A multimodal study of pinning selection for restoration of a historic statue

Materials and Design 98 (2016) 294–304

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A multimodal study of pinning selection for restoration of a historic statue Jessica Rosewitz a, Christina Muir b, Carolyn Riccardelli c, Nima Rahbar a,⁎, George Wheeler c,d a

Department of Civil and Environmental Engineering, Worcester Polytechnic Institute, 100 Institute Rd, Worcester, MA 01609, United States Jan Hird Pokomy Associates, 39 West 37th Street, New York, NY, United States c The Metropolitan Museum of Art, Objects Conservations Department, 1000 Fifth Avenue, New York, NY 10028, United States d Historic Preservation Program, Columbia University, 400 Avery, 1172 Amsterdam Avenue, New York, NY 10027, United States b

a r t i c l e

i n f o

Article history: Received 5 October 2015 Received in revised form 21 February 2016 Accepted 2 March 2016 Available online 4 March 2016 Keywords: Finite element Pin restoration Marble Structural Historical Conservation Restoration

a b s t r a c t Current practices for repair of fractured stone architecture and monuments rely on drilling into the substrate and installing metal pins, providing component alignment and resisting shear and tensile stresses. Adhesives such as acrylic resin may reinforce the pins at the interface with the stone. This research studies failure modes in the repaired areas of the statue Adam (Tullio Lombardo c. 1490–95) to ensure the artwork's longevity. Six materials as pins were investigated to repair fractured Carrara marble specimens. Furthermore, the results of finite element simulations were correlated with experiments on pinned join repairs. The simulations and experiments concluded that fiberglass pins outperformed metal pins. The fiberglass pins provided maximum strength to withstand the static forces of the repaired sculpture, without damaging the substrate before pin failure. From the simulation results, a ranking of the pin materials quantified the overall efficiency of the system. The ratio of join displacements at the tension stress limit to the compression stress limit in Carrara marble indicates the join performance, where 1.0 represents equal strength in tension and compression. The fiberglass pin achieves a ratio of about 0.80, from which we conclude that sudden join failure may be prevented, a desirable trait for monumental conservation. © 2016 Elsevier Ltd. All rights reserved.

1. Introduction This paper investigates and categorizes pin performance in the repair of fractured marble, supporting the restoration of the statue Adam by Tullio Lombardo c. 1490–95. The goals of this research are to study the failure modes in repaired areas, to analyze repair methods for adverse effects to the artwork's longevity, and to maintain relevance to both preservation and conservation of historic artifacts and architecture. The statue was repaired by conservators and restored in 2014 after the pedestal supporting the statue collapsed in 2002. The accident caused the sculpture to fracture into 28 large pieces and hundreds of smaller ones. Further information on the history of the statue and the subsequent research and treatment from the art conservator's point of view can be found in [1–3] for the interested reader. Previous work conducted on the glued joins can be found in [4,5]. Ultimately, only three joins were selected for structural pinning. In general, conservation of sculptures is the process to repair and make a sculpture whole again. Generally, conservators follow several principles. The original materials should remain intact and the repairs should not cause long-term damage. The restoration should be completely reversible, if possible. In the case of using a pinning repair to reconnect a break, the pinning site should not cause crack initiation ⁎ Corresponding author. E-mail address: [email protected] (N. Rahbar).

http://dx.doi.org/10.1016/j.matdes.2016.03.004 0264-1275/© 2016 Elsevier Ltd. All rights reserved.

in the sculpture. The process is difficult and time-consuming since the methods can be invasive. Therefore, the traditional method of drilling and installing pins is never undertaken lightly. Specifically within the bounds of the conservation of Adam, the goal was to maintain a tight join and a thin bond line. The breaks were fresh and the mating surfaces still fit tightly together, much different than with other historic sculpture with breaks that may be centuries old. Selecting adhesives to make the thinnest bond thickness was critical to recreate Adam as he was, reported in [4,5]. A second but equally important consideration was to design a repair system that would be as minimally invasive as possible with the least number of pins and drilled holes. This required careful analysis of the stresses on the sculpture in its entirety and across the join locations. Along with the pin number and locations, the pin material was a critical choice. From considerable study of the history and past applications in [3,6,7], conservators needed a pin that would not create stresses above what Carrara marble can endure. Here we combine experimental and numerical studies of structural pin materials in the high stress zones of the Adam statue that was in need of repair. Six pin materials were selected for experimental study to reconnect two halves of a cored marble cylinder, cut at a 45° angle, and secured by a pin to create a join repair scenario similar to the actual fracture of the Adam statue. Two repair methods were studied, one without an adhesive and one with an epoxy adhesive, termed dry and wet repairs, respectively. In the wet join repair, the epoxy secured the pin in drilled holes in the marble substrate. No epoxy was permitted

