# On the Use of a Simplified Slip Limit Equation to Predict Screw Self-Loosening of Dental Implants Subjected to External Cycling Loading

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## Featured Application

**A methodology to study screw self-loosening phenomenon in preliminary design stages of dental implants is presented.**

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Background: Loosening Torque

_{h}and r

_{t}are respectively the screw head and thread effective contact radii obtained by considering the preload to be uniformly distributed under the bolt head and on the thread surface:

#### 2.2. Simplified Model for the Loosening Torque

#### 2.3. Methodology to Study Self-Loosening in Dental Implants

#### 2.4. Experimental Setup

^{®}IIPUCA3313 implant with a 3.3 mm body diameter and a 4.1 mm Universal Platform with a four-lobe anti-rotation connection, a BTI INPPTU44 titanium abutment (used for direct restorations) and an INTTUH retaining screw with TiBlack

^{®}coating (see Figure 4). The half-angle of the thread profile is $\alpha $ = 30° and the helix angle is $\beta $ = 5.75° (0.35 mm pitch). The screw head and thread effective radii are ${r}_{h}$ = 1.115 mm and ${r}_{t}$ = 0.810 mm. The friction coefficients are ${\mu}_{t}={\mu}_{h}=0.17$ for the screw contacts and 0.21 for the implant-abutment contact, as measured in a MicroTest SMT-A/0200 pin-on-disk tribometer (Microtest S.A., Madrid, Spain) in a previous work by the authors (see Figure 5) [36]. The experimental tests were carried out by applying a cyclic load on the implant by means of an INSTRON 8801 servo-hydraulic direct stress test bench (Instron, Barcelona, Spain). Force control was used to apply the load cycles using a DYNACELL

^{TM}2527-129 load cell (±2 kN load range). The dental implant was attached to the specimen holder hole by using Loctite 401, which is an embedding material that meets the specifications of [37].

#### 2.5. Finite Element Model

^{®}19 R1 software (Ansys Iberia S.L, Madrid, Spain) to run the analyses, which consist of two load steps: in the first one, the preload calculated in step 2 of the methodology was applied to the screw via pretension section. As explained, Equation (3) was used to calculate the preload ${F}_{p}$ for each of the three tightening torques applied, namely 232 N the corresponding preload for 10 Ncm, 349 N for 15 Ncm and 465 N for 20 Ncm. In the second load step, the external load $F$ was applied to the abutment through the ring shown in Figure 7 in order to reproduce the experimental conditions described in the previous section. Implant and abutment are made of grade 4 commercially pure titanium (Ti CP4) and the prosthetic screw is made of Ti6Al4V ELI (Ti Gr5). Chemical composition of both materials is described in Table 1. Both materials were modeled as linear elastic, with E = 103 GPa, ν = 0.35 for CP4 and ν = 0.31 for GR5.

^{®}to be used to test the self-loosening state using Equation (8).

