain elements as
well as three different generalized plane-strain type approaches were performed. The computed skin and flange strains, transverse
tensile stresses and energy release rates were compared to results obtained from three-dimensional simulations. The study showed
that for strains and energy release rate computations the generalized plane-strain assumptions yielded results closest to the full threedimensional
analysis. For computed transverse tensile stresses the plane-stress assumption gave the best agreement. Based on this
study it is recommended that results from plane-stress and plane-strain models be used as upper and lower bounds. The results from
generalized plane-strain models fall between the results obtained from plane-stress and plane-strain models. Two-dimensional
models may also be used to qualitatively evaluate the stress distribution in a ply and the variation of energy release rates and mixed
mode ratios with delamination length. For more accurate predictions, however, a three-dimensional analysis is required.
R. Krueger, T. K. O'Brien, and P. J. Minguet.
Application of the Shell/3D Modeling Technique
for the analysis of Skin-Stiffener Debond Specimens.
In Proceedings of the American Society for Composites - 17th Annual Technical Conference on Composite Materials,
C. T. Sun and H. Kim, Eds.: CRC Press LLC, 2002. - (373kB)
ABSTRACT:
The application of a shell/3D modeling technique for the simulation of skin/stringer debond in a
specimen subjected to three-point bending is demonstrated. The global structure was modeled with
shell elements. A local three-dimensional model, extending to about three specimen thicknesses on
either side of the delamination front was used to capture the details of the damaged section.
Computed total strain energy release rates and mixed-mode ratios obtained from shell/3D
simulations were in good agreement with results obtained from full solid models. The good
correlations of the results demonstrated the effectiveness of the shell/3D modeling technique for the
investigation of skin/stiffener separation due to delamination in the adherents.
ABSTRACT:
An overview of the virtual crack closure technique is presented. The approach used is discussed, the history summarized, and insight into 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 three-dimensional solid elements as well as plate/shell elements are also provided. Necessary modifications for the use of the method with
geometrically nonlinear finite element analysis and corrections required for elements at the crack tip with different lengths and widths are discussed. The
problems associated with cracks or delaminations 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.
ABSTRACT:
The influence of two-dimensional finite element modeling assumptions on the debonding prediction for skin-stiffener specimens was investigated.
Geometrically nonlinear finite element analyses using two-dimensional plane-stress and plane-strain elements as well as three different generalized
plane strain type approaches were performed. The computed deflections, skin and flange strains, transverse tensile stresses and energy release rates
were compared to results obtained from three-dimensional simulations. The study showed that for strains and energy release rate computations the
generalized plane strain assumptions yielded results closest to the full three-dimensional analysis. For computed transverse tensile stresses the
plane stress assumption gave the best agreement. Based on this study it is recommended that results from plane stress and plane strain models be used
as upper and lower bounds. The results from generalized plane strain models fall between the results obtained from plane stress and plane strain models.
Two-dimensional models may also be used to qualitatively evaluate the stress distribution in a ply and the variation of energy release rates and mixed mode
ratios with delamination length. For more accurate predictions, however, a three-dimensional analysis is required.
ABSTRACT:
A methodology is presented for determining the fatigue life of composite structures based on fatigue characterization data and geometric nonlinear
finite element analyses. To demonstrate the approach, predicted results were compared to fatigue tests performed on specimens which consisted of a tapered
composite flange, representing a stringer or frame, bonded onto a composite skin. In a first step, quasi-static tension and fatigue tests were performed to
evaluate the debonding mechanisms between the skin and the bonded stringer. Specimen edges were examined under the microscope to document the damage occurrence.
In a second step, a two-dimensional finite element model was developed to analyze the tests. To predict matrix cracking onset, the relationship between the
externally applied tension load and the maximum principal stresses transverse to the fiber direction was determined through geometrically nonlinear analysis.
