## Abstract

Ultrasonic welding (USW) is one of the joining technologies that can be applied to short carbon fiber thermoplastic composites. In this study, the USW of Nylon 6 reinforced by short carbon fibers created using injection molding is used to investigate the USW process without energy directors. In addition to process parameters and performance parameters, a new category of parameters is introduced to characterize the behavior of base materials to control USW without energy directors. These parameters, named morphological parameters, are the degree of crystallinity (DoC) and the ratio of the crystalline phases of Nylon 6 (α/γ ratio). One method of controlling the morphological parameters is annealing. A design of experiments is carried out using 5 replicates and 7 annealing temperatures above the glass transition temperature (Tg) and below the melting temperature (Tm) of Nylon 6 to investigate the influence of annealing on the morphological parameters. The DoC and α/γ ratio are measured for each replicate by utilizing differential scanning calorimetry and X-ray diffraction. The results show that the DoC becomes uniform and the α/γ ratio increases after annealing. Consequently, the variation in weld strength decreases and the average weld strength increases by controlling the morphological parameters through annealing.

## 1 Introduction

The short cycle time of ultrasonic welding (USW) and its adaptability for automation has spurred its recent use for joining thermoplastic composites in the automotive, aerospace and energy, and packaging industries [13]. Joining using USW is characterized by a set of process parameters, such as the vibration frequency and amplitude, welding force, vibration time (energy), holding time, and solidification force, which influence the formation of a weld and determine its performance parameters (i.e., weld area and strength) [4,5].

Numerous researchers have studied the effect of the USW process parameters on weld performance with energy directors. Villegas and Bersee [6] showed that transverse energy directors reduced the scatter of welding performance compared to parallel energy directors. Similarly, Palardy and Villegas [7] studied the effect of an energy director's thickness and shape on weld strength. Liu and Chang [8] optimized the welding time, welding force, holding time, solidification force, vibration amplitude, and the shape of an energy director to obtain the maximum weld strength of Nylon 6 composites reinforced by glass fiber. These studies showed that the parameters with the strongest influence on weld performance are the vibration amplitude, welding time, and energy director shape. Energy directors are pre-molded [9] or supplied as a film that is positioned between the coupons to be welded [4]. In general, an energy director triggers joining by introducing a less stiff area between the coupons to be welded and concentrates the vibration energy in this area, where melting is initiated earlier compared with the rest of the composite [9]. Despite the positive role of energy directors on weld formation, their manufacture involves additional costs related to tools and equipment. Moreover, their presence at the interface between composites locally modifies the structure of composites, leading to a non-uniform distribution of fibers in the weld area [4,10]. Hence, the current industrial practice seeks to eliminate the use of energy directors.

There is limited research on the USW of composites without an energy director. Luo et al. proposed the use of external thermal or chemical sources during USW without energy directors to promote bonding between two surfaces [11]. The main application of these methods is the micro bonding of poly (methyl methacrylate), which produces low-strength welds. These methods are not suitable for joining large components for which weld strength must reach extremely high values (between 2 kN and 4 kN).

In recent years, Wang et al. investigated the effect of the process parameters of USW without energy directors on the weld strength of Nylon-6-based reinforced composites [5]. Wang et al. determined the empirical relationships between weld attributes and strength [2,5] without investigating the mechanism of bonding. However, their studies show large variations in weld strength—even when process parameters are maintained constant—and relatively lower average values compared to the strength of base composite materials. Li et al. developed a blank holder to focus welding under a horn. Their study shows that the blank holder with critical release time increases weld strength, but the variation in weld strength is still large [12]. This variability may be explained by the instability of weld formation and consolidation and the surface waviness produced when preprocessing coupons. The origin of this instability can be associated with changes in material behavior in the presence of heat generated through USW at the interface between coupons [13,14] combined with the fiber distribution in weld areas. Moreover, the mechanical behavior of a material depends on the volume fraction of its fibers. It is not known how fibers and their distribution in a weld contribute to weld formation. In the case of thermoplastic materials used as a matrix, the volume fraction of a crystalline phase determines the viscoelastic behavior of the materials, and the crystalline phase is influenced by heating and cooling [15,16]. In summary, it is evident that weld performance is influenced by different categories of parameters, such as process parameters and material parameters related to morphology, and the kinematics of weld formation. Because USW processes with energy directors produce consistent weld performance, this study focuses on understanding the role of energy directors in the bonding mechanism and the effect of eliminating energy directors on weld performance. Moreover, annealing is proposed as a method to compensate for the impact of eliminating energy directors in stabilizing the USW process and enhancing weld performance. To apply this method, morphological parameters are considered to characterize the phenomenological changes in the material behavior during USW.

