Effect of Layer-wise Fiber Orientation on the Mechanical Response of Laminated Composites: A Finite Element Simulation Approach

Recent advances in modeling and experimental approaches have addressed many aspects of hybrid architectures and damage evolution in fiber-reinforced laminates subjected to impact forces using FEM and XFEM of the grain structure [7-14]. Bonding between fiber layers plays a crucial role in bullet resistance and energy absorption, but prior studies have mostly focused on three- or four-layer setups. High-aspect-ratio multilayer systems are common in aerospace and defense composites, but little attention has been paid to this specific geometry. Moreover, although finite element damage models have been successful in simulating interlaminar delamination and crack propagation, single-impact or low-velocity validation has limited their use, leaving layer orientation and mixed-velocity effects largely unaddressed.

Although efforts to investigate fiber orientation have focused primarily on evaluating stress distribution and residual velocity, the understanding of interlayer stress transfer, a vital factor in energy dissipation and failure prevention in laminated composites, remains elusive. This work seeks to address this shortage by developing a six-layer finite-element model. A finite-element-based model will be applied to examine the effects of fiber orientation, bond strength, and impact velocity on the resulting stress distribution, deformation patterns, and interlaminar energy transfer across a wide range of impact velocities. In line with this, this robust simulation methodology emphasizes the damage tolerance, crack-arrest capacity, and energy-absorption efficiency of multilayered fiber layups. The subsequent work will aim to align numerical predictions with the current design principles governing the behavior of composite materials.

The study of composite panels under various ballistic conditions is important for understanding their performance, as it enables simulations with varying fiber orientations to assess the effectiveness of fabric-oriented composite panels. To assess the impact of ballistics, projectile material, and size, and design and implementation of composite systems, a finite-element model was used. Within the framework of composite panels, precise mathematical and computational modeling, as well as the dynamic behavior of compounds, are also mandatory at various levels of the system [22]. Numerical studies on composite panels have been conducted, and several studies have reported on the high-velocity impact response of damaged panels [23, 24]. These experiments provide insight into the ballistic characteristics, energy absorption, and damage mechanisms of composite panels with varying orientation sequences.

4.1 System deformation (0°, 45°, 90°)

LS-DYNA simulations of a 6-layered ballistic impact composite with a stacking sequence of [0, 45, 90] depicted in Figure 4(a) and (b) provide an in-depth understanding of interactions between fiber orientation, interlaminar mechanics, and damage evolution in these high-velocity-loaded composites. The layers lie at 0°, which is essential for initial impact resistance, and the 0° orientation provides high in-plane stiffness and serves as the initial line of defense against projectiles. These layers absorb and retain most of the incident kinetic energy, thereby reducing penetration and increasing tensile and compressive strengths along their principal axes.

(a)

(b)

Figure 4. Six-layer system deformation (0°, 45°, 90°)

The adjacent 45° layers also provide oblique load paths; they redistribute shear stress, thereby reducing interlaminar shear forces, and direct energy into neighboring layers, thereby reducing the interfacial resistance across layers with different fiber orientations.

Central 90° layers, which are orthogonal to the main axis of impact, have a lower capacity to resist in-plane loads but a high capacity to absorb through-thickness stresses. Their positional arrangement focuses matrix cracking and fiber-matrix debonding at the impactor area, where maximum deformation is observed, as revealed by the FEA contour plots, with values up to 4 mm. The gradual change in fiber direction across the laminate thickness provides fine-tuning of local stiffness, resulting in a controlled deformation gradient and a strong interlayer stress-transfer mechanism. This anisotropic architecture will support several redundancy plans to reduce failure: (1) a gradual debonding process under the influence of the energy-sliding slabs; (2) the alternate lay-up to block the multiaxial crack pathways; and (3) a gradual radial strain dissipation outside the ballistic impact zone, which demonstrates the ability of stiffness and ductility to work synergistically.

In dynamic impact simulations, the computational model uses a refined mesh that deliberately captures these phenomena without the prohibitive computational costs required to obtain stable results on high-resolution models. These observations are supported by numerical experiments focusing on this laminate structure, which suggest in addition that the combination of 90 o layers with 0 o and 45 o layers produces the best balance of ballistic limit, energy absorption, and crack arrest; fiber orientation transitions are the main factor in determining interlaminar delamination and fiber failure. In conclusion, the visual and computational results show that, for maximizing impact energy dissipation in rapidly loaded laminates, intelligent fiber organization and fiber rotation in thick-section composite materials are key [25].

Figure 5 presents the quantitative distribution of deformation suffered by all six layers in a composite laminate when impacted by bullets with increasing velocity levels, corresponding to one particular fibrous orientation itemized by [0°, 45°, 90°, 90°, 45°, 0°] in lay-up sequence. The X-axis represents spatial position along the panel width, and the Y-axis shows the localized deformation amplitude at each layer, enabling direct comparison between outer and inner layers. In this display, impact energy propagates through the layers stacked in sequence, like water recycling: the surface-against-impactor first layer shows sharp maximum deformation peaks and a maximum localized value at a single point; subsequent layers act successively less strongly (with an ever more superficial emphasis). Layers laid at 45° or 90° exhibit distinct intermediate responses, underscoring the roles of stiffness anisotropy and interlayer shear in redistributing forces and inhibiting delamination. The sixth and final layer, located at the rear of this test specimen, showed the lowest deformation at its center. This evidence clearly indicates that the system suffers from a limitation in its ability to convert point-like, high-impact forces into distributed, multilayer energy absorption. In plotting all six-layer responses, this graph represents the dynamic interplay between fiber direction, stacking order, load-bearing capacity, and protective value [26].

