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Research Papers

Interfacial Strength Between Single Wall Carbon Nanotubes and Copper Material: Molecular Dynamics Simulation OPEN ACCESS

[+] Author and Article Information
Ibrahim Awad

Department of Mechanical Engineering,
University of Connecticut,
191 Auditorium Road,
Unit 3139, Storrs, CT 06269
e-mail: ibrahim.awad@uconn.edu

Leila Ladani

Department of Mechanical Engineering,
University of Connecticut,
191 Auditorium Road,
Unit 3139, Storrs, CT 06269
e-mail: lladani@engr.uconn.edu

Manuscript received December 4, 2013; final manuscript received February 20, 2014; published online March 12, 2014. Assoc. Editor: Abraham Wang.

J. Nanotechnol. Eng. Med 4(4), 041001 (Mar 12, 2014) (6 pages) Paper No: NANO-13-1084; doi: 10.1115/1.4026939 History: Received December 04, 2013; Revised February 20, 2014

Due to their promising mechanical and electrical properties, carbon nanotubes (CNTs) have the potential to be employed in many nano/microelectronic applications e.g., through silicon vias (TSVs), interconnects, transistors, etc. In particular, use of CNT bundles inside annular cylinders of copper (Cu) as TSV is proposed in this study. To evaluate mechanical integrity of CNT-Cu composite material, a molecular dynamics (MD) simulation of the interface between CNT and Cu is conducted. Different arrangements of single wall carbon nanotubes (SWCNTs) have been studied at interface of a Cu slab. Pullout forces have been applied to a SWCNT while Cu is spatially fixed. This study is repeated for several different cases where multiple CNT strands are interfaced with Cu slab. The results show similar behavior of the pull-out-displacement curves. After pull-out force reaches a maximum value, it oscillates around an average force with descending amplitude until the strand/s is/are completely pulled-out. A linear relationship between pull-out forces and the number of CNT strands was observed. Second order interaction effect was found to be negligible when multiple layers of CNTs were studied at the interface of Cu. C–Cu van der Waals (vdW) interaction was found to be much stronger than C–C vdW's interactions. Embedded length has no significance on the average pull-out force. However, the amplitude of oscillations increases as the length of CNTs increases. As expected when one end of CNT strand was fixed, owing to its extraordinary strength, large amount of force was required to pull it out. Finally, an analytical relationship is proposed to determine the interfacial shear strength between Cu and CNT bundle.

FIGURES IN THIS ARTICLE
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Since their discovery by Iijima [1], CNTs have shown many superior mechanical properties such as Young's modulus and tensile strength [2-4]. CNTs have been utilized in many different applications from composite materials and biomedical applications to microelectronics and interconnect in hopes to enhance some property or functionality. Vast research is dedicated to inclusion and use of CNTs in micro/nanoelectronics. However, issues with electrical and mechanical integrity of CNTs at the interface of existing materials have been prohibitive. Due to the very small scale (nanoscale and microscale), mechanical and electrical testing of a single CNT strand is overly challenging and not very accurate. At this scale, simulation can be used as guiding tool to provide insights on mechanical integrity and long term reliability of these interconnects. The forces at the interface of CNTs and Cu are governed by molecular interactions. Therefore, regular finite element simulations at the continuum level are not capable of modeling this interface behavior. MD simulation is used, initially, to determine the interface behavior of CNTs and Cu material.

