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Progressive damage analysis as a design tool for composite bonded joints
Composites Part B 77 (2015) 474e483
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Composites Part B journal homepage: www.elsevier.com/locate/compositesb
Progressive damage analysis as a design tool for composite bonded joints vila a, Donato Girolamo b Frank A. Leone a, *, Carlos G. Da a b
NASA Langley Research Center, Hampton, VA, 23681, USA North Carolina State University, Raleigh, NC, 27695, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 April 2014 Received in revised form 11 March 2015 Accepted 14 March 2015 Available online 20 March 2015
This paper discusses the application of progressive damage analysis (PDA) methods as a design tool. Two case studies are presented in which the effects of changing design features on the strength of bonded composite joints are evaluated. It is shown that the trends of parametric evaluations performed with fullfeatured PDA models can be unintuitive and the trends can be opposite to those obtained with traditional design criteria. The joint configurations that were tested exhibit multiple damage modes, requiring several different PDA tools to accurately predict the structural peak loads. For damage tolerant structures that exhibit complex sequences of multiple failure mechanisms, traditional failure prediction tools are insufficient. Parametric PDA models encompassing a bonded joint specimen's design space have the potential to reveal unintuitive and advantageous design changes. Published by Elsevier Ltd.
Keywords: C. Finite element analysis (FEA) B. Adhesion A. Honeycomb D. Mechanical testing
1. Introduction Fiber-reinforced polymer laminates can exhibit several failure mechanisms, including fiber fracture, matrix cracking, delamination, etc. The first predicted occurrence of one of these failure mechanisms typically does not coincide with structural failure, especially for structures that have been designed according to damage tolerance requirements. Often, structural failure is the result of several different damage mechanisms joining together, progressing from a series of stable and/or locally unstable failure processes up to a globally unstable failure process. For structures whose collapse is preceded by a sequence of different interacting damage mechanisms, the structural strength can be significantly higher than the load that corresponds to the first instance of damage. Failing to take into account the effects of non-critical damage on a structure's ability to carry higher loads can lead to overly conservative structures. In order to accurately predict the strength of a composite structure, it is necessary to predict both the formation of all relevant failure mechanisms and the effects that those failures have on load redistribution. Progressive damage analysis (PDA) is a broad label applied to several modeling approaches that allow for the prediction of the
* Corresponding author. E-mail address: [email protected] (F.A. Leone). http://dx.doi.org/10.1016/j.compositesb.2015.03.046 1359-8368/Published by Elsevier Ltd.
initiation and evolution of damage. The development and application of PDA tools to advanced composite materials and structures is an active field of research, with several branching technologies that are intended to predict different composite failure mechanisms. Cohesive elements (e.g., [1e3]), for example, excel at discretely representing the formation and evolution of cracks in the finite element (FE) framework when the locations and orientations of cracks are known a priori (e.g., delaminations). Continuum damage mechanics (CDM) methods (e.g., [4e8]), rather than discretely representing cracks, represent the presence of various failure mechanisms by changing terms of the local material compliance tensor. CDM-based methods work without having prior knowledge of either the location or orientation of the damage. All PDA methods, however, have multiple strengths and technical limitations in their current state [9]. Having a proper understanding of the capabilities of each method is crucial to selecting the right tool(s) for any given progressive damage modeling application. Often, it is a combination of damage modeling techniques that is required to properly model the initiation and progression of a structural failure process, especially in structures composed of multiple advanced composite materials. In this paper, the structural response and damage mechanisms of two bonded composite joint concepts from a previous test and analysis campaign are presented [10]. It was observed that several different mechanisms contributed to the eventual failure of the specimens, and that the load at which damage was initially
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observed was well below the structural strength. A combination of PDA tools was used to model the observed sequences of damage events, and good agreement in terms of peak load and failure mode sequence was attained. Utilizing parametric FE models, it is herein attempted to improve upon the designs of the tested bonded composite joint concepts. Two case studies exploring the integration of PDA methods into the design process are presented. Performing parametric analyses with integrated PDA tools has the potential to yield significantly more efficient designs, to reveal advantageous, unintuitive design improvements, and to reduce the number of physical experiments required to identify optimal configurations.
2. Background 2.1. Test specimens The development of durable bonded joint technology for assembling composite structures for launch vehicles is an essential component of NASA's Space Launch System. Several joint designs intended for lightly-loaded minimum-gauge space structures were tested in tension, compression, and four-point bending as part of an experimental test campaign at NASA Langley Research Center [11]. Two joint designs from this test campaign are discussed in this paper: a conventional splice joint (CSJ) and a new Durable Redundant Joint (DRJ) concept [12]. Each design involves a honeycomb core with carbon/epoxy facesheets joined with adhesively bonded carbon/epoxy doublers. The data considered in this paper is limited to tensile loading cases. The sandwich panels used in this study are composed of six-ply carbon/epoxy facesheets and a 25.4-mm-thick Hexcel CRIII-1/85052-.0007P-3.1 aluminum honeycomb core. The facesheet material is made of grade 190 TE-1 tapes (toughened epoxy/T800) [13]. The stacking sequence of the facesheets is [þ60/0/60]S, with the 0 fiber direction aligned with the specimen length. The facesheet plies have a nominal thickness of 0.19 mm. The CSJ specimens measure 559 mm long and 76.2 mm wide and consist of two sandwich panels joined by two 139.7-mm-long, six-ply doublers bonded to the exterior faces of the sandwich with Cytec FM-300M film adhesive, as shown in Fig. 1. At their thickest, the doublers have the same stacking sequence as the facesheets. The doublers have internal ply terminations and ply drops, with cascading ply terminations spaced at 6.4-mm intervals from the doubler edges. Design specifications for the joint specimens allow
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for a 2.54-mm gap between the sandwich panels. A 12.7-mm-long Teflon film strip was inserted in-line with the adhesive layer at the joint center to decrease the severity of the stress concentration in the doubler at that location. The DRJ concept expands upon the CSJ design by adding a 96.5mm-long laminated structural insert in place of honeycomb core at the joint center, as shown in Fig. 2. The insert contains three ±45 hollow, rectangular cells. Six additional plies were laid-up above and below the cells with a stacking sequence of [þ60/0/60]S, with the outermost þ60 ply wrapped around all three hollow cells. The DRJ inserts were bonded to the interior surface of the sandwich facesheets using FM-300M adhesive. The inserts are intended to increase the ability of the joint to withstand impact damage and provide nearly symmetric load paths about the facesheet centerlines. Additional details regarding the CSJ and DRJ concepts, their design, and fabrication can be found in Ref. [11]. 2.2. Experimental test results 2.2.1. Conventional splice joint Two CSJ specimens were loaded in tension to failure. The specimens failed within the joint at peak loads of 109 and 113 kN in similar modes. The first instance of observable damage occurred in the adhesive near the outer edge of the Teflon tape, as shown in Fig. 3a. The asymmetry of the load path in the vicinity of the Teflon tape caused the facesheet to bend away from the Teflon. The bending of the facesheet compressively loaded the core. Because of the light-gauge core used, the two core cells nearest the joint center crushed at approximately two-thirds of the specimen failure load. Without the transverse support of the core beneath the Teflon tape, the facesheet and doubler were free to separate, which induced a mode I loading component of the adhesive and ply interfaces. Since FM-300M adhesive is tougher than the epoxy matrix [10], the delamination transitioned from the adhesive layer to the inner þ60 /0 interface of the doubler, as confirmed by inspection of the fracture surfaces in Fig. 3c. Unstable delamination propagation ensued shortly thereafter. 2.2.2. Durable redundant joint Two DRJ specimens were also loaded in tension to failure. The two DRJ specimens failed at loads of 140 and 130 kN. Failure was observed to initiate as delaminations at two sites in the facesheet: (1) below the outermost doubler 0 ply termination, and (2) above
Fig. 1. Schematic of the conventional splice joint (CSJ) cross section [11].
