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Abstract

The structural efficiency of composite T-joints is critically dependent on the design features, which minimize the governing stress concentrations and delay failure. This study first analyzes the failure initiation mechanism, and the results show that the regions around the deltoid are the primary areas of stress concentration, resulting in filler debonding and fracture failure. The second part, through Pearson linear correlation coefficient analysis, shows that the L-rib laminate stacking sequence, filler geometry, and filler material are critical design features to delay failure. The final part includes the investigation of five different L-rib laminate stacking sequence designs, revealing that the transverse tensile stiffness (E₂) primarily determines the ultimate load-carrying proficiency in T-joints under tensile pull-out. Premature transverse cracking caused a 68% decrease in strength in a shear-optimized sequence with an insufficient 90° ply content. Conversely, by appropriately optimizing axial, transverse, and shear stiffnesses, a hybrid sequence with ±30° plies produced a superior failure load of 24.3 kN. Furthermore, compliant polyvinyl chloride (PVC) foam filler outperformed stiff carbon/epoxy fillers, reducing interlaminar shear stress by 94% and increasing ultimate strength by 5% by permitting efficient stress redistribution. This study provided new design principles for efficient joint manufacturing under tensile loading.

Keywords

Composite T-joint compliant fillers interlaminar shear stresses damage tolerance shear stiffness

Highlights

• Hierarchical design study of T-joints from load bearing to stress-management.

• Eminence of transverse stiffness (E₂) on ultimate pull-out strength for joints

• L-rib laminate stacking sequence effect on stiffness and load carrying capacity

• PVC Foam filler energy absorption and reduction in interlamianr shear stresses

• Non-linear interaction study between filler and L-rib stacking based on DOE

Introduction

Composite T-joints are commonly used for load transfer in lightweight structures for aerospace, marine, wind energy, and automotive applications. T-joints provide an orthogonal connection between the skins and stiffeners, resulting in high specific stiffness and strength. Nevertheless, the geometric discontinuities at the flange-web intersection, combined with the heterogeneous and anisotropic nature of laminated composites and adhesive interfaces, precipitate complex multi-axial stress states and damage mechanisms, challenging conventional metallic joint design practice.^1–3 The region at the intersection of the web-flange creates a deltoid region, which is often filled with a filler material.^4,5 The filler material is often a point of concern because it determines the load-carrying capacity and often the damage initiation point of debonding and fracture failure.⁶

Out-of-plane loads are the main area of concern when working on these joints, as the weak polymer matrix and fiber matrix interface are the main load-carrying members, which results in debonding or delamination failure.⁷ High stress concentrations, usually transverse normal stress and shear stress at the deltoid region, result in failure initiation.⁸ The complex 3-D geometry of the T-joint, particularly the fillet radius and the transition from the web to the flange, creates a multi-axial stress state that cannot be simplified to 2-D. A 2-D (plane stress or plane strain) analysis makes a critical simplification of the stress components through the thickness (the z-direction) as zero or negligible, sets σ₃ = τ₁₃ = τ₂₃ = 0. However, in T-joints, these stress calculations are necessary to determine the damage mechanisms at the web–skin interface and filler fracture failure.

In the literature, numerous studies have focused on exploring the mechanical behavior of joints, but mostly focused on the failure mechanism experimentally and focused on one parametric effect study. Huang et al.⁹ focused on the effect of the adhesive interface, while Liu et al. focused on the buckling behavior of J-joints experimentally.¹⁰ Progressive damage analysis of joints^11,12 under tensile loading shows that the debonding between the skin panel and the stringer and the delamination of the skin panel had less of an effect on the strength of the stiffened composite panels than the delamination of a stringer. Similarly, work related to the failure mechanism of stiffened panels is presented in Ref. 13–15. Tan et al.¹⁶ studied the effect of impact damage in joints under compression are studied by Tan et al.¹⁶ and the effect of the cohesive zone model CZM on the tensile behavior of the delamination behavior¹⁷ shows the importance of experimental results for fracture analysis. Similarly, work related to delamination was found in Ref. 18–20.

Numerous strategies have been developed to improve the low-through-thickness mechanical properties, impact damage tolerance, delamination resistance, and through-thickness direction of composite T-joint laminates. Manufacturing choice co-cured, co-bonded, or secondary bonded layups, inclusion of z-reinforcement (stitching, tufting, pins) ^21–23 and the use of tapered laminates or interleaves strongly affect damage onset and growth, creating a multi-physics design space that couples structural performance with process constraints and quality variability. Experimental validation remains essential because of the sensitivity of the joint performance to manufacturing details and boundary conditions.^24,25 Representative sub-component test pull-off, three- or four-point bending of stiffened panels, and tensile/compression web loading are used to calibrate the CZM and intra-laminar damage parameters and verify the predicted failure sequences.^26–28

Modeling T-joint behavior typically combines shell/solid submodeling with detailed interface representations.^29,30 Cohesive zone models (CZM) with traction separation laws remain the important factor for predicting initiation and propagation of debonding and adhesive failure, while virtual crack closure techniques (VCCT) ^31,32 and energy-based delamination criteria are employed for laminate interfaces.^33,34 Intralaminar damage is often captured via Hashin, Puck, or LaRC failure criteria embedded in progressive damage frameworks with stiffness degradation laws.³⁵ Pinho’s damage model, which was developed at the ply level to distinguish between matrix cracking, fiber kinking, and fiber tension failure in the second World-Wide Failure Exercise (WWFE-II), considers the complexity of the non-linear material response of composites for three-dimensional (3D) stress states.^36,37

Optimization of composite T-joints must therefore navigate a high-dimensional, constrained, and often non-convex design landscape.³⁸ Decision variables include span laminate architecture (ply angles, stacking sequence, thickness distribution, ply drop patterns), geometric features (flange width, web thickness, taper ratios, fillet/spew radii), and interfacial parameters (adhesive thickness, spew geometry, interleaf properties, and z-reinforcement density).^39,40 Objectives usually include maximizing the load-carrying capacity or damage tolerance, lowering the mass, limiting the peak interfacial peel/shear tractions, and reducing the manufacturing complexity or cost. Given the computational expense of high-fidelity finite element analyses with progressive damage and cohesive elements, surrogate-assisted strategies such as response surface models, kriging/GP,^41–43 radial basis functions, and polynomial chaos expansions are commonly paired with space-filling design of experiments (DoE) and global search algorithms such as NSGA-II, particle swarm optimization, differential evolution, or Bayesian optimization.⁴⁴