The interface between CNT and other materials has been studied by many scientists. Maiti and Ricca [5] have theoretically investigated the wetting properties of CNTs to different metals e.g., Au, Pt, and Pd with different configurations using density function theory. Nemec et al. [6] applied ab initio density function theory to distinguish between poor and strong contacts of metals to CNTs and observed superiority of Pd to Ti in metal-nanotube hybridization. They have also suggested that the optimum metal-nanotube contact combines a weak hybridization with a large contact length of few hundred nanometers between the metal and the nanotube. Banhart [7] has reviewed the interaction between metals and CNTs in different material systems. The interface reaction between the CNTs and metallic materials are classified into side and end contact interactions. It is assumed that, for weakly bonded metal to CNT contacts, only van der Waals (vdW) interactions exist and covalent bonds are absent. Tsuda et al. [8] experimentally evaluated the interfacial shear strength (IFSS) of CNT/poly-ether-ether-ketone (PEEK) composite. An individual multiwalled CNT (MWCNT) was pulled out from the composite using a testing system installed inside a scanning electron microscope. The pull-out force was measured by the deformation of an atomic force microscope (AFM) cantilever. The IFSS of MWNT/PEEK composite was measured as 3.5–7 MPa. However, when specimens were heat treated, the IFSS increased to 6–14 MPa as a result of interfacial bonds' recovery. The results agree with the macroscopic stress–strain behavior of MWNT/PEEK. The experiments have shown that vdW forces are dominant in the interface. The authors have found that the reported results of IFSS from MD simulations are small (<10 MPA) when considering vdW interactions only. Wernik et al. [9] investigated the interfacial properties of CNT reinforced polymers through atomistic-based continuum model by simulating CNT pull-out experiment. The interface between CNT and polymer matrix was constituted by Lennard Jones constitutive relation that represents vdW interactions. Although pull-out force is not affected by CNT's embedded length, the authors claimed the IFSS decay significantly with the embedded length. They calculated IFSS by dividing maximum force by interfacial area of various CNT lengths. In the same way, increasing CNT diameters increases pull-out forces but decreases IFSS. Their study also illustrates the effect of different CNT capping scenarios showing that incorporating an end cap in the simulation yields high initial pull-out peaks that better correlate with experimental findings. Kim et al. [10] examined the effect of interfacial bonding between CNT and Si on the mechanical properties. Only vdW interactions are considered in C–Si and are represented by Lennard Jones relationship. They observed that Young's modulus, maximum tensile strength and toughness are increased steadily with increasing Si–C bonding strength (ε, the potential well depth in Lennard Jones constitutive relationship). Toprak and Bayazitoglu [11] created MD simulation to predict the thermal conductivity of a single wall CNT filled with a Cu nanowire for different lengths with different temperatures at the two ends; 320 °K and 280 °K. It was found that the thermal conductivity of the CNT/Cu nanowire is higher than that of a pure CNT and estimated to be lower than that of a pure Cu nanowire. Hartmann et al. [12] performed a tensile test and pull-out test of a single walled CNT embedded inside gold using MD simulation. They reported the influence of the embedded length and the temperature on the pull-out force. The results show that embedded length has minor effect. The temperature has a small effect on the maximum pull-out force as well.

Many studies have investigated the interaction between polymers and CNTs. Studies in the area of interaction between metals and CNTs are scarce. However, metal composites with CNTs have promising mechanical and electrical properties that make them potentially suitable for many micro/nanoelectronic applications e.g., TSVs, interconnects, transistors, etc. Therefore, a study of the mechanical interactions between the CNTs and the metallic material typically used for interconnects such as Cu is of paramount importance. In this study, MD simulation is used to explore the interfacial strength and behavior of metallic CNTs at the interface of Cu. The interface properties extracted from this study can be beneficial in multiscale modeling of the hybrid or composite material made using CNTs and Cu.

Large-scale atomic/molecular massively parallel simulator (LAMMPS) code [13] was employed to simulate the force-displacement relations in a simple model that consists of SWCNTs interfaced with a Cu slab. Our study focuses on TSVs. Figure 1 shows a cylindrical TSV made of vertically oriented CNTs embedded inside an annular cylinder of Cu. A bundle of embedded CNTs contains thousands of them, which makes it challenging and time consuming to model by MD. To make the model computationally feasible, only a few strands of CNT have been modeled as shown in Fig. 1. Displacement controlled loading has been applied to pull the CNTs out of the Cu slab. The resulted force-displacement curves show the interfacial strength.

