Vibration welding offers a robust method for physically joining thermoplastics to fabricate complex hollow assemblies from simpler injection-molded articles without using an external heat source, adhesives, or mechanical fasteners. Vibration welding involves a complex interplay of several phenomena—solid (Coulomb) friction, melting, high strain-rate, pressure-driven, strong (high-strain) melt flows, solidification, and microstructure development—which ultimately govern the strength and integrity of the weld. Defects in the weld region may lead to catastrophic failure of the welded assembly. In this article, the current understanding of the processing–structure–property relationships in the context of vibration welding of thermoplastics and polymer-matrix composites is reviewed. Experimental as well as analytical methods of investigation of the vibration welding process phenomenology are presented. The interrelationships between the microstructure in the weld region and the resulting weld strength and fatigue behavior are then discussed in the light of this phenomenological information for neat polymers, filled polymers, polymer blends, and foams. This review is also aimed at identifying the areas requiring further investigation with regard to understanding vibration welding phenomenology and weld structure–property relationships. POLYM. ENG. SCI., 2011. © 2010 Society of Plastics Engineers
JOINING OF PLASTICS
The need for joining components arises in situations where the whole part is difficult to fabricate in a single manufacturing step due to the involvement of different materials and geometrical constraints and complexities. Joining may be accomplished by mechanical fastening (using, for example, nuts and bolts), chemical bonding (using adhesives), or physical bonding, also referred to as welding. The method used depends on the material being joined, the size of the part, the geometrical details in the region of joining, the rate of production of parts, the service conditions and performance requirements of the assembly, the cost constraints, and the aesthetic requirements .
Thermoplastics typically lend themselves quite well to complex shaping—involving large-strain deformations, small radii of curvatures, and sharp thickness gradients—via processing operations such as extrusion, injection molding, and thermoforming. This has led to the widespread use of several plastics in automotive applications where they bring the additional advantage of weight savings, and higher part throughput rates. However, parts such as air intake manifolds (AIMs), battery casings, and lighting assemblies entail complex geometrical details, and single step manufacturing of the entire part is not feasible . Similar challenges are faced with shaping of continuous-fiber-reinforced plastics (CFRP), which, while offering superior mechanical properties, are limited by the extent of geometrical details that may be captured in stamping and compression molding operations .
Such challenges, imposed by the geometry (AIMs) or the material (CFRP) can be overcome by specialized processing operations, such as lost-core injection molding [2, 4] or joining operations . In lost-core molding, the polymer is extruded or injection-molded over a mold or core made with low-melting metals and alloys, such as tin alloys . The over-molded core is melted out after polymer solidification, and may be reused. The major disadvantages of the lost-core molding process are the high capital costs and complexities associated with the additional metal forming, melting, and core removal operations.
Alternatively, joining operations may be used to build up injection-molded components into more complex assemblies. The additional geometrical details can be added by strategically juxtaposing ribs, bosses, and other local geometrical details in the injection-molded or thermoformed components . However, conventional joining techniques such as mechanical fastening and adhesive bonding may not be optimal for complex hollow assemblies. Mechanical fastening requires additional exposed surface (flanges) to facilitate the inclusion of nuts and bolts. Also, mechanical fastening may not always be sufficient when the resulting hollow assemblies are required to hold and distribute liquids or gases, in which case, the joints also need to serve as seals to contain the fluids. The complexity and size of geometrical features that need to be bonded may pose a challenge for robotic application of adhesives. Moreover, adhesive bonds, containing a material different from the bulk, may provide weak points during harsh service conditions or in scenarios where organic liquids or acids are involved. Adhesives may also fill small hollow geometrical details. In such scenarios, physical bonding (or welding) techniques offer several advantages: the joint may be evenly established throughout the bonding surfaces (in contrast to mechanical fastening); the joint is limited only to the area where it is required; good bonding may be obtained even when the area to be bonded is narrow (e.g., ribs); and the joint is composed of the same material as the bulk (in contrast to adhesive bonding).
All physical bonding or welding processes for plastics typically involve the following steps : (1) Nesting of the plastic parts in grips; (2) Provision of heat in the areas to be joined leading to localized melting; (3) Joining under pressure; (4) Cooling of the weld and surrounding areas; and (5) Welded part removal from the welding tool. Welding processes can be typically grouped into (a) methods involving external heat application (thermal welding), (b) methods involving inductive or resistive heat generation with conductive implants or fillers (electromagnetic welding), and (c) methods involving heat generation through mechanical means (mechanical welding) (refer to Grimm , and Grewell and Benatar  for an overview of the various categories of thermoplastic welding).
The focus of this review is vibration welding of thermoplastic parts, a mechanical welding technique which does not require an external heat source. Vibration welding is carried out by rubbing the surfaces to be joined in an oscillatory manner against each other , under pressure, as shown in the schematic in Fig. 1. Generally, the plastic pieces to be welded are gripped in an upper vibrating frame and a lower nonvibrating platen. The material at the weld interface is heated due to the frictional work, and eventually becomes fluid as the interface temperature rises beyond the melting point or the glass transition temperature of the polymer. After the onset of the melt-film, vibration is continued for a sufficient amount of time to allow pressure-driven flow and intermixing within the film. Finally, vibration is stopped and the molten film is allowed to cool and solidify under pressure, resulting in the welded joint. The controlled process parameters in vibration welding are the frequency, n, and the amplitude, a, of the vibratory motion, the weld pressure, p0, and the duration of welding . Commercial vibration welders typically offer a frequency range of 180–240 Hz, with amplitudes ranging from 1.0 to 1.8 mm (controlled using a digital vibrator drive), and clamp forces of up to 27,000 N (typically maintained using hydraulic clamps) [8, 9]. Several researchers have also reported lab-scale tests with smaller vibration welders [7, 10] with variable vibration frequency.
The schematic in Fig. 1 represents one specific method of vibration welding, termed “longitudinal” vibration welding, in which the weld specimens are vibrated in a direction that is parallel to the longer edge of the specimens. On the other hand, vibration of the specimens in a direction parallel to the shorter edge constitutes “transverse” or “cross-thickness” vibration welding  (in a deviation from the terminology of Stokes , throughout this article, the shorter specimen dimension in the weld plane will be referred to as width, instead of thickness; thus transverse welding would be equivalent to “cross-width” welding). Together, longitudinal and transverse vibration welding methodologies comprise “linear” vibration welding, in which the trajectory of vibratory motion remains linear and constant. By contrast, in “orbital” vibration welding, vibration may be carried out in several directions.
Vibration welding, in its wide applicability, competes with hot-plate welding and ultrasonic welding as the method of choice for joining plastics. Hot plate welding  is suited for joining of large parts, and typically results in welds with low residual stress and orientation; but it may be prone to accumulation of voids and bubbles in the weld region . Vibration welding and ultrasonic welding do not require pre-heat of the parts prior to assembly, and therefore offer greater thermal efficiency. Although ultrasonic welding is better suited to joining parts of low stiffness, it entails greater frequency vibration (up to 40 kHz) with an ultrasonic horn , and requires better surface preparation compared to vibration welding. Vibration welding is most suited for parts of relatively higher stiffness, and offers the advantages of robust machinery, simple processing without accessories such as the ultrasonic horn, high throughput rates, and minimal polymer degradation . Vibration welding does not require elaborate weld surface preparation; any surface impurities are automatically removed since the welding operation results in depletion of the initial part surface (as explained in the next section) . Vibration welding is versatile in its applicability to joining of large parts, irregularly shaped parts, and parts having multi-plane or curved surfaces [8, 9], and can be conveniently used to make sealed hollow regions in complicated geometries, such as AIMs, fuel tanks, lighting assemblies, and battery casings. On the other hand, vibration welding is also known to offer a stronger flow-field in the weld region when compared to hot-plate or ultrasonic welding , making it more prone to development of residual stresses and orientation.
In this article, the current understanding of the processing–structure–property relationships in the context of thermoplastic vibration welding is reviewed. First, experimental as well as analytical methods of investigation of the vibration welding process phenomenology are presented in the next section. Subsequently, the interrelationships between the microstructure in the weld region and the resulting weld strength and fatigue are discussed in the light of this phenomenological information, for neat polymers, filled polymers, polymer blends, and foams. This review is also aimed at identifying the areas requiring further investigation with regard to understanding vibration welding phenomenology and weld structure–property relationships, and these aspects are reiterated in the final section.
VIBRATION WELDING PROCESS PHENOMENOLOGY
Since vibration welding involves oscillatory motion parallel to the weld plane (refer to Fig. 1), the measurement of shear forces at the weld interface is a natural choice to gain insights into the vibration welding process phenomenology. Stokes  used a combination of measurements of the load at the weld specimen interface (using a pressure gage), and the force used to drive the moving-frame-grip assembly (using a Kistler gage) to determine the interfacial shear force during welding at low frequencies. Measurements with piezoelectric shear-force transducers can provide additional insights into the evolution of interfacial forces .