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Fig. 2. Schematic of the durable redundant joint (DRJ) cross section [11].
Fig. 3. Digital photographs of (a) a CSJ specimen during loading, (b) a DRJ specimen during loading, and (c) a CSJ specimen post-test with the fracture surfaces exposed.
the outside edge of the DRJ insert. The delamination originating at site (1) grew stably until reaching the DRJ structural insert, as shown in Fig. 3b. Final failure occurred shortly thereafter, with the two delaminations unstably propagating inward and the facesheet pulling out from between the external doubler and the internal structural insert. The DRJ structural inserts were able to share load with the external doublers and reduce bending near the joint center. As a result, no matrix cracks or delaminations were observed in the
vicinity of the Teflon tape before the joint failure. No crushing of the core or insert web was observed. 3. Progressive damage analysis methods For both the CSJ and DRJ specimens, failure was observed to occur within the joint rather than in the pristine material outside the joint, which is undesirable for optimal strength. Both joints also exhibited multiple sequential failure modes before structural
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failure, originating from different locations. Instances of adhesive failure, matrix cracking, interply delamination, and honeycomb core crushing were visible in the CSJ post-test, as shown in Fig. 3c. Each successive failure mode can redistribute loads in the joint, which can cause stress concentrations in locations not revealed by standard FE analyses. In order to predict and represent each instance of damage, multiple PDA tools are required. Intraply damage is modeled with a CDM approach. Interply delamination and adhesive damage are implemented using cohesive elements. Honeycomb core crushing is modeled using a specialized onedimensional damage model.
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a result of crushing under compressive normal loads [16]. This damage model separates the compressive normal response of a honeycomb material into three parts: (1) the initial linear-elastic response, characterized by the Young's modulus; (2) the crushing of the core, during which the material has a negative tangent stiffness; and (3) post-crushed response, characterized by a significantly reduced modulus. In addition, the core crush damage model is capable of representing the unloading/reloading response of either a partially or fully crushed material. This damage model represents only the normal response of the core, neglecting the transverse shear response of the core.
3.1. Cohesive zone modeling 4. Finite element models Cohesive elements are specialized nonlinear finite elements that are designed to predict the initiation and evolution of cracks when the potential propagation paths are known a priori, e.g., Turon et al. [1]. Layers of zero-thickness cohesive elements were used between all plies of different orientations to account for potential delaminations in the bonded joint models. The constitutive response of cohesive elements is defined in terms of local traction versus crack opening displacement. Prior to the prediction of damage initiation, a high cohesive penalty stiffness keeps the crack surfaces closed. Upon satisfying a failure criterion, the stiffness properties of the element soften with further deformation until the element completely fails. The crack opening displacements corresponding to damage initiation and complete failure are dependent on the mode I and mode II strengths and fracture toughness values, as well as the local mode mixity. No inplane loads are carried by cohesive elements. 3.2. Continuum damage mechanics Continuum damage mechanics is a PDA method that allows for the prediction of damage initiation and evolution without modifying the original finite element mesh. Rather than modeling cracks by the direct insertion of discrete discontinuities into the original finite element mesh, CDM approaches represent the effects of cracks by softening certain components of the constitutive stiffness tensor. Different damage modes are accounted for with a set of scalar damage state variables. After the initiation of damage, the affected stiffness terms are softened according to relevant fracture toughness properties and the local characteristic element size. As a result, in order to accurately predict the initial linear elastic response, the initiation of damage, and the evolution of damage, it is necessary to have a set of material property data including the elastic moduli, strengths and fracture toughness values for each potential failure mechanism. The LaRC03 [14] failure criteria were used for the CDM model predictions. LaRC03 consists of stress-based analytical equations that predict the onset of failure mechanisms such as matrix cracking, fiber fracture, and fiber kinking. The prediction of damage evolution was implemented through an updated version of the CDM approach originally proposed by Maimí et al. [7,8]. The improvements to the CDM approach that are relevant to this work include: (1) an extension of failure criteria to account for threedimensional stress states, as well as extensions to the corresponding damage evolution laws and stiffness tensor degradation algorithms, and (2) the development of a mixed-mode matrix damage evolution law [15]. 3.3. Honeycomb core damage model A new user-written one-dimensional damage model was developed to represent the loss of stiffness of a honeycomb core as
The finite element models of the joint specimens were solved using Abaqus/Explicit [20]. User-written subroutines were used to define the constitutive responses of carbon/epoxy plies and the honeycomb core material. Elements were not removed after failing. Both the CSJ and DRJ FE models are defined parametrically to enable the efficient analysis of different joint configurations. Model dimensions, such as the length of the external doublers, the length/ presence of the Teflon tape, the thicknesses of the plies and the adhesive, the locations of the ply terminations, and the length of the ply drops can be easily changed as desired. Each ply in the facesheets and doublers is represented with a single layer of 3D solid elements through the thickness. The in-plane element size is set to be approximately equal to the ply thickness. Layers of zerothickness cohesive elements are located between all plies of different orientations. The honeycomb core is represented by a layer of two-node T3D2 truss elements, oriented normal to the facesheet. The adhesive layers are modeled using finite-thickness COH3D8 cohesive elements. The Teflon tape near the joint gap is represented by setting the strength and fracture toughness properties of the adhesive elements in the span of the Teflon to negligibly low values, which causes them to fail early in the analyses. The CSJ FE mesh is shown in Fig. 4a. The DRJ model expands on the parametric definition of the CSJ model. The honeycomb sandwich and exterior doublers of the DRJ and CSJ specimens are identical, and, as a result, only the removal of the inner 50.8 mm of the honeycomb core truss elements from the CSJ model is required to accommodate the DRJ inserts. It was assumed that no significant damage would develop in the DRJ inserts. The inserts are modeled with S4R shell elements with linear elastic stiffness properties and are not capable of accounting for damage. The layer of adhesive connecting the DRJ inserts to the interior surface of the facesheets is modeled with COH3D8 cohesive elements. The shell elements representing the DRJ inserts are tied to the bottom surface of the cohesive elements that represent the adhesive. The DRJ FE mesh is shown in Fig. 4b. To account for the residual thermal strains caused by the cooling of the specimen after curing, the models were solved in two steps: the first step accounts for the thermal contraction that follows the curing process, and the second step consists of tensile mechanical load application. Thermal contraction in the joints is modeled in a single simplified step by applying a temperature difference of 152 C uniformly throughout the model volume. Because the model is held at a uniform temperature at all times, no heat transfer is modeled. In the second step, the applied temperature difference is held, and tensile mechanical loads are applied by uniformly displacing the nodes on outer face of the facesheet in the þx1-direction. Two planes of symmetry are assumed: one at the joint center, and one through the center of the honeycomb core. It is assumed that there is no gap between the two sandwich panels at the joint center in the models.
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Fig. 4. FE meshes for the (a) conventional splice joint and (b) durable redundant joint.