The structure is built by atomic simulation environment ASE [14] using Python coding software. For the current case, a few CNTs of chirality (7,7) (armchair electrically conductive CNT) and a length of 26 Å have been modeled. Cu slab is assumed to be FCC (100) in the direction of CNT axis. Embedded atom method potential [15] is used for interatomic potential between Cu atoms. Adaptive intermolecular reactive empirical bond order (AIREBO) [16,17] interatomic potential is used for carbon atoms as [18-20]. (AIREBO) model is a function to calculate the potential energy of covalent bonds, interatomic force and the long-ranged interaction between atoms. For the interatomic potential between Cu and carbon atoms, only vdW potential occurs and that has been implemented in LAMMPS by the use of Lennard Jones interatomic potential [11,21]. The Lennard Jones parameters used for C–Cu interactions are (σ = 3.088 Å and ε = 0.025 eV), where σ is the finite distance and ε is the depth of the potential well. For the intertube (CNT-CNT) potential only vdW interaction is considered as in Refs. [22-24]. Lennard Jones parameters used for CNT-CNT interaction are (σ = 3.4 Å and ε = 0.00284 eV).

The energy of the structure was first minimized using conjugate gradient algorithm [12,20]. The minimization was done to place the atoms in more stable positions where it is geometrically optimized. The system was then heated up to the desired temperature using NPT ensemble where N, the number of atoms, P, the pressure of the system and T, the temperature, are kept constant. The pressure was kept at zero to mimic the experimental condition of an AFM experiment conducted at vacuum pressure. The system is heated to 1 °K for 50 ps as an arbitrary value because it was reported that temperature has little effect on the pull-out force [12]. NPT equilibration process is followed by NVE and Berendsen thermostat [25] integrations for 50 ps where V is the volume and E is the total energy which were kept constant. Berendsen thermostatkeeps the temperature constant at 1 °K. Displacement was applied on carbon atoms using discrete displacements in a displacement controlled manner. The two uppermost rings of the CNT were subjected to discrete displacements of 0.1 Å until the CNT strand is pulled out completely. The system is equilibrated using NVE ensemble and Berendsen thermostat for 10 ps after each step in order to avoid energy build-up and destabilization. Both NVT and NVE combined with Berendsen thermostat are used in literature to create a thermostat in order to keep the temperature constant and perform time integration. NVE and Berendsen thermostat function as NVT equilibration to converge to the environment temperature after applying the displacement [12,26,27]. NVT ensemble performs both Nose-Hoover thermostating and time integration while Berendsen thermostat performs only Nose-Hoover thermostating. Therefore, another ensemble is necessitated to perform time integration, which is NVE. When combined with Berendsen thermostat, NVE does not keep the energy constant and the system exchanges energy with the environment to bring the temperature down to 1 °K. To make sure that the effect are the same a model was run with NVT and NVE combined with Berendsen thermostat. As shown in Fig. 2 the results are identical.

First, the effect of the number of aligned CNTs is explored. Figure 3 depicts the simulation models for four arrangements at different stages; before minimization and equilibration, after minimization and equilibration, during pull-out and after pull-out. The last vertical layer of Cu atoms not in contact with the CNTs is fixed in all directions during simulation. Pull-out force is calculated by summing up carbon atoms' forces in Z-direction.

Figure 4 shows the resulted force-displacement curves. The common behavior of the four simulated arrangements is that the force increases to a certain value at the beginning then it oscillates with constant decreasing amplitude until force drops to zero at the end of the pull-out. These oscillations are due to vdW interactions' separation and re-attraction with Cu atoms i.e., (stick-slip behavior [28]); when separation occurs there is a sudden drop in force but this is followed by re-attraction of C–Cu vdW interactions with adjacent atom of CNT. After the first peak, force oscillates around a constant average value until the last three maxima when significant deterioration is observed.

Generally, fracture is neither observed in CNT or Cu. The CNT was completely pulled-out with no further rearrangement in the Cu atoms. So, the separation is attributed to the weak interatomic interaction between CNT and Cu modeled by Lennard-Jones potential. According to Amonton's friction law with adhesion [29], the total friction force is given byDisplay Formula

(1)F=μL+Fo

where μ, L, and Fo are the coefficient of friction, external normal force, and internal force due to adhesion, respectively.