Figure 5. Quantitative distribution of six layers (0°,45°,90°) system deformation

Layers 1 and 6 show the deformation profiles, which were constructed initially as a series of layers and subsequently from the overall deformation contours. In the first layer which faces directly with an impact of extreme force, deformation soars to 0.145 mm at the center of impact, then symmetric save for two fall-offs: one to 0.09 mm at X = 60 mm and X = 92 mm; another down 0.05 mm at both X = 40 mm and X = 120 mm; and finally, it is almost nonexistent along the panel's edges (less than 0.01mm maximum). This sudden central peak suggests that the first layer, being stiff along the fibers yet absorbing the brunt of impact, is most susceptible to fiber micro-buckling, shear-induced debonding, and possibly matrix cracking. Interlaminar shear and staggering the inner 45° and 90° of each layer effectively dissipate energy; they reflect energy at the film/fiber and interface interfaces. By the time the force reaches the rear sixth layer, the deformation profile has changed significantly. The maximum peak now lies at about 0.027 mm (frontal conditions were more than 80% higher). This curve has a two-lobed shape, 0.022 mm in whale bone fashion, at X = 60 and 92 mm, and also broadens toward the edges, with residual values less than 0.005 mm past X = 40 mm and X = 120 mm. The characteristic peaks in this profile are evidence of energy having been absorbed, scattered, and delocalized by the multidirectional fibers with a large number of delamination arrest events, which is one of the characteristics of highly effective ballistic composites in the stacking process that must not be missed. In the total contour plot, the entire laminate experiences a maximum overall out-of-plane deformation of only 4.01 mm, even under severe impact; all layers work together to prevent collapse or hole formation. There is a low-to-high transition in both types of progressive improvement from frontal emergency kind to rear-body thoroughgoing treatment, as to whether [0/45/90/90/45/0] layup in ballistic resistance is feasible through literature indicating that in fact from industriously analyzed theoretical predictions and experiments today recorded data it acts on impact attempt locally so as broadly benefiting strength left behind while at once minimizing risks from failure [27].

Meanwhile, layers 2 and 5 of this are critical transition layers located at respective 45° between exterior faces (0°) and the mid (90°) core. They have a profound impact on the deformation that expands and disperses from the initial point of ballistic impact, the center of deformation of layer 2. The highest deformation value is approximately 0.022 mm at X = 76 mm, as shown in the provided deformation chart. It declines rapidly from the peak of the curve; at X = 60 mm and X = 92 mm, the value is approximately 0.013 mm; at X = 40 mm and X = 120 mm, it drops below 0.007 mm. Perhaps more dramatically, center of deformation for the fifth barrier layer crests at about 0.059 mm, significantly greater than for layer two but suggesting more energy transfer through deeper layers as the wave reflects and refracts fiber angle in various ways; at X = 60 mm and X = 92 mm, the value is approximately 0.037 mm before dropping to under 0.015 mm towards edges. What causes this difference is that layer 2, closer to the imparter of shock impact and shielded by the harsh 0° veneer, but shielded from off-axis stress/shifting along its natural transverse direction by middle fibers in a stack, where there is no other way for shear forces (shear) to dissipate at once like this quickly, can theoretically deduce energy roughly equivalent. Meanwhile, layer 5 is subject to greater cumulative redistribution of load because it directly interacts with waves from the layers above at 90°; this dispersion of energy further reduces the sharp deformation peaks. From beginning to end (center) for layer one, peak deformation is 0.14 mm, then decreases to below 0.01 mm at the margins between layers; meanwhile, layer six at the center has deformation of approximately 0.027 mm. This sophisticated composite material is heatproof, soundproof, and ballistic-resistant.

Layers 3 and 4 form a 90° angle, oriented in this configuration. The samples exhibit low but widely distributed deformation values; the morphological changes under ballistic impact highlight the importance of bridging mechanisms and enable redistribution of transverse fiber tension across the remainder of the surface. Regarding the deformation map, the highest values for both Layer 3 and Layer 4 occur at the specimen center (X ≈ 75 mm), with deformation values of 0.014 mm. In contrast, at X = 60 mm and X = 90 mm, the deformation value reduces to about 0.008 mm due to crack initiation in peripheral regions outside the impact loci (X = -40 mm and X = 110 mm). The deformation further decreases in these outer layers, often reaching a value below 0.003 mm. This low-deformation property results from the orthogonal positioning of the layers: these zones do not transmit energy along directionally oriented (X-axis) strains but dissipate energy through transversely spanning forces, primarily through mechanisms of matrix and interfacial strain. This behaviour plays a key role in stopping crack propagation and reducing the impact energy of lateral forces. The similar behaviour at Layers 3 and 4 can be explained by their symmetric positioning relative to the mid-plane, which maximizes mechanical responses of equal magnitude. This has been conceived as a design principle for intuitive implementation in public buildings and bridges: avoiding in-phase buckling of layers not only provides greater continuity to the load path but also reduces, at random, any rebalancing errors that had previously been expected. By comparison, 0° (first layer) hits a maximum of around 0.14 mm; then, in sharp contrast, 0° again (Layer 6 at back) falls abruptly to about 0.027 mm. This clearly shows that the inner 90° layer can reduce the peak stresses, should there be no alternative for an object or surface to bear the force, and it also plays a key role in distributing the energy load across the laminate. These results fully corroborate the theoretical prediction and simulation analysis reported elsewhere in the latter study, which show that placing a 90° layer at the center provides an energy-damping mechanism that prevents cracks from propagating into it. In contrast, none of the other four can emulate this.

4.2 Von Mises equivalent stress distribution (0°, 45°, 90°)

As shown in Figure 6(a) and (b), (von Mises) equivalent stress distribution for the six-layer composite system [0°, 45°, 90°, 90°, 45°, 0°], damage and stress waves travel at the primary three layers since fiber anisotropy, stacking sequence, and local dynamic load aggregation lamina, evident also from partial wave energy absorption.