To reduce the number of required explicit solution increments, the loading and cooling rates were selected to be as fast as possible without inducing any significant dynamic forces. The temperature difference (in step 1) and the displacement (in step 2) were applied sinusoidally to reduce any accelerations applied to the models. Variable mass scaling was used to decrease the solution time by increasing the minimum stable time increment to 2.e07 s throughout the models. Mass scaling factors were updated every 500 solution increments. To reduce the analysis times, a nearly two-dimensional state of damage was assumed, and the CSJ and DRJ models were therefore solved with reduced widths of 1.52 mm and 2.48 mm, respectively. Only 101.6 mm along the length of the quarter-specimen are modeled. Therefore, a relatively uniform strain state is assumed to be present away from the end of the doubler. Due to the reduced dimensions of the models, it was necessary to scale-up the loads and displacements for comparison with the experimental results. The loads in the models were increased by scale factors equal to the ratio of the width of the full specimen to the width of the model and accounting for the quarter symmetry of the models. To obtain model displacements that can be compared to the experimental applied displacements, it was necessary to take into account the displacement along the span of the specimen that was not modeled. This additional displacement is a function of the reaction load, the length not included in the model, the laminate stiffness, and the cross-sectional area of the laminate. The ply material properties for the carbon/epoxy facesheets and doublers are shown in Table 1. The elastic, thermal, and strength properties were provided by The Boeing Company [13]. The mode I and mode II matrix fracture toughness properties, GIc and GIIc, and the Benzeggagh-Kenane exponent h, are those of IM7/977-2 [17]. These properties are used for the prediction of matrix cracking and delaminations. Due to a lack of available fiber fracture toughness properties for IM7/977-2, properties from material system using the same fibers and a similar toughened epoxy matrix, IM7/8552, are used [18,19]. A thorough characterization study of FM-300M film adhesive was conducted by Girolamo [21]. The adhesive was found to exhibit nonlinear hardening and softening behaviors prior to complete failure. This nonlinear response is represented in the model by
Table 1 TE-1 Grade 190 Type 35 Carbon/Epoxy tape material properties. Elastic properties 142.0 7.8 7.8 4.0 4.0 2.8 0.34 0.34 0.40
GPa GPa GPa GPa GPa GPa
3.60e8 3.24e5 3.24e5
/ C / C / C
2606. 1682. 72.4 116. 112. 299.
MPa MPa MPa MPa MPa MPa
146.7 106.3 0.26 1.40 1.4 2.33
N/mm N/mm N/mm N/mm
E11 E22 E33 G12 G13 G23
n12 n13 n23
Thermal properties
a11 a22 a33 Strength properties XT XC YT SL ST b YC Fracture properties GXTa GXCa GIcc GIIcc
hc
GYCb a b c
N/mm
IM7/8552 properties [18,19]. Calculated. IM7/977-2 properties [17].
using two superposed layers of finite-thickness cohesive elements. The material properties for the two layers of cohesive elements are listed in Table 2. The aluminum honeycomb material has a compressive normal modulus and strength of 517 MPa and 2 MPa, respectively, according to the manufacturer. A post-crush characterization of the honeycomb material used here was not available. As a result, it is assumed to behave similarly to the core characterized by Ratcliffe
F.A. Leone et al. / Composites Part B 77 (2015) 474e483 Table 2 FM-300M material properties. Elastic properties KI-A KII-A KI-B KII-B
N/mm3 N/mm3 N/mm3 N/mm3
23,823 2000 444 200
Strength properties
sI-A sII-A sI-B sII-B
71. 46. 9. 22.
MPa MPa MPa MPa
0.70 3.50 0.55 7.79 2.6 2.2
N/mm N/mm N/mm N/mm
Fracture properties GIc-A GIIc-A GIc-B GIIc-B
hA hB
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the termination of the last 0 doubler ply at 40 kN applied load (not shown), and (2) in the bottom þ60 ply of the doubler near the end of the Teflon tape at 45 kN applied load, shown in Fig. 6. These cracks initially have no effect on the global load-displacement response. The bending of the facesheet near the end of the Teflon tape causes compressive loads in the honeycomb core in excess of its strength. At an applied load of 78 kN, the two rows of cells closest to the joint center in the model become crushed, as illustrated in Fig. 6a. Widespread matrix cracking is predicted to begin outside the joint area at 79 kN. At 123 kN, þ60 /0 delaminations develop at the locations of the two initial þ60 matrix cracks. The delamination originating from site (2) is shown in Fig. 6b. The delaminations at sites (1) and (2) are approximately 1.3 mm long at this load level. The delaminations at each location grow stably until unstable delamination propagation occurs at a predicted peak load of 125 kN, as shown in Fig. 6c. The matrix and adhesive are predicted to crack where the two delaminations meet. 5.2. Durable redundant joint
et al. [16]. It is assumed that after exceeding its compressive strength, the core crushes and the reaction load drops by half at 0.8% deformation. Further compression of the core causes the load to increase with a tangent stiffness of one percent of the elastic stiffness. 5. Comparison of experimental and model results 5.1. Conventional splice joint The predicted load-displacement curve for the CSJ tension specimen is shown in Fig. 5a. The predicted peak load of the CSJ specimen is 125 kN, compared to the experimentally observed strengths of 109 and 113 kN. Prior to the predicted failure of the specimen, several instances of localized damage development occur in the model. At 15 kN applied load, prior to the prediction of any intraply or interply cracks, the adhesive begins to soften immediately ahead of the Teflon tape. The softening of the adhesive is a very gradual process due to the high fracture toughness determined during the material characterization work [21]. No appreciable loss of structural stiffness occurs due to the initial softening of the adhesive, as can be observed in Fig. 5a. Localized matrix cracking is predicted to occur initially at two sites in the CSJ model: (1) in the top þ60 ply of the facesheet near
The predicted load-displacement curve for the DRJ tension specimen is shown in Fig. 5b. The predicted peak load of the DRJ specimen is 139 kN, compared to the experimentally observed strengths of 140 and 130 kN. Intraply matrix cracks are predicted to form initially at two sites in the facesheet: (1) in the top þ60 ply of the facesheet near the termination of the last 0 doubler ply, and (2) in the bottom þ60 ply of the facesheet near the outside edge of the DRJ structural insert. These two cracks form at 40 and 61 kN, respectively. Cracks originating at these two locations were observed experimentally, as shown in Fig. 3b. Softening of the adhesive at sites (1) and (2) is predicted to begin at low loads, but the softened regions do not grow to a significant length before matrix cracking is predicted. Widespread matrix cracking is predicted to begin outside the joint area in the facesheet at 77 kN applied load. A delamination between the þ60 and 0 plies of the facesheet forms at site (1) at 90 kN applied load, as shown in Fig. 7a. At this load, the region of softened adhesive extends 1.0 mm from site (1) and 0.8 mm from site (2). This delamination propagates toward the joint center until reaching an approximate length of 1.5 mm at the predicted peak load of 139 kN, as shown in Fig. 7b. After reaching the peak load, damage propagates inward toward the Teflon tape (i.e., to the left in Fig. 7c) from both sites (1) and (2). These two damage fronts are predicted to link up with the Teflon tape, at which point the facesheet completely separates from the inner and
Fig. 5. Load-displacement plots of the (a) CSJ and (b) DRJ.
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Fig. 6. Schematic representation of the predicted failure process for CSJ. The adhesive, delamination, matrix, and core damage locations are shown superposed on the deformed model results.
Fig. 7. Schematic representation of the predicted failure process for DRJ. The adhesive, delamination, matrix, and core damage locations are shown superposed on the deformed model results.
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The good correlation between the observed and predicted failure loads and failure mechanisms in the CSJ and DRJ panels provides an indication of validity of the PDA model. Therefore, this model can be used with relative confidence to explore the design space of the joints and search for design improvements. Two studies are conducted herein. The first examines the effect of the length of the Teflon tape on the joint strength of the CSJ. The second study investigates the effect of the length of the external doubler of the DRJ.
mechanism is insensitive to the occurrence of adhesive softening, and further increases in the length of the Teflon tape do not improve the predicted CSJ performance. The 25.4-mm insert model also predicts failure at a peak load of 138 kN, though failure is predicted to occur via þ60 /0 delamination originating near the outer 0 ply terminationdthe same mechanism observed experimentally for the tested DRJ specimens. By increasing the length of the embedded Teflon tape at the joint center, the CSJ model is predicted to transition from exhibiting the experimentally observed sequence of failures in the CSJ specimen to that which was observed experimentally for the DRJ specimen. Increasing the length of the Teflon tape from 12.7 mm to 19.1 mm amounts to an 11% increase in predicted structural strength with a negligible increase in structural weight.