Transverse tension fatigue life data were used to generate an onset fatigue life P-N curve for matrix cracking. The resulting prediction was in good agreement
with measured data from the fatigue tests. In a third step, a fracture mechanics approach based on geometrically nonlinear analysis was used to determine the
relationship between the externally applied tension load and the critical energy release rate. Mixed mode energy release rate fatigue life data from DCB, 4ENF
and MMB tests were used to create an fatigue life onset G-N curve for delamination. The resulting prediction was in good agreement with data from the fatigue
tests. Additionally, the prediction curve for cumulative life to failure was generated from the matrix onset and delamination onset fatigue life curves.
The results were in good agreement with data from the fatigue tests which demonstrated that the methodology offers a significant potential to predict cumulative
fatigue life of composite structures.
ABSTRACT:
The transverse tension fatigue life of S2/8552 glassÐepoxy and IM7/8552 carbonÐepoxy was characterized using flexure tests of
90-degree laminates loaded in 3-point and 4-point bending. The influence of specimen polishing and specimen configuration on
transverse tension fatigue life was examined using the glassÐepoxy laminates. Results showed that 90-degree flexure specimens
with polished machined edges and polished tension-side surfaces had lower fatigue lives than unpolished specimens when cyclically
loaded at equal stress levels. The influence of specimen thickness and the utility of a Weibull scaling law were examined using
the carbonÐepoxy laminates. The influence of test frequency on fatigue results was also documented for the 4-point bending con-figuration.
A Weibull scaling law was used to predict the 4-point bending fatigue lives from the 3-point bending curve fit and vice
versa. Scaling was performed based on maximum cyclic stress level as well as fatigue life. The scaling laws based on stress level
shifted the curve fit SÐN characterizations in the desired direction, however, the magnitude of the shift was not adequate to accurately
predict the fatigue lives. Furthermore, the scaling law based on fatigue life shifted the curve fit SÐN characterizations in the opposite
direction from measured values. Therefore, these scaling laws were not adequate for obtaining accurate predictions of the transverse
tension fatigue lives of heterogeneous, fiber reinforced, polymer matrix composites.
ABSTRACT:
The influence of two-dimensional finite element modeling assumptions
on the debonding prediction for skin-stiffener specimens was investigated.
Geometrically nonlinear finite element analyses using two-dimensional plane-stress
and plane-strain elements as well as three different generalized plane
strain type approaches were performed. The computed skin and flange strains,
transverse tensile stresses and energy release rates were compared to results
obtained from three-dimensional simulations. The study showed that for
strains and energy release rate computations the generalized plane strain
assumptions yielded results closest to the full three-dimensional analysis.
For computed transverse tensile stresses the plane stress assumption gave
the best agreement. Based on this study it is recommended that results
from plane stress and plane strain models be used as upper and lower bounds.
The results from generalized plane strain models fall between the results
obtained from plane stress and plane strain models. Two-dimensional models
may also be used to qualitatively evaluate the stress distribution in a
ply and the variation of energy release rates and mixed mode ratios with
delamination length. For more accurate predictions, however, a three-dimensional
analysis is required.
ABSTRACT:
The objective of the case study presented here was to compare the difference
in delamination onset predictions based on the type and location of the
assumed initial damage in a specimen consisting of a tapered flange laminate
bonded to a skin laminate. From previous experimental work, the damage
consists of a matrix crack in the top skin layer followed by a delamination
between the top and second skin layer (+45º/-45º interface).
Finite Elements analysis were performed for three different assumed flaws
and the results show a considerable reduction in critical load if the matrix
crack initiation is ignored, both under tension and bending loads. For
a crack length corresponding to the peak in the strain energy release rate,
the delamination onset load for an assumed initial flaw in the bondline
is slightly higher than the critical load for delamination onset from an
assumed skin matrix crack, both under tension and bending loads. As a result,
assuming an initial flaw in the bondline is simpler while providing a critical
load relatively close to the real case. For the configuration studied,
assuming an initial flaw of 12.7 mm (0.5") is unconservative for the tension
load while it is conservative for the bending load.
