**Contents**

## **About the Editors**

**Giovanni Bruno** studied Dentistry at the University of Padua in 2017 with the maximum evaluation cum laude, discussing original research on dental agenesis in patients affected by cleft lip and palate. In 2016, he was a visiting student at the Craniofacial Center at the University of North Carolina. He has participated in several post-graduate courses in orthodontics and pediatric dentistry and has published more than 40 research articles in international journals. He is currently enrolled in a three-year Master of Science program in pediatric dentistry that ends in 2021.

**Alberto De Stefani** studied Dentistry at the University of Padua in 2017 with the maximum evaluation cum laude, discussing original research on skeletal age evaluation in growing patients. In 2016, he was a visiting student at the Craniofacial Center at the University of North Carolina. He has participated in several post-graduate courses in orthodontics and pediatric dentistry and has published more than 40 research articles in international journals. He is currently enrolled in a three-year Master of Science program in pediatric dentistry that ends in 2021.

**Antonio Gracco** graduated from the University of Padua in 2003 and specialized in orthodontics in 2006 at the University of Ferrara with the maximum evaluation. He coordinated research activities in orthodontics at the University of Ferrara and, later, at the University of Padua. He is currently associate professor at the University of Padua and Head of the Pediatric Dentistry Master of Science program. He has published more than 100 original pieces of research in international journals.

## **Preface to "Mechanical Properties of Materials"**

In the oral environment, restorative and prosthetic materials and appliances are exposed to chemical, thermal and mechanical challenges. The mechanical properties of a material define how it responds to the application of a physical force. The mechanical properties which are of importance in dentistry include brittleness, compressive strength, ductility, elastic modulus, fatigue limit, flexural modulus, flexural strength, fracture toughness, hardness, impact strength, malleability, Poisson's ratio, shear modulus, shear and tensile strength, torsional strength and Young's modulus. All of these are measures of the resistance of materials to deformation, crack or fracture under an applied force or pressure. Measured responses can be both elastic (reversible on force removal) and plastic (irreversible on force removal). Recent advances in nanotechnology and 3D printing have rapidly spread and manufacturers continuously develop new materials and solutions to provide high-quality dental care, with particular attention being paid to long-term follow-up. Restorative dentistry, prosthodontics, oral surgery, implants, periodontology and orthodontics are all involved in this continuing evolution. This Special Issue focuses on all the recent technology that can enhance the mechanical properties of materials used in all of the different branches of dentistry.

> **Giovanni Bruno, Alberto De Stefani, Antonio Gracco** *Editors*

#### *Article*

## **Comparison of the E**ff**ects Caused by Three Di**ff**erent Mandibular Advancement Devices on the Periodontal Ligaments and Teeth for the Treatment of Osa: A Finite Element Model Study**

**Giovanni Bruno 1,\*, Alberto de Stefani 1,\*, Manila Caragiuli 2, Francesca Zalunardo 1, Alida Mazzoli 3, Daniele Landi 2, Marco Mandolini <sup>2</sup> and Antonio Gracco <sup>1</sup>**


Received: 29 July 2020; Accepted: 27 September 2020; Published: 3 October 2020

**Abstract:** AIM: The purpose of this study is to compare the stress effects developed on the periodontal ligaments and teeth by three different types of mandibular advancement devices (MADs) using a finite element method (FEM) analysis. Introduction: Obstructive sleep apnea (OSA) is a disease with a high prevalence and, in recent years, the use of MADs as an alternative or support treatment to the continuous positive airway pressure (CPAP) has spread. Their use finds relative contraindications in the case of partial edentulism and severe periodontal disease. Given the widespread of periodontal problems, it is essential to know the effects that these devices cause on the periodontal ligament of the teeth. Materials and methods: Starting from the computed tomography (CT) scan of a patient's skull, 3D reconstructions of the maxilla and mandible were implemented. Three different MADs were prepared for the patient, then 3D scanned, and lastly, coupled with the 3D models of the jaws. The devices have two different mechanics: One has a front reverse connecting rod (OrthoapneaTM), and two have lateral propulsion (SomnodentTM and HerbstTM). A FEM analysis was performed to calculate the stress applied on periodontal ligaments, on every single tooth and the displacement vectors that are generated by applying an advancement force on the mandible. Results: HerbstTM and SomnodentTM devices present very similar stress values, mainly concentrated on lateral teeth, but in general, the forces are very mild and distributed. The maximum stresses values are 3.27 kPa on periodontal ligaments and 287 kPa on teeth for SomnodentTM and 3.56 kPa on periodontal ligaments and 302 kPa on teeth for HerbstTM. OrthoapneaTM has, instead, higher and concentrated stress values, especially in the anterior maxillary and mandibular area with 4.26 kPa and 600 kPa as maximum stress values, respectively, on periodontal ligaments and teeth. Conclusions: From the results, it is concluded that devices with a bilateral mechanism generate less and more distributed stress than an anterior connecting rod mechanism. Therefore, they may be advisable to patients with compromised periodontal conditions in the anterior area.

**Keywords:** dental materials; orthodontics; obstructive sleep apnea; mandibular advancement device; finite element method

#### **1. Introduction**

Obstructive sleep apnea (OSA) is characterized by various and recurring episodes of reduction (hypopnea) or cessation (apnea) of the airflow during sleep. It results from the obstruction due to the collapse of the upper airway [1]. The pathophysiology of OSA is multifactorial and includes a reduction in upper airway dimensions that is caused by both anatomical and functional alterations (obesity or maxillofacial structural changes) and increased pharyngeal collapsibility due to reduced neuromuscular compensation and lack of the pharyngeal protective reflex during sleep [2–6].

OSA is one of the most prevalent chronic respiratory disorders. In recent population-based studies, the estimated prevalence of moderate to severe sleep-disordered breathing ranges from 3% to nearly 50% depending on the age group and sex. Recent studies suggest an increase in the incidence that is probably related to the growing prevalence of overweight and obese individuals [7,8].

Extensive population-based studies have shown that untreated moderate or severe OSA is associated with severe complications. The most important are the increased cardiovascular and cerebrovascular disease, stroke, chronic inflammation, hypertension, and metabolic syndrome resulting in increased morbidity and mortality. The main symptoms are snoring, day sleepiness, nocturia, frequent nocturnal waking caused by choking or gasping sensations, psychological or cognitive dysfunction, morning headaches, low concentration, irritability, and erectile dysfunction. Many patients report a reduction in their life quality due to obstructive sleep apnea [9–13].

OSA is an under-estimated problem even though there are many screening tools such as the STOP-BANG questionnaire, Epworth scale, and Berlin questionnaire [14–17]. The gold standard for the diagnosis of OSA is polysomnography (level I study), which consists of an instrumental examination carried out in dedicated structures.

Polysomnography involves the collection of seven or more data channels, including respiratory, electrocardiogram, electroencephalogram, and electrooculogram for sleep staging and electromyogram. Another solution for the diagnosis is the home-based polygraphy [18–20].

CPAP (continuous positive airway pressure) is the gold standard treatment for severe OSA, but since the 1980s, even mandibular advancement devices (MADs) were used as a therapy for OSA. MADs are widely used for mild and moderate OSA treatment, and several studies have demonstrated their effectiveness even in the treatment of severe OSA [21,22]. MADs present higher compliance and are more convenient for the patient than CPAP [23–27].

Although mandibular advancement devices represent the gold standard in the treatment of mild and moderate OSA, they cause skeletal and dental modifications due to their use [28].

MADs are responsible for a small but statistically significant change in the dentition of long-term wearers. Skeletal changes are generally secondary to dental changes. Major dental modifications feature the tendency towards a reduction of overbite and overjet, maxillary incisors palatal tipping and mandibular incisor labial tipping. A moderate linkage exists between the length of treatment time (how long the device is worn), and the number of dental changes experienced [29].

Even if the modifications are not significant compared to the benefits that the use of the MAD brings, it is crucial to evaluate the periodontal consequences of these devices. Periodontal health is defined to be a state free from inflammatory periodontal disease. This situation, in turn, means that absence of inflammation associated with gingivitis or periodontitis [30]. An analysis of the literature reveals an epidemiological picture of the uneven periodontal disease with methodological discrepancies that make it difficult to compare the prevalence and severity of data [31].