## 2 Materials and Methods

### 2.1 Materials.

The materials used in this study are HiFill PA6 CF30 and HiFill PA6 (Techmer PM, TN). HiFill PA6 CF30 is a short carbon fiber reinforced (CFRP) composite with a Nylon 6 matrix and HiFill PA6 is pure Nylon 6. The weight fraction of short carbon fibers in the CFRP is 30%. The average diameter and length of the carbon fibers are approximately 8 µm and 250 µm, respectively. For reference, HiFill PA6 coupons were used along testing the HiFill PA6 CF30 to reveal the role of the fibers in changing the thermomechanical properties during fabrication of the coupons and their welding.

The coupons for USW were manufactured by injection molding HiFill PA6 CF30 pellets with a diameter of 7 mm. A similar fabrication process was used for HiFill PA6 coupons. Their glass transition temperature (Tg) and melting temperature (Tm) are 60 °C and 220 °C, respectively. The pellets were dried at 80 °C for 4 h to reduce their moisture to less than 0.12%. After injection molding, the coupons were kept dry in a sealed plastic bag. The dimensions of the molded coupons were 127 mm × 38 mm × 3 mm. Nylon 6 is a semicrystalline thermoplastic polymer with amorphous and crystalline phases. The crystalline phase of Nylon 6 has two forms—α and γ (Fig. 1)—which have different structures and properties.

Fig. 1
Fig. 1
Close modal

The α form has a monoclinic structure, and it is generated using a relatively high-temperature crystallization process with a slow cooling rate. The γ form has a hexagonal or pseudohexagonal structure, and it is generated using a relatively low-temperature crystallization process with a rapid cooling rate [17]. The Young's modulus and stability of the α form are higher than those of the γ form. The different mechanical and physical properties of the two forms are shown in Table 1. The γ form can be transformed into the α form by treatments such as annealing and stretching [17,18].

Table 1

Mechanical and physical properties of α and γ crystalline forms [17,18]

Propertyα Formγ Form
Crystal structureMonoclinicHexagonal/pseudohexagonal
Lattice constantsa = 9.587 Åa = 4.931 Å
b = 17.602 Åb = 17.267 Å
c = 7.760 Åc = 8.810 Å
β = 69 degβ = 126.8 deg
Density (g/cm3)1.231.16
Heat of fusion, $ΔHm∘$ (J/g)241239
Young's modulus (GPa)235.29131.97
Propertyα Formγ Form
Crystal structureMonoclinicHexagonal/pseudohexagonal
Lattice constantsa = 9.587 Åa = 4.931 Å
b = 17.602 Åb = 17.267 Å
c = 7.760 Åc = 8.810 Å
β = 69 degβ = 126.8 deg
Density (g/cm3)1.231.16
Heat of fusion, $ΔHm∘$ (J/g)241239
Young's modulus (GPa)235.29131.97

The weight fraction of the crystalline phase over the amorphous phase and the ratio of the two crystalline forms influence the mechanical and physical properties of the semicrystalline polymer. The quantitative influence of this weight fraction and ratio on the mechanical properties of the material is presented in the following sections.

### 2.2 Welding Coupons and Measurement of Weld Strength.

An iQ Servo USW machine (Dukane, IL) was used for USW at a vibration frequency of 20 kHz. A circular horn with a diameter of 9.5 mm was used to weld the coupon samples. Lap joint bonds were created with an overlap area of 12.7 mm × 12.7 mm after the milling of the edge region to prevent edge welding (Fig. 2). The milling depth was 0.5 mm (16% of coupon thickness). The previous studies [5] provided proper process parameters of USW without energy directors to make a normal weld and prevent an over-weld. The other processing parameters were a welding speed of 0.1 mm/s, a trigger force of 150 N, an amplitude of 50 µm, and a holding time of 3 s.

Fig. 2
Fig. 2
Close modal
Single lap shear tests were conducted on the welded coupons using a 3300 series universal test machine (Instron, MA) with a 5 kN load cell at a test speed of 2 mm/min. The setup for the single lap shear tests is shown in Fig. 3(a). In the tests, the loading direction was tilted because of the horizontal gap between the upper and lower fixtures. The maximum load divided by the overlapped area (AOverlap) during the test was used to evaluate weld strength (τ).
$τ=Finterface/AOverlap=Floadingcos(α)/AOverlap$
(1)
Fig. 3
Fig. 3
Close modal

A digital image correlation system (DIC) was used to collect titling data during the single-lap shear tests. The tilting angle was calculated from the initial position of specimens at the beginning of the tests. The maximum titling angle during the tests was below 5 deg. For this tilting angle, cos α in Eq. (1) was 0.9962. This shows that the tilting during the lap shear tests is negligible. The tilting angle distribution immediately before the break in the single-lap shear tests is shown in Fig. 3(a), and the evolutions of the tilting angle for the five replicates are shown in Fig. 3(b).