The external normal force may come from nonuniformity of connection between CNT and Cu, such as waviness of CNT and mismatch in coefficient of thermal expansion (CTE) or an applied external force. In this study, there is no applied normal force (L) and the interface is deemed perfect. Thus, the force to consider is only the internal force due to adhesion (Fo) i.e., vdW force that dominates the pull-out force.

Figure 5 shows the maximum, force (F), average force (Favg), and the maximum amplitude (Fmax − Fmin) of oscillation for each arrangement. It is clear that (F) and (Favg) are linearly proportional with the same slope to the number of adjacent CNTs (N). The trend of the maximum and average forces could be estimated for more CNTs by extrapolating these relationships

From Fig. 5, the maximum amplitude is almost constant in all cases. This is discussed in the next part when embedded length effect is studied.

The effect of the CNT embedded length has been studied as well. Different lengths of single CNTs are simulated. The simulated lengths are 26 Å, 36 Å, and 52 Å. Figure 6 shows the resulted pull-out force-displacement curves for these three cases. As seen in this figure, the average force is the same for CNTs with different lengths. However, the amplitude of the oscillation is increasing as the length of the CNT increases. The amplitude is believed to be the result of summation of the forces between each pair of CNT-Cu atoms in stick and slip situation. As the number of CNT atoms that are in contact with Cu atoms increases, the force summation increases, resulting in larger amplitude in the oscillation in longer CNTs. That could explain the constant amplitude observed in Fig. 5, as the embedded length is the same for all the cases in that figure.

To evaluate the adhesion between the CNTs themselves, in one case, the load was only applied on one CNT while the other CNT strand was left standing freely adjacent to it. The model and the force displacement results are shown in Fig. 7. As seen in this figure, the amount of force that is required for this case is less than the force applied to both CNTs. One CNT moves out of Cu and the other remains attached to it. This is because C–Cu vdW interaction is stronger than CNT-CNT vdW interaction. As the number of the dominant C–Cu interactions is fewer in this case, pull-out force will decrease as shown in Fig. 7. This case is also compared with pulling-out one CNT (Fig. 7). The force required to pull-out one standalone CNT is less than the force of the current case. This is attributed to that more force is required to overcome, both, C–Cu and CNT-CNT vdW interactions instead of only C–Cu interactions, however, C–Cu interaction is still dominant as it has major effect on the pull-out force.

In the case of CNT bundle inside an annular copper cylinder, the CNTs may also be connected to the bottom of TSVs (end-contact). Therefore the boundary condition on the bottom side of the CNTs may play a significant role. Therefore, it's important to evaluate the effect of end contact connections on the interfacial strength. For this reason, another model is built in which the boundary condition for the CNTs base was changed such that the two lowermost rings of one of the CNTs were completely fixed. As expected, witness to strong bond between CNT atoms, the amount of force that is required to pull out the CNTs increases exponentially to mid-hundred eV/A as seen in Fig. 8. The oscillating behavior is eliminated in the results or perhaps absorbed in the magnitude of this force and not discernible. In this case, the CNT behaves as being loaded in tensile test and what is measured in load-displacement curve is essentially the strength of the CNT strand. After maximum force is attained, the force drops in several increments. Each increment corresponds to a C–C bond breaking. After all the bonds are broken, the forces reaches zero.

If CNTs are used as bundle in interconnects, inevitably some CNTs will be in contact with Cu and some will be in contact with other CNTs and won't have a direct contact with Cu. It is essential to know if adding more CNT strands which are not directly adjacent to metallic material has the same effect as adding them adjacent to Cu. So in another arrangement, the original case of two CNTs adjacent to the Cu was changed and one CNT strand was added on top of two CNTs such that it did not have any contact with Cu. This arrangement is shown in Fig. 9.

Interestingly, the amount of average force that is required to pull-out new three strands of CNTs in this case is the same as the amount of average force to pull out two CNTs which are directly adjacent to Cu (Fig. 10). The average force is the force used in calculation of the shear strength and therefore of more interest to this study.