A schematic representing the typical transient of the shear force at the weld interface during vibration welding (capturing the key features of the experimental shear-force transient measurements reported by Stokes  and Dai et al. ) is shown in Fig. 2. As soon as vibration is started, a peak in shear force (point A in Fig. 2) is observed, which has been attributed to static friction or any initial interlocking between the parts due to geometrical asperities . The magnitude of the initial peak force increases with weld pressure; the direct proportionality between the shear-force and the applied normal stress is characteristic of Coulomb friction . Also, the shear force is found to be in phase with the sliding velocity (2πna), confirming that the forces are purely frictional in nature (viscous forces are absent) ; this implies that Coulomb friction is the sole mechanism for heating of the weld interface in the initial stages of welding. The magnitudes of the frictional forces display only a weak dependence on the sliding velocity .
The end of the Coulomb-friction dominated initial phase is marked by an upturn in the interfacial shear forces (point B in Fig. 2), that has been associated with the onset of viscous shear  (indicating the formation of a melt-film at the weld interface). Following this, the interfacial shear forces remain almost constant for the major duration of welding, and are found to be out of phase with the sliding velocity, confirming the viscous nature of the forces . In this latter steady-state, viscous dissipation is the dominant mechanism for heat generation at the interface. Depending on the viscosity of the melt and the shear rates in the interfacial region, the shear forces in the viscous-shear regime may be higher than those in the solid- (Coulomb-) friction phase [7, 16]. Upon stopping of vibration (point C in Fig. 2), the shear forces do not instantly decay to zero, indicating that some degree of flow or deformation (driven by the weld pressure) occurs even after stopping the vibration.
Measurement of Weld Penetration
Shear-force transient measurements typically become more challenging at high-frequency vibration welding as the force signals get convoluted with inertial effects associated with the mass of the moving assembly . A more convenient method of studying the phenomenology of vibration welding is the measurement of a variable known as “meltdown” or “weld penetration.” The cartoon shown in Fig. 3 helps in visualizing the changes occurring in a butt-weld interface during the course of vibration welding, and in understanding the concept of weld penetration. Frictional force leads to heating and melting of the polymer at the weld interface. Under externally applied normal pressure, this polymer is squeezed out into a weld-bead. With progressive growth of the bead, there is a corresponding reduction in the separation between the grips holding the weld specimens (cf. Fig. 3). This is called meltdown or weld penetration. The transients of weld penetration can be measured with precision in a wide variety of commercial and research grade vibration welders [7–10], and over a broad spectrum of process parameters, using a linear displacement transducer. The penetration transient can be understood in terms of a mass balance in the vicinity of the welding interface: the evolution of weld penetration is indicative of the balance (or imbalance) between the rate at which new material from within the bulk melts (inflow), thus feeding the melt-film (accumulation), and the rate at which this melt-film is depleted through squeeze-out into the weld-bead (outflow).
On the basis of the transients of weld penetration, the vibration welding process may be represented to occur in four phases as shown schematically in Fig. 4: I—solid friction, II—unsteady evolution of penetration, III—steady growth of penetration, and IV—solidification . These four phases have been observed during vibration welding of a variety of unfilled polymers (e.g., ) filled polymers , polymer blends [7, 18], polymer foams , and dissimilar polymers . The controlled parameters of vibration welding—the frequency (n), and amplitude (a) of vibration, the weld pressure (p0), and the specimen width (b)—significantly impact the weld penetration, η, the penetration rate, , and the duration of each phase of welding; the typical experimental trends have been schematically summarized in Fig. 5, and are discussed in detail below.
In phase I of vibration welding, dominated by solid (Coulomb) friction, no weld penetration is recorded. This indicates that the normal pressure does not result in any collapse of the interface as long as the material is solid. The first displacement signals on the linear displacement transducer (at time t1 in Fig. 4) indicate the onset of the melt-film at the interface, marking the end of phase I. Higher weld pressures and higher vibration amplitudes (while keeping the weld-geometry and the remaining weld-parameters constant) typically result in faster onset of melting at the interface—or shorter durations of phase I (t1) [7, 21]. t1 is not impacted by the width of the sample being welded .
The onset of weld penetration marks the beginning of the regime of flow and viscous dissipation within the melt-film. Initially, the penetration rate evolves with time; this is indicative of an unsteady state in which the rate of inflow of new melt into the melt-film is not matched by the rate of outflow into the weld-bead. This indicates an effective accumulation of melt, implying the growth of the melt-film (cf. Fig. 3). However, after time t2 (cf. Fig. 4) the penetration grows linearly with time resulting in a constant penetration rate. This indicates that a steady-state has been established with the rate of fresh melt formation being matched by the rate of melt-outflow into the weld-bead—implying a zero rate of accumulation, or a constant melt-film thickness.
Stokes's measurements of the duration of phase II (t2−t1) (cf. Fig. 4) during longitudinal vibration welding of polycarbonate [7, 21] indicate that steady states are established more quickly [shorter durations of phase II, or smaller (t2−t1)] at higher weld pressures (while keeping the weld-geometry, and the vibration amplitude and frequency constant). Higher pressures may cause a quicker establishment of the lateral squeeze-flow-field. The weld geometry and other weld settings remaining constant, the duration of phase II increases at higher frequencies and lower amplitudes [7, 21]. Increase in the width of the weld sample (while keeping the vibration amplitude and frequency, and the weld pressure, constant) also results in longer durations of phase II . An increase in sample width is equivalent to an increase in the entry-flow region of the squeeze-flow (x-direction distance, cf. Fig. 1), and, therefore, will lead to longer times to establish steady flow in that direction.
In the steady phase III, the lateral outward extrusion of the material results in the growth of the weld-bead (refer to Fig. 3). Stokes's measurements for longitudinal vibration welding [7, 21] indicate that the steady-state penetration rates ( ) increase with increase in weld pressure (while keeping the weld geometry, and the vibration amplitude and frequency constant). With the melt-film thickness remaining constant in phase III, the primary consequence of higher normal pressure would be in pushing new material from the bulk into the solid–melt interface at a faster rate, thereby increasing the penetration rate. Increase in vibration amplitude (while keeping the vibration frequency, and the weld pressure, constant) also results in higher penetration rates . These higher rates may be correlated to quicker melting of the polymer at the weld interface, due to greater viscous dissipation at higher amplitudes (as discussed in detail in the context of melt-film variables).
For transverse welds, even though the general trends in process variables with respect to the process parameters remain the same, the durations of the phases II and III are longer, and the steady penetration rates are lower  compared to longitudinal welds (with the same specimen width) carried out at the same vibration amplitude, frequency, and weld pressure; this may be attributed to the greater exposure of the melt-films in transversely welded surfaces to the ambient, and, therefore, greater convective cooling of the film [4, 11]. Increase in specimen width (while keeping the welding parameters constant) also typically leads to lower penetration rates in the steady state . This can be understood based on the fact that at larger sample widths, any new material arriving at the weld interface has to be laterally squeezed for a longer distance before it gets incorporated in the weld-bead.
The steady state of vibration welding is more complicated in welds of dissimilar polymers . The “apparent” steady state, indicated by the measured constant penetration rate, in welds of dissimilar polymers is dominated by the higher melting rates and the higher flow rates of the polymer that has the lower melting point. The melt-film of the higher melting polymer may continue to grow during the apparent steady phase, and a “true” steady state, in which the melt-film thicknesses of both the polymers become constant, is only achieved at substantially greater penetrations. In a study of weld penetration transients during welding in different geometries, it was also noted that T-welds display longer weld cycles (lower penetration rates) compared to butt welds . This was attributed to the variable effective width of the weld as the web penetrates into the flange in case of T-welds.
In phase IV, in the absence of frictional work or viscous dissipation, the film cools and solidifies, resulting in the final weld. The solidification time reported for typical industrial components is of the order of 1s . The typical measured bead sizes of welded automotive components such as air intake manifolds are in the range of 3–4 mm, and are similar to the bead sizes observed in research butt welds .
The study of penetration transients, discussed in the earlier section, offers some significant insights into the phenomenology of vibration welding—particularly regarding the kinematic conditions prevailing at the evolving melt-film at the weld interface. In addition to this kinematic information, detailed quantitative understanding of the melt-film variables—such as the thickness of melt-film, and the temperatures and stresses within the melt-film—is required to establish logical correlations between the processing conditions, and the weld microstructure and strength.
Measurements of melt-film variables are severely limited by the uncertainties arising from the small thickness of the melt-film and the large gradients of the variables within the melt-film. Although attempts to measure temperatures in the melt-film in situ during vibration welding by using embedded thermocouples , and infra-red cameras [26–28] have been reported, the experimental assessment of variables such as melt-film thickness, and shear rates and stresses within the melt-film is quiet challenging, and typically, only indirect qualitative assessments about the same may be made through inspection of post-weld microstructure (as discussed in later sections of this article). The impact of weld pressure and vibration amplitude and frequency on these variables, therefore, needs to be investigated using mathematical models for each phase of vibration welding. The steady-state weld penetration in phase III constitutes the longest phase of vibration welding, and has a significant impact on microstructure development, orientation and residual stresses at the weld interface. The phase III of vibration welding has, therefore, received the most attention in modeling studies [7, 21, 24, 29–32].
Model for Flow and Heat Transfer in the Melt-Film During Steady Penetration.
