Influence of the insertion of shape memory wires in composite materials on impact response

Abstract

In recent decades, the quest for high-performance materials—those that combine low weight with high mechanical strength—has intensified. A promising solution involves composites reinforced with fiber and a polymeric matrix. However, these composite materials often exhibit deficiencies in crashworthiness. To address this issue, we investigated the incorporation of shape memory alloys, specifically nickel–titanium (NiTi), into the laminate structure. This study aimed to develop an equation, using a design of experiments approach, capable of predicting the energy absorption capacity of fiberglass and epoxy resin matrix composites upon impact, with integrated NiTi wires. Additionally, we proposed a model through numerical simulation using the finite element method to correlate with experimental analyses, thereby establishing a reliable model for future research. We selected the appropriate NiTi alloy (martensitic or superelastic) for the impact specimens through a full factorial design and dynamic mechanical analysis. After choosing the statistically superior superelastic wire, we manufactured test specimens using vacuum assisted resin transfer molding. These specimens, designed with three variables (diameter, spacing, and position in the laminate), followed a fractional factorial design. The drop-weight impact tests, conducted according to the ASTM D7136 standard, demonstrated increased energy absorption when NiTi wire was included in the composite. A non-linear numerical simulation (dynamic analysis) was performed, and its results—showing an excellent correlation with experimental data (above 95%)—validated the model.

Introduction

Advanced technology industries, such as the aerospace and automotive sectors, are experiencing an increasing demand for parts and components that are lighter yet strong enough to withstand high loads. One effective solution is the use of fiber-reinforced composites with a polymer matrix, notably those using carbon fiber or fiberglass combined with an epoxy matrix. These materials significantly reduce the weight of structures and offer additional benefits, including enhanced mechanical strength, toughness, corrosion resistance, noise attenuation, and damping capacity [4].

However, a notable deficiency in these composites is their limited crashworthiness—the capability of a structure to protect occupants during a collision event [5]. Crashworthiness involves energy absorption through controlled mechanisms and failure modes, creating a gradual load profile during absorption to ensure occupant safety [1]. Addressing this challenge necessitates research into solutions that enhance impact energy absorption. One promising approach is the integration of smart materials, such as shape memory alloys (SMA), into the composite laminate as active structures that adapt their properties in response to environmental conditions. Among smart materials, SMA or, in the case of this work, shape memory alloy wires (SMAWs) can change their mechanical properties based on the temperature to which they are exposed [6].

Among smart materials, nickel–titanium (NiTi) wires, commercially known as nitinol, are particularly valuable. These wires are typically classified by their activation temperature (A_f) into martensitic and superelastic types. Martensitic wires exhibit martensite as the stable crystal structure at room temperature, whereas superelastic wires maintain austenite as the stable phase [7].

Understanding the thermomechanical properties of shape memory materials (SMMs), such as SMAs and shape memory polymers (SMPs), is crucial for advancing and applying these materials in intelligent elements across various fields. SMAs, like TiNi alloys, are notable for their ability to recover from large deformations through the shape memory effect and superelasticity. Similarly, SMPs, such as polyurethane SMPs, exhibit remarkable shape recovery and fixity capabilities that can be utilized in SMP elements [3]. Tobushi et al. highlight that the deformation behavior of these materials significantly varies depending on the thermomechanical loading conditions, such as strain rate, stress rate, temperature, subloop loading, temperature-controlled condition, strain holding condition, and cyclic loading. This understanding is essential for the proper design and functionalization of SMM elements, which could lead to significant innovations in various industrial and technological applications. The study by [3] on the thermomechanical properties of TiNi shape memory alloy, polyurethane shape memory polymer (SMP), and their composites provides a fundamental basis for exploring these unique properties in smart composites.

In comparison to other smart materials, SMA offer some advantages such as high reversible deformations (up to 6%) and shape recovery, high damping capacity, significant reversible alteration of mechanical and physical characteristics, and the ability to generate high recovery stresses when prevented from returning to their original shape. These alloys can be in the form of wires, facilitating their integration into polymer composite materials. Additionally, SMA wires can bring additional functionality without drastically disrupting the initial microstructure and structural properties, thus preserving the low weight of composites. As a result, composite materials with SMA wires can exhibit functions such as shape change, controlled thermal expansion, change in the natural vibration frequency of the component after activation, possible damage reduction, and repair [9].

In this work, we present a novel approach to enhancing the impact response of composite materials by integrating SMAWs, specifically Superelastic NiTi wires, into fiberglass and epoxy resin matrix composites. Unlike previous studies which have primarily focused on the mechanical reinforcement provided by SMAWs, our research introduces a comprehensive methodology combining experimental tests and numerical simulation. This dual approach not only verifies the enhanced impact resistance capabilities of these composites but also leads to the development of a predictive model using the design of experiments (DoE). This model facilitates a deeper understanding of the variables influencing energy absorption, thereby paving the way for optimized composite structures tailored for specific impact resistance applications [2]. Furthermore, our study explores the effect of variable wire configurations (diameter, spacing, and laminate positioning), providing insights that extend beyond the commonly studied parameters, thus offering a significant contribution to the field of smart composite materials.

Theoretical background

Shape memory alloys embedded in composite materials

The term composite material, as per Strong [11], refers to the union of two or more different materials that combine to form a third material. If well designed and manufactured, the new material exhibits better structural properties than its individual components. One of these components is called reinforcement or reinforcing phase, which aims to strengthen the composite in terms of supporting structural loads. The second component is called the matrix and is responsible for bonding and load transfer within the composite [12].

The focus of this work is on structural composites, with the most common reinforcement materials being carbon fiber, fiberglass, and aramid fiber [13]. For composite material processing, the most widely used method in the industry is the stacking of layers of fabric, whether unidirectional or bidirectional, with a predefined orientation. However, one of the limiting aspects of using these materials is their low impact resistance associated with low fracture toughness [14].

Since their discovery, SMAs have been increasingly studied and applied in various fields of knowledge as a viable solution to engineering-related problems [15]. Numerous research efforts have focused on expanding and exploring efficient ways to harness or even enhance their unique properties related to their mechanical performance [16]. In their work, Ashby and Br´echet [17] outlined two possible approaches to improving SMA performance: (i) the development of new alloys or (ii) the creation of hybrid materials that combine the characteristics of existing materials to improve their properties. Studies related to the development of new alloys have led to the acquisition of high-temperature shape memory alloys (HTSMA) [18], magnetic shape memory alloys (MSMA) [19], and SMPs [20].

The second approach proposed by Ashby and Br´echet [17] has seen more studies related to SMAs because, by combining one or more alloys with other materials, new composites with thermoelastic, mechanical, and more efficient phase transformations can be created. This concept incorporates materials with distinct phases, including the use of SMAs as reinforcement or matrix in a porous medium. In the late 1980s, Rogers and Robertshaw [21] incorporated NiTi wires into a polymer matrix composite for the first time, classifying this material as an adaptive material that they defined as a composite containing fibers and SMAWs in such a way that the material can be reinforced or controlled by heat addition.

Shape memory alloys were discovered in the twentieth century, specifically in 1932 with the first observations of the gold-cadmium alloy, which is highly expensive and toxic [68]. In the 1960s, SMA based on NiTi that were more accessible and non-toxic were discovered [15]. The majority of SMAs exhibit three main properties (Fig. 1): (i) shape memory after heating from a deformed martensitic state, with possible bidirectional shape memory effects during alloy training, (ii) damping in the martensitic state, and (iii) superelastic behavior in the austenitic state. To simplify, the alloy that exhibits shape memory at room temperature is the Martensitic alloy, which, as the name suggests, has martensite as the crystal structure and stable phase at room temperature. The Superelastic alloy, on the other hand, has austenite as the stable phase at room temperature [23].

Fig. 1 [Images not available. See PDF.]

Stress–strain diagrams of SMAs and their respective crystal structures at their respective temperatures. aT >> A_f, bT > A_f, and cT < M_f (adapted from [8])

The earliest studies on composites with SMA focused on using activation effects combined with material properties adjustment and deformation energy tuning [24]. Property tuning refers to the transformation of undeformed SMA wires from their martensitic state to the austenitic state to take advantage of the increased modulus of elasticity, which can be very useful in vibration, damping, and structural control. For active deformation energy tuning, initially elongated wires are heated back to their austenitic form. The induced wire contraction leads to high internal stresses (and deformation energy), which, in addition to the modulus change, can provide even greater control over vibration, damping, or other structural features [25].

In their study, Baz and Ro [26] extended this concept, taking into account the dissipation of energy inherited from martensitic transformation along with changes in composite stiffness to achieve optimal vibration control across a wide frequency spectrum. The shape memory effect was also utilized to enhance the strength of composites with SMAs due to internal forces associated with thermal recovery, as initially proposed by Yamada [27] and demonstrated by Armstrong and Kino [28]. Paine [29] also used SMA with a polymer matrix-reinforced NiTi system to alleviate stress peaks in pressure vessels under tension. Table 1 shows some related works on the incorporation of SMAs for improving the mechanical properties of composite materials.