6.1. Case study on CSJ Teflon tape length
6.2. Case study on DRJ external doubler length
A computational study was conducted on the effect of changing the length of the Teflon tape in the CSJ models on the predicted strength and failure mechanisms when subjected to tensile loading. The length of the Teflon tape in the CSJ model was increased in 6.4mm increments from 0.0 to 25.4 mm. All other material properties and configuration details were kept constant. The loaddisplacement results of this study are shown in Fig. 8. For models with insert lengths less than 12.7 mm, the predicted failure mechanism remains unchanged from the tested configuration: unstable þ60 /0 delamination propagation from the center of the joint, preceded by matrix cracking and core crushing. Fig. 8 shows that the predicted peak loads for the 0.0-, 6.4-, and 12.7mm configurations were 114, 118, and 125 kN, respectively. This trend of increasing peak load with increasing Teflon tape length is related to the development of longer fracture process zones in the adhesive for the configurations with longer lengths of Teflon. A longer process zone decreases the severity of the stress concentration in the þ60 /0 interface of the doubler by transferring load from the facesheet to the doubler more gradually. Longer Teflon inserts cause more severe stress concentrations in the adhesive, which causes longer process zones to develop and delays the onset of matrix cracking and interply delamination in the doubler. While the peak þ60 /0 interlaminar stresses in the doubler decrease as the fracture process zone of the adhesive develops, the eccentricity of the load path continues to causes a stress concentration in the bottom 0 ply of the doubler. For the 19.1-mm insert, fiber fracture is predicted in the bottom 0 ply of the doubler near the end of the Teflon tape at 138 kN applied load. This failure
Ideally, a joint in a structure is as strong as the pristine components being joined. That is, the joint should be designed so that failure of the virgin material outside the span of the joint coincides with failure in the joint. For both the CSJ and DRJ test specimens, however, failure was observed to occur within the span of the joint. For the CSJ concept, whether failure originates near the joint center, as was experimentally observed, or at the doubler ply terminations, as is predicted to occur with longer Teflon tape lengths, it is the eccentricity of the load path in the facesheet/doubler combination that leads to premature failure. Because the facesheets of the DRJ concept are supported both internally and externally, it was thought that design changes to the DRJ that reduce local bending in the facesheets would improve the joint performance. A computational study was conducted on the effect of changing the external doubler length on the predicted strength and failure mechanisms of the DRJ concept when subjected to tensile loading. The length of the doubler was increased in 12.7-mm increments from 88.9 to 165.1 mm. All other material properties and geometries were kept constant. The predicted failure loads for each of the cases analyzed are shown in Fig. 9a. It was found that lengths of the external doublers shorter than the tested configuration yield higher predicted peak loads. The predicted peak load of 166 kN for the model with the shorter 114.2mm doubler was 19% higher than the tested configuration with the 139.7-mm doubler, while the weight was decreased by approximately 3% for the model with the shorter doubler. As the distance between the outer edge of the doubler and the outer edge of the structural insert decreases, less bending occurs within the
outer doublers. The predicted sequence of failures agrees with the final damage state of the DRJ specimens. 6. Discussion
Fig. 8. The predicted CSJ peak loads and failure mechanisms for various Teflon tape lengths.
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Fig. 9. (a) The predicted DRJ peak load and failure mechanism change with doubler length. Shorter doublers yield far-field fiber fracture while longer doublers yield bendinginduced delaminations at lower peak loads. (b) The load corresponding to adhesive softening is generally constant for the modeled DRJ doubler lengths.
facesheet, delaying the onset of unstable interply delamination. When the edges of the doubler and the structural insert are in close proximity, facesheet bending is sufficiently reduced so as to change the predicted failure mechanism to far-field fiber fracture outside the joint area. The trend of increasing structural strength with decreasing doubler length between the 114.3-mm and 139.7-mm cases is shown in Fig. 9a. An increase in the length of the doubler beyond 139.7 mm causes a small decrease in the predicted peak load, down to a steady-state minimum of 134 kN, where further increases in doubler length do not affect the peak load. For doubler lengths longer than 152.4 mm, the presence of the structural insert does not affect the facesheet bending, and no gains are to be had from installing longer external doublers. The trend of shorter external doubler lengths yielding higher joint strengths is not evident if PDA tools are not applied. For example, if the initial softening of the adhesive is used as a criterion for failure prediction, a slight increasing trend of load versus doubler length is observed, shown in Fig. 9bdopposite the trend predicted via PDA. Similar trends that do not agree with the PDA peak load results were attained when using other individual failure mode predictions as indicators of joint strength (not shown). Without utilizing PDA tools that can predict all major damage modes and their interactions, a designer runs the risk of either not finding the optimal solution or errantly being guided toward a solution that will perform worse in terms of overall structural strength. 7. Conclusions Progressive damage finite element analyses were conducted for two composite sandwich adhesively bonded joint designs to predict the load-displacement response and failure mechanism(s) and to compare the results with experimental results. The two joint designs evaluated consist of a conventional composite splice joint (CSJ) and a Durable Redundant Joint (DRJ) design. A series of experiments were conducted to determine strength and failure mechanism for each joint design. One of the major driving forces behind the development and application of new progressive damage analysis methods is the potential reduction of the experimental testing required to validate and optimize new structures and systems. By developing a sufficiently fine model and experimentally validating it for bounding cases, intermediate values of design parameters can be evaluated quickly and efficiently. For the joint designs considered herein, two separate multi-mode failure sequences were observed experimentally and predicted accurately using a combination of
advanced progressive damage analysis tools. The effects of changing certain design features of the joints were explored, with attention paid to the predicted joint peak loads and associated failure mechanisms. Using PDA as a design tool, potential increases in joint failure load of 11% and 19% were identified for the CSJ and DRJ designs, respectively, without requiring any appreciable increase in the weight of the joints. Similar applications of PDA tools and methodologies within the design process of advanced composite structures have the potential to significantly reduce testing and lead to innovative structural concepts and configurations.
References vila CG. A damage model for the simulation [1] Turon A, Camanho PP, Costa J, Da of delamination in advanced composites under variable-mode loading. Mech Mater 2006;38:1072e89. [2] Nguyen VP, Kerfriden P, Bordas SPA. Two- and three-dimensional isogeometric cohesive elements for composite delamination analysis. Compos Part B 2014;60:193e212. [3] Airoldi A, Baldi A, Bettini P, Sara G. Efficient modelling of forces and local strain evolution during delamination of composite laminates. Compos Part B 2015;72:137e49. [4] Matzenmiller A, Lubliner J, Tayler RL. A constitutive model for anisotropic damage in fiber-composites. Mech Mater 1995;20:125e52. [5] Barbero EJ, Lonetti P, Sikkil KK. Finite element continuum damage modeling of plain weave reinforced composites. Compos Part B 2006;37:137e47. [6] Lapcyzyk I, Hurtado JA. Progressive damage modeling in fiber-reinforced materials. Compos Part A 2007;38:2333e41. vila CG. A continuum damage model for [7] Maimí P, Camanho PP, Mayugo JA, Da composite laminates: part I e constitutive model. Mech Mater 2007;39: 897e908. vila CG. A continuum damage model for [8] Maimí P, Camanho PP, Mayugo JA, Da composite laminates: part II e computational implementation and validation. Mech Mater 2007;39:909e19. vila CG, Leone FA. Analysis methods for progressive damage of [9] Rose CA, Da composite structures. NASA/TMe2013-218024. [10] Leone FA, D avila CG, Girolamo D. Progressive damage analysis of bonded composite joints. NASA/TMe2012-217790. [11] Lin S-Y, Splinter SC, Tarkenton C, Paddock DA, Smeltzer SS, Ghose S, et al. Fabrication and testing of durable redundant and flute-core joints for composite sandwich structures. SAMPE 2013 Conference. Long Beach, CA May, 2013. [12] Smeltzer SS, Lundgren EC. (2014) Systems, apparatuses, and methods for using durable adhesively bonded joints for sandwich structures. Patent US 8,697,216 B2. Washington, DC: U.S. Patent and Trademark Office. [13] Ghose S. The Boeing Company. 2012 [Personal communication]. vila CG, Camanho PP. Failure criteria for FRP laminates in plane stress. [14] Da NASA/TMe2003-212663. vila CG. Mixed-mode matrix damage evolution in continuum [15] Leone FA, Da damage mechanics. In: 16th international conference on composite structures. Porto, Portugal; June, 2011. [16] Ratcliffe JG, Czabaj MW, Jackson WC. A model for simulating the response of aluminum honeycomb structure to transverse loading. In: 2012 American society for composites 27th technical conference; 15th
F.A. Leone et al. / Composites Part B 77 (2015) 474e483 US-Japan conference on composite materials meeting. Arlington, VA; October, 2012. [17] Reeder JR. 3D mixed-mode delamination fracture criteriaean experimentalist's perspective. In: 21st annual technical conference of the American society for composites. Dearborn, MI; September, 2006. [18] Camanho PP, Maimí P, D avila CG. Prediction of size effects in notched laminates using continuum damage mechanics. Compos Sci Technol 2007;67: 2715e27.