In 2007, the Centers for Disease Control and Prevention and the American Academy of Periodontology determined that population-based epidemiological studies should use the definition of moderate and severe periodontitis proposed by Page and Eke [32]. In the European area, the prevalence of moderate periodontitis is between 33.3% and 50%, while the severe one is between 17.6% and 35% [33–35]. Periodontal disease is a prevalent problem; it is estimated that more than 46% of the population in the United States is affected. The advanced forms of periodontitis that result in severe loss of supporting structures and substantial tooth loss affect 8.9% of the population [36].

The American Academy of Sleep Medicine stated that edentulism and severe periodontal disease represent a counter indication to the use of MADs. However, it is not verified how the stresses related to wearing MADs are discharged on the periodontal ligament of teeth [37].

Ethical or instrumental limits and increased complexity often put a limitation to research, and many questions cannot be answered given the impossibility of obtaining satisfactory results. In these cases, reverse engineering (RE) with the finite element method (FEM) represents a solution. RE is a technique used to generate a 3D virtual model from a real-world tangible object. FEM is an engineering instrument used to calculate stress and deformations in complex structures and has been widely applied in biomedical research. In the field of structural engineering, the use of FEM aims to establish the state of tension and deformation of a solid subjected to external actions.

By taking advantage of this engineering resource in orthodontics, it is possible to model and analyze any dental and maxillofacial material or structure [38]. The FEM principle is based on the division of complex structures into smaller sections called elements in which physical properties are applied to study the response of the object to external stimulation such as an orthodontic force. All this represents a significant advantage since the degree of simplification can be controlled.

The study aims to analyze how different types of MADs stress and deform teeth and periodontal ligaments of the individual dental elements of both arches, using a finite element method analysis. To the author's knowledge, this is the first work that compares the effects of three different types of MADs through a FEM. The predictable behavior of teeth and periodontal ligaments (PDLs) suggests to the clinicians the choice of the most suitable OSA treatment device depending on the patient's dental condition.

#### **2. Materials and Methods**

The finite element model employed in this study included the maxilla and the mandible with associated teeth and periodontal ligaments and a mandibular advancement device (Figure 1). The model was developed according to the dental cone beam computed tomography (CBCT) (Voxel size 75 micron, FOV 11 × 13 cm. NewTom Giano, Cefla, Italy) images of a 29-year-old female patient. The patient is in good health and does not suffer from OSA or mandibular disorders. Before proceeding with the CT scan, the patient was informed of the purpose of the study and gave her consent to the procedure. Her data were used anonymously in the simulations. The volumetric image of the anatomy was reconstructed in Mimics (v.12.11, Materialise NV, Leuven, Belgium) using an appropriate threshold based on the Hounsfield unit. The periodontal ligaments (PDLs) were reconstructed through the 3D modelling software Rhinoceros (v.5.0 by McNeel & Associates, Seattle, WA) since soft tissues are not identifiable in CT scans. Although the average thickness of periodontal ligament is 0.15 to 0.38 mm and it has an hourglass shape (it is thinnest at the middle third of the root [39]), PDLs were modelled by offsetting each tooth root surface of 0.3 mm to fill the space between each tooth and the alveolar socket [38,40,41]. The devices chosen are among the most used in OSA therapy. The authors have selected to consider two different types of mechanics: Lateral and anterior propulsion. In Herbst'sTM case, two lateral telescopic arms protrude the mandible. SomnodentTM also has a lateral mechanism, but the propulsion is no longer given by arms but by two screws that push the wings of the lower splint forward as they move forward. OrthoapneaTM is an entirely different device that has an anterior inverse connecting rod that is activated through the central screw that produces the protrusion of the mandible. In the simulations, SomnodentTM was reproduced without vertical elastics that are used to improve the outcome of the therapy. To simulate the effect of different MAD models, three MADs were created through a RE approach starting from the physical prototype due to the personalised nature. An optical laser scanner (Konica Minolta Range 7) was used for digitising a model of MAD to be used as a reference for the design of the two other devices. All the triangular mesh models were further processed and reconstructed to obtain the non-uniform rational basis spline (NURBS) models ready to be imported into Ansys v.19 R1 (Canonsburg, PA, USA) for the final arrangement of the model in terms of material properties, meshing, boundary conditions, and loading conditions.

**Figure 1.** 3D finite element model.

The material properties of teeth and MAD as presented in Table 1 were assumed to be linear elastic, homogeneous, and isotropic. At the same time, a hyperelastic law was used to simulate large non-linear strains associated with the non-linear nature of PDLs [42].

**Table 1.** Material properties used in the finite element model.


A 2nd-order Ogden model was used to define the strain energy function [43–45]. The parameter values listed in Table 2 were obtained through the fitting of uniaxial experimental data by Natali et al. [46].


**Table 2.** Parameters of the second-order Ogden model.

Perfect bonding was assumed between the bodies since MADs are anchored on teeth to force the mandible to a protruded position, and PDLs strongly bind the tooth root to the supporting alveolar bone. Thus, a continuous mesh (shared topology) has been created between MAD and teeth and teeth and PDLs with common nodes at the boundary between the parts. The contact between the bone and the PDL was set as bonded meaning that no sliding or separation is allowed. The two splints of the MAD were coupled in a configuration that will enable mutual sliding without separation. The bony components were assumed as rigid bodies since they have more rigid behaviour than PDLs. Moreover, they were constrained in all directions to prevent rigid body motion.

The authors decided to not differentiate bone in its cortical and cancellous components since the main objective of the study is to compare the results in the three devices. The results, therefore, must be understood as comparative and not in absolute terms.

As a boundary condition, a load associated with the force applied by the MAD to protrude the mandible was applied in the connecting region between the two MAD splints. According to the methodology developed by Bruno et al. [47], it was possible to correlate the amount of advancement of the mandible due to the MAD settings to the magnitude of the force exerted by the device and experimentally determined by Cohen-Levy et al. [48]. The application of a pressure transducer to a MAD allowed measuring the force produced by a progressive mandibular advancement. The advancement to which the MADs have been subjected is 9.5 mm, a reasonable value for the treatment of OSA [38]. Thus, an overall force of 11.18 N was applied on each splint in correspondence of the connection mechanism. The 3D models were then discretised in 5,705,381 linear tetrahedral elements with three degrees of freedom per node. A mean mesh size of 1 mm was used to discretize the model. A mesh convergence study was performed to ensure the adequacy of the results from the simulation. The obtained numerical solution will tend toward a unique value of Von Mises stress by increasing the mesh density in the PDLs from 0.26 to 0.154 mm. The physical memory of the workstation did not support further mesh refinement (0.118 mm). Thus, according to the values provided in Table 3 an element size of 0.2 mm was considered an acceptable trade-off between the quality of the mesh and the computational effort of the workstation. A dense and tight mesh was obtained in the thickness of the bodies ensuring at least two elements in the ligaments' wall.



#### **3. Results**

In this study, three finite element simulations were carried out by varying the MAD design to analyze the stress distribution and deformation of teeth and PDLs. Tooth movement and pain are the biomechanical response of the stress that develops in teeth and PDLs under the application of a load. Therefore, to evaluate the teeth that are more loaded and the areas that are prone to be compressed and stretched, results in terms of von Mises stress and deformation of teeth and PDLs were presented. (Figure 2).

**Figure 2.** Three models of mandibular advancement devices: OrthoApnea (**a**), Herbst (**b**), Somnodent (**c**).

Regarding the analysis of stress on the periodontal ligaments, significant differences emerge between OrthoapneaTM (Grupo Dental Ortoplus, Malaga, Spain), HerbstTM (Somnomed, Sydney, Australia), and SomnodentTM (Somnomed, Sydney, Australia).

In the case of OrthoapneaTM, which has an anterior reverse rod activation mechanism, the stresses on the individual teeth develop mainly on the coronal portion, while apically, the stresses are minor. The most involved teeth are the lower and upper incisors, with the PDLs exhibiting a maximum expression of strength in correspondence of the anterior cervical margin reaching 4.26 kPa (kilopascal). The teeth of the posterior sectors (premolars and molars) are less stressed. The stresses are slightly uneven in the various portions of the arches, as shown in Figure 3.

**Figure 3.** Contour plots. Periodontal ligaments (PDLs) stress distribution (kPa), frontal and occlusal view.

HerbstTM is a bilateral telescopic activation device. It presents periodontal stresses that are concentrated in the most coronal portion of the teeth similarly to OrthoapneamTM. The main difference with the first device is that tensions caused by HerbstTM are much more uniform in the arches. The most stressed teeth are the upper and lower premolars and molars (but the differences are not significant while compared with other teeth). The PDLs are mainly affected by stress in the medio-distal cervical region with a peak of pressure that reaches 3.56 kPa.