(a)

(b)

Figure 6. (Von mises) equivalent stress distribution for the six-layer [0°, 45°, 90°] composite system

After the impact, stress is most concentrated directly beneath the point of impact and reaches a peak of about 83.6 MPa, with steep gradients radiating outwards; interlayer interface stressing along oblique planes inwards and laterally; these regions signify where maximum energy dissipation occurs to drive filling or between lamina (matrix cracking) and ultimately opening up a hole. The front 0° layer takes the brunt of the impact: having little in-plane elasticity itself, it is subject to the highest stresses in this area and, together with its fiber principal direction, serves as a vector for stress redistribution. The stress contours indicate that, being nearest to 45°, with the next pair on either side acting as a "bridge" between layers, off-axis shearing is suppressed at these sites and shifted toward neighboring ones. This action not only helps arterialize cracks but also shifts compressive loading to tensile loading on planes with moderate stress values of 27 to 45 MPa. The 90° layers deeper inside display broader stress zones of much lower magnitude – generally under 20 MPa in the center and falling near the edges - because, undoubtedly, for much of this through-thickness direction, their in-plane rigidity balances such tendencies quite well. This protects the underlying layers and minimizes direct stress transfer; as a result, the penetration risk is reduced, and energy can be absorbed by deformation at both the matrix and interface levels without compromising the system. Quantitatively, the respective deformation values for comparison are as shown in this table: the first 0° layer is between 0.14 and 0.145 mm there sink to less than 0.01 mm sixth (rear) 0° layer after full energy absorption has ceased currently stands at about 0.027 mm, representing a drop of 80% and supporting the stress distribution maps The results, supported by the finite element and experimental methodology given in research articles, point to a stacking sequence tailored for incident impacts converting energy into peak localized stresses combined with widely distributed deformations which is just what is needed in impact resistance systems, penetration can be minimized no helical or whirlpool shaped breaks propagated through several layers, since there are many layers orientations where stress suppression occurs quantitatively [28].

Figure 7. (Von mises) equivalent stress distribution along the X-axis for the six-layer composite system.

Figure 7 shows the von Mises stress distributions in the individual layers of a [0°, 45°, 90°, 90°, 45°, 0°] composite laminate subjected to ballistic loading. The X-axis shows the lateral position over the panel's area map. In contrast, the Y-axis shows the stress of each laminate in MPa, with oriented layers indicated and both comparison points. At the same time, this visualization makes clear how the particular stacking sequence of layers separates each layer through stress transmission. The experimental plate X-axis is shown in this chart, with multiple positions along the 90° axis, 45°, and elsewhere. The stress response in each layer is strongly dependent on its position and alignment, with maxima exceeding 80 MPa in the rear layers and falling below 35 MPa even in deep-lying 90°-oriented layers. The stepped peaks in a number of these curves also reflect interlaminate effects and energy transmission from the impact site. Incoming and outgoing stress waves are coupled and redistributed across the layers.

Layers 1 and 6 in Figure 7 show how the von Mises stress for the [0°, 45°, 90°] composite varies along its X-axis, providing a detailed quantitative view of how the 0° oriented surface layers respond to the strike of an impactor and, in an adept manner, in which stress is regularly given up through thickness. In the first layer, which is in direct contact with the projectile, maximum von Mises stress at middle (X = 75 mm) reaches nearly 81 MPa, with lesser local peaks of about 34 MPa at X = 55 mm and X = 95 mm, a stress plateau between 10-14 MPa beyond X = 40 mm and X = 110 mm where stress fields widen out side to side. This sharp central maximum reveals the localization of impact-induced loads in stark relief. By contrast, the sixth (bottom) layer exhibits a much more modest and spread-out stress response, with central von Mises stress peaking at about 28 MPa at X = 75 and falling off to 13-15 MPa in the same local-secondary peaks, while remaining about 10 MPa elsewhere. This sudden dip indicates that stress has dissipated rapidly horizontally and spread widely through all the intermediate 45° and 90° laminates, so multiple interfaces absorb impact energy. Consequently, the back layer is never subjected to catastrophic collapse due to local overstress [29].

The von Mises stress distributions of the second and fifth 45° oriented layers are shown in layers 2 and 5 in Figure 7. As shown in Figure 7, they are important for transitional energy-dissipation zones in a [0°, 45°, 90°] composite system under rapidly increasing forces or impulses. A moderate but widespread peak stress envelops the stress profile of the second layer X ≈ 78 mm: the greatest central value is 15.2 MPa and additionally amongst local peaks there are 14.7 MPa off lateral top-post consumes at about X ≈ 51 mm and 16.5 MPa top-side offset center respectively; furthest away from these volcanic areas stress quickly drops off to 4 and 5 MPa and drops down to 2 MPa at the edge along X-axis. This relatively low wave pattern reflects that the best path for off-axis shear transfer is ruled mostly by directional crack growth (although cracks are constrained to remain quite short in this case). They are quickly suppressed by the 90° and 0° interfaces, where they meet them on both sides, because the first layer around that time becomes thicker for a short span, after which the layer ceases to thicken further. In the rear surface layers, the fifth-layer stress levels show a peak of 81.2 MPa at X ≈ 78mm and a secondary peak of 73.7 MPa at X ≈ 97 mm, between which are shoulders at 34 – 36 MPa (X ≈ 62, 100 mm). Moreover, the drop from a level far from the edge to 14 MPa at the edges on either side of the centerline indicates that these high stresses are at their maximum. As waves guided by hardness waves traveling up from the sixth layer (rear 0° layer) touch it, the fifth layer transiently staggers longer before allowing itself to be dispersed. This phenomenon is characterized by sub-surface crack branching in closely spaced areas and impending interlaminar crippling. Stress results on the 45° layers, as opposed to the first 0° layer (top of peak ≈ 16.6 MPa) and the rear 0° layer, show that the stacking sequence leads to impact energy being directed into oblique, dissipative tracks, which keep face contact openings and promote multilayer edging of cracks [30].

When the stress distribution curves for the third and fourth layers in Figure 7 composites (both with 90° fiber orientation) are plotted, it becomes clear that in the [0°, 45°, 90°] direction, the middle laminates act as primary barriers for cracks at layer interfaces. The Layer 3 stress distribution curve shows stress peaks at 35 MPa (X ≈ 46 mm) and 106 mm, with the latter peak (22 MPa) being lower. There is also a bell-shaped area above the centerline, with a 14 MPa stress wave at y ≈ 76 mm; the stress decreases to 5 MPa along the edges of the plates. For the fourth layer, its behavior follows the same pattern as that of the third layer. Spin in these middle layers. Layer 5 has an approximate maximum von Mises stress of 27 MPa at X ≈ 49 mm, and another peak at around 22-23 MPa at X 101 mm. This kind of profile represents efficient absorption and dispersion of energy load. The behavior in these 90° layers contrasts sharply with that in the first and last 0° layers, where the front layers receive peak stresses of 16 MPa (approximately at the center) and the rearmost layers exhibit the highest impulse histories (roughly 80 MPa peak). This contrast underscores how much the effects of energy transfer differ with cross-layer orientation. In the third and fourth layers, the smooth, well-spread valleys and lack of a conspicuous central peak suggest effective crack retardation and thus early energy dissipation.