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[19] Catalanotti G, Camanho PP, Xavier J, D avila CG, Marques AT. Measurement of resistance curves in the longitudinal failure of composites using digital image correlation. Compos Sci Technol 2010;70:1986e93. [20] ABAQUS. Abaqus 6.13 online documentation. Providence, RI, USA: Dassault mes; 2013. Syste [21] Girolamo D. Progressive damage analysis of bonded composite joints [Master’s Thesis]. TU Delft; 2012.
Contents lists available at ScienceDirect
Composites Part B journal homepage: www.elsevier.com/locate/compositesb
Progressive damage analysis as a design tool for composite bonded joints vila a, Donato Girolamo b Frank A. Leone a, *, Carlos G. Da a b
NASA Langley Research Center, Hampton, VA, 23681, USA North Carolina State University, Raleigh, NC, 27695, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 April 2014 Received in revised form 11 March 2015 Accepted 14 March 2015 Available online 20 March 2015
This paper discusses the application of progressive damage analysis (PDA) methods as a design tool. Two case studies are presented in which the effects of changing design features on the strength of bonded composite joints are evaluated. It is shown that the trends of parametric evaluations performed with fullfeatured PDA models can be unintuitive and the trends can be opposite to those obtained with traditional design criteria. The joint configurations that were tested exhibit multiple damage modes, requiring several different PDA tools to accurately predict the structural peak loads. For damage tolerant structures that exhibit complex sequences of multiple failure mechanisms, traditional failure prediction tools are insufficient. Parametric PDA models encompassing a bonded joint specimen's design space have the potential to reveal unintuitive and advantageous design changes. Published by Elsevier Ltd.
Keywords: C. Finite element analysis (FEA) B. Adhesion A. Honeycomb D. Mechanical testing
1. Introduction Fiber-reinforced polymer laminates can exhibit several failure mechanisms, including fiber fracture, matrix cracking, delamination, etc. The first predicted occurrence of one of these failure mechanisms typically does not coincide with structural failure, especially for structures that have been designed according to damage tolerance requirements. Often, structural failure is the result of several different damage mechanisms joining together, progressing from a series of stable and/or locally unstable failure processes up to a globally unstable failure process. For structures whose collapse is preceded by a sequence of different interacting damage mechanisms, the structural strength can be significantly higher than the load that corresponds to the first instance of damage. Failing to take into account the effects of non-critical damage on a structure's ability to carry higher loads can lead to overly conservative structures. In order to accurately predict the strength of a composite structure, it is necessary to predict both the formation of all relevant failure mechanisms and the effects that those failures have on load redistribution. Progressive damage analysis (PDA) is a broad label applied to several modeling approaches that allow for the prediction of the
* Corresponding author. E-mail address: [email protected] (F.A. Leone). http://dx.doi.org/10.1016/j.compositesb.2015.03.046 1359-8368/Published by Elsevier Ltd.
initiation and evolution of damage. The development and application of PDA tools to advanced composite materials and structures is an active field of research, with several branching technologies that are intended to predict different composite failure mechanisms. Cohesive elements (e.g., [1e3]), for example, excel at discretely representing the formation and evolution of cracks in the finite element (FE) framework when the locations and orientations of cracks are known a priori (e.g., delaminations). Continuum damage mechanics (CDM) methods (e.g., [4e8]), rather than discretely representing cracks, represent the presence of various failure mechanisms by changing terms of the local material compliance tensor. CDM-based methods work without having prior knowledge of either the location or orientation of the damage. All PDA methods, however, have multiple strengths and technical limitations in their current state [9]. Having a proper understanding of the capabilities of each method is crucial to selecting the right tool(s) for any given progressive damage modeling application. Often, it is a combination of damage modeling techniques that is required to properly model the initiation and progression of a structural failure process, especially in structures composed of multiple advanced composite materials. In this paper, the structural response and damage mechanisms of two bonded composite joint concepts from a previous test and analysis campaign are presented [10]. It was observed that several different mechanisms contributed to the eventual failure of the specimens, and that the load at which damage was initially
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observed was well below the structural strength. A combination of PDA tools was used to model the observed sequences of damage events, and good agreement in terms of peak load and failure mode sequence was attained. Utilizing parametric FE models, it is herein attempted to improve upon the designs of the tested bonded composite joint concepts. Two case studies exploring the integration of PDA methods into the design process are presented. Performing parametric analyses with integrated PDA tools has the potential to yield significantly more efficient designs, to reveal advantageous, unintuitive design improvements, and to reduce the number of physical experiments required to identify optimal configurations.