Table 1. Some works related to the incorporation of SMAs in composite materials

Fiber type	SMA model	SMA composition	References
Carbon	Wire	NiTi	[43]
Carbon	Wire	NiTi	[31–34]
Carbon/Kevlar	Wire	NiTi	[35]
Kevlar	Wire	NiTi	[36]
Kevlar	Wire	NiTiCu	[37–40]
Glass Fiber	Wire	NiTiCu	[41, 44–46]
Glass Fiber	Wire	NiTi	[47]

Shape memory alloys in impact response

In the advancement of composite materials development, one of the main motivations has been the increasing need for materials with high stiffness and specific mechanical strength. Recently, the development of composite materials has leveraged their inherent heterogeneity and anisotropy to combine their traditional load-bearing functions with new functionalities in the form of embedded elements. These new adaptive or “smart materials” can integrate actuators or sensors so that they can adapt and respond to their service environment, allowing for efficiency gains and not just reducing structural weight but also integrating functions directly related to the structure. In this context, one of these smart materials is SMAs [6].

The subject of this study, Paine and Rogers [48] demonstrated for the first time the use of NiTi wires (0.4 mm in diameter) to improve the impact response of low-velocity impact-damaged composites. In their work, they integrated NiTi wires into carbon prepregs, parallel to the fibers in the 0° direction in the layers below the neutral axis of the structure. Overall, the volumetric fraction of the wires was 2.8%. This strategy allowed for a 25% increase in delamination resistance at the time of impact compared to composites without SMA wires. The wires also prevented the structure from being pierced by the impactor.

To further benefit from the properties of SMA wires, pre-strain can be applied to the wires before integrating them into the structure. Birman [49] used a micromechanical model based on the multicellular method to model SMA-reinforced fibers under pre-tension. Their results confirmed the effectiveness of SMA embedded in composite layers to improve low-velocity impact properties, provided they were pre-tensioned, and their contraction was avoided during composite manufacturing, thereby creating tensile stresses.

In another study, Tsoi [7] experimentally investigated the potential of pre-tensioned LMFs in fiberglass/epoxy composites to enhance impact damage properties. They integrated superelastic and martensitic NiTi wires (0.15 mm in diameter), as well as stainless steel wires for comparison, into fiberglass epoxy prepregs. To enable the integration of pre-tensioned wires, a special structure was designed to maintain deformation during the composite curing process (which was above the wire transformation temperature). Pre-deformation levels of 0%, 1%, 5%, and 3% were investigated for NiTi wires. The influence of position and volumetric fraction was investigated with NiTi wires, which were integrated between the reinforcement layers at different positions and volumetric fractions of 0.45%, 0.89%, and 1.8%, corresponding to 0.5, 1, and 2 wires per millimeter in the structure, respectively. Overall, the results showed that

(i) delaminated area decreased with increasing LMF pre-tension level, (ii) LMFs needed to be integrated between the layers, in the lower half of the laminate, especially in the bottom layer, to reduce fiber breakage damage, and (iii) increasing wire density increased delamination resistance.

Pappada [50], in two publications, evaluated the mechanical, damping, and impact characteristics of hybrid fiberglass and vinyl ester matrix composites with inserted LMF wires. Three plates for Charpy impact testing [50] were manufactured: (i) plates with 0.1 mm diameter unidirectional superelastic NiTi wires, (ii) plates with unidirectional steel wires to understand the influence of LMF alloys, and (iii) plates with chopped superelastic NiTi wires. All plates had approximately 1% volume of wires and were produced using the vacuum-assisted resin transfer molding (VARTM) process. While samples with chopped wires showed a 37% increase in Charpy impact energy, samples containing unidirectional steel wires and LMF wires did not show a significant change in impact characteristics. The authors concluded that the improvement in the configuration of chopped LMF wires was related to the lower elastic modulus compared to LMFs integrated within the structure. Additionally, they stated that the lack of adhesion in the matrix of unidirectional superelastic wires contributed to the composite’s low performance. The authors continued their work by conducting low-velocity impact tests on laminates with LMFs produced again by VARTM with a vinyl ester resin and a fiberglass fabric [51]. Aluminum supports were used to align the superelastic NiTi wires in the 0° and 90° directions, and the wire volume in the composite was approximately 3%. Impact test curves, measured for energy ranging from 1 to 500 J, showed a slight but marginal increase in delamination for the composites. However, when measuring the resulting damage area by C-Scan, a considerable decrease in the damage area (up to 60%) was observed, especially for impact energies below 10 J.

To observe the influence of LMF wires on improving energy absorption in low-energy composite materials, Aurrekoetxea et al. [30] proposed the use of a thermoplastic matrix with superelastic NiTi wires (0.5 mm in diameter) at a volume fraction of 2.3%. The wires were integrated into a carbon fiber fabric with a poly(butylene terephthalate) matrix. The laminates were processed at 230 °C to allow better impregnation of the thermoplastic resin into the laminate. Impact tests were then conducted with energies ranging from 0.1 to 6.8 J. The results showed that at energy levels above 1.1 J, there is better energy dissipation upon impact in the thermoplastic composites.

To assess the effects of environmental conditions (temperature) on the impact response of laminates, Kang and Kim [42] produced test specimens with 24 layers of a glass/epoxy prepreg and superelastic LMF wires inserted at the neutral axis of the laminate, i.e., between layers 12 and 13. Impact tests were conducted at room temperature and at three different temperatures: 293 K, 263 K, and 233 K. The results showed that the insertion of wires improved the impact response. However, with decreasing temperature, the laminate’s brittleness increased, resulting in decreased impact energy absorption capacity.

In their study, Lau [52] fabricated a composite with 10 layers of stitched (stitching technique) glass fiber/epoxy fabric using 0.22 mm diameter superelastic NiTi wires. Impact tests were conducted at an energy level of 3.4 J, and the results showed that, with LMF wires, the specimens reduced delamination energy, the number of translaminar cracks, and increased the tensile modulus and damping ratio of the composites compared to non-stitched specimens. In the same research line, Vachon [53] produced a composite with 16 layers of stitched carbon fiber/epoxy fabric with LMF and Aramid. The authors observed a reduction of 7% and 19% in impact delamination area (at an energy level of 1 J/mm) for LMF and Kevlar, respectively. Furthermore, with stitching, there was a 1% increase for LMF and an 8% increase for Aramid in the CAI response compared to unstitched specimens. The authors also concluded that these property variations could be improved by increasing the volume fraction of LMF wires in the composite.

In light of the various studies on the insertion of LMF wires into polymer matrix composites, it can be observed that there are numerous parameters to be studied. Among them, we can highlight wire type (superelastic or martensitic), diameter, position, and spacing in the laminate. Additionally, an equation involving all these parameters would make a significant contribution to the technological development of smart materials and their applications. Therefore, this work aims to develop an equation capable of predicting energy absorption capacity in impact and post-impact compression events, as well as conducting more detailed analyses of the influence of each design variable. To arrive at this equation, it was necessary to perform some preliminary steps to assist in selecting the most suitable NiTi wire for the work’s development. For this purpose, dynamic mechanical analysis (DMA) was used, which is a faster and cheaper method for evaluating the viscoelastic properties of the material and whether the wire’s insertion would improve composite properties, allowing for the inference and study of composite deformation over time under constant tension and temperature. This type of analysis uses temperature as an activator for the smart material to adjust its properties. Vilar and colleagues [54] obtained results in the DMA test, finding that shape memory wires inserted into composites obtained with unidirectional carbon fiber prepreg showed a substantial increase in stiffness when heated to a temperature high enough to promote phase transformation. The observed increase in the elastic modulus of nitinol wires indicates great potential for obtaining active structures. Thus, the DMA analysis is justified as a starting point for selecting the NiTi wire to be used in composite impact analysis.

Design of experiments

Design of experiments is a statistical method developed to determine which variables are most significant in a process and the conditions under which these variables should operate to optimize it. It was introduced in the 1920s by Sir Ronald A. Fisher in England in the field of agricultural research [55]. Since then, many scientists and statisticians have contributed to the development of DoE and its application in various research fields.

According to Montgomery [56], experiments are usually conducted to discover something about a specific process or system. An experiment is a test or a series of tests in which intentional changes are made to the input variables so that it is possible to observe and identify the reasons for the changes that may occur in the output response(s).

In the industrial field and scientific development, input variables are considered as control parameters, and the output variables are the response to the problem. As an example, in the study to be developed in this study, the control parameters considered are the variation in wire type, diameter, position, and spacing in the laminate. The response variable will be the energy absorption upon impact and post-impact compression.

Therefore, the experimental design incorporates all the parameters considered in the problem into an experimental design that will be statistically analyzed through Analysis of Variance (ANOVA) [57].

Experimental designs can be categorized by the degree of the characteristic polynomial, i.e., a first-degree polynomial (first order) shown in Eq. 1 or a second-degree polynomial (second order) shown in Eq. 2 [58]. Within the definitions of the experimental design, the most commonly used first-order ones are the full or fractional factorial design, and for second order, there are the central composite design (CCD) and Box-Behnken design (BBD) [56].