## 3. Results and Discussion

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Patterson, E.A.; Johns, R.B. Theoretical analysis of the fatigue life of fixture screws in osseointegrated dental implants. Int. J. Oral Maxillofac. Implants
**1992**, 7, 26–33. [Google Scholar] - Bickford, J.H. Introduction to the Design and Behavior of Bolted Joints. In Introduction to the Design and Behavior of Bolted Joints; CRC Press: New York, NY, USA, 2008; pp. 1–14. [Google Scholar]
- Barbosa, G.S.; da Silva-Neto, J.P.; Simamoto-Júnior, P.C.; das Neves, F.D.; da Gloria Chiarello de Mattos, M.; Ribeiro, R.F. Evaluation of screw loosening on new abutment screws and after successive tightening. Braz. Dent. J.
**2011**, 22, 51–55. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Theoharidou, A.; Petridis, H.; Tzannas, K.; Garefis, P. Abutment screw loosening in single-implant restorations: A systematic review. Int. J. Oral Maxillofac. Implants
**2007**, 23, 681–690. [Google Scholar] - Dixon, D.L.; Breeding, L.C.; Sadler, J.P.; McKay, M.L. Comparison of screw loosening, rotation, and deflection among three implant designs. J. Prosthet. Dent.
**1995**, 74, 270–278. [Google Scholar] [CrossRef] - Mericske-Stern, R.; Geering, A.H.; Bürgin, W.B.; Graf, H. Three-dimensional force measurements on mandibular implants supporting overdentures. Int. J. Oral Maxillofac. Implants
**1998**, 13, 36–43. [Google Scholar] - Stüker, R.A.; Teixeira, E.R.; Beck, J.C.P.; Da Costa, N.P. Preload and torque removal evaluation of three different abutment screws for single standing implant restorations. J. Appl. Oral Sci.
**2008**, 16, 55–58. [Google Scholar] [CrossRef] [Green Version] - Zeno, H.A.; Buitrago, R.L.; Sternberger, S.S.; Patt, M.E.; Tovar, N.; Coelho, P.; Kurtz, K.S.; Tuminelli, F.J. The Effect of Tissue Entrapment on Screw Loosening at the Implant/Abutment Interface of External- and Internal-Connection Implants: An In Vitro Study. J. Prosthodont.
**2016**, 25, 216–223. [Google Scholar] [CrossRef] - Paepoemsin, T.; Reichart, P.A.; Chaijareenont, P.; Strietzel, F.P.; Khongkhunthian, P. Removal torque evaluation of three different abutment screws for single implant restorations after mechanical cyclic loading. Oral Implantol.
**2016**, 9, 213–221. [Google Scholar] - Schwarz, M.S. Mechanical complications of dental implants. Clin. Oral Implants Res.
**2000**, 11, 156–158. [Google Scholar] [CrossRef] - Jeng, M.-D.; Lin, Y.-S.; Lin, C.-L. Biomechanical Evaluation of the Effects of Implant Neck Wall Thickness and Abutment Screw Size: A 3D Nonlinear Finite Element Analysis. Appl. Sci.
**2020**, 10, 3471. [Google Scholar] [CrossRef] - Khraisat, A.; Abu-Hammad, O.; Dar-Odeh, N.; Al-Kayed, A.M. Abutment screw loosening and bending resistance of external hexagon implant system after lateral cyclic loading. Clin. Implant Dent. Relat. Res.
**2004**, 6, 157–164. [Google Scholar] [CrossRef] [PubMed] - Chaar, M.S.; Att, W.; Strub, J.R. Prosthetic outcome of cement-retained implant-supported fixed dental restorations: A systematic review. J. Oral Rehabil.
**2011**, 38, 697–711. [Google Scholar] [CrossRef] - Jung, R.E.; Pjetursson, B.E.; Glauser, R.; Zembic, A.; Zwahlen, M.; Lang, N.P. A systematic review of the 5-year survival and complication rates of implant-supported single crowns. Clin. Oral Implants Res.
**2008**, 19, 119–130. [Google Scholar] [CrossRef] [PubMed] - Simon, R.L. Single implant-supported molar and premolar crowns: A ten-year retrospective clinical report. J. Prosthet. Dent.
**2003**, 90, 517–521. [Google Scholar] [CrossRef] [PubMed] - Aboyoussef, H.; Weiner, S.; Ehrenberg, D. Effect of an antirotation resistance form on screw loosening for single implant-supported crowns. J. Prosthet. Dent.
**2000**, 83, 450–455. [Google Scholar] [CrossRef] - Cavazos, E.; Bell, F.A. Preventing loosening of implant abutment screws. J. Prosthet. Dent.
**1996**, 75, 566–569. [Google Scholar] [CrossRef] - Kirov, D.; Stoichkov, B. Factors affecting the abutment screw loosening. J. IMAB–Annu. Proceeding Sci. Pap.
**2017**, 23, 1505–1509. [Google Scholar] [CrossRef] - Arshad, M.; Shirani, G.; Refoua, S.; Yeganeh, M.R. Comparative study of abutment screw loosening with or without adhesive material. J. Adv. Prosthodont.
**2017**, 9, 99–103. [Google Scholar] [CrossRef] - Yeo, I.-S.; Lee, J.-H.; Kang, T.-J.; Kim, S.-K.; Heo, S.-J.; Koak, J.-Y.; Park, J.-M.; Lee, S.