Influenced by this gap, the current study examined the optimization of the design of a composite sandwich T-joint under pull-out loads, focusing on the relationship between web/flange geometry, fillet filler configuration, and L-rib design. There were three phases in this investigation. To determine the failure modes and crucial regions that control the onset of degradation under pull-out loads, the damage initiation processes in the baseline T-joint were investigated thoroughly. The impact of important design factors, such as the skin thickness and stacking sequence, fillet radius, filler material, L-rib stacking sequence, and number of plies, on the load-carrying capacity was then assessed using parametric analysis. Third, the most important parameters of the filler material, fillet (filler) radius, and L-rib stacking sequence were determined by this screening. These three factors are then the subject of a focused investigation to measure their individual and combined effects on pull-out behavior and derive design recommendations for improved performance.

The remainder of this paper is organized as follows. The T-joint configuration, material systems, and numerical/experimental methodology, which includes the definition of design variables and failure criteria, are covered in the methodology section. The study on the start of damage in the baseline joint is presented in damage and failure assesment. The parametric study used to determine the most important design parameters is described in parametric screening. The results part, analyze the effects of the filler material, fillet radius, and L-rib stacking sequence on pull-out performance. Finally, conclusion part highlights the important observations and provides recommendations for the design of composite sandwich T-joints. The methodology is shown in Figure 1.

Figure 1.

Methodology for T-joint Pull-out behavior damage sensitivity study and optimization for enhanced performance.

Methodology

The base design configuration for the composite T-joint consists of two L-ribs connected to the skin through a co-curing process, and the deltoid region in the center, which is often filled with a filler material, as shown in Figure 2. The overall length of the T-joint was 200 mm with a height and width of 150 mm. The critical area that determines the load-carrying capacity of the T-joint is the area around the filler, which is often prone to stress gradients and damage initiation.

Figure 2.

Carbon Epoxy T-Joint Front and Side View along with dimensions and thickness.

The dimensions of each rib were 100 × 150 × 150 (Length, Width, and Height). All dimensions were measured in millimeters. The stacking sequence of each rib is [45/-45/0/90/-45/0/90/-45/90]_S. The maximum thickness of each rib was 1.75 mm. Skin (sole-plate): The dimensions of the soleplate were 200 × 150 × 150. The stacking sequence was [45/0/-45/90/45/0/-45]_S. The thickness of the soleplate is 7 mm. Deltoid: The deltoid had a radius of curvature of 5 mm. It is filled with a unidirectional prepreg of the same material as the L ribs. For the composite layup, for T-joint fiber direction was specified along the length, and the normal direction was out-of-plane. The direction of the deltoid was defined along the length of the deltoid in the z-direction.

The T-joint was made of T700/QY9611 carbon-epoxy material. The material properties are listed in Table1, taken from AVIC Composites Corporation Ltd. technical datasheet for T700/QY9611 prepreg system.

Table 1.

Elastic and Strength properties of the T700/QY9611 Composite T-joint.

Elastic properties	E11 [GPa]	E22 [GPa]	E33 [GPa]	G12 [GPa]	G13 [GPa]	G23 [GPa]	$ν_{12}$	$ν_{13}$	$ν_{23}$
T700/QY9611	128	8.46	8.46	3.89	3.89	3.89	0.32	0.32	0.35
Strength properties	$X_{1}^{T}$ [MPa]	$X_{2}^{T}$ [MPa]	$X_{1}^{C}$ [MPa]	$X_{2}^{C}$ [MPa]	$S_{12}$ [MPa]	$S_{13}$ [MPa]	$S_{23}$ [MPa]
T700/QY9611	2372	50	1234	178	107	80.7	80.7

Finite element modeling

The T-joint model was modeled using a coupled approach involving ANSYS Composite PrepPost (ACP) and ANSYS Static Structural software to accurately simulate the complex behavior of a T-joint under static loading. The composite layup and material orientations were defined in the ACP module, which then generated a detailed layered solid model. The solid model provides detailed 3D stress states and interlaminar shear stresses, particularly in critical areas of the joint interface and free edges. SOLID185 is used for the 3D modeling of solid structures, defined by eight nodes with three degrees of freedom at each node: translations in the nodal x, y, and z directions. This element type is well suited for the 3D modeling of solid structures and is efficient for generating a volume mesh in composite laminates. The edges of the structures were constrained using the fixed-support option U1 = U2 = U3 = RX = RY = RZ = 0, and the specimen was loaded at a constant rate of 0.5 mm/min as shown in Figure 3. The material behavior for each ply was modeled as orthotropic elastic with progressive stiffness degradation governed by the experimentally calibrated failure criteria.

Figure 3.

Composite T-joint Mesh and Refine Mesh Area around Deltoid region.

Damage and failure modeling

The failure behavior of the composite T-joint is governed by a combination of interlaminar and intralaminar damage mechanisms. Interlaminar failures, such as adhesive debonding and delamination between plies, were modeled using cohesive zone elements with bilinear traction-separation laws. This approach specifically models the non-linear behavior of the interface between plies, allowing the simulation to track the initiation and subsequent propagation of a crack along the defined interface (cohesive zone). The traction-separation law (TSL) governs the behavior of these elements or contact surfaces. The behavior is dictated by the input material properties that define the cohesive material response: the maximum interface strengths $σ_{\max}, τ_{\max}$ the normal and shear directions, respectively, and the corresponding critical fracture toughness values $G_{I c}, G_{I I c}, G_{I I I c}$ .

The damage evolution was controlled using an internal damage variable D that ranged from 0 (undamaged) to 1 (fully separated). The effective traction T acting on the interface was calculated based on the initial traction T _0:

T = (1 - D) T_{0}

(1)

The initiation of damage in a mixed-mode loading scenario (a combination of Mode I, II, and III openings) is often determined using a quadratic interaction criterion, which defines when the cohesive elements begin to soften.