SomnodentTM is activated with two lateral propulsion screws and this case also presents concentrated stresses, especially in the coronal portion of the teeth. Stresses are concentrated in the periodontal ligaments of the second molars and, with a minor component, the anterior teeth of both arches. The stress mainly affects the medio-distal cervical sides of PDLs and the lingual sides of mandibular PDLs associated with molars. The maximum pressure achieved is about 3.27 kPa. SomnodentTM is the device that generates the least stresses among the three considered in the study. In Figure 4, the stress analysis of dental elements reflects periodontal tensions. In OrthoapneaTM, the most loaded teeth are the upper and lower incisors. The most affected dental portions are the incisal margins with a maximum value of 600 kPa. HerbstTM has less intense stresses that are concentrated mainly in the maxillary molars and the mandibular premolars. The maximum load value reached is 302 kPa. SomnodentTM has stresses concentrated on the upper molars and mandibular second premolars in correspondence of the splint's wings. The highest pressure is 287 kPa. The analyses also allowed us to obtain images, from the occlusal view, representing the stresses and deformations on periodontal ligaments (Figure 3) and teeth (Figure 4).

**Figure 4.** Colour plots. Stress distribution (kPa) in the teeth, frontal and occlusal view.

A lateral representation of the arches shows the deformation vectors to which the individual dental elements of both arches are submitted to (Figure 5). The model shows a right-side view, but the left side is considered symmetrical. In all three devices, the forces tend to displace the teeth of the upper arch downwards and backwards when considering the anterior teeth. In contrast, the deformations on the posterior teeth are directed back and upwards. The deformations are more significant in OrthoapneaTM; in particular, incisor teeth are the most affected teeth, as shown in Figure 5, while the deformations are more uniform in HerbstTM and in particular in SomnodentTM, which is characterized by the lowest intensity of deformation (Figure 5). This image does not report the advancement of the 9.5 mm MAD at which the simulations were made but is only indicative of the direction of displacement.

**Figure 5.**Deformation (mm) on teeth from a lateral view. Arrows indicate the direction of tooth displacement and its intensity (red for higher displacement; blue and grey for lower displacement).

#### **4. Discussion**

Mandibular advancement devices are efficient in reducing the apnea-hypopnea index (AHI) under the score of 5, a value below which sporadic apnea episodes are considered physiological, in both mild and severe OSA. The resolution of the apneic syndrome is obtained in 48% of treated patients who presented a mild-severe OSA and AHI under 10 in 64% of the patients, which is considered a good result starting from a severe OSA [18,49]. The reduction of snoring and daily sleepiness, which are the most common symptoms of sleep apnea, is referred in 82% of patients who wears a mandibular advancement device [50–52].

The effectiveness of MAD therapy has been widely verified in the literature. Still, it is essential also to consider the side effects caused by the treatment. The treatment is indicated for the entire duration of the subject's life. Therefore, as this is not a short-term treatment, the consequences at the dental, skeletal, and articular level have to be taken into consideration. Even though a slight mandibular advancement can also be considered a safe procedure for an extended period and should not cause permanent side effects on the temporomandibular joint [51], dental effects are more evident, resulting in a reduction of both overjet and overbite [53].

Dental displacement is the result of the application of the MAD forces on the attachment system of the teeth and the consequent remodeling at the periodontal level. A study that uses a finite element analysis to investigate the optimal orthodontic force establishes that in a range of orthodontic pressure between 4.7 kPa and 16 kPa, dental movements are generated in the biological respect of the periodontal and dental structure [54]. The pressures highlighted by our study turned out to be lower than this range of optimal orthodontic forces. Therefore, a slight tooth movement is obtained, which is compatible with wearing the MAD for long periods. This conclusion is supported by the results of a study showing that occlusal changes (reduction in overjet and overbite) occur in 86.7% of patients [55]. Another recent research evaluating a 10-year follow-up also demonstrates the presence of dental modifications resulting from the use of MAD; these changes are progressive over time [56]. Given the significant prevalence of the periodontal disease, it is crucial to know the stress levels generated at the level of the individual dental elements in the different types of appliance.

Previous studies investigated the effects of forces applied on periodontal ligaments by orthodontic appliances on both healthy and reduced periodontal attachment. It has been demonstrated that the maximum stress value is located in the ligament portion close to the alveolar crest, because of the pressure generated by the mandibular advancement splint on the arch [57–59].

The analysis found that the SomnodentTM and HerbstTM appliances exhibited lower levels of stress than an OrthoapneaTM device. OrthoapneaTM releases the activation forces in a concentrated manner on the anterior teeth of both arches. At the same time, Herbst and SomnodentTM concentrate their stresses on the posterior teeth. This result agrees with a previous study demonstrating a stress concentration at the molars wearing a MAD with the lateral mechanism [38]. The results of the paper agree on a study comparing the dental effects of using a SomnodentTM device and TAPTM (which is a MAD that has the same mechanics as OrthoapneaTM). In the study, it was shown that the dental modifications are lower in the case of SomnodentTM [60]. According to the authors, the difference depends on the two different mechanics that promote the activation of the three devices. SomnodentTM has a bilateral activation screw located at the level of the molar teeth, HerbstTM has two telescopic technology pistons that join the two arches bringing the jaw forward. Even in this case, the point of application of the forces is at the latero-posterior level on both sides. OrthoapneaTM, on the other hand, has an anterior reverse connecting rod, which discharges the forces on the frontal elements of both arches. The advantages of using a device such as OrthoapneaTM are, in particular, the possibility of having lateral excursions, useful, for example, in the bruxist patient and the ability of the device to force the jaw to advance further if the patient tends to open mouth during sleep. This phenomenon, which is a typical tendence in OSA, decreases the efficiency of MAD (causing mandibular postrotation and retroposition) and, therefore, the effectiveness of the therapy [61,62]. In lateral mechanical devices such as SomnodentTM or HerbstTM, since there is no real limit to the opening of the mouth, vertical elastics of adequate length and strength can be used to keep the two parts of the splint in contact. The use of elastics is not necessary in the case of OrthoapneaTM, having included this feature in its mechanics. Devices such as HerbstTM and SomnodentTM, on the other hand, have the advantage of being less

aggressive with regards to the stresses applied at the periodontal level and therefore represent a better option in the case of periodontally compromised patients in the anterior mandible area.

Since it is not possible to perform an in vivo validation of this study, a comparison of the results with previous studies assessed its reliability. Earlier articles on orthodontic tooth loading and mandibular advancement devices evaluation from both a clinical point [60] of view and an engineering point of view (finite element analysis) [38,57–59] have been taken into account.

A study carried out using FEM simulations has shown that in the case of a reduced periodontium it is necessary to reduce the application of orthodontic forces to generate lower and more uniform stresses that do not worsen the already compromised situation [59]. This result aids practitioners in deciding the type of appliance to be used so that the applied forces are uniform. The forces applied to the MAD do not depend only on the type of device, but also on the degree of activation: Higher activations correspond to higher stresses. In particular, when 70% of the maximum advance is exceeded, the risk of root resorption begins to increase (PDL pressure exceeds 4.7 kPa). A study shows that only below 40% of advancement is safe to avoid root resorption, but this is not a sufficient advancement to obtain the therapeutic effect of MAD [38].

This study provides critical clinical results that may influence the choice of the device. The analysis, however, has some limitations: The stress simulations are static, no load cycles have been performed, so they detach from the model of orthodontic forces applied intermittently. The simulation focuses on the investigation of the response of the periodontal ligament disregarding the effects at the bone level. Since the study is comparative with a focus on the behavior of the three devices, the authors decided to not discriminate bone in its cortical and cancellous components; this represents a limitation of the study, but as future work, the discrimination between cortical and cancellous bone will be considered following the approach proposed by Toniolo et al. [63]. With this improvement, it will be possible to analyze patients suffering from periodontitis (bone resorption and edentulism). The model used to carry out the analyses refers to a young female, without significant temporomandibular or orthodontic problems, not affected by periodontal disease and who has all the dental elements of both arches. In clinical practice, it is difficult to find patients with these characteristics. Therefore, the authors plan to continue the work with analysis on the reduced periodontium and with cases of partial edentulism or implant rehabilitations to make the study more comparable with the cohorts of adult patients with OSA. Other simulations can be performed using different levels of MADs' activation.