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on the diagonal join surface. The numerical analyses were performed using finite element analysis (FEA). The FEA were validated by the results from the experimental work. FEA were also used to study the failure mechanisms in the repaired system. The stresses in the marble substrate around the repair area and the pin were simulated as the result of an enforced joint displacement. By understanding the possible failure mechanisms in the join repair, this study identified the pin material most suitable to repair this statue. The locations in need of a structural pin were identified previously [6] as the left knee and both ankles of Adam. Because of the inclination angle of the anticipated pins to the fracture lines, the pins in those locations needed to resist both tensile and shear stresses. For the structural repairs to be successful, the pin should not cause any further damage to the marble once placed, and thus not adversely affect the artwork's longevity. This project highlights the implications of engineering mechanics and numerical modeling in the conservation of art, sculptures, monuments, and buildings. 1.1. Background The importance of combining science and conservation has not been understated. Idelson succinctly put it “The most authentic and irreplaceable contribution that conservation scientists can bring to the knowledge of heritage and to the improvement of the conservation techniques is in the different point of view that derives from the prevalence of natural sciences in their formation” [8]. Simply put, conservation needs science and vice versa. Outlined below are a few recent examples of collaboration between these engineering disciplines and conservation that are relevant to the work presented here on Tullio Lombardo's Adam. The marble statue of Neptune, dating from the 3rd century CE, was retrieved from the Rhone River and restored in 2012. Neptune is currently on display at the Arles Museum of Antiquity in Arles, France. Michel et al. reported in [9,10] the results of numerical analysis that supplemented the physical repair of this monumental sculpture. This included 3D digital imaging of the individual pieces to evaluate reassembly options. Then, alignment pins and high-tension tie rods were installed to connect the components. A numerical analysis was performed that included grout between pieces, specific interface elements, and 1D structural elements representing the pins and tie rods. This analysis yielded stresses in the rock substrate that did not exceed accepted limits as found in the literature. However, the zone surrounding the structural elements was not analyzed for local stresses caused by anchorage. The behavior of the marble in simulations was considered linear elastic, and the stresses in marble were evaluated at the end of the analyses with regard to tension and compression stress limits. Additionally, anisotropy was neglected. The contact surface between marble pieces was modeled by frictional constraints. Components of the grand scale project to restore the Acropolis of Athens monuments, including the Parthenon temple, were reported by Kourkoulis et al. in several publications: [11–14]. Of most interest to this work is [15], in which the effect of inclination angle to the fracture line of a threaded titanium rod was studied. The rod was installed to repair fractured epistyle pieces of Pentelic marble, and secured in the substrate with cement mortar. Scale model join repairs were fabricated and tested, and then modeled in FE using linear elastic material properties with isotropic behavior. The interfaces between the rod, mortar, and marble were defined with frictional constants. The finite element results were validated by comparing the force-displacement results of the repaired join with the experimental result, finding good correlation. And while not reported on scientifically, the restoration of the statue Juno, 2nd century CE, by the Objects Conservation and Scientific Research Labs at the Museum of Fine Arts, Boston approached the problem in a similar manner over a two-year process of analysis and design which finished in 2013 [16]. The goddess' head, attached sometime

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after her initial creation, had been installed using an iron rod. This rod corroded over time, severely damaging the neck. Furthermore, a fracture spanned across her midsection. The conservators chose a posttension rod to stabilize her torso, installed by drilling through down through the neck and anchored by plate beneath the waist. A new stainless steel pin reattached her head. Other pins were also installed at the base of the sculpture for stabilization through the supporting pedestal. Common themes persist in the conservation efforts. First, NDT techniques are used to determine the stability of monumental pieces and any existing pins. Second, a 3D scan is performed to obtain a full digital model of the monument. Third, FE modeling supplemented either the physical restoration or specimen mockups of the restoration. The FE modeling may be created from the 3D scans or simplified geometry. Within the FE modeling, most often elastic properties are assumed and the contact between surfaces is greatly simplified by frictional constants. 2. Materials and methods The mechanical performance of six pinning materials as join reinforcement for the marble statue Adam were studied: super-corrosionresistant 316 stainless steel, high-strength lightweight carbon fiber reinforced polymer, highly corrosion-resistant grade 2 titanium, structural fiberglass reinforced polymer, impact-resistant polycarbonate, and Teflon® PTFE. The pin materials were commercially available at the time of experiments (McMaster-Carr, Elmhurst, IL, USA). The behavior of the each material as join reinforcement was then experimentally and numerically investigated. 2.1. Carrara marble Carrara marble is a metamorphic rock quarried from the northwestern part of the Alpi Apuane region surrounding Carrara, Italy. It is a natural building material, and as such is characterized by microcracking [17]. It is widely used in monumental sculpture because of its homogeneity in appearance and composition. Furthermore, it is highly workable due to its rather low stiffness. It is a medium-grained white marble with intersecting grey veins. Composition is 99% calcite; the remainder is pyrite, quartz, albite, and white mica. Due to the nearly homogenous fabric, this marble has been used in rock-deformation experiments, where it has been shown to be nearly isotropic in relation to crystallographic orientation [2,18]. During metamorphic formation, it is prone to annealing which removes visible traces of deformation, and under large shear strains the grains are highly twinned [19]. It exhibits a high degree of dilatancy, where the material expands as it shears due to highly interlocked grains [20]. Microcracking is highly anisotropic and propagates inter and intra-granularly along grain boundaries. Flexural strength is dependent on specimen size, but is notch insensitive in testing, [17], and at confining pressures below 30 MPa Carrara marble is characterized by brittle fracture [21,22]. Alber and Hauptfleisch report the Young's modulus of Carrara marble is 49 GPa (7100 ksi), Poisson's ratio is 0.19, density is 2.65 g/cm3, and porosity is 0.4% [22]. Jaeger and Hoskins report the uniaxial tensile strength is 6.9 MPa (1000 psi) [23], and Wong and Einstein report the uniaxial compressive strength is 84.63 MPa (12,200 psi) [24]. Consistent among experiments regarding microcracking of Carrara marble, a distinct transformed white area forms prior to coalescence of microcracking, which is needed to accommodate plastic deformation [25]. This white area is a location to three types of microcracking: interand intra-granular and spalling. The white areas also lead to tensile wing cracks and shear cracks; the white area was classified as a microcrack development zone [26]. These white patches were also found to coincide with macroscopic crack development, but white patches and cracks developed slightly differently under quasistatic and dynamic strain rates [27].