In addition to the lap shear tests, tensile tests were conducted to determine the ultimate tensile strength of the coupons. A hydraulic universal testing machine (MTS, MN) with a 100 kN load cell was used to perform the tests at a speed of 2 mm/min. A minimum of five replicates were used for each test.

## 3 Bonding Mechanisms in Ultrasonic Welding With Energy Director Versus USW Without Energy Director

### 3.1 Bonding Mechanisms in Ultrasonic Welding of Polymer Composites.

In USW processes, weld performance is determined by the bonding between the two parts to be assembled, in this paper referred to as coupons. The bonding mechanism of polymeric composites is polymer–polymer interface healing, which is the same as the bonding mechanism for thermoplastics. Therefore, the bonding mechanism in USW of the Nylon 6 short carbon fiber composite is dominated by the Nylon 6 behavior. However, the role of the fibers is also considered in changing the behavior of Nylon 6 during fabrication of the coupons and USW.

Generally, in interface healing, a polymer–polymer interface gradually disappears and the mechanical strength at the interface develops when two coupons are brought into close contact at a temperature above the glass transition temperature (Tg) [19].

Wool and O'Connor [20] studied the interface healing process and divided it into five sequential stages, i.e., (1) surface adjusting, (2) surface approach, (3) wetting, (4) diffusion, and (5) diffusion and randomization [21]. A molecular dynamic model created in material studio software visually represents these five stages (Fig. 4).

Fig. 4
Fig. 4
Close modal

In stages (1) and (2), vibrations are applied to the overlapped coupons. The two surfaces of the upper coupon and the bottom coupon rearrange and approach until all the asperities of the surfaces erode. The next stage is characterized by intimate contact between the two surfaces similar to the wetting (stage 3). In this stage, polymer chains are free to diffuse at the interface between the two coupons by the end of this stage. Stages (4) and (5) are the most important stages because the characteristic strength of welded joints appears in these stages.

### 3.2 Models for Bonding Mechanisms in Ultrasonic Welding.

According to the presented interface healing process, two common models are developed to describe the five stages, namely, intimate contact and autohesion.

1. Intimate contact model describes stages (1–2) and (3). The surface irregularities of the coupons such as roughness or waviness are considered identical rectangles uniformly distributed on the surface of the coupons and they are characterized by a height (ao), a width (bo), and the distance between two rectangles (w0). The degree of intimate contact is given as [2224]
$Dic=11+w0b0[1+5(1+w0b0)(a0b0)2∫0tcpappηmfdt]1/5≈1w*(a*∫0tcpappηmfdt)1/5$
(2)
where papp is the applied pressure, ηmf is the viscosity of the matrix–fiber system, $w*=1+(w0/b0)$, and a* = $5w*(a0/b0)2$.
2. Autohesion model describes the stages that follow achieving intimate contact. The interdiffusion of polymer chains occurs owing to thermal motion. As time passes, a part of the chains from one coupon diffuses at the interface and entangles with the polymer chains on the other coupon. In these stages, Wool and O'Connor [20] provides the relationship between the mechanical strength and the diffusion related parameters
$σσ∞∝t1/4M−3/4fort
(3)
where σ is the mechanical strength at a time t, σ is the mechanical strength at an infinite time, M is the molecular weight, and tr is the reptation time, which is related to temperature and can be obtained using the “tube” model [25] as follows:
$tr=ζN3b4π2kBTa2$
(4)
where ζ is the monomeric friction coefficient, N is the number of monomers in the polymer, a is the tube persistence length, b is the polymer statistical segment length, and kB is the Boltzmann constant.

Hence, the critical healing process starts when intimate contact is achieved and ends when tube renewal time tr has elapsed, which is defined as the duration for a polymer chain to completely exit the original tube in which it is confined.

The degree of autohesion is introduced to monitor the development of molecular diffusion as a function of time, which is defined in Ref. [26] as
$Dau=σσ∞=(ttr)1/4=(π2kBTa2tζN3b4)1/4$
(5)
Hence, the degree of bonding (i.e., bonding efficiency) in the region where intimate contact and autohesion have occurred can be expressed as [26]
$Db=DicDau=1w*(a*∫0tcpappηmfdt)1/5(π2kBTa2tζN3b4)1/4$
(6)

From the above equation, it can be seen that during the ultrasonic welding process, coupon surface roughness, welding pressure, welding time, and welding temperature have an important impact on bonding efficiency (or joint strength), wherein welding pressure, welding time, and welding temperature have a positive effect.