#### **5. Conclusions**

This work represents a step of more complex work for evaluating the effects caused by a mandibular advancement device for OSA treatment. The study, which is based on FEM, allowed authors to assess stress and deformation caused by MADs on periodontal ligaments and teeth surfaces.

The findings of this study suggest that by changing the design of the mandibular advancement device, there is a significant difference in terms of stress between a bilateral propulsion mechanism and an anterior rod system. In the case of the anterior mechanism model, the stresses are much more concentrated and intense in the anterior area, creating a situation that could be contraindicated in patients presenting periodontal problems. In a subsequent study, stress and deformations applied to a patient with a reduced periodontium and partial edentulism can be studied.

**Author Contributions:** Conceptualization, G.B., A.d.S., A.M. and M.M.; Investigation, M.C. and F.Z.; Methodology, G.B., A.d.S., M.C., D.L. and M.M.; Supervision, A.G.; Validation, A.G.; Writing—original draft, G.B., A.d.S., Francesca Zalunardo, M.C. and M.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 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/).

### *Article* **Temperature Changes in Composite Materials during Photopolymerization**

**Leszek Szalewski 1, Magdalena Szalewska 1,2,\*, Paweł Jarosz 3, Michał Wo´s <sup>4</sup> and Jolanta Szyma ´nska <sup>1</sup>**


**Abstract:** During polymerization, composite materials cause a temperature rise which may lead to irreversible changes in the dental pulp. The mechanical properties of composite materials depend on a number of factors, such as the composition of the material, the type of polymerization unit, the polymerization mode, and the duration of polymerization. The objective of this study was to assess the temperature rise values and flexural strength of composite materials, as obtained using different modes and times of polymerization. A total of six composite materials were used in the study. Samples of each of the materials were cured using seven polymerization protocols. A CMP-401 digital meter (Sonel, Swidnica, Poland), complete with a type K thermocouple (NiCr-Ni), was used ´ to record the temperature increases during the light curing of the resin composites. Temperature rises were recorded beneath the composite disc in an acrylic matrix. The specimens were tested for flexural strength using a Cometech QC-508M2 testing machine. The lowest results for the increased mean temperature were obtained for Fast-Cure 3 s (39.0 ◦C), while the highest results were obtained for Fast-Cure 20 s (45.8 ◦C). The highest average temperature values for all tested protocols were recorded for the Z550 Filtek material. Mean flexural strengths as measured in each test group were higher than the minimum value for composite materials as per the ISO:4049 standard. In the case of deep caries with a thin layer of dentin separating the filling from pulp, a base layer or a short polymerization duration mode is recommended to protect pulp from thermal injury.

**Keywords:** temperature rise; composites; polymerization; flexural strength

#### **1. Introduction**

Composite materials are widely used in every dental practice. As the result of many years of technological development and improvements, as well as changes in their composition, composite materials are very durable, while being esthetically pleasing and popular among dentists. At the same time, numerous manufacturers have introduced increasingly advanced units featuring modifying polymerization programs and power adjustments, so as to ensure the best mechanical performance of composite materials. However, many dentists fail to use polymerization units in the correct manner, by focusing mainly on the anatomical representation and the esthetics of fillings. In the survey carried out by Kopperud et al., almost one third of dentists failed to use proper eye protection against blue light while up to 78.3% of respondents were unaware of the irradiance values of the polymerization lamp they used [1]. Many respondents did not check the quality of the light produced by the polymerization unit. Other studies have shown that preclinical dental students and dentists in their internship years use polymerization lamps in an incorrect manner, not delivering the required amount of energy to the composite layer.

**Citation:** Szalewski, L.; Szalewska, M.; Jarosz, P.; Wo´s, M.; Szyma ´nska, J. Temperature Changes in Composite Materials during Photopolymerization. *Appl. Sci.* **2021**, *11*, 474. https://doi. org/10.3390/app11020474

Received: 29 November 2020 Accepted: 2 January 2021 Published: 6 January 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 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 (https:// creativecommons.org/licenses/by/ 4.0/).

Following a briefing on the use of polymerization tips, the number of study subjects who failed to deliver the minimum required energy to the filling was significantly reduced [2]. Many dentists do not analyze polymerization unit power and modes before purchasing, study instructions of dental composite polymerization protocols, or obey polymerization procedures. This is an essential element, which can affect the final treatment result.

As materials science advanced, more and more dental practitioners abandoned the use of base layers, even in deep caries; combined with the increased lamp powers and changes in composite material compositions, this might lead to increased temperatures being achieved during polymerization, and leading to pulp damage. The critical value for pulp damage (temperature increased by 5.5 ◦C) was first reported by Zach and Cohen in 1965 on the basis of a study conducted in five adult rhesus macaque monkeys. The authors demonstrated necrosis of 15% of the tissue as the pulp temperature was increased by 5.5 ◦C [3]. However, not all studies confirmed this value as critical for pulp damage. Gross et al. observed no histological changes within the pulp as its temperature increased by 5.5 ◦C [4]. In the study by Runnacles et al., a 60-s exposure led to the highest increase in pulp temperatures, exceeding 5.5 ◦C for certain teeth. However, the authors noted that the critical temperature of pulp damage leading to potential necrosis had been determined by testing the teeth of monkeys rather than humans [5]. There are various methods of protecting the pulp against thermal injury: cooling with water during preparation or using liners, such as calcium hydroxide, mineral trioxide aggregate (MTA), or glass-ionomer cements (GIC) [6–8]. Polymerization lamp choice is essential to avoid pulp overheating. On the other hand, the lamps emitting lower levels of energy can disturb the process of polymerization, thus disabling the acquisition of optimal mechanical parameters, including the tensile strength and the flexural strength.

Since the tensile strength of composites is much lower than their compressive strength, and since tensile strength is typically much more affected by internal flaws, this property is likely the most appropriate test of strength. However, it is usually substituted by measurements of flexural strength as a potentially simpler testing method, well-related to tensile failure. Flexure testing is the standard means for the strength testing of dental composites (ISO 4049), and has been shown to correlate with material wear in some studies [9]. Manufacturers keep upgrading their composite materials using different resins or fillers. Sideridou et al. confirmed that the higher the percentage content of the filler, the higher the flexural strength [10]. The mechanical characteristic of composite materials is affected not only by the composition of materials, but also by the polymerization mode [11–15].

The main objective of this study was to assess the temperature rise values as observed for composite materials during polymerization, and to further assess whether different polymerization durations and modes affect the mechanical properties of materials as exemplified by their flexural strength. The null hypothesis was that the different modes and durations of polymerization would have no effect on the rise of the temperature and flexural strength of the composite materials.

#### **2. Materials and Methods**

#### *2.1. Composites*

A total of 6 composite materials in A2, Medium Dentin, and Universal shades were used in the study. These included: Essentia: Universal and Medium Dentin (GC Corporation, Tokyo, Japan), GrandioSO, Polofil Supra (VOCO GmbH, Cuxhaven, Germany), Filtek Z550 (3M ESPE, Minneapolis, MN, USA), and Boston (Arkona LFS, Nasutów, Poland). One half of the materials consisted of nano-hybrid materials, while the other half consisted of micro-hybrid materials (Figure 1). The weight content of the filler material in the study group of materials ranged from 76.5% to 89%. All materials featured resin-based matrices: Bis-GMA, TEGDMA, UDMA (with the exception of GrandioSO), and Bis-EMA (with the exception of Polofil Supra); the materials differed by the addition of resins such as Bis-MEPP (Essentia), PEGDMA (Filtek Z550), and HEMA (Polofil Supra). The detailed compositions of the materials used in the study are given in Table 1.


**Figure 1.** The experimental study design and distribution of samples in groups with curing protocol.


**Table 1.** Characteristics of composite materials used in the study.

#### *2.2. Light Curing Unit*

The composite materials examined were polymerized using a high-powered LED LCU (Mini LED III Supercharged, Acteon Group, Merignac, France). According to the manufacturer's information, polymerization power 2000 mW/cm2 when a 7.5-mm diameter tip was used. Three samples of each tested material were cured using 7 polymerization protocols: 4 Fast-Cure modes (full power for 3, 5, 10, and 20 s (double 10-s program), 2 Pulse-Cure modes (5 and 10 shots of 1-s exposures at full power) and 1 Step-Cure mode (soft start with progressive cycle lasting 9 s). In this study, the total energy ranged from

6 J/cm2 (Fast-Cure, 3 s) to 40 J/cm2 (Fast-Cure, 20 s). Table 2 shows details pertaining to the LED unit and its polymerization modes.



