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Characterization of adhesive joints under high-speed normal impact: Part I – Experimental studies
Journal Pre-proof Characterization of Adhesive Joints Under High-Speed Normal Impact: Part I – Experimental Studies Kenneth Gollins, Niell Elvin, Feridun Delale PII:
S0143-7496(19)30281-7
DOI:
https://doi.org/10.1016/j.ijadhadh.2019.102529
Reference:
JAAD 102529
To appear in:
International Journal of Adhesion and Adhesives
Received Date: 21 September 2019 Accepted Date: 2 December 2019
Please cite this article as: Gollins K, Elvin N, Delale F, Characterization of Adhesive Joints Under HighSpeed Normal Impact: Part I – Experimental Studies, International Journal of Adhesion and Adhesives, https://doi.org/10.1016/j.ijadhadh.2019.102529. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Elsevier Ltd. All rights reserved.
Characterization of Adhesive Joints Under High-Speed Normal Impact: Part I – Experimental Studies Kenneth Gollinsa, Niell Elvina†, Feridun Delalea a. Department of Mechanical Engineering, City College of New York, New York, NY 10031, USA † Corresponding Author, email: [email protected]
Abstract This two-part article presents an experimental method with numerical verification of the characterization of adhesive bonds under normal impact loading. Part I presents experimental results of the mechanical behavior of two different adhesives (a methacrylate and an epoxy). Though the two adhesives have similar static behavior, their impact strengths are significantly different. Thus adhesives that are to be used under impact loading need their own dynamic characterization tests.
Here we present
an impact test that is analogous to the commonly used blister test for static adhesive testing. One major advantage of the present impact test is that existing apparatus and methods that are currently used for ballistic penetration can be readily adopted for the proposed dynamic test. The average dynamic stress as well as energy absorbed by the adhesive are experimentally determined by the proposed method.
Keywords D. mechanical properties of adhesives; D. impact; C. dynamic mechanical analysis; C. destructive testing
1
Introduction One of the major challenges facing the aerospace, commercial vehicular and defense industries is the
need to decrease cost and increase fuel economy without sacrificing performance. Adhesive materials are ideally suited to address these challenges, permitting the construction of lightweight assemblages by replacement of heavier conventional joints such as bolts or weldments. However, achieving the desired 1
savings without sacrificing performance requires that these adhesive joints possess sufficient survivability under both quasi-static and impact loading. The joints between the elements of the structure have the potential to introduce critical structural vulnerability if not designed properly. Current static failure strength test methods such as tensile, compressive and shear tests are well established and understood, but the current methods are not as reliable for testing the dynamic failure strengths. The most commonly used methods to test adhesive joint specimens under impact loading are pendulums, drop weight impactors and split Hopkinson pressure bars [1]. Early impact tests were performed by Perry [2] on an instrumented pendulum rig (ASTM D950-78) to measure the failure load and energy absorption of adhesively bonded butt-joints. It was found that the response was equivalent to an elastic spring and thus the energy absorbed is proportional to the square of the failure stress. However, as noted by Adams [3] the energies from this impact test do not necessarily reflect the energy absorbing capability of the adhesive itself, but rather the compliance of the test system, thus making the result machine sensitive. Using a modified drop weight impact test, Galliot et al. [1] explored the dynamic behavior of adhesively bonded lap joints in shear (mode II) failure at impact velocities between 1 and 4 m/s. Their test results indicated that the stiffness, the failure load and the absorbed energy all increased with the loading rate. They also found that the extension at failure was the only rate insensitive parameter since it remained constant for all impact velocities. Despite these findings, Galliot et al. concluded that the influence of local and overall parameters were identical under quasi-static and impact loading. Thus, for moderate loading velocities (< 4 m/s), the design of the adhesive joints could be based on static material properties. Using a split Hopkinson pressure bar, Goglio et al. [4], found that a bi-component epoxy adhesive is
highly sensitive to strain-rate. At an applied strain-rate on the order of 10 s-1, the bulk adhesive strength,
with respect to the static value, was observed to increase by a factor of three under compression and a factor of five under tension. The elastic modulus was also seen to increase with strain-rate, however no conclusive modulus data was reported from these tests due to the small-time scale at which these tests were performed i.e. equilibrium conditions were approximately reached at the same time in which the stress reached the elastic limit, thus limiting the ability to measure the elastic modulus. Bezemer et al. [5] devised a new type of adhesive joint specimen for high speed dynamic testing to simulate pure shear loading condition. In addition to the limitations noted early, the pendulum impact tests are not suitable for speeds above 5 m/s. Therefore, higher velocities were achieved with a drop weight machine, for speeds up to 10 m/s, and an air gun for speeds up to 100 m/s. These authors conclude that for each of the three tested adhesives (epoxy, polyurethane and an anaerobic adhesive) the energy absorption of the adhesive increases with the load. It was also seen that a ductile adhesive shows a larger
2
energy absorption at impact than a brittle adhesive. Thirdly, optimum adhesive thicknesses were found at each test speed for each adhesive. Considerable efforts have been undertaken to understand the behavior of adhesively bonded joints by many researchers. The most well understood is the lap joint because in most structural applications, adhesive bonds are loaded in shear due to their greater load carrying capacity. Lap joints exhibit local plastic zones at the bond edges and are thus less susceptible to failure than adhesives loaded in a normal direction to the adherends i.e. in bending. While many researchers have studied the bending failure mode, the breadth of work has been with quasi-static loading and little is known about the dynamic aspects of bonded joints under bending. Dynamic testing is critical for any design that may experience high strain rates or types of transient loads. Currently, there is no standard for the dynamic testing of adhesively bonded joints under impact loading, especially at very high strain rates. As such, a robust and repeatable dynamic testing protocol for characterizing adhesively bonded joints has been devised. These tests were designed to provide a dynamic analog to the static blister test by subjecting the joint to a transverse impulse load to transmit a stress wave through the adhesive. The methods defined in this work differentiate from previous studies through the following: (i) A method for determining the critical failure velocity and energy under transverse dynamic loading was developed. (ii) A method to determine the energy absorption under impact load was developed. (iii) A protocol was developed to measure the residual strength of the bond post-impact and how to report the observed behavior over a range of test velocities. The objective of this paper is to experimentally analyze the behavior and failure modes of adhesively bonded joints under high strain rate loading, namely ballistic impact. One advantage of the new test is that standard experimental equipment used for ballistic penetration testing can be readily modified to find the dynamic strength of a transversely loaded joint. This joint can be viewed as an axisymmetric lap joint for the purpose of transverse loading. The dynamic forces required to rupture the adhesive bond, the remaining strength of the bond post-impact (for non-failure cases) and the energy absorption of the adhesive have been characterized for two types of adhesives, a methacrylate and an epoxy.
2 2.1
Materials and Experimental Procedure Specimen Design
3
The experiment was designed to facilitate predominantly tensile Mode I type failure of an adhesive material between two adherends subjected to ballistic impact. The test specimen (as shown in Figure 2-1) consists of three parts: the back plate, the patch (the so called adherends) and the adhesive. The back plate has a two-inch diameter hole to allow the projectile to impact the adhered three-inch diameter patch in predominantly tensile loading as also shown in Figure 2-1. The adhesive thickness for all bonds was 0.254 mm with a bond width of 12.7 mm. The projectile delivered the high speed impulse required to create the high strain rate necessary to study the dynamic effect of impact in the adhesive. This specimen was designed to reduce any shear and torsional stresses, predominately allowing for normal stresses only. The specimen design is similar to the blister test by Updike [6], however it was modified to accommodate impact. The back plate diameter was shorter and the thickness was increased to transfer the bulk of the load to the adhesive. One metal adherend, AISI-1018 steel, was investigated with two adhesives. The chosen adhesives were both thermosetting adhesives, the first an acrylic and the second an epoxy. The first adhesive was a poly(methyl methacrylate) (PMMA) produced by SCIGRIP (Methacrylate SG805). The second adhesive was epoxy produced by Hysol (EA 9309NA). Two material combinations were tested in the experiments i.e. (1) steel- methacrylate and (2) steel-epoxy. The ratio between the Young's modulus of steel (~200 GPa) and the adhesives (~ 3 GPa) is high enough to consider relative deformation in the steel adherends to be negligible compared to that in the adhesive. In all cases, both the back plate and patch were the same material (i.e. steel); dissimilar adherends should be studied in future investigations.
4
Figure 2-1 Dimensions of the test specimens.
2.2
Static Testing
2.2.1
Tensile Tests
Owing to reported deviations between the bulk and thin adhesive bond mechanical properties, bulk material properties are not sufficient to use when determining the dynamic behavior of adhesively bonded joints. This is caused by strain constraining effects of the adherends in bonded assemblies, and also by typical mixed mode crack propagation in adhesive bonds [7]. In bulk materials, cracks tend to grow perpendicularly to the direction of the maximum principal stress [8]. However, in thin adhesive bonds, cracks are forced to follow the bond line because the adhesive is weaker and more compliant than the adherends. Thus, additional tests were performed to determine the tensile properties of the joints as the manufacturers data is provided for the bulk material only [9].
5
By using an axially loaded butt-joint (ASTM D2095) the tensile properties of the methacrylate and epoxy were determined. Theoretically, if the two adherends are infinitely rigid in relation to the adhesive, the stress-strain curve can be generated by isolating the strains within the adhesive. This material relation is not representative of the intrinsic adhesive behavior due to the adherend constraining effect and can only correspond correctly to the joint properties, not the adhesive bulk properties. The adherends do not allow the adhesive to contract laterally, thus introducing additional stresses perpendicular to the loading direction, which is indicative of bonded joint behavior. A set of five methacrylate and five epoxy butt-joint specimens were tested with an MTS 464 universal hydraulic testing machine at room temperature. Each of the steel adherends was 100 mm long, 25.4 mm wide and 6.35 mm thick. The adhesive was 0.254 mm thick. The specimens were positioned so that 25 mm of each side of the steel adherends was held within the hydraulic clamping jaws of the testing machine. The loading rate was set to 2 mm/min to simulate a quasi-static rate. An extensometer (MTS 634.12E-25) was positioned symmetrically across the bond line to measure the displacement of the adherends on both sides of the adhesive. The force and the extensometer displacement were recorded.
2.2.2
Bending Strength
Static tests were performed both on virgin specimens, to establish baseline characteristics, as well as on non-failed post ballistic impact specimens to measure the residual strength of the bond. The residual strength of a non-failed adhesive bond after ballistic impact, discussed in the following section, was measured by performing a static bending test on all surviving specimens. The static bending tests were performed using a universal testing machine (Instron-5882) at room temperature. The indentor, as shown in Figure 2-2, was modified to match the projectile diameter of 7.6 mm that was used in the impact tests as described in Section 2-3. The top portion of the indentor was threaded to fit inside of the existing testing machine; the bottom portion of the indentor was turned down on the lathe to a 7.6 mm diameter. The specimen was placed on top of a rigid steel base plate with a 50.8 mm center opening. The loading rate was set to 2 mm/min to simulate quasi-static conditions. The force and displacement were recorded from the testing machine.