2. Background 2.1. Test specimens The development of durable bonded joint technology for assembling composite structures for launch vehicles is an essential component of NASA's Space Launch System. Several joint designs intended for lightly-loaded minimum-gauge space structures were tested in tension, compression, and four-point bending as part of an experimental test campaign at NASA Langley Research Center [11]. Two joint designs from this test campaign are discussed in this paper: a conventional splice joint (CSJ) and a new Durable Redundant Joint (DRJ) concept [12]. Each design involves a honeycomb core with carbon/epoxy facesheets joined with adhesively bonded carbon/epoxy doublers. The data considered in this paper is limited to tensile loading cases. The sandwich panels used in this study are composed of six-ply carbon/epoxy facesheets and a 25.4-mm-thick Hexcel CRIII-1/85052-.0007P-3.1 aluminum honeycomb core. The facesheet material is made of grade 190 TE-1 tapes (toughened epoxy/T800) [13]. The stacking sequence of the facesheets is [þ60/0/60]S, with the 0 fiber direction aligned with the specimen length. The facesheet plies have a nominal thickness of 0.19 mm. The CSJ specimens measure 559 mm long and 76.2 mm wide and consist of two sandwich panels joined by two 139.7-mm-long, six-ply doublers bonded to the exterior faces of the sandwich with Cytec FM-300M film adhesive, as shown in Fig. 1. At their thickest, the doublers have the same stacking sequence as the facesheets. The doublers have internal ply terminations and ply drops, with cascading ply terminations spaced at 6.4-mm intervals from the doubler edges. Design specifications for the joint specimens allow
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for a 2.54-mm gap between the sandwich panels. A 12.7-mm-long Teflon film strip was inserted in-line with the adhesive layer at the joint center to decrease the severity of the stress concentration in the doubler at that location. The DRJ concept expands upon the CSJ design by adding a 96.5mm-long laminated structural insert in place of honeycomb core at the joint center, as shown in Fig. 2. The insert contains three ±45 hollow, rectangular cells. Six additional plies were laid-up above and below the cells with a stacking sequence of [þ60/0/60]S, with the outermost þ60 ply wrapped around all three hollow cells. The DRJ inserts were bonded to the interior surface of the sandwich facesheets using FM-300M adhesive. The inserts are intended to increase the ability of the joint to withstand impact damage and provide nearly symmetric load paths about the facesheet centerlines. Additional details regarding the CSJ and DRJ concepts, their design, and fabrication can be found in Ref. [11]. 2.2. Experimental test results 2.2.1. Conventional splice joint Two CSJ specimens were loaded in tension to failure. The specimens failed within the joint at peak loads of 109 and 113 kN in similar modes. The first instance of observable damage occurred in the adhesive near the outer edge of the Teflon tape, as shown in Fig. 3a. The asymmetry of the load path in the vicinity of the Teflon tape caused the facesheet to bend away from the Teflon. The bending of the facesheet compressively loaded the core. Because of the light-gauge core used, the two core cells nearest the joint center crushed at approximately two-thirds of the specimen failure load. Without the transverse support of the core beneath the Teflon tape, the facesheet and doubler were free to separate, which induced a mode I loading component of the adhesive and ply interfaces. Since FM-300M adhesive is tougher than the epoxy matrix [10], the delamination transitioned from the adhesive layer to the inner þ60 /0 interface of the doubler, as confirmed by inspection of the fracture surfaces in Fig. 3c. Unstable delamination propagation ensued shortly thereafter. 2.2.2. Durable redundant joint Two DRJ specimens were also loaded in tension to failure. The two DRJ specimens failed at loads of 140 and 130 kN. Failure was observed to initiate as delaminations at two sites in the facesheet: (1) below the outermost doubler 0 ply termination, and (2) above
Fig. 1. Schematic of the conventional splice joint (CSJ) cross section [11].
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Fig. 2. Schematic of the durable redundant joint (DRJ) cross section [11].
Fig. 3. Digital photographs of (a) a CSJ specimen during loading, (b) a DRJ specimen during loading, and (c) a CSJ specimen post-test with the fracture surfaces exposed.
the outside edge of the DRJ insert. The delamination originating at site (1) grew stably until reaching the DRJ structural insert, as shown in Fig. 3b. Final failure occurred shortly thereafter, with the two delaminations unstably propagating inward and the facesheet pulling out from between the external doubler and the internal structural insert. The DRJ structural inserts were able to share load with the external doublers and reduce bending near the joint center. As a result, no matrix cracks or delaminations were observed in the
vicinity of the Teflon tape before the joint failure. No crushing of the core or insert web was observed. 3. Progressive damage analysis methods For both the CSJ and DRJ specimens, failure was observed to occur within the joint rather than in the pristine material outside the joint, which is undesirable for optimal strength. Both joints also exhibited multiple sequential failure modes before structural
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failure, originating from different locations. Instances of adhesive failure, matrix cracking, interply delamination, and honeycomb core crushing were visible in the CSJ post-test, as shown in Fig. 3c. Each successive failure mode can redistribute loads in the joint, which can cause stress concentrations in locations not revealed by standard FE analyses. In order to predict and represent each instance of damage, multiple PDA tools are required. Intraply damage is modeled with a CDM approach. Interply delamination and adhesive damage are implemented using cohesive elements. Honeycomb core crushing is modeled using a specialized onedimensional damage model.
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a result of crushing under compressive normal loads [16]. This damage model separates the compressive normal response of a honeycomb material into three parts: (1) the initial linear-elastic response, characterized by the Young's modulus; (2) the crushing of the core, during which the material has a negative tangent stiffness; and (3) post-crushed response, characterized by a significantly reduced modulus. In addition, the core crush damage model is capable of representing the unloading/reloading response of either a partially or fully crushed material. This damage model represents only the normal response of the core, neglecting the transverse shear response of the core.
3.1. Cohesive zone modeling 4. Finite element models Cohesive elements are specialized nonlinear finite elements that are designed to predict the initiation and evolution of cracks when the potential propagation paths are known a priori, e.g., Turon et al. [1]. Layers of zero-thickness cohesive elements were used between all plies of different orientations to account for potential delaminations in the bonded joint models. The constitutive response of cohesive elements is defined in terms of local traction versus crack opening displacement. Prior to the prediction of damage initiation, a high cohesive penalty stiffness keeps the crack surfaces closed. Upon satisfying a failure criterion, the stiffness properties of the element soften with further deformation until the element completely fails. The crack opening displacements corresponding to damage initiation and complete failure are dependent on the mode I and mode II strengths and fracture toughness values, as well as the local mode mixity. No inplane loads are carried by cohesive elements. 3.2. Continuum damage mechanics Continuum damage mechanics is a PDA method that allows for the prediction of damage initiation and evolution without modifying the original finite element mesh. Rather than modeling cracks by the direct insertion of discrete discontinuities into the original finite element mesh, CDM approaches represent the effects of cracks by softening certain components of the constitutive stiffness tensor. Different damage modes are accounted for with a set of scalar damage state variables. After the initiation of damage, the affected stiffness terms are softened according to relevant fracture toughness properties and the local characteristic element size. As a result, in order to accurately predict the initial linear elastic response, the initiation of damage, and the evolution of damage, it is necessary to have a set of material property data including the elastic moduli, strengths and fracture toughness values for each potential failure mechanism. The LaRC03 [14] failure criteria were used for the CDM model predictions. LaRC03 consists of stress-based analytical equations that predict the onset of failure mechanisms such as matrix cracking, fiber fracture, and fiber kinking. The prediction of damage evolution was implemented through an updated version of the CDM approach originally proposed by Maimí et al. [7,8]. The improvements to the CDM approach that are relevant to this work include: (1) an extension of failure criteria to account for threedimensional stress states, as well as extensions to the corresponding damage evolution laws and stiffness tensor degradation algorithms, and (2) the development of a mixed-mode matrix damage evolution law [15]. 3.3. Honeycomb core damage model A new user-written one-dimensional damage model was developed to represent the loss of stiffness of a honeycomb core as
The finite element models of the joint specimens were solved using Abaqus/Explicit [20]. User-written subroutines were used to define the constitutive responses of carbon/epoxy plies and the honeycomb core material. Elements were not removed after failing. Both the CSJ and DRJ FE models are defined parametrically to enable the efficient analysis of different joint configurations. Model dimensions, such as the length of the external doublers, the length/ presence of the Teflon tape, the thicknesses of the plies and the adhesive, the locations of the ply terminations, and the length of the ply drops can be easily changed as desired. Each ply in the facesheets and doublers is represented with a single layer of 3D solid elements through the thickness. The in-plane element size is set to be approximately equal to the ply thickness. Layers of zerothickness cohesive elements are located between all plies of different orientations. The honeycomb core is represented by a layer of two-node T3D2 truss elements, oriented normal to the facesheet. The adhesive layers are modeled using finite-thickness COH3D8 cohesive elements. The Teflon tape near the joint gap is represented by setting the strength and fracture toughness properties of the adhesive elements in the span of the Teflon to negligibly low values, which causes them to fail early in the analyses. The CSJ FE mesh is shown in Fig. 4a. The DRJ model expands on the parametric definition of the CSJ model. The honeycomb sandwich and exterior doublers of the DRJ and CSJ specimens are identical, and, as a result, only the removal of the inner 50.8 mm of the honeycomb core truss elements from the CSJ model is required to accommodate the DRJ inserts. It was assumed that no significant damage would develop in the DRJ inserts. The inserts are modeled with S4R shell elements with linear elastic stiffness properties and are not capable of accounting for damage. The layer of adhesive connecting the DRJ inserts to the interior surface of the facesheets is modeled with COH3D8 cohesive elements. The shell elements representing the DRJ inserts are tied to the bottom surface of the cohesive elements that represent the adhesive. The DRJ FE mesh is shown in Fig. 4b. To account for the residual thermal strains caused by the cooling of the specimen after curing, the models were solved in two steps: the first step accounts for the thermal contraction that follows the curing process, and the second step consists of tensile mechanical load application. Thermal contraction in the joints is modeled in a single simplified step by applying a temperature difference of 152 C uniformly throughout the model volume. Because the model is held at a uniform temperature at all times, no heat transfer is modeled. In the second step, the applied temperature difference is held, and tensile mechanical loads are applied by uniformly displacing the nodes on outer face of the facesheet in the þx1-direction. Two planes of symmetry are assumed: one at the joint center, and one through the center of the honeycomb core. It is assumed that there is no gap between the two sandwich panels at the joint center in the models.