1

$$y={\beta }_0+\sum _{i=1}^k{\beta }_i{x}_i+\epsilon ,$$

2

$$y={\beta }_0+\sum _{i=1}^k{\beta }_i{x}_i+\sum _{i=1}^k{\beta }_{\mathit{ii}}{x}_i^2+\sum _{i=1}^k{\beta }_{\mathit{ij}}{x}_i{x}_j+\sum _{i=1}^k{\beta }_{\mathit{ij}}{x}_i{x}_j+\epsilon ,$$where: y represents the real function to be modeled; β₀ represents the constant term of the model; β_i represents the coefficients of the linear terms; β_ii represents the coefficients of the quadratic terms; β_ij represents the coefficients of the interaction terms between factors; and ε represents the residual associated with the estimated model.

In these types of experiments, all factors under study vary simultaneously to obtain a more realistic view of the joint operations of a process. Instead of studying one factor at a time and its response factor, we can study the effects in conjunction with other factors on the response variable. This joint evaluation allows the study of the interaction between factors.

When dealing with factorial experiments, each factor is set at two or more levels, depending on the experimental situation. To study the effect of a factor, it is necessary to have at least two levels. In the industrial area, factors are usually tested at the same number of levels, ranging from 2 to 3.

The analysis methodology used in this work, the full factorial design (FFD), and the fractional factorial design, are robust statistical tools that cover the entire sample space and their respective variables. In other words, they are experimental combinations of variables, combined in such a way that each independent variable is experimented with an equal number of times at each of its levels, defined as the upper (positive) and lower (negative) limits [60]. Thus, FFD designs are balanced and orthogonal (the sum of the signs of the upper and lower limits is zero) [61]. The number of experiments to be performed in a full factorial design is related to the number of input variables and can be demonstrated by Eq. 3.

3

$$N=2^k,$$where N represents the number of experiments; and k represents the number of problem variables.

The number of experiments in a full factorial design grows in a geometric progression with a ratio of 2 as a function of the input variables, making its use very expensive in some cases (Table 2).

Table 2. Number of experiments in a full factorial design

Number of variables	Number of experiments (No replicas)
1	2
2	4
3	8
4	16
5	32
6	64
7	128
8	256
9	512
10	1024
…	…
15	32,768
…	…
20	1,048,576

As the number of problem variables increases, higher-order interactions (interactions between 3 or more factors) also increase significantly. However, according to [56], these higher-order interactions usually have little or almost no significance. For example, with 4 input variables, we obtain 6 second-order interactions, 4 third-order, and 1 fourth-order. When working with experimentation, in addition to the costs involved in conducting experiments, replications and triplicates are necessary for the purpose of comparing the process and validating the results, making them more reliable.

Therefore, when there are 3 or more input variables in experiments and cost limitations, the fractional factorial design becomes an excellent mathematical and statistical tool. The number of experiments to be performed in a fractional factorial design is related to the number of input variables and can be demonstrated by Eq. 4.

4

$$N=2^{k-1},$$where N represents the number of experiments and k represents the number of problem variables.

Numerical simulation by the finite element method (FEM)

Numerical simulation using the finite element method (FEM) has been used for some time as the most widely used modeling and structural calculation method for obtaining approximate solutions to engineering problems [62]. The FEM is a numerical technique used to determine the approximate solution for structural calculations, for partial differential equations (PDEs) on a defined domain. To solve the PDE, the main challenge is to create a basis function that can approximate the solution. There are many ways to build the approximation basis, and how this is done is determined by the selected formulation.

The FEM performs very well when solving partial differential equations over complex domains that may vary with time. This method emerged in the mid-1950s as an analytical tool and had a rapid development in the 1960s with the demand from the space sector [63]. Its application has become quite extensive, and it can be applied in both the structural calculation part (linear and non-linear analysis) as well as in the fluid and thermal areas.

Numerical simulation using the FEM applied to composite materials reinforced with SMAWs has been the subject of study in some works. Xu [64] proposed a generic 3D multiscale FEM (FE2) to model the pseudoelasticity and shape memory effects in fiber-reinforced composites with shape memory alloy fibers. The composites were separated into a macroscopic level and a microscopic level, where the constitutive behavior of each integration point at the macroscopic level is represented by the effective behavior of a corresponding representative volume element (RVE). This effective behavior was calculated using the FEM under the RVE meshed by volumetric element. The transition of real-time information between the two levels was performed in the ABAQUS commercial software through its user-defined subroutine (UMAT). A thermodynamic model was adopted to describe the total constitutive behavior of the SMA. This model considers three path-dependent deformation mechanisms related to phase transformation, martensite reorientation, and accommodation through the derivation of Gibbs free energy. Several thermodynamic tests from the literature subjected to tensile-compression and bending loads were studied to validate the multiscale model, which showed good accuracy and reliability.

In his work, Brinson [65] developed a procedure through the nonlinear FEM that incorporated a thermodynamically derived constitutive law for the behavior of shape memory alloy materials. The constitutive equations include the internal variables necessary to explain material transformations and were used in a one-dimensional finite element procedure that captures the unique responses of shape memory alloy materials and the pseudo-elasticity of shape memory effects at all temperatures, stress levels, and loading conditions. The solution to the nonlinear problem was obtained by applying Newton’s method, where a sequence of linear problems is solved numerically due to consistent linearization, achieving quadratic convergence. Several test cases were presented to illustrate the potential of the finite element procedure. These cases simulated the stress-strain behavior of a shape memory alloy bar under simple uniaxial loading, as well as restricted recovery responses at different temperatures. The results of these analyses showed a good correlation with analytical results, and the methodology for using the finite element procedure in general cases was demonstrated. The finite element procedure proved to be a powerful tool for studying various applications of SMA.

In another work, Cho [66] presented a nonlinear finite element analysis approach for the modeling procedure of laminated hybrid composite shells with SMAW subjected to structural and thermal loads. Numerical analyses of SMA-reinforced composite laminates were performed by synergizing the nonlinear laminated shell element with Brinson’s model of SMA constitutive law. To verify the proposed procedure, rectangular laminated panels fixed along one side were used. The results of the numerical analysis showed very good agreement with experimental results.

Low-velocity impact-induced damage in symmetric and asymmetric laminates was the subject of study by Singh [67]. A generalized lay-up sequence was proposed for asymmetric laminates. The asymmetric laminate manufactured according to the proposed lay-up sequence has a stiffness characteristic almost identical to that of symmetric laminates. The proposed placement sequence in the work provides a laminate that behaves as almost isotropic. A low-velocity impactor with a mass of 5.23 kg was launched with velocities of 3 m/s, 4 m/s, and 6 m/s. The damage pattern and the energy-time relationship of the proposed asymmetric laminate are compared to symmetric laminates with similar stiffness matrices. The results obtained showed that the damage height and width for the symmetric laminate by numerical analysis were 4.25 mm and 22.96 mm, respectively. For the asymmetric laminate, the damage height and width were 5.67 mm and 23.34 mm, respectively. Thus, it can be seen that these damage predictions are very close to the experimental results.

In his work, Chang [68] developed a damage model based on the Hashin criterion for simulating low-velocity and high-velocity impact in composite plates reinforced with shape memory alloy. The effect of impact velocity on the composite plate with shape memory alloy under fixed boundary conditions was investigated using the FEM, as well as the state of damage. Initially, a low-velocity impact was applied to the model to illustrate the accuracy of the parameters and procedures by comparing them with experimental data. In another step, various impact velocities

Materials and methods

This section describes all the stages of the work’s development, starting from the selection of NiTi wire, through experimental planning and manufacturing, and ending with experimental tests and nonlinear numerical simulations. Figure 2 illustrates the flowchart with the stages of the development of this work.

Fig. 2 [Images not available. See PDF.]

General flowchart

Materials

For the fabrication of specimens for DMA tests, eight layers of plain weave fiberglass fabric with a grammage of 200 g/m² from the manufacturer Fibertex were used. This type of fabric is compatible with various commercial resins, with each warp and weft composed of 300 threads with a diameter of 13 µm, tensile strength of 1500 MPa, and elastic modulus of 75 GPa. The polymer matrix used for the composite plate fabrication was epoxy resin AR21 with the Slow hardener in a 100:33 ratio.

The SMAWs used in the composites of this work were NiTi #1 (superelastic nitinol wire) and NiTi #6 (martensitic nitinol wire) provided by FW Metals, both with a diameter of 0.7 mm. The nickel/titanium ratio of the martensitic wire is 54.70%/45.12% with a tensile strength of 1516 MPa and an elongation percentage greater than 3, while the superelastic wire has a ratio of 56.02%/43.93% with a tensile strength of 1475 MPa and an elongation percentage greater than 10.

The consumable materials used for the DMA specimen fabrication via the VARTM process are listed in Table 3.