6
Load
Figure 2-2 Bending static test configuration.
2.3
High Strain Rate Tests High strain rate in the adhesive was accomplished by performing high velocity impact tests. These
tests were conducted using a gas gun shown in Figure 2-3. The gas gun, controlled by a solenoid valve, was powered by either compressed air, for lower velocities, or helium for higher velocity impacts. The cylindrical projectile, with length 25.4 mm, diameter 7.6 mm and made from O1-tool steel, was seated in front of a modified sabot and front loaded into the barrel. Using a constant pressure, the depth at which the projectile was inserted down the barrel determined the velocity of the projectile. For instance, with the pressure set to a maximum of 12.4 MPa and at full depth insertion of 110cm, the projectile was capable of reaching a velocity of approximately 250 m/s. However, by using helium at the same depth, the projectile could be propelled up to 400 m/s. The specimen was mounted inside a ballistic chamber which is equipped with 25.4 mm thick transparent safety glass. Four C-clamps were used to attach the specimen to two rails in the ballistic chamber. The positions of C-clamps were 12.5mm from the back-plate edge, sufficiently far from the adhesive to ensure that the reflected waves from the clamps and back-plate edge had no chance of reaching the adhesive before it failed.
This allowed the ballistic event to be safely viewed with the
Phantom V710 high-speed camera (not shown in Figure 2-3). The high-speed camera was used to record 7
the displacements of the projectile and various specimen pieces to calculate the kinetic energies of all components throughout the system. The laser trap at the end of the barrel was used to trigger the camera when the projectile passed through the laser.
Figure 2-3 Experimental ballistic test setup, the high-speed camera is not shown for clarity.
The displacements of the projectile, plate and patch, were measured by incorporating tracking markers to each component of the system. Each component was tracked via custom-written software (Matlab®) during post processing. The algorithm used standard image processing techniques to filter the relative contrast between the feature points and the background and tracking the centroids of these features. The projectile, marked as blue, and the plate and patch, marked as red, are shown in Figure 3-3. The projectile incident speed, rebound speed and the patch speed if the adhesive failed were collected for all tests. The failure/non-failure of the adhesive layer was recorded to determine the critical incident projectile velocity that was required to rupture the bond.
2.4
Surface Preparation and Bonding The integrity of an adhesive bond is driven in large part by good surface adhesion between the
adhesive and the base adherend material. A meticulous surface preparation method was followed to ensure a good cohesive bond. For the steel adherend, the method required bulk cleaning of the base material, followed by a mechanical abrasion of the bond surface. Care was taken to not contaminate the bond surface during and after coupon preparation. Bonding was thus conducted within 30 minutes of 8
completion of the preparation procedure to minimize exposure time to potential contaminants. The methacrylate adhesive required only standard grit-blasting, whereas the epoxy adhesive also required an additional silane chemical treatment of the adherends. Silane is a coupling agent that helps bond the organic epoxy polymers to the inorganic metallic surface of the adherends. The surface preparation techniques were followed as per the description by Jensen [10]. When bonding with the epoxy adhesive, the additional silane treatment was as follows: after grit blasting the adherends, the adherends were placed into a silane bath for 90 seconds and then baked in the oven at 120°C for one hour. After removing the adherends from the oven, they were cooled to room temperature before being be set onto the jig for bonding. After the surface preparation was completed and the bonding surface was cleaned one final time with the inert gas spray, the adherends were then set in the jig for bonding, shown in Figure 2-4. The square bottom plate was located by placing the adherend against pins set in the jig bottom, while the patch was located similarly in the jig top. The bond-line thickness of the coupons was maintained by placing a 0.254 mm disk shim on to the center-post of the jig. Guided by set pins, the jig top (housing the patch) was placed on to the adhesive and pressed down with a 10-kg mass. The two manufacturers recommend the adhesives remain under pressure on the jig at room temperature until 80% of the final strength is reached. For the methacrylate, this takes 30 minutes and the epoxy requires 12 hours. Full bond strength is reached after 48 hours for methacrylate and 72 hours for epoxy. Due to the pressure applied to the patch, some of the adhesive was squeezed out of both the inner and outer diameters of the joint. This spew was left in place during curing and testing.
9
Patch Top
Spacer Plate Guide rails
Base
Figure 2-4 Manufacturing jig with specimen parts on manufacturing jig.
3
Experimental Results and Discussion
3.1 Static Testing 3.1.1
Tensile Testing
The strain within the adhesive can be extracted by isolating the displacement of the adhesive from the total displacement measured by the extensometer. Figure 3-1 illustrates the locations where the measurements were taken.
10
Force
Force
Figure 3-1 Gauge length and displacements in the axially loaded butt-joint
The strain in the adhesive can be derived using a uniaxial stress assumption in both the adhesive and adherends. The total displacement is defined as
=
+
Inserting the strain definition, (3.1) becomes: =
+
+
(3.1)
+
(3.2)
From (3.2), the strain in the adhesive can be obtained as: =
−
+
(3.3)
Substituting the stress definition, the equation for the strain within the adhesive in its final form is: = where ,
,
respectively.
, and
,
and
+
(3.4)
are the displacements of the total system, adherend 1, adherend 2 and adhesive, are the strains in the adherends and adhesive.
the adhesive to the extensometer and cell,
−
the cross-sectional area and
is the adhesive thickness.
and
are the distances from
is the measured force from the load
the adherend’s Young’s modulus.
The characteristic results for the quasi-static tests of 5 samples each of methacrylate and epoxy buttjoints are plotted below in Figure 3-2. As seen, the epoxy was stiffer and stronger, but the fracture strain was equivalent for both adhesives. The material properties are listed in Table 3-1. The stress-strain curves 11
did not start at the zero point because a small, initial load was applied to the specimen when the grip head was closed. Note that the load recorded by the load-cell after each specimen failed was taken as the zero load condition, and the initial load was offset accordingly.
Epoxy
Methacrylate
Figure 3-2 Characteristic stress-strain curve for the axially loaded butt-joints bonded with epoxy and methacrylate.
Table 3-1 Adhesive material properties from an axially loaded butt-joint
Methacrylate Epoxy
Young's Modulus [GPa] 1.5 ± 0.3 3.3 ± 0.3
The static energy absorption
Max. Stress [MPa] 28.7 ± 1.0 36.1 ± 2.2
Failure Strain 0.12 ± 0.01 0.12 ± 0.02
Energy [J] 0.13± 0.02 0.16± 0.04
of the adhesives can be calculated by integrating the stress-strain curves
(i.e. σ-ε curves) in Figure 3-2 and multiplying it by the adhesive volume, V: =
(3.5)
The energy absorption for each adhesive is shown in Table 3-1. 12
3.1.2
Static Bending Strength
The bending specimens were loaded to failure under quasi-static conditions using a point load indenter (Figure 2-2). Three specimens of each material combination were tested to determine the failure strength of the bond. The experimental results showed that the bending static strength was equivalent for the methacrylate and epoxy joints. Despite the epoxy having a 25% higher tensile strength (as obtained from the butt joint test), the tensile strength of these two adhesives (as obtained from the static bending test) is essentially equivalent. The results are listed in Table 3-2 below.
Table 3-2 Average static bending strength of the adhesive joint.
Adhesive Methacrylate Epoxy
Strength [MPa] 13.5 ± 1.3 13.0 ± 1.2
3.2 Critical Failure Velocity Specimens were tested at increasing incident projectile velocities to find the critical failure velocity (CFV). The CFV is defined as the velocity range that causes full rupture within the adhesive. It is analogous to the ballistic limit velocity V50 commonly used in single-layer metallic specimens [11]. However, full degradation of the adhesive bond is not always apparent near the CFV with a more ductile adhesive. Under dynamic loading, there could be considerable plastic flow in the epoxy adhesive as the stress wave passes through the bond. It is thus possible that at velocities close to the CFV for the epoxy bonded specimens, the growth rate of the void nucleation was not fast enough for a full rupture, leaving the bond partially cracked [12]. With partial cracking, the bond remains visually intact, but the load carrying capacity of the bond could be significantly compromised. Thus all non-failed specimens underwent quasi-static testing to measure their post-impact residual strength. This additional destructive evaluation procedure would also allow the determination of the type of failure observed, i.e. brittle or ductile. Lastly, for design purposes, it is important to present both the failure points, i.e. the critical rupture and the residual strength, to define a viable range for these adhesives to be used both during and after impact loading.
13
An example of the measurement technique is shown in Figure 3-3 with video images captured at three significant times during the ballistic event. The displacements from each white feature point are tracked and averaged for the particular component of the specimen. The velocities are obtained from the timehistory of the displacement measurements and recorded for both the projectile and patch. The kinetic energy of each component is also calculated by using the known masses and recorded velocities of the components.
a
b
c Figure 3-3 A sequence of high speed images taken at a frame rate of 126,669 fps with a resolution of 384 x 120 pixels showing a methacrylate adhesive joint (a) just before impact, (b) during impact and (c) after impact.
14
The data for the critical failure speeds for the two types of adhesives, plotted below in
12
Patch Speed [m/s]
10
Exp: Methacrylate Jonas-Lambert: Methacrylate Exp: Epoxy Jonas-Lambert: Epoxy
8
6
4
2
0 50
100
150
200 250 300 350 Projectile Speed [m/s]
400
450
Figure 3-4, utilizes the Lambert-Jonas approximation for ballistic impact as a best-fit model. The Lambert-Jonas [13] correlation is based on the conservation of energy between the impactor and target to predict the ballistic limit, or
, of a material based on experimental ballistic tests. The concept of the
patch detaching from the back plate during total adhesive rupture is akin to the ballistic limit of projectile perforation and thus the Lambert-Jonas correlation is a good approximation for this type of test. The Lambert-Jonas correlation is given by: " !
where
!
is the residual speed of the target,
#
=
" #
−$
(3.6)
is the incident speed of the projectile, A is a fit parameter
based on the mass ratio of the projectile and target, B is a fit parameter that predicts the CFV, and P is a fit parameter based on the rigidity of the impact. Using P = 2, approximating a rigid collision, the Lambert-Jonas fit plotted for all cases is: !