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Fig. 4. FE meshes for the (a) conventional splice joint and (b) durable redundant joint.
To reduce the number of required explicit solution increments, the loading and cooling rates were selected to be as fast as possible without inducing any significant dynamic forces. The temperature difference (in step 1) and the displacement (in step 2) were applied sinusoidally to reduce any accelerations applied to the models. Variable mass scaling was used to decrease the solution time by increasing the minimum stable time increment to 2.e07 s throughout the models. Mass scaling factors were updated every 500 solution increments. To reduce the analysis times, a nearly two-dimensional state of damage was assumed, and the CSJ and DRJ models were therefore solved with reduced widths of 1.52 mm and 2.48 mm, respectively. Only 101.6 mm along the length of the quarter-specimen are modeled. Therefore, a relatively uniform strain state is assumed to be present away from the end of the doubler. Due to the reduced dimensions of the models, it was necessary to scale-up the loads and displacements for comparison with the experimental results. The loads in the models were increased by scale factors equal to the ratio of the width of the full specimen to the width of the model and accounting for the quarter symmetry of the models. To obtain model displacements that can be compared to the experimental applied displacements, it was necessary to take into account the displacement along the span of the specimen that was not modeled. This additional displacement is a function of the reaction load, the length not included in the model, the laminate stiffness, and the cross-sectional area of the laminate. The ply material properties for the carbon/epoxy facesheets and doublers are shown in Table 1. The elastic, thermal, and strength properties were provided by The Boeing Company [13]. The mode I and mode II matrix fracture toughness properties, GIc and GIIc, and the Benzeggagh-Kenane exponent h, are those of IM7/977-2 [17]. These properties are used for the prediction of matrix cracking and delaminations. Due to a lack of available fiber fracture toughness properties for IM7/977-2, properties from material system using the same fibers and a similar toughened epoxy matrix, IM7/8552, are used [18,19]. A thorough characterization study of FM-300M film adhesive was conducted by Girolamo [21]. The adhesive was found to exhibit nonlinear hardening and softening behaviors prior to complete failure. This nonlinear response is represented in the model by
Table 1 TE-1 Grade 190 Type 35 Carbon/Epoxy tape material properties. Elastic properties 142.0 7.8 7.8 4.0 4.0 2.8 0.34 0.34 0.40
GPa GPa GPa GPa GPa GPa
3.60e8 3.24e5 3.24e5
/ C / C / C
2606. 1682. 72.4 116. 112. 299.
MPa MPa MPa MPa MPa MPa
146.7 106.3 0.26 1.40 1.4 2.33
N/mm N/mm N/mm N/mm
E11 E22 E33 G12 G13 G23
n12 n13 n23
Thermal properties
a11 a22 a33 Strength properties XT XC YT SL ST b YC Fracture properties GXTa GXCa GIcc GIIcc
hc
GYCb a b c
N/mm
IM7/8552 properties [18,19]. Calculated. IM7/977-2 properties [17].
using two superposed layers of finite-thickness cohesive elements. The material properties for the two layers of cohesive elements are listed in Table 2. The aluminum honeycomb material has a compressive normal modulus and strength of 517 MPa and 2 MPa, respectively, according to the manufacturer. A post-crush characterization of the honeycomb material used here was not available. As a result, it is assumed to behave similarly to the core characterized by Ratcliffe
F.A. Leone et al. / Composites Part B 77 (2015) 474e483 Table 2 FM-300M material properties. Elastic properties KI-A KII-A KI-B KII-B
N/mm3 N/mm3 N/mm3 N/mm3
23,823 2000 444 200
Strength properties
sI-A sII-A sI-B sII-B
71. 46. 9. 22.
MPa MPa MPa MPa
0.70 3.50 0.55 7.79 2.6 2.2
N/mm N/mm N/mm N/mm
Fracture properties GIc-A GIIc-A GIc-B GIIc-B
hA hB
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the termination of the last 0 doubler ply at 40 kN applied load (not shown), and (2) in the bottom þ60 ply of the doubler near the end of the Teflon tape at 45 kN applied load, shown in Fig. 6. These cracks initially have no effect on the global load-displacement response. The bending of the facesheet near the end of the Teflon tape causes compressive loads in the honeycomb core in excess of its strength. At an applied load of 78 kN, the two rows of cells closest to the joint center in the model become crushed, as illustrated in Fig. 6a. Widespread matrix cracking is predicted to begin outside the joint area at 79 kN. At 123 kN, þ60 /0 delaminations develop at the locations of the two initial þ60 matrix cracks. The delamination originating from site (2) is shown in Fig. 6b. The delaminations at sites (1) and (2) are approximately 1.3 mm long at this load level. The delaminations at each location grow stably until unstable delamination propagation occurs at a predicted peak load of 125 kN, as shown in Fig. 6c. The matrix and adhesive are predicted to crack where the two delaminations meet. 5.2. Durable redundant joint
et al. [16]. It is assumed that after exceeding its compressive strength, the core crushes and the reaction load drops by half at 0.8% deformation. Further compression of the core causes the load to increase with a tangent stiffness of one percent of the elastic stiffness. 5. Comparison of experimental and model results 5.1. Conventional splice joint The predicted load-displacement curve for the CSJ tension specimen is shown in Fig. 5a. The predicted peak load of the CSJ specimen is 125 kN, compared to the experimentally observed strengths of 109 and 113 kN. Prior to the predicted failure of the specimen, several instances of localized damage development occur in the model. At 15 kN applied load, prior to the prediction of any intraply or interply cracks, the adhesive begins to soften immediately ahead of the Teflon tape. The softening of the adhesive is a very gradual process due to the high fracture toughness determined during the material characterization work [21]. No appreciable loss of structural stiffness occurs due to the initial softening of the adhesive, as can be observed in Fig. 5a. Localized matrix cracking is predicted to occur initially at two sites in the CSJ model: (1) in the top þ60 ply of the facesheet near
The predicted load-displacement curve for the DRJ tension specimen is shown in Fig. 5b. The predicted peak load of the DRJ specimen is 139 kN, compared to the experimentally observed strengths of 140 and 130 kN. Intraply matrix cracks are predicted to form initially at two sites in the facesheet: (1) in the top þ60 ply of the facesheet near the termination of the last 0 doubler ply, and (2) in the bottom þ60 ply of the facesheet near the outside edge of the DRJ structural insert. These two cracks form at 40 and 61 kN, respectively. Cracks originating at these two locations were observed experimentally, as shown in Fig. 3b. Softening of the adhesive at sites (1) and (2) is predicted to begin at low loads, but the softened regions do not grow to a significant length before matrix cracking is predicted. Widespread matrix cracking is predicted to begin outside the joint area in the facesheet at 77 kN applied load. A delamination between the þ60 and 0 plies of the facesheet forms at site (1) at 90 kN applied load, as shown in Fig. 7a. At this load, the region of softened adhesive extends 1.0 mm from site (1) and 0.8 mm from site (2). This delamination propagates toward the joint center until reaching an approximate length of 1.5 mm at the predicted peak load of 139 kN, as shown in Fig. 7b. After reaching the peak load, damage propagates inward toward the Teflon tape (i.e., to the left in Fig. 7c) from both sites (1) and (2). These two damage fronts are predicted to link up with the Teflon tape, at which point the facesheet completely separates from the inner and
Fig. 5. Load-displacement plots of the (a) CSJ and (b) DRJ.