Table 3. Materials used in the VARTM infusion process

Material	Model	Manufacturer
Vacuum bag	Flexnyl MLA SF	MAP
Peel ply fabric	MAP Ply—MT	MAP
Edge sealant	TAPE 9880-13A	MAP
Distribution media	INFLUX-E 110-M 1220-100	MAP
Vacuum hose	120-WA-120-160	MAP
Spiral hose	–	–
Infusion line fitting	–	–

Selection of SMA wire

For the wire selection stage, DMA test specimens were standardized with 8 layers of fiberglass fabric and dimensions of 45 mm × 12 mm × 3 mm (width, length, and thickness). Initially, the NiTi wires were uniformly inserted into the laminate along the neutral plane, i.e., between the fourth and fifth layers of fiberglass, as illustrated in Fig. 3. For the selection, three different types of composites were fabricated, in addition to the base sample (B) (composite without the presence of NiTi wire), which were the martensitic (M) and superelastic (S) composites.

Fig. 3 [Images not available. See PDF.]

Positioning of NiTi wires in the laminate

Starting from the wire insertion into the laminate, the resin infusion process via VARTM (Fig. 4) was initiated. In summary, in this process, the layers of fibers (laminate) are positioned against a mold and wrapped in a plastic film whose purpose is to compact the laminate and serve as a flexible counter-mold simultaneously. Then, consumable materials (peel ply fabric, distribution media, resin transport duct) are added, and the system is sealed using edge sealant tape. A vacuum pump connected to a resin outlet is used to apply vacuum, which allows resin infusion through the laminate, impregnating the fibers.

Fig. 4 [Images not available. See PDF.]

Positioning of martensitic and superelastic wires in the laminate (a) and impregnation of fibers via VARTM (b)

According to the manufacturer, after infusion, it is recommended to use a curing cycle to achieve better composite properties. Thus, the composite was placed inside a Solab SL-1152L oven with a controlled temperature of 80 °C for 4 h to ensure complete curing.

To ensure dimensional accuracy, the test specimens were cut on a CNC SHG Router available at NTC UNIFEI. Following ASTM D7028, 12 samples were selected, with 4 of each composite type, for DMA testing with dimensions of 12mm (width) × 45 mm (length) × 3mm (thickness).

DMA tests were performed on a SEIKO SII EXSTAR 6000 DMS instrument, where the base, martensitic, and superelastic samples were tested in dual cantilever mode using a frequency of 1.0 Hz, an amplitude of 20 µm, and 0.01% of the sample’s effective length. The samples were heated from room temperature (∼ 25 °C) to 220 °C at a heating rate of 3 °C/min.

Obtaining equations for DMA

After selecting the superelastic nitinol wire, and considering the various parameters to be studied through the insertion of SMAWs in composite materials, equations were developed to predict the composite’s storage modulus (E^′) and glass transition temperature (T_g) using DMA tests. The T_g of the material can be obtained in DMA tests through the tangent of delta (tan δ). Both the storage modulus and tan δ can be expressed by Eq. 5.

5

$$\text{tan}\delta =\frac{E^{″}}{E^{\prime }},$$where tan δ represents the glass transition temperature of the material; E^′ represents the storage modulus of the material; and E^′′ represents the loss modulus or viscosity of the material.

In this context, the statistical tool used was a full factorial design, where the equation is obtained through linear regression using the least squares method, according to Eq. 6 [59]:

6

$$y={\beta }_0+\sum _{i=1}^k{\beta }_i{x}_i+\sum _{i=1}^k\sum {\beta }_{\mathit{ij}}{x}_{\mathit{ij}}{\beta }_0+\epsilon ,$$where y represents the real function to be modeled; β₀ represents the model’s constant term; β_i represents the coefficients of the linear terms; β_ij represents the coefficients of the interaction terms between factors; and ε represents the residue associated with the estimated model.

For the fabrication of test specimens, an experimental design was conducted using MiniTab, employing a full factorial design (2ⁿ) with 2 factors (quantity of wires and position in the laminate), 2 replications, and 3 center points, generating 11 experiments (Table 4). The wire spacing and laminate position were the parameters adopted to analyze the significance in relation to the quantity and whether their position interferes with the energy absorption and glass transition temperature of the composite through DMA analysis.

Table 4. Factorial design in terms of wire quantity and position in the laminate

Control variables	Symbol	Levels
		Lower (− 1)	Center point (0)	Upper (+ 1)
Position	x1	− 1.125	0	1.125
Quantity of wires	x2	1	2	3

The neutral plane was positioned in the laminate’s center; therefore, the values − 1.125, 1.125, and 0 correspond to the position below the neutral plane (between layers 7 and 8), above the neutral plane (between layers 1 and 2), and on the neutral plane (between layers 4 and 5), respectively.

Experimental design for low-velocity impact tests

To prepare specimens for low-velocity impact tests, an experimental design (DOE) was conducted using Minitab, employing a fractional factorial design (2^n−k) with 3 factors (NiTi wire diameter, wire spacing, and position in the laminate), 3 replicates, and 3 center points, resulting in 15 experiments. In other words, 15 composite laminate plates with different configurations were created. Regarding the specimens manufactured for the DMA test, wire spacing and position in the laminate were also adopted parameters, with the inclusion of the NiTi wire diameter to analyze its significance concerning the amount of energy absorbed by the composite in the low-velocity impact test.

The decision to use a fractional factorial design was made to reduce costs since a full factorial design would have required approximately 27 experiments, making the work economically burdensome due to the high costs involved, such as epoxy resin, fiberglass, NiTi wires, machine hours for specimen cutting, machine hours for impact tests, etc. Furthermore, the use of a fractional factorial design does not result in significant losses in the model because higher-order interactions usually do not have a high degree of significance, which does not compromise the analysis of the work (Tables 5, 6).

Table 5. Fractional factorial design for NiTi wire diameter, spacing, and position in the laminate

Experiment	NiTi wire diameter (mm)	Wire spacing in laminate (mm)	Position in laminate (mm)
1	0.3	10	1.125
2	0.7	10	− 1.125
3	0.3	50	− 1.125
4	0.7	50	1.125
5	0.3	10	1.125
6	0.7	10	− 1.125
7	0.3	50	− 1.125
8	0.7	50	1.125
9	0.3	10	1.125
10	0.7	10	− 1.125
11	0.3	50	− 1.125
12	0.7	50	1.125
13	0.5	30	0
14	0.5	30	0
15	0.5	30	0

Table 6. Experiments generated by the fractional factorial design

Control variables	Symbol	Levels
		Lower (− 1)	Center point (0)	Upper (+ 1)
NiTi wire diameter (mm)	x1	0.3	0.5	0.7
Wire spacing in laminate (mm)	x2	10	30	50
Position in laminate	x3	− 1.125	0	1.125

Manufacturing specimens for impact

The manufacturing process of the specimens for low-velocity impact testing was VARTM, the same process described for DMA specimen manufacturing. Unlike the manufacturing for DMA, an additional control variable was included, which was the diameter of the NiTi wire. The positions of the NiTi wires were the same as those adopted and illustrated in Fig. 3, where the neutral line is located between layers 4–5, and the positions − 1.125 and 1.125 correspond to the insertion between layers 7–8 and 1–2, respectively. The manufacturing of the specimens for impact testing followed the configurations generated by the DoE.

The variation in wire spacing used in the composite plates for impact testing is illustrated in Fig. 5. This spacing was applied horizontally along the length of the plate, with the wires positioned parallel to each other. To ensure that the same testing conditions were replicated for all specimens at the moment of impact, it was adopted that the initial wire placement was in the center of the plate. Consequently, the spacing was applied as illustrated in Fig. 5. This ensured that the impactor always hit the region where at least one NiTi wire was inserted.

Fig. 5 [Images not available. See PDF.]

Spacing of NiTi wires in the laminate: a 10 mm; b 30 mm; and c 50 mm

In the process of manufacturing the specimens for impact, to ensure the correct wire spacing in the laminate, a printed paper mold was used for marking, and adhesive tape was used to prevent the wires from detaching from the fiberglass fabric. An example of how this fixation on the fabric was done is illustrated in Fig. 6, where a wire diameter of 0.3 mm and a spacing of 10 mm were used. It is worth noting that a surplus of material was left in the composite plate design, including where the adhesive tape was positioned, so that it would not interfere with the laminate, and it would remain outside the specimen during cutting. To ensure dimensional accuracy, the specimens were cut using the CNC SHG Router equipment available at NTC—UNIFEI (Fig. 6).

Fig. 6 [Images not available. See PDF.]

Attachment of NiTi wires to ensure correct spacing (a) and (b) cutting of specimens for impact testing

As can be observed in Table 2, the 15 specimens resulting from the experimental design generate 5 different configurations, each with three replicates. Additionally, to provide a parameter for comparing the effect of NiTi wires inserted in the composite, three base samples were manufactured without the wire. Thus, Table 7 was created for a better understanding and organization of these configurations, which will be the subject of this study.