=%
#
−$
(3.7)
15
12
Patch Speed [m/s]
10
Exp: Methacrylate Jonas-Lambert: Methacrylate Exp: Epoxy Jonas-Lambert: Epoxy
8
6
4
2
0 50 As seen in
100
150
200 250 300 350 Projectile Speed [m/s]
400
450
Figure 3-4, there is a clean rupture for the steel-methacrylate bond. The rupture CFV for the steelmethacrylate bonded specimens is B ≈ 170 m/s. The CFV for the steel-epoxy bond lies between 311 m/s and 343 m/s, with the Jonas-Lambert CFV fit parameter, B ≈ 320 m/s. The CFV values calculated from the Jonas-Lambert model for both adhesives are listed in Table 3-3. The steel-epoxy bonds do not exhibit a clean rupture like the methacrylate. The CFV band is wider for steel-epoxy, leading to less certainty of the dynamic failure point. As explained above, this is typical for a ductile adhesive where void nucleation growth is slower, therefore within this impact velocity range, the crack does not have enough energy to fully propagate. Additionally, this result is indicative that the fracture strain of the epoxy has a wider range of values than the methacrylate, causing the relatively large spread in CFV. Note that in this paper, the Jonas-Lambert fit has been used purely for curve-fitting purposes in order to obtain the CFV from the experimental data.
16
12 Exp: Methacrylate Jonas-Lambert: Methacrylate Exp: Epoxy Jonas-Lambert: Epoxy
Patch Speed [m/s]
10
8
6
4
2
0 50
100
150
200 250 300 350 Projectile Speed [m/s]
400
450
Figure 3-4 Critical failure speed for the two adhesively bonded steel joints.
Table 3-3 Critical Failure velocity based on the Jonas-Lambert model.
Adhesive Methacrylate Epoxy
3.3
Critical Failure Speed (m/s) ~170 ~320
Basic dynamics of the system No direct measurements of impact forces were made for the ballistic impact experiments performed
in the present research; thus to estimate the impact force of the projectile on the target, Newton's second law can be used to calculate the average impact forces. Consider the impulse-momentum diagram shown for the closed system containing the projectile and target, during and after impact in Figure 3-5 below. 17
/ ∆(
mvi 13a.
mvf 13b.
13c.
Figure 3-5 A schematic of the impulse and momentum of the projectile: (a) just before impact, (b) during impact and (c) after impact. Part of the plate (dashed lines) is shown for reference.
From the principle of impulse-momentum in the direction of impact: &=
' (=
) * = )*+ − )*# = ' ∆(
or '=
)-*+ − *# .
∆(
=
)∆*
∆(
(3.8)
(3.9)
where & denotes the impulse imparted to the body, / the average impact force, ) the mass of the projectile, vi the incident projectile velocity before impact, vf the projectile rebound velocity after impact, and ∆t is the impact time. Experimentally the projectile mass, incident velocity and rebound velocity can be readily measured. However, directly measuring the impact time is significantly more challenging. An estimate of the contact time was obtained by increasing the frame rate of the high-speed camera to 280,991 fps (the highest without sacrificing spatial resolution) and repositioning the camera in such a way that the projectile contact event was visible. In these experiments it was found that the target metal plate reflected the mirror image of the projectile and this allowed for a relatively simple visual initiation of the contact. Additionally, the impact flash observed for the higher speed impacts (>250 m/s) served as another helpful benchmark to determine contact initiation. (The impact flash duration from the camera was < 4 µs which was significantly less than the impact duration). The end of the impact event was calculated to be the zero crossing in the tracked velocity-time history of the projectile. With the specified frame rate, the impact time measurement was estimated to have an error of ±3.5 μs.
Contact force was also calculated using Taylor impact theory [14]. Taylor [14] conducted an analysis on the deformation produced by the impact of cylinders against a rigid wall. Taylor’s impact theory predicts that when a cylindrical projectile, shown in Figure 3-6, of length
impacts a target at velocity
18
vi, the following simple non-dimensional relationship can be used to estimate the dynamic yield strength, 23
of the projectile material. 4*#
23
=
2
−5 −
ln
1
(3.10)
5
where x is the length of the undeformed section of the cylinder and L1 is the final length of the projectile. During deformation, the stress within the region that has plastically deformed is assumed to be constant and equal to the dynamic yield stress of the material at that strain rate. *#
89 5 −5 (b)
(a)
Figure 3-6 Sequence of deformation of cylindrical projectile (a) before and (b) after impact against a rigid wall
The beauty of the Taylor approximation is that simple geometric measurements of the projectile after impact can be used to estimate the dynamic yield stress of the material. The projectiles were photographed after each experiment and digital measurements were taken to obtain accurate dimensions of the plastic zone. An example of this technique is shown in Figure 3-7. The Taylor relationship is used to calculate the dynamic yield strength (i.e.
23
in equation 3.10) for each experiment and is plotted in
Figure 3-8. A quadratic least-square curve-fit of the data presented in Figure 3-8 is also plotted. The experimental results shown in Figure 3-8 are for all the ballistic experimental results which include both the epoxy and methacrylate and for velocities above and below the CFVs of the adhesives.
19
/
Figure 3-7 Projectile measurements (all dimensions in mm) after impact.
= 0.103 E
4*# /
4*F 2 G
H − 0.446 E
4*F 2 G
H+1
23
Figure 3-8 Theoretical and experimental results for :; /:= as a function of >?@ A /BCD . The curve labeled ‘Taylor’ is a quadratic polynomial least square fit of the data.
As a further verification, the measured dynamic yield stress was compared with the Johnson-Cook constitutive model. The Johnson-Cook model is a rate-dependent plasticity model to predict a material's stress response under high strain-rate loading. Neglecting temperature effect, the Johnson-Cook model is expressed as [15]:
20
23
where ̅9 =
RS TRU RS
= J + $ 9̅ L M N1 + O ln E
9P
P
H Q
(3.11)
is the effective plastic strain, P the reference strain rate, 9P the applied strain-rate, and
A, B, C, and n are material dependent constants.
The Johnson-Cook constitutive model constants for O1 tool steel were experimentally determined by McClain et al. [16] and are listed in Table 3-4. The experimental data is plotted for comparison in Figure 3-9. Here the experimental dynamic stress
23 was
obtained from Taylor’s approximation (i.e. equation
3.10). It is seen that there is a good fit between the measured values for the dynamic stress and the Johnson-Cook model.
Table 3-4 Johnson-Cook parameters for O1 tool steel (McClain et al. [16]).
A (MPa) B (MPa) C(-) n(-) P (s T 9P (s T
391.3 723.9 0.1144 0.3067 1 103
21
Figure 3-9 Johnson-Cook constitutive model for O1 tool steel compared with experimental data.
The projectile impact force F can now be estimated using the dynamic stress as: =
23 9
(3.12)
where Ap is the plastic area which is the entire area of the projectile that has come in contact with the patch (Ap = π Dp2/4 in Figure 3-6). The average impact force for various projectile speeds is shown in Figure 3-10. Note that this experimental approach cannot recreate a force-time history plot, thus leaving the peak force unknown. Figure 3-10 also compares the average impact force as calculated using projectile impulse and contact time estimated with the high-speed camera (i.e. equation 3.8) to the Taylor approximation. As shown, the high-speed camera method has a much larger scatter than the Taylor approach and is thus potentially a worse approximation of the impact duration than the Taylor method.
22
Figure 3-10 Average impact force as a function of projectile velocity utilizing the Taylor impact approximation and the projectile’s impulse and contact time as measured with the high-speed camera.
The average impact force of the projectiles (as calculated from the Taylor approximation) at the experimental specimen’s CFVs are listed in Table 3-5. This table also shows a comparison between the dynamic and static strengths of the bonds. The so-called strength of the bond is calculated as the failure load divided by the bond area and oversimplifies the complex dynamic stresses due to impact. As such, the strength is an average for the full bond length and could be a useful parameter for design purposes. Furthermore, Table 3-5 clearly illustrates the dynamic effect within the bond. The dynamic strength of the epoxy is 3.5 times higher than that of the static strength, while the dynamic strength of the methacrylate is more than double its static strength.
Table 3-5 Average impact force and strengths at CFV for the two adhesives.
Adhesive Methacrylate Epoxy
Incident Speed (m/s) ~170 ~320
Projectile Impact Force (kN) 78 119
Static Strength (MPa) 14 13
Dynamic Strength (MPa) 31 47
23
3.4
Residual Strength For some epoxy bonded specimens, within the CFV range, there is visible cracking in the bond, yet
the patch remains attached to the back plate. This observation led to testing the residual strength of the unbroken specimens. Shown below in Figure 3-11 are the results for the quasi-static tests for all material combinations including both the virgin and the post-impact specimens. Three virgin (i.e. not subjected to impact) specimens for each adhesive were tested. The results from these tests are listed below in Table
Stress [MPa]
3-6 for visualization purposes. The data were fitted with an exponential curve.
Figure 3-11 Residual strength of methacrylate and epoxy bonds after impact.
Table 3-6 Projectile velocity where bond line stress is equal to B/A
Joint Materials Steel-Methacrylate Steel-Epoxy
B/A (MPa) 6.8 6.6
Velocity (m/s) ~100 ~300
24
These residual strength tests results show a degradation in bond strength as the dynamic impact force increases in magnitude. The residual strength of methacrylate adhesive bonds degrade at a much faster rate than the epoxy bonds, indicative of a brittle failure at high loading rates, while the slower degradation within the epoxy indicates some ductility at high loading rates. It has been shown by Gledhill et al. [17] and Kinloch et al. [12] that three distinct types of crack propagation may be observed in adhesives. These are defined as: (A) Stable Ductile Propagation where the crack grows steadily in a controlled manner and the crack propagation rate is constant. The fracture surfaces will be rough and torn in appearance. This type of crack growth is often observed at higher test temperatures or low-test rates. (B) Unstable Brittle Propagation where the type of crack growth is essentially brittle in nature, but the crack propagates intermittently in a stick-slip manner. This type of crack growth is associated with an increase in crack-tip plasticity and is typically observed at a somewhat higher test temperature or intermediate test rate. (C) Stable Brittle Propagation where the fracture surfaces are relatively featureless and smooth, which is indicative of brittle failure. This type of crack growth is associated with lower test temperatures or hightest rates. These three regimes can be seen from the post mortem micrographs of the failed specimens. In Figure 3-12 it is apparent that the fracture surface is different for the static and impact loading for methacrylate. The fracture surface from the slow test-rate (quasi-static) tests appeared to be rough and torn, corresponding to a Type A failure. The fracture surface for the specimen that failed upon impact corresponded to a Type C failure, which is indicative of a brittle fracture. The fracture surface of the specimen loading in the intermediary range was similar in appearance, which indicated that either this adhesive does not demonstrate Type B failure, or the ductile to brittle transition happens too quickly for observation.
1 mm
1 mm
(a)
1 mm
(b)
(c)
Figure 3-12 Micrograph of the methacrylate adhesive fracture surface for failure from (a) quasi-static test rate, (b) quasi-static residual strength testing after non-failure impact (71 m/s), and (c) impact loading (175 m/s)
25
In Figure 3-13 it is apparent that the fracture surface is different for the static and impact loading for epoxy. The fracture surface from the low test-rate (quasi-static) tests appeared to be rough and torn, corresponding to a Type A failure. The fracture surface for the specimen that failed upon impact corresponded to a Type C failure, which is indicative of a brittle fracture. The fracture surface on the specimen that did not fail upon impact (Figure 3-12 b), but rather upon quasi-static loading after impact, appeared to have a surface similar in appearance to both Type A and Type B fracture surfaces. This is indicative of the transition between ductile to brittle failure.