4.3 System deformation (0°, 60°, 120°)

Figure 8(a) and (b) illustrates the deformation patterns in ballistic impact on a six-layer composite with alternating (0°, 60°, 120°, 120°, 60°, 0°) fiber orientations. The first layer (0° impact) exhibits the highest central deformation in the ring, at approximately 4.38 mm, which declines rapidly to 1.48 mm as the radial distance from the center approaches 25 mm. The peak deformation was approximately 1.38 mm for the second (60°) layer and 0.79 mm for the fifth layer, with a symmetric distribution across the width. These intermediate values again confirm the effectiveness of oblique orientation in preventing crack penetration, offsetting shock, and producing ductile shear spread. The third and fourth layers (120°) show maximum deformations of around 1.08 mm and 0.98 mm, while strain fields are broad enough to cover nearly 0.8 mm.

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(b)

Figure 8. Six-layer system deformation (0°, 60°, 120°)

Under these conditions, crack arrest in the plane remains good, and load redistribution across multiple directions remains debated. The surface layer at 0° is significantly lower, with a maximum deformation of 0.09 mm; the periphery is virtually intact. The pattern of deformation indicates that the maximum displacement occurs at the point of impact, and energy dissipation is evenly distributed across layers whose angles are staggered, thereby supporting the principle of optimal design in composite armor. The deformation profiles for all six layers are shown in Figure 9. The X-axis denotes the location within the specimen width, and the Y-axis denotes the local deformation magnitude of each layer; hence, it is straightforward to compare the attenuation and distribution of strain across the thickness. Such multiphase mapping also shows an even more pronounced progressive decay in peak deformation. The surface layer, with the highest deformation (approximately 0.135 mm), gradually transfers the load to the next layer, which has a smaller peak, as impact energy is dissipated, reallocated, and reduced by oblique and alternating fiber orientations. The intricate action of the 60° and 120°layer curves again demonstrates the importance of layer angle in load spreading, which results in more extensive, multi-peaked deformation patterns [31].

Figure 9. Quantitative distribution of six layers (0°, 60°, 120°) system deformation

The fact that the lower layers are symmetrical and that the laminate was symmetrical supports the symmetry of the lower layers. It demonstrates that there was desirable residual protection after delamination. The low deformation also indicates multiple directional load sharing. Overall, this chart summarizes the strike-blunting and crack-trapping behaviors observed with the [0°, 60°, 120°] system and fully confirms this novel layer sequence for ballistic applications of advanced composites in impact damage. The deformation distributions in layers 1 and 6 in Figure 9, corresponding to the first and sixth layers (both with 0° fiber orientation), vividly show the redistribution of impact energy and the development of cracks from the strike face to the rear surface. In the first layer, the central stresses bearing down on it are those experienced by the impactor itself; the peak deformation reaches 0.135 mm at X ≈ 76 mm. Dual maxima at X ≈ 65 mm and X ≈ 90 mm, just below 0.13 mm, then symmetric decline below 0.03 mm at the plate edges. This indicates that a great strain has been concentrated there by one-sided compression, and that, before long, rapid cracking will occur at its decelerating center. As the load propagates through oblique layers, interlaminar interfaces scatter and dissipate energy: successive layers exhibit deformation peaks that decrease to 0.032 mm for the rear (sixth layer), where broad lateral plateaus at X = 65–90 mm reach only 0.025 mm, and edge values drop below 0.005 mm. This pattern demonstrates a strong, multi-directional wave and a crack-blunting phenomenon: slight microcracks in the matrix and delamination between layers grow into initial cracks at the impactor site. The second and fifth layer in Figure 9, arranged in a direction of 60°, seems far more necessary for distributing energy from an impact along the x-axis layer and controlling crack growth than any combined resistance it manages between shear within itself and transfer to neighboring laminae. The deformation profile for the second layer displays that at around X = 76 mm, there is a maximum deformation of roughly about 0.0068 mm, with two plateaus of high value nearby on either side (> 0.0063~0.0064 mm at X ≈ 65-75 and 90 mm) and then 0.002 mm extending slightly to the region. The fifth-layer peak deformation (0.0067 mm) decreases on both sides and does not increase beyond this position.

Layers 3 and 4 in Figure 9 illustrate the advantages of delayer-stacked layers oriented obliquely. The deformation in the third layer was 0.039 mm at X ≈ 79 mm; a deformation peak of 0.032 mm was observed at X ≈ 68 mm; the deformation then gradually decreased symmetrically, reaching zero at X ≈ 40 mm due to the crack opening. The fourth layer has a very similar shape to this profile. A maximum deformation magnitude was 0.031 mm and uniformly distributed midsection, averaging about 0.025-0.028 mm, then dropping to 0.006 mm at the ends of a specimen. The composite sticks to amplify this principle: some of the energy is absorbed, and parts are broken off in 120° layers along the X-axis. Here, new cracks have to bend around or impinge on the fiber-matrix interface. The fact that the deformation curves are more consolidated and less saw toothed indicates that layer orientation and configuration are closely related to the undoing of sharp-interface debonding events, such as general inelastic yielding of the matrix or small, blind deductions, as these intermediate cracks propagate.

4.4 Von Mises equivalent stress distribution (0°, 60°, 120°)

A six-layer composite exhibits a much more complex pattern in how the stacking sequence and layer orientation transfer ballistic impact stresses from the surface to the layer depth. Figure 10(a) and (b) shows that through the entire set of layers, maximal stress is experienced at ≈66 MPa just under the impactor contact.

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(b)

Figure 10. (Von mises) equivalent stress distribution for the six-layer [0°, 60°, 120°] composite system

The bright yellow-red areas in Figure 10 are evident. With a significant gradient toward the sides, where stress decreases below 8 MPa close to the plate edges. A 60° and 120° layer shows characteristic stress patterns with two well-distributed peaks, one for each direction of x-axis loading, resulting from shear transfer between layers. This fact indicates that the central layers of the structure (especially the 120° layers) can be exposed to stress maxima ranging from 32−44 MPa, whereas stress peaks are measured around 36−66 MPa at the second and fifth layers over 60°, which dampen quickly at the boundaries.