#### *2.3. Temperature Measurement*

One hundred and twenty-six specimens were prepared overall, with a total of twentyone specimens for each composite material, whereby three specimens (*n* = 3) were polymerized using one of the seven curing modes. All specimens were prepared in an acrylic resin matrix of the same shape (7.5 mm in diameter, 2 mm deep). The tip of the light curing unit touched the composite resin through a protective cover to simulate the situation of filling a tooth within the oral cavity. The scheme of the test stand is shown in Figure 2.

**Figure 2.** Scheme of the test stand for measuring temperature changes.

All measurements were taken in a temperature-controlled room at a constant temperature of 29 <sup>±</sup> <sup>1</sup> ◦C. A CMP-401 digital meter (Sonel, Swidnica, Poland) complete with ´ a type K thermocouple (NiCr-Ni) was used to record the temperature increases during the light curing of the resin composites. Temperature rises were recorded beneath the composite disc in the acrylic matrix. Two measurements were recorded during each session, namely the initial temperature and then the maximum temperature achieved in the time of polymerization. The obtained results were analyzed statistically.

#### *2.4. Flexural Strength Test*

Seventy specimens were prepared for flexural strength test according to the ISO standard 4049:201012, using the Boston (Arkona LFS, Nasutów, Poland) composite resin (shade A2). Rectangular specimens (25 mm × 2 mm × 2 mm) were produced using a steel mold and placed on a microscope slide to achieve a flat surface. Subsequently, one portion of composite resin was condensed with a dental plugger and flattened by being pressed using another microscope slide. The composite material was then polymerized across a layer of polyethylene film in order to eliminate oxygen inhibition at the surface. Samples were polymerized using a high-powered LED LCU (Mini LED III Supercharged, Acteon Group, Merignac, France) using 7 different modes; the same as for the temperature measurement tests. Ten specimens were used for each mode and duration. Each rectangular sample was polymerized at 4 points. After polymerization, the specimens were released from the mold. Next, the specimens were examined for the presence of air bubbles and defective specimens were excluded from the study. Specimens were then immersed in distilled water at a temperature of 37 ◦C for 24 h. Next, the specimens were tested for flexural strength using the Cometech QC-508M2 testing machine (Cometech Testing Machines Co., Taichung City, Taiwan) with the opening width of 20 mm, initial gripping force of 1 N and the crosshead speed of 0.75 mm/min. The specimens were measured to an accuracy of 0.01 mm before the test. The test end was marked by the specimen being crushed.

Flexural strength was calculated using the following equation:

$$\mathbf{S} = \mathbf{3}\mathbf{F}\mathbf{L} / (\mathbf{2}\mathbf{B}\mathbf{H}^2)$$

where F is the maximum load in Newtons exerted on the specimens, L is the distance (20 mm) between the supports, accurate to ±0.01 mm, B is the width (2 mm ± 0.01 mm) of the specimens measured immediately prior to testing and H is the height (2 mm ± 0.01 mm) of the specimens measured immediately prior to testing.

#### *2.5. Statistical Analysis*

The mean maximum temperatures at the assigned measurement sites and flexural strength were analyzed using ANOVA and Shapiro–Wilk tests. The analyses were conducted using Statistica software version 13 (Statsoft, Warszawa, Poland) at the significance level of 0.05.

#### **3. Results**

The specific values of the average temperatures before and during the test along with the standard deviations are summarized in Table 3.

The statistical analysis (Shapiro–Wilk test for normality) showed a significance level for Fast-cure 3 s (W = 0.96364, *p*-value = 0.6732), Fast-cure 5 s (W = 0.95208, *p*-value = 0.4585), Fast-cure 10 s (W = 0.96143, *p*-value = 0.6294), Fast-cure 20 s (W = 0.97366, *p*-value = 0.863), Pulse-cure 5 s (W = 0.96143, *p*-value = 0.6294), Pulse-Cure 10 s (W = 0.95192, *p*-value = 0.4559), and Step-Cure 9 s (W = 0.9568, *p*-value = 0.5412). We cannot reject normality in the test groups. The lowest average results were obtained for Fast-Cure 3 s (39.0 ◦C ± SD 2.7), while the highest average results were obtained for Fast-Cure 20 s (45.8 ◦C ± SD 2.0). The temperature increase was the lowest for 3 s of continuous polymerization, amounting to 10.1 ◦C, while being the highest for 20 s of continuous polymerization (16.3 ◦C). The highest average temperature values for all tested protocols were recorded for the Z550 Filtek material. The variance estimated based on the variability within the group showed a statistical significance for polymerization time (F = 1.4778) and for the type of filler (F = 2.2404). (Table 4).


**Table3.**Meantemperaturevaluesandstandarddeviations(SD)forthecompositematerialsandlightcuringmodesevaluated.

Standard deviations are in parentheses. Values with identical superscript letters are similar within the same temperatures (*<sup>p</sup>* > 0.05). T0, beginning temperature; T1, maximum temperatureduring polymerization.


**Table 4.** Multiple factor ANOVA test for the time of polymerization and the type of filler.

Mean flexural strengths as measured in each test group were higher than the minimum value for composite materials as per the ISO:4049 standard, i.e., 80 MPa (Figure 3).

**Figure 3.** Mean values of flexural strength (MPa) and standard deviations.

The statistical analysis (Shapiro–Wilk test for normality) showed a significance level for Fast-cure 3 s (W = 0.97125, *p* = 0.90220), Fast-cure 5 s (W = 0.97324 *p* = 0.91020), Fast-cure 10 s (W = 0.95863, *p* = 0.86159), Fast-cure 20 s (W = 0.95945, *p* = 0.90257), Pulse-cure 5 s (W = 0.99865, *p* = 0.97432), Pulse-cure 10 s (W = 0.96699, *p* = 0.91351), and Step-cure 9 s (W = 0.95980, *p* = 0.90619). We cannot reject normality in the test groups. The lowest flexural strength was measured for the Fast-Cure 3 s protocol, while the highest flexural strength was measured for the Fast-Cure 20 s protocol, the differences being statistically significant (*p* = 0.02060).

#### **4. Discussion**

The research results show that the change of the polymerization time has a great impact on the mechanical properties, such as flexural strength. Furthermore, the increase of the material temperature was influenced by the polymerization time. Hence, the null hypothesis was rejected. The results demonstrated that in our study the average temperature

as measured for all test materials did not exceed 42.0 ◦C for Fast-Cure 3 s mode. This value was exceeded for the remaining polymerization modes, reaching a maximum value of 45.8 ◦C for Fast-Cure 20 s. This value is particularly important for deep cavities with only a thin layer of dentin separating the composite material from the pulp. High temperatures can cause irreversible damage to pulp tissue, and therefore require endodontic treatment.