1 mm
1 mm
(a)
1 mm
(b)
(c)
Figure 3-13 Micrograph of the epoxy adhesive fracture surface for failure from (a) quasi-static test rate, (b) quasi-static residual strength testing after non-failure impact (305 m/s), and (c) impact loading (312 m/s)
Depending on the failure mode, a new failure definition is required. We suggest that for ductile adhesives, the CFV should be redefined as the projectile velocity at which the residual strength has been reduced by 50% of the virgin static strength (shown as σ/2 in Figure 3-11). The choice of defining the CFV at 50% of the virgin static strength is relatively arbitrary and is left to the discretion of the designer; here it is chosen to give a safety factor of 2 most commonly used in design. For brittle adhesives, the CFV should be left as the rupture speed. This allows for a practical definition of impact resistance of an adhesive joint that a designer could use to estimate joint survivability during and after impact.
3.5 Energy Absorption A comparative test outlined by Adams and Harris [18] suggests that an estimation of the energy imparted to the adhesive after fracture can be found by testing an unbonded specimen. The difference in kinetic energy between the unbonded and bonded experiments should provide an estimate for the energy absorbed by the adhesive provided that the deformation in both cases is the same. Though this result may be lower because only the translational kinetic energy can be experimentally calculated. Other energy in the system such as energy due to vibration, rotational kinetic energy, damping etc. cannot be calculated. 26
The underlying assumption in the experimental method is that the overall stiffness of the adhesive is small in comparison to the overall stiffness of the patch and back-plate and thus do not affect the overall dynamics of the impact. To have an empirical measurement of the energy absorbed due to the presence of each adhesive, additional ballistic tests were performed. The experimental setup is similar to the tests described above, except that the patch is now unbonded and held to the back plate with a low strength adhesive tape. In the ballistic test, all the input energy into the system consists of the initial kinetic energy of the projectile. Upon impact, the energy is converted into various other forms of energy including plastic dissipation in the projectile and patch, fracture of the adhesive layer, heat and lastly as kinetic energy of the rebounding projectile and the free-flying patch. Post-impact, the translational kinetic energy of the patch can be calculated by measuring its velocity through a digital tracking software. It is impractical to try to account for all of the energy contributions. However, the sum of all the unaccounted absorbed energies and final kinetic energy must equal the energy input. Here we assume that the difference in the final measured kinetic energies is equal to the difference in total absorbed energy by the adhesive for the two tests with the same initial input energy. After completing the bonded and unbonded tests, it is seen that the deformations in the projectile and patch are similar for both cases. Measurements of the projectile lengths before and after impacts for both the bonded and unbonded cases at comparable projectile velocities were within 10% of each other over the range of tested projectile velocities. Thus, the method outlined above is a practical measure for the energy absorption of the adhesive. For the ballistic bending specimens, tests at the CFV defined by residual strength will not cause the patch to detach; therefore, there is no kinetic energy of the patch after the impact. The resulting kinetic energy of an unbonded patch impacted at the same velocity is considered to be the energy absorbed due to the presence of the adhesive. Figure 3-14 shows the unbonded patch energies and the bonded patch energies for all experiments. The critical energy, i.e. the projectile kinetic energy at the CFV determined by the residual strength, is also shown. The intersection of this critical energy and the linear fit denotes the energy absorbed by the adhesive. For instance, the kinetic energy at the CFV (i.e. the critical energy) of the methacrylate bond is 134.5 J.
The patch kinetic energy at this critical energy (the energy
absorption of the bond) is 4.1 J, or the energy absorbed per unit area of the bond is 1.6 kJ/m . The absorbed impact energy results are presented in Table 3-7.
27
Patch Kinetic Energy [J]
Epoxy
Methacrylate
Figure 3-14 Energy absorption for the methacrylate and epoxy adhesives
Table 3-7 Adhesive energy absorption at CFV for the two adhesives.
Adherend-Adhesive Steel-Methacrylate Steel-Epoxy
Critical Projectile Energy (from B/A (J) 135 384
Energy Absorption (J) 4.0 16
Energy Absorption YZ/[A 1.6 6 28
4
Conclusions We have presented a novel experimental protocol for the dynamic characterization of adhesively
bonded joints under ballistic impact loading. The test is meant to be a dynamic analog to the commonly used static blister test. The new dynamic test has the advantages that it requires relatively small scale test specimens and that standard ballistic penetration equipment can be used. The parameters obtained through this testing program include: (1) the critical failure velocity for each bond type, (2) the average critical failure force and energy, (3) the energy absorbed by the adhesive under impact loading, and (4) the nature of the bond failure (cohesive or interfacial). The proposed method relies only on measuring the velocities of the projectile and patch obtained from a high-speed camera which is standard for any ballistic testing facility. Relatively accurate average impact forces also can be obtained using Taylor impact theory and measurements of the projectile deformation after impact. The current study has also shown that adhesives that have nearly identical strengths under static loading (such as the methacrylate and the epoxy adhesives used in the study) can perform substantially differently under impact loading. The epoxy was seen to withstand an average projectile impact force 40% higher than that of the methacrylate. Furthermore, the dynamic strength of the epoxy is shown to be 3.5 times greater than that of its static strength, while the dynamic strength of the methacrylate is more than double compared to its static strength. Thus, static strength is not a good indication of dynamic strength and should be separately characterized for adhesives operating under impact conditions. Residual strength tests were conducted to determine the loss of strength of the adhesive bond as the dynamic load approached the failure load. From these tests it was apparent that there was a structural degradation within the adhesive bond as the dynamic load increased. Micrographs of the failed adhesive surfaces showed that the epoxy adhesive behaved more like a ductile material under dynamic loading, while the methacrylate behaved more like a brittle material. The adhesive fracture surfaces were observed to be cohesive with the fracture surface being through the adhesive (as opposed to interfacial), indicating that the inherent strength of the adhesive was being measured. (The test was not designed to measure interfacial strength which should be characterized separately and is not part of the present study). An auxiliary experiment was devised to determine the energy absorption of the adhesive bond. The comparative test between the unbonded and bonded joint assumed the only difference in energy was due to the contribution of the adhesive. At failure, the epoxy adhesive was shown to absorb nearly 4 times more energy compared to the methacrylate. Again this is in stark contrast to the static butt-joint tests which showed that the epoxy only had approximately 30% greater energy absorption than the methacrylate adhesive.
29
5
Acknowledgements
This work was supported by U.S. Army- TARDEC (currently US Army- GVSC) under contract #69201511 through NAMC. We thank Dr. Robert Jensen of ARL and Daniel Schaffren of US Army – GVSC (previously TARDEC) who provided their expertise on surface preparation and bonding. Additionally, we thank our colleagues Dr. Bruno Zamorano and Dr. Jack Chiu for their insightful discussions and contribution to this work.
References [1]
[2] [3]
[4]
[5]
[6] [7]
[8] [9] [10]
[11] [12]
[13]
[14]
C. Galliot, J. Rousseau, and G. Verchery, “Drop weight tensile impact testing of adhesively bonded carbon/epoxy laminate joints,” International Journal of Adhesion and Adhesives, vol. 35, pp. 68–75, 2012. H. A. Perry, Adhesive Bonding of Reinforced Plastics. McGraw-Hall, 1959. R. D. Adams and J. A. Harris, “A critical assessment of the block impact test for measuring the impact strength of adhesive bonds,” International Journal of Adhesion and Adhesives, vol. 16, no. 2, pp. 61–71, 1996. L. Goglio, L. Peroni, M. Peroni, and M. Rossetto, “High strain-rate compression and tension behaviour of an epoxy bi-component adhesive,” International Journal of Adhesion and Adhesives, vol. 28, no. 7, pp. 329–339, 2008. A. A. Bezemer, C. B. Guyt, and A. Vlot, “New impact specimen for adhesives: optimization of high-speed-loaded adhesive joints,” International Journal of Adhesion and Adhesives, vol. 18, no. 4, pp. 255–260, 1998. D. P. Updike, “Effect of adhesive layer elasticity on the fracture mechanics of a blister test specimen,” International Journal of Fracture, vol. 12, no. 6, pp. 815–827, 1976. T. Andersson and U. Stigh, “The stress-elongation relation for an adhesive layer loaded in peel using equilibrium of energetic forces,” International Journal of Solids and Structures, vol. 41, no. 2, pp. 413–434, 2004. H. Chai, “Experimental Evaluation of Mixed-mode Fracture in Adhesive Bonds by Herzl Chai,” Experimental Mechanics, vol. 34, no. 4 December, pp. 296–303, 1992. G. P. Zou, K. Shahin, and F. Taheri, “An analytical solution for the analysis of symmetric composite adhesively bonded joints,” Composite Structures, vol. 65, no. 3–4, pp. 499–510, 2004. R. Jensen, D. Deschepper, D. Flanagan, G. Chaney, and C. Pergantis, “Adhesives : Test Method , Group Assignment , and Categorization Guide for High-Loading- Rate Applications – Preparation and Testing of Single Lap Joints ( Ver . 2 . 2 , Unlimited ),” 2016. J. A. Zukas, Penetration and Perforation of Solids. Impact Dynamics. 1982. A. J. Kinloch, S. J. Shaw, D. A. Tod, and D. L. Hunston, “Deformation and fracture behaviour of a rubber-toughened epoxy: 1. Microstructure and fracture studies,” Polymer, vol. 24, no. 10, pp. 1341–1354, 1983. J. P. Lambert and G. H. Jonas, “Towards Standardization in Terminal Ballistics Testing: Velocity Representation,” no. BRL-1852, Army Ballistics Research Lab Abderdeen Proving Ground MD, January, 1976. G. Taylor, “The Use of Flat-Ended Projectiles for Determining Dynamic Yield Stress. I. 30
Theoretical Considerations,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 194, no. 1038, pp. 289–299, 1948. [15] G. R. Johnson and W. H. Cook, “Fracture characteristic of three metals subjected to various strains, strain rates, temperatures and pressures,” Engineering Fracture Mechanics, vol. 21, no. 1, pp. 31–48, 1985. [16] B. McClain, S. A. Batzer, and G. I. Maldonado, “A numeric investigation of the rake face stress distribution in orthogonal machining,” Journal of Materials Processing Technology, vol. 123, no. 1, pp. 114–119, 2002. [17] R. A. Gledhill, A. J. Kinloch, S. Yamini, and R. J. Young, “Relationship between mechanical properties of and crack progogation in epoxy resin adhesives,” Polymer, vol. 19, no. 5, pp. 574– 582, 1978. [18] R. D. Adams and J. A. Harris, “The influence of local geometry on the strength of adhesive joints,” International Journal of Adhesion and Adhesives, vol. 7, no. 2, pp. 69–80, 1987.