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2.2. Experimental method The six pinning materials exhibit a wide range of Young's moduli. Therefore, mock join repair specimens were fabricated and tested to study the effects of stiffness and strength of the pins on the overall mechanical performance of the repair. Two sample sets of dry (without adhesive) and wet (with adhesive) join repairs were designed to study the contribution the pin material has on the join strength. A wet join repair is commonly used in sculpture conservation, as opposed to dry join repair. In a normal conservation scenario on a work of art, a conservator would always use adhesive in the pin holes and on the join surfaces. These experiments provided insight into the overall behavior of a pinned join under loading, and guidance on the best pin material to use in this conservation effort. A simulated join repair was fabricated using the proposed pin materials. Cylinders were cored from Carrara marble in 101.6 mm (4 in) diameter sections, each 203.2 mm (8 in) long. These cores were then cut in half along a 45° angle at the middle of each specimen using a 24″ slab saw (Buehler®, Lake Bluff, IL, USA) to simulate the most acute and therefore critical fractures in the Adam statue. These locations are the left knee and the ankles. The cut surfaces were mechanically sanded using a grinder with a 240 grit grinding plate (Buehler®). The specimens were then sanded smooth by hand using a glass plate and mixture of 240 grit silicon carbide powder (Buehler®) and water in a figureeight motion. The specimens were held by template while a 15.9 mm (0.626 in) hole was drilled into the center of each specimen to a maximum depth of 63.5 mm (2.5 in) using a 14 mm I.D. diamond core drill (Lunzer Tech. Inc., NY, NY, USA). Loose debris was removed from the sanded surfaces, and then the surfaces were cleaned with deionized water. The two halves were pinned together with a 15.7 mm (0.618 in) diameter pin, simulating a dry join, or without adhesive, repair of an actual 45-degree fracture that occurred in the accident. A close tolerance between the pin and drilled hole, of 0.1 mm (0.004 in) was chosen to limit the gap and create a tight join. This method repaired the join by vertically pinning the two halves of marble together (Fig. 1). The total height of each repaired specimen was 203.2 mm (8 in). Three specimens for each pin material were prepared, for 18 specimens.

Fig. 1. Schematic of the simulated join repair.

The second repair method was the wet repair using an epoxy (Akemi® Akepox® 2000, Akemi®, Nürnberg, Germany) to adhere the pins in the top and bottom marble halves (Fig. 2). These specimens were prepared by placing approximately 1.25 mL of epoxy in the 15.9 mm (0.626 in) diameter drilled hole using a syringe; 14.4 mm (0.569 in) diameter pins were used for the wet join repair. The gap between the pin and the hole is larger than the dry repair to facilitate epoxy placement in a 0.75 mm (0.030 in) gap. Small shims were temporarily placed around the pin to center it in the hole. After curing overnight, the shims were removed and the remaining gap filled with epoxy. Then, the assembly was inverted and the hole in the top core half was filled with epoxy. The two halves were then pinned together and allowed to cure for 2 weeks. The total height of each repaired specimen was 203.2 mm (8 in). This resulted in 18 specimens using epoxy. The specimens were prepared at the Department of Objects Conservation at The Metropolitan Museum of Art (MMA). Uniaxial compression tests were performed on the dry and wet join repair specimens to simulate the overall load capacity (Fig. 3). The specimens were tested using an Instron® 8501 (Instron®, Norwood, MA, USA) servo-hydraulic system in compression until failure with a maximum capacity 100 kN load cell, similar to the procedure in ASTM D7012–07 [28]. The load was applied at a rate of 0.001 mm/s until visible fracturing or excessive displacement occurred, or until a preset maximum force of 95 kN was reached. The schematics of the dry and wet repair specimens are presented in Figs. 1 and 2, respectively. The experimental setup applies shear stress in the pin and combined compression/tension and shear stresses in the marble substrate. 2.3. Numerical analysis: elastic analysis of structural pin material in Carrara marble FEA of the experimental setup was performed to further understand the mechanical performance of the join repair. The Abaqus/CAE 6.12–2 (Dassault Systèmes Simulia Corp., Johnston, RI, USA) software package was used to perform the simulations. Three-dimensional models of three parts, two marble halves and one pin, were prepared and meshed

Fig. 2. Schematic of the simulated wet join repair with epoxy to bond the pin to the marble cores.