{(\frac{〈 T_{n} 〉}{N_{\max}})}^{2} + {(\frac{T_{s}}{S_{\max}})}^{2} + {(\frac{T_{t}}{T_{\max}})}^{2} = 1

(2)

where

T_{n}, T_{s}, T_{t}

are the current normal and shear tractions, respectively, and

N_{\max}, S_{\max}, T_{\max}

are the respective maximum strengths. Macaulay’s operator

″ < >^{″}

indicates that the compression component cannot initiate damage in the structure.

Once the damage is initiated, the rate at which the material softens is governed by the energy release rate. The material fully delaminates when the total energy released reaches the critical mixed-mode fracture toughness,

G_{m c}

. This mixed-mode toughness is often calculated using the Benzeggagh (BK) law within composite damage models:

G_{mC} = G_{I C} + (G_{I I C} - G_{I C}) {(\frac{G_{S}}{G_{T}})}^{η}

(3)

where

G_{S}

is the total shear energy release rate

(G_{II} + G_{III}), G_{T}

is the total energy release rate

(G_{I} + G_{S})

and

η

is a material parameter that governs the mixed-mode behavior (the BK exponent). The value of the coefficient η, which aims for simulation convergence, ranges from 1 to 2 for glass fibers and 2 to 3 for carbon fiber materials. The value in our case is taken as 2.28 from the reference paper. This equation dictates when the element fails and can no longer transfer load across the interface. Table 2 provide information on the cohesive element properties.

Table 2.

T-joint cohesive element parameters.

Property	$T_{n}$ (MPa)	$T_{s}$ (MPa)	$T_{t}$ (MPa)	$G_{I c}$ (J/m²)	$G_{I I c}$ (J/m²), $G_{I I I c}$ (J/m²),
Value	50	110	110	432	910

Mode I ( $T_{n}$ = 50 MPa) and Mode II/III ( $T_{s}$ = $T_{t}$ = 110 MPa) strengths were calibrated using experimental results for the T700/QY9611 system because to the difficulties in directly measuring interfacial strengths. Table 2 shows Mode I and Mode II fracture toughness values obtained experimentally using DCB (ASTM D5528) and ENF (ASTM D7905) testing, respectively. Mode III toughness is considered to be the same as Mode II, which is a reasonable approximation for transversely orthotropic composites.

Intralaminar damage, including fiber breakage in tension and compression, is calculated using the Hashin failure criterion, whereas matrix failure in compression or tension is calculated using the PUCK failure criterion. The equations are shown in Table 3:

p_{⊥ II}^{(-)}, p_{⊥ II}^{(+)}

= Slopes of the fracture envelope for carbon fiber = 0.3 & 0.5. Progressive failure analysis was implemented through gradual stiffness reduction, enabling the simulation of load redistribution following local failures. Thus, the combined interlaminar-intralaminar modeling framework provides a physically consistent basis for predicting the ultimate load-carrying capacity and failure sequences.

Table 3.

Failure Criteria for damage initiation and evolution.

Failure modes	Failure criterion
For fiber tension (Longitudinal direction)	$F_{f}^{t} = {(\frac{σ_{11}}{X^{T}})}^{2} + α {(\frac{τ_{12}}{S^{L}})}^{2} + α {(\frac{τ_{13}}{S^{L}})}^{2} a n d σ_{11} \geq 0$
For fiber compression (Longitudinal direction)	$F_{f}^{c} = {(\frac{σ_{11}}{X^{C}})}^{2} a n d σ_{11} \leq 0$
Matrix cracking (tension)	$\sqrt{{(\frac{τ_{21}}{S_{21}})}^{2} + {(1 - p_{⊥ ∥}^{(+)} \frac{Y_{T}}{S_{21}})}^{2} {(\frac{σ_{2}}{Y_{T}})}^{2}} + p_{⊥ ∥}^{(+)} \frac{σ_{1}}{S_{21}} = 1 - \| \frac{σ_{1}}{σ_{1 D}} \|$
Matrix cracking (tension)	$σ_{2} \geq 0$
Matrix cracking (compression)	Mode I
	$\frac{1}{S_{21}} (\sqrt{τ_{21}^{2} + {(p_{⊥ ⊥}^{(-)} σ_{2})}^{2}} + p_{⊥ ∥}^{(-)} σ_{2}) = 1 - \| \frac{σ_{1}}{σ_{1 D}} \|; σ_{2} < 0$
	Mode II
	${(\frac{τ_{21}}{2 (1 + p_{⊥ ⊥}^{(-)}) S_{21}})}^{2} + {(\frac{σ_{2}}{Y_{C}})}^{2}] \frac{Y_{C}}{(- σ_{2})} = 1 - \| \frac{σ_{1}}{σ_{1 D}} \|; σ_{2} < 0$
Interface delamination	${(\frac{〈 T_{n} 〉}{N_{\max}})}^{2} + {(\frac{T_{s}}{S_{\max}})}^{2} + {(\frac{T_{t}}{T_{\max}})}^{2} = 1$
Interface delamination propagation	$G_{mC} = G_{I C} + (G_{I I C} - G_{I C}) {(\frac{G_{S}}{G_{T}})}^{η}$
Inverse reverse factor (IRF)	Ultimate Load/Ultimate strength; IRF >1 failureIRF <1 safe

Damage and failure assessment

The pull-off test experimental data show that⁴⁵ damage initiation mainly occurs around the edge of the deltoid filler sections; this occurrence is explained by the presence of geometric stress concentration points, as shown in Figure 4. Finite element analyses (FEA) support these findings by demonstrating that localized stress intensification is caused by abrupt geometric discontinuities at the vertices and edges of the deltoid filler. These sites are critical for the stress singularity under tensile or out-of-plane loading conditions. The main damage modes include debonding failure between the L-ribs and deltoid as the starting point of damage initiation. As the tensile deformation along the z-axis increases, the debonding between the L-ribs and deltoid follows the radial curvature path, finally resulting in skin-stiffener debonding Figure 4. The load–displacement curve shows a difference of 2.3 %. The numerically calculated value is 20.196 kN compared to the experimental value of 20.691 kN Figure 5(b). The Figure 5(a) shows the shear stress and normal stress variations across the out of plane axis.