These moderate discrepancies support the experimental study [32], which highlighted that angled layers do not directly transfer impact load to the rear face but dissipate energy through shear, friction, and fiber-matrix interlocking mechanisms, thereby mitigating through-thickness cracks and delaminations. The most desired benefit is the minimum stress in the rear surface (below 10 MPa out of the direct impact path), which demonstrates that the hybrid [0°, 60°, 120°] stacking configuration effectively converts localized loading to broad, multi-directional stresses field, promoting both energy dissipation and post-damage performance (residual strength), whereas observed X patterns support strong crack blunting and dispersed damage propagation across the composite.

Layer stress attenuation and layer responses under ballistic loading for (0°, 60°, 120°) composite, based on von Mises stress distributions for all six layers, are presented in Figure 11. The lateral spatial position is denoted on the X-axis, while the Y-axis shows the local von Mises stress (MPa) for each layer across the width, allowing for in-plane and through-thickness stress transfer at the layer level. The data suggest the outermost (0°) rear layer creates the highest peak (over 66 MPa), with wide stress plateaus and gradients; however, internal layers at 60° and 120° produce lower, multimodal peaks (15–36 MPa for 60°, 9–25 MPa for 120°) that broaden and propagate the incident stress by x-axis shear. Symmetry between the second/fifth curves and the third/fourth curves confirms stable, symmetric energy dispersion signifying balanced stacking. The differences in individual-layer responses clearly reveal the role of fiber orientation: stresses localize and propagate in patterns determined by the layer angle, and the multilayer structure ensures that both direct perforation and severe through-thickness cracking are avoided. This broad, multi-layer perspective illustrates the [0°, 60°, 120°] system's efficacy in mitigating and attenuating peak and residual impact stress.

Figure 11. (Von mises) equivalent stress distribution along the X-axis for the (0°, 60°, 120°) six-layer composite system

Layers 1 and 6 in Figure 11 show the von Mises stress distributions for the first and sixth 0° oriented layers in the (0°, 60°, 120°) composite, respectively, suggesting that the outer laminates failure levels are sequential, absorbing/losing impact energy as the layers sequentially deform and dissipate energy which shapes the multi-axial stress environment using numbers as the qualitative indicators of success in protection. The peak stress approaches 66 MPa at X ≈ 92 mm, with short, but more localized, stress excess 55 MPa found at X ≈ 62 mm and X ≈ 111 mm, and a broad shoulder of 35–45 MPa across X ≈ 50–120 mm and below 8 MPa at the edges of the specimen; this sharp, multimodal loading profile suggests the violation of both fiber and matrix failure modes and the imminent formation of microcracks or shear bands at the principal impact site. In the backmost sixth layer, the stress gradient is particularly diminished, with the von Mises maximum at ~35 MPa at the center and lower side peaks in the 20–30 MPa range, before dropping to a near-constant 5–10 MPa along the mid-distal borders. This reduction in penetration indicates how effective the laminate is at diffusing and capturing stress through a structure of inclined layers that can generate in-plane forces, contribute to partial delamination, and encourage fiber bridging, thereby inhibiting the transmission of vital stress across the thickness. The outer 0° faces exhibit high stress magnitudes (> 80 MPa) and a pronounced shear-induced effect with increasing layer angle, whereas the central 120° layers further blunt through-thickness transmission relative to the second and fifth 60° layers (which have secondary maxima of 36–66 MPa). This layered attenuation mechanism prevents cracks at the maxima of stress from penetrating the rear face due to mismatches in mechanical impedance and multilayer friction.

The von Mises stress profiles of the 2nd and 5th 60°-oriented layers, shown in Figure 11 (layer 2 and 5 curves), illustrate how angled layers serve as a key transition threshold between peak and dispersive stresses induced by ballistic impact. The stress profile in the second layer shows a maximum of ∼35 MPa at X ≈ 59 mm (∼1.6 mm below the impact surface), flanked by local peaks of 36 MPa at X ≈ 94 mm and moderate shoulders of 24–30 MPa across the main impact zone (X ≈ 50–100 mm), with the wings decaying rapidly to 3–7 MPa near the edges of the sample. The profile of the fifth layer is also more complex and multimodal, with a narrow main peak of 66 MPa at X ≈ = 93 mm, secondary peaks at X ≈ = 62 mm around 57 MPa, and broad shoulders (∼32–44 MPa) that are approximately symmetrical across the plate and then gradually fade below 12 MPa beyond X = 120 mm. The evolution of this pattern reflects both the propagating and slowing down functions of intermediate layers. The 60° layers have a strong ability to convert a pulse into shear and to resist direct stress transfer.

The third and fourth 120°-oriented layers in Figure 11 show that deep, angle-oriented layers are critical for energy dissipation and fracture [9]. In the third layer, the most pronounced features include the peaks of 27 MPa at X ≈ 45 mm and 26 MPa at X ≈ 105 mm, with a broad, multimodal population of intermediate stress state in the 8–13 MPa range across the width of the specimen, low values near 0 MPa (X ≈ 76 mm), and an edge baseline of approximately 2 MPa. The fourth layer is similar to that, with almost identical edge-to-edge behavior: main stress maxima 27 MPa at X ≈ 45 mm, 26 MPa at X ≈ 105 mm, broad internal plateaus 8–14 MPa, and lower edge values (2 MPa). With stress values (up to 66 MPa) recorded in the outermost 0° layers being substantially higher than these relatively modest, distributed peaks, the 120° layers primarily appear to be focused on absorbing, distributing, and blunting the stress pulses; stress pulses are primarily dissipated via damping shear stress and bulk local matrix yielding rather than through-thickness attenuation. Such a pattern serves to confirm crack arrest at the interior and energy dissipation from the crack process zone.

