DAMAGE TOLERANCE AND NOTCH SENSITIVITY TEST METHOD DEVELOPMENT FOR SANDWICH COMPOSITES Daniel O. Adams, Bradley Kuramoto, and Marcus Stanfield Department of Mechanical Engineering University of Utah Salt Lake City, UT 84112 ABSTRACT Although the development of coupon-level test methods for notch sensitivity and damage tolerance of monolithic composites has reached a high level of maturity, less attention has been directed towards the development of standardized test methods for sandwich composites. For monolithic composites, these test methods are commonly performed as part of composite materials characterization programs to provide design allowables associated with notch sensitivity and damage tolerance. Additionally, results from such tests have been used to validate numerical modeling approaches for simulating damage progression in composite laminates. The objective of this research is to develop and evaluate candidate notch sensitivity and damage tolerance test methodologies for sandwich composites and to propose specific methodologies and configurations for standardization. Two test methodologies have been developed for damage tolerance testing of sandwich composites. The first utilizes an end-loaded Compression After Impact (CAI) configuration. The second methodology consists of a four-point flexure test configuration in which the damaged facesheet of the composite sandwich panel may be loaded in compression or tension. For both test methodologies, research has focused on their limits of applicability, the required sandwich specimen dimensions, and their recommended testing procedures. For notch sensitivity, initial research has focused on the development of test methods for sandwich composites under in-plane loading, with an expected progression to more complex out-of-plane loading cases. Additionally, finite element analysis with progressive damage modeling is being assessed for use in predicting strength reductions of sandwich composites with impact damage and notches (open holes). Previously developed analysis methodologies for monolithic composite laminates are being extended to sandwich composites using ABAQUS with add-on software NDBILIN. Experimental validation is being aided through the use of Digital Image Correlation (DIC) to provide full-field deformations and strain fields associated with damage progression. INTRODUCTION Damage tolerance test method development for monolithic composite laminates has reached a high level of maturity relative to sandwich composites. There currently exists a standardized damage resistance test method (ASTM D7136 [1]), as well as a damage tolerance standard (ASTM D7137 [2]) for monolithic composites. For sandwich composites, relatively little effort has been placed towards arriving at one or more standardized damage tolerance test methods for sandwich composites until recently. However, the need for such a standardized test recently has been identified by the aviation industry in general, and ASTM Committee D30 on Composites specifically. In October 2009, a joint SAMPE/ASTM D30 Panel Session on “Damage Resistance and Damage Tolerance of Sandwich Structures” was held in Wichita, KS. This panel, organized by the PI of this research project, focused on the current status and future needs of damage resistance and damage tolerance test methods for sandwich composites. Considerable interest was identified for standardized damage resistance and damage tolerance test methods for sandwich composites, and work commenced towards a damage resistance test method. In 2011, a damage resistance standard practice for sandwich composites (ASTM D7766 [3]) was published by ASTM Committee D30. Later in 2011, a second joint SAMPE/ASTM D30 Panel on “Damage Resistance of Composite Sandwich Structures” was held in Ft. Worth, TX. At this panel, interest in a subsequent damage tolerance test method for sandwich composites was reaffirmed. At a subsequent ASTM D30 meeting, the University of Utah (Dr. Dan Adams) was identified as the lead institution to lead the effort towards the development of a standardized test method in damage tolerance. One objective of this research is to identify and develop one or more test methodologies for assessing the damage tolerance of sandwich composites. The possibility of having multiple test methods or practices exists in order to accommodate the largest number of sandwich configurations and loading conditions as well as intended usages of sandwich composites. Additionally, efforts have focused on investigating possible methodologies