Figure 4.

Damage Initiation and Final Failure of T-joint during tensile loading.

Figure 5.

(a) Shear Stress XY (in-plane), Shear Stress YZ, XZ (out of plane) and Normal Stress along Z-Direction (b) Load Displacement Curve for experimental and numerical simulation.

Parametric screening of design variables

The geometric and material parameters (fillet radius, filler material, L-rib stacking sequence and number of plies, skin stacking sequence, and thickness) were varied systematically to understand the effect on the mechanical performance, and a sensitivity analysis was performed to determine which parameters had the strongest influence on the load-carrying capacity and damage initiation. The parameters used in this study are shown in Figure 6.

Figure 6.

Design parameters selection for T-joint.

For the stacking sequence of L-ribs and skin, three stacking sequences are taken for study, denoted as Case A, B, and C. The stacking sequence for case A is [45, 0, 90, −45, 45, −45, 0, 90, 45, −45, −45, 45, 90, 0, −45, 45, −45, 45]. For case B Stack: [45, 0, 90, −45, 45, −45, 45, −45, 0, −45, 45, 90, 45, −45, 45, −45, 0, 45] and for case C Stack: [45, 0, 90, −45, 0, 45, 90, −45, 45, −45, −45, 45, −45, 90, 45, 0, −45, 45]. Table 4 represents the concentration of ply contents for different orientations.

Table 4.

Concentration of plies for case A, B and C.

Case	±45° Content	0° plies	90° plies
Balanced (Case A)	61%	17%	22%
Peel-optimized (Case B)	66%	17%	17%
Damage-tolerant (Case C)	55%	22%	22%
Experimental Case	11.1% (45); 33.3% (−45°)	22.2%	33.3%

There was a significant reduction in the load-carrying capacity compared with the experimental results. The key results obtained from the finite element analysis show that the high ±45° cases have fewer 0° plies (Case A 17% 0°, Case B: 17% 0°, Case C: 22% 0°). In the pull-off test of a T-joint, failure is often dominated by axial separation (tension in the flange). The 0° plies were the primary load-carrying plies in tension. Reducing 0° plies by 5-10% (from 22% in the Experimental Case to 17% in Cases B and C) reduced the axial strength significantly Figure 7(a). The ±45° plies are excellent for shear and peel resistance, but in a pull-off test, if the failure is driven by axial tension, then the 0° plies are critical. The graph indicates that the failure mode was dominated by axial failure rather than peel/shear failure.

Figure 7.

(a) Load Displacement Curve for Case A, B and C, compared with experimental results (b) Filler Material Ultimate Load Value (1) PVC FOAM (2) Resin Epoxy (3) T700/QY9611 (4) Epoxy Carbon UD (c) Filler Radius effect on ultimate load(d) Skin Laminate Thickness effect on final load value for composite T-joint.

For the filler material, four types were considered in the study: PVC FOAM, resin epoxy, unidirectional, and epoxy carbon UD, as shown in Figure 7(b). Two of the filler materials, PVC Foam and Resin Epoxy, have isotropic properties, and both materials have Young’s moduli (102 MPa and 3780 MPa), which are less than those of Carbon Epoxy UD Pre-peg (209 GPa) and T700/QY9611 (128 GPa). Another important aspect is the stiffness effect of the filler on damage behavior. Less stiff fillers have fewer stress concentration points and absorb more deformation, but cracking can occur at lower load values, which results in a low load-carrying capacity of the joints. Similarly, radius of filler also have a significant effect on the load carrying capacity as increases from 18.6 kN to 22.05 kN for 7 mm radius, as shown in Figure 7(c).

For the skin, the load-carrying capacity shows an upward trend with the increase in thickness of the skin laminate, as shown in Figure 7(d). The total laminate thickness for the experimental case is 7 mm, with each layer of 0.5 mm; the force obtained for that case is experimentally 20.19 kN, whereas numerically the value obtained is 20.477 kN. With the decrease in the skin laminate thickness, there is a substantial decrease in the load-carrying capacity. For a skin thickness of 5.6 mm, the ultimate load value is reduced by 36% and for a thickness of 4.2 mm, the ultimate load value is reduced by 62.9%.

After obtaining the parametric response in terms of the maximum Reaction Force (N), Shear Stress (XY in-plane, XZ, YZ out-of-plane), and maximum strain energy, as shown in Appendix A, a parametric response relationship was obtained using the Pearson linear correlation coefficient, while the range was defined from −1 to +1.

\begin{array}{l} Range : - 1 \leq r \leq + 1 \\ | r | > 0.7 \to strong linear link \\ 0.3 < | r | < 0.7 \to moderate \\ | r | < 0.3 \to weak / negligible \\ r = \frac{n (\sum x y) - (\sum x) (\sum y)}{\sqrt{[n \sum x^{2} - {(\sum x)}^{2}]} - [n \sum y^{2} - {(y)}^{2}]} \end{array}

(4)

n

= number of data points,

\sum x y

= sum of the product of the x- and y-values for each point. From the correlation heat map, it is concluded that the radius has a maximum impact on the reaction force with r = 0.94 Figure 8(a); an increase in radius will increase the load carrying capacity, but at the same time, an increase in radius causes the joint stiffer to decrease the maximum strain energy absorption. Similarly, stacking sequence A reduces the in-plane shear stresses as compared to stacking sequences B and C. From the correlation map, three aspects of T-joints have the greatest effect on mechanical performance: the stacking sequence, filler radius, and material properties. Appendix B presents the correlation values. These three influential parameters were studied to determine the optimal design principles for joint manufacturing.

Figure 8.

(a) 2-D Correlation Map for T-joint parametric evaluation (b) 3-D Response Surface w.r.t Filler Radius and Material effect on Maximum Load Carrying Capacity.