Table 7. Naming of impact test specimens

Configuration	NiTi wire diameter (mm)	Wire spacing (mm)	Position in laminate (mm)	Replicates	Naming
1	0.3	10	1.125	3	A
2	0.3	50	− 1.125	3	B
3	0.7	10	− 1.125	3	C
4	0.7	50	1.125	3	D
5	0.5	30	0	3	E
6		Without the presence of the wire		3	F

Low-velocity impact test

The low-velocity free-fall impact test (commonly known as the drop-weight impact test) is a method governed by the ASTM D7136/D7136M standard [10]. This test determines the damage resistance of multidirectional polymer matrix composite laminates subjected to a free-falling weight impact event. According to the standard, sample dimensions should be approximately 3 mm thick, 150 mm long, and 100 mm wide, with a dimensional tolerance of ± 0.25 mm.

The impact tests were conducted at LEL—Lightweight Structures Unit of IPT—Technological Research Institute in S˜ao Jos´e dos Campos—SP. The equipment used for the impact test was the Instron 9340 machine, equipped with a spherical punch approximately 16 mm in diameter, and an impactor mass (Fig. 7) of 1.215 kg. This equipment features a Rebound Catcher mechanism, capable of capturing the impactor after it collides with the tested sample, preventing a second impact event. This type of safety mechanism is one of the standard requirements for increased reliability in results.

Fig. 7 [Images not available. See PDF.]

Low-velocity impact testing machine Instron 9340 (a) and (b) type of impactor according to ASTM D7136/D7136M [10] and Instron 9340 impactor

According to the standard, the impact energy (E) is calculated based on the impact velocity (v_i), the displacement of the impactor (δ), and time (t) according to Eqs. 7–9.

7

$$E\left(t\right)=\frac{m(v_i^2-v{\left(t\right)}^2)}{2}+mg\delta \left(t\right),$$

8

$$v_i=\frac{w_{12}}{t_2-t_1}+g{t}_i-\frac{t_1-t_2}{2},$$

9

$$\delta \left(t\right)={\delta }_i+v_{i}t+\frac{g{t}^2}{2}-{\int }_0^t{\int }_0^t\frac{F\left(t\right)}{m}\text{d}t\text{d}t,$$where w₁₂ is the distance between velocity sensors 1 and 2 that measure the impactor’s speed; t₁ is the time of the impactor passing through sensor 1; t₂ is the time of the impactor passing through sensor 2; t_i is the time related to initial contact point with the sample surface; g represents gravity acceleration; δ_i is the impactor displacement at time t = 0 s; F(t) is the impactor contact force measured at time t; and m is the impactor mass.

The total impact energy E_T is the sum of the energy absorbed by the material (AEI) and the elastic energy (E_E) related to the impactor’s rebound, and it can be calculated by Eq. 10.

10

$$E_{\text{T}}=\text{AEI}+E_{\text{E}}.$$

The strain rate ε(t) can be calculated using Eq. 11.

11

$$\epsilon \left(t\right)=\frac{\text{d}\epsilon }{\text{d}t}=\frac{\text{d}}{\text{d}t}\frac{L\left(t\right)-L_0}{L_0}=\frac{1}{L_0}\frac{\text{d}L}{\text{d}t}t=\frac{v\left(t\right)}{L_0},$$where: L₀ is the initial length of deflection; L(t) is the length at each time t; and v(t) is the falling velocity at time t.

The test conditions adopted for low-velocity impact are presented in Table 8 and were conducted according to ASTM D7136/D7136M.

Table 8. Boundary conditions of the impact experiment

Total impact mass	3.215 kg
Total impact energy	31.5 J impact
Acceleration	4.429 m/s2 plate
Dimensions	100 × 150 × 3 mm
Safety mechanism	Rebound catcher

Numerical impact simulation using the finite element method

As seen in previous sections of this work, several previously cited authors have used numerical simulation to propose a model that could somehow correlate and predict the experimental behavior of certain test specimens under various boundary conditions. In this work, the proposed model corresponds to the parameters of variation of the diameter, spacing, and position of NiTi wires in the fiberglass composite with epoxy matrix under low-velocity impact conditions. Therefore, a nonlinear dynamic analysis was performed using the finite element software Altair Hyperworks with the Hypermesh mesh generator and the Radioss solver.

The geometries required for the numerical simulation, such as the support base of the composite plate and the impactor, were designed using SolidWorks software. The dimensions of the geometry were based on the real model of the experiment. For the impactor geometry, a cylinder with a height of 50 mm and a diameter of 16 mm was used (Fig. 8). Due to the simplification in the impactor’s geometry, a correction of the specific mass was made to maintain a total impact mass of 3.214 kg in the dynamic simulation model.

Fig. 8 [Images not available. See PDF.]

Numerical model details

The base support for the test specimens was modeled with a rectangle geometry of 250 × 200 × 6 mm, representing the real base support of the Instron 9340 testing machine.

The geometry of the test specimen consists of eight layers of fiberglass with dimensions of 1500 × 100 mm, with each layer having a thickness of 0.375 mm. In this work, the geometry of only one layer was modeled, and multiple imports into the simulation software were performed to achieve a thickness of 3 mm for the laminate. As discussed earlier, the numerical simulation process was performed using Altair HyperWorks.

In the modeling step of the test specimen in the software, three models with wires and a base model without the NiTi wire were used according to Table 9. Figure 9 illustrates the geometry in the finite element software for Model C.

Table 9. Nomenclature of the geometries used in numerical simulation

Model	Diameter (mm)	Spacing (mm)	Position (mm)
A	No wire inserted
B	0.3	10	1.125
C	0.5	30	0
D	0.7	10	− 1.125

Fig. 9 [Images not available. See PDF.]

Geometry of Model C in the finite element software (a) and symmetric geometry applied for model simplification (b)

In numerical simulations, as for experimental analyses, there are also certain costs, such as computational cost, which becomes more expensive for nonlinear simulations compared to linear ones. This cost is directly related to the geometries and the number of elements (mesh) involved in the modeling. Due to the symmetrical nature of the components in this study and to reduce computational cost, a longitudinal symmetrical cut was made in the geometry. This form of geometry simplification through element symmetry does not impact or vary the results in a numerical simulation.

After importing and adjusting the geometry, meshing was applied to the punch, base, composite plate, and wires inserted into the plate. The NiTi wires were modeled using beam-type elements with an appropriate mesh size (1 mm) to coincide with the nodes of the mesh used in the composite plate. Figure 10 illustrates the mesh of the NiTi wires applied to the composite plate for all models used in the nonlinear numerical simulation.

Fig. 10 [Images not available. See PDF.]

Mesh of the NiTi wire inserted in the composite plate

In the step of applying the mesh to the composite plate, three cuts on the surface were made, dividing it into regions to better adapt the mesh to the wires and the impactor’s contact region. In the first region, a circular cut was made at the contact interface of the plate with the impactor, with the average size of the mesh elements equal to 1 mm. This mesh refinement was applied for better adaptation and better results in the impact region. In the region adjacent to the impact zone, a mesh with elements of an average size of 1.5 mm was applied. In the rest of the surface, elements with an average size of 2 mm were applied. This mesh configuration was chosen after successive mesh convergence tests, seeking the best cost/benefit for the available hardware.

The generated mesh elements are first-order and have 3 (three) degrees of freedom per node and only one integration point. Additionally, these elements were also configured to be applied to the problem of geometric nonlinearity (large deformations).

After the mesh generation step for the composite plate, meshing of the base and the impactor was performed. For this model, it is assumed that the impactor and the base support have negligible deformations, which provides mechanisms for simplifying the geometry. Therefore, the support base was modeled with 2D elements after extracting the average surface from the geometry, and the impactor was modeled using 3D tetrahedral elements, with both geometries having a mesh size of 2 mm.

Regarding the boundary conditions of the simulation, three-movement constraints were used in the model. The first constraint was applied to prevent the movement of the base support, where a fixation of all degrees of freedom was applied, preventing the base from translating or rotating.

In the second constraint, all degrees of freedom of the contact element created between the composite plate and the base support were also fixed. This contact simulates the Toggle Clamp specified in ASTM D7136 and was modeled to ensure the correct positions in which the plate would be fixed.

The third constraint aims to ensure that the movement of the impactor occurs only in translation in the direction of the composite plate (Z-axis). To achieve this, a motion restriction was applied to 5 degrees of freedom of the impactor, leaving only the degree of translation in the direction of the plate free.

The impact velocity between the composite and the impactor was another boundary condition inserted in the simulation model, where this velocity was applied to the principal node of the rigid element that connects all the nodes of the impactor. This velocity acts in the direction of the plate with a value of 4.429 m/s, and together with the impactor’s mass of 3.215 kg, generates a Total Impact Energy of 31.5 J according to experimental boundary conditions. After the step of mesh generation and application of boundary conditions, the material properties were assigned to the geometries in the finite element software. For the base and impactor, since they are made of isotropic metallic material, it was sufficient to enter the values of the elastic modulus of 210 GPa and a specific mass of 7.8 g/cm³.