SUMMARY:
Finite element (FE) analysis was performed on 3-point and 4-point bending
test configurations of ninety degree oriented glass-epoxy and graphite-epoxy
composite beams to identify deviations from beam theory predictions. Both
linear and geometric non-linear analyses were performed using the ABAQUS®
finite element code. The 3-point and 4-point bending specimens were first
modeled with two-dimensional elements. Three-dimensional finite element
models were then performed for selected 4-point bending configurations
to study the stress distribution across the width of the specimens and
compare the results to the stresses computed from two-dimensional plane-strain
and plane-stress analyses and the stresses from beam theory. Stresses for
all configurations were analyzed at load levels corresponding to the measured
transverse tensile strength of the materials.
For 3-point bend test configurations, both the linear and geometric non-linear 2D plane-strain and plane-stress analyses yielded similar results. The maximum tensile stresses under the center load nose calculated from the FE analysis were slightly lower than stresses predicted by beam theory. The difference (maximum of 4%) was greatest for the shortest span analyzed.
For 4-point bend test configurations, both the plane-stress and plane-strain 2D linear analysis results agreed closely with beam theory except right below the load points. However, 2D geometric non-linear analyses deviated slightly from beam theory throughout the inner span as well as below the load points. Plane-stress results deviated from beam theory more than plane-strain results. The maximum tensile stresses between the inner span load points were slightly greater than the beam theory result. This difference was greatest (maximum of 4%) for configurations with the shortest spans between inner and outer load points. A contact analysis was also performed in order to investigate the influence of modeling the roller versus modeling the support as a simple boundary condition at one nodal point. A configuration with the shortest span between inner and outer load points was modeled for the 24-ply and 36-ply IM7/8552 layups and the 24-ply S2/8552 layup. Generally, for all configurations investigated, the discrepancy between the FE and beam theory results became smaller (max. 2%) when the rollers were modeled in conjunction with contact analysis. Hence, the beam theory yields a reasonably accurate value for the maximum tensile stress in bending compared to 2D FE analysis.
The 3D linear FE analysis of the 4-point configurations agreed closely with beam theory, except right below the load points. The 3D linear FE results at the specimen edge agreed with 2D plane-stress results, and the 3D linear FE results in the center of the specimen agreed with 2D plane-strain results. The 3D geometric non-linear analyses deviated slightly from beam theory throughout the inner span as well as under load points. The 3D geometric non-linear FE results at the specimen edge agreed with the 2D plane-stress results. For the 12.7 mm (0.50 in.) wide IM7/8552 specimens, the 3D geometric non-linear FE results in the center of the specimen agreed with 2D plane-strain results. However, for the 6.35 mm (0.25 in.) wide S2/8552 specimens, the 3D geometric non-linear FE results in the center were less than 2D plane-strain results, indicating that these specimens were not wide enough to achieve full constraint.
The utility of the FE results is primarily for guidance in the choice
of beam thickness, width, and configuration. For the 3-point bend configuration,
longer spans are preferred to minimize the error in beam theory data reduction.
Similarly, for the 4-point bend configurations, a longer span between the
inner and outer load noses, at least equal to the span between the inner
load noses, results in less error compared to beam theory. In addition,
these FE results indicate that the span between the inner load noses should
not be too long to avoid obtaining a non-uniform maximum stress between
the inner load noses. Finally, the 3D analysis indicates that specimens
should be sufficiently wide to achieve a fully constrained state of plane-strain
at the center of the specimen width.
ABSTRACT:
The transverse tension fatigue life of S2/8552 glass-epoxy and IM7/8552
carbon-epoxy was characterized using flexure tests of 90-degree laminates
loaded in 3-point and 4-point bending. The influence of specimen polishing
and specimen configuration on transverse tension fatigue life was examined
using the glass-epoxy laminates. Results showed that 90-degree flexure
specimens with polished machined edges and polished tension-side surfaces
had lower fatigue lives than unpolished specimens when cyclically loaded
at equal stress levels. The influence of specimen thickness and the utility
of a Weibull scaling law were examined using the carbon-epoxy laminates.