In Figure 8(b), the red dots represent the values calculated through simulations and show a trend with the effect of an increase in the radius and filler material properties on the load-carrying capacity of T-joints, with resin epoxy providing a maximum of 22.3 kN of reaction force.

Laminate stacking sequence impact on mechanical performance

The performance of a composite T-joint under pull-out loading is highly dependent on the stacking sequence of its constituent laminates, particularly L-ribs, which experience complicated multi-axial stress states dominated by bending and interlaminar shear. The principal design objective is to delay the onset and mitigate the propagation of critical damage mechanisms specifically delamination, matrix cracking, and fiber failure, while at the same time maximizing joint stiffness, strength, and resistance to damage. The following fundamental design concepts govern the development of the five stacking sequences examined in this study, each of which prioritizes a distinct structural performance metric:

• Symmetry: To prevent coupling between bending and extension, all laminates were symmetric about the mid-plane [B] = 0.

• Balance: Every sequence has an equal number of +θ and -θ plies, making it balanced (especially for the ±45° pairs). This assures that the extension-shear coupling (A₁₆ = A₂₆ = 0) is eliminated, which is essential for preserving structural stability and consistent in-plane deformation.

• Contiguity and Disorientation: The number of contiguous plies with the same orientation is limited to a maximum of four to prevent large resin-rich areas and inhibit the propagation of intralaminar cracks. Furthermore, the change in fiber angle between adjacent plies is limited to a maximum of 45° (e.g., 45° to 0° to −45° is a common progression) to reduce interlaminar shear stresses and minimize the risk of delamination initiation.

• 10% Rule: A minimum of 10% of plies are allocated to each of the four principal directions (0°, 90°, +45°, −45°). This ensures the baseline stiffness and strength in all in-plane directions.

Five stacking sequences were designed for study based on multi-loading scenarios, as shown in Figure 9:

• Sequence 1: Balanced Quasi-Isotropic [45, 0, −45, 90, 45, 0, −45, 45, 90]s, With a ply distribution of 22.2% 0°, 22.2% 90°, 33.3% + 45°, and 22.2% −45°, it achieves a nearly perfect quasi-isotropic state, where the in-plane stiffness is approximately equal in all directions (A₁₁/A₂₂ ≈ 1.05).

• Sequence 2: Shear-Optimized [45, 0, −45, 45, 0, 90, −45, 0, 45]s,this sequence was engineered to enhance the resistance to shear stresses, which are predominant in the web of the L-rib under pull-out loading. It features a high percentage of ±45° plies (55.6% combined), which are most effective in carrying shear loads. The increased number of 0° plies (33.3%) provided additional bending stiffness to resist the opening moment.

• Sequence 3: Impact-Tolerant [45, 90, 0, −45, 90, 45, 0, 90, −45]s designed for scenarios involving potential low-velocity impact (e.g., tool drop), which prioritizes through-thickness strength. It features a very high percentage of 90° plies (44.4%), which is crucial for resisting impact damage and improving compression-after-impact (CAI) strength by providing support to the primary load-bearing 0° plies. The outer layers are composed of ±45° plies, which protect the internal 0° plies from scratches and surface impacts, and provide resistance to buckling.

• Sequence 4: Hybrid Angle [45, 30, −45, 0, 45, 90, −45, 0, −30]s, this sequence explores the use of non-standard angles (±30°) to tailor the stiffness properties more precisely. The inclusion of ±30° plies (33.3%) provided stiffness properties intermediate between 0° and ±45° directions, potentially optimizing the load path for specific stress trajectories within the joint’s bend radius. It adheres to the 10% rule in all principal directions while providing a distinct stiffness profile that can enhance off-axis performance and reduce stress concentrations in complicated geometric features.

• Sequence 5: Compression-Dominant [45, 0, 90, −45, 0, 90, 45, 0, −45] s. This arrangement is optimized for configurations considering global buckling or crippling of the vertical rib as a principal concern. It features an equal and high spreading of 0° and 90° plies (33.3% each), which maximizes the axial,transverse, and compressive stiffness as well as the strength.

Figure 9.

Methodology for five design cases to analyze L-ribs stacking sequence effect on Load carrying capacity.

This study examines a matrix of sequences, each based on a different scientific assumption, to identify the stacking sequence mechanism that most successfully improves the pullout performance and damage tolerance of composite T-joints.

Results and discussion

Effect on stacking sequence on the load carrying capacity

The data shown in Table 5 show that the maximum load varies significantly, from a low of 14.5 kN (Case-02) to a high of 24.3 kN (Case-04). This 68% performance increase demonstrates that stacking sequence is an essential design parameter rather than a minor attribute. There was no direct correlation between the final strength and any stiffness parameter (E1, E2, or G12) when comparing the stiffness and strength of the T-joint. The highest E1 (Case-02, 56.6 GPa) exhibited the lowest strength. This implies that failure is not a straightforward material limit failure but rather is caused by a complicated combination of stresses (interlaminar, bending, and shear). The vertical leg (L-rib) of the T-joint bent primarily during the pull-out test. This causes strong interlaminar shear stresses throughout the thickness and large tensile strains on the outer surface of the bending radius. Sequences that are resilient to these stresses perform well.

Table 5.

Laminate Stacking Sequence Cases and their effect of longitudinal, transverse and shear stiffness of L-ribs.