### 3.3 Differences Between Bonding Mechanisms in Ultrasonic Welding With Energy Director Versus Ultrasonic Welding Without Energy Director.

The difference between the bonding mechanisms of USW with and without energy directors is mainly in stages (1), (2), and (3). This difference is caused by an initial discontinuous contact surface between energy directors (built in on the surface of the upper coupon) and the bottom coupon in the case of USW with energy directors and almost full contact between the two coupons in the case of USW without energy directors. Owing to localized contact between the energy directors and bottom coupon, the wetting step is reached faster compared to nonlocalized contact (theoretical infinite contact) in the case of no energy director. Moreover, the high-speed camera recording of USW without energy directors shows that contact is initiated on a circumferential area under the horn leading to weld formation. A schematic representation of contact initiation and propagation for USW with and without energy directors is presented in Fig. 5.

Fig. 5
Fig. 5
Close modal

It should be noted that the main differences between the two processes are in the initiation and propagation directions of intimate contact, which strongly depends on the uniformity of the coupon structure in the superficial layer and coupon flatness (or roughness). These two attributes of coupons are determined during injection molding, and they generally depend on the DoC and the distribution of fibers [27]. In annealing, slow heating and cooling rates are used to remove the heat history of a material carried from precursor manufacturing processes such as injection molding [28]. Moreover, in semicrystalline thermoplastic materials, such as Nylon 6, the DoC is the sum of the percentages of the α and γ forms over the total (composed of amorphous and crystalline phases). Different combinations of heating and cooling rates generate different DoCs and α/γ ratios [2830]. As these two crystalline forms have different mechanical and physical properties, changing the relative amount of each crystalline form modifies the mechanical and physical properties of a material.

Thus, the following hypothesis is considered in this work: the variation in welding performance in USW without energy directors can be reduced by controlling the uniformity of the DoC and the ratio of α to γ by changing the surface conditions of developing the bonding mechanism in the diffusion and randomization steps.

It is assumed that annealing influences stages (4) and (5) from the bonding mechanism, leading to higher strength and a more uniform shape of the weld compared with the no annealing case. This can be explained using the autohesion model, where reptation time tr is related to the movement of entangled polymer chains. Lin et al. [31] demonstrated that annealing determines the increase in chain entanglement density resulting from the increased efficiency of chain packing and entanglement recovery. Annealing above glass transition temperature Tg strongly affects segmental motion, including transition temperature and dynamics. In other words, Tg and relaxation time (τmax) increase owing to increased entanglement density and decreased molecular mobility.

The following sections demonstrate the effect of annealing on the weld performance by measuring the morphological parameters. The methods presented in Sec. 2—the USW process, lap shear tests, and tensile tests—are used for analyzing the influence of annealing on the welding performance through controlling the morphological parameters.

## 4 Annealing the Coupons of HiFill PA6 CF30 and HiFill PA6

The HiFill PA6 CF30 and HiFill PA6 coupons were annealed prior to their welding. Annealing parameters were the heating and cooling rates, heating temperature, and the holding time at a selected temperature. In the annealing processes of polymers, it is typically recommended to use heating and cooling rates of less than 120 °C/h and a holding time of more than 15 min per 1 mm of thickness. A sensitivity study was performed using two heating and cooling rates, i.e., 10 °C/h and 120 °C/h, at a constant holding time of 2 h and an annealing temperature of 160 °C. Lap shear tests were carried out on the annealed coupons to measure the maximum load of the weld. Figure 6 shows (a) the applied annealing treatment and (b) the plot of the maximum load of the weld for each case.

Fig. 6
Fig. 6
Close modal

The results show that the heating and cooling rates have a negligible influence on the welding performance measured through the maximum load (0.8% difference). Consequently, only one heating/cooling rate, 10 °C/h, was selected for further experiments. The reference for this comparison was the result of the lap shear test of nonannealed welded coupons. A new experimental plan was created for analyzing the influence of annealing temperature on welding performance. The temperature varied between 80 °C and 180 °C in increments of 20 °C while maintaining all other parameters constant (heating and cooling rates: 10 °C/h; holding time: 2 h). For all experiments, three replicates were annealed for each condition in a Blue M furnace (Lindberg/MPH). After annealing, the coupons were stored in sealed bags to prevent moisture absorption.

Three simultaneous campaigns were developed using the annealed coupons for (1) measuring the morphological parameters of the annealed coupons, (2) tensile testing for determining the mechanical properties post-annealing, and (3) welding and lap shear testing for measuring weld performance. The results are presented in the following sections.