to scale test results from small-scale sandwich panel tests to larger sandwich structures. Following an initial assessment of candidate test methodologies, two have been selected for further development: edgewise compression after impact and four-point flexure after impact. Testing has been conducted to evaluate these methods, and finite element analysis performed using ABAQUS/NDBILIN to investigate specimen configurations and predict the residual strength of the specimens. Another objective of this research is to investigate the notch sensitivity of sandwich composites. Although the development and numerical modeling of couponlevel test methods for notch sensitivity of monolithic composite laminates has reached a high level of maturity, little research has been performed towards the development of such test methods and numerical modeling methodologies for sandwich composites. Two standardized tests currently exist for notched monolithic composites under in-plane loading: open-hole tension (ASTM D 5766 [4]) and open-hole compression (ASTM D 6484 [5]). However, currently no standardized test methods exist for assessing notch sensitivity of sandwich composites. A survey of the literature has been conducted to determine candidate notched sandwich composite test methods. Based on this review, the initial focus of this research has been on an open-hole edgewise compression test. Emphasis has been placed on both suitable specimen and hole sizing as well as the numerical simulation of the test specimen to predict the notched strength. Digital Image Correlation (DIC) is used during testing to provide full-field deformations and strain fields. LITERATURE REVIEW Research began with a literature review to identify candidate damage tolerance test methodologies for sandwich composites. Emphasis was focused on both papers and reports in the open literature as well as common practices in the aerospace industry and from commercial test labs. From the candidate test configurations identified, two were selected for investigation and further development. The first methodology utilizes an end-loaded compression after impact (CAI) test configuration. Second, a four-point flexure test methodology was identified for evaluating post-impact performance where the damaged facesheet can be loaded in compression or tension depending on specime en setup. Further de evelopmentt and evalu uation of th he two ide entified dam mage toleranc ce test meth hodologies is currently y underway.. Additionally, A h identifie ed several potential n notch sensiitivity a literaturre review has tests tha at could be investigate ed for sand dwich comp posites. A b brief descrip ption follow ws for each ca andidate tes st method identified. The first ccandidate ttest is an in n-plane loa aded, open-ho ole sandwic ch compression test. This T candida ate test wo ould incorpo orate aspeccts of two existing stan ndardized tests: the edgewise e compresssion test for sand dwich composites (ASTM M C364 [6 6]) and th he open-ho ole compre ession testt of mono olithic M D6484 [5 5]). This ca andidate te st would fe eature a ce entered cirrcular composites (ASTM hole, eitther through h the entire e sandwich specimen or through h one facessheet. Thiss test methodo ology, also used in a previous research r invvestigation by Tombliin et al. [7]] has been selected as th he initial foc cus of this research r in vestigation n. Another A can ndidate test is an in-p plane loade ed, open-hole sandwich tensile test. While a standardiz zed open-h hole tension n test existts for monolithic com mposites (A ASTM D5766 [4]), [ no sta andardized in-plane te ensile tests exist for ssandwich ccomposites.. To introduc ce sufficientt tensile loa ad into the sandwich s sspecimen, rrelatively co omplex fixtu uring is expec cted to be required, as a evidence ed by the open-hole tension tesst configuration used pre eviously by Tomblin ett al. [7]. The T out-of-plane flexu ural streng gth of notcched sandw wich comp posites can n be determin ned using a four-pointt flexure test configurration as sh hown in Fig gure 1. Su uch a test wo ould be pe erformed similarly s to the stand dardized fo our-point fflexure test for monolith hic compos sites (ASTM M D7249 [8 8]), but witth modificattions to acccommodatte an open-ho ole composiite sandwic ch specimen n. Figure 1. Four-point F t flexure te est for notc ched sandw wich comp posites. A three-poin nt flexure test t configuration hass been used to indu uce an in-p plane bending moment in n a sandwic ch composite