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of 128,273 elements, and there are 10,010 elements in the pin. The assembly is composed of 266,556 total elements. The mesh was created with free tetrahedral elements. The bottom surface of the lower marble half is fixed in all directions as the only boundary condition in the simulations. Displacement is applied on the top surface of the upper marble half in one step with linear ramping of the displacement from zero. The top surface of the upper marble half is permitted to translate laterally, similar to what was observed in the experiments. Areas not in contact with another part, such as the top and bottom surfaces in the assembly, are meshed with larger elements for computational efficiency. Several factors were monitored during the simulations, in particular the overall force-displacement curve. Further, the FEA provided detailed stress distribution in the marble substrate around the hole, which was of importance when deciding which of the pin materials repaired the two join components in the most beneficial or least damaging way. 3. Results 3.1. Experimental results

Fig. 3. Experimental setup (specimen #8, dry repair with fiberglass pin).

using solid tetrahedral elements. The components in the model follow the same dimensions as the experiments [7] (Fig. 1). Prior to the wet and dry join repair compression testing, conservators at the MMA determined the flexural elastic moduli from flexural testing in 3-point bend. We simulated these flexural tests using the software Abaqus CAE 6.12–2 and found the simulations matched the experimental tests well. These mechanical properties for all materials used in the FE simulations are presented in Table 1. The surface contact between the two halves of the marble core along the join was modeled with static friction. The static coefficient of friction between the smooth join surfaces of the marble cores was chosen as 0.05. This coefficient of friction was experimentally determined using an inclined surface test, where the coefficient of static friction is the tangent of the angle from the horizontal at which the surfaces begin to slide. Smooth, hard contact controlled the interaction between the pin and interior face of the marble hole. A downward vertical displacement was then applied on the horizontal surface of the top core half. Since the FEA model was built to the same dimensions as the dry join repair, the diameter of the pin was slightly smaller in than the diameter of the hole in the marble. Therefore a slight amount of flexural deformation occurred before contact between the sides of the pin and the marble. The boundary conditions and interaction properties implemented into the 3D model are presented here. Each marble half is composed Table 1 Mechanical properties of materials used in the finite element simulations. Material

Young's modulus, GPa

Poisson's ratio

Carrara marble Carbon fiber reinforced polymer Fiberglass, structural Polycarbonate Stainless steel, Type 316 Teflon® PTFE Titanium, Grade 2 Akemi® Akepox® 2000 epoxy

49.0 28.2 14.8 3.90 200 1.80 100 3.3

0.19 0.30 0.30 0.37 0.27 0.46 0.37 0.30

3.1.1. Dry join repair specimens Testing results showed that metal pins could withstand a larger force before failure than fiber-reinforced and resin pins. Failure was characterized as excessive horizontal join misalignment or visible fracture through the marble. The testing apparatus used, Instron® 8501, had a maximum load cell capacity of 95 kN. This load is quite large in comparison to the estimated loads carried by the statue. Therefore, the testing was conducted until either visible failure of the marble substrate, the pin sheared, or the machine reached maximum load. In the case of the stainless steel and titanium pins, the latter occurred. The pin's Young's modulus and strength control this behavior. The stiff metal pins, stainless steel and titanium, crush the substrate at the interface around the pin, possibly densifying or pulverizing the marble into powder. The less stiff fiber pins, fiberglass and carbon fiber, are sheared along the diagonal join surface, and/or caused the marble core to fracture through or near the pin hole. The weakest resin pins, polycarbonate and Teflon®, exhibit excessive horizontal displacement, indicative of early pin shear failure. There is then inconsistent damage to the pin and marble at the interface in the dry repair specimens across the six pin material selections. The dry repair specimens exhibited several consistent trends in the force-displacement curves from the experiments, and in observations on join misalignment and marble fracture. The force-displacement presents an initial soft behavior for the join, but then swiftly hardens nonlinearly into a steep linear relationship indicative of the hard contact with frictional behavior. Experiments with the stainless steel pin exhibit a stiffer behavior, and thus, reach maximum force earlier than the experiments with the less stiff titanium pin. The experimental results for the stainless steel and titanium pins are shown in Figs. 8 and 9, respectively. The dry repair specimens using metal pins showed little horizontal join misalignment and no visual marble surface fracture, with the exception of minor crushing of uneven edges on the top and bottom bearing surfaces. Additionally, all specimens with metal pins fused together and were unable to be separated manually once testing completed. This may be due to the soft nature of Carrara marble in comparison with the stiff metal pins. While the interface between the pin and hole could not be observed during the experiment, one may hypothesize that as the repair specimens were loaded, the stiff pin crushed the soft marble locally near the pin hole. High compressive stresses fused the marble and metal pins, locking the crushed join together. The experimental results for the carbon fiber (Fig. 10) and fiberglass pin (Fig. 11) show an initial soft behavior, which slowly converts into a stiffer linear relationship. However, once a certain elastic limit is reached, the curve softens and plastic behavior is observed. This plastic behavior can be explained by breakage of the pin's fibers, shearing, and