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Fig. 6. Schematic representation of the predicted failure process for CSJ. The adhesive, delamination, matrix, and core damage locations are shown superposed on the deformed model results.
Fig. 7. Schematic representation of the predicted failure process for DRJ. The adhesive, delamination, matrix, and core damage locations are shown superposed on the deformed model results.
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The good correlation between the observed and predicted failure loads and failure mechanisms in the CSJ and DRJ panels provides an indication of validity of the PDA model. Therefore, this model can be used with relative confidence to explore the design space of the joints and search for design improvements. Two studies are conducted herein. The first examines the effect of the length of the Teflon tape on the joint strength of the CSJ. The second study investigates the effect of the length of the external doubler of the DRJ.
mechanism is insensitive to the occurrence of adhesive softening, and further increases in the length of the Teflon tape do not improve the predicted CSJ performance. The 25.4-mm insert model also predicts failure at a peak load of 138 kN, though failure is predicted to occur via þ60 /0 delamination originating near the outer 0 ply terminationdthe same mechanism observed experimentally for the tested DRJ specimens. By increasing the length of the embedded Teflon tape at the joint center, the CSJ model is predicted to transition from exhibiting the experimentally observed sequence of failures in the CSJ specimen to that which was observed experimentally for the DRJ specimen. Increasing the length of the Teflon tape from 12.7 mm to 19.1 mm amounts to an 11% increase in predicted structural strength with a negligible increase in structural weight.
6.1. Case study on CSJ Teflon tape length
6.2. Case study on DRJ external doubler length
A computational study was conducted on the effect of changing the length of the Teflon tape in the CSJ models on the predicted strength and failure mechanisms when subjected to tensile loading. The length of the Teflon tape in the CSJ model was increased in 6.4mm increments from 0.0 to 25.4 mm. All other material properties and configuration details were kept constant. The loaddisplacement results of this study are shown in Fig. 8. For models with insert lengths less than 12.7 mm, the predicted failure mechanism remains unchanged from the tested configuration: unstable þ60 /0 delamination propagation from the center of the joint, preceded by matrix cracking and core crushing. Fig. 8 shows that the predicted peak loads for the 0.0-, 6.4-, and 12.7mm configurations were 114, 118, and 125 kN, respectively. This trend of increasing peak load with increasing Teflon tape length is related to the development of longer fracture process zones in the adhesive for the configurations with longer lengths of Teflon. A longer process zone decreases the severity of the stress concentration in the þ60 /0 interface of the doubler by transferring load from the facesheet to the doubler more gradually. Longer Teflon inserts cause more severe stress concentrations in the adhesive, which causes longer process zones to develop and delays the onset of matrix cracking and interply delamination in the doubler. While the peak þ60 /0 interlaminar stresses in the doubler decrease as the fracture process zone of the adhesive develops, the eccentricity of the load path continues to causes a stress concentration in the bottom 0 ply of the doubler. For the 19.1-mm insert, fiber fracture is predicted in the bottom 0 ply of the doubler near the end of the Teflon tape at 138 kN applied load. This failure
Ideally, a joint in a structure is as strong as the pristine components being joined. That is, the joint should be designed so that failure of the virgin material outside the span of the joint coincides with failure in the joint. For both the CSJ and DRJ test specimens, however, failure was observed to occur within the span of the joint. For the CSJ concept, whether failure originates near the joint center, as was experimentally observed, or at the doubler ply terminations, as is predicted to occur with longer Teflon tape lengths, it is the eccentricity of the load path in the facesheet/doubler combination that leads to premature failure. Because the facesheets of the DRJ concept are supported both internally and externally, it was thought that design changes to the DRJ that reduce local bending in the facesheets would improve the joint performance. A computational study was conducted on the effect of changing the external doubler length on the predicted strength and failure mechanisms of the DRJ concept when subjected to tensile loading. The length of the doubler was increased in 12.7-mm increments from 88.9 to 165.1 mm. All other material properties and geometries were kept constant. The predicted failure loads for each of the cases analyzed are shown in Fig. 9a. It was found that lengths of the external doublers shorter than the tested configuration yield higher predicted peak loads. The predicted peak load of 166 kN for the model with the shorter 114.2mm doubler was 19% higher than the tested configuration with the 139.7-mm doubler, while the weight was decreased by approximately 3% for the model with the shorter doubler. As the distance between the outer edge of the doubler and the outer edge of the structural insert decreases, less bending occurs within the
outer doublers. The predicted sequence of failures agrees with the final damage state of the DRJ specimens. 6. Discussion
Fig. 8. The predicted CSJ peak loads and failure mechanisms for various Teflon tape lengths.
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Fig. 9. (a) The predicted DRJ peak load and failure mechanism change with doubler length. Shorter doublers yield far-field fiber fracture while longer doublers yield bendinginduced delaminations at lower peak loads. (b) The load corresponding to adhesive softening is generally constant for the modeled DRJ doubler lengths.
facesheet, delaying the onset of unstable interply delamination. When the edges of the doubler and the structural insert are in close proximity, facesheet bending is sufficiently reduced so as to change the predicted failure mechanism to far-field fiber fracture outside the joint area. The trend of increasing structural strength with decreasing doubler length between the 114.3-mm and 139.7-mm cases is shown in Fig. 9a. An increase in the length of the doubler beyond 139.7 mm causes a small decrease in the predicted peak load, down to a steady-state minimum of 134 kN, where further increases in doubler length do not affect the peak load. For doubler lengths longer than 152.4 mm, the presence of the structural insert does not affect the facesheet bending, and no gains are to be had from installing longer external doublers. The trend of shorter external doubler lengths yielding higher joint strengths is not evident if PDA tools are not applied. For example, if the initial softening of the adhesive is used as a criterion for failure prediction, a slight increasing trend of load versus doubler length is observed, shown in Fig. 9bdopposite the trend predicted via PDA. Similar trends that do not agree with the PDA peak load results were attained when using other individual failure mode predictions as indicators of joint strength (not shown). Without utilizing PDA tools that can predict all major damage modes and their interactions, a designer runs the risk of either not finding the optimal solution or errantly being guided toward a solution that will perform worse in terms of overall structural strength. 7. Conclusions Progressive damage finite element analyses were conducted for two composite sandwich adhesively bonded joint designs to predict the load-displacement response and failure mechanism(s) and to compare the results with experimental results. The two joint designs evaluated consist of a conventional composite splice joint (CSJ) and a Durable Redundant Joint (DRJ) design. A series of experiments were conducted to determine strength and failure mechanism for each joint design. One of the major driving forces behind the development and application of new progressive damage analysis methods is the potential reduction of the experimental testing required to validate and optimize new structures and systems. By developing a sufficiently fine model and experimentally validating it for bounding cases, intermediate values of design parameters can be evaluated quickly and efficiently. For the joint designs considered herein, two separate multi-mode failure sequences were observed experimentally and predicted accurately using a combination of
advanced progressive damage analysis tools. The effects of changing certain design features of the joints were explored, with attention paid to the predicted joint peak loads and associated failure mechanisms. Using PDA as a design tool, potential increases in joint failure load of 11% and 19% were identified for the CSJ and DRJ designs, respectively, without requiring any appreciable increase in the weight of the joints. Similar applications of PDA tools and methodologies within the design process of advanced composite structures have the potential to significantly reduce testing and lead to innovative structural concepts and configurations.
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