### 4.1 Measuring the Morphological Parameters of Annealed Coupons

#### 4.1.1 Measurement of the Degree of Crystallinity by Differential Scanning Calorimetry.

A Discovery DSC machine (TA Instruments, DE) was used to measure the DoC. The weight of DSC samples was approximately 10 mg, and data were collected from nine different locations on the coupon after injection molding for the annealed and as-received samples, as shown in Fig. 7.

Fig. 7
Fig. 7
Close modal

In DSC, the samples were heated from 25 °C to 270 °C at a rate of 10 °C/min, maintained at 270 °C for 5 min, and cooled to 25 °C at a rate of 10 °C/min.

The DoC was calculated from the heating cycle using the following equation:
$DoCDSC(%)=ΔHm(1−wf)ΔHm0×100$
(7)
where ΔHm is the melting enthalpy of the samples as measured during the heating cycle, wf is the weight fraction of short carbon fibers (0.3 in this study), and $ΔHm0$ is the melting enthalpy of the 100% crystalline form of Nylon 6 (240 J/g) [32].

#### 4.1.2 Measurement of the α/γ Ratio by X-ray Diffraction.

XRD was used to investigate the structure and the morphology of the material [32]. A Miniflex X-ray diffractometer (Rigaku Americas Corporation, TX) was used to obtain XRD patterns, which were utilized to calculate the fraction of constituent crystalline forms in the material. The XRD scan speed was 1 deg/min, and the diffraction angle (2θ) ranged from 10 deg to 30 deg. A Cu Kα metal target was used, and voltage and current were 30 kV and 10 mA, respectively. XRD measurements were conducted for the annealed and as-received coupons using specimens prepared by cutting the coupons from the position where USW was performed. The dimensions of the specimens were 9 mm × 9 mm × 3 mm.

XRD pattern data were obtained from the completed measurements according to diffraction angles. The XRD pattern data were fit to curves using the adjacent averaging method based on 20 data points from the original experimental data (Fig. 8). The background of XRD curves was not removed for the deconvolutions of the XRD curves because the randomly oriented polymers in the amorphous phase were included the background in all regions of the XRD curves between 2θ = 10 deg and 30 deg. Each phase of the CFRP contains 2θ locations. The peaks at 2θ ≈ 20 deg (α1) and 23.7 deg (α2) represent the α forms. The peaks at 2θ ≈ 21.3 deg (γ1) and 22 deg (γ2) represent the γ forms [17,2830]. The peak of carbon fibers is at 2θ ≈ 25.5 deg [30]. The peak of the amorphous phase is at 2θ ≈ 21.43 deg [17]. Each peak curve was calculated using a Gaussian shape model with manual adjustments of the heights and widths of peaks at the beginning to provide reasonable starting points. The agreement between experimental data and the prediction obtained from the Gaussian shape model satisfied the yielding coefficients of determination (R2) above 0.98. The curve fitting functions in the origin data analysis software were used to calculate the area under the curves for each peak ($Aα1$, $Aα2$, $Aγ1$, $Aγ2$, Aamorpous, Acarbonfiber). The fractions of the α phase $(Xα)$ and γ phase $(Xγ)$ and the α/γ ratio were calculated from the equations given below (Eqs. (8)(10)).
$Xα=Aα1+Aα2Aα1+Aα2+Aγ1+Aγ2+Aamorphous$
(8)
$Xγ=Aα1+Aγ2Aα1+Aα2+Aγ1+Aγ2+Aamorphous$
(9)
$αγ(%)=XαXγ(%)$
(10)
Fig. 8
Fig. 8
Close modal

### 4.2 Influence of the Annealing on the Degree of Crystallinity.

The DoC results measured via DSC are shown in Fig. 9. The DoC of the as-received CFRP is not uniform, which implies that the distribution of material morphology is not even. After annealing, the DoC values become more uniform even though the average DoC on the coupon surface remains the same. When these annealed coupons are welded, the weld strength results of the lap shear tests show significantly reduced scatter.

Fig. 9
Fig. 9
Close modal

The injection molding process used to manufacture the coupons unevenly distributes the crystalline structure during cooling. Annealing the base material at a temperature higher than its glass transition temperature (Tg) induces a change in the crystalline structure [29]. Pure Nylon 6 shows less DoC variation compared to the CFRP, as the thermal conductivity of the carbon fibers is considerably higher compared to Nylon 6. Therefore, the carbon fibers accelerate cooling during CFRP manufacture. These results show that annealing can control the DoC, which is a key morphological parameter.