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Fig. 4. a, b: Fiber pin failure, dry repair. a) Fiberglass pin fiber damage showing fiber shear (specimen #7, bottom half). b) Carbon fiber pin damage showing fiber pullout and kinking (specimen #15, top half).

pullout within the pin matrix material (Fig. 4). In these scenarios, the join repair fails by pin shear and/or marble fracture, and load carrying capacity diminishes. This is marked by sharp drops in the forcedisplacement curves. All dry join specimens repaired with fiberglass pins showed the same failure modes. The fiberglass pin shears along the repair plane and the marble fractures tangentially to the pin hole through the entire marble specimen (Fig. 5a). Typically, only one of the marble halves fractured, but it was inconsistently the top or bottom half. Specimens repaired with the carbon fiber pin showed similar behavior to both the fiberglass pin specimens and the metal pin specimens. Two carbon fiber repair specimens fused together at the

conclusion of the experiments, similar to the metal pin specimens. In the remaining carbon fiber specimen, the pin sheared and one marble half fractured along a line tangential to the pin hole, similar to the fiberglass pin specimens (Fig. 5b). The experiments of the polycarbonate pin (Fig. 12) and Teflon® pin (Fig. 13) showed the initial soft behavior, which slowly stiffened. The curves for polycarbonate and Teflon® pins do not develop a linear elastic relationship; instead, the curvature reverses and displays plastic behavior. The experiments were stopped at the maximum force of 95 kN representing a large amount of force needed to shear the pins. The dry repair with polycarbonate pin showed large horizontal displacement

Fig. 5. a–d: Marble fracture, dry repair. a) Fiberglass pin shear and marble fracture tangential to the pin hole (specimen #5, bottom). b) Carbon fiber pin kinking and marble fracture tangential and radial to pin hole (specimen #15, top, left; bottom, right). c) Crushing, powdering, and densification of marble around fiberglass pin (specimen #7). d) Necking of Teflon® pin (specimen #1).

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without marble fracture, indicating the pin failure occurred much earlier than marble failure. None of the marble cores fractured in the dry repair with polycarbonate pins. The dry repair with Teflon® pin also showed large horizontal displacement with marble fracture, proving the pin failure occurred earlier than marble failure. The Teflon® pin showed sufficient plasticity to deform severely and undergo necking before complete failure (Fig. 5d). Marble fractures in the dry repair with Teflon® pin occur tangential to the pin hole and radial across the pin hole, fracturing the entire specimen. While, Teflon® and polycarbonate are capable of absorbing most of the energy and keeping the marble safe, the excessive join misalignment under load suggest these two materials may not be suitable for sculpture repair.

3.1.2. Wet join repair specimens In the wet join repair specimens, epoxy was used to fill the gap between the pin and the walls of the drilled holes. The epoxy covered nearly the entire length of the pin, but not the joining surface of the two marble halves. In all other respects, the experiments were performed in the same manner as the dry join repair. Marble fracture occurred at a consistently lower value of vertical displacement when compared with the dry join repair specimens. Additionally, for all wet join repair specimens the force-displacement curves reached the maximum force at lower displacement when compared with the dry join repair specimens.

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The stiffness of the pin material controls the behavior of the wet join repair specimens. For this set of tests, the carbon fiber and fiberglass pins protected the marble cores and provided excellent load resistance. Additionally, these pins failed in shear well before the marble fractured for the majority of cases. The weakest pins, polycarbonate and Teflon®, caused large join displacements before pin failure at lower forces. The stiffer metal pins, stainless steel and titanium, caused early marble fracture at high forces and low displacement. Across the various pins, failure occurs by one of three methods: the marble fractures, the pin shears, or the pin begins to exhibit non-linear behavior and damage causing visible join displacement. The first occurring failure is not clear from simply observing the maximum force from the force-displacement curves. All wet join repair specimens with metal pins failed consistently. The stainless steel and titanium pins retained join alignment to such a degree that the marble fractured around the pin. The crack most often initiated outward from the pin in a tri-fold pattern (Fig. 6a–b). This is perhaps because of the large mismatch between elastic moduli of the metal pins and marble. This is also in contrast to the dry join repair specimens with metal pins that did not initiate cracks in marble but rather crushed the area around the hole. For a wet join, a distinct compressive ring in the marble formed around the pin hole at the join surface, and no powdering or pulverizing of the marble occurred (Fig. 6c). This is because the epoxy formed a protective (strong) layer between the pin and the hole. The epoxy prevented the marble from crushing and pulverizing into powder, as were observed in the dry join repair specimens

Fig. 6. a–d: Marble fracture, wet repair. a) Tri-axial radial marble fracture pattern on top and bottom cores (specimen #34, stainless steel pin; top, left; bottom, right). b) Lateral radial marble fracture pattern (specimen # 36, stainless steel pin; top, left; bottom, right). c) Compressive ring in marble substrate around pin hole with fracture (specimen #28, titanium pin; top). d) Compressive ring in marble substrate around pin hole without fracture (specimen #32, carbon fiber pin; bottom).