For the composite plate, the material adopted in the finite element software was an orthotropic- elastic material. In the elastic phase, the calculation of Stress-Strain relation is calculated according to the relationships shown in Eqs. 12–17.

12

$${\epsilon }_{11}=\frac{1}{E_{11}}{\sigma }_{11}-\frac{{\nu }_{21}}{E_{22}}{\sigma }_{22}-\frac{{\nu }_{31}}{E_{33}}{\sigma }_{33},$$

13

$${\epsilon }_{22}=\frac{1}{E_{22}}{\sigma }_{22}-\frac{{\nu }_{12}}{E_{11}}{\sigma }_{11}-\frac{{\nu }_{32}}{E_{33}}{\sigma }_{33},$$

14

$${\epsilon }_{33}=\frac{1}{E_{33}}{\sigma }_{33}-\frac{{\nu }_{13}}{E_{11}}{\sigma }_{11}-\frac{{\nu }_{23}}{E_{22}}{\sigma }_{22},$$

15

$${\gamma }_{12}=\frac{1}{2G_{12}}{\sigma }_{12}\frac{{\nu }_{21}}{E_{22}}=\frac{{\nu }_{12}}{E_{11}},$$

16

$${\gamma }_{23}=\frac{1}{2G_{23}}{\sigma }_{23}\frac{{\nu }_{32}}{E_{33}}=\frac{{\nu }_{23}}{E_{22}},$$

17

$${\gamma }_{31}=\frac{1}{2G_{31}}{\sigma }_{31}\frac{{\nu }_{13}}{E_{11}}=\frac{{\nu }_{31}}{E_{33}}.$$

In the numerical simulation, at each increment, an analysis is conducted to determine whether the composite plate material is in the elastic or nonlinear phase. This is done using the Tsai-Wu criterion, which checks whether F (σ) is less than or greater than F (W_p^∗, ε), as expressed in Eqs. 18 and 19, respectively. For the calculation of F (σ), the resistance coefficients F_i and F_ij are expressed in Eqs. 20–31.

18

$$\begin{array}{c}F\left(\sigma \right)=F_1{\sigma }_1+F_2{\sigma }_2+F_3{\sigma }_3+F_{11}{\sigma }_1^2\\ +F_{22}{\sigma }_2^2+F_{33}{\sigma }_3^2+F_{44}{\sigma }_{12}^2+F_{55}{\sigma }_{23}^2\\ +F_{66}{\sigma }_{31}^2+2F_{12}{\sigma }_1{\sigma }_2+2F_{23}{\sigma }_2{\sigma }_3+2F_{13}{\sigma }_1{\sigma }_3,\\ \end{array}$$

19

$$F(W_p^{\ast },\epsilon )=[1+B(W_p^{\ast })]_{}^{\ast }{]}^n\ast \left[1+c\ast ln\frac{\dot{\epsilon }}{{\dot{\epsilon }}_0}\right],$$

20

$$F_1=-\frac{1}{{\sigma }_{1y}^c}+\frac{1}{{\sigma }_{1y}^t},$$

21

$$F_2=-\frac{1}{{\sigma }_{2y}^c}+\frac{1}{{\sigma }_{2y}^t},$$

22

$$F_3=-\frac{1}{{\sigma }_{3y}^c}+\frac{1}{{\sigma }_{3y}^t},$$

23

$$F_{11}=\frac{1}{{\sigma }_{1y}^c{\sigma }_{1y}^t},$$

24

$$F_{22}=\frac{1}{{\sigma }_{2y}^c{\sigma }_{2y}^t},$$

25

$$F_{33}=\frac{1}{{\sigma }_{3y}^c{\sigma }_{3y}^t},$$

26

$$F_{44}=\frac{1}{{\sigma }_{12y}^c{\sigma }_{12y}^t},$$

27

$$F_{55}=\frac{1}{{\sigma }_{23y}^c{\sigma }_{23y}^t},$$

28

$$F_{66}=\frac{1}{{\sigma }_{31y}^c{\sigma }_{31y}^t},$$

29

$$F_{12}=-\frac{1}{2}\sqrt{F_{11}{F}_{22}},$$

30

$$F_{23}=-\frac{1}{2}\sqrt{F_{22}{F}_{33}},$$

31

$$F_{13}=-\frac{1}{2}\sqrt{F_{11}{F}_{33}}.$$

When the stress value reaches the limits σ_ti of the material, a new reduced stress is calculated using a damage value (D). This value is updated at each time increment through the damage parameter (δ). The damage calculation is done according to Eq. 32, and the reduced stress is calculated following the relationship shown in Eq. 33.

32

$$D_i=\sum _i\ast {\delta }_i,$$

33

$${\sigma }^{\text{reduced}}=(1-D_i){\sigma }_{\mathit{ti}}.$$

The mechanical properties of the composite material used in the nonlinear numerical simulation are presented in Table 10 [67].

Table 10. Composite material properties (adapted from [67])

Elastic modulus (GPa)		Poisson’s ratio		Shear modulus (GPa)
Ex	26	vxy	0.10	Gxy	3.8
Ey	26	Vyz	0.25	Gyz	2.8
Ez	8	Vxz	0.25	Gxz	2.8

Tensile strength (MPa)		Compressive strength (MPa)		Shear strength (MPa)
XT	850	XC	720	S12	105
YT	850	YC	720	S13	65
ZT	120	ZC	500	S23	65
Interlaminar normal failure stress 35 MPa			Interlaminar shear failure stress 65 MPa

The material model adopted in the finite element software for the NiTi alloy was represented by the Johnson-Cook criterion. In this model, during each increment, its plastic deformation and stress are described in terms of strain according to Eq. 34.

34

$$\sigma =(a+b{\epsilon }_p^n)\left(1+c\ast ln\frac{\dot{\epsilon }}{{\dot{\epsilon }}_0}\right).$$

In the Solver Radioss Card, by selecting the option I_flag = 1 for the material, the software itself calculates the parameters a, b, and n based on the yield stress, ultimate stress, and rupture strain of NiTi. Additionally, it was necessary to input the elastic modulus and the specific mass of the material for calculations in the elastic phase. All material data, as presented in Table 11, were provided by the manufacturer Sandinox Biomateriais under quality certificate 34424/19 ISO 9001.

Table 11. Mechanical properties of NiTi wires

Mechanical properties	Diameter (mm)
	0.3	0.5	0.7
Density ρ (g/cm3)	5.54	5.61	6.75
Elastic modulus E (GPa)	35	35	35
Yield stress σY (MPa)	566	536	586
Ultimate stress σU (MPa)	1519	1496	1475
Yield strain εY (%)	14.3	14.8	15.9

Numerical-experimental results and discussions

Selection of nitinol wire

As previously reported, the selection of the Nitinol wire to be used in the impact test was carried out through DMA experiments to evaluate its influence on the composite storage modulus (E^′). Figure 11 shows the composite plate manufactured to obtain test specimens categorized as base samples (B), martensitic samples (M), and superelastic samples (S).

Fig. 11 [Images not available. See PDF.]

Composite plate with superelastic and martensitic wires (a) and Test specimens for superelastic, base, and martensitic DMA samples, respectively (b)

With the test specimens obtained, DMA tests were performed to obtain the storage moduli (E^′). The storage modulus is directly related to the material’s ability to absorb energy and return it in elastic form, resulting in the assertion that one material absorbs more or less energy than another. The results from dynamic-mechanical analysis in terms of storage modulus (E^′) can be seen in Table 12.

Table 12. Storage moduli from DMA tests

Sample	Base (B) (GPa)	Martensitic (M) (GPa)	Superelastic (S) (GPa)
1	6.1	7.7	8.3
2	5.8	7.6	8.3
3	6.7	6.9	9.2
4	6.6	7.2	8.0
Average	6.3	7.3	8.4

To ensure quantitative comparability of the DMA test results, various statistical analyses, including ANOVA and t-tests, were conducted. For the ANOVA with factor B × M × S, the null hypothesis (H₀) stated that the variances of base (B), martensitic (M), and superelastic (S) are equal, while the alternative hypothesis (H_A) posited unequal variances. The resulting p-value was 0.000, indicating significant differences in means among the three treatments. Subsequent t-tests were performed for pairwise comparisons: B × M, B × S, and M × S. For each test, the null hypothesis assumed equal means, and the alternative hypothesis suggested that the mean of the first factor is less than the mean of the second factor. The corresponding p-values were 0.007, 0.001, and 0.011, respectively. These results further supported the rejection of null hypotheses, signifying differences in storage moduli. Consequently, the Superelastic Nitinol wire, associated with the highest storage capacity, will be employed in the remainder of the work for manufacturing composites intended for low-velocity impact testing.

Equation for storage modulus and glass transition temperature in DMA

As described in previous sections, a composite plate was manufactured via VARTM with wire positions and quantities in accordance with a full factorial design. DMA tests were conducted following the ASTM D7028 standard, and the results of the storage modulus and tan δ for each experiment were collected and entered into MiniTab for factorial statistical analysis as shown in Table 13.