The influence of test frequency on fatigue results was also documented
for the 4-point bending configuration. A Weibull scaling law was used to
predict the 4-point bending fatigue lives from the 3-point bending curve
fit and vice-versa. Scaling was performed based on maximum cyclic stress
level as well as fatigue life. The scaling laws based on stress level shifted
the curve fit S-N characterizations in the desired direction, however,
the magnitude of the shift was not adequate to accurately predict the fatigue
lives. Furthermore, the scaling law based on fatigue life shifted the curve
fit S-N characterizations in the opposite direction from measured values.
Therefore, these scaling laws were not adequate for obtaining accurate
predictions of the transverse tension fatigue lives of heterogeneous, fiber
reinforced, polymer matrix composites.
ABSTRACT:
A methodology is presented for determining the fatigue life of composite
structures based on fatigue characterization data and geometric nonlinear
finite element analyses. To demonstrate the approach, predicted results
were compared to fatigue tests performed on specimens which consisted of
a tapered composite flange, representing a stringer or frame, bonded onto
a composite skin. In a first step, quasi-static tension and fatigue tests
were performed to evaluate the debonding mechanisms between the skin and
the bonded stringer. Specimen edges were examined under the microscope
to document the damage occurrence. In a second step, a two-dimensional
finite element model was developed to analyze the tests. To predict matrix
cracking onset, the relationship between the externally applied tension
load and the maximum principal stresses transverse to the fiber direction
was determined through geometrically nonlinear analysis. Transverse tension
fatigue life data were used to generate an onset fatigue life P-N curve
for matrix cracking. The resulting prediction was in good agreement with
measured data from the fatigue tests. In a third step, a fracture mechanics
approach based on geometrically nonlinear analysis was used to determine
the relationship between the externally applied tension load and the critical
energy release rate. Mixed mode energy release rate fatigue life data from
DCB, 4ENF and MMB tests were used to create an fatigue life onset G-N curve
for delamination. The resulting prediction was in good agreement with data
from the fatigue tests. Additionally, the prediction curve for cumulative
life to failure was generated from the matrix onset and delamination onset
fatigue life curves. The results were in good agreement with data from
the fatigue tests which demonstrated that the methodology offers a significant
potential to predict cumulative fatigue life of composite structures.
ABSTRACT:
A shell/3D modeling technique was developed for which a local three-dimensional
solid finite element model is used only in the immediate vicinity of the
delamination front. The goal was to combine the accuracy of the full three-dimensional
solution with the computational efficiency of a plate or shell finite element
model. Multi-point constraints provided a kinematically compatible interface
between the local three-dimensional model and the global structural model
which has been meshed with plate or shell finite elements. Double Cantilever
Beam (DCB), End Notched Flexure (ENF), and Single Leg Bending (SLB) specimens
were modeled using the shell/3D technique to study the feasibility for
pure mode I (DCB), mode II (ENF) and mixed mode I/II (SLB) cases. Mixed
mode strain energy release rate distributions were computed across the
width of the specimens using the virtual crack closure technique. Specimens
with a unidirectional layup and with a multidirectional layup where the
delamination is located between two non-zero degree plies were simulated.
For a local three-dimensional model, extending to a minimum of about three
specimen thicknesses on either side of the delamination front, the results
were in good agreement with mixed mode strain energy release rates obtained
from computations where the entire specimen had been modeled with solid
elements. For large built-up composite structures modeled with plate elements,
the shell/3D modeling technique offers a great potential for reducing the
model size, since only a relatively small section in the vicinity of the
delamination front needs to be modeled with solid elements.
ABSTRACT:
Three simple procedures were developed to determine strain energy release
rates, G, in composite skin/stringer specimens for various combinations
of uniaxial and biaxial (in-plane/out-of-plane) loading conditions. These
procedures may be used for parametric design studies in such a way that
only a few finite element computations will be necessary for a study of
many load combinations. The results were compared with mixed mode strain
energy release rates calculated directly from nonlinear two-dimensional
plane-strain finite element analyses using the virtual crack closure technique.