### 4.3 Influence of the Annealing on the α/γ Ratio.

The fractions of the α and γ forms and the α/γ ratio are illustrated in Fig. 10(a) for the CFRP and Fig. 10(b) for Nylon 6. Annealing at 80 °C facilitates the transformation from the amorphous phase to the γ form crystalline phase [29]. The same phenomenon is observed in annealing between 80 °C and 100 °C, in which the weight fraction of the γ crystalline phase increases. However, when annealing is started at a temperature of 120 °C—with significant transformation occurring at an annealing temperature of 180 °C—the weight fraction of the α form increases because of the transformation from the γ form to the α form [33]. Yan et al. showed that the transformation of crystalline forms differs depending on the presence or absence of carbon fibers and that carbon fibers facilitate transformation at low annealing temperatures [30].

Fig. 10
Fig. 10
Close modal

The γ crystalline form dominates at the surface layer of an injection-molded base material, whereas the α crystalline form is dominant in its core layer [34]. Moreover, the thermal conductivity of carbon fibers is considerably higher compared to that of Nylon 6. This facilitates rapid cooling during injection molding, which further leads to a high weight fraction of the γ form. In this experiment, the ratio of the weight fractions of the two forms was measured on the surface of an injection-molded base material. The weight fraction of the γ form is higher than that of the α form. For Nylon 6, the α/γ ratio increases rapidly after annealing at 180 °C, which shows easier change in the crystalline structure compared to the CFRP at a high annealing temperature.

The measurements of the DoC and α/γ ratio with different annealing temperatures confirm that the annealing process changes the crystalline structure. Annealing results in a uniform DoC throughout the material, and the crystalline structure transforms according to the annealing temperature. These changes in the morphology of the material alter its viscoelastic and mechanical properties. The evolution of viscoelastic and mechanical properties caused by the annealing process is discussed in the following sections. The lap shear test results of USW are shown to evaluate the changes in weld strength corresponding to the variations in morphological parameters and viscoelastic and mechanical properties caused by the annealing process.

## 5 Influence of Annealing on the Elasto-Viscoplastic Behavior of the CFRP

### 5.1 Influence of the Annealing on the Ultimate Tensile Strength.

The ultimate tensile strength of the material is shown in Fig. 11, which illustrates that the ultimate tensile strength increases with annealing temperature. This phenomenon can be explained by the increase in the α crystalline form, which improves the tensile strength, in the material after annealing. The higher tensile strength of the base material influences the weld strength after USW.

Fig. 11
Fig. 11
Close modal

### 5.2 Influence of the Annealing on the Viscoelastic Properties.

The dynamic mechanical behavior of a material is determined using a DMA, in which sinusoidal stress is applied and the response of the material is measured through strain [32,35]. The delay between the stress and strain is expressed as phase angle δ. The following equations (Eqs. (11)(16)) show the relationship between stress σ, strain ɛ, and phase angle δ at time t [36,37].
$σ(t)=σ0sin(ωt+δ)$
(11)
$ε(t)=ε0sin(ωt)$
(12)
$σ=σ0sin(ωt)cosδ+σ0cos(ωt)sinδ$
(13)
$E′=σ0ε0cosδ$
(14)
$E′′=σ0ε0sinδ$
(15)
$tanδ=E′′E′$
(16)
where σ0 is the maximum sinusoidal stress, ω is the oscillation frequency, and ɛ0 is the strain at the maximum stress. Storage modulus E′ and loss modulus E″ represent the elastic and viscous behaviors of the material. These properties are related to intermolecular friction heating during USW [4,14,3840]. As expressed in the preceding equations, the moduli of viscoelastic materials, such as polymers, are a function of time at a constant temperature or a function of temperature at a constant time. The master curve for the viscoelastic properties of a polymer can be predicted using the time–temperature superposition method, in which several sets of frequency sweep results at various temperatures are used to create the master curve. This method is used to predict the viscoelastic properties in conditions under which experimental measurements cannot be performed such as high frequencies and temperatures. Here, the viscoelastic properties of the material were predicted with a temperature sweep at 20 kHz (the USW vibration frequency). The Williams-Landel-Ferry model was used to calculate the shift factors of the master curve [37].

A DMA machine (TA instruments, DE) was used to measure the storage and loss moduli with a three-point bending fixture. The dimensions of the DMA specimens were 10 mm × 37 mm × 1 mm, and the span length of the fixture was 25 mm. The specimens were obtained by cutting and softly sanding the coupons created using injection molding. The frequency–temperature sweep method was used in a temperature range of 25–80 °C and a frequency range of 0.05–10 Hz. A convection-controlled heating chamber was employed to stabilize temperature, with a soaking time of 300 s before dynamic loading.