31
S0143-7496(19)30281-7
DOI:
https://doi.org/10.1016/j.ijadhadh.2019.102529
Reference:
JAAD 102529
To appear in:
International Journal of Adhesion and Adhesives
Received Date: 21 September 2019 Accepted Date: 2 December 2019
Please cite this article as: Gollins K, Elvin N, Delale F, Characterization of Adhesive Joints Under HighSpeed Normal Impact: Part I – Experimental Studies, International Journal of Adhesion and Adhesives, https://doi.org/10.1016/j.ijadhadh.2019.102529. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Elsevier Ltd. All rights reserved.
Characterization of Adhesive Joints Under High-Speed Normal Impact: Part I – Experimental Studies Kenneth Gollinsa, Niell Elvina†, Feridun Delalea a. Department of Mechanical Engineering, City College of New York, New York, NY 10031, USA † Corresponding Author, email: [email protected]
Abstract This two-part article presents an experimental method with numerical verification of the characterization of adhesive bonds under normal impact loading. Part I presents experimental results of the mechanical behavior of two different adhesives (a methacrylate and an epoxy). Though the two adhesives have similar static behavior, their impact strengths are significantly different. Thus adhesives that are to be used under impact loading need their own dynamic characterization tests.
Here we present
an impact test that is analogous to the commonly used blister test for static adhesive testing. One major advantage of the present impact test is that existing apparatus and methods that are currently used for ballistic penetration can be readily adopted for the proposed dynamic test. The average dynamic stress as well as energy absorbed by the adhesive are experimentally determined by the proposed method.
Keywords D. mechanical properties of adhesives; D. impact; C. dynamic mechanical analysis; C. destructive testing
1
Introduction One of the major challenges facing the aerospace, commercial vehicular and defense industries is the
need to decrease cost and increase fuel economy without sacrificing performance. Adhesive materials are ideally suited to address these challenges, permitting the construction of lightweight assemblages by replacement of heavier conventional joints such as bolts or weldments. However, achieving the desired 1
savings without sacrificing performance requires that these adhesive joints possess sufficient survivability under both quasi-static and impact loading. The joints between the elements of the structure have the potential to introduce critical structural vulnerability if not designed properly. Current static failure strength test methods such as tensile, compressive and shear tests are well established and understood, but the current methods are not as reliable for testing the dynamic failure strengths. The most commonly used methods to test adhesive joint specimens under impact loading are pendulums, drop weight impactors and split Hopkinson pressure bars [1]. Early impact tests were performed by Perry [2] on an instrumented pendulum rig (ASTM D950-78) to measure the failure load and energy absorption of adhesively bonded butt-joints. It was found that the response was equivalent to an elastic spring and thus the energy absorbed is proportional to the square of the failure stress. However, as noted by Adams [3] the energies from this impact test do not necessarily reflect the energy absorbing capability of the adhesive itself, but rather the compliance of the test system, thus making the result machine sensitive. Using a modified drop weight impact test, Galliot et al. [1] explored the dynamic behavior of adhesively bonded lap joints in shear (mode II) failure at impact velocities between 1 and 4 m/s. Their test results indicated that the stiffness, the failure load and the absorbed energy all increased with the loading rate. They also found that the extension at failure was the only rate insensitive parameter since it remained constant for all impact velocities. Despite these findings, Galliot et al. concluded that the influence of local and overall parameters were identical under quasi-static and impact loading. Thus, for moderate loading velocities (< 4 m/s), the design of the adhesive joints could be based on static material properties. Using a split Hopkinson pressure bar, Goglio et al. [4], found that a bi-component epoxy adhesive is
highly sensitive to strain-rate. At an applied strain-rate on the order of 10 s-1, the bulk adhesive strength,
with respect to the static value, was observed to increase by a factor of three under compression and a factor of five under tension. The elastic modulus was also seen to increase with strain-rate, however no conclusive modulus data was reported from these tests due to the small-time scale at which these tests were performed i.e. equilibrium conditions were approximately reached at the same time in which the stress reached the elastic limit, thus limiting the ability to measure the elastic modulus. Bezemer et al. [5] devised a new type of adhesive joint specimen for high speed dynamic testing to simulate pure shear loading condition. In addition to the limitations noted early, the pendulum impact tests are not suitable for speeds above 5 m/s. Therefore, higher velocities were achieved with a drop weight machine, for speeds up to 10 m/s, and an air gun for speeds up to 100 m/s. These authors conclude that for each of the three tested adhesives (epoxy, polyurethane and an anaerobic adhesive) the energy absorption of the adhesive increases with the load. It was also seen that a ductile adhesive shows a larger
2
energy absorption at impact than a brittle adhesive. Thirdly, optimum adhesive thicknesses were found at each test speed for each adhesive. Considerable efforts have been undertaken to understand the behavior of adhesively bonded joints by many researchers. The most well understood is the lap joint because in most structural applications, adhesive bonds are loaded in shear due to their greater load carrying capacity. Lap joints exhibit local plastic zones at the bond edges and are thus less susceptible to failure than adhesives loaded in a normal direction to the adherends i.e. in bending. While many researchers have studied the bending failure mode, the breadth of work has been with quasi-static loading and little is known about the dynamic aspects of bonded joints under bending. Dynamic testing is critical for any design that may experience high strain rates or types of transient loads. Currently, there is no standard for the dynamic testing of adhesively bonded joints under impact loading, especially at very high strain rates. As such, a robust and repeatable dynamic testing protocol for characterizing adhesively bonded joints has been devised. These tests were designed to provide a dynamic analog to the static blister test by subjecting the joint to a transverse impulse load to transmit a stress wave through the adhesive. The methods defined in this work differentiate from previous studies through the following: (i) A method for determining the critical failure velocity and energy under transverse dynamic loading was developed. (ii) A method to determine the energy absorption under impact load was developed. (iii) A protocol was developed to measure the residual strength of the bond post-impact and how to report the observed behavior over a range of test velocities. The objective of this paper is to experimentally analyze the behavior and failure modes of adhesively bonded joints under high strain rate loading, namely ballistic impact. One advantage of the new test is that standard experimental equipment used for ballistic penetration testing can be readily modified to find the dynamic strength of a transversely loaded joint. This joint can be viewed as an axisymmetric lap joint for the purpose of transverse loading. The dynamic forces required to rupture the adhesive bond, the remaining strength of the bond post-impact (for non-failure cases) and the energy absorption of the adhesive have been characterized for two types of adhesives, a methacrylate and an epoxy.
2 2.1
Materials and Experimental Procedure Specimen Design
3
The experiment was designed to facilitate predominantly tensile Mode I type failure of an adhesive material between two adherends subjected to ballistic impact. The test specimen (as shown in Figure 2-1) consists of three parts: the back plate, the patch (the so called adherends) and the adhesive. The back plate has a two-inch diameter hole to allow the projectile to impact the adhered three-inch diameter patch in predominantly tensile loading as also shown in Figure 2-1. The adhesive thickness for all bonds was 0.254 mm with a bond width of 12.7 mm. The projectile delivered the high speed impulse required to create the high strain rate necessary to study the dynamic effect of impact in the adhesive. This specimen was designed to reduce any shear and torsional stresses, predominately allowing for normal stresses only. The specimen design is similar to the blister test by Updike [6], however it was modified to accommodate impact. The back plate diameter was shorter and the thickness was increased to transfer the bulk of the load to the adhesive. One metal adherend, AISI-1018 steel, was investigated with two adhesives. The chosen adhesives were both thermosetting adhesives, the first an acrylic and the second an epoxy. The first adhesive was a poly(methyl methacrylate) (PMMA) produced by SCIGRIP (Methacrylate SG805). The second adhesive was epoxy produced by Hysol (EA 9309NA). Two material combinations were tested in the experiments i.e. (1) steel- methacrylate and (2) steel-epoxy. The ratio between the Young's modulus of steel (~200 GPa) and the adhesives (~ 3 GPa) is high enough to consider relative deformation in the steel adherends to be negligible compared to that in the adhesive. In all cases, both the back plate and patch were the same material (i.e. steel); dissimilar adherends should be studied in future investigations.
4
Figure 2-1 Dimensions of the test specimens.
2.2
Static Testing
2.2.1
Tensile Tests
Owing to reported deviations between the bulk and thin adhesive bond mechanical properties, bulk material properties are not sufficient to use when determining the dynamic behavior of adhesively bonded joints. This is caused by strain constraining effects of the adherends in bonded assemblies, and also by typical mixed mode crack propagation in adhesive bonds [7]. In bulk materials, cracks tend to grow perpendicularly to the direction of the maximum principal stress [8]. However, in thin adhesive bonds, cracks are forced to follow the bond line because the adhesive is weaker and more compliant than the adherends. Thus, additional tests were performed to determine the tensile properties of the joints as the manufacturers data is provided for the bulk material only [9].
5
By using an axially loaded butt-joint (ASTM D2095) the tensile properties of the methacrylate and epoxy were determined. Theoretically, if the two adherends are infinitely rigid in relation to the adhesive, the stress-strain curve can be generated by isolating the strains within the adhesive. This material relation is not representative of the intrinsic adhesive behavior due to the adherend constraining effect and can only correspond correctly to the joint properties, not the adhesive bulk properties. The adherends do not allow the adhesive to contract laterally, thus introducing additional stresses perpendicular to the loading direction, which is indicative of bonded joint behavior. A set of five methacrylate and five epoxy butt-joint specimens were tested with an MTS 464 universal hydraulic testing machine at room temperature. Each of the steel adherends was 100 mm long, 25.4 mm wide and 6.35 mm thick. The adhesive was 0.254 mm thick. The specimens were positioned so that 25 mm of each side of the steel adherends was held within the hydraulic clamping jaws of the testing machine. The loading rate was set to 2 mm/min to simulate a quasi-static rate. An extensometer (MTS 634.12E-25) was positioned symmetrically across the bond line to measure the displacement of the adherends on both sides of the adhesive. The force and the extensometer displacement were recorded.
2.2.2
Bending Strength
Static tests were performed both on virgin specimens, to establish baseline characteristics, as well as on non-failed post ballistic impact specimens to measure the residual strength of the bond. The residual strength of a non-failed adhesive bond after ballistic impact, discussed in the following section, was measured by performing a static bending test on all surviving specimens. The static bending tests were performed using a universal testing machine (Instron-5882) at room temperature. The indentor, as shown in Figure 2-2, was modified to match the projectile diameter of 7.6 mm that was used in the impact tests as described in Section 2-3. The top portion of the indentor was threaded to fit inside of the existing testing machine; the bottom portion of the indentor was turned down on the lathe to a 7.6 mm diameter. The specimen was placed on top of a rigid steel base plate with a 50.8 mm center opening. The loading rate was set to 2 mm/min to simulate quasi-static conditions. The force and displacement were recorded from the testing machine.