Figure 6 shows the geometry for modeling steady-state flow and heat transfer within the melt-film of constant (unknown) thickness, h0, bounded on two sides by solid–melt interfaces, at y = 0 (nonvibrating lower solid–melt interface) and y = h0 (vibrating upper solid–melt interface). The thickness of the melt-film is maintained constant through a balance between the inflow of fresh melt [driven by the steady penetration velocity, (measured)] at the two solid–melt interfaces, and the outflow of the melt into the weld-bead through the pressure-driven squeeze-flow along the width (b) of the specimen. In addition to h0, there are two more unknowns in this problem: the temperature field [T(x,y)] and the melt viscosities (μ) (or the viscous stresses) within the melt-film. This problem is further complicated by the shear-rate and temperature dependence of viscosity. The shear rates are governed, in turn, by the thickness of the melt-film, and the viscosity of the melt.
Stokes  ignored the shear-rate and temperature dependence of viscosity, and used the Newtonian model (constant viscosity) for the melt, to solve the momentum balances in the vibration direction (z-direction) and the squeeze-flow plane (x–y plane). Momentum balance in the squeeze-flow direction was solved using the stream function approach to relate the applied pressure to the melt viscosity and film thickness. Heat transfer was modeled using a macroscopic heat balance, which involved equating the heats associated with temperature rise and phase change in the melt to the heat generation from viscous heating. The viscous heating term took into account the shear rate in the vibration direction alone, and not in the squeeze-flow direction. This macroscopic formulation of the heat transfer problem does not account for the spatial variation of temperature in the melt-film. Therefore, Stokes's problem definition does not yield three independent equations required to solve for the three variables. Stokes  was required to assume an arbitrary constant viscosity and then solve for the melt-film thickness.
Chung et al.  also used the Newtonian model for momentum balance within the melt-film. In their model, the momentum balance in the squeeze-flow direction was reduced to a one-dimensional problem using the lubrication approximation (flow in the x-direction with gradients in y-direction). In an improvement to Stokes's approach , the heat transfer problem, formulated using a differential equation, accounted for the spatial variation of temperature within the melt-film. The heat generation term involving viscous heating, took into account the shear rate in both the vibration direction and the squeeze-flow direction. By accounting for spatial variation in temperature, the model of Chung et al.  is able to exploit the temperature boundary conditions at the solid–melt interfaces, to arrive at two additional independent equations to solve for the three variables. This approach is described in greater detail below.
The momentum balance for Newtonian (constant viscosity, μ) melt flow in the film under the applied pressure p0 may be expressed in the form of the Stokes equation  (no inertial effects)
The boundary conditions on the velocity components v(u,v,w) are (cf. Fig. 6a):
In the steady state, the component of the velocity in the y-direction, indicative of melt penetration, is governed by the steady penetration rate (measurable). The solution of the momentum balance in the z-direction with the boundary conditions in Eq. 2, ignoring any gradients in the z-direction, and assuming w = w(y), yields the cycle-averaged velocity w and time-averaged shear rate in the vibration direction :
Chung et al.  applied the lubrication approximation in the thin melt-film region (u ≫ v) to obtain the steady-state x-direction (lateral squeeze-flow direction) velocity u and shear rate
The steady-state pressure drop dp/dx (refer to  for details) due to the squeeze-flow in the x-direction can be averaged over the sample width b to obtain the applied weld pressure, p0.
The temperature distribution in the melt-film was related to the viscous dissipation due to the vibration-flow in the z-direction and the squeeze-flow in the x-direction.
Equation8, when solved with the temperature boundary conditions, T = Tg (or Tm) at y = 0 and y = h0 [implying that the temperature of the melt-film is equal to the glass-transition temperature (of the amorphous polymer) or the melting point (of the semi-crystalline polymer) at both the solid–melt interfaces], gives the temperature distribution within the melt-film.
At the solid–melt interfaces, the heat flux is consumed to bring about glass transition in the case of amorphous polymers or melting in case of semi-crystalline polymers. This may be expressed as:
Equations7, 9, and 11 provide the three independent relationships required to solve for the steady-state thickness of the melt-film, the viscosity of the melt, and the temperature field. The solution of the momentum and heat balances requires input of material properties and process parameters and variables. The material property inputs are: thermal conductivity, k, the specific heat, C, the density, ρ, and the latent heat of fusion ΔHmelting (for semi-crystalline polymers), of the melt and the melting point, Tm, (for semi-crystalline polymers) or the glass transition temperature, Tg (for amorphous polymers). The process parameter inputs are: the width, b, of the weld specimens, the frequency, n, and the amplitude, a, of vibration, and the weld pressure, p0. The process variable input required is the experimentally measured steady-state penetration rate, .
The key insights from the model about the magnitudes of the melt-film variables, and their variation with respect to vibration amplitude, frequency, and weld pressure will now be briefly discussed, with original results in the context of vibration welding of polycarbonate (PC), using material and process inputs from Stokes's study [7, 21] (Chung et al.  presented their analysis for Nylon). This discussion will also bring out some inherent limitations of the Newtonian analytical approach.
Model Estimates of Melt-Film Variables.
Estimates of the steady-state melt-film thickness, h0, for polycarbonate vibration butt welds (obtained by solving Eq. 11, after substituting for μ with the expression obtained by rearrangement of Eq. 7) are plotted at different weld pressures (with the vibration amplitude and frequency held constant) in Fig. 7a. The corresponding estimates for melt viscosities (obtained by re-substituting the estimates for h0 into Eq. 7) are plotted in Fig. 7b. The estimates for shear rates in the vibration direction, (calculated by substituting the estimates for h0 into Eq. 4) and the shear rates in the squeeze-flow direction, , at the exit of the squeeze-flow channel (at x = b/2) (calculated by substituting the estimates for h0 into Eq. 6) are plotted in Fig. 7c and d, respectively.
An increase in weld pressure, while keeping other process parameters constant, leads to reduction of the melt-film thickness (Fig. 7a). The decrease in melt-film thickness in turn results in higher vibration direction shear rates, (Fig. 7c). Weld pressure impacts the squeeze-flow direction shear rates, (Fig. 7d), more directly by increasing the flow rates within the melt-film (refer to Eq. 6), in addition to the reduced melt-film thickness. It may be inferred from Fig. 7 that with increase in weld pressure, the reduction in melt-film thickness (Fig. 7a), combined with the higher shear rates (Fig. 7c and d) would result in greater orientational effects within the melt-film, which can hinder polymer chain inter-diffusion and, therefore, can be detrimental to weld strength.
A quick inspection of Eqs. 4 and 6 shows that does not vary spatially in the melt-film, while varies in both x and y directions. The variation of in the thickness (y−) direction, with the maximum magnitudes at the two solid–melt interfaces, is also captured in Fig. 7d. Along the x− direction, the magnitudes of increase from zero at x = 0 (the stagnation point at the center of the specimen width), to the maximum values at the exit into the melt bead (x = b/2, plotted in Fig. 7d). Inspection of Fig. 7c and d reveals that the highest magnitudes of in the melt-film are significantly lower than those of at comparable weld pressures. This difference is especially pronounced at lower weld pressures. This would imply that plays a more significant role in governing the viscous dissipation driven temperature rise within the melt-film (cf. Eq. 8).
An inspection of Fig. 7b–d also reveals an inconsistency in the Newtonian analytical model. Even though the momentum balance has been solved using a constant viscosity Newtonian fluid model, the magnitudes of viscosity estimated from the model for different processing conditions can vary significantly. Moreover, a comparison of the estimated trends with increasing weld pressure, in shear rates (direct relationship, cf. Fig. 7c and d) and viscosities (also direct relationship, cf. Fig. 7b) implies an erroneous trend of increase in viscosity at higher shear rates, which is inconsistent with the slightly shear thinning nature of polycarbonate. These inconsistencies arise due to the fact that the estimate of melt viscosity using either Eq. 7 or 11 does not account for either the temperature dependency (such as the WLF equation ), or the shear-rate dependency (such as Cross law ), and does not have a reference value for the viscosity of the material. The predictions of melt-film thickness can be improved by incorporating the melt viscosities in a more fundamental manner in the analysis.
The effect of vibration-amplitude on the predicted steady-state melt-film thickness has been plotted in Fig. 8a. It is clear that increasing weld amplitude results in an increase of steady-state melt-film thickness, associated with lower orientational effects. However, higher amplitudes also result in an increase in (cf. Eq. 4) as plotted in Fig. 8b. Thus, high amplitudes can significantly increase orientational effects when combined with high weld pressures.
The temperature-fields in the melt-film (estimated using Eq. 9), with substitution of the estimated magnitudes of melt-film thickness, h0, and the viscosity, μ, are plotted in Fig. 9a and b. It is clear that the melt temperature is equal to the glass transition temperature of PC at y = 0 and y = h0, the two solid–melt interfaces, as prescribed by the boundary conditions. Away from the solid–melt interfaces, viscous dissipation results in progressive increase of the temperatures beyond the glass transition, towards the center of the melt-film. The maximum temperature of the melt occurs at approximately the middle of the melt-film. With increase in vibration amplitude, the maximum temperature in the melt-film increases (cf. Fig. 9a)—this increase is driven by the increase in . The maximum temperatures estimated based on the properties of polycarbonate, are only about 4°C above the glass transition temperature of the polymer, as seen in Fig. 9b. In the analysis of vibration welding of nylon butt welds, Chung et al.  concluded that to predict temperature increases of up to 37°C above the melting point of the polymer (consistent with the measurements of Zou et al. ), the associated viscosity estimates were unrealistically high. This once again underscores the need to incorporate fundamental relationships governing temperature and shear-rate dependence of viscosity into the analysis.