Table 13. DMA analysis responses in full factorial design

Continuous variables	Experiment
Wire quantity	Position (mm)	Storage modulus (E′) (Gpa)	Glass transition temperature (tan δ) (C)
1	− 1.125	7.08	99.79
1	− 1.125	6.92	99.67
1	1.125	6.10	100.09
1	1.125	6.04	100.08
2	0	6.67	99.78
2	0	6.88	99.65
2	0	6.66	99.67
3	− 1.125	6.33	99.56
3	− 1.125	6.38	99.32
3	1.125	6.78	100.20
3	1.125	6.78	100.18

With the data entered into MiniTab, an analysis of variance (Table 14) was performed to obtain the results and study the variables that are most significant.

Table 14. ANOVA p-value responses for E^′ and tan δ

Factor	p-value (E′)	p-value (tan δ)
Wire quantity	0.623	0.190
Position	0.007	0.000
Wire quantity × position	0.000	0.020
Constant (ε)	0.000	0.000

Analyzing the results, the p-value values for E′ and tan δ, it can be observed that the most significant variable is the wire position in the laminate and the second-order variable corresponding to the interaction between wire quantity versus position in the laminate. The numerical results in the tables can also be seen and confirmed graphically through the pareto effects plot (Fig. 12) and the main effects plot (Fig. 13).

Fig. 12 [Images not available. See PDF.]

Pareto effects plot

Fig. 13 [Images not available. See PDF.]

Main effects plots

In the main effects plot for E^′ (Fig. 13), corresponding to wire quantity, it can be seen that the points are close to the reference axis of the model’s central mean, indicating that they do not have significant effects on the results. In contrast to wire quantity, the Position in the laminate shows a significant deviation from the model’s central mean, which has a great impact on the results.

The main effects plot for tan δ, the lines regarding wire quantity are nearly parallel to the central mean of the model, indicating that this variable is not significant. In contrast, the lines regarding the Position of the wires in the laminate are mostly horizontal, indicating a significant effect.

In addition to the analysis of the pareto charts and main effects plots, the ANOVA data brought an excellent fit with R² of approximately 96% for E^′ and 94% for tan δ as shown in Table 15.

Table 15. R² responses for E^′ and tan δ

Response	R2 (E′)	R2adj (E′)	R2pred (E′)	R2 (tan δ)
Storage modulus (E′)	95.99%	93.32%	88.63%	–
Tan delta (tan δ)	–	–	–	94.02%

The mathematical model for the behavior of the storage modulus (E^′) and glass transition temperature (tan δ) as a function of wire position and quantity in the laminate is based on DoE equations in previous sections. Using linear regression, Eqs. 35 and 36 were obtained. As can be observed, the most significant factors for increasing E^′ and tan δ correspond to the terms x₁ and x₁x₂, where the sign is positive (+), unlike the term x₂, which has a negative sign (−), meaning it decreases the value of the storage modulus.

35

$$E^{\prime }=1.61\times 10^7\left(x_1\right)-2.85\times 10^8\left(x_2\right)+1.2\times 10^8\left(x_1{x}_2\right)+6.52\times 10^9,$$

36

$$\text{tan}\delta =0.0276\left(x_1\right)-0.0470\left(x_2\right)+0.0355\left(x_1{x}_2\right)+99.9593,$$where E^′ is storage modulus in DMA; and tan δ is the glass transition temperature; x₁ is wire position in the laminate; and x₂ is wire quantity inserted in the laminate.

Figure 14 represents the three-dimensional graphs related to the mathematical models for the storage modulus and glass transition temperature. It was observed that E^′ and tan δ decrease as a result of the positioning of the superelastic NiTi wires in the layers below the neutral axis of the composite, meaning that the further below the neutral axis the wires are positioned, the lower the storage modulus and the tangent delta. As the wire position is changed to the upper layers, i.e., above the neutral axis, the storage modulus increases significantly. The interaction between the wire quantity and position also leads to changes in the values of E^′ and tan δ. This interaction becomes more significant because there are more regions where the storage modulus increases, unlike this interaction effect does not substantially modify the values of the tangent delta.

Fig. 14 [Images not available. See PDF.]

Surface plots

The results showed that the correct insertion of superelastic NiTi wires can bring significant benefits to the composite by increasing the elastic zone and working temperature. These aspects are important factors in most engineering projects. For example, in the automotive industry, the increase in the tangent delta and the elastic portion extends the use and application of this material, ensuring project safety.

It is also worth mentioning that the insertion of superelastic NiTi wires increases the glass transition temperature of the composite, possibly due to the high conductivity of the wires, as they are metallic materials that provide homogenous temperature dispersion throughout the composite material.

Analysis and results for experimental impact tests

As previously explained, all 15 test specimens were generated by the fractional factorial design, plus the 3 specimens without the NiTi wire. Figure 15 illustrates Model E (with the NiTi wire) and F (without the NiTi wire) with their respective replicas.

Fig. 15 [Images not available. See PDF.]

Test specimens for Models E and F

After manufacturing the test specimens, all samples were taken to the LEL—Lightweight Structures Laboratory of IPT for impact tests. The samples were tested according to ASTM D7136 using an Instron 9340 machine. Figure 16 illustrates a sample without the NiTi wire attached to the equipment’s support base for low-speed impact experiments. Figure 17 shows the samples for Models E and F after the low-speed impact test. Analyzing the images of the damage caused by the punch, it can be identified that the composite plates conform to ASTM D7136, where the external damage was of Type I—indentation/depression.

Fig. 16 [Images not available. See PDF.]

Sample without NiTi wire fixed to the machine for impact test

Fig. 17 [Images not available. See PDF.]

Damage caused by impact on samples of Models E and F

The impact energy absorption results of all 18 samples, both those generated by the fractional factorial design and those without the NiTi wire, are summarized in Table 16 and illustrated through curves in Fig. 18.

Table 16. Impact energy absorption results

Sample	Wire diameter (mm)	Spacing (mm)	Position in laminate (mm)	Energy	Average energy
				(J)	(J)
1	0.3	10	1.125	27.57
2	0.3	10	1.125	27.67	27.54
3	0.3	10	1.125	27.37
4	0.3	50	− 1.125	27.99
5	0.3	50	− 1.125	27.29	27.70
6	0.3	50	− 1.125	27.82
7	0.7	10	− 1.125	28.29
8	0.7	10	− 1.125	28.32	28.25
9	0.7	10	− 1.125	28.14
10	0.7	50	1.125	28.54
11	0.7	50	1.125	28.58	28.52
12	0.7	50	1.125	28.44
13	0.5	30	0	29.26
14	0.5	30	0	29.74	29.52
15	0.5	30	0	29.56
16		Without NiTi wire		26.48
17		Without NiTi wire		26.71	26.63
18		Without NiTi wire		26.70

Fig. 18 [Images not available. See PDF.]

Curves of average (of three specimens) absorbed energies as a function of punch displacement

In the first analysis, it can be observed that all models containing the NiTi wire inserted into the composite plate obtained greater impact energy absorption compared to the base sample without the wire.

At this stage, we are comparing only average values without a mathematical statistical basis; therefore, a more rigorous analysis requires further investigation. With the experimental results in hand, MiniTab was used to perform factorial statistical analysis. With the data inputted, an analysis of variance (ANOVA) was performed to obtain the results and study the most significant variables according to the p-Value, which are presented in Table 17.

Table 17. ANOVA response p-value for impact energy absorption

Factor	p-value
Wire diameter	0.000
Spacing	0.111
Position in laminate	0.684
Constant (ε)	0.000
Curvature (Pt Ct)	0.000

Analyzing the results with the p-value values for impact energy absorption E, it can be observed that the most significant variable is the wire diameter. Additionally, in this analysis, it can be seen that there is a curvature in the model. The numerical results in the table can also be observed and confirmed graphically through the pareto effects curve and the main effects mean curve (19) (Fig. 19).

Fig. 19 [Images not available. See PDF.]

Pareto effects (a) and main effect plots (b)

In both the pareto curve and the main effects mean curve for impact energy absorption E, it can be observed that the points corresponding to spacing and position in the laminate are close to the central mean axis and do not show significant effects on the results. However, the wire diameter exhibits a significant deviation from the central mean axis, indicating its high significance in the results.

It is worth noting that although spacing does not show statistical significance in this experimental test according to the pareto curve, this variable has a high probability of being statistically significant. One justification for this analysis is that in this experiment following ASTM D7136, a small impact region was used, considering a 16 mm diameter impactor and a composite plate of 150 × 100 × 3 mm. In the case of an aircraft impact test (Bird Strike), for example, a projectile with a diameter ranging from 100 to 200 mm impacts an aircraft test specimen at a velocity of approximately 175 m/s [69–71], where the wire spacing would most likely show statistical mathematical significance.

In addition to the pareto curve and main effects analysis, by using analysis of variance, the ANOVA data brought an excellent fit with an R² of approximately 94% for impact energy absorption E, as shown in Table 18. Therefore, with this R² result, the experimental data are reliable and can be statistically validated.