Design Cases	Orientation Percentage %	E1 (GPa)	E2 (GPa)	G12 (GPa)	Max. Force (kN)
Case-01	0° (4) 22.2%90° (4) 22.2%+45° (6) 33.3%−45° (4) 22.2%	45.507	45.507	19.74	21.548
Case-02	0° (6) 33.3%90° (2) 11.1%+45° (6) 33.3%−45° (4) 22.2%	56.6	33.4	19.75	14.513
Case-03	0° (4) 22.2%90° (6) 33.3%+45° (4) 22.2%−45° (4) 22.2%	45.15	57.4	16.821	20.523
Case-04	0° (4) 22.2%90° (2) 11.1%+45° (4) 22.2%−45° (4) 22.2%±30° (4) 22.2%	50.83	30.99	20.520	24.321
Case-05	0° (6) 33.3%90° (4) 22.2%+45° (4) 22.2%−45° (4) 22.2%	57.45	45.15	16.82	21.148
Experimental Case	0° (4) 22.2%90° (6) 33.3%+45° (2) 22.2%−45° (6) 22.2%	43.53	56.15	15.54	20.19

The Quasi-Isotropic Case-01 with balanced stiffness, E1 = E2 = 45.5 GPa, result in a very reliable and predicted performance of 21.5 kN, when each case is compared individually. This is a great benchmark, exhibiting satisfactory, but not optimum, strength. The worst performance was given by Case-02, which was optimized for shear stress bearing. It failed catastrophically early at a load value of 14.5 kN, while having the highest shear stiffness G12 = 19.75 GPa and axial stiffness E1 = 56.6 GPa. Its significant weakness is its extremely low transverse stiffness (E2 = 33.4 GPa, which is the lowest of all the instances, providing the most critical outcome. At the bend radius, the plies experienced strong tensile stresses acting transversely (90°) owing to the bending force. Because of the low E2 value, the laminate is less resilient to these stresses, which results in delamination and matrix cracking, ultimately resulting in early failure. A large number of 0° plies cannot stop the effect of this failure mode.

The numerical model was validated against experimental data in Case-03 of the Impact-Tolerant, which is near the stacking sequence of the experimental one and has an almost equal performance of ∼20.5 kN. Their outstanding performance is explained by their high 90° content, which offers great resilience to the transverse tensile stresses. Due of their lower shear stiffness (G12 ∼16.8 GPa vs 19.7 GPa), which makes them more vulnerable to interlaminar shear, their strength is marginally lower than Case-01.

With a load value of 21.1 kN, Case-05 of compression dominance performed exceptionally well, second only to Case-04. High E1 (57.45 GPa) for bending stiffness and high E2 (45.15 GPa) results in stopping transverse splitting because of its high and balanced 0° and 90° content (33.3% each), resulting in a combination effect that successfully manages the complex bend stress condition.

The hybrid angle Case-04 exhibits the most impressive result (24.3 kN), which was 13% greater than Case-01. These two elements are responsible for the performance. The first is customized stiffness, where additional stiffness between 0° and 45° is provided by the presence of ±30° plies. The stress concentrations decrease as a result of a more consistent and effective load transmission into the bend radius. The second is the optimal stiffness combination, because this stacking sequence produces the maximum shear stiffness (G12 = 20.52 GPa) to withstand interlaminar shear and the highest axial stiffness (E1 = 50.83 GPa) to withstand bending. Although its E2 value is modest (30.99 GPa), this weakness tends to be successfully mitigated by its improved handling of bending and shear. As a result, ±30° plies offer a strong barrier to prevent delamination.

Force-displacement curve analysis

The load–displacement graph of Figure 10(a) demonstrates that all cases have a comparable initial linear slope, suggesting that the failure strength is more sensitive to the sequence than the global stiffness. Until the abrupt collapse, the curves were primarily linear, suggesting brittle failure modes of catastrophic delamination or matrix fracture. Owing to its low transverse strength, Case-02 fails at a significantly lower peak load (14.5 kN) and exhibits an extended post-failure residual load-carrying capacity, indicating progressive damage propagation rather than catastrophic collapse. With failure loads ranging from 14.5 kN to 24.3 kN, a difference of more than 68%, the numerical analysis demonstrated a significant impact of the laminate stacking sequence on the final pull-out capacity of the composite T-joints (Figure 10(a), Table 5).

Figure 10.

(a) Force Displacement Curves for different Laminate Stacking Sequence and Experimental Case (b) Shear Stress XZ, YZ out of plane comparison for Resin Epoxy, FOAM and Woven Filler.

The most critical finding was the performance of Case-02 which resulted in the lowest failure load (14.5 kN). Its substantial transverse stiffness deficiency (E₂ = 33.4 GPa) is the reason for this, and the laminate is ill-suited for the considerable tensile stresses that are induced in the transverse direction by the bending moment at the T-joint radius. The advantages of its high axial (E₁ = 56.6 GPa) and shear (G₁₂ = 19.75 GPa) properties were negated by the premature failure caused by matrix cracking and delamination at these transverse stresses. On the other hand, laminates with improved transverse resistance perform good with failure loads of 20.5 kN and 20.2 kN were attained by Case-03, which had a high 90° ply content (33.3%), and the experimental case. The correctness of the finite element model was also confirmed by its strong agreement with the experimental results.

Stress concentrations are decreased by the more gradual and effective transition of loads around the geometrically essential bend radius made possible by the customized load transfer caused by the presence of ±30° plies. This laminate effectively mitigates its considerably lower transverse stiffness by balancing the high axial stiffness (E₁ = 50.83 GPa) with greater shear resistance.

Analysis of Filler Material Effect (Constant Geometry)

While maintaining the same fillet geometry, a controlled study was conducted to determine the impact of the filler material stiffness on the T-joint performance. Three materials were assessed: a very high-stiffness Epoxy Carbon Woven prepreg, high-stiffness Solid Epoxy Resin, and low-stiffness PVC Foam (60 kg/m³). The findings show that the failure mechanism and structural efficiency are significantly affected by filler compliance. Importantly, as shown in Table 6, the compliant PVC foam filler outperformed both stiff fillers in terms of the ultimate load-carrying capability (20.7 kN).

Table 6.

Filler Materials (Resin Epoxy, PVC FOAM, and Epoxy Carbon) load carrying capacity, strain energy and shear stresses.

Design Cases	Deltoid assignment	Force reaction maximum total	Shear stress XZ (Out of plane)	Inverse reserve factor maximum	Shear stress YZ (Out of plane)	Shear stress XY (In-plane)	Strain energy maximum
Units		N	MPa		MPa	MPa	mJ
1	Resin Epoxy	20,473	14.7	0.9	34.3	16.0	21.6
2	PVC foam (60 kg m^-3)	20,715	4.1	0.7	2.1	1.7	22.4
3	Epoxy carbon woven (395 GPa) prepreg	19,789	21.7	0.7	31.9	23.7	20.2

The stress distributions revealed the mechanism underlying the improved performance. Compared with the rigid fillers, the compliant foam reduced the maximum contact stress by 72–81% and the maximum interlaminar shear stress by more than 94%, as shown in Figure 10(b). This suggests that the primary purpose of the foam is to serve as a stress-redistribution element rather than to bear a load. Owing to its low modulus, it can deform, delaying the onset of delamination and matrix degradation by neutralizing harmful stress concentrations at the geometrically significant bend radius.