specime en by placin ng the sand dwich on its side otch was used u in th he compos ite sandwicch specimen, which was [9]. An edge V-no ed to both static and fatigue testing. Thiss three poin nt flexure cconfiguratio on is subjecte limited to o a notch lo ocated on the t tension side of the e sandwich. However, if the test w were modified d to four-po oint flexure as shown in Figure 2 2, the edge e notch cou uld be place ed at the tension or compression sid de or a dou uble edge n notch could be used. Fig gure 2. Fo our-point in n-plane flex xure for no otched san ndwich com mposites. Parmigiani P et e al. at Orregon State e Universityy [10] has d developed an out-of-p plane shear (M Mode III te earing) test method to o investigatte the notcch sensitivitty in mono olithic composites. As sho own in Figu ure 3, this test t uses a keyhole no otch in the specimen. This test methodology will need to t be inves stigated further for its possible applicability to sandwic ch composittes. Figure F 3. Out-of-plan O ne shear te est for notc ched sandw wich comp posites. RESEAR RCH FOCU US: SANDWICH COM MPOSITE D DAMAGE T TOLERANC CE The T primary y focus of th he sandwich damage ttolerance e effort is to e evaluate the e two general test metho odologies, edgewise e compressio c n and four--point flexu ure, for posssible standard dization. However, a secondary focus is to pro ovide a residual stre ength comparison of sand dwich pane els with idea alized dam mage as well as impact damage u using both of the t propose ed test methodologies. Additiona lly, digital im mage corre elation and finite elementt analyses have bee en performed to esta ablish prop per specim men sizing and predictin ng failure sttrengths of damaged sandwich s pa anels. osite Edgew wise Comp pression A After Impac ct Sandwich Compo One O of the most com mmonly us sed method ds to asse ess damag ge tolerancce of sandwic ch compos sites is edgewise e compression testing g. Typicallly, end-loa aded Compression After Impact (CAI) testing on sandwich structures has been performed using ASTM D7137 [2], the standardized method for CAI testing of monolithic composite plates, as a reference. This test method requires that the loading ends of the specimen are machined to be parallel within tight tolerances, and then loaded edgewise until failure. The specimen sides are typically supported along their edges to prevent buckling failure of the sandwich panel. This test methodology has been used previously on Nomex honeycomb panels as well as stitched and unstitched foam panels with success [11-14]. On undamaged or barely damaged high-strength specimens, however, edgewise loading using this test configuration can lead to undesired failure modes such as end crushing before failure in the gage section [12]. Tomblin et al. [11-12] and Butterfield and Adams [13-14] have used edgewise compression to assess the damage tolerance of sandwich composites. The sandwich panels tested in both laboratories were 216 mm (8.5 in.) wide by 267 mm (10.5 in.) in height. Impactor diameters of 25 mm and 76 mm (1.0 in. and 3.0 in.) were used. Whereas the Wichita State University researchers [11-12] used honeycomb core sandwich panels, the subsequent University of Utah investigation [13-14] focused on unstitched and stitched foam sandwich composites. In both investigations, sandwich composites with 9.5 mm and 19 mm (0.375 in. and 0.75 in.) thick cores were tested. Composite sandwich specimens were clamped on the upper and lower loading edges, and knife-edge supports were used on the specimen sides. The test fixture used for the University of Utah investigation is shown in Figure 4. In this investigation, strain gages were placed 25 mm (1.0 in.) from the lower corners in order to align the panels prior to testing. A hemispherical alignment stage, placed under the test fixture, was used in conjunction with the corner strain gages and a small preload to provide proper panel alignment. Figure 4. Comp pression After A Impac ct (CAI) test fixture fo or composiite sandwich panells used at the t Univerrsity of Uta ah. Based B on th he review of o the litera ature as w well as from m past experiences of the authors, several aspects a of sandwich CAI C testing g have bee en identified that requ uired further investigatio on prior to o test stan ndardizatio n. For ma any core materials, it is necessa ary to reinfforce the core c at the e specimen n ends to allow prop per end loa ading without premature end failure es due to eiither facesh heet broom ming or buckling. Sincce