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with metal pins. Instead, the marble fractured due to local mode-I stresses. The wet join repairs with carbon fiber pins failed by pin shear failure, with no significant marble fracture. The carbon fiber pin was sufficiently stiff enough to cause the same compression ring in the marble around the pin hole, similar to what was seen with the metal pins (Fig. 6d). The ring of marble stressed in compression around the hole began to separate and lift away from the surface of the specimens before the carbon fiber pin failed in shear. None of the specimens repaired with the fiberglass pin caused fracture in the marble, and all specimens failed by the failure of pin in shear. The same compression ring phenomenon formed around the pin hole at the join surface, but did not separate or lift off of the specimen before the fiberglass pin sheared. The wet join repair specimens with polycarbonate pin showed similar results to the specimens with fiberglass and carbon fiber pins. The pin sheared at the join, but no marble fracture occurred. The compression ring formed around the pin hole at the join surface, and some specimens caused that area to separate or lift off the marble before the polycarbonate pin sheared. The adhesion of the epoxy failed before the experiment in two of the wet join repair specimens with a Teflon® pin. This is obviously due to the low surface roughness of Teflon®, and the low adhesion energy between Teflon® with epoxy due to high resistance to van der Waals forces [29]. These two characteristics combine to make it difficult to bond anything to a Teflon® surface. The join repairs failed by pin shear, and no marble fracture occurred. The same compression ring formed, and did separate or lift away from the marble at the join surface, occurring prior to pin failure. 3.2. FEA simulation results 3.2.1. Dry join repair simulation The FEA was used to simulate the dry join repair for the six pin materials, using the geometry and properties of materials in the system. A model was also created using a Carrara marble pin, the results of which are included here. The finite element simulations can accurately predict the overall behavior of the systems (Figs. 8–13). The initial part of each FEA force-displacement curve shows a shallow slope, representing the deformation of the pin in the larger hole. The forcedisplacement curve clearly presents the initiation of contact shown by a stiffening as the pin is brought into contact with the marble. The failure of the marble can be described by two predominant modes: a) fracture of marble due to mode-I cracks (Fig. 5), and b) crushing of marble under compression, which can be seen around the pin-to-hole interface (Fig. 5c). While the crack growth in marble is not simulated in the model, the stress propagates through the marble around the pin in the following process. To begin, downward displacement is applied on the horizontal surface of the top marble half. The relatively low coefficient of static friction allows the top marble core to slide along the diagonal, but the pin restrains lateral movement. The gap between the pin and the hole is 0.1 mm on each side (pin diameter is 15.7 mm; hole diameter is 15.9 mm). This small gap permits the pin to displace laterally and to bend in the hole. As the marble cores slide against one another, the 45° acute angled marble edge is pushed against the pin. The compression stress in the acute edge exceeds the marble's ultimate strength of about 84.63 MPa (Fig. 7a–b), and the marble crushes and is pulverized into a combination of small fragments and powder (Fig. 4a–b). This happens in both the top and bottom halves, as the acute edge of the halves are pushed against opposite sides of the pin. The marble surface in contact opposite the acute edge is compressed as the top half slides against the bottom half. As the acute edge goes into compression, a half ring of tension forms underneath as the compressed region is pushed laterally outward from the core (Fig. 7b–c). The tensile stress exceeds the ultimate tensile strength of about 6.9 MPa and the compressed portion breaks away from the marble (Fig. 5c). The opposite half compresses the 135° obtuse angled marble edge. At the perimeter of this compression

Fig. 7. a–e: Principal stress propagation in the bottom half of the marble core, section cut (top half similar). Black zone exceeds compressive stress limit of 84.63 MPa, grey zone exceeds tensile stress limit of 6.9 MPa.

zone below the obtuse edge is another tension zone around the hole (Fig. 7d–e). Because of this tension zone, the compressed portion also separates from the marble half, fragmenting and pulverizing into powder. Table 2 shows the reaction force and vertical displacement when the maximum principal stress in marble exceeds the compression or tension limit stresses of 84.63 MPa and 6.9 MPa, respectively. Fig. 14 displays the corresponding vertical displacement when the maximum principal stress in marble exceeds the tension or Table 2 Force and vertical displacement at maximum principal compression and tension stresses in marble. Pin material

Stainless steel, Type 316 Titanium, Grade 2 Carrara marble Carbon fiber reinforced polymer Structural fiberglass Polycarbonate Teflon® PTFE