The study of Khaksaran et al. measured the temperatures following polymerization of bonding systems (N Bond, G-Bond, OptiBond XTR, Clearfil SE, Adper Single Bond 2 and V Bond) on pre-prepared dentin discs obtained from human third molars. The study environment temperature of experiments was 37 ◦C. The irradiation time was 20 s, and the minimum and maximum temperature rise growth in all subgroups was 1.7 ◦C and 2.8 ◦C, respectively. In the case of the 20 s polymerization protocol, no dangerous rise in temperature (5.5 ◦C) was obtained for either of the bonding systems tested [16]. Our research findings revealed that the maximum temperature increase for the 20 s mode (Fast-cure, 2 × 10 s) was 17.8 ◦C, for the Filtek Z550 material, with the lowest of 7.25 ◦C for the Essentia Medium Dentin 3 s mode. In our study the initial temperature was maintained at 29 ± 1 ◦C. The critical pulp temperature values were not exceeded in the case of Fastcure 3 s mode. Jo et al., in their study, performed on 30 extracted human molars with class I cavities filled using a nano-hybrid material (Filtek Bulk Fill Posterior Restorative (BFP, 3M ESPE)), found the maximum temperature increase during polymerization at 0.625 mm apically from the top and center of the defect. On the basis of their results, the authors concluded that replacing pulsed or soft start modes with continuous irradiation might reduce the risk of damage to the pulp [17]. The authors' research does not confirm this thesis. For the 5 s modes (Fast-cure and Pulse-cure) and 10 s (Fast-cure, Pulse-cure and Step-cure 9 s) temperature rises were similar: ±14 ◦C (5 s modes) and ±15.5 ◦C (10 s modes). Another study (Braga et al.) compared the rise in the temperature during polymerization of two materials (SDR, Dentsply and AURA, SDI) polymerized using two lamps (Bluephase G2, Ivoclar Vivadent, and VALO Cordless, Ultradent) in the standard output power mode. An increase of 6 ◦C was observed for the Bluephase G2 lamp, as compared to 4 ◦C for the VALO Cordless lamp for the light curing adhesive system (20 s mode without microcirculation) [18]. Our study demonstrated that for fast-cure 20 s mode (2 × 10 s) the highest temperature increase was 17.8 ◦C, in the case of Filtek Z550 material. There was no simulated pulpal microcirculation. On the other hand, Kim et al. measured the temperature rise in class I cavities in third molars in the course of layered filling with a composite material (Filtek Z250, Shade A2, lot N506344, 3M ESPE, St. Paul, MN, USA). The temperature was measured for 110 s using eight thermocouples. The authors demonstrated that the rise in the temperature within the cavity was significantly higher during polymerization of the first layer of material (59.8 ◦C) compared to the next layer (58.5 ◦C) [19]. The authors' findings do not demonstrate such a temperature increase, even in 20 s mode. This might support the idea of shorter polymerization durations being used for the deepest layers of composite fillings. In a subsequent examination of six composites (Admira, Filtek P60, Premise, Tetric Flow, Tetric Ceram, and Filtek Z250) polymerized using different modes (standard (10 s, full power), pulsed (10 consecutive one-second exposures at full power) or soft start (progressive cycle lasting 20 s)), with a type L thermocouple being used for temperature measurements, higher temperature rises were observed for soft start exposures (in the case of Admira and Tetric Flow materials). The lowest rise in temperature was observed for the Premise material irradiated using the pulsed protocol. None of the exposure protocols tested resulted in temperature being raised to the critical value [20]. In the authors' research the lowest temperature rise was observed for Essentia Medium Dentin and Fast-cure 3 s mode (7.25 ◦C). No significant differences in temperature rise were found between modes with similar durations. In another study, three polymerization units were compared, one halogen lamp (QTH LCU XL2500 (3M/ESPE), two LED lamps (Freelight LED LCU (3M/ESPE), and Ultrablue (DMC Equipamentos LTDA) on a one composite material (Filtek Z250, 3M/ESPE). Five types of photoactivation modes were used: 20 s with each of the three light curing units according to the manufacturer's instructions, 50 s with

the Freelight LED lamp, and 30 s with the Ultrablue IS lamp. The authors demonstrated that for photoactivation times as per the manufacturer's recommendations, both LED lamps produced a lower temperature rise than the QTH lamp (average temperature rise values in degrees Celsius: Ultrablue LED 1.13 (0.05), Freelight LED 1.05 (0.16) vs. QTH XL 2500 1.57 (0.13)). However, the authors stressed that the choice of the type of the polymerization lamp affected the average temperature rises [21]. However, other studies did not confirm the reports suggesting that LED lamps generated lower temperature rise values. A study using 96 fragments of bovine teeth revealed that higher temperatures were obtained during polymerization of composite materials using a LED lamp as compared to halogen lamps. However, the temperature increase was above 5.5 ◦C for both tested lamps, which could be considered as a critical value [22]. The authors' study demonstrated that the temperature rise was lower than the critical temperature value only for the 3 s Fast-cure mode. For other modes and durations, the final temperature was higher than the critical temperature value. Santini et al. used two LED lamps (Bluephase, Elipar Freelight 2) and a halogen lamp (Prismatics). The authors demonstrated that for all light curing units, the exposure of the bonding system resulted in temperature rises being significantly higher than those observed for the exposure of composite materials. However, higher temperatures were achieved during the polymerization of bonding systems and resin-based composite materials using both LED lamps compared to the halogen lamp [23]. Bagis et al. demonstrated that for the output values of all units tested (halogen, plasma, LED), the temperature rise exceeded 5.5 ◦C; and the temperature rose along with increasing polymerization duration [24].

Type of polymerization unit and irradiation modes also affect the mechanical properties of composite materials. One such parameter is flexural strength. The study by Pieniak et al. revealed no impact on flexural strength when a LED lamp was used instead of a halogen lamp to polymerize the Filtek Silorane (3M ESPE) and Herculite XRV (Kerr) composite materials. However, a rise in flexural strength was demonstrated as being due to increased polymerization duration when using a halogen lamp for polymerization of Filtek Silorane. In the study, lower values of flexural strength were obtained for methacrylate resin-based materials (Gradia Direct Anterior and Gradia Direct Posterior, GC Japan) [25]. According to our findings, polymerization time affected flexural strength, not the mode of light curing. Another study revealed higher flexural strength values for hybrid composite materials compared to nanofill resins. The authors used two composite materials with different filler types, namely the Filtek P60 3M ESPE (hybrid) and Filtek Supreme 3M ESPE (nanofill) [26]. Another study using the Z250 (3M ESPE) composite and the Scotchbond Multi-purpose Plus (3M ESPE) bonding system revealed that the photoactivation method applied had no impact on the performance of the composite material (including flexural strength), regardless of the material storage medium (water vs. ethanol) [27]. The Filtek Z250 (3M ESPE) and Heliomolar (Ivoclar Vivadent) composite materials were tested by Calheiros et al. at polymerization energy doses of 6–24 J/cm2. A rise in flexural strength was observed for increasing energy doses for the Filtek Z250 material, whereas no changes in mechanical properties were observed for the Heliomolar composite [28]. The authors' results confirmed the hypothesis that the polymerization energy dose influences the flexural strength value.

All in vitro studies have their limitations. The baseline test stand temperature in our study was lower than the temperature within the cavity. However, even starting at lower temperatures, some values exceeded the limit value of 42 ◦C. The effects of thermal absorption within the dentin tissue, potentially leading to lower values during polymerization, were not taken into account in the tests. In addition, in the case of deep cavities, it is not always possible to reach the composite layer with the polymerization tip, and the energy dose, leading to the rise in the temperature, is reduced with increasing distance. The effect of the bonding system on the temperature rise was not taken into account in our study, so as to maintain constant conditions for all materials for which different bonding systems are recommended by their manufacturers.

Subsequent studies should be based on the model of human teeth, in which natural heat dissipation in hard tissues will be obtained. In addition, it would be advisable to examine how liners and their thickness affect the transmission of thermal energy to the tooth pulp. Such studies would allow obtaining a safe clinical procedure for the treatment of deep carious lesions.

#### **5. Conclusions**

Based on the results of this in vitro study, the following conclusions were drawn:


In the case of deep caries with a thin layer of dentin separating the filling from pulp, a base layer or a short duration polymerization mode is recommended to protect pulp from thermal injury during polymerization of the composite materials.

**Author Contributions:** Conceptualization, L.S., M.S. and J.S.; methodology, L.S. and P.J.; software, M.W.; formal analysis, M.S. and J.S.; investigation, L.S. and P.J.; resources, J.S.; data curation, P.J. and M.W.; writing—original draft preparation, L.S. and M.S.; writing—review and editing, P.J., M.W. and J.S.; visualization, L.S. and M.W.; supervision, J.S.; project administration, M.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author, [MS], upon reasonable request.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **Anisotropic Yield Criterion of Rolled AZ31 Magnesium Alloy via Nanoindentation**

#### **Zai Wang 1, Xin Hao 1, Ji Qiu 2, Tao Jin 1,3, Xuefeng Shu 1,2,\* and Xin Li 4,\***


Received: 20 November 2020; Accepted: 11 December 2020; Published: 16 December 2020

**Abstract:** In this paper, the anisotropic mechanical properties of rolled AZ31 magnesium alloys are investigated using nanoindentation tests at room temperature. Nanoindentation was carried out at four angles, including the rolling direction (0◦), diagonal direction (45◦), transverse direction (90◦), and vertical direction (ND). Experimental results show that hardness increases as the rolling angle increases from 0◦ to 90◦ and is lowest in the ND direction. The hardness independent of the effect of indentation depth is obtained by analyzing the indentation size effect and then converting hardness values into yield strengths. A new criterion is proposed on the basis of the Hill48 yield criterion. The data obtained through the above experiments are used to determine the parameters in the new criterion. Finally, a solution to the challenge of modeling a function that accurately describes the anisotropic yielding behavior of AZ31 magnesium alloys is proposed using the nanoindentation technique to solve the requirements of specimen size and experimental methods of the macro test.