After pull-out force calculation, interfacial shear strength (S) can be determined. In this study, we assumed a perfect interface. There is no waviness of CNT, mismatch in coefficient of thermal expansion (CTE) or an applied normal force. So, from Eq. (1), we getDisplay Formula

(4)F=Fo

Consequently, the interfacial shear strength will be induced only by C–Cu vdW interaction. If we assumed the common assumption that (S) is constant along the embedded length and (S) is calculated by dividing maximum (F) by interfacial area as in Ref. [9], pull-out force (F) will vary with the change of length during pull-out, which contradicts with the previous force-displacement results. Thus, this assumption is inappropriate for a perfect interface. Moreover, according to this assumption, when CNT's length is extremely long (∞), the interfacial shear strength approaches to zero, which is irrational. Therefore, shear strength is only contributed by separation and rejoining of C atoms i.e., (stick-slip) behavior as shown in Fig. 11. The same rationale was used to obtain the interfacial shear strength by Li et al. [30-32]. When an atom of C is pulled out of two Cu atoms the oscillatory behavior takes place. Apparently, as seen in Fig. 11, oscillations are attributed to stick-slip behavior. The wave length of this oscillation is (a). This process repeats itself every specific displacement (a) and takes place along the CNTs. Moreover, (a) denotes the atomic spacing of Cu. The work (w) done by this force to overcome vdW interaction is given by the area under the curve

where (Favg) is the average force.

On the other handDisplay Formula

(6)w=0aF(x)dx

As F(x) is induced by the interfacial shear strength (τ), and (τ) is assumed to be uniform along the distance (a)Display Formula

(7)w=0aτcadx

where (c) is the interfacial length For example, in the case of two CNTs in contact with Cu (Fig. 12), (c) is the distance given by (c1 + c2)

From Eqs. (5)–(7)Display Formula

(8)w=Favga=0aτcadxFavg=τc(x)0a=τcaτ=Favgca

(Favg) could be predicted from Eq. (3). From Fig. 12, only 90% of C atoms, of both strands, are in contact with Cu. Therefore, for a bundle of CNTs, (c) is 0.9 (2πr), where r is the radius of the bundle. Thus, interfacial shear strength could be predicted.

Molecular Dynamics simulation was employed to examine the interfacial strength of CNT/Cu interface. Many arrangements of CNT/Cu have been simulated to study their effect. From MD simulation, increasing the number of CNTs in contact with Cu linearly increases the pull-out force. This relationship can be used to predict the total pull out force for a bundle of CNTs. Embedded length has no effect on the average pull-out forces. Only amplitude of oscillation increases because of (stick-slip) behavior but the average force is almost the same. When one CNT strand adjacent to another CNT strand and Cu slab is pulled-out of Cu, C–Cu vdW interaction was found to be stronger than C–C vdW interaction. The CNTs were found to have a very strong C–C bonding. Adding interior CNTs which are not in contact with Cu, will not affect the value of average pull-out force. Interfacial shear strength is independent of the embedded length but dependent on the average force (Favg) and work done by the pull-out force. The interfacial shear strength can be predicted for a bundle of CNTs by considering the previous effects.

This paper is based upon work supported by the National Science Foundation under CMMI Grant No. 1415165. The authors greatly appreciate the support from NSF. We also thank University of Connecticut for the use of their computational facilities

 