Figures 1214 show the storage modulus, loss modulus, and tanδ, respectively, for the as-received and annealed coupons of the CFRP and Nylon 6. The storage modulus of the CFRP decreases with increasing temperature (Fig. 12(a)). However, it increases during annealing because of the change in the crystalline structure. The loss modulus increases at temperatures higher than the glass transition temperature of CFRP (Fig. 13(a)). This trend is also observed in Nylon 6 (Figs. 12(b) and 13(b)). The apex of tanδ corresponds to the glass transition temperature of the thermoplastic polymer (Figs. 14(a) and 14(b)). The as-received sample has the lowest glass transition temperature, and the obtained sample has the highest glass transition temperature after annealing at 180 °C. Hence, the glass transition temperature of the material increases with annealing temperature. These results influence the heat generation in the USW process.

Fig. 12
Fig. 12
Close modal
Fig. 13
Fig. 13
Close modal
Fig. 14
Fig. 14
Close modal
At temperatures less than the glass transition or melting temperatures of the materials used for USW, the interfacial friction heating mechanism is dominant in the USW process. At temperatures higher than the glass transition or melting temperatures, the intermolecular friction heating mechanism becomes dominant in the USW process [4,14,38,39]. Equations (17) and (18) are used to calculate the heat generation rate of the interfacial friction heating mechanism and intermolecular friction heating mechanism. Their summation is the total heat generation rate in the USW process.
$Q˙interfacial=αh2ωπμ|σyy*δu*|$
(17)
$Q˙intermolecular=αh2ωε02E′′2$
(18)
where $Q˙$ is the heating rate, αh is the empirical hammering correction factor, μ is the friction coefficient, $σyy*$ is the vertical stress on the horizontal interface, ω is the vibration frequency, and $δu*$ is the horizontal displacement discontinuity across the interface [38].

The equations illustrate that the heat generated during USW by interfacial friction increases with the storage modulus, if other parameters remain the same. In contrast, the heat generated by intermolecular friction increases with the loss modulus. Increased heat generation improves welding quality (before reaching temperatures at which the heat degradation of the material occurs). Among the processing parameters, welding energy is related to the total heat generation. A higher heating rate results in rapid heating with the same welding energy. Wang et al. [2] showed that higher welding energy results in increased weld strength up to energy levels at which the material degrades. After the material melts, welding energy is used to entangle molecules in the welded area, and this results in a better weld performance.

The viscoelastic behavior of semicrystalline polymers contributes differently to the heat generation during USW at various temperatures. The storage modulus of a semicrystalline polymer is maintained up to the melting temperature and decreases considerably thereafter, implying that interfacial friction is dominant until the melting temperature is reached. Intermolecular friction is dominant above the melting temperature. The loss modulus of a semicrystalline polymer is maintained at relatively low values up to the melting temperature and increases rapidly close to the melting temperature. The loss modulus decreases rapidly above the melting temperature [38]. This material used in this study, i.e., the CFRP, is stiffer and more heat resistant compared to a pure Nylon 6 owing to its reinforcement with short carbon fibers, which contribute to larger interfacial friction compared to intermolecular friction.

Annealing this material increases its stiffness, as expressed by the storage modulus, and its resistance, as expressed by the glass transition temperature. These increases lead to higher heat generation by interfacial friction and improve the welding process at the same welding energy level compared with as-received samples.

The elasto-viscoplastic behavior of the annealed and as-received coupons was used in a thermomechanical finite element model of the USW with heat generation driven by Eqs. (17) and (18) [41]. The results of the prediction of the temperature generated at the interface (overlapped area, 38 mm × 38 mm) of the coupons show that the temperature maps in the weld area are more uniform for annealed coupons compared with as-received including the center area and consequently, the weld area is larger and circular as shown in Fig. 15. Consistent shape and bonding of the weld for the coupons weld with the same USW process parameters is desired for leading to fracture surfaces almost similar and, consequently, a reduced variation in the weld strength. The performance of the weld was also experimentally tested and validated, as presented in Sec. 6.1.

Fig. 15
Fig. 15
Close modal

## 6 Results and Discussion

### 6.1 Enhanced Weld Strength.

The weld strength results obtained in the single lap shear test are shown in Fig. 16. The maximum lap shear strength increases with annealing temperature. These results prove the influence of the morphological parameters and viscoelastic and mechanical properties on USW. For annealing at 160 °C, various welding energy levels (600, 700, and 800 J) were used to validate the influence of the morphological parameters and viscoelastic and mechanical properties on weld strength (Fig. 17).