-Y. The Effect of Abutment Screw Length on Screw Loosening in Dental Implants with External Abutment Connections After Thermocycling. Int. J. Oral Maxillofac. Implants
**2014**, 29, 59–62. [Google Scholar] [CrossRef] - Wu, T.; Fan, H.; Ma, R.; Chen, H.; Li, Z.; Yu, H. Effect of lubricant on the reliability of dental implant abutment screw joint: An in vitro laboratory and three-dimension finite element analysis. Mater. Sci. Eng. C
**2017**, 75, 297–304. [Google Scholar] [CrossRef] - Elias, C.N.; Figueira, D.C.; Rios, P.R. Influence of the coating material on the loosing of dental implant abutment screw joints. Mater. Sci. Eng. C
**2006**, 26, 1361–1366. [Google Scholar] [CrossRef] - Park, C.I.; Choe, H.C.; Chung, C.H. Effects of surface coating on the screw loosening of dental abutment screws. Met. Mater. Int.
**2004**, 10, 549. [Google Scholar] [CrossRef] - Yao, K.T.; Kao, H.C.; Cheng, C.K.; Fang, H.W.; Yip, S.W.; Hsu, M.L. The effect of clockwise and counterclockwise twisting moments on abutment screw loosening. Clin. Oral Implants Res.
**2012**, 23, 1181–1186. [Google Scholar] [CrossRef] [PubMed] - Siamos, G.; Winkler, S.; Boberick, K.G. The relationship between implant preload and screw loosening on implant-supported prostheses. J. Oral Implantol.
**2002**, 28, 67–73. [Google Scholar] [CrossRef] [Green Version] - Lang, L.A.; Kang, B.; Wang, R.F.; Lang, B.R. Finite element analysis to determine implant preload. J. Prosthet. Dent.
**2003**, 90, 539–546. [Google Scholar] [CrossRef] [PubMed] - Norton, M.R. Assessment of cold welding properties of the internal conical interface of two commercially available implant systems. J. Prosthet. Dent.
**1999**, 81, 159–166. [Google Scholar] [CrossRef] - Junker, G.H. New criteria for self-loosening of fasteners under vibration. SAE Trans.
**1969**, 78, 314–335. [Google Scholar] - Junker, G.H. Criteria for Self Loosening of Fasteners Under Vibration. Aircr. Eng. Aerosp. Technol.
**1973**, 44, 14–16. [Google Scholar] [CrossRef] - Haviland, G.S. Unraveling the Myths of Fastener World; SAE Technical Papers; SAE International: Warrendale, PA, USA, 1981. [Google Scholar]
- Nassar, S.A.; Yang, X. A mathematical model for vibration-induced loosening of preloaded threaded fasteners. J. Vib. Acoust.
**2009**, 131, 2–13. [Google Scholar] [CrossRef] - Nassar, S.A.; Xianjie, Y. Novel formulation of the tightening and breakaway torque components in threaded fasteners. J. Press. Vessel Technol. Trans. ASME
**2007**, 129, 653–663. [Google Scholar] [CrossRef] - Fort, V.; Bouzid, A.H.; Gratton, M. Analytical Modeling of Self-Loosening of Bolted Joints Subjected to Transverse Loading. J. Press. Vessel Technol. Trans. ASME
**2019**, 141, 1–11. [Google Scholar] [CrossRef] - Motosh, N. Development of design charts for bolts preloaded up to the plastic range. J. Manuf. Sci. Eng. Trans. ASME
**1976**, 98, 849–951. [Google Scholar] [CrossRef] - Juvinall, R.C.; Saunders, H. Fundamentals of Machine Component Design, 5th ed.; John Wiley & Sons, INC: Hoboken, NJ, USA, 2012; Chapter 10; pp. 411–471. ISBN 13 9781118012895. [Google Scholar]
- Armentia, M.; Abasolo, M.; Coria, I.; Albizuri, J. Fatigue Design of Dental Implant Assemblies: A Nominal Stress Approach. Metals
**2020**, 10, 744. [Google Scholar] [CrossRef] - ISO 14801:2007 Dentistry. Dynamic Fatigue Test for Endosseous Dental Implants; ISO: Geneva, Switzerland, 2007. [Google Scholar]
- Horváth, P.; Tóth, P. Nondestructive Bolt Preload Measurement. Athens J. Τechnology Eng.
**2018**, 5, 91–110. [Google Scholar] [CrossRef] - Little, R. Manual on Statistical Planning and Analysis, 17th ed.; ASTM International: Philadelphia, PA, USA, 1975. [Google Scholar]
- Guda, T.; Ross, T.A.; Lang, L.A.; Millwater, H.R. Probabilistic analysis of preload in the abutment screw of a dental implant complex. J. Prosthet. Dent.
**2008**, 100, 183–193. [Google Scholar] [CrossRef] - Kim, S.K.; Lee, J.B.; Koak, J.Y.; Heo, S.J.; Lee, K.R.; Cho, L.R.; Lee, S.S. An abutment screw loosening study of a Diamond Like Carbon-coated CP titanium implant. J. Oral Rehabil.
**2005**, 32, 346–350. [Google Scholar] [CrossRef] [PubMed] - Sun, F.; Wang, L.; Li, X.C.; Cheng, W.; Lin, Z.; Ba, D.C.; Song, G.Q.; Sun, C.S. Effect of surface modification on the long-term stability of dental implant abutment screws by plasma nitriding treatment. Surf. Coat. Technol.
**2020**, 399, 126089. [Google Scholar] [CrossRef] - Bulaqi, H.A.; Mousavi Mashhadi, M.; Geramipanah, F.; Safari, H.; Paknejad, M. Effect of the coefficient of friction and tightening speed on the preload induced at the dental implant complex with the finite element method. J. Prosthet. Dent.
**2015**, 113, 405–411. [Google Scholar] [CrossRef] - Yang, X.; Nassar, S.A.; Wu, Z. Criterion for preventing self-loosening of preloaded cap screws under transverse cyclic excitation. J. Vib. Acoust.
**2011**, 133, 041013. [Google Scholar] [CrossRef]