For polycarbonate, the predicted maximum temperatures in the melt-film show a gradual increase with increase in pressure, as shown in Fig. 9b. However, Chung et al.  estimated that maximum melt temperatures decrease with increase in pressure for Nylon-6, again consistent with experimental observations of Zou et al. . The opposite dependencies of the temperature fields in PC and nylon on the weld pressure may be because of the different manners in which the weld pressure impacts the penetration velocities. For example, in case of nylon-6, the measured penetration velocities showed a weak dependence on the weld pressure [24, 25] compared to the strong dependence shown by polycarbonate in Stokes's welding experiments [7, 21]. Of course, in a truly Newtonian analysis, in which the melt viscosity would remain a constant at all shear rates (as in the approach of Stokes ) this model would predict an increase in melt-film temperatures with increasing weld pressures. The impact of amplitude and pressure on the trends in temperature in the melt-film is also governed by, in addition to temperature and shear-rate dependence of viscosity , the viscoelasticity of the melt, and the heat capacity of the melt. In the calculations of Stokes  and Chung et al. , temperature and shear-rate dependence of viscosity is not accounted for, and viscoelastic effects have been ignored. Viscoelastic effects may become quite significant in the welding of polyolefins and thermoplastic olefinic blends.
Other Modeling Approaches.
The modeling approaches of Nonhof et al.  and Bates et al.  made an attempt to incorporate shear-rate dependence of viscosity using the Cross law (cf. ). However, the shear-rate dependence was not in-built into the formulation of the momentum and heat balances. In the analytical model of Bates et al. , the momentum-balance formulation was the same as that of Stokes  using Newtonian constant viscosity. The Cross law was used only after the integration of the momentum balance, to modify the resulting algebraic relations between applied pressure, viscosity, and penetration rate. Similarly, in the iterative finite element model of Nonhof et al. , the viscous heating term in the heat balance was the same as that of Stokes  derived for a Newtonian fluid. The Cross-WLF relationship was used only for substituting the magnitude of viscosity in the resulting expression. Therefore, in the strictest sense, these approaches cannot be considered to be full-fledged nonNewtonian solutions. More recently, Patham and Foss  have developed an iterative finite element approach that accounts for both the shear-rate and temperature dependence of viscosity in a fundamental fashion by incorporating the Cross-WLF dependence of viscosity in the formulation of the momentum balance as well as in the viscous heating term in the heat balance. An alternative modeling approach by Lee et al.  employs the measurement of shear-force amplitude to directly calculate the shear stresses (ratio of shear-force and sheared area) in the melt-film; the input of these measured shear stresses, in addition to the penetration transient measurements, into the model can enable the direct calculation of the shear-rate dependent melt-film viscosities and viscous dissipation functions, without resorting to an iterative approach. However, as pointed out earlier, measurement of shear force at the interface is quite challenging, and requires additional complex experimentation.
The final phase of vibration welding, phase IV, in which the vibratory motion is stopped and the melt-film cools under pressure, is the most difficult to study experimentally because of its short and transient nature. This phase is also the least investigated through analytical or finite element models. This is primarily due to the complexities associated with modeling of the strong microstructural dependence of the residual stress development in a solidifying melt. Bushko and Stokes [37, 38] have analyzed the solidification of thermo-viscoelastic melts in the context of injection molding. Doufas et al. , and more recently, Kohler and McHugh  have modeled solidification during high speed thermoplastic melt spinning accounting for flow-enhanced crystallization.
A complete model for Phase IV of vibration welding will therefore have to draw on the understanding from such modeling studies [37–40] to evaluate the effect of polymer orientation at the weld interface on the crystalline structure (where applicable) and residual stress development during solidification. Currently, the phenomenology and impact of process parameters during phase IV can be best assessed only by an analysis of post-weld microstructure. Zou et al.'s study , involving careful measurements of temperature transients in the melt-film during vibration welding of nylons revealed a significantly high cooling rate after the vibratory motion stops—it was reported that a temperature drop of more than 20°C from the melt temperature to the re-crystallization temperature of nylon was accomplished in only 40 ms. As the melt-film cools under pressure, additional material is forced into the weld-zone due to the normal pressure. This deformation imparted in a high-viscosity rapidly cooling melt can be of significance in governing the orientation and residual stresses in the weld, and ultimately impact its strength. The strength and microstructural aspects of vibration welds are discussed in the next section.
MICROSTRUCTURE AND PERFORMANCE OF VIBRATION WELDS
One of the most important measures of performance of a welded assembly is its strength. In the case of automotive components such as air intake manifolds, the strength of the part is typically quantified using a burst test . For test welds, the tensile strength of the T-welded or butt-welded specimens is measured, after suitable sample preparation, to evaluate the performance of the weld (refer to Stokes:  for butt weld, and  for T-weld sample preparation). Stokes  concluded that the butt weld geometry is the most suitable to obtain the true measure of the tensile strength of the weld. The measurements of weld tensile strength using T-weld geometries are complicated by the presence of re-entrant corners and the associated residual stress fields, and may result in a gross under-estimation of the strength [42, 43]. The tensile strength of vibration butt welds have been reported with or without removing the weld-bead prior to testing. Stokes  argued that the presence of weld-bead does not add any excess load-bearing area, and that the presence of beads may in fact present notches around which failure may develop at lower strains during testing. Corroboration for Stokes's premise may be found in the assessment (using environmental stress cracking studies) of residual strains of up to 5% in the weld-beads in vibration welds of poly(vinylidene fluoride) (PVDF) .
If a weld develops an inferior strength compared to the bulk, then the weld can act as the weakest link and result in part failure. Indeed, even in optimally welded specimens, the failure in tensile loading has been observed in the weld . The weld performance may, therefore, be evaluated by defining a “weld factor” or “relative weld strength” as the ratio of the tensile strength of the welded part and that of the bulk (un-welded, as-molded) plastic.
Weld factors close to 1 will ensure that the weld fails at loadings similar to that at which the bulk polymer would fail. For systems with weld factors significantly less than 1, the effective area of the weld must be increased to support the loads imposed on the weld by the part requirements. In the subsequent sections of this article, the weld processing–microstructure–strength interrelationships are reviewed for vibration welds of neat polymers, filled polymers, polymer blends, and polymeric foams. The magnitudes of maximum achievable relative weld strengths for a wide range of neat polymeric systems are included in the Appendix. It should be noted that the majority of the trends discussed in this section are obtained for butt welds effected using longitudinal vibration welding.
Stokes  reported that transverse welds did not typically attain the strength entitlements achievable with longitudinal welds. It should be noted that in actual components, weld surfaces may undergo a combination of longitudinal and transverse vibratory motion. In a study on vibration welding of nonplanar geometries (weld angles different from 0°) welded with vibration axis oriented in different angles with respect to part axis (a vibration angle of 0° implying a longitudinal weld, and 90° implying a transverse weld) [45, 46], it was observed that increasing the vibration angle typically resulted in reduction of weld strength; this was attributed to increased convective cooling in case of transverse vibration welding. At comparable welding conditions, weld strength also decreased with increasing weld angle (weld plane different from vibration plane).
Welds of Neat Polymers
For neat polymers, under optimal weld processing conditions, the vibration welds develop strengths that are equivalent to that of the bulk (unwelded, as-molded) polymer. Data on strength entitlements of vibration butt welds are available for PC , poly(butylene terephthalate) (PBT) , poly(etherimide) (PEI) , modified poly(phenylene oxide) (PPO) , polypropylene (PP) [48, 49], polyamides (PA) [13, 50], poly(vinyl chloride) (PVC) , PMMA , and acrylonitrile-butadiene-styrene (ABS) [53–55], and acrylonitrile-styrene-acrylate (ASA) . In case of welds involving dissimilar polymers, the weld strengths are governed by the mutual affinity of the two polymers ; if the two polymers are not compatible, the weld factors can be substantially lower than 1.0, relative to the less stronger polymer; for example, polymer pairs such as PMMA–PBT , ABS–PPO , ABS–PEI , PPO–PC , PPO–PPO/PA (blend of PPO and PA) , and PPO/PA–PC , develop vibration weld strengths that are significantly lower than the strength of the weaker polymer (refer to the Appendix). For compatible polymer pairs, the weld strengths under optimal processing conditions can be as high as the bulk strength of the weaker of the two polymers (refer to the Appendix for data on strong welds of dissimilar polymer pairs such as PC–PEI , PMMA–PPO , PC–PBT , PC–PC/PBT (blend of PBT and PC) , and PBT–PEI ). In the remaining portion of this section, the interrelationships between the weld processing conditions, the microstructure in the weld region, and the resulting weld strength and fatigue behavior of neat polymers will be discussed with the aim of identifying the key weld process parameters and variables that govern the weld strength.