The first procedure involved solving three unknown parameters needed to
determine the energy release rates. Good agreement was obtained when the
external loads were used in the expression derived. This superposition
technique, however, was only applicable if the structure exhibits a linear
load/deflection behavior. Consequently, a second modified technique was
derived which was applicable in the case of nonlinear load/deformation
behavior. The technique, however, involved calculating six unknown parameters
from a set of six simultaneous linear equations with data from six nonlinear
analyses to determine the energy release rates. This procedure was not
time efficient, and hence, less appealing.
Finally, a third procedure was developed to calculate mixed mode energy
release rates as a function of delamination lengths. This procedure required
only one nonlinear finite element analysis of the specimen with a single
delamination length to obtain a reference solution for the energy release
rates and the scale factors. The delamination was subsequently extended
in three separate linear models of the local area in the vicinity of the
delamination subjected to unit loads to obtain the distribution of G
with
delamination lengths. This set of sub-problems was solved using linear
finite element analyses, which resulted in a considerable reduction in
CPU time compared to a series of nonlinear analyses. Although additional
modeling effort is required to create the local sub-model, this superposition
technique is very efficient for large parametric studies, which may occur
during preliminary design where multiple load combinations must be considered.
ABSTRACT
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-of-plane 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, delaminations of various lengths were simulated in two locations
where delaminations were observed during the tests. The analyses showed
that at the loads corresponding to matrix ply crack initiation computed
strain energy release rates exceeded the values obtained from a mixed mode
failure criterion in one location. Hence, unstable delamination propagation
is likely to occur as observed in the experiments.
ABSTRACT:
A methodology is presented for determining the fatigue life of bonded
composite skin/stringer structures based on delamination fatigue characterization
data and geometric nonlinear finite element analyses. Results were compared
to fatigue tests on stringer flange/skin specimens to verify the approach.
ABSTRACT
A shell/3D modeling technique was developed for which a local three-dimensional
solid finite element model is used only in the immediate vicinity of the
delamination front. The goal was to combine the accuracy of the full three-dimensional
solution with the computational efficiency of a plate or shell finite element
model. Multi-point constraints provided a kinematically compatible interface
between the local three-dimensional model and the global structural model
which has been meshed with plate or shell finite elements. Double Cantilever
Beam (DCB), End Notched Flexure (ENF), and Single Leg Bending (SLB) specimens
were analyzed first using three-dimensional finite element models to obtain
reference solutions. Mixed mode strain energy release rate distributions
were computed across the width of the specimens using the virtual crack
closure technique. The analyses were repeated using the shell/3D technique
to study the feasibility for pure mode I (DCB), mode II (ENF) and mixed
mode I/II (SLB) cases. Specimens with a unidirectional layup and with a
multidirectional layup where the delamination is located between two non-zero
degree plies were simulated. For a local three-dimensional model, extending
to a minimum of about three specimen thicknesses on either side of the
delamination front, the results were in good agreement with mixed mode
strain energy release rates obtained from computations where the entire
specimen had been modeled with solid elements. For large built-up composite
structures the shell/3D modeling technique offers a great potential for
reducing the model size, since only a relatively small section in the vicinity
of the delamination front needs to be modeled with solid elements.
ABSTRACT
A shell/3D modeling technique was developed for which a local solid
finite element model is used only in the immediate vicinity of the delamination
front. The goal was to combine the accuracy of the full three-dimensional
solution with the computational efficiency of a plate or shell finite element
model. Multi-point constraints provide a kinematically compatible interface
between the local 3D model and the global structural model which has been
meshed with plate or shell finite elements. For simple double cantilever
beam (DCB), end notched flexure (ENF), and single leg bending (SLB) specimens,
mixed mode energy release rate distributions were computed across the width
from nonlinear finite element analyses using the virtual crack closure
technique. The analyses served to test the accuracy of the shell/3D technique
for the pure mode I case (DCB), mode II case (ENF) and a mixed mode I/II
case (SLB). Specimens with a unidirectional layup where the delamination
is located between two 0° plies, as well as a multidirectional layup
where the delamination is located between two non-zero degree plies, were
simulated. For a local 3D model extending to a minimum of about three specimen
thicknesses in front of and behind the delamination front, the results
were in good agreement with mixed mode strain energy release rates obtained
from computations where the entire specimen had been modeled with solid
elements. For large built-up composite structures modeled with plate elements,
the shell/3D modeling technique offers a great potential, since only a
relatively small section in the vicinity of the delamination front needs
to be modeled with solid elements.