an y imposed on the san ndwich pan nel at the e ends, external clamp-type restraint is typically o the entirre end of th he sandwic ch specime en is not de esirable. R Rather, the core potting of material may be filled f or re eplaced witth a highe er strength potting orr filler material. Addition nally the choice of side e supports must be cconsidered. Such sup pports may take the form m of knife edge supp ports or cla amp-type ssupports, d depending on the typ pe of boundarry condition n desired; knife edge e supports are used tto replicate e a pinned joint whereas s clamped supports are a used to o minimize e panel rottation at th he edges. The selection n of suppo ort condition ns are imp portant whe en considerring scaling g the resullts of CAI san ndwich pan nel testing to larger size structtures. The e best-suitted size off the sandwich panel as well as the boundary conditions may both be selected to represent the composite structure of interest. Tomblin et al. [11-12] investigated the effects of scaling the planar dimensions of sandwich specimen both experimentally and using finite element analysis. For sandwich configurations with thin facesheets, the residual strength increased with panel width. However, this increase was not observed for sandwich configurations with thicker facesheets. Results suggest that CAI-level tests may be useful for scaling if the width-to-damage ratio is sufficient to avoid edge effects. This topic is currently under investigation as part of the standardized test method development. Testing conducted to evaluate the sandwich edgewise CAI test method used composite sandwich panels fabricated from 1.5 mm (0.06 in.) thick G11 fiberglass/epoxy and 0.38 mm (0.015 in.) thick carbon/epoxy facesheets bonded to 13 mm (0.5 in.) thick Nomex honeycomb core using FM300 film adhesive. The sandwich specimens were machined to 216 mm (8.5 in.) in width by 267 mm (10.5 in.) in height, the same dimensions as used in previous studies [11-14]. To prevent the loaded ends from crushing prior to failure in the gage section, they were potted using a room temperature cure epoxy potting compound. In order to minimize the variability in initial test results due to variations in damage states from impact testing, the use of idealized damage in the form of circular holes machined in one facesheet was employed rather than actual drop-weight impacting. By testing these sandwich configurations with and without the idealized damage, these tests provided an initial comparison of residual strength between different damage sizes. Following these initial idealized damage states, actual impact damage was created in composite sandwich panels. Testing was conducted using the same fixture as used in previous testing at the University of Utah (Figure 4). The specimens were preloaded and subsequently aligned using the hemispherical stage to adjust the strain readings from strain gages bonded near the bottom corners of both facesheets. Two different idealized damage sizes, 25 mm (1 in.) and 76 mm (3 in.) through holes on the damaged facesheet were compared to undamaged and impact damaged specimens. The impact damaged specimens were impacted at an energy level of 3.4J (30 in-lbf) in accordance with ASTM D7766 [3]. As shown in Figure 5, the damage state had a significant impact on the residual strength, especially for the sandwich composites with the relatively thin carbon/epoxy facesheets. The strength reduction of the impacted specimens with carbon/epoxy facesheets was between that measured in specimens with a 25 mm (1 in.) and 76 mm (3 in.) hole. The sandwich composites with the thicker G11 facesheets were not affected as significantly, Normalized Compression Strength with less strength reduction due to all forms of damage investigated. 1.0 Glass/Epoxy 0.9 Carbon/Epoxy 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 Undamaged 1" Hole 3" Hole Impacted Figure 5. Normalized results of edgewise compression after impact testing. Sandwich Four-Point Flexure After Impact The second test method selected for investigating damage tolerance of sandwich composites is the four-point flexure after impact test. As shown in Figure 6, this test configuration allows for a constant bending moment and zero shear stress in the central gage section of the specimen. The four-point flexure configuration allows for the damaged facesheet to be placed under either compression or tension loading depending on how the specimen is placed into the fixture (damaged facesheet placed either upward or downward). In a