6
Load
Figure 2-2 Bending static test configuration.
2.3
High Strain Rate Tests High strain rate in the adhesive was accomplished by performing high velocity impact tests. These
tests were conducted using a gas gun shown in Figure 2-3. The gas gun, controlled by a solenoid valve, was powered by either compressed air, for lower velocities, or helium for higher velocity impacts. The cylindrical projectile, with length 25.4 mm, diameter 7.6 mm and made from O1-tool steel, was seated in front of a modified sabot and front loaded into the barrel. Using a constant pressure, the depth at which the projectile was inserted down the barrel determined the velocity of the projectile. For instance, with the pressure set to a maximum of 12.4 MPa and at full depth insertion of 110cm, the projectile was capable of reaching a velocity of approximately 250 m/s. However, by using helium at the same depth, the projectile could be propelled up to 400 m/s. The specimen was mounted inside a ballistic chamber which is equipped with 25.4 mm thick transparent safety glass. Four C-clamps were used to attach the specimen to two rails in the ballistic chamber. The positions of C-clamps were 12.5mm from the back-plate edge, sufficiently far from the adhesive to ensure that the reflected waves from the clamps and back-plate edge had no chance of reaching the adhesive before it failed.
This allowed the ballistic event to be safely viewed with the
Phantom V710 high-speed camera (not shown in Figure 2-3). The high-speed camera was used to record 7
the displacements of the projectile and various specimen pieces to calculate the kinetic energies of all components throughout the system. The laser trap at the end of the barrel was used to trigger the camera when the projectile passed through the laser.
Figure 2-3 Experimental ballistic test setup, the high-speed camera is not shown for clarity.
The displacements of the projectile, plate and patch, were measured by incorporating tracking markers to each component of the system. Each component was tracked via custom-written software (Matlab®) during post processing. The algorithm used standard image processing techniques to filter the relative contrast between the feature points and the background and tracking the centroids of these features. The projectile, marked as blue, and the plate and patch, marked as red, are shown in Figure 3-3. The projectile incident speed, rebound speed and the patch speed if the adhesive failed were collected for all tests. The failure/non-failure of the adhesive layer was recorded to determine the critical incident projectile velocity that was required to rupture the bond.
2.4
Surface Preparation and Bonding The integrity of an adhesive bond is driven in large part by good surface adhesion between the
adhesive and the base adherend material. A meticulous surface preparation method was followed to ensure a good cohesive bond. For the steel adherend, the method required bulk cleaning of the base material, followed by a mechanical abrasion of the bond surface. Care was taken to not contaminate the bond surface during and after coupon preparation. Bonding was thus conducted within 30 minutes of 8
completion of the preparation procedure to minimize exposure time to potential contaminants. The methacrylate adhesive required only standard grit-blasting, whereas the epoxy adhesive also required an additional silane chemical treatment of the adherends. Silane is a coupling agent that helps bond the organic epoxy polymers to the inorganic metallic surface of the adherends. The surface preparation techniques were followed as per the description by Jensen [10]. When bonding with the epoxy adhesive, the additional silane treatment was as follows: after grit blasting the adherends, the adherends were placed into a silane bath for 90 seconds and then baked in the oven at 120°C for one hour. After removing the adherends from the oven, they were cooled to room temperature before being be set onto the jig for bonding. After the surface preparation was completed and the bonding surface was cleaned one final time with the inert gas spray, the adherends were then set in the jig for bonding, shown in Figure 2-4. The square bottom plate was located by placing the adherend against pins set in the jig bottom, while the patch was located similarly in the jig top. The bond-line thickness of the coupons was maintained by placing a 0.254 mm disk shim on to the center-post of the jig. Guided by set pins, the jig top (housing the patch) was placed on to the adhesive and pressed down with a 10-kg mass. The two manufacturers recommend the adhesives remain under pressure on the jig at room temperature until 80% of the final strength is reached. For the methacrylate, this takes 30 minutes and the epoxy requires 12 hours. Full bond strength is reached after 48 hours for methacrylate and 72 hours for epoxy. Due to the pressure applied to the patch, some of the adhesive was squeezed out of both the inner and outer diameters of the joint. This spew was left in place during curing and testing.
9
Patch Top
Spacer Plate Guide rails
Base
Figure 2-4 Manufacturing jig with specimen parts on manufacturing jig.
3
Experimental Results and Discussion
3.1 Static Testing 3.1.1
Tensile Testing
The strain within the adhesive can be extracted by isolating the displacement of the adhesive from the total displacement measured by the extensometer. Figure 3-1 illustrates the locations where the measurements were taken.
10
Force
Force
Figure 3-1 Gauge length and displacements in the axially loaded butt-joint
The strain in the adhesive can be derived using a uniaxial stress assumption in both the adhesive and adherends. The total displacement is defined as
=
+
Inserting the strain definition, (3.1) becomes: =
+
+
(3.1)
+
(3.2)
From (3.2), the strain in the adhesive can be obtained as: =
−
+
(3.3)
Substituting the stress definition, the equation for the strain within the adhesive in its final form is: = where ,
,
respectively.
, and
,
and
+
(3.4)
are the displacements of the total system, adherend 1, adherend 2 and adhesive, are the strains in the adherends and adhesive.
the adhesive to the extensometer and cell,
−
the cross-sectional area and
is the adhesive thickness.
and
are the distances from
is the measured force from the load
the adherend’s Young’s modulus.
The characteristic results for the quasi-static tests of 5 samples each of methacrylate and epoxy buttjoints are plotted below in Figure 3-2. As seen, the epoxy was stiffer and stronger, but the fracture strain was equivalent for both adhesives. The material properties are listed in Table 3-1. The stress-strain curves 11
did not start at the zero point because a small, initial load was applied to the specimen when the grip head was closed. Note that the load recorded by the load-cell after each specimen failed was taken as the zero load condition, and the initial load was offset accordingly.
Epoxy
Methacrylate
Figure 3-2 Characteristic stress-strain curve for the axially loaded butt-joints bonded with epoxy and methacrylate.
Table 3-1 Adhesive material properties from an axially loaded butt-joint
Methacrylate Epoxy
Young's Modulus [GPa] 1.5 ± 0.3 3.3 ± 0.3
The static energy absorption
Max. Stress [MPa] 28.7 ± 1.0 36.1 ± 2.2
Failure Strain 0.12 ± 0.01 0.12 ± 0.02
Energy [J] 0.13± 0.02 0.16± 0.04
of the adhesives can be calculated by integrating the stress-strain curves
(i.e. σ-ε curves) in Figure 3-2 and multiplying it by the adhesive volume, V: =
(3.5)
The energy absorption for each adhesive is shown in Table 3-1. 12
3.1.2
Static Bending Strength
The bending specimens were loaded to failure under quasi-static conditions using a point load indenter (Figure 2-2). Three specimens of each material combination were tested to determine the failure strength of the bond. The experimental results showed that the bending static strength was equivalent for the methacrylate and epoxy joints. Despite the epoxy having a 25% higher tensile strength (as obtained from the butt joint test), the tensile strength of these two adhesives (as obtained from the static bending test) is essentially equivalent. The results are listed in Table 3-2 below.
Table 3-2 Average static bending strength of the adhesive joint.
Adhesive Methacrylate Epoxy
Strength [MPa] 13.5 ± 1.3 13.0 ± 1.2
3.2 Critical Failure Velocity Specimens were tested at increasing incident projectile velocities to find the critical failure velocity (CFV). The CFV is defined as the velocity range that causes full rupture within the adhesive. It is analogous to the ballistic limit velocity V50 commonly used in single-layer metallic specimens [11]. However, full degradation of the adhesive bond is not always apparent near the CFV with a more ductile adhesive. Under dynamic loading, there could be considerable plastic flow in the epoxy adhesive as the stress wave passes through the bond. It is thus possible that at velocities close to the CFV for the epoxy bonded specimens, the growth rate of the void nucleation was not fast enough for a full rupture, leaving the bond partially cracked [12]. With partial cracking, the bond remains visually intact, but the load carrying capacity of the bond could be significantly compromised. Thus all non-failed specimens underwent quasi-static testing to measure their post-impact residual strength. This additional destructive evaluation procedure would also allow the determination of the type of failure observed, i.e. brittle or ductile. Lastly, for design purposes, it is important to present both the failure points, i.e. the critical rupture and the residual strength, to define a viable range for these adhesives to be used both during and after impact loading.
13
An example of the measurement technique is shown in Figure 3-3 with video images captured at three significant times during the ballistic event. The displacements from each white feature point are tracked and averaged for the particular component of the specimen. The velocities are obtained from the timehistory of the displacement measurements and recorded for both the projectile and patch. The kinetic energy of each component is also calculated by using the known masses and recorded velocities of the components.
a
b
c Figure 3-3 A sequence of high speed images taken at a frame rate of 126,669 fps with a resolution of 384 x 120 pixels showing a methacrylate adhesive joint (a) just before impact, (b) during impact and (c) after impact.
14
The data for the critical failure speeds for the two types of adhesives, plotted below in
12
Patch Speed [m/s]
10
Exp: Methacrylate Jonas-Lambert: Methacrylate Exp: Epoxy Jonas-Lambert: Epoxy
8
6
4
2
0 50
100
150
200 250 300 350 Projectile Speed [m/s]
400
450
Figure 3-4, utilizes the Lambert-Jonas approximation for ballistic impact as a best-fit model. The Lambert-Jonas [13] correlation is based on the conservation of energy between the impactor and target to predict the ballistic limit, or
, of a material based on experimental ballistic tests. The concept of the
patch detaching from the back plate during total adhesive rupture is akin to the ballistic limit of projectile perforation and thus the Lambert-Jonas correlation is a good approximation for this type of test. The Lambert-Jonas correlation is given by: " !
where
!
is the residual speed of the target,
#
=
" #
−$
(3.6)
is the incident speed of the projectile, A is a fit parameter
based on the mass ratio of the projectile and target, B is a fit parameter that predicts the CFV, and P is a fit parameter based on the rigidity of the impact. Using P = 2, approximating a rigid collision, the Lambert-Jonas fit plotted for all cases is: !
=%
#
−$
(3.7)
15
12
Patch Speed [m/s]
10
Exp: Methacrylate Jonas-Lambert: Methacrylate Exp: Epoxy Jonas-Lambert: Epoxy
8
6
4
2
0 50 As seen in
100
150
200 250 300 350 Projectile Speed [m/s]
400
450
Figure 3-4, there is a clean rupture for the steel-methacrylate bond. The rupture CFV for the steelmethacrylate bonded specimens is B ≈ 170 m/s. The CFV for the steel-epoxy bond lies between 311 m/s and 343 m/s, with the Jonas-Lambert CFV fit parameter, B ≈ 320 m/s. The CFV values calculated from the Jonas-Lambert model for both adhesives are listed in Table 3-3. The steel-epoxy bonds do not exhibit a clean rupture like the methacrylate. The CFV band is wider for steel-epoxy, leading to less certainty of the dynamic failure point. As explained above, this is typical for a ductile adhesive where void nucleation growth is slower, therefore within this impact velocity range, the crack does not have enough energy to fully propagate. Additionally, this result is indicative that the fracture strain of the epoxy has a wider range of values than the methacrylate, causing the relatively large spread in CFV. Note that in this paper, the Jonas-Lambert fit has been used purely for curve-fitting purposes in order to obtain the CFV from the experimental data.