 Nomenclature
  • F =

    total friction force

  • Favg =

    average pull-out force

  • Fo =

    internal force due to adhesion

  • L =

    normal force

  • Μ =

    coefficient of friction

  • N =

    number of adjacent CNT

  • S =

    interfacial shear strength

  • w =

    work done by the pull-out force

  • x =

    displacement

  • τ =

    interfacial shear strength

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References

Iijima, S., 1991, “Helical Microtubules of Graphitic Carbon,” Nature, 354(6348), pp. 56–58. [CrossRef]
Jorio, A., Dresselhaus, G., and Dresselhaus, M., 2008, Topics in Applied Physics, (Carbon Nanotubes: Advanced Topics in the Synthesis, Structure, Properties and Applications) Springer, Berlin, Germany.
Saito, S., Dresselhaus, G., and Dresselhaus, M. S., 1998, Physical Properties of Carbon Nanotubes, Imperial College Press, London.
Harris, P. J. F., 2009, Carbon Nanotube Science: Synthesis, Properties and Applications, Cambridge University, Cambridge, UK.
Maiti, A., and Ricca, A., 2004, “Metal–Nanotube Interactions–Binding Energies and Wetting Properties,” Chem. Phys. Lett., 395(1–3), pp. 7–11. [CrossRef]
Nemec, N., Tománek, D., and Cuniberti, G., 2006, “Contact Dependence of Carrier Injection in Carbon Nanotubes: An Ab Initio Study,” Phys. Rev. Lett., 96(7), p. 076802. [CrossRef] [PubMed]
Banhart, F., 2009, “Interactions Between Metals and Carbon Nanotubes: At the Interface Between Old and New Materials,” Nanoscale, 1(2), pp. 201–213. [CrossRef] [PubMed]
Tsuda, T., Ogasawara, T., Deng, F., and Takeda, N., 2011, “Direct Measurements of Interfacial Shear Strength of Multi-Walled Carbon Nanotube/PEEK Composite Using a Nano-Pullout Method,” Compos. Sci. Technol., 71(10), pp. 1295–1300. [CrossRef]
Wernik, J. M., Cornwell-Mott, B. J., and Meguid, S. A., 2012, “Determination of the Interfacial Properties of Carbon Nanotube Reinforced Polymer Composites Using Atomistic-Based Continuum Model,” Int. J. Solid Struct., 49(13), pp. 1852–1863. [CrossRef]
Kim, B.-H., Lee, K.-R., Chung, Y.-C., and Gunn, L. J., 2012, “Effects of Interfacial Bonding in the Si-Carbon Nanotube Nanocomposite: A Molecular Dynamics Approach,” J. Appl. Phys., 112(4), p. 044312. [CrossRef]
Toprak, K., and Bayazitoglu, Y., 2013, “Numerical Modeling of a CNT–Cu Coaxial Nanowire in a Vacuum to Determine the Thermal Conductivity,” Int. J. Heat Mass Transfer, 61, pp. 172–175. [CrossRef]
Hartmann, S., Wunderle, B., and Hölck, O., 2012, “Pull-Out Testing of SWCNTs Simulated by Molecular Dynamics,” Int. J. Theory Appl. Nanotechnol., 1(1), pp. 59–65. [CrossRef]
Plimpton, S., 1995, “Fast Parallel Algorithms for Short-Range Molecular Dynamics,” J. Comput. Phys., 117(1), pp. 1–19. [CrossRef]
Center for Atomic-Scale Materials Design (CAMd), 2012, ATOMIC SIMULATION ENVIRONMENT, DTU Physics, Technical University of Denmark, Lyngby, Denmark.
Acklandab, G. J., Tichyc, G., Vitekd, V., and Finnisa, M. W., 1987, “Simple N-Body Potentials for the Noble Metals and Nickel,” Philos. Mag. A, 56(6), pp. 735–756. [CrossRef]
Stuart, S. J., Tutein, A. B., and Harrison, J. A., 2000, “A Reactive Potential for Hydrocarbons With Intermolecular Interactions,” J. Chem. Phys., 112(14), pp. 72–86. [CrossRef]
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Figures

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Fig. 5

Pull-out force—Number of CNTs curve

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Fig. 4

Number of aligned CNTs' effect

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Fig. 3

Simulation of aligned CNTs

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Fig. 2

NVT versus (NVE + Berendsen thermostat)

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Fig. 1

Schematic of the TSV and a sample of the molecular dynamics structure used in our study

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Fig. 12

Illustration of the interfacial length

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Fig. 6

Embedded length's effect

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Fig. 7

Point of loading's effect

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Fig. 8

Applicaton of load when CNT strand is completely fixed at one side

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Fig. 9

The MD simulation structure when CNT strand is added to the top

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Fig. 10

Force-displacement curve to show the second order interaction effect

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Fig. 11

Illustration of the work done by pull-out forces

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