majority of studies performed to date, the damaged facesheet has been loaded in compression. The University of Utah test set-up for fourpoint flexure testing of sandwich composites is shown in Figure 7. Fig gure 6. She ear and be ending mom ment diagrram for fou ur point fle exure test. Figure e 7. Four point p flexurre test fixtu ure used fo or assessin ng damage e tolerance e of sandwich composite es at the University o of Utah. Based on a review of the literature and past experiences of the authors, a number of aspects of sandwich four-point flexure testing are under investigation in anticipation of test standardization. The central test section, or region of the sandwich panel between the inner supports, must be of sufficient length and width such that the damage present in the panel is not influenced by the panel edges or the presence of the inner loading rollers. Similarly the outer spans of the panel must be of sufficient length to generate an adequate bending moment in the central test section prior to shear failure in the outer spans or compression failure at the load application points. Shear failure of the core in the outer spans can be avoided through the use of a higher density core material, or the filling of the cells of a honeycomb core material. Similarly, precautions must be taken to avoid crushing failure of the facesheet and/or core at the loading points. Thus, the sandwich panel and span lengths of the test fixture must be properly designed to prevent undesirable failure modes from occurring under four-point flexure loading. An initial round of testing was conducted to evaluate four-point flexure loading for assessing damage tolerance of sandwich composites. The sandwich specimens were sized in accordance with the ASTM D7249 [8] sizing guidelines. The sandwich panels were fabricated using 0.5 mm (0.02 in.) carbon/epoxy facesheets bonded to 13 mm (0.5 in.) thick Nomex honeycomb core using FM300 film adhesive. The sandwich specimens were machined to 216 mm (8.5 in.) in width by 813 mm (32 in.) in length, the same dimensions as used in previous studies [13-14]. Initial tests were performed using a 760 mm (30 in.) outer support span and 229 mm (9 in.) inner loading span. Due to the relatively low shear strength of the Nomex honeycomb, a higher density honeycomb core material was spliced in the outer section to prevent core shear failures. Testing was performed using idealized damage in the form of 25 mm (1 in.) and 76 mm (3 in.) circular holes machined in one facesheet. Additionally, sandwich panels without damage were tested to determine strength reductions due to the idealized damage. As shown in Figure 8 the two idealized damage states had a significant effect on the residual strength of the sandwich composites. The 25 mm (1 in.) facesheet hole produced a 42% reduction in strength and the 76 mm (3 in.) hole produced a 60% reduction in strength. When discussing these test results at a recent ASTM Committee D30 on Composites meeting, it was suggested that to simplify the specimen preparation procedures (avoiding the splicing of higher density core in the outer sections), a greater core thickness could be used in the test specimen, even if this thickness was greater than for the intended application. The rationale was that the damage tolerance of a sandwich composite under flexure is sensitive to facesheet damage, but insensitive to the core thickness. Thus, the core thickness can be used as a design variable towards preventing undesirable failure modes from occurring. However, the core thickness must be sufficient to prevent damage from occurring in the opposite facesheet during the impact event. Normalized Flexural Strength 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 No Hole 1" Hole 3" Hole Figure 8. Normalized four-point flexure after impact strength of idealized damage specimens. RESEARCH FOCUS: SANDWICH COMPOSITE NOTCH SENSITIVITY The initial focus of the sandwich notch sensitivity research has focused on the measurement and prediction of the open-hole compression strength of composite sandwich specimens. The selected specimen size was 114.3 mm (4.5 in.) in width and 152.4 mm (6.0 in.) in height. The diameter of the through-hole in the center of the specimen was 19 mm (0.75 in.), producing the same 6:1 specimen width-to-hole diameter ratio used with monolithic open-hole composite specimens [4-5]. The test fixture was the same as used in ASTM D7137 [2] for compression-after-impact testing of monolithic composite specimens Fixed end conditions were used on