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A failure criterion for notched plates in compression was developed. The criterion is based on experimentally observed kinking failure of fibers around a notch combined compressive and shear stresses. Experimental results for plates with a crack or a hole are used to verify the failure model, and design studies are performed to demonstrate the use of the model.
Models of surface fractures due to volcanic loading an elastic plate are commonly used to constrain thickness of planetary lithospheres, but discrepancies exist in predictions of the style of initial failure and in the nature of subsequent fracture evolution. In this study, we perform an experiment to determine the mode of initial failure due to the incremental addition of a conical load to the surface of an elastic plate and compare the location of initial failure with that predicted by elastic theory. In all experiments, the mode of initial failure was tension cracking at the surface of the plate, with cracks oriented circumferential to the load. The cracks nucleated at a distance from load center that corresponds the maximum radial stress predicted by analytical solutions, so a tensile failure criterion is appropriate for predictions of initial failure. With continued loading of the plate, migration of tensional cracks was observed. In the same azimuthal direction as the initial crack, subsequent cracks formed at a smaller radial distance than the initial crack. When forming in a different azimuthal direction, the subsequent cracks formed at a distance greater than the radial distance of the initial crack. The observed fracture pattern may explain the distribution of extensional structures in annular bands around many large scale, circular volcanic features.
A quasi-three dimensional, nonlinear elastic finite element stress analysis of finite width composite laminates including curing stresses is presented. Cross-ply, angle-ply, and two quasi-isotropic graphite/epoxy laminates are studied. Curing stresses are calculated using temperature dependent elastic properties that are input as percent retention curves, and stresses due to mechanical loading in the form of an axial strain are calculated using tangent modulii obtained by Ramberg-Osgood parameters. It is shown that curing stresses and stresses due to tensile loading are significant as edge effects in all types of laminate studies. The tensor polynomial failure criterion is used to predict the initiation of failure. The mode of failure is predicted by examining individual stress contributions to the tensor polynomial.
The results of a failure analysis of finite width (+ or - theta)s T300/5208 graphite-epoxy laminates subjected to thermal curing loads and applied tensile strain are presented. Stress distributions obtained from linear elastic and linear thermoelastic finite element stress analyses are used in conjunction with the tensor polynomial failure criterion to predict the mode and location of first failure in laminates with fiber angles ranging from five to seventy-five degrees. It is shown that the mode of failure is predominantly interlaminar shear for small fiber angles, shifts to combined interlaminar normal, in-plane shear and in-plane normal for intermediate angles, and is primarily transverse tension for large fiber angles. The location of initial failure shifts from the (+ or - theta)s interface for small fiber angles to the midplane for large fiber angles.
In this study, a progressive failure analysis is used to investigate leakage in internally pressurized non-circular composite cylinders. This type of approach accounts for the localized loss of stiffness when material failure occurs at some location in a structure by degrading the local material elastic properties by a certain factor. The manner in which this degradation of material properties takes place depends on the failure modes, which are determined by the application of a failure criterion. The finite-element code STAGS, which has the capability to perform progressive failure analysis using different degradation schemes and failure criteria, is utilized to analyze laboratory scale, graphite-epoxy, elliptical cylinders with quasi-isotropic, circumferentially-stiff, and axially-stiff material orthotropies. The results are divided into two parts. The first part shows that leakage, which is assumed to develop if there is material failure in every layer at some axial and circumferential location within the cylinder, does not occur without failure of fibers. Moreover before fibers begin to fail, only matrix tensile failures, or matrix cracking, takes place, and at least one layer in all three cylinders studied remain uncracked, preventing the formation of a leakage path. That determination is corroborated by the use of different degradation schemes and various failure criteria. Among the degradation schemes investigated are the degradation of different engineering properties, the use of various degradation factors, the recursive or non-recursive degradation of the engineering properties, and the degradation of material properties using different computational approaches. The failure criteria used in the analysis include the noninteractive maximum stress criterion and the interactive Hashin and Tsai-Wu criteria. The second part of the results shows that leakage occurs due to a combination of matrix tensile and compressive, fiber tensile and compressive, and inplane shear failure modes in all three cylinders. Leakage develops after a relatively low amount of fiber damage, at about the same pressure for three material orthotropies, and at approximately the same location.