The effect of weld pressure on the weld strength of unfilled polymers is shown in Figs. 10 and 11. In Fig. 10, data for weld strength have been presented for PC , PBT  (both welded at 25 Hz frequency), and for PP [48, 49], and Nylon-6  (both welded in a commercial welder at about 210 Hz frequency). The data have been chosen such that, in comparing the strengths at various pressures, the weld amplitude has been maintained constant for each material. From Fig. 10, no single trend emerges from the data presented for the four polymers.
In Fig. 11, the weld strengths have been plotted for PC  over a wider range of weld pressures, but in this case, the data is presented for different pressures at the same vibration frequency (with different vibration amplitudes employed at certain frequencies). This figure presents a more realistic scenario in which there is lesser freedom in terms of choice of weld amplitudes, especially at higher vibration frequencies. From Fig. 11, it is clearer compared to Fig. 10 that an increase in weld pressure results in reduction in weld strengths. Schlarb and Ehrenstein  observed that the impact strength of vibration welds also progressively decreases with increasing weld pressures. For vibration welds, the “strength-life equal-rank assumption” seems to hold, and the weld conditions that yield high tensile strengths also yield better fatigue performance [59, 60]. Tsang et al. [59, 60] observed that the fatigue life of nylon-6 vibration welded at low pressures was one to four orders of magnitudes higher than that welded at higher pressures, depending on the fatigue test stress used.
Stokes [41, 47] observed that during tensile testing of the vibration welded specimens of PC and PBT, the ones that demonstrated the highest weld strength first developed a stable neck away from the weld which propagated up to the weld. Analysis of fracture surfaces in vibration welded specimens that failed during fatigue testing revealed a thumbnail fatigue fracture pattern , also seen in fatigue failure of metals. The stress intensity in the fractured surface was found to be the highest at the edge of the specimen, due to the notch effect. The shape or location of the fatigue fracture pattern was not affected by the welding pressure or vibration amplitude, suggesting similar mechanisms for fatigue fracture for specimens welded under different conditions . Stokes [61, 62] observed that the failure during fatigue testing at low stresses occurred away from the weld, for welds of PC, PPO, and PBT. PC welded specimens failed away from the welds for all testing conditions. In case of PBT welds, Stokes observed that samples that failed away from the welds typically failed due to void development in the necking region, while samples that failed at the weld always failed catastrophically due to weld imperfections .
For weld angles different from 0° (nonplanar weld surfaces), it was observed that weld strength can increase with increasing weld pressures , in contrast to the trend observed for planar welds (as discussed previously). This increase may be attributed to better mating of the surfaces under higher pressures. Similarly, Stokes  observed that higher pressures resulted in higher weld strengths for welds involving wider specimens. Higher pressures aid in reducing the duration of the unsteady phase in wider samples and increasing the steady-state penetration rates.
In investigations of the macroscopic appearance of the heat affected zone (HAZ) in vibration welds, Krishnan et al. , and Stokes  observed that the typical thickness of the heat affected zone is of the order of 0.2–0.3 mm. The thickness of the HAZ was observed to be uniform for the entire width (x-direction) of the weld, except at the edges . Stokes  also observed that in contrast to a uniform bead structure in hot-tool welds, vibration welds typically resulted in nonuniform, bi-layer, foamed beads; the bi-layer structure may be attributed to the oscillatory motion in vibration welding, and the foaming may be caused by the degassing of the melt during squeeze-flow. Using polarized light microscopy of vibration welded specimens, Bates et al.  observed that higher weld pressures resulted in thinner HAZ. Similarly, Schlarb and Ehrenstein  observed that the thickness of the HAZ, developed at low pressure vibration welding, was approximately three times that developed at high pressure vibration welding. From Eq. 7, during steady state, p0 ∝ v0/h, which is qualitatively consistent with the experimentally observed HAZ thicknesses.
Vibration welding is known to yield narrow weld lines with high molecular orientation . Estimates of film thickness and shear rates in the melt-film of the vibration weld, obtained from the model described earlier, indicate that the vicinity of the weld line experiences strong (high-deformation) flow. Krishnan et al. , Schlarb and Ehrenstein , Stokes , Chung and Kamal [65, 66], Cakmak et al. , and Varga et al.  have analyzed the microstructure of vibration welds of nylon-6 [58, 65, 66], PBT , poly(ethylene naphthalate) (PEN) , and PP , all semi-crystalline polymers, and PC [15, 63], an amorphous polymer, using techniques such as optical microscopy, polarized light microscopy, high magnification transmission electron microscopy (TEM), and wide-angle X-ray scattering (WAXS). Microscopic assessment of the welds of semi-crystalline polymers is relatively easier due to the presence of spherulitic microstructure, which is absent in amorphous polymers.
For semi-crystalline polymers, Schlarb and Ehrenstein , Chung and Kamal [65, 66], and Varga et al. , concluded that the typical microstructures in the heat affected zone of welds with the best strength performance consisted of four regions, as shown in a simplistic cartoon in Fig. 12. In the immediate vicinity of the weld-line lies a region without any visible crystallinity (indicative of rapid quenching), and has been labeled “amorphous” in Fig. 12. Adjacent to this inner region is a “trans-crystalline” region, a re-crystallized zone with spherulites of different sizes (indicative of melting, flow, and re-solidification). Between the trans-crystalline region and the region of bulk microstructure, a “transition zone of deformed spherulites” may be observed. It has been suggested that such multilayer microstructure may result in a more efficient stress transfer at the weld, resulting in superior mechanical properties .
Schlarb and Ehrenstein  and Chung and Kamal  observed that the trans-crystalline region was most prominent at lower pressures. More specifically, Chung and Kamal  observed that when weld pressure was increased while maintaining the vibration amplitude during vibration welding, the size of spherulites in the trans-crystalline region decreased. The spherulitic morphology in the trans-crystalline region was observed to be most prominent in samples welded at higher amplitudes. As discussed earlier in the context of the modeling of melt-film variables for PC, and also from Chung et al.'s analysis  and Zou et al.'s measurements  for nylon, it is clear that vibration welding at higher amplitudes results in higher temperatures in the melt-film (cf. Fig. 9a). As seen from Eq. 4, higher amplitudes also result in higher shear rates and consequently higher shear stresses in the melt-film, which may in turn cause stress-induced crystallization at higher temperatures. This would imply that nylon-6 samples welded at lower pressures and higher amplitudes would be characterized by the commencement of crystallization at higher temperatures and at relatively lower cooling rates (with additional stress-induced crystallization due to high amplitudes), resulting in large spherulitic microstructure, consistent with the observations of Chung and Kamal . The prominent spherulitic microstructure in the trans-crystalline region has been identified as key to developing high weld strengths [58, 65].
Higher shear stress induced nucleation can also be brought about by using higher molecular weight polymers, as demonstrated by the improvement in weld impact properties with lower melt-flow polypropylenes . The crystallinity of the trans-crystalline region was observed to be the lowest at high pressures and high amplitudes, and the corresponding welds had the lowest strengths . In a study involving modified polypropylenes with beta nucleators, the maximum improvement in impact strength due to β-crystallization was observed with low pressure vibration welding . From the foregoing, it is clear that a combination of low pressures and high amplitudes results in ideal microstructures for developing high strength.
Chung and Kamal  also observed an increase in the thickness of the deformed-spherulites zone in welds formed at higher weld pressures. The deformed-spherulites zone also showed a lower degree of molecular orientation compared to the trans-crystalline zone, implying insufficient melting . These observations indicate that the deformed-spherulites zone may be the result of the additional melt squeeze-out during the cooling (phase IV) of the vibration weld. The high-strain deformation in phase IV (in the absence of melting and re-crystallization) that would result in the type of microstructure observed in the deformed-spherulites zone, would also result in an accumulation of residual stresses. Therefore, a prominent deformed-spherulites zone is associated with lower weld strengths  due to the residual stresses. During tensile testing, Chung and Kamal  observed that the welded samples failed at the interface between the re-crystallized trans-crystalline region and the deformed-spherulites region.
In case of welds of amorphous polymers, for example, PC, which are devoid of spherulitic microstructure, birefringence is the only way of assessing flow-induced molecular orientation and residual stresses in the weld zone. However, a systematic study of variation of birefringence with change in weld pressure has not been reported for amorphous polymers. The measurement of birefringence can be challenging in these systems, because of the high magnitudes of residual stresses developed during vibration welding (resulting in very bright fringes in a narrow region, which can be difficult to resolve) . In the case of PC, however, the residual stresses do not seem to have a significant consequence on the weld strength; In Stokes's study  PC welds were found to develop high relative weld strengths, O(1), over a wide range of weld parameter settings. However, a more complex picture is offered by poly(etherimide) (PEI), also an amorphous polymer. PEI develops higher strengths at higher weld pressures . For PEI, the weld strengths also show a strong dependence on the frequency of welding . Both these observations are outliers compared to the typical trends observed for a majority of polymers. These phenomena need to be investigated further with the aid of microstructural studies for PEI welds.