the top and bottom ends of the specimen and knife edge supports were used on specimen edges. The composite sandwich panels were fabricated using 0.5 mm (0.02 in.) carbon/epoxy facesheets bonded to 13 mm (0.5 in.) Nomex honeycomb core using FM300 film adhesive. The specimens were machined to their final measurements and the core region at the specimen ends were potted using a room-temperature cure epoxy to prevent end crushing during loading. The central through-hole was milled using a UKAM Universal Metal Bond Core Drill. Four strain gages were bonded 25 mm (1 in.) from the bottom and side edges for use in aligning the fixture at a given preload. The front face was painted white and speckled using black ink for Digital Image Correlation (DIC) measurements. The load and crosshead displacements were also measured during the test. Initial test results from the notched sandwich composite specimen show a 32% reduction in compression strength compared to the unnotched specimen. Axial strains measured using DIC and bonded strain gages were found to be in good agreement as shown in Figure 9. 5.00E‐03 4.50E‐03 4.00E‐03 Strain (in/in) 3.50E‐03 3.00E‐03 DIC Left 2.50E‐03 Left Gage 2.00E‐03 DIC Right 1.50E‐03 Right Gage 1.00E‐03 5.00E‐04 0.00E+00 0 20 40 60 80 100 120 DIC Index Figure 9. Axial strain gage and DIC comparison from open-hole compression testing of composite sandwich specimens. FINITE ELEMENT MODELING The failure analysis of notched sandwich specimens was modeled using the commercial finite element code ABAQUS. NDBILIN, a user-defined nonlinear material model (UMAT) developed by Materials Sciences Corporation [15, 16] was used for stiffness degradation based progressive damage modeling. Using this UMAT, stiffness degradation is prescribed at the lamina level within the composite facesheets and is shaped by inputting the failure criteria (ex: max stress/strain, Hashin, phase averaged constituent), the stiffness degradation factors, and stiffness transition factor. A graphical representation of the material model is shown in Figure 10. NDBILIN allows for two different material inputs for fiber stiffness degradation and matrix stiffness degradation. When matrix damage occurs, the stiffness reduction is applied to all matrix modes (22, 33, 12, 13, and 23). Figure F 10. NDBILIN stiffness s de egradation n model. In nitial progrressive dam mage anallysis using g ABAQUS S/NDBILIN focused o on a monolith hic compos site open-h hole tension specime en. The m modeled sp pecimen was a quasi-iso otropic lam minate of IM M7/8552 carbon/epoxyy, and pred dictions were compare ed to experimental resu ults from three t spec cimens tessted. The e predicted load ve ersus displace ement resu ults, shown in Figu ure 11, were in go ood agreem ment with the experimental resultts. Figure 11. ABAQUS S/NDBILIN open-hole o tension re esults and model. Following F th he initial modeling m off the mono olithic com mposite ope en-hole ten nsion specime en, the AB BAQUS/NDB BILIN mod deling meth hodology w was applied d to open--hole compres ssion testin ng of the co omposite sa andwich spe ecimens. F Full-field strains meassured during mechanical m testing usin ng DIC werre in good a agreement with prediccted strain ffields from AB BAQUS/ND DBILIN analysis as sh hown in Fig gure 12. These initial results w were useful in n determinin ng minimum m specimen n sizing req quirements to produce e far-field strains at the specimen boundaries and at the location o f the strain n gages. R Results sug ggest 4.5 in.) wide and 152 mm (6.0 in n.) tall speccimen with a 19 mm ((0.75 that the 114 mm (4 in.), center hole is suitable s forr investigating notch se ensitivity un nder in-plan ne compresssion loading in composite sandwich specimen ns. Figu ure 12. Comparison of Digital Image Corrrelation (le eft) and finite elemen nt analy ysis results s. Although A the e predicted d strain field ds in the viicinity of the open holle were in g good agreeme ent with ex xperimental results, th he initial an nalysis did not accura ately predicct the failure load. As shown s in Figure 13, the finite element ssimulation predicts fu urther s reduction and a con nsiderably higher h com mpression ffailure load than obse erved stiffness experimentally. These differrences sug ggest that a additional ffailure mod des need to be included d into the finite elem ment simula ations to p roperly mo odel the fa ailure sequence occurring in sandw wich open-hole compression tesst. As a rresult, additional modeling nding as w well as face esheet bucckling capabilitties to simulate both facesheet//core debon are currrently underr investigattion. The use u of cohe esive eleme ents is und der investigation for face esheet/core debonding g, whereas s the posssibility of in ncorporating an insta ability analysis s is being ex xplored. 