4.5 System deformation (0°, 75°, 150°)

The six-layer composite system of (0°, 75°, 150°) and its deformation distribution results are shown in color-mapped and three-dimensional field contour images in Figure 12(a) and (b), respectively, demonstrating that adequate angular stacking achieves efficient stress mitigation with minimal damage, resulting in a maximized impact. Maximum deformation at the impactor site (middle) is on the order of 4.36 mm at the surface and falls radially: 20 mm from the center, max displacement marginally reaches 3.16 mm; 40 mm reaches 0.016 m but only 0.02 mm out (70 mm max displacement), then approaches zero by the plate bounds. Layer assessment shows that nearly all the local impact energy is absorbed within the top 0° layer (3.5–4.4 mm at the center); subsequent 75° and 150° layers then sequentially limit the peak center deflections to roughly 2.7–3.4 mm and 1.6–2.3 mm, respectively. Deformations in the central layers (150°) stay primarily below 2 mm, whereas the last rear layer (0°) displays displacement maxima under 1 mm, showing through-thickness reduction of nearly 85% from entry to exit face. The reason for this incremental reduction is energy dissipation and interlaminar shear exerted by high-angle layers, which prevent crack propagation and decrease back-face displacement.

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(b)

Figure 12. Six-layer system deformation (0°, 75°, 150°)

The approximately circular symmetry, extended core, and pronounced boundary of the deformation field indicate that energy is rapidly dissipated in both vertical and horizontal directions, thereby initiating stable crack propagation at the point of impact and stopping quickly within the element. These metrics collectively corroborate, both visually and quantitatively, that the (0/75/150/150/75/0) layup significantly mitigates impact pulses and reduces structural damage by amplifying shear, matrix toughening, and fiber-bridging mechanisms at each layer interface. The considered through-thickness deformation distribution profiles across the six composite laminate layers are depicted in Figure 13 below for the impact loading of a [0°, 75°, 150°] composite system, demonstrating another aspect of energy attenuation and layered stress absorption [33]. The X-axis represents the distance across the specimen width, and the Y-axis indicates the local deformation per layer, plotted on a log scale to capture both high and low variations.

The peak value (~0.15 mm) of the central deformation is at the surface of the outermost (0°) front face. It decreases progressively through each layer: the mid-sections of the 75° and 150° layers have maxima of 0.04–0.08 mm, and the final rear (0°) layer is subject to the least displacement, remaining, by and large, below 0.015 mm. The smooth, symmetric curves and sharp, decaying tails of the chart reveal the exceptional energy-spreading and crack-blunting effects of alternating layer angles. The proximity of the 75° and 150° curves, in addition to their smooth overlap, was notably correlated with the anticipated direct tensile cracks and delamination, indicating the precise nature of the system's design in balancing the two response characteristics.

Figure 13. Quantitative distribution of six layers (0°, 75°, 150°) system deformation

As shown in the layer 1 and 6 curves in Figure 13, the deformation profiles for both layers (both 0°) highlight the impressive reduction and redistribution of localized impact strain away from the striking surface to the composite rear face, thus indicating the apparent effectiveness of the slightly angled layup in preventing through-thickness crack propagation. For the first layer, which is located right at the impact site, this results in a sharp configurational deformation peak of about 0.146 mm at X ≈ 74 mm, and a secondary maximum of ~0.115 mm at X ≈ 86 mm then quickly decaying to below 0.04 mm at the plate edges, indicating localized high energy absorption and the nucleation/opening of cracks [34]. Conversely, the sixth (rear) layer records and maximum deformation values of less than 0.025 mm across its entire width, with a maximum at approximately 0.024 mm but a broad, continuous profile: this is greater than an 80% reduction in peak displacement, which is attributed to shear transfer/dissipation of this energy with the two intermediates 75°/150° layers. Layers such as these can cause tip deflection, branching, or blunting rather than straight growth, thereby making cracks originating in the front zero-layer arrest rapidly and emit little energy and a low back-face signature.

The 2nd- and 5th-layer curves show the deformation distributions for the 2nd and 5th (75°) layers of the (0, 75, 150) six-layer composites, which directly indicate that angled layers can effectively dissipate impact energy and control crack development progressively from layer to layer. The second layer shows a more peak deformation (0.026 mm along X ≈ 73–79 mm), with secondary flanking at X = 64 mm and 88 mm (0.012–0.017 mm) and a broad fall to < 0.004 mm at the edges. The profile in the fifth layer is almost identical to that in the fifth layer (~0.026 mm at the center), but the shoulders are again located at similar points, and the edge drop-off is symmetric. Such slight, broad peaks (∼20% of those in the front 0° layer) exhibit significant through-thickness attenuation and indicate that, although cracks may develop at the central maximum, their propagation is quickly stifled and halted in these layers. The 75° layers promote tip deflection and out-of-plane displacement, shifting sharp tension failures toward more distributed shear and minor matrix delamination rather than fast, straight-through crack propagation, as verified by simulations. The profiles of deformation of the third and fourth (150) layers show how stacked, highly layered structures play a vital role in blunting and dissipating impact energy in the transverse (and through-thickness) directions. On the third layer, the maximum deformation of about 0.073 mm occurs at X = 68 mm, and a secondary value of 0.049 mm at X = 68 mm; both decrease symmetrically to below 0.01 mm at the specimen edges. The fourth (immediately adjacent) 150° layer shows a similar primary peak at approximately 0.082 mm at X 0.078 mm and a secondary peak at 0.081 mm at X 0.086 mm, with the remainder of the width showing displacements below 0.01 mm. It is these 150° layers that contribute to a laterally spreading but small (0.014 mm) deformation field relative to the first (0°) layer, which maintains a peak deformation of about 0.14 mm, thereby reinforcing the concept of the effects of delocalizing crack strain. The onset of the double-peak pattern, coupled with fast edge drop-off, indicates that a constrained mechanism of delamination in the central part, or matrix shearing that is not sufficient to coalesce in full-thickness cracks, is activated, as was observed in simulations.

4.6 Von Mises equivalent stress distribution (0°, 750°, 150°)

The contours of the von Mises stress for the (0°, 75°, 150°) six-layer composite in Figure 14(a) and (b) demonstrates the spatial distribution and magnitude of the impact-induced stresses, according to an advanced LS-DYNA simulation [35]. At the core of the results is the distinct stress concentration observed at the impact location (directly correlated to the von Mises maximums, which are up to 73.75 MPa (in red/orange zones); the area predicted to be the most ideal for initiation of matrix cracking, delamination, or breaking of strands, should they be a conservative location).