16
12 Exp: Methacrylate Jonas-Lambert: Methacrylate Exp: Epoxy Jonas-Lambert: Epoxy
Patch Speed [m/s]
10
8
6
4
2
0 50
100
150
200 250 300 350 Projectile Speed [m/s]
400
450
Figure 3-4 Critical failure speed for the two adhesively bonded steel joints.
Table 3-3 Critical Failure velocity based on the Jonas-Lambert model.
Adhesive Methacrylate Epoxy
3.3
Critical Failure Speed (m/s) ~170 ~320
Basic dynamics of the system No direct measurements of impact forces were made for the ballistic impact experiments performed
in the present research; thus to estimate the impact force of the projectile on the target, Newton's second law can be used to calculate the average impact forces. Consider the impulse-momentum diagram shown for the closed system containing the projectile and target, during and after impact in Figure 3-5 below. 17
/ ∆(
mvi 13a.
mvf 13b.
13c.
Figure 3-5 A schematic of the impulse and momentum of the projectile: (a) just before impact, (b) during impact and (c) after impact. Part of the plate (dashed lines) is shown for reference.
From the principle of impulse-momentum in the direction of impact: &=
' (=
) * = )*+ − )*# = ' ∆(
or '=
)-*+ − *# .
∆(
=
)∆*
∆(
(3.8)
(3.9)
where & denotes the impulse imparted to the body, / the average impact force, ) the mass of the projectile, vi the incident projectile velocity before impact, vf the projectile rebound velocity after impact, and ∆t is the impact time. Experimentally the projectile mass, incident velocity and rebound velocity can be readily measured. However, directly measuring the impact time is significantly more challenging. An estimate of the contact time was obtained by increasing the frame rate of the high-speed camera to 280,991 fps (the highest without sacrificing spatial resolution) and repositioning the camera in such a way that the projectile contact event was visible. In these experiments it was found that the target metal plate reflected the mirror image of the projectile and this allowed for a relatively simple visual initiation of the contact. Additionally, the impact flash observed for the higher speed impacts (>250 m/s) served as another helpful benchmark to determine contact initiation. (The impact flash duration from the camera was < 4 µs which was significantly less than the impact duration). The end of the impact event was calculated to be the zero crossing in the tracked velocity-time history of the projectile. With the specified frame rate, the impact time measurement was estimated to have an error of ±3.5 μs.
Contact force was also calculated using Taylor impact theory [14]. Taylor [14] conducted an analysis on the deformation produced by the impact of cylinders against a rigid wall. Taylor’s impact theory predicts that when a cylindrical projectile, shown in Figure 3-6, of length
impacts a target at velocity
18
vi, the following simple non-dimensional relationship can be used to estimate the dynamic yield strength, 23
of the projectile material. 4*#
23
=
2
−5 −
ln
1
(3.10)
5
where x is the length of the undeformed section of the cylinder and L1 is the final length of the projectile. During deformation, the stress within the region that has plastically deformed is assumed to be constant and equal to the dynamic yield stress of the material at that strain rate. *#
89 5 −5 (b)
(a)
Figure 3-6 Sequence of deformation of cylindrical projectile (a) before and (b) after impact against a rigid wall
The beauty of the Taylor approximation is that simple geometric measurements of the projectile after impact can be used to estimate the dynamic yield stress of the material. The projectiles were photographed after each experiment and digital measurements were taken to obtain accurate dimensions of the plastic zone. An example of this technique is shown in Figure 3-7. The Taylor relationship is used to calculate the dynamic yield strength (i.e.
23
in equation 3.10) for each experiment and is plotted in
Figure 3-8. A quadratic least-square curve-fit of the data presented in Figure 3-8 is also plotted. The experimental results shown in Figure 3-8 are for all the ballistic experimental results which include both the epoxy and methacrylate and for velocities above and below the CFVs of the adhesives.
19
/
Figure 3-7 Projectile measurements (all dimensions in mm) after impact.
= 0.103 E
4*# /
4*F 2 G
H − 0.446 E
4*F 2 G
H+1
23
Figure 3-8 Theoretical and experimental results for :; /:= as a function of >?@ A /BCD . The curve labeled ‘Taylor’ is a quadratic polynomial least square fit of the data.
As a further verification, the measured dynamic yield stress was compared with the Johnson-Cook constitutive model. The Johnson-Cook model is a rate-dependent plasticity model to predict a material's stress response under high strain-rate loading. Neglecting temperature effect, the Johnson-Cook model is expressed as [15]:
20
23
where ̅9 =
RS TRU RS
= J + $ 9̅ L M N1 + O ln E
9P
P
H Q
(3.11)
is the effective plastic strain, P the reference strain rate, 9P the applied strain-rate, and
A, B, C, and n are material dependent constants.
The Johnson-Cook constitutive model constants for O1 tool steel were experimentally determined by McClain et al. [16] and are listed in Table 3-4. The experimental data is plotted for comparison in Figure 3-9. Here the experimental dynamic stress
23 was
obtained from Taylor’s approximation (i.e. equation
3.10). It is seen that there is a good fit between the measured values for the dynamic stress and the Johnson-Cook model.
Table 3-4 Johnson-Cook parameters for O1 tool steel (McClain et al. [16]).
A (MPa) B (MPa) C(-) n(-) P (s T 9P (s T
391.3 723.9 0.1144 0.3067 1 103
21
Figure 3-9 Johnson-Cook constitutive model for O1 tool steel compared with experimental data.
The projectile impact force F can now be estimated using the dynamic stress as: =
23 9
(3.12)
where Ap is the plastic area which is the entire area of the projectile that has come in contact with the patch (Ap = π Dp2/4 in Figure 3-6). The average impact force for various projectile speeds is shown in Figure 3-10. Note that this experimental approach cannot recreate a force-time history plot, thus leaving the peak force unknown. Figure 3-10 also compares the average impact force as calculated using projectile impulse and contact time estimated with the high-speed camera (i.e. equation 3.8) to the Taylor approximation. As shown, the high-speed camera method has a much larger scatter than the Taylor approach and is thus potentially a worse approximation of the impact duration than the Taylor method.
22
Figure 3-10 Average impact force as a function of projectile velocity utilizing the Taylor impact approximation and the projectile’s impulse and contact time as measured with the high-speed camera.
The average impact force of the projectiles (as calculated from the Taylor approximation) at the experimental specimen’s CFVs are listed in Table 3-5. This table also shows a comparison between the dynamic and static strengths of the bonds. The so-called strength of the bond is calculated as the failure load divided by the bond area and oversimplifies the complex dynamic stresses due to impact. As such, the strength is an average for the full bond length and could be a useful parameter for design purposes. Furthermore, Table 3-5 clearly illustrates the dynamic effect within the bond. The dynamic strength of the epoxy is 3.5 times higher than that of the static strength, while the dynamic strength of the methacrylate is more than double its static strength.
Table 3-5 Average impact force and strengths at CFV for the two adhesives.
Adhesive Methacrylate Epoxy
Incident Speed (m/s) ~170 ~320
Projectile Impact Force (kN) 78 119
Static Strength (MPa) 14 13
Dynamic Strength (MPa) 31 47
23
3.4
Residual Strength For some epoxy bonded specimens, within the CFV range, there is visible cracking in the bond, yet
the patch remains attached to the back plate. This observation led to testing the residual strength of the unbroken specimens. Shown below in Figure 3-11 are the results for the quasi-static tests for all material combinations including both the virgin and the post-impact specimens. Three virgin (i.e. not subjected to impact) specimens for each adhesive were tested. The results from these tests are listed below in Table
Stress [MPa]
3-6 for visualization purposes. The data were fitted with an exponential curve.
Figure 3-11 Residual strength of methacrylate and epoxy bonds after impact.
Table 3-6 Projectile velocity where bond line stress is equal to B/A
Joint Materials Steel-Methacrylate Steel-Epoxy
B/A (MPa) 6.8 6.6
Velocity (m/s) ~100 ~300
24
These residual strength tests results show a degradation in bond strength as the dynamic impact force increases in magnitude. The residual strength of methacrylate adhesive bonds degrade at a much faster rate than the epoxy bonds, indicative of a brittle failure at high loading rates, while the slower degradation within the epoxy indicates some ductility at high loading rates. It has been shown by Gledhill et al. [17] and Kinloch et al. [12] that three distinct types of crack propagation may be observed in adhesives. These are defined as: (A) Stable Ductile Propagation where the crack grows steadily in a controlled manner and the crack propagation rate is constant. The fracture surfaces will be rough and torn in appearance. This type of crack growth is often observed at higher test temperatures or low-test rates. (B) Unstable Brittle Propagation where the type of crack growth is essentially brittle in nature, but the crack propagates intermittently in a stick-slip manner. This type of crack growth is associated with an increase in crack-tip plasticity and is typically observed at a somewhat higher test temperature or intermediate test rate. (C) Stable Brittle Propagation where the fracture surfaces are relatively featureless and smooth, which is indicative of brittle failure. This type of crack growth is associated with lower test temperatures or hightest rates. These three regimes can be seen from the post mortem micrographs of the failed specimens. In Figure 3-12 it is apparent that the fracture surface is different for the static and impact loading for methacrylate. The fracture surface from the slow test-rate (quasi-static) tests appeared to be rough and torn, corresponding to a Type A failure. The fracture surface for the specimen that failed upon impact corresponded to a Type C failure, which is indicative of a brittle fracture. The fracture surface of the specimen loading in the intermediary range was similar in appearance, which indicated that either this adhesive does not demonstrate Type B failure, or the ductile to brittle transition happens too quickly for observation.
1 mm
1 mm
(a)
1 mm
(b)
(c)
Figure 3-12 Micrograph of the methacrylate adhesive fracture surface for failure from (a) quasi-static test rate, (b) quasi-static residual strength testing after non-failure impact (71 m/s), and (c) impact loading (175 m/s)
25
In Figure 3-13 it is apparent that the fracture surface is different for the static and impact loading for epoxy. The fracture surface from the low test-rate (quasi-static) tests appeared to be rough and torn, corresponding to a Type A failure. The fracture surface for the specimen that failed upon impact corresponded to a Type C failure, which is indicative of a brittle fracture. The fracture surface on the specimen that did not fail upon impact (Figure 3-12 b), but rather upon quasi-static loading after impact, appeared to have a surface similar in appearance to both Type A and Type B fracture surfaces. This is indicative of the transition between ductile to brittle failure.