3500 3000 Nyy (lbf/in) 2500 2000 1500 Experimental 1000 ABAQUS/NDBILIN 500 0 0 0.002 0.004 Strain (in/in) 0.006 0.008 Figure 13. Open-hole compression load versus strain comparison. SUMMARY The two candidate test configurations under development for damage tolerance of sandwich composites, edgewise compression after impact and four-point flexure after impact, appear to be well suited for future ASTM standardization. The current focus of the sandwich damage tolerance research is the evaluation of progressive damage modeling approaches for predicting strength reductions in composite sandwich structures. Additionally, a combined experimental/numerical methodology for scaling of damage tolerance results from smaller test specimens to larger sandwich structures is under investigation. Research into the notch sensitivity of sandwich composites has focused initially on in-plane compression loading of sandwich composites with centrally located open holes. Progressive-damage finite element analysis has been performed using ABAQUS with a user-defined nonlinear material model, NDBILIN. This modeling approach, used previously for monolithic composite laminates, appears to be a promising approach for sandwich composites. Experimental validation is being aided through the use of Digital Image Correlation (DIC) to provide full-field deformations and strain fields associated with damage progression. REFERENCES 1. ASTM D7136, “Standard Test Method for Measuring the Damage Resistance of a Fiber-Reinforced Polymer Matrix Composite to a Drop-Weight Impact Event,” ASTM International, West Conshohocken, PA, 2007. 2. ASTM D7137, “Standard Test Method for Compressive Residual Strength Properties of Damaged Polymer Matrix Composite Plates,” ASTM International, West Conshohocken, PA, 2007. 3. ASTM D7766, “Standard Practice for Damage Resistance Testing of Sandwich Constructions,” ASTM International, West Conshohocken, PA, 2011. 4. ASTM D5766, “Standard Test Method for Open-Hole Tensile Strength of Polymer Matrix Composite Laminates," ASTM International, West Conshohocken, PA, 2011. 5. ASTM D6484, “Standard Test Method for Open-Hole Compressive Strength of Polymer Matrix Composite Laminates," ASTM International, West Conshohocken, 2009. 6. ASTM C364, “Standard Test Method for Edgewise Compressive Strength of Sandwich Constructions," ASTM International, West Conshohocken, PA, 2007. 7. Tomblin, J.S., Raju, K.S., Walker, T., and Acosta, J. F., "Damage Tolerance of Composite Sandwich Airframe Structures - Additional Results," DOT/FAA/AR-05/33, 2005. 8. ASTM D7249, “Standard Test Method for Facing Properties of Sandwich Constructions by Long Beam Flexure," ASTM International, West Conshohocken, PA, 2012. 9. Shafiq, B. and Quispitupa, A., "Fatigue Characteristics of Foam Core Sandwich Composites," International Journal of Fatigue, Vol. 28, pp. 96-102, 2006. 10. Parmigiani, J.P., Atanasov, N., and Hyder, I., “Failure of Notched Laminates Under Out-of-Plane Bending,” proceedings of the 2014 FAA JAMS Technical Review Meeting, Seattle, WA, March 25-26 2014. 11. Tomblin, J.S., Raju, K.S., Liew, J., and Smith, B.L., “Impact Damage Characterization and Damage Tolerance of Composite Sandwich Airframe Structures,” Final Report, DOT/FAA/AR-00/44, 2001. 12. Tomblin, J.S., Raju, K.S., and Arosteguy, G., “Damage Resistance and Tolerance of Composite Sandwich Panels – Scaling Effects,” Final Report, DOT/FAA/AR-03/75, 2004. 13. Butterfield, J.M and Adams, D.O., “Effects of Stitching on the Compression After Impact Strength of Sandwich Composites”, Proceedings of the 49th International SAMPE Symposium and Exhibition, Long Beach, CA, May 2004. 14. Butterfield, J.M., “Damage Tolerance of Stitched Carbon Composite Sandwich Structures,” M.S. Thesis, Department of Mechanical Engineering, University of Utah, 2006. 15. Schutte, J., Meeker, J.C., and Clay, S., "Improved Methodologies for Damage Tolerant Composite Structure Qualification." 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 20th AIAA/ASME/AHS Adaptive Structures Conference 14th AIAA. 2012. 16. Hayduke, D. and Meeker, J., "NDBILIN-AF: Sub-Cell Level Damage UMAT Users Manual V2.0", Materials Sciences Corporation, Horsham, PA, December 2012.
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