Tension failure in marble

Compression failure in marble

Force kN

Displacement mm

Force kN

Displacement mm

0.15 0.13 0.12 0.11 0.11 0.06 0.06

0.11 0.16 0.21 0.27 0.28 0.30 0.30

0.59 0.59 0.63 0.56 0.53 0.67 0.76

0.24 0.28 0.30 0.32 0.35 0.49 0.65

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compression limits from FEA of the dry join repair. The location of the maximum principal stress in the model is at the sharp edge of the pin hole at the join surface. For the selected pin material, fiberglass, if the join was to displace vertically at about 0.28 mm, the marble would be stressed at the tension limit of 6.9 MPa, and at a displacement of 0.33 mm, it would be stressed at the compression limit of 84.63 MPa. Creating a join displacement ratio, T/C, for each pin material compares the join strength in tension vs. compression. The variable “T” is the join displacement at tension stress limit and “C” is the compression stress limit in Carrara marble. This ratio, representing the overall efficiency of the system, is presented in Fig. 15. Theoretically, a pin that provides equal join strength in tension and compression has a T/C ratio approaching 1.0. Fiberglass and carbon fiber pins nearly achieve that ratio, at 0.8 and 0.84 respectively. A T/C ratio closer to 1.0 is desirable because it indicates the highest mechanical performance in the join, or the ability of the join to carry the highest forces before failure. The results in Table 2 show that the stress limits are reached at low force and displacement values. However, Figs. 8–13 show elastic behavior of the entire dry join repair. Hence, internal damage at the pin hole occurs at very low displacements, and the complete join failure occurs at higher displacements. Since the intent of this analysis is to prevent damage to marble, then a pin material that holds the join together but is still less stiff than the substrate is the obvious choice. When taken in tandem with the experiments, structural fiberglass is the optimum pin material. The pin is less stiff than the marble, and the internal damage occurs at about 0.1 kN in tension and 0.5 kN in compression. Fig. 11 shows that the entire join repair fails at about 20 kN. The difference between the first internal damage and the final join failure is due to complex interaction between the join surfaces and pin post-failure.

3.2.2. Wet join repair simulation The FEA simulations of the wet join repair modified the previous model by adding two sleeves of the epoxy in each hole surrounding half of the pin, for a total of five parts in the assembly (Fig. 2). Similar to the dry join repair, the six pin materials were studied. The bond between epoxy and both the marble and pin was modeled as a perfect rigid bond between interfaces. A near perfect bond was assumed during experimentation, but upon further investigation of the epoxy and comparison of FEA with the experimental results, this indeed may not be the case. The bonding agent, Akemi Akepox 2000®, is specified for use as a superior adhesive for either natural or cast stone. The bond is stronger to silicate-bound stones than carbonate-bound stones, and the bonding agent easily bonds to damp stone. It is also specified to bond wood and ceramics, and works well with glass fibers and polycarbonate.

Fig. 8. Stainless steel pin force-displacement vs. FEA simulation results.

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Fig. 9. Titanium pin force-displacement vs. FEA simulation results.

For the tested wet join repairs with pin materials compatible with epoxy, the samples reached higher join strengths at lower join vertical displacements than the dry join repair specimens. This can be seen in Fig. 10 for the carbon fiber pin, Fig. 11 for the fiberglass pin, and Fig. 12 for the polycarbonate pin, in which the linear portion of the force-displacement curves are stiffer for the wet join repair than the dry join repair. However, for pin materials incompatible with epoxy, both sets of dry and wet repair results match. This can be seen in Fig. 8 for the stainless steel pin and Fig. 9 for the titanium pin, in which the linear slope of the force-displacement curves are indistinguishable. The results for the Teflon® pin are inconsistent (Fig. 13), and confirm observations that this pin material is not suitable to maintain join alignment or contribute to join strength, nor can it be used with the selected epoxy. Selected FEA results are presented here for the wet join repair with the carbon fiber pin (Fig. 10) and the fiberglass pin (Fig. 11) to illustrate the disparity between the FEA and experimental results of the wet join repair. The possible differences between the FEA and experimental results are hypothesized in the following. For the wet join repair, the epoxy was applied between the pin and marble using a small syringe. This process may have introduced some inadvertent air pockets or bubbles within the body of the epoxy sleeve. Furthermore, the epoxy consisted of a two-part mix of resin and hardener, and the mixing was likely to have incorporated air within the epoxy even before it was placed. These imperfections could have led to early initial epoxy failure by cracking, or caused discrete locations of a weaker bond between the marble and pin.

Fig. 10. Carbon fiber pin force-displacement vs. FEA simulation results.

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Fig. 11. Fiberglass pin force-displacement vs. FEA simulation results.

Fig. 13. Teflon® PTFE pin force-displacement vs. FEA simulation results.

The method of setting the pins for testing the wet join repair also may have introduced incomplete bond between the interfaces. The setting putty at the base of the pin displaced a small volume of the epoxy, leaving locations where no bond occurred between pin and marble. This may have reduced the effectiveness of the epoxy sleeve, creating locations where early failure might occur. Finally, there may have been an air gap at the interfaces. A reasonable explanation of this thinking is that the thermal expansion and contraction is different for each material. For example, the coefficient of thermal expansion for type 304 stainless steel is 17 to 18 × 10−6C−1 [30], while for Carrara marble it is 2.4 to 6.7 × 10−6C−1 [20]. Before testing the wet join repair, it was left to cure for 1 week at the MMA, then transported for testing and allowed to cure for another week. The location change and long curing times likely caused temperature fluctuations across the join materials leading to expansion and contraction at the interfaces and interference in the bond to the epoxy.