A systems approach was adopted to study the pocketing phenomena on a solid rocket nozzle liner. The classical thermoelastic analysis was used to identify marginally strained regions on the composite liner erosion surface and at a depth coincident with the peak value of the across ply coefficient of thermal expansion. A failure criterion was introduced which included a thermal term and permitted failure assessment over the charred liner. The method was verified by satisfactory application to a reported related experiment. Liner pocketing mechanism was attributed to very localized material degradation caused during manufacturing process either by reduction of fiber strength and/or by concentration of resin volume fraction. Pocketing scenario over the degraged material was constructed with supporting formulation to predict size of fissures with respect to degraded material size and location in the liner and with burn time. Sensitivities of liner material parameters were determined to influence test programs designed to update mechanical data base of carbon cloth phenolic over the char temperature range.
The problem of an existing through-the-thickness center notch in a unidirectional fibrous composite is investigated using a homogeneous anisotropic elasticity analysis in conjunction with various crack growth criteria. Tensor polynomial, strain energy density, and normal stress ratio criteria are applied as crack growth direction criteria and compared to experimental observations. For the cases and criteria studied, only the normal stress ratio criterion exhibits an ability to correctly predict crack growth direction. The normal stress ratio criterion is subsequently applied to the same cases as a failure criterion. Comparison with experiment indicates that these predictions exhibit reasonable correlation with observed critical stresses. Finally, the macroscopic approach to the problem used in this study is compared to a microscopic shear lag analysis of experimental results in the literature. The comparison indicates that both approaches yield essentially identical predictions. The comparisons made with other criteria and approaches indicate that application of the normal stress ratio within a macroscopic level analysis has great potential as an approach to modeling composite crack growth.
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.
A comprehensive experimental and analytical evaluation of the tensor polynomial failure criterion was undertaken to determine its capability for predicting the ultimate strength of a composite limina subject to a plane stress state. Results are presented demonstrating that a quadratic formulation is too conservative and a cubic representation is required. Strength comparisons with test data derived from glass/epoxy and graphite/epoxy tubular specimens are also provided to validate the cubic strength criterion. Environmental effects including ambient temperature, exposure to vacuum, length of post-cure time, and rate of cool down were also investigated. Behavior changes associated with polymer (epoxy) matrix composites were determined in terms of variations in stiffness and tensile strength.
An experimental study conducted to evaluate the effect of laminate orthotropic properties and panel width on the compression strength of 48-ply graphite-epoxy laminates with drilled holes is described. The test results are evaluated on the basis of hole size and specimen width and are used in determining parameters necessary for predicting trends using the point stress failure criterion. Good agreement is obtained between experimental and predicted values of failure for panels fabricated from two quasi-isotropic laminates and one orthotropic laminate. The results suggest that panels of different widths having holes that are large in relation to the failure prediction parameter should be included in any test program conducted to develop prediction trends that may be used in design applications.
A research program is in progress to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. Strain rate dependent inelastic constitutive equations have been developed to model the polymer matrix, and have been incorporated into a micromechanics approach to analyze polymer matrix composites. The Hashin failure criterion has been implemented within the micromechanics results to predict ply failure strengths. The deformation model has been implemented within LS-DYNA, a commercially available transient dynamic finite element code. The deformation response and ply failure stresses for the representative polymer matrix composite AS4/PEEK have been predicted for a variety of fiber orientations and strain rates. The predicted results compare favorably to experimentally obtained values.
Splitting, ultimate failure load and the damage path in center notched composite specimens subjected to in-plane tension loading are predicted using progressive failure analysis methodology. A 2-D Hashin-Rotem failure criterion is used in determining intra-laminar fiber and matrix failures. This progressive failure methodology has been implemented in the Abaqus/Explicit and Abaqus/Standard finite element codes through user written subroutines "VUMAT" and "USDFLD" respectively. A 2-D finite element model is used for predicting the intra-laminar damages. Analysis results obtained from the Abaqus/Explicit and Abaqus/Standard code show good agreement with experimental results. The importance of modeling delamination in progressive failure analysis methodology is recognized for future studies. The use of an explicit integration dynamics code for simple specimen geometry and static loading establishes a foundation for future analyses where complex loading and nonlinear dynamic interactions of damage and structure will necessitate it.
The interaction equation was used to predict failure in Ti-4V-6Al joints brazed with Al 1100 filler metal. The joints used in this study were geometrically similar to the joints in the brazed beryllium metering structure considered for the ATLAS telescope. This study confirmed that the interaction equation R(sub sigma) + R(sub Tau) = 1, where R(sub sigma) and R(sub Tau)are normal and shear stress ratios, can be used as conservative lower bound estimate of the failure criterion in ATLAS brazed joints as well as for construction of the Failure Assessment Diagram (FAD).