Polyesters, such as poly(ethylene naphthalate) (PEN), with glass transition temperature (Tg ∼ 120°C) significantly above the room temperatures, and without much separation between the Tg and the melting point (Tm ∼ 240°C), are quite interesting in that the rubbery properties as well as the melt rheology play an important role in the microstructure development at the interface. Vibration welding of as-molded PEN specimens, which are predominantly amorphous to begin with, was shown to result in substantially greater crystalline orientation at the weld interface (and correspondingly lower weld strengths) compared to welding of annealed specimens, which develop significant initial crystallinity . The pronounced crystalline orientation in the welds of as-molded specimens may be correlated with the substantially greater chain orientation in the rubbery state (above Tg, but below Tm) in the vicinity of the weld interface, compared to the annealed specimens .
In investigations of the morphology of welds of dissimilar polymers [20, 53, 56], it was observed that at lower penetrations, when a “true” steady state (in which both the resins have melted and intermixed in the weld region) has not been obtained, mechanical interlocking between the two dissimilar polymers may provide the only mechanism of weld strength development, as indicated by the highly convoluted or banded weld interface in welds of PC and PEI . Once a steady melt flow-field has been established for both the polymers being welded, the weld region shows a planar microstructure without any striations, and the weld strength increases, apparently driven by increased polymer inter-diffusion across the weld interface [20, 56] In another study, the differential scanning calorimetry (DSC) of the welded regions of low-strength butt welds of PA-6 and PA-66 , (obtained at high weld pressures) revealed crystalline peaks for the lower melting PA-6 alone, whereas, the DSC of high-strength welds (obtained at low weld pressures) contained peaks of both PA-6 and PA-66, indicating better intermixing of the two resins. The impact of difference in melting temperatures between the PA-6 and PA-66 was found to be even more pronounced in T-welds: low-pressure T-welds with the lower melting PA-6 in the web region were up to 1.5 times stronger than those with the PA-66 in the web region, at comparable penetrations . This difference was attributed to the modification of the residual stress field in the T-weld by the location and shape of the weld interface : the location and width of the weld interface would be significantly affected by whether the lower melting polymer is located in the flange or the web, since the effective width of the weld varies as the web penetrates into the flange .
Welds of Filled Polymers
As discussed in the foregoing, under optimal vibration welding conditions, vibration welds of unreinforced polymers can attain strengths equivalent to that of the un-welded bulk material. However, in case of glass-fiber-reinforced polymers (with discontinuous-fiber reinforcements), it has been observed that weld strengths are substantially lower than that of the bulk composite. Under optimal conditions, the strengths of vibration welds of composites with discontinuous fibrous reinforcements have been shown at best to only slightly exceed that of the unreinforced bulk matrix [70, 71]. Such reduction in weld strength relative to the un-welded bulk composite could be attributed to the weld region being depleted of fibers (and therefore having an inherently lower composite strength) or unfavorable orientations of the fibers in the weld interface . Microscopy of vibration welds of glass-fiber-reinforced polymers with superior weld strength typically reveals some glass fibers oriented perpendicular to the plane of vibration welding, and some even crossing the weld interface . Poor weld strengths are typically associated with glass fibers “bundled” together at the weld interface  in the plane of the weld.
A SEM comparison of the tensile fracture specimens of un-welded (as-molded) and vibration welded glass-fiber-reinforced PBT  revealed two major differences: first, the un-welded fractured specimens showed several glass fibers pulled out of the fracture surface (indicating an orientation perpendicular to the fracture surface), while the fracture surfaces of welded specimens that failed at the weld revealed the majority of the fibers to be aligned with the fracture (or vibration) plane. Second, and more importantly, it was observed that the pulled out fibers in the fractured surfaces of un-welded specimens were coated with plastic, while the exposed fibers in the fractured surfaces of specimens that failed at the weld were devoid of any polymer coating. This brings out two critical factors that govern the strength of fiber-filled composite welds: the orientation of glass fibers with respect to the vibration direction, and the wetting of glass fibers by the resin in the weld region.
Under similar welding conditions, the strength of vibration welds has been shown to decrease with increase in loadings of short glass fibers beyond 14 wt% . Kagan and Roth , and Stokes [17, 74, 75] observed that the tensile strength of the welded glass-fiber-reinforced composite specimens, relative to the un-welded specimens was lower at higher glass-fiber loadings. The relative weld strengths at similar glass-fiber loadings for two glass-fiber-reinforced materials, with significantly different bulk (un-welded) strengths, were found to be remarkably similar . Typically, welds achieved at lower pressures develop greater strength compared to those achieved at higher weld pressures . Vibration welded short-glass-fiber-reinforced nylons also showed longer fatigue life when welded at lower pressures . Vibration welded air intake manifolds made with a variety of glass-fiber-reinforced resins generally showed greater burst pressures when welded at lower weld pressures [4, 77].
Microscopic studies of welds of glass-fiber-reinforced polymers also show that just as in the case of neat polymers, welding at lower pressures results in wider heat affected zones [73, 78, 79]. A wider heat affected zone has been associated with a more random-fiber orientation in the weld melt-film, increasing the probability of fiber orientation perpendicular to the weld plane, and also diffusion of fibers across the weld interface . On the other hand, some microscopic analyses have suggested that wider heat affected zones may not necessarily randomize fiber orientation in the film, but help in increasing the fiber concentration in the weld zone, thereby increasing the weld strength [78, 79]. Higher pressures typically result in very thin heat affected zones in which the polymer as well as fiber orientations may be parallel to the vibration weld plane; and this may result in lower weld strengths. However, some studies have shown that higher pressures combined with lower amplitudes result in strengths equivalent to those achieved at low weld pressures. Lower amplitudes imply a lower probability of the fibers to orient in the vibration direction, thereby making the higher pressures more effective in re-orienting the fibers perpendicular to the vibration plane [78, 79].
For welds of composites, the initial microstructure of the composite, that is, fiber orientation and distribution, in the vicinity of the surface being welded, is of great significance in governing the ultimate microstructure in the weld. This initial microstructure results from the flow experienced by the composite during the molding operation (similar strong correlations between the initial processing-induced specimen microstructure and the final weld microstructure and strength are in general observed in all multi-phase or multi-material systems including blends and foams, as will be detailed later). A detailed study of the impact of welding direction relative to the direction of fiber orientation in injection-molded parts was undertaken by Dai and Bates [73, 80]. To facilitate the understanding of the impact of the choice of vibration-direction relative to the injection-molding flow-direction on the strength of the welds of short-fiber composites, a simplistic cartoon depicting the various scenarios investigated by Dai and Bates  (capturing the key microstructural features described by them) is presented in Fig. 13. Dai and Bates  observed that short-fiber-reinforced composites typically yielded higher weld strength when welded in a plane perpendicular to the primary flow direction during injection molding (i.e., when welded in the x–y plane in the schematic shown in Fig. 13a). The measured weld strengths were found to be substantially lower when welded in flow plane (the y–z plane as shown in Fig. 13a). As seen in Fig. 13a, injection molding flow can result in orientation of short glass fibers in the flow direction. Therefore, if the vibration welding of an as-molded bar in Fig. 13a is carried out “transverse” to the flow, then the initial fiber orientations will be perpendicular to the vibration plane; this initial fiber orientation is conducive to fiber diffusion across the interface, and should, therefore, result in higher weld strength. By contrast, if the vibration welding of an as-molded bar in Fig. 13a is carried out in “flow” direction, then the initial fiber orientations of the fibers will be parallel to the vibration plane; this initial fiber orientation requires greater re-orientation to enable fiber diffusion across the weld interface, and should, therefore, result in relatively lower weld strengths.
Dai and Bates  also compared the vibration welds of as-molded and “machined” samples. The typical initial orientations of the short-glass-fibers in the weld planes of “transverse” and “flow” direction machined samples can be schematically represented as shown in Fig. 13b and c. In the absence of significant edge effects in case of short-fiber orientation, Dai and Bates observed that the trends obtained in weld strengths were similar for as-molded and machined samples .
Like short-fiber-reinforced composites, the relative weld strengths of vibration welded discontinuous-long-fiber-reinforced composites typically decrease with increasing fiber content . However, unlike short-fiber-reinforced composite welds, increase of weld pressure can result in slight to substantial improvement of weld strength in case of vibration welds of long-fiber-reinforced composites . In welds achieved at low weld pressures, short-fiber-reinforced composites typically developed greater weld strength compared to long-fiber-reinforced composite welds . Analysis of fracture surfaces in low-pressure-welded long-fiber-reinforced composites revealed polymer “bundles” lying parallel to the weld surface, indicating that welds achieved at low pressures do not have sufficient quantity of “reoriented” long glass fibers to achieve high weld strengths . To facilitate the understanding of the impact of the choice of vibration-direction relative to the injection-molding flow-direction on the strength of the welds of long-fiber composites, a simplistic cartoon depicting the various scenarios investigated by Dai and Bates  (and capturing the key microstructural features described by them) is presented in Fig. 14. As depicted in Fig. 14a, injection molding of discontinuous-long-fiber composites can result in a substantially different initial microstructure in the as-molded article compared to short discontinuous-fiber-reinforced composites. Two key differences may be noted by comparing Figs. 13a and 14a: first, long-fibers are not easily oriented by the injection molding flow, resulting in a more isotropic fiber orientation distribution compared to that in short-fiber composites, and second, mold-edge induced fiber orientation effects are much more prominent in long-fiber-reinforced composites compared to short-fiber-reinforced composites. From Fig. 14a, it can be assessed that owing to the strong edge effects, the initial fiber orientation will typically be parallel relative to the vibration plane whether the vibration of the “as-molded” article is carried out in the flow (y–z) plane or the transverse (x–y) plane—this initial fiber orientation in the as-molded article is not conducive to fiber diffusion across weld interface, and may require higher weld pressures to reorient the fibers in an optimal fashion. This initial microstructure may also explain the presence of fiber bundles lying parallel to the vibration plane.