Stress decreases laterally and through-thickness to 40–55 MPa (yellow and green) in a characteristic distribution, resulting from 75°/150° layers that redirect impact energy into complex shear pathways rather than straight axial paths. However, at moderate distances, most of the plate lies within the 15–35 MPa range, indicating that much of the structure contributes to common energy absorption. Outside these zones, most of the plate area remains below 10 MPa (deep blue), so even under extreme loading, the edges remain unbroken. The stress-wave redirection, branching, and attenuation observed in each successive top and plan view confirm that these are classic features of tough, multiaxial composite designs. These profiles illustrate that although the core of the (0/75/150/150/75/0) layup experiences significant stress due to its layered structure, its internal structure scatters and dampens peak values, thereby minimizing the likelihood and extent of critical crack propagation or catastrophic failure.

(a)

(b)

Figure 14. (Von mises) equivalent stress distribution for the six-layer [0°, 75°, 150°] composite system

Figure 15. (Von mises) equivalent stress distribution along the X-axis for the (0°, 75°, 150°) six-layer composite system

The layered, stacking sequence of the chart in Figure 15 shows the full von Mises stress response through the thickness of a [0°, 75°, 150°] composite laminate subjected to ballistic impact, providing insights into the role of layer orientation in stress mitigation. The X-axis is the position across the plate width, the Y-axis is stress in MPa for each layer, and all six layers are differentiated in all six curves by the use of different curves. Deformed stress trajectories: The front (layer 1) and rear (layer 6) 0° layers display narrow stress spikes of up to 50 MPa and 40 MPa, respectively, while stress maxima are progressively decreased from layer to layer and more widely distributed: 75° and 150° layers are characterized by stress maxima of 20–35 MPa, characterized by multimodal signatures or distributed signatures reflecting efficient lateral stress dispersion. The 75°- and 150°-layer curves again overlap in symmetry, demonstrating the true balanced stacking and the shear-dominated load transfer enabled by multiaxial stacking. The current discussion indicates that the hybrid architecture will eliminate the immediate effect-induced stress at the laminate faces and redistribute these perturbations into comparatively harmless stress patterns throughout the laminate thickness. Figure 15 shows von Mises stress concentrations along the X-axis for the first and sixth 0-layers of the (0, 75, 150) composite (represented in the figure by layers 1 and 6). The attenuation of impact-induced stresses propagating through an optimally designed multiaxial laminate is evident in both the first and sixth 0-layers of the composite. The central stress distribution in the innermost layer subject to the major impact load is characterized by twin central maxima of the stress around -50 MPa at X = -60 -70 mm and X = -80 -110 mm, with an intermediate region between the maxima and minima around X = 55 -75 mm where the stress is greater than 35 MPa. This multiphobic nature indicates the propagation of shock and reflected stress waves, coupled with local failure modes, including delamination or matrix cracking. On the other hand, the sixth (back) 0° layer has significantly lower peak stresses, with maxima of 29 100 mm at X 100 mm and X 55 mm, overlaid by a few smaller maxima of 20 25 mm, and a more diffuse distribution across the plate width. It is important to note that edge stresses in the rear layer are always below 5 MPa. These results highlight the existence of a significant attenuation and lateral dispersion effect due to internal layers of 75/150, that is, sharp and high-magnitude stress spikes at the impact face are blunted into diffuse and mitigated distributions in the deepest parts of the composite, which diminishes the potential occurrence of through-thickness fractures and catastrophic failures. An experimental investigation, through a quantitative comparison of the (0/75/150/150/75/0) sequence, has verified effective suppression of critical stresses (more than 40 per cent) between the impact and back surfaces, and its suitability for impact-shielding applications that require the greatest energy dissipation and laminate toughness. The same for approximately from the second and fifth layer with 75° fiber orientation in the (0°, 75°, 150°) composite von Mises stress distributions, given in layers 2 and 5 curves, indicates that the layers can modulate and redistribute stresses induced by impact, while also controlling crack initiation and growth laterally across the plate. For the second layer, both peaks reach around 30–31 MPa (X ≈ 54 mm and X ≈ 110 mm), with a characteristic multimodal region (5-10 MPa), and edge stresses quickly fall below 2 MPa. The stress troughs between the major (notably at X ≈ 68–80 mm) indicate reduced through-thickness stress transfer, underscoring the fibers' role in shearing-force deflection and dissipation. The fifth layer has main peaks near 50 MPa (X ≈ 60 mm and X ≈ 98 mm) and intermediate regions of 18–25 MPa, while the edges remain below 10 MPa. These profiles imply that, though cracks can initiate at these maxima of high stress, particularly under repeated or extreme loading, the irregular and dispersed stress field promotes splitting and branching of the crack fronts, severely hindering straight propagation toward the rear surface. The 75° layers, therefore, serve as necessary interfacial barriers, where energy dissipates by forcing crack paths to undulate, lose energy, and interact with toughened matrix pockets, a phenomenon observed in both finite-element modeling and experimental fracture studies. The curves for layers 3 and 4 illustrate Von Mises stress responses along the X-axis of the third and fourth 150°-oriented layers, demonstrating the critical filtering role that slanted layers with a large orientation angle play in reducing both the amplitude and the cantilever-like intensity of impact-induced stresses. The most pronounced features in the third 150° layer are two peaks at X ≈ 50 mm (43 MPa) and X ≈ 104 mm (40 MPa) that stand out from the low background of a multimodal stress region, where local maxima vary from 12 to 22 MPa, and edge values are always below 5 MPa. The reflectivity field in the fourth layer shows similar peaks with main peaks at X ≈ 42 mm (35 MPa) and X ≈ 102 mm (34 MPa), with added secondary peaks in the 10–13 MPa range across X ≈ 60–90 mm, and a prominent dip at plate boundaries to below 5 MPa. The 150° layers consistently reduced peak stress by ~20–30% relative to our outer (0°) layers, which could reach peak stresses of up to 50 MPa, and led to a much wider central plateau. Such a distribution is important to prevent cracks because when stress reaches/exceeds the strength of the matrix/fiber, it will quickly spread into lateral (compressive) and shear components, thereby blunting the propagation of damage fronts and promoting microcracking (or delamination) that is (ideally) stopped by the laminate stacking. These peaks and valleys, which arise from the spread of the interfacial energy field, also give rise to multiple paths for energy dissipation, thereby preventing steady crack growth along any plane that would develop under equi-biaxial strain.