Results from an experimental and analytical study of the local buckling, postbuckling, and crippling (failure) behavior of channel, zee, and I- and J-section stiffeners made of AS4/3502 graphite-epoxy unidirectional tape are presented. Thirty-six specimens were tested in axial compression. Experimental results indicate the existence of a number of damage initiation modes, all of which involve either delamination in some part of the specimen or local material strength failure in a corner of the specimen. The flange width-to-thickness ratio is found to influence the mode of damage initiation. The inner corner radius strongly affects the crippling stress for the I- and J-section specimens, but was not found to have a significant effect on the crippling stress of channels and zees. Geometrically nonlinear analyses of five specimens were performed with the STAGS general purpose computer code. Correlation between analytical and experimental results is excellent through buckling, but agreement degrades in postbuckling. The discrepancies in postbuckling are attributed to neglect of transverse shearing deformations in the analysis and development of damage in the specimens. Hashin's compressive fiber mode failure criterion correlates reasonably well with the first major damage event in a first ply failure analysis.
A research program is being undertaken to develop rate dependent deformation and failure models for the analysis of polymer matrix composite materials. In previous work in this program, strain-rate dependent inelastic constitutive equations used to analyze polymers have been implemented into a mechanics of materials based composite micromechanics method. In the current work, modifications to the micromechanics model have been implemented to improve the calculation of the effective inelastic strain. Additionally, modifications to the polymer constitutive model are discussed in which pressure dependence is incorporated into the equations in order to improve the calculation of constituent and composite shear stresses. The Hashin failure criterion is implemented into the analysis method to allow for the calculation of ply level failure stresses. The deformation response and failure stresses for two representative uniaxial polymer matrix composites, IM7/977-2 and AS4-PEEK, are predicted for varying strain rates and fiber orientations. The predicted results compare favorably to experimentally obtained values.
To obtain a better understanding the response of the structural adhesives used in the Space Shuttle's Reusable Solid Rocket Motor (RSRM) nozzle, an extensive effort has been conducted to characterize in detail the failure properties of these adhesives. This effort involved the development of a failure model that includes the effects of multi-axial loading, temperature, and time. An understanding of the effects of these parameters on the failure of the adhesive is crucial to the understanding and prediction of the safety of the RSRM nozzle. This paper documents the use of this newly developed multi-axial, temperature, and time (MATT) dependent failure model for modeling failure for the adhesives TIGA 321, EA913NA, and EA946. The development of the mathematical failure model using constant load rate normal and shear test data is presented. Verification of the accuracy of the failure model is shown through comparisons between predictions and measured creep and multi-axial failure data. The verification indicates that the failure model performs well for a wide range of conditions (loading, temperature, and time) for the three adhesives. The failure criterion is shown to be accurate through the glass transition for the adhesive EA946. Though this failure model has been developed and evaluated with adhesives, the concepts are applicable for other isotropic materials.
Solutions are developed for the two dimensional region containing unidirectional fibers with initial damage in the form of a notch, a rectangular cut out, and a circular hole. An ultimate stress failure criterion is used for both the fibers and the matrix, simple tension for the fibers, and shear failure for the matrix. Models which account for longitudinal matrix yielding and splitting as well as transverse matrix yielding and fiber breakage as a function of initial damage, material properties, and applied stress are presented. For ductile matrix composites the results indicate that longitudinal matrix yielding and transverse notch extension are the most significant forms of damage. The extent of the stable transverse damage is shown to be approximately constant, independent of initial notch length. In the case of brittle matrix composites (graphite/epoxy) longitudinal splitting is shown to be the dominant form of damage.
Although graphite fibers behave in an essentially elastic manner, the polymeric matrix of graphite/epoxy composites is a viscoelastic material which exhibits creep and delayed failures. The creep process is quite slow at room temperature, but may be accelerated by higher temperatures, moisture absorption, and other factors. Techniques are being studied to predict long-term behavior of general laminates based on short-term observations of the unidirectional material at elevated temperatures. A preliminary numerical procedure based on lamination theory is developed for predicting creep and delayed failures in laminated composites. A modification of the Findley nonlinear power law is used to model the constitutive behavior of a lamina. An adaptation of the Tsai-Hill failure criterion is used to predict the time-dependent strength of a lamina. Predicted creep and delayed failure results are compared with typical experimental data.