specimens with metal pins fused together at the conclusion of the experiments. The joins containing the polycarbonate and Teflon® pins are not strong enough as the force-displacement curves plateaus at relatively small force. The polycarbonate and Teflon® pins are failed in shear at low load and cause excessive horizontal displacement and sometimes fracture in marble. The Teflon® pin also caused marble fracture in all specimens. The diagonal join surface creates shear failures in the fiberglass and carbon fiber pins with some marble fracture. Two carbon fiber repair specimens fused together at the conclusion of the experiments, similar to the metal pin specimens. In the remaining carbon fiber specimen, the pin sheared and one marble half fractured. Of the fiberglass specimens, only one out of three fused together at conclusion of experiment. Furthermore, all the fiberglass specimens caused marble fracture after pin shear, an important result since this signifies the pin is sacrificial with respect to the marble. The dry join result is complemented by the experimental results from the wet join repair specimens. The wet joint repair more closely resembles actual repair techniques used by art conservators. However, conservators would have applied a reversible adhesive to the join surface. In the wet join repair specimens, marble fractured at smaller vertical displacement and reached maximum force at lower displacement versus the dry join repair specimens. The stainless steel and titanium pins retained join alignment to such a degree that the marble fractured around the pins. The wet join repairs with carbon fiber pins failed by pin shear failure, with no marble fracture. Therefore, these pins, and the

4. Discussion and conclusions Testing the dry join repair specimens provided a systematic approach for selecting the proper pin material for this specific marble sculpture and repair of historical marble. Due to their high stiffness and strength, the stainless steel, titanium, and carbon fiber pins cause damage to the diagonal join surface and the interior pin hole by crushing the marble. These specimens showed little horizontal join misalignment and no fracture was visible on the marble surface. All

Fig. 12. Polycarbonate pin force-displacement vs. FEA simulation results.

Fig. 14. Join displacement (mm) characterized by pin material at tension and compression limits in Carrara marble.

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locations, the most notable result from the treatment of Adam is that approximately 20 major joins were repaired with a completely reversible adhesive. This follows a common principal in conservation to leave materials intact wherever possible. The traditional method of pinning is irreversible, since holes must be drilled to install the pins, thus damaging the substrate and removing portions of the original artwork. By combining the experimental method and the FE simulations, we conclude that a join repair using a fiberglass pin is the most efficient join with regard to ultimate strength. Most importantly, since the fiberglass pin failed in shear before the marble fractures, it should not cause long-term damage to the artwork. Acknowledgements We acknowledge the generous gift from the Objects Conversation Department at The Metropolitan Museum of Art. References Fig. 15. Join displacement ratio T/C by pin material Young's modulus (T = join displacement at tension stress limit in Carrara marble; C = join displacement at compression stress limit in Carrara marble).

carbon fiber pin were precluded because of marble failure by fracture. None of the specimens repaired with the fiberglass pin caused fracture in the marble. The polycarbonate pin went through shear failure at the join, but the marble did not fracture. The remaining differences between polycarbonate and fiberglass pins were minimal in the wet repair case, but fiberglass clearly outperforms in the experiments. The FEA simulation results matches well with the experimental results for the dry join repair. The highest stress concentrations are in the marble at the pin hole at the join surface in both compression and tension on opposite sides of the pin. These are the sites of crack propagations observed in the specimens. The finite element simulations perfectly predict the behavior of the dry join repairs. From the simulation results, the join displacement T/C ratio ranks the different pin materials. The T/C ratio compares the join displacement at the tension stress limit to the compression stress limit in Carrara marble, quantifying the overall efficiency of the system. At 1.0, this ratio represents a pin that provides equal join strength in tension and compression. The fiberglass and carbon fiber pins nearly achieve that ratio, at 0.80 and 0.84 respectively, more desirable than the other pins indicating high mechanical performance in the join. Most importantly, this join will prevent sudden or catastrophic join failure, a desirable trait for sculpture conservation and preservation. Using FEA, the experimental conclusion that fiberglass is the most optimal material for pinning repair of Carrara marble is upheld with the least potential to damage the marble substrate. A complete finite element model of Adam was constructed after the sculpture was fractured, from 3D laser scans of the major fragments [3]. Analysis of the FE model loaded with the self-weight of the sculpture provided stresses across each fracture plane in the sculpture, from which the highest compressive and tensile stresses occur between the left calf and ankle fragments. The maximum compressive stress is 0.924 MPa at the front, and the tensile stress is 0.524 MPa at the back [3]. This FE model did not account for the pinning repair at the left knee, or left or right ankles. The magnitudes of the maximum compressive and tensile stresses from the full FE model of Adam are quite low when compared to the tensile (6.9 MPa) and compressive (84.63 MPa) limits of Carrara marble. Therefore fiberglass, the selected pin material can also withstand the highest forces on the sculpture. While the result of this study is a matched pair of a pin and a substrate, a designed repair for pinning a particular stone substrate, the methods reported herein can be expanded to other conservation efforts with sculpture and architecture. The proposed repair should also be evaluated to preclude drilling and inserting a pin, instead using a reversible adhesive as reported in [3–5]. While the experimental and FE simulations support the conservator's installing fiberglass pins in three

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