1 mm
1 mm
(a)
1 mm
(b)
(c)
Figure 3-13 Micrograph of the epoxy adhesive fracture surface for failure from (a) quasi-static test rate, (b) quasi-static residual strength testing after non-failure impact (305 m/s), and (c) impact loading (312 m/s)
Depending on the failure mode, a new failure definition is required. We suggest that for ductile adhesives, the CFV should be redefined as the projectile velocity at which the residual strength has been reduced by 50% of the virgin static strength (shown as σ/2 in Figure 3-11). The choice of defining the CFV at 50% of the virgin static strength is relatively arbitrary and is left to the discretion of the designer; here it is chosen to give a safety factor of 2 most commonly used in design. For brittle adhesives, the CFV should be left as the rupture speed. This allows for a practical definition of impact resistance of an adhesive joint that a designer could use to estimate joint survivability during and after impact.
3.5 Energy Absorption A comparative test outlined by Adams and Harris [18] suggests that an estimation of the energy imparted to the adhesive after fracture can be found by testing an unbonded specimen. The difference in kinetic energy between the unbonded and bonded experiments should provide an estimate for the energy absorbed by the adhesive provided that the deformation in both cases is the same. Though this result may be lower because only the translational kinetic energy can be experimentally calculated. Other energy in the system such as energy due to vibration, rotational kinetic energy, damping etc. cannot be calculated. 26
The underlying assumption in the experimental method is that the overall stiffness of the adhesive is small in comparison to the overall stiffness of the patch and back-plate and thus do not affect the overall dynamics of the impact. To have an empirical measurement of the energy absorbed due to the presence of each adhesive, additional ballistic tests were performed. The experimental setup is similar to the tests described above, except that the patch is now unbonded and held to the back plate with a low strength adhesive tape. In the ballistic test, all the input energy into the system consists of the initial kinetic energy of the projectile. Upon impact, the energy is converted into various other forms of energy including plastic dissipation in the projectile and patch, fracture of the adhesive layer, heat and lastly as kinetic energy of the rebounding projectile and the free-flying patch. Post-impact, the translational kinetic energy of the patch can be calculated by measuring its velocity through a digital tracking software. It is impractical to try to account for all of the energy contributions. However, the sum of all the unaccounted absorbed energies and final kinetic energy must equal the energy input. Here we assume that the difference in the final measured kinetic energies is equal to the difference in total absorbed energy by the adhesive for the two tests with the same initial input energy. After completing the bonded and unbonded tests, it is seen that the deformations in the projectile and patch are similar for both cases. Measurements of the projectile lengths before and after impacts for both the bonded and unbonded cases at comparable projectile velocities were within 10% of each other over the range of tested projectile velocities. Thus, the method outlined above is a practical measure for the energy absorption of the adhesive. For the ballistic bending specimens, tests at the CFV defined by residual strength will not cause the patch to detach; therefore, there is no kinetic energy of the patch after the impact. The resulting kinetic energy of an unbonded patch impacted at the same velocity is considered to be the energy absorbed due to the presence of the adhesive. Figure 3-14 shows the unbonded patch energies and the bonded patch energies for all experiments. The critical energy, i.e. the projectile kinetic energy at the CFV determined by the residual strength, is also shown. The intersection of this critical energy and the linear fit denotes the energy absorbed by the adhesive. For instance, the kinetic energy at the CFV (i.e. the critical energy) of the methacrylate bond is 134.5 J.
The patch kinetic energy at this critical energy (the energy
absorption of the bond) is 4.1 J, or the energy absorbed per unit area of the bond is 1.6 kJ/m . The absorbed impact energy results are presented in Table 3-7.
27
Patch Kinetic Energy [J]
Epoxy
Methacrylate
Figure 3-14 Energy absorption for the methacrylate and epoxy adhesives
Table 3-7 Adhesive energy absorption at CFV for the two adhesives.
Adherend-Adhesive Steel-Methacrylate Steel-Epoxy
Critical Projectile Energy (from B/A (J) 135 384
Energy Absorption (J) 4.0 16
Energy Absorption YZ/[A 1.6 6 28
4
Conclusions We have presented a novel experimental protocol for the dynamic characterization of adhesively
bonded joints under ballistic impact loading. The test is meant to be a dynamic analog to the commonly used static blister test. The new dynamic test has the advantages that it requires relatively small scale test specimens and that standard ballistic penetration equipment can be used. The parameters obtained through this testing program include: (1) the critical failure velocity for each bond type, (2) the average critical failure force and energy, (3) the energy absorbed by the adhesive under impact loading, and (4) the nature of the bond failure (cohesive or interfacial). The proposed method relies only on measuring the velocities of the projectile and patch obtained from a high-speed camera which is standard for any ballistic testing facility. Relatively accurate average impact forces also can be obtained using Taylor impact theory and measurements of the projectile deformation after impact. The current study has also shown that adhesives that have nearly identical strengths under static loading (such as the methacrylate and the epoxy adhesives used in the study) can perform substantially differently under impact loading. The epoxy was seen to withstand an average projectile impact force 40% higher than that of the methacrylate. Furthermore, the dynamic strength of the epoxy is shown to be 3.5 times greater than that of its static strength, while the dynamic strength of the methacrylate is more than double compared to its static strength. Thus, static strength is not a good indication of dynamic strength and should be separately characterized for adhesives operating under impact conditions. Residual strength tests were conducted to determine the loss of strength of the adhesive bond as the dynamic load approached the failure load. From these tests it was apparent that there was a structural degradation within the adhesive bond as the dynamic load increased. Micrographs of the failed adhesive surfaces showed that the epoxy adhesive behaved more like a ductile material under dynamic loading, while the methacrylate behaved more like a brittle material. The adhesive fracture surfaces were observed to be cohesive with the fracture surface being through the adhesive (as opposed to interfacial), indicating that the inherent strength of the adhesive was being measured. (The test was not designed to measure interfacial strength which should be characterized separately and is not part of the present study). An auxiliary experiment was devised to determine the energy absorption of the adhesive bond. The comparative test between the unbonded and bonded joint assumed the only difference in energy was due to the contribution of the adhesive. At failure, the epoxy adhesive was shown to absorb nearly 4 times more energy compared to the methacrylate. Again this is in stark contrast to the static butt-joint tests which showed that the epoxy only had approximately 30% greater energy absorption than the methacrylate adhesive.
29
5
Acknowledgements
This work was supported by U.S. Army- TARDEC (currently US Army- GVSC) under contract #69201511 through NAMC. We thank Dr. Robert Jensen of ARL and Daniel Schaffren of US Army – GVSC (previously TARDEC) who provided their expertise on surface preparation and bonding. Additionally, we thank our colleagues Dr. Bruno Zamorano and Dr. Jack Chiu for their insightful discussions and contribution to this work.
References [1]
[2] [3]
[4]
[5]
[6] [7]
[8] [9] [10]
[11] [12]
[13]
[14]
C. Galliot, J. Rousseau, and G. Verchery, “Drop weight tensile impact testing of adhesively bonded carbon/epoxy laminate joints,” International Journal of Adhesion and Adhesives, vol. 35, pp. 68–75, 2012. H. A. Perry, Adhesive Bonding of Reinforced Plastics. McGraw-Hall, 1959. R. D. Adams and J. A. Harris, “A critical assessment of the block impact test for measuring the impact strength of adhesive bonds,” International Journal of Adhesion and Adhesives, vol. 16, no. 2, pp. 61–71, 1996. L. Goglio, L. Peroni, M. Peroni, and M. Rossetto, “High strain-rate compression and tension behaviour of an epoxy bi-component adhesive,” International Journal of Adhesion and Adhesives, vol. 28, no. 7, pp. 329–339, 2008. A. A. Bezemer, C. B. Guyt, and A. Vlot, “New impact specimen for adhesives: optimization of high-speed-loaded adhesive joints,” International Journal of Adhesion and Adhesives, vol. 18, no. 4, pp. 255–260, 1998. D. P. Updike, “Effect of adhesive layer elasticity on the fracture mechanics of a blister test specimen,” International Journal of Fracture, vol. 12, no. 6, pp. 815–827, 1976. T. Andersson and U. Stigh, “The stress-elongation relation for an adhesive layer loaded in peel using equilibrium of energetic forces,” International Journal of Solids and Structures, vol. 41, no. 2, pp. 413–434, 2004. H. Chai, “Experimental Evaluation of Mixed-mode Fracture in Adhesive Bonds by Herzl Chai,” Experimental Mechanics, vol. 34, no. 4 December, pp. 296–303, 1992. G. P. Zou, K. Shahin, and F. Taheri, “An analytical solution for the analysis of symmetric composite adhesively bonded joints,” Composite Structures, vol. 65, no. 3–4, pp. 499–510, 2004. R. Jensen, D. Deschepper, D. Flanagan, G. Chaney, and C. Pergantis, “Adhesives : Test Method , Group Assignment , and Categorization Guide for High-Loading- Rate Applications – Preparation and Testing of Single Lap Joints ( Ver . 2 . 2 , Unlimited ),” 2016. J. A. Zukas, Penetration and Perforation of Solids. Impact Dynamics. 1982. A. J. Kinloch, S. J. Shaw, D. A. Tod, and D. L. Hunston, “Deformation and fracture behaviour of a rubber-toughened epoxy: 1. Microstructure and fracture studies,” Polymer, vol. 24, no. 10, pp. 1341–1354, 1983. J. P. Lambert and G. H. Jonas, “Towards Standardization in Terminal Ballistics Testing: Velocity Representation,” no. BRL-1852, Army Ballistics Research Lab Abderdeen Proving Ground MD, January, 1976. G. Taylor, “The Use of Flat-Ended Projectiles for Determining Dynamic Yield Stress. I. 30
Theoretical Considerations,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 194, no. 1038, pp. 289–299, 1948. [15] G. R. Johnson and W. H. Cook, “Fracture characteristic of three metals subjected to various strains, strain rates, temperatures and pressures,” Engineering Fracture Mechanics, vol. 21, no. 1, pp. 31–48, 1985. [16] B. McClain, S. A. Batzer, and G. I. Maldonado, “A numeric investigation of the rake face stress distribution in orthogonal machining,” Journal of Materials Processing Technology, vol. 123, no. 1, pp. 114–119, 2002. [17] R. A. Gledhill, A. J. Kinloch, S. Yamini, and R. J. Young, “Relationship between mechanical properties of and crack progogation in epoxy resin adhesives,” Polymer, vol. 19, no. 5, pp. 574– 582, 1978. [18] R. D. Adams and J. A. Harris, “The influence of local geometry on the strength of adhesive joints,” International Journal of Adhesion and Adhesives, vol. 7, no. 2, pp. 69–80, 1987.
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