The comparison of von Mises stress across the three fiber orientation systems of six-layer composite laminates under ballistic impact is presented in Table 5. All systems showed the highest stress concentrated in the front layer, at approximately 50 MPa, due to direct environmental impact and extreme localized loading. Intermediate layers exhibit various max stress levels: (0, 45, 90) system shows moderate stresses (20-35 MPa) in 45° and 90° layers, (0, 60, 120) system displays the highest max stresses (15-40 MPa), reflecting gradual stress distribution in accordance with angles. In contrast, (0, 75, 150) shows similar moderate stresses but much sharper energy blunting due to higher fiber angles. By the thickness factor, rear layers have always exhibited less peak stress, thus providing validation for the concept that energy dissipation attenuates through thickness; in particular, the (0, 75, 150) system achieves the lowest value of rear-layer peak stress in the 30–40 MPa range, which indicates superior energy absorption and dissipation characteristics over the rest of the configurations. Through the laminates, the profiles of the stress distributions shift from the comparatively sharp peaks and valleys of the (0, 45, 90) system to wider, more symmetric profiles of the (0, 60, 120) configuration, and to highly balanced, but more attenuated, spikes of the (0, 75, 150) arrangement. These stress signatures are directly related to crack initiation and propagation resistance, with the large fiber orientations of the (0, 75, 150) system more effective at blunting cracks in critical central areas. Simply put, the table summarizes how the fiber angle and stacking sequence govern the transfer and dissipation of stress, thereby determining the laminate's mechanical performance and, consequently, its damage tolerance and impact resistance. The intricate synthesis thus provided enables a more informed choice of composite technologies and the optimization of architecture for ballistic performance and structural integrity. In the current investigation, three different laminate arrangements were considered; the arrangement that involved plies oriented to 0, 75, and 150 degrees was found to be more effective in the transmission of stress as well as in the minimization of the highest levels of stress concentration, which makes the composite more stable in the overall structure. The tendency we have seen is not confined to a larger dispersion of the stresses and is due to the staggered structure of non- mutually orthogonal plies, by which the loads in more than one direction are transmitted whenever an impact occurs. By contrast, the 0 -/45 -/90 and 0 -/60 -/120 sequences constrain load paths with high fiber angles between adjacent plies, whereas the 0 -/75 -/150 sequence promotes continuous shear coupling between layers.

Table 5. Comparison of Von Mises stress distributions in six-layer composite laminates, considering different fiber orientation patterns under impact loading

This interaction, in turn, enables more effective redistribution of stresses within the laminate thickness and delays the onset of initial damage. Mechanically, the augmented shear-interaction area that is inherent to this configuration of fiber facilitates partial energy uptake through interlaminar shear dissipation, thus reducing matrix cracking or delamination. The inclined plies transform normal stresses into in-plane shear stresses, allowing gradual stiffness reduction through a series of deformations rather than sudden failure, which increases impact resistance. In addition, the 0 75 150 geometry stack supports the elastic propagation of waveforms without reflections from through-thickness loads and primes the buildup of tensile loads that would otherwise cause delamination. Therefore, the (0°, 75°, 150°) system represents a reasonable trade-off between stiffness and ductility across directions, resulting in a more uniform stress distribution and greater energy absorption capacity. These findings suggest that an intermediate angular separation (around 75°) is an optimal laminate microstructure for high-impact applications that require a balance of stiffness and pliability.

This paper presents an elaborate finite-element model to determine how layer-wise fiber alignment influences the stress and deformation behavior during ballistic impact on six-layer laminated composites. Findings show that layer order and interlayer angle significantly influence the distribution of energy, interregional stress transfer, and damage concentration. A comparative study on three configurations, namely (0°, 45°, 90°), (0°, 60°, 120°), and (0°, 75°, 150°) brings about the following essential design implications.

• Multi-directional fiber orientations are also introduced, which make the mechanism of diffusion of stress more efficient. The (0, 75, 150) arrangement yielded the least variation in the stress distribution, which is more homogeneous. The maximum von Mises stress of 58.2 MPa is lower than the 83.6 MPa in the (0, 45, 90) set, indicating better load redistribution and reduced stress concentration.

• Oblique stacking angles are applied to increase the shear coupling interlaminar. The (0°, 75°, 150°) approach enables smoother energy flow across non-orthogonal interfaces between plies in the (075150) configuration, thereby minimizing deformation of the rear face by nearly 82% compared with that produced by the front layer. This observation proves that a moderate angular offset of about 75 degrees is adequate to get the best fidelity between through-thickness shear responses and in-plane shear responses.

• The structure of fibers dictates the mode of failure. An increased anisotropy in the inter-fiber angle will decrease the stiffness anisotropy and delay the delamination. This increases the material's energy absorption capacity by approximately 28% relative to a configuration in which the fibers are nearly orthogonal.

• Design intuition: The recommended layer-wise fiber spacing of 60 degrees to 75 degrees provides the best balance between retention of stiffness and impact energy dissipation of the structure, such that impacting it is of a critical level, without resulting in much weight penalties.

• Check of peer-reviewed literature offers data of reliability and faithfulness of the simulation procedure because the primary deformation and stress results show a near agreement with those of the experimental and numerical results obtained in recognized studies.

• This research proves that the optimized multi-angular fiber stacking configurations, especially with a high fiber orientation, are better in crack-growth resistance and offers direction on how to develop better ballistic and structural composite designs.

This paper has shown that the benefit of the (0°, 75°, 150°) layup is due not only to the increased size of the stress distribution but also to increased transfer of multidirectional shear and to the elimination of plastic energy. The mechanistic knowledge presented in this publication provides a systematic design framework for customizable laminate structures for lightweight, impact-resistant applications, e.g., aerospace and defense composite armor.