ABSTRACT
Three simple procedures were developed to determine strain energy release
rates, G, in composite skin/stringer specimens for various combinations
of uniaxial and biaxial (in-plane/out-of-plane) loading conditions. These
procedures may be used for parametric design studies in such a way that
only a few finite element computations will be necessary for a study of
many load combinations. The results were compared with mixed mode strain
energy release rates calculated directly from nonlinear two-dimensional
plane-strain finite element analyses using the virtual crack closure technique.
The first procedure involved solving three unknown parameters needed to
determine the energy release rates. Good agreement was obtained when the
external loads were used in the expression derived. This superposition
technique, however, was only applicable if the structure exhibits a linear
load/deflection behavior. Consequently, a second modified technique was
derived which was applicable in the case of nonlinear load/deformation
behavior. The technique, however, involved calculating six unknown parameters
from a set of six simultaneous linear equations with data from six nonlinear
analyses to determine the energy release rates. This procedure was not
time efficient, and hence, less appealing.
Finally, a third procedure was developed to calculate mixed mode energy
release rates as a function of delamination lengths. This procedure required
only one nonlinear finite element analysis of the specimen with a single
delamination length to obtain a reference solution for the energy release
rates and the scale factors. The delamination was subsequently extended
in three separate linear models of the local area in the vicinity of the
delamination subjected to unit loads to obtain the distribution of G
with
delamination lengths. This set of sub-problems was solved using linear
finite element analyses, which resulted in a considerable reduction in
CPU time compared to a series of nonlinear analyses. Although additional
modeling effort is required to create the local sub-model, this superposition
technique is very efficient for large parametric studies, which may occur
during preliminary design where multiple load combinations must be considered.
ABSTRACT
The objective of this work was to investigate the damage mechanisms
in composite bonded skin/stringer constructions under uniaxial and biaxial
(in-plane/out-of-plane) loading conditions as typically experienced by
aircraft crown fuselage panels. The specimens for all tests were identical
and 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-of-plane
bending loads simultaneously. Specimen edges were examined on the microscope
to document the damage occurrence and to identify typical damage patterns.
The observations showed that, for all three load cases, failure initiated
in the flange, near the flange tip, causing the flange to almost fully
debond from the skin.
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, principal stresses exceeded the transverse
strength of the material in the flange area. Additionally, delaminations
of various lengths were simulated in two locations where delaminations
were observed. The analyses showed that unstable delamination propagation
is likely to occur in one location at the loads corresponding to matrix
ply crack initiation for all three load cases. However, the current two-dimensional
plane-strain finite element model may not fully account for the complex
three-dimensional damage pattern observed. A detailed investigation of
this damage pattern may require a local three-dimensional analysis of the
damaged area.
ABSTRACT
The objective of this work was to investigate the damage mechanisms
in composite bonded skin/stringer constructions under uniaxial and biaxial
(in-plane/out-of-plane) loading conditions as typically experienced by
aircraft crown fuselage panels. The specimens for all tests were identical
and 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 loads simultaneously. Microscopic
investigations of the specimen edges were used to document the damage occurrence
and to identify typical damage patterns. The observations showed that,
for all three load cases, failure initiated in the flange near the flange
tip causing the flange to almost fully debond from the skin.
A two-dimensional plain-strain finite element model was developed to
analyze the different test cases using a geometrically nonlinear solution.
For all three loading conditions, principal stresses exceeded the transverse
strength of the material in the flange area. Additionally, delaminations
of various lengths were simulated in the locations where delaminations
were experimentally observed. The analyses showed that unstable delamination
propagation is likely to occur at the loads corresponding to matrix ply
crack initiation for all three loadings.
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