By contrast, machined samples (shown schematically in Fig. 14b and c) when welded at low pressures resulted in substantially higher strengths compared to welds made from as-molded articles . During low pressure welding of machined samples, higher loadings of long-fibers resulted in greater relative weld strength, in contrast to the trend observed with the welds of as-molded samples. In fact, with 40% long-glass-fiber-reinforced PPs, the weld strengths of machined samples welded at low pressures were observed to be nearly 1.5 times that of the matrix strength, and close to the bulk composite strength. This drastic increase in strength in machined samples with low pressure welding may be attributed to the dilution of edge effects, and an initial configuration of long-fibers which are relatively easier to reorient (refer to the cartoons in Fig. 14b and c). However, when welded at high pressures, the machined samples showed drastic reduction in strength, in stark contrast to welds of as-molded samples which showed increases in strength with increasing pressures. This reduction in strength at higher pressures was attributed to “collapse” of random orientations at high shear rates associated with high pressures, leading to reorientation of long-fibers parallel to the weld plane .
Vibration welds with continuous-fiber fabric reinforced composites develop high weld strengths—corresponding to about 400% increase compared to the tensile strength of the unreinforced matrix . In welds of woven-fabric-reinforced composites, development of high strength has been associated with the entanglement of the continuous glass fibers that were initially oriented perpendicular to the weld plane (weft fibers) . The entanglement density, and consequently the strength of the weld, shows a strong dependence on the weld penetration . At low pressures, the orientational effects are less and the initial glass-fiber orientation in the part surface is not disturbed with progressive increase in penetration. In this scenario, weft–weft welds (which have a greater density of fibers aligned perpendicular to the weld plane compared to a warp–warp weld) achieve higher strengths compared to warp–warp welds. At high pressures, the orientational effects are very strong, and the fibers (whether they are initially oriented in the warp or weft direction) tend to preferentially orient parallel to the weld plane during the course of welding. Therefore, at high pressures, lower weld strengths are achieved compared to low pressure welds, and the warp–warp and weft–weft weld strengths become comparable .
In two different studies involving vibration welding of lap shear joints with unidirectional fiber-reinforced composites [81, 82], and butt-joints with random-glass-mat reinforced thermoplastics  it was found that the duration of vibration welding (in other words, the penetration distance) has a significant impact on the strength; however, the trend in strength versus weld-duration (or penetration distance) displayed a maximum at an intermediate weld duration. The reduction in strength at longer weld durations in the lap shear joints was attributed to preferential depletion of the matrix into the weld-bead at long times . Also, high-pressure welding for short duration was shown to yield higher strengths compared to low-pressure vibration welding in case of lap shear joints , whereas weld strengths monotonically decreased with increasing weld pressures for fiber-mat-reinforced composite butt welds . Again, the drop in strength in case of butt welds was attributed to preferential depletion of matrix combined with fiber orientation at high pressures . These studies [81–83] highlight a challenge (preferential matrix depletion in the weld zone) that is very specific to welding of fiber-mat (or continuous-fiber) reinforced composites.
The other category of filled polymers that has been studied in the context of welding involves polymer nanocomposites. Welding studies on nanoclay-composites with polypropylene and HDPE as matrices have revealed that addition of nano fillers significantly reduces the weld strength relative to the weld strength of the un-reinforced polymer [48, 49, 84]. This is attributed to the alignment of clay platelets parallel to the weld surface [48, 49]. The reduction in weld strength with increasing clay loadings in nylon-clay nano-composites  is not as pronounced as in the case of polypropylene. This indicates that the degree of clay exfoliation, the polarity of the matrix (nylon is more polar than polypropylene), and the solubility of the clay functionality with the matrix polymer would be of significance in governing the reorientation of the clay platelets at the weld interface.
Welds of Block-Copolymers, Polymer Blends, and Foams
Block Copolymers and Polymer Blends.
The strength of vibration welds in polymer blends is governed by the microstructure developed in the weld vicinity. Just as in the case of neat polymers and fiber-reinforced polymers, high degrees of orientation parallel to the vibration plane are often detrimental to the weld strength. In a comparative study of hot plate welding and vibration welding of a PC/ABS blend (Shieu and Wang ), the hot plate welded samples developed a weld strength of about 14 MPa, while the vibration welded samples showed a weld strength of 36 MPa, which was equivalent to a weld factor of 0.8. This significant difference in weld strengths was related to the morphology of the welds, assessed through transmission electron microscopy. The low strength hot plate welds showed a drastic change in the weld morphology at the weld interface compared to the bulk morphology, with pronounced orientation and laminar morphology near the welds. The morphology difference between hot plate welding and vibration welding observed by Shieu and Wang  is surprising, given the fact that vibration welding typically results in a stronger flow-field and narrower heat affected zones compared to hot plate welding . Shieu and Wang  do not indicate if the two welding techniques resulted in comparable flow conditions or overall penetrations. In the absence of such information, the weld strengths resulting from the two methods cannot be compared. However, the correlation between weld strength and blend morphology at the weld interface would be independent of the welding method used. In another study on the morphology of vibration welds of ABS, a block copolymer, Stokes  observed significant orientation of the styrene-acrylonitrile (SAN) rubber phase in the weld region, the degree of orientation increasing with reduction in the degree of crosslinking of SAN phase.
As in the case of glass-fiber-reinforced materials, the microstructure development in the weld interface, and consequently the strength of vibration welds are strong functions of the initial blend morphology in the injection-molded articles that are welded. High shear rates typically lead to greater deformation of the dispersed phase in the flow direction, and result in the development of a laminar morphology in the blend. The laminar morphology is more pronounced in thinner injection-molded articles  because thin molds result in greater shear rates during injection molding. Stokes  demonstrated that butt welds of PC/ABS blends made from thin specimens, which had a pronounced layered structure resulted in poorer strengths at comparable welding conditions. The strength of vibration welds in polymer blends typically increases with increase in weld pressure. It may be argued that the increase in pressure causes the injection-molded microstructure to get randomized, thereby negating any detrimental effects of the oriented microstructures on the strength; this randomization may not be possible at lower weld pressures.
Vibration welding studies have been done with a variety of polymer blends—including High impact polystyrene (PS)/PPO , PC/PBT [57, 87], PPO/poly(propylene sulfide) (PPS) , PC/ABS [85, 86], and PPO/nylon  blends. Weld factors >80% have been obtained with all these blends under optimal welding conditions. For a majority of these blends (except PC/ABS ), however, there is no information regarding morphology, orientation, and microstructure development in the weld region. Also, microstructural studies on fractured surfaces of polymer blends, analogous to those reported for glass-fiber-reinforced polymer composites, are not widely reported. Stokes's microscopic study of ABS weld fractures  revealed that the failure of the ABS welds are primarily brought about by cavitation and crazing rather than plastic deformation in the weld region; this was attributed to the inability of the SAN phase to reorient during tensile loading. This may explain the poor relative strengths observed for dissimilar welds involving ABS  (also see Appendix), and weld factors of as low as 0.46 for welds of ASA . The availability of such microscopic information for other polymer blends would provide significant clues to improving their weld performance.
Vibration welding has been studied with foams of PP , PS , and PPO . The evolution of weld penetration during vibration welding of foams is similar to that observed in neat polymers—the typical four stages of vibration welding are observed for foams also. However, the duration of the phases and the cycle time of welding are substantially shorter due to the cellular structure of the foam . The vibration welding cycle times become progressively lower with decreasing foam density (increasing void fraction) . In structural foams, which have an outer layer of compact (nonporous) polymer “skin” covering a foamed “core,” pressure fluctuations are observed when weld penetration progresses from the skin to the core, owing to the sudden change in effective load-bearing surface . The pressure fluctuations last until the solid material is entirely incorporated into the squeeze-flow zone and the solid–melt interface is entirely occupied by the foamed material.
The analysis of the impact of welding conditions on the strength of vibration welds in foams is complicated by the inherent variation of local densities in an injection-molded base specimen . It has been observed that there is a drastic variation in density and the moduli of the foam, depending on the location of measurement with respect to the injection gate. At increasing linear distance from the gate, the density, and the corresponding moduli and ultimate stress decrease. This intra-part variation is more drastic for lower density foam (high void fraction). The local properties of the foam, as governed by the localized density, typically have a greater impact on the weld strength as compared to weld pressure or amplitude . Weld strength may show a weak direct dependence on the weld pressure . Relative to the weld strength of the un-welded foamed article, weld factors of 0.8, 0.9, and 1.0 have been achieved for vibration welded PS , PP , and PPO , respectively. In case of structural foams, higher weld factors may be achieved if the steady-state penetration rate is established prior to the depletion of the solid skin layer . As in the case of polymer blends, information regarding interrelationships between weld process, foam microstructure (in the weld and fracture surfaces), and weld strength interrelationships is lacking.