The strain energy statistics, which show that the foam absorber had the greatest energy (22.4 mJ) prior to failure, further support this stress-redistribution role. The stiff carbon filler generated the highest interfacial shear stresses at the filler-skin and filler-rib interface, the lowest total failure load (19.8 kN) despite having the lowest Inverse Reserve Factor (0.66), which indicates a significant safety buffer against a particular failure mode. This suggests that its high stiffness creates a brittle failure condition, making it the least effective choice for maximizing joint strength.

To summarize, for a fixed geometry, the ideal filler is the most compliant material rather than the stiffest. A compliant filler improves the joint strength by efficiently regulating the stress concentrations and not by increasing the structural stiffness, allowing the primary composite structure to reach its maximum load-carrying capacity. This marks a paradigm shift from a “load-carrying” to a “stress-management” stress-management’ approach to filler design.

Effect of Filler Geometry

The filler geometry is assumed to be circular because it provides a much better stress distribution from the flange to the skin. Variations in the radius of the fillet were studied to analyze the behavior of the stress distribution and load-carrying capacity of the joint. With the increase in radius from 3 mm to 7 mm for the filler, the load carrying capacity changes from 18.36 kN to 22.034 kN, with overall increase of 34.8% in strength of T-joint as shown in Figure 11(a). There is also an increase in the displacement value for failure, as for 3 mm the material fails at a displacement value of 2.56 mm as compared to 2.95 mm for 7 mm radius, with a difference of 13.22%. When comparing the 5 mm and 7 mm radii, the change in load carrying capacity is 7.33 % (5 mm 20.4 kN, 7 mm 22.034 kN). While for displacement failure, 5 mm radius had a displacement failure 2.99 mm with a difference of 1.3 %. This provides a critical tradeoff when designing T-joints as the overall stiffness of the structure increases with the increase in radius; however, after the critical radius R_c, the change in load-carrying capacity will be minimal. A further increase in the radius will increase the weight of the structure and will be more prone to impact from debris or maintenance tools because of the larger surface of the deltoid area.

Figure 11.

(a) Load Displacement Curve for filler radius of 3 mm, 5 mm, 7 mm (b) Shear Stress Variation for filler radius of 3 mm, 5 mm and 7 mm.

With an increase in radius, there was a decrease in the interlaminar shear stress (ILSS) concentration, as shown in Figure 11(b). A larger radius provided a uniform distribution of stresses from the flange to the skin and reduced the peak stress points. However, by analyzing the shear stress distribution in Figure 11(b), there is a decrease in the shear stress distribution for 5 mm and 7 mm as compared to the 3 mm deltoid filler. However, the damage mechanism of composite joints is complex and is based on the interaction between normal and shear stress components. Figure 12(a) provides information regarding the Inverse Reverse Factor IRF, strain energy, while Figure 12(b) provides normal stress variations with increasing radius.

Figure 12.

(a) Inverse Reverse Factor (IRF) and Strain Energy for filler radius of 3 mm, 5 mm and 7 mm (b)Normal Stress Distribution along X, Y (In-Plane) and Z (Out of Plane) Direction for filler radius of 3 mm, 5 mm and 7 mm.

Conclusions

The study conclusively demonstrates that the ultimate load-carrying capacity of a composite T-joint under pull-out loading is not only dependent on axial and shear stiffness, but also critically dependent on the laminate’s transverse stiffness and its resistance to transverse tensile stresses (quantified by E₂). This is evidenced by the catastrophic premature failure of the shear-optimized sequence (Case-02), resulting in a 68% decrease in ultimate pull-out strength. Conversely, sequences with high 90° ply content (Case-03, Case-05) exhibited robust performance. The maximum load varies significantly, ranging from a low of 14.5 kN (Case-02) to a high of 24.3 kN (Case-04). This 68% gain in performance shows that stacking sequence is not a minor detail, but a fundamental design parameter.

A hybrid sequence with ±30° plies (Case-04) outperformed a regular orthogonal laminate in terms of performance. This arrangement effectively combined the highest shear stiffness (G₁₂), high axial stiffness (E₁), and enough transverse reinforcement to offset its lower E₂. This result demonstrates that using non-standard ply angles strategically is a powerful tool for advanced stiffness tailoring. Compared to traditional 0°/±45°/90° stacks, this enables designers to produce laminates that more effectively control the complicated, multi-axial stress condition at the T-joint radius, resulting in significant improvements in ultimate strength and structural efficiency.

Increasing the fillet radius significantly enhanced the load-carrying capacity and reduced the stress concentrations at the bend radius by promoting a more efficient load transition. With the increase in radius from 3 mm to 7 mm for the filler, the load carrying capacity changes from 18.36 kN to 22.034 kN, with overall increase of 34.8% in strength. However, for 5 mm and 7 mm radius, the change in the load-carrying capacity is 7.33 % (5 mm 20.4 kN, 7 mm 22.034 kN). While for displacement failure, 5 mm radius has a displacement failure at 2.99 mm as compared to 2.95 mm for 7 mm radius, with a difference of 1.3 %. This identifies a crucial design optimization point, suggesting that the resources allocated to increasing the radius beyond this threshold are inefficient.

Furthermore, the filler material acts as a critical damage mitigation component. The compliance and failure strain of the filler material are paramount for enhancing joint performance. With the use of PVC foam, the failure load increased by 5% and the destructive interlaminar shear stresses by 94% through effective energy absorption and stress redistribution, identifying compliant fillers as essential stress-damping components. This study provides a design framework for joints with enhanced performance under pull-out loading.