**Keywords:** AZ31 magnesium alloy; nanoindentation; indentation size effect; anisotropic yielding criterion

#### **1. Introduction**

Magnesium alloys have aroused great research interest and are used in many applications on account of their excellent properties, which include high strength and good wear resistance, corrosion resistance, and thermal stability. However, although magnesium alloys present many advantages over other alloys, they are not perfect metals, because of their poor formability and corrosion resistance at ambient temperature. Magnesium alloys have a hexagonal closed-packed crystal structure with a limited number of available slip systems (basal {0001}, prismatic {1010}, and pyramidal {1011}), which leads to their poor formability during cold working [1]. While cast magnesium alloys are used more extensively than deformed magnesium alloys, the strength, ductility, and mechanical properties of the former are poorer than those of the latter. AZ31 is one of the most widely used alloys currently available. Rolling is an important means to improve the properties of this type of alloy. Under annealing and mechanical twinning, magnesium can show anisotropy at room temperature; thus, the nature of the plastic deformation of magnesium is quite complex [2]. Studies on the deformation and damage behavior of magnesium indicate that anisotropy clearly occurs during magnesium alloy deformation. Initial textures can impact the shape and stress–strain behavior of the samples [1]. The anisotropic mechanical characteristics of AZ31 magnesium alloys have a significant influence on their plastic

deformation. Therefore, obtaining a comprehensive understanding of the anisotropic mechanical behavior of magnesium alloys is important.

An accurate description of the magnesium alloy yielding behavior is essential to predict its forming processes. Industrial applications require an overall understanding of the mechanical properties of rolled AZ31 alloys. An accurate mathematical description is significant for predicting material deformation and yielding behaviors; thus, researchers have exerted considerable efforts over the last several decades to establish a solid foundation through which the magnesium yielding and deformation behaviors may be described. In 1864, Tresca established a phenomenological model to describe the yield of materials using the concept of maximum shear stress. Hu proposed an anisotropic yield criterion that satisfies the anisotropic presentation under uniaxial and equibiaxial tension [3]. Masse et al. [4] concluded that taking plastic anisotropy into account obviously improves the estimation of the final width. Many reports on the measurement of mechanical properties at the macro scale have been published. However, the in situ acquisition of the micro-scale mechanical properties of AZ31 alloys has yet to be conducted. Basu et al. [5] investigated size-dependent plastic responses by nanomechanical testing, high-resolution microscopy, and phase analysis and showed that the local microstructure has an obvious influence on small-scale plastic responses. Knowledge of the micro-scale mechanical properties of AZ31 alloys could provide a fundamental basis for its applications.

Most traditional experimental approaches, such as compression, tension, and torsion, are based on conventional bulk-scale testing, are destructive, and require a large number and volume of materials. The nanoindentation testing technique, a non- or semi-destructive approach, is considered a reliable, convenient, and robust approach with which to study the mechanical properties of materials at the nano- and micro-scales. Many scholars have proposed a series of simple mechanical properties for AZ31 alloys determined from indentation tests. However, in-depth studies of the mechanical properties of AZ31 alloys obtained via nanoindentation must be carried out, which can solve the impact due to the local deformation of the indentation test and complex operating conditions. In this study, nanoindentation tests were conducted using the continuous stiffness measurement technique (CSM), and the hardness of AZ31 alloys independent of size effects is obtained from the Nix model. The hardness values obtained are converted into strength values by using Tabor's factor, and the material parameters in the criteria were calculated to establish the anisotropic yield criterion of AZ31 alloys.

#### **2. Materials and Experimental Procedure**

The chemical composition of the material was Mg-90 wt.% Al-0.3 wt.% Zn-0.1 wt.%. The magnesium sheet was produced by the traditional rolling method. As shown in Figure 1, the specimens were machined into dimensions of 5 mm × 5 mm × 5 mm in the rolling direction (0◦), diagonal direction (45◦), transverse direction (90◦), and vertical direction (ND). The nanoindentation tests were performed using a Nanoindenter G200 test system produced by Agilent Technologies with a triangular pyramid Berkovich diamond indenter. The optical microscopic images were performed using the GX53 Metallographic Microscope produced by OLYMPUS. Prior to indentation testing, the test surface was ground using a series of SiC sand papers with gradually finer grains and polished to a scratch-free mirror-like finish. In this study, the maximum indentation depth was set to 2000 nm and the indentation strain rate was 0.001. Each test was performed at room temperature and repeated thrice. The mean hardness was used for the following discussion. The maximum indentation depth and Poisson's ratio of the AZ31 alloys were set to 2000 nm and 0.28, respectively. A constant indentation strain rate was implemented by maintaining a constant loading rate (. *p*/*p*) during the test. The hardness values were obtained during loading in CSM mode [6,7], and the dwell time at a constant load of 45 mN was set to 100 s.

**Figure 1.** Schematic of the loading of rolled AZ31 alloys in four directions.

#### **3. Results and Discussion**

Figure 2 shows the optical microscopic images of the rolled AZ31 samples in the 0◦, 45◦, 90◦, and ND directions (these directions are marked by the arrows in Figure 1); coarse grains of 5–20 μm could be observed in the samples. Barnett et al. found that grain size affects the mechanical responses of wrought magnesium [8]. The grain sizes of the rolled samples in the four directions were significantly different, which could explain the observed differences in their strength. The nanoindentation experiments were carried out in four directions, as shown in Figure 1.

**Figure 2.** Optical microscopic images of the rolled AZ31 samples in the 0◦, 45◦, 90◦, and vertical (ND) directions.

In CSM mode, the function of contact stiffness can be expressed as follows [6]:

$$S = \left[\frac{1}{\left(F\_{\rm amp} / h\_{\rm amp}\right)\cos\phi - \left(K\_s - m\omega^2\right)} - \frac{1}{K\_f}\right]^{-1} \tag{1}$$

where *S*, *Famp*, and *hamp* are the contact stiffness, amplitude of the harmonic excitation force, and response displacement amplitude, respectively. In addition, φ is the phase shift, ω = 2π*f* is the angular frequency (*f* = 45Hz), and *Ks*, *Kf* , and m are the spring constant in the vertical direction, frame stiffness, and mass of the indenter, respectively. The contact stiffness increases nearly linearly with indentation depth in the three directions, as shown in Figure 3.

**Figure 3.** Nanoindentation contact stiffness-depth curves obtained during the loading of rolled AZ31 alloys in four directions.

The projected contact area *Ac* of a perfect Berkovich diamond indenter can be calculated as follows [9,10]:

$$A\_c = 24.56h\_c^2\tag{2}$$

where *hc* is the contact depth and calculated by the equation:

$$h\_{\varepsilon} = h - \varepsilon \frac{p}{s} \tag{3}$$

where *P* and ε = 0.75 are the contact load and a contact for the Berkovich indenter, respectively. Hardness (*H*) is defined by the follow equation:

$$H = \frac{P}{A\_c} \tag{4}$$

where *P* is the contact load. The hardness–depth curves of the samples in four directions can then be obtained. As shown in Figure 4, the experimental data of 45◦ have better repetition.

**Figure 4.** Nanoindentation hardness-depth curves of 45◦ from three repeated experiments.

The hardness values of rolled AZ31 alloys during loading in the 0◦, 45◦, 90◦, and ND directions clearly differ, as shown in Figure 5. As the indentation depth increases, the hardness values decrease. The hardness increases as the angle increases from 0◦ to 90◦ and is smallest in the ND direction. Hardness is affected by the plate texture during rolling and shows significant anisotropy. Some factors of uncertainty and error in nanoindentation tests include surface roughness and surface texture, among others. In this study, the maximum penetration depth of the sample was approximately 2000 nm; such a depth is sufficiently large to assume that the contribution of surface inconsistencies is negligible. The hardness values observed in the 0◦, 45◦, 90◦, and ND directions are listed in Table 1.

**Figure 5.** Nanoindentation hardness-depth curves obtained during the loading of rolled AZ31 alloys in four directions.