**Figure 7.**Experimental test: (

**a**) test bench, (

**b**) detail of the designed loading jig for tests, (

**c**) drawing of the loading jig, (

**d**) section view.

**Figure 8.**(

**a**) Boundary conditions of the finite element (FE) model of the dental implant under study; (

**b**) mesh.

**Figure 10.**Calculation of F

_{exp}using the staircase method under 10, 15 and 20 Ncm tightening torques (left vertical axis) and $\frac{{F}_{exp}}{{T}_{T}}$ coefficient of each test (right vertical axis) ×: loosened; o: non loosened; grey marker: discarded value.

**Table 1.**Chemical composition of materials used in implant and prosthetic component manufacturing process.

Ti 6Al 4V ELI (TI GR5) | TI CP4 | ||
---|---|---|---|

Composition | Wt.% | Composition | Wt.% |

Al | 5.5–6.5 | N(max) | 0.05 |

V | 3.5–4.5 | C(max) | 0.08 |

Fe(max) | 0.25 | Fe(max) | 0.5 |

O(max) | 0.13 | O(max) | 0.4 |

C(max) | 0.08 | H(max) | 0.0125 |

N(max) | 0.05 | - | - |

H(max) | 0.012 | - | - |

**Table 2.**Calculated load values that cause self-loosening in the dental implant under study using the methodology.

${\mathit{T}}_{\mathit{T}}\left(\mathit{N}\mathit{c}\mathit{m}\right)$ | ${\mathit{F}}_{\mathit{c}\mathit{r}\mathit{i}\mathit{t}}\left(\mathit{N}\right)$ | ${\mathit{F}}_{\mathit{a}}\left(\mathit{N}\right)$ | ${\mathit{F}}_{\mathit{e}}\left(\mathit{N}\right)$ |
---|---|---|---|

10 | 64.5 | 217.7 | 36.1 |

15 | 96.7 | 326.1 | 53.7 |

20 | 128.3 | 433.9 | 72.6 |

**Table 3.**External load values that cause self-loosening in the dental implant under study: methodology vs. experimental.

${\mathit{T}}_{\mathit{T}}\left(\mathit{N}\mathit{c}\mathit{m}\right)$ | ${\mathit{F}}_{\mathit{e}\mathit{x}\mathit{p}}\left(\mathit{N}\right)$ | ${\mathit{\sigma}}_{\mathit{e}\mathit{x}\mathit{p}}\left(\mathit{N}\right)$ | Error (%) |
---|---|---|---|

10 | 67.9 | 5.9 | 5 |

15 | 100.8 | 9.9 | 4.1 |

20 | 138.9 | 6.2 | 7.6 |

Source of Variation | SS | DoF | MS | F | p-Value | F_{crit} |
---|---|---|---|---|---|---|

Between groups | 0.75 | 2 | 0.38 | 1.29 | 0.28 | 3.11 |

Within groups | 23.48 | 81 | 0.29 | |||

Total | 24.23 | 83 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Armentia, M.; Abasolo, M.; Coria, I.; Bouzid, A.-H.
On the Use of a Simplified Slip Limit Equation to Predict Screw Self-Loosening of Dental Implants Subjected to External Cycling Loading. *Appl. Sci.* **2020**, *10*, 6748.
https://doi.org/10.3390/app10196748

**AMA Style**

Armentia M, Abasolo M, Coria I, Bouzid A-H.
On the Use of a Simplified Slip Limit Equation to Predict Screw Self-Loosening of Dental Implants Subjected to External Cycling Loading. *Applied Sciences*. 2020; 10(19):6748.
https://doi.org/10.3390/app10196748

**Chicago/Turabian Style**

Armentia, Mikel, Mikel Abasolo, Ibai Coria, and Abdel-Hakim Bouzid.
2020. "On the Use of a Simplified Slip Limit Equation to Predict Screw Self-Loosening of Dental Implants Subjected to External Cycling Loading" *Applied Sciences* 10, no. 19: 6748.
https://doi.org/10.3390/app10196748