Footnotes

Acknowledgements

The researchers involved in this project appreciate the assistance of the National Natural Science Foundation of China under Grants 12072288 and 12272319.

Author Contributions

CRediT: Shakir Hussain Chaudhry: Conceptualization, Formal analysis, Investigation, Methodology, Visualization, Writing- original draft, Final review & Editing; Pu Xue: Supervision, Funding Acquisition, Resources; Ameer S. Zirjawi; Resources, Final Review & Editing.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: National Natural Science Foundation of China (12072288 and 12272319).

ORCID iD

Shakir Hussain Chaudhry

Appendix

Appendix A.

Design cases with specific stacking sequence, filler radius and their corresponding performance parameters.

Design Cases	Stacking Sequence	Radius	Deltoid Material Assignment	Force Reaction Maximum	Shear Stress XZ (Out of Plane)	Directional Deformation	Inverse Reserve Factor Maximum	Shear Stress YZ (Out of Plane)	Shear Stress XY (In-Plane)	Strain Energy Maximum
				N	MPa	mm		MPa	MPa	mJ
1	A	5	Resin Epoxy	20,399.05	29.60	1.40	0.78	87.59	17.00	19.96
2	A	5	PVC foam (60 kg m^-3)	20,912.02	4.19	1.40	0.76	1.86	1.70	21.31
3	A	5	Epoxy carbon woven (395 GPa) prepreg	20,290.20	58.28	1.35	0.90	36.28	14.79	19.50
4	B	5	Resin Epoxy	20,277.37	22.77	1.40	0.62	54.37	26.06	19.63
5	B	5	PVC foam (60 kg m^-3)	20,851.32	5.01	1.40	0.77	1.81	1.82	21.92
6	B	5	Epoxy carbon woven (395 GPa) prepreg	19,682.48	21.32	1.40	0.62	31.92	20.67	18.18
7	C	5	Resin Epoxy	20,023.60	28.04	1.40	1.61	45.11	12.62	19.87
8	C	5	PVC foam (60 kg m^-3)	20,543.60	3.89	1.40	0.78	1.97	1.74	21.33
9	C	5	Epoxy carbon woven (395 GPa) prepreg	19,453.79	21.01	1.40	1.37	34.38	8.64	18.52
10	A	3	Resin Epoxy	18,725.46	48.16	1.40	0.70	85.58	25.13	10.53
11	A	3	PVC foam (60 kg m^-3)	18,299.75	7.36	1.78	0.63	6.51	2.20	10.47
12	A	3	Epoxy carbon woven (395 GPa) prepreg	18,432.12	25.65	1.40	0.70	20.93	19.43	10.19
13	B	3	Resin Epoxy	18,655.67	35.60	1.40	0.68	66.39	24.44	9.91
14	B	3	PVC foam (60 kg m^-3)	18,452.83	12.52	2.48	0.77	19.46	4.47	10.10
15	B	3	Epoxy carbon woven (395 GPa) prepreg	18,808.11	59.34	1.20	0.72	67.33	49.57	10.27
16	C	3	Resin Epoxy	18,832.22	70.85	1.20	0.73	140.68	44.94	10.07
17	C	3	PVC foam (60 kg m^-3)	18,452.83	12.52	2.48	0.77	19.46	4.47	10.10
18	C	3	Epoxy carbon woven (395 GPa) prepreg	18,808.11	59.34	1.20	0.72	67.33	49.57	10.27
19	A	7	Resin Epoxy	22,110.02	98.05	1.77	0.74	452.49	71.63	4.98
20	A	7	PVC foam (60 kg m^-3)	21,710.87	9.14	1.75	0.70	7.03	8.42	16.19
21	A	7	Epoxy carbon woven (395 GPa) prepreg	21,871.10	3.45	1.40	0.63	252.44	50.77	4.43
22	B	7	Resin Epoxy	23,274.28	96.94	1.82	0.69	521.59	107.23	5.57
23	B	7	PVC foam (60 kg m^-3)	22,377.39	9.67	1.77	0.71	8.67	9.38	16.32
24	B	7	Epoxy carbon woven (395 GPa) prepreg	21,807.32	2.91	1.40	0.61	242.30	52.23	3.98
25	C	7	Resin Epoxy	21,770.72	96.98	1.69	1.58	463.16	75.71	4.73
26	C	7	PVC foam (60 kg m^-3)	20,511.73	8.01	1.64	0.74	6.50	2.29	14.68
27	C	7	Epoxy carbon woven (395 GPa) prepreg	21,523.64	3.73	1.40	1.48	263.49	52.68	4.30

Appendix B.

Top 10 strongest linear correlations from heat map.

Correlation parameters	Value
Maximum reaction force vs radius	+0.939
Maximum strain Energy vs design cases	−0.763
Shear stress XY (in-plane) vs filler material PVC	−0.631
Shear stress XZ (out of plane) vs filler material RE	+0.627
Shear stress XZ (out of plane) vs filler material PVC	−0.550
Shear stress YZ (out of plane) vs design cases	+0.529
Shear stress XY (in-plane) vs design cases	+0.522
Shear stress YZ (out of plane) vs radius	+0.522
Shear stress YZ (out of plane) vs filler material PVC	−0.487
Shear stress YZ (out of plane) vs filler material RE	+0.480

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. Sensitivity study of debonding damage to load-carrying capacity of composite T-Joints under tensile loading. J Aero Eng 2023; 36(4): 04023023. https://doi.org/10.1061/JAEEEZ.ASENG-4890

Optimizing the stress concentrations by tailoring laminate stacking sequencing and compliant fillers for superior composite T-joint performance

Abstract

Keywords

Highlights

Introduction

Methodology

Finite element modeling

Damage and failure modeling

Damage and failure assessment

Parametric screening of design variables

Laminate stacking sequence impact on mechanical performance

Results and discussion

Effect on stacking sequence on the load carrying capacity

Force-displacement curve analysis

Analysis of Filler Material Effect (Constant Geometry)

Effect of Filler Geometry

Conclusions

Footnotes

Acknowledgements

Author Contributions

Declaration of conflicting interests

Funding

ORCID iD

Appendix

References