Table 18. R² response for impact energy absorption E

Response	R2	R2adj	R2pred
Impact Energy absorption E	94.18%	91.86%	86.92%

The mathematical model for the impact energy absorption behavior (E) as a function of the wire diameter, spacing, and position in the laminate is based on DoE regression equations. Through the linear regression process, we can obtain Eq. 37. As observed, the most significant factors for increasing E correspond to the term x₁. It is worth noting that the term x₁x₂x₃ in the fractional factorial design confounded with the center point (x₃) of the experiment due to significant curvature in the region. In addition, Fig. 20 shows the surface plot obtained from Eq. 37:

37

$$IAE=1.1912\left(x_1\right)+0.00541\left(x_2\right)+0.0093\left(x_3\right)+1.522\left(x_1{x}_2{x}_3\right)+26.885,$$where E is impact energy absorption; x₁ NiTi wire diameter; x₁ wire spacing in the laminate; and x₃ wire position inserted in the laminate.

Fig. 20 [Images not available. See PDF.]

Surface plots for the absorbed energy

Analysis and results for nonlinear impact numerical simulations

In this section, the results for impact energy absorption through nonlinear numerical simulations using the FEM will be analyzed and discussed. As highlighted in Sect. 2, the purpose of analyzing these results is to find a numerical correlation to validate a model capable of predicting the impact energy absorption behavior in a composite plate. Thus, numerical simulations were performed for all four models proposed and their energy absorption curves are illustrated in Fig. 21.

Fig. 21 [Images not available. See PDF.]

Absorbed energy for the models A, B, C and D

The curves generated by the Altair Hyperworks finite element software differ slightly from the experimental results, but this does not affect the analyses. The experimental results curves were plotted against punch displacement for better visualization of the impact energy absorption curves [4]. For an identical reproduction of the numerical simulation graphs in relation to the experimental ones, the punch should be positioned exactly at the same height and at the exact moment in time as the contact between the plate and the impactor.

For a better analysis, the results of the nonlinear numerical simulation for impact energy absorption are presented in Table 19. Analyzing the results, it can be observed that, despite the numerical values being slightly higher than the experimental ones, they followed the same response pattern as the experimental analysis, indicating a good fit for the model.

Table 19. Numerical simulation results for impact energy absorption E

Model	Diameter (mm)	Spacing (mm)	Position (mm)	Energy (J)
A		No wire		27,35
B	0,3	10	1125	28,93
C	0,5	30	0	29,84
D	0,7	10	− 1125	29,65

To validate the numerical model, the experimental and numerical results for impact energy absorption are presented in Table 20 along with the correlation values.

Table 20. Correlation between experimental and numerical results for impact energy absorption E

Model	Experimental	Numerical	Correlation
	(J)	(J)	(%)
A	26.63	27.35	97.36
B	27.54	28.93	95.19
C	29.52	29.84	98.92
D	28.25	29.65	95.28

Analyzing Table 20, the correlation values between the results obtained by numerical simulation and experimentation were all above 95%, with all variations within a 10% margin. For Model C, the variation was only 1.08% [72, 73]. This means that the finite element model adopted for the numerical simulations of these tests is consistent and can be used in future projects involving the insertion of NiTi wires in composites to enhance impact energy absorption.

Another important factor for validating the finite element model is related to the dynamic behavior of nonlinear numerical simulations. Figure 22 illustrates the shear stress values in the composite plate for Models A, B, C, and D.

Fig. 22 [Images not available. See PDF.]

Shear stresses for the Models A, B, C and D

Analyzing the figure, it can be seen that there is a failure in the composite due to the high shear stress generated by the impact. It can be verified that, in accordance with the experimental results, the impactor also did not penetrate the composite plate. It is worth noting that, although Solver Radioss in its 2022 version uses the Tsai-Wu criterion in its damage calculation, it does not export results based on this criterion.

As explained, damage is calculated at each moment in time and at each increment of the model, generating a stress field until the damage ceases and the equation stabilizes. At this exact moment, it was possible to verify that the composite failure ceases at a certain moment in time (exactly at 5.7 ms) because there is evidence of impact energy absorption, correlated with the experimental results, and the start of the impactor’s rebound. In the boundary conditions of the model, the nonlinear numerical simulation stops when the impactor returns because there are no relevant results justifying further computational usage.

In addition to the composite analysis, the behavior of the NiTi Wire and its influence on impact energy absorption was verified. This work has demonstrated that inserting the wire results in increased energy absorption. To illustrate this behavior, Fig. 23 shows the stress field according to the Von Mises criterion.

Fig. 23 [Images not available. See PDF.]

Von Mises stresses for the models B, C and D

Analyzing the stress results in Fig. 23, it was possible to verify that the NiTi wires inserted into the composite exhibit points of plastic deformation. Through these results, this analysis justifies one of the reasons for the increase in impact energy absorption by the test specimen, as the wire proves efficient in absorbing some of the energy, transforming it into internal deformation. The curves in Fig. 24 illustrate the results of the internal energy absorbed by the NiTi wires for Models B, C, and D. The results show that there is indeed a portion of impact energy that is transformed into internal energy absorbed by the wires, leading to improved experimental results.

Fig. 24 [Images not available. See PDF.]

Internal energy absorbed by NiTi wires for Models B, C and D

The variation in internal energy absorption across Models B, C, and D can be primarily attributed to differences in wire diameter, spacing, and positioning within the laminate. In Model B, which uses a wire diameter of 0.3 mm and a spacing of 10 mm, the energy absorption capacity was lower compared to Models C and D. The smaller diameter of the wires in Model B limits their ability to deform elastically and absorb energy efficiently, which is crucial for mitigating impact forces. Conversely, Model D, where wires are positioned at − 1.125 mm closer to the impact surface, exhibited increased energy absorption. This positioning allows the wires to engage more directly with the impact forces, thus absorbing more energy before it is transmitted deeper into the composite. Model C demonstrated the optimal interaction between the NiTi wires and the fiberglass-epoxy matrix due to its balanced configuration of a 0.5 mm wire diameter at a 30 mm spacing, facilitating better energy distribution and absorption within the material.

These findings underscore the significant influence of wire geometry and positioning on the performance of SMAW-enhanced composites under impact loading. Each configuration presents unique interactions within the composite that lead to different levels of energy absorption efficiency.

Conclusion

This study assessed the feasibility of enhancing the impact energy absorption of composite materials through the integration of NiTi wires. An equation was developed using the DoE to predict the absorption capacity, adhering to the ASTM D7136 standard for low-velocity impact on composite materials. Statistical analysis via fractional factorial design demonstrated that the inclusion of NiTi wires significantly increases energy absorption compared to base samples (without wires), enabling the formulation of an equation based on three design variables: diameter, spacing, and position in the laminate.

Dynamic mechanical analysis (DMA) was employed to identify the most suitable shape memory metal alloy (martensitic or superelastic) for impact energy absorption in composite materials. Results analyzed through ANOVA and t-tests revealed that the Superelastic alloy exhibited superior mechanical properties compared to both the Martensitic alloy and the base sample. Further analysis through DoE, including pareto curves and main effects mean, highlighted that the most influential factors were the position in the laminate and the interaction between position and wire quantity. This led to the development of an equation predicting behavior in terms of increased storage modulus (E^′) and glass transition temperature (tan δ).

The DoE technique identified the factors (wire diameter, spacing between wires, and position in the laminate) that most significantly influence impact energy absorption according to ASTM D7136 standards. Statistical analysis indicated that NiTi wire diameter and the interaction between wire diameter, spacing, and position in the laminate (x₁x₂x₃) were the most influential. The significance of wire spacing in the laminate (x₂) under different impact conditions, such as bird strikes on aircraft, was also noted.

Nonlinear numerical simulation (dynamic analysis) demonstrated a strong correlation between numerical and experimental results, with error margins below 10%. Specifically, Model C achieved an accuracy rate exceeding 98%, confirming the reliability of the numerical simulation model. The analysis of results from the nonlinear numerical simulation demonstrated its robustness, even with proposed simplifications to reduce computational time. This model offers various possibilities for analyzing the impact event, enabling detailed examinations of the composite’s stress and energy dynamics, and the specific influence of the inserted NiTi wire. Thus, this model is a promising tool for predicting the behavior of composite material plates with NiTi wires, aimed at enhancing energy absorption in impact events.

Looking forward, we recommend that future research explore the application of SMAW-enhanced composites in automotive crash tests and high-velocity impact scenarios like bird strikes, which are critical in aerospace applications. Additionally, studying the rheology of these materials under dynamic loading could provide deeper insights into their behavior and energy absorption/dissipation capacities. Such investigations would validate and expand upon the current study’s findings, contributing to the development of more resilient and efficient materials for critical automotive and aerospace applications.

Acknowledgements

The authors would like to acknowledge the support from the National Council for Scientific and Technological Development (CNPq), Coordination for the Improvement of Higher Education Personnel (CAPES), and Research Support Foundation of the State of Minas Gerais (FAPEMIG).

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Declarations

Conflict of interest

The authors declare no conflict of interest.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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