Fig. 16
Fig. 16
Close modal
Fig. 17
Fig. 17
Close modal

Figure 17 shows that the average weld strength increases and the variation in weld strength decreases. This demonstrates that the better DoC distribution and higher weight fraction of the α crystalline form compared to the γ crystalline form result in better welding performance. These parameters can be defined as the morphological parameters that influence the viscoelastic and mechanical properties of the material. These changes allow for a more stable and efficient welding process. Weld strength is improved through the enhancement of the mechanical properties of the material. In this study, the average weld strength improves by 46% and the variation in weld strength decreases by 61% on average.

### 6.2 Enhanced Bonding in Ultrasonic Welding of the Annealed Coupons.

USW generates heat at the interface between the coupons to be welded. However, there is no standard method for measuring the temperature at the interface. To measure the heat generation during the USW process at the interface of two coupons, type K thermocouples (OMEGA, CT) with a diameter of 0.13 mm and a maximum temperature of 593 °C were placed on the top surface of the bottom coupon where the top coupon would be overlapped, as shown in Fig. 18. These thermocouples were triggered with the USW process so that the start of their recordings corresponded to the initiation of the ultrasonic effect. Data were recorded using an Arduino development board with a time interval of 0.01 s. The temperature was recorded for the USW of five annealed and five as-received coupons.

Fig. 18
Fig. 18
Close modal

The maximum temperature during USW and the evolution of temperature were measured, and the evolution of temperature is shown in Fig. 19(a). Figure 19(a) confirms that the temperature evolutions for the USW of the as-received and annealed coupons are different. Annealing at 180 °C leads to the most rapid temperature increase and the highest maximum temperature. The maximum temperatures during USW are shown for five replicates in Fig. 19(b).

Fig. 19
Fig. 19
Close modal

The maximum temperatures of the USW of the as-received coupons are not uniform. Comparatively, the variations in the maximum temperatures of the USW of the annealed coupons are smaller. Additionally, the highest maximum temperature of the as-received samples is lower than that of the annealed samples, proving that the increased α/γ ratio and uniform DoC improve mechanical and viscoelastic properties, which lead to higher heat generation by interfacial and intermolecular friction.

## 7 Conclusions

In this paper, a new category of parameters for USW is introduced to study the USW of short carbon fiber polymer composite materials without energy directors and their difference compared with the USW using energy directors. This category of parameters characterizes the morphology of the material and impacts its elasto-viscoplastic behavior during USW. It was shown through experiments that DoC and the ratio of the weight fractions of the crystalline forms of Nylon 6 play a very important role in weld formation and stability of the weld in the USW process. These parameters, named morphological parameters, can be controlled through annealing. Experimental campaigns were conducted annealing coupons at different temperatures and further welding them. The changes in viscoelastic and mechanical properties alter heat generation during USW and the resulting weld strength. The conclusions of the study are as follows:

1. Morphological parameters, i.e., the DoC and α/γ ratio, influence the viscoelastic and mechanical properties of the material, which are important parameters for USW. Morphological parameters must be considered to control USW.

2. Annealing can be used to control the morphological parameters of the material and induce a uniform DoC distribution. The α/γ ratio increases with annealing temperature.

3. The uniform DoC and increased α/γ ratio obtained by annealing increase the storage and loss moduli and the glass transition temperature of the material, which results in more efficient USW in terms of heat generation by interfacial and intermolecular friction. These changes in the morphological parameters also increase the ultimate tensile strength of the material.

4. The improved viscoelastic and mechanical properties increase weld strength and decrease the variation in weld strength.

## Acknowledgment

This research is supported by the General Motors Collaborative Research Laboratory at the University of Michigan.

## Funding Data

• General Motors Collaborative Research Laboratory at the University of Michigan (N017367-06; Funder ID: 10.13039/100014076).

## Nomenclature

• a =

tube persistence length

•
• b =

polymer statistical segment length

•
• M =

molecular weight

•
• N =

number of monomers

•
• E′ =

storage modulus, GPa

•
• E″ =

loss modulus, GPa

•
• $Q˙$ =

heating rate, W/m3

•
• kB =

Boltzmann constant

•
• papp =

applied pressure

•
• tr =

reptation time

•
• αh =

empirical hammering correction factor

•
• δ =

phase angle, deg

•
• $δu*$ =

horizontal displacement discontinuity across the interface, m

•
• ΔHm =

melting enthalpy, J/g

•
• ɛ =

strain

•
• ηmf =

viscosity of the matrix–fiber system

•
• ζ =

monomeric friction coefficient

•
• σ =

stress, Pa

•
• σ =

mechanical strength at infinite time

•
• $σyy*$ =

vertical stress on the horizontal interface, Pa

•
• μ =

friction coefficient

•
• ω =

frequency of oscillation, Hz

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