SUMMARY AND UNRESOLVED ISSUES
Importance of Vibration Welding
Vibration welding (including longitudinal, transverse, and orbital vibration welding) offers a robust method of physical joining of thermoplastics without using an external heat source or adhesives, and offers the advantages of minimal surface preparation requirements and low polymer degradation. This method can be used for relatively stiff plastics to fabricate complex hollow assemblies from simpler injection-molded objects.
Vibration Welding Phenomenology
In vibration welding, frictional heat generated through vibration of the mating surfaces against each other is used to melt the mating surfaces, normal pressure is used to drive the flow and intermixing in the melt-film, and the solidification of this film effects the weld. This process involves a complex interplay of several phenomena: solid (Coulomb) friction, melting, high strain-rate, pressure-driven strong (high-strain) melt flows, solidification, and microstructure-development. The key process (controllable) parameters are the amplitude and frequency of vibration, the pressure applied during welding, and the weld time.
The process can be divided into four characteristic phases: (I) Coulomb friction leading to the melting of the solid surfaces, (II) unsteady flow in, and growth of, the melt-film, (III) steady flow in a melt-film of constant thickness, and (IV) transient cooling and solidification under pressure. The various stages of vibration welding have been studied experimentally by tracking an important process variable—weld penetration, the parameter that captures the reduction in the length of the part perpendicular to the weld plane due to squeeze-flow. A threshold penetration is required to achieve the strength entitlement of the weld.
Increased vibration-amplitude and weld-pressure typically lead to faster onset of melt-film at the interface (during phase I), quicker establishment of the steady-state flow in the melt-film (during phase II), and higher steady penetration rates (during phase III). The impact of process parameters on the melt-film thickness, the temperature-field, the shear rates, and the melt-viscosities in the melt-film are difficult to measure in situ during welding.
The steady-state flow (phase III) of vibration welding has been most extensively studied, both through experimental measurements and analytical models. Current models using Newtonian viscosities estimate an increase of steady-state melt-film thickness at lower weld-pressures and higher vibration-amplitudes. The impact of pressure and amplitude on the temperature fields within the melt-film are primarily governed by how the weld pressure impacts the steady-state penetration velocity. However, a more detailed model, accounting in a fundamental fashion, for the temperature and shear-rate dependence of viscosity and viscoelasticity, is required for better estimation of melt-film thickness and temperature fields.
Phase IV of vibration welding, involving cooling and solidification under pressure is a relatively less understood aspect of vibration welding, and has not been investigated in detail experimentally. However, this phase may involve large deformations of a high-viscosity cooling melt, and affects the weld microstructure significantly. Models for solidification, crystallization-kinetics, and residual stresses for oriented melts have not been applied to the context of vibration welding. This aspect of vibration welding needs further investigation.
Also, fundamental vibration welding experiments on model geometries such as butt welds, (analogous to those conducted by Stokes [7, 41] on a variety of neat and filled polymers and polymer blends) need to be conducted on a variety of new material systems of relevance to practical applications. This is important to establish a body of data—on the processing–structure–property relationships of these systems—that is currently not available. Fundamental welding data on multi-material systems—in which there are more than two materials/phases involved, such as glass-fiber or nano-filler reinforced polymer blends, or nano-composite-foams—is of particular relevance. Another aspect that needs to be investigated is the impact of resin architecture on weld strength. It is clear that viscous heating plays an important role in governing the temperature fields and melt-film thickness; viscous heating is significantly impacted by the molecular architecture and polydispersity of the resin.
Processing–Structure–Property Relationships in Vibration Welds
It may be concluded that when the constituents of the part—including the polymer, the reinforcement (such as glass fibers, micro-fillers, or nano-fillers), or the dispersed phase (such as elastomers, dispersed polymers, impact modifiers)—are oriented along the weld plane, the resulting weld is weak. Orientation in the weld region can be affected by the thickness of the melt-film, but this is not always the case.
Welds obtained under optimal vibration welding conditions typically develop strengths equivalent to that of the un-welded bulk component. Failures starting within the weld can be driven by welding-induced defects and may be brittle in nature.
Weld pressure and amplitude are two parameters of greatest impact on the strength of the weld. Between these, however, under practical conditions involving high frequencies and large parts, only pressure can be extensively varied, and, therefore, turns out to be the most critical controllable welding parameter.
Trends in Neat Polymers.
Increase in weld pressure typically leads to lowering of weld strength. This can be attributed to greater orientation effects at higher pressure. In addition, welds of semi-crystalline polymers prepared at low pressures typically develop a more complex layered microstructure—including a re-crystallized zone—that may result in more efficient stress transfer. High pressure welding results in a narrower heat affected zone with the re-crystallized zone less prominent. In amorphous polymers, high pressures may lead to higher magnitudes of residual stresses and birefringence in the weld zone—this aspect has not been fully investigated in complex amorphous systems such as poly(etherimides).
Trends in Fiber-Reinforced Polymers.
The strength of vibration welds of fiber-reinforced polymers is primarily governed by three factors—the density of fibers in the weld zone relative to that in the bulk, the orientation of fibers at the weld interface, and the adhesion between the fibers and polymers in the weld zone. The strength of the vibration weld is also significantly impacted by the initial injection-molded microstructure of the weld specimen since the initial fiber orientation in the parts has a strong effect on the orientation in the weld.
In short-fiber-reinforced polymers, lower pressure welding results in higher strength. Low pressures widen the heat affected zones, and this may result in more random fiber orientation in the melt-film and also greater fiber density in the film—both of which can improve weld strength. As in the case of neat polymers, higher pressures lead to short-fiber orientation along the weld plane, resulting in loss of strength. Low weld pressures, along with high weld penetrations, also improve weld strength in continuously reinforced thermoplastic composites.
On the other hand, higher pressures can aid in improving strength in welds of discontinuous-long-fiber-reinforced composites. Micrographs suggest that higher pressures are more effective in randomizing the fiber orientation in the weld zone. In fiber-reinforced polymers, while extensive attention has been paid to fiber orientation in the weld zone, there is little understanding of how the fiber orientation affects the polymer-matrix orientation, solidification, and crystallinity.
Trends in Polymer Blends and Foams.
Strength development in vibration welding of polymer blends is governed by the initial injection-molded microstructure of the specimen. Higher pressures typically tend to improve the strength of the weld. Microstructural and crystallographic information on the as-welded and fractured surfaces of vibration welds of polymer blends has not been reported for a wide range of blend systems.
In case of welds of polymeric foams, the local density reduction brought about by the foam production typically turns out to be far more significant in governing the strength of the weld compared to the weld process parameters. Higher strengths are achieved in structural foams with an un-foamed skin if the steady-state flow is achieved during welding prior to the depletion of the skin. Once again, microstructural and crystallographic information on the welds and the fracture surfaces are lacking in case of welds of polymer foams.
The authors thank William Rodgers, Howard Cox, and Mark Verbrugge, for motivating discussions, and acknowledge the comments and feedback from the reviewers.
vibration amplitude (m)
vibration weld specimen width (m)
specific heat of the melt (J/kg/K)
thickness of the melt-film in the weld region (m)
thermal conductivity of the melt (W/m/K)
vibration frequency (s−1)
isotropic component of the stress tensor (pressure) (Pa)
weld pressure (Pa)
heat Flux (W/m2/K)
instantaneous temperature at a given location within the melt-film (K)
ambient temperature (temperature at a substantially large distance from the solid–melt interface) (K)
glass transition temperature (K)
melting point (K)
duration of phase I (Coulomb friction phase) of vibration welding; it is the time at which first displacement is recorded by the transducer during vibration welding (s)
- v = (u,v,w)
velocity vector (m/s)
steady penetration velocity, the rate at which the solid–melt interface moves during the steady penetration phase of vibration welding (m/s)
cycle averaged vibration (z−) direction velocity (m/s)
specimen width direction (m)
weld thickness direction (parallel to the direction of application of pressure) (m)
vibration direction (m)
latent heat of fusion (J/kg)
shear rate due to gradient of z− (vibration) direction velocity along the melt-film thickness (y− direction) (s−1)
shear rate due to gradient of x− (squeeze-flow) direction velocity along the melt-film thickness (y− direction) (s−1)
viscous dissipation function in the vibration (z−) direction averaged over 1 s (s−2)
viscous dissipation function in the squeeze-flow (x−) direction (s−2)
weld penetration (m)
steady weld penetration rate (m/s)
viscosity (Newtonian) of the melt (Pa s)
density of the melt (kg/m3)
strength of the un-welded (as-molded) bulk specimen (Pa)
weld factor, or relative weld strength of the vibration weld
strength of the welded specimen (Pa)
- ω = 2πn
cyclic frequency of vibration (rad/s)