**Table 1.** Fitting values of hardness under different angles.


The indentation size effect refers to the variation in the indentation hardness (or indentation stress) as a function of indentation depth [11]. The effects of indentation depth on the mechanical properties of metals must be considered. Under the limit of infinite depth, Nix et al. [12,13] proposed a hardness model to investigate the indentation size effect of metal hardness as follows:

$$\frac{H}{H\_0} = \sqrt{1 + \frac{h^\*}{h}}\tag{5}$$

$$H^2 = H\_0^2 h^\* \cdot \frac{1}{h} + H\_0^2 \tag{6}$$

where *H*<sup>0</sup> is the hardness in the limit of infinite depth and *h*<sup>∗</sup> is the characteristic length. The relationship between the square of hardness (*H*2) and the reciprocal of indentation depth (1/*h*) should be linear, as shown in Equation (6). We performed the linear fitting of *H*<sup>2</sup> vs. 1/*h*. Based on the indentation data collected between 500 and 1500 nm, the slope and intercept of the fitted straight line are *H*<sup>2</sup> <sup>0</sup> · *<sup>h</sup>*<sup>∗</sup> and *<sup>H</sup>*<sup>2</sup> 0, respectively. Thus, *H*<sup>0</sup> independent of the indentation size effect can be obtained (Figure 6).

**Figure 6.** H<sup>2</sup> versus 1/*h* curves of the rolled AZ31 alloys in four angles.

*H*<sup>0</sup> may be determined from the results of linear fitting, as shown in Table 2.


**Table 2.** Fitting values of *H*<sup>0</sup> under different angles.

A Tabor's factor of 3 can be used to convert the hardness values into yield stress values [14]:

$$H = \mathbf{3}\sigma\tag{7}$$

The strength of magnesium alloys can be obtained using Equation (7). The yield stresses in different directions are presented in Table 3

**Table 3.** Strength of the magnesium AZ31 alloys.


The anisotropy yield criterion of rolled AZ31 magnesium alloys is established according to the Hill 1948 yield function. The three-dimensional yield function proposed by Hill [15] is defined as follows:

$$f\_{\mathcal{Y}} = F\_{\mathcal{Y}} \left(\sigma \mathfrak{z} 2 - \sigma \mathfrak{z} \mathfrak{z}\right)^2 + G\_{\mathcal{Y}} \left(\sigma \mathfrak{z} 3 - \sigma\_{11}\right)^2 + H\_{\mathcal{Y}} \left(\sigma\_{11} - \sigma \mathfrak{z}\right)^2 + 2L\_{\mathcal{Y}} \sigma \mathfrak{z}^2 + 2M\_{\mathcal{Y}} \sigma\_{31}^2 + 2N\_{\mathcal{Y}} \sigma\_{12}^2 - \overline{\sigma}\_{\mathcal{Y}}^2 \tag{8}$$

where *Fy*, *Gy*, *Hy*, *Ly*, *My*, *Ny* are used to describe direction-dependent yield stresses.

These coefficients can be obtained by considering the uniaxial compression at some angle relative to the rolling direction and denoting the uniaxial compressive yield stress σθ. The stress components in the Cartesian axis system are:

$$
\sigma\_{11} = \sigma\_0 \cos^2 \theta \,\,\sigma\_{12} = \sigma\_0 \sin \theta \cos \theta \,\,\sigma\_{22} = \sigma\_0 \sin^2 \theta \tag{9}
$$

Substituting (9) for σ11, σ12, σ<sup>22</sup> in Equation (8) yields:

$$\sigma\_{\theta} = \left( (1)((F\_{\mathcal{Y}} + H\_{\mathcal{Y}})\sin^{4}\theta) + (G\_{\mathcal{Y}} + H\_{\mathcal{Y}})\cos^{4}\theta - 2H\_{\mathcal{Y}}\sin^{2}\theta\cos^{2}\theta + 2N\_{\mathcal{Y}}\sin^{2}\theta\cos^{2}\theta \right)^{-1})^{1/2}\tilde{\sigma}\_{\mathcal{Y}} \tag{10}$$

Based on the primitive function, the uniaxial compressive yield stresses for the rolling direction (0◦), diagonal direction (45◦), and transverse direction (90◦) are formulated as follows:

$$\begin{array}{l} \sigma\_{0} = \left(\frac{1}{G\_{y} + H\_{y}}\right)^{1/2} \overline{\sigma}\_{y\_{\prime}}\\ \sigma\_{045} = \left(\frac{4}{F\_{y} + G\_{y} + 2N\_{y}}\right)^{1/2} \overline{\sigma}\_{y\_{\prime}}\\ \sigma\_{90} = \left(\frac{1}{F\_{y} + H\_{y}}\right)^{1/2} \overline{\sigma}\_{y}. \end{array} \tag{11}$$

The yield stress in the rolled-plane direction, which is denoted σ*Z*, can be concisely expressed as follows (12):

$$
\sigma\_z = \left(\frac{1}{F\_y + G\_y}\right)^{1/2} \overline{\sigma}\_y \tag{12}
$$

The following expression can be acquired by finding the primitive function, and four anisotropic parameters are formulated by solving Equations (11) and (12) as follows:

$$F\_y = \frac{1}{2} (\frac{1}{\sigma\_{90}^2} - \frac{1}{\sigma\_0^2} + \frac{1}{\sigma\_z^2}) \overline{\sigma}\_y 2 \tag{13}$$

$$G\_{\mathcal{Y}} = \frac{1}{2} (\frac{1}{\sigma\_0^2} - \frac{1}{\sigma\_{\mathcal{Y}0}^2} + \frac{1}{\sigma\_z^2}) \overline{\sigma}\_y \,^2 \tag{14}$$

$$H\_{\rm Y} = \frac{1}{2} (\frac{1}{\sigma\_0^2} + \frac{1}{\sigma\_{90}^2} - \frac{1}{\sigma\_z^2}) \overline{\sigma}\_{\rm y}^{\prime 2} \tag{15}$$

$$N\_y = (\frac{2}{\sigma\_{45}^2} - \frac{1}{2\sigma\_z^2})\overline{\sigma}\_y^2 \tag{16}$$

Through-thickness anisotropic parameters related to shear *Ly* and *My* are assumed to be identical to the anisotropic parameters of *Ny* and calculated as follows [16]:

$$L\_{\!\!\!} = M\_{\!\!\!\!} = N\_{\!\!\!\!\!} \tag{17}$$

The yield stress clearly increases as the angle along the rolling direction increases. This result is consistent with the results of macroscopic compression yield strength. The anisotropic parameters in the yield function can be calibrated using the data in Table 2. The yield stress in the vertical direction σ*<sup>z</sup>* is used to represent the effective yield stress σ*y*. The calibrated anisotropic parameters are summarized in Table 4.

**Table 4.** Anisotropic parameters in the Hill yield function for rolled AZ31 alloys.


The anisotropic yield function determined via the nanoindentation test is utilized to describe the yield behavior of rolled AZ31 magnesium alloys. The following expression can be acquired by obtaining the primitive function:

$$\begin{array}{ll} f\_{\overline{y}} = 0.406(\sigma\_{22} - \sigma\_{33})^2 + 1.184(\sigma\_{33} - \sigma\_{11})^2 + 0.468(\sigma\_{11} - \sigma\_{22})^2 + 0.723\sigma\_{23} \\ \qquad + 0.723\sigma\_{31}^2 + 0.723\sigma\_{12}^2 - \overline{\sigma}\_{y}^2 \end{array} \tag{18}$$

#### **4. Conclusions**

The Hill48 yield function is calibrated using data obtained from nanoindentation tests because the proposed plasticity model is applied to the rolling process, during which materials mainly experience compression. The mechanical behavior of the AZ31 alloys is investigated via nanoindentation tests with the CSM technique. The indentation hardness exhibits anisotropic behavior and is relatively large under high angles along the rolling direction, that is, the hardness values increase as the angle increases from 0◦ to 90◦. The hardness in the ND direction is smallest among the values obtained. The anisotropic mechanical behavior of the alloys is analyzed, and the hardness independent of the effect of indentation depth is calculated. Tabor's factor can be used to convert hardness values into yield stress values. The Hill48 yield function of rolled AZ31 magnesium alloys is calibrated using the experimental results.

**Author Contributions:** Conceptualization, Z.W. and T.J.; methodology, T.J.; software, X.H.; validation, J.Q., X.L. and T.J.; formal analysis, X.S.; investigation, Z.W.; resources, Z.W. and T.J.; data curation, J.Q.; writing—originaldraft preparation, X.S.; writing—review and editing, T.J., Z.W. and X.H.; supervision, X.S.; project administration, X.L. and X.H.; funding acquisition, T.J. and X.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China [11772215, 11772217, and 11802199]. Tao Jin is grateful to the Open Fund of the State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi'An Jiaotong University [SV2019-KF-15] for its support. All financial contributions are gratefully acknowledged. And The APC was funded by [11772215].

**Conflicts of Interest:** Authors have no conflict of interest to declare.

#### **References**


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