Submitted Successfully!
To reward your contribution, here is a gift for you: A free trial for our video production service.
Thank you for your contribution! You can also upload a video entry or images related to this topic.
Version Summary Created by Modification Content Size Created at Operation
1
Masum Bellah
 -- 5080 2023-08-08 18:25:36 |
2 format change
Peter Tang
 -11 word(s) 5069 2023-08-09 02:55:52 | |
3 The Description section has been updated.
Masum Bellah
 -76 word(s) 4993 2023-08-10 03:34:48 |

Video Upload Options

Do you have a full video?
Send video materials Upload full video

Confirm

Are you sure to Delete?
Yes No
Cite
If you have any further questions, please contact Encyclopedia Editorial Office.
Bellah, M.; Nosonovsky, M.; Rohatgi, P. Shape Memory Alloy Reinforced Self-Healing Metal Matrix Composites. Encyclopedia. Available online: https://encyclopedia.pub/entry/47805 (accessed on 31 August 2024).
Bellah M, Nosonovsky M, Rohatgi P. Shape Memory Alloy Reinforced Self-Healing Metal Matrix Composites. Encyclopedia. Available at: https://encyclopedia.pub/entry/47805. Accessed August 31, 2024.
Bellah, Masum, Michael Nosonovsky, Pradeep Rohatgi. "Shape Memory Alloy Reinforced Self-Healing Metal Matrix Composites" Encyclopedia, https://encyclopedia.pub/entry/47805 (accessed August 31, 2024).
Bellah, M., Nosonovsky, M., & Rohatgi, P. (2023, August 08). Shape Memory Alloy Reinforced Self-Healing Metal Matrix Composites. In Encyclopedia. https://encyclopedia.pub/entry/47805
Bellah, Masum, et al. "Shape Memory Alloy Reinforced Self-Healing Metal Matrix Composites." Encyclopedia. Web. 08 August, 2023.
Shape Memory Alloy Reinforced Self-Healing Metal Matrix Composites
Edit
This entry is adapted from the peer-reviewed paper 10.3390/app13126884

Shape-memory alloys (SMAs) are among the newest and most popular smart/intelligent materials that can recover their original shape when heated above a critical temperature. Self-healing refers to the remarkable ability of a material to repair damage inflicted upon it, such as cracks or voids. A Metal Matrix Composite (MMC) is a composite material that consists of at least two constituent parts: a metal (or alloy) matrix and typically a ceramic or metallic reinforcement (which can be particles, fibers, or whiskers) to enhance strength, stiffness, and other specific properties.

self-healing metal matrix composites shape-memory alloys crack closure phase transformation

1. Introduction

Self-healing refers to the remarkable ability of a material to repair damage inflicted upon it, such as cracks or voids. The concept of self-healing in materials finds its inspiration from the regenerative properties found in biological tissues, which can heal themselves naturally following an injury or bleeding. This fascinating phenomenon has been observed in various living systems, ranging from plants and animals to humans. Scientists and engineers aim to mimic and harness these inherent healing mechanisms to design materials that can autonomously repair themselves when subjected to damage [1]. The concept of self-healing in materials represents the shift of the current materials design strategy from “damage prevention” to “damage management” [2]. Self-healing has so far been most successfully applied to polymerics [3][4][5][6][7][8][9][10][11][12][13], ceramics [14][15][16][17][18], and cementitious materials [19][20][21][22][23][24][25][26]. Developing self-healing properties in metals or metal composites is challenging due to their strong metallic bonds, which provide exceptional strength and stability. However, this strength limits the necessary atom mobility and rearrangement for effective self-healing. Additionally, the small size and low diffusion rate of potential healing atoms, particularly at operating temperatures, further hinder the achievement of self-healing properties in these materials [27].
Self-healing materials find applications in a wide range of industries, including automotive, electronics, aerospace, defense, manufacturing, construction, healthcare, and consumer goods. Similarly, Self-healing Metal Matrix Composites (SHMMCs) are anticipated to play a crucial role in aerospace, automotive, electronics, energy conversion, and energy storage-related sectors [28][29][30][31][32]. SHMMCs are proposed for spacecraft, extraterrestrial planet surface rovers, and deep-sea applications that are currently impractical or impossible to repair while in service [33]. SHMMCs offer significant potential for application in a wide range of aircraft structural components, providing enhanced performance and durability in fuselage skin, stingers, frames, ribs, longerons, stiffeners, doors, fuel tanks, landing gears, wheel wells, fuel lines, shock struts, empennage structures, avionics enclosures, and floor beams [34]. These advanced materials hold promise in spacecraft structures, including hulls, frames, trusses, panels, and support structures, enabling extended missions with improved reliability. Furthermore, the utilization of SHMMCs in the oil and gas industry could revolutionize structures such as oil-well casings, pipelines, offshore platforms, and drilling equipment, delivering enhanced structural integrity and maintenance capabilities. Similarly, extraterrestrial planet surface rovers could greatly benefit from SHMMCs in various critical structures, encompassing chassis, body panels, wheels, suspension components, robotic arms, and other load-bearing and protective elements, enabling reliable exploration and operation. Additionally, deep-sea applications stand to benefit from the use of SHMMCs in structures like underwater vehicles, submersibles, remotely operated vehicles (ROVs), and offshore oil and gas exploration equipment, enhancing their durability and performance in challenging marine environments.
Shape-memory alloys (SMAs) are among the newest and most popular smart/intelligent materials that can recover their original shape when heated above a critical temperature [35][36].

2. Classification of Self-Healing Metal Matrix Composites

SHMMCs are classified on the basis of self-healing mechanism, phase transformation involved during healing, characteristic length scale of the healed damage, and autonomy. SMA clamp-and-melt-based self-healing, solder tube/capsule-based self-healing, and nano-SMA dispersoid-based self-healing are among the self-healing mechanisms studied so far for metal matrix composites. SHMMCs are classified by Manuel [37] based on the type of phase transformation involved during healing, such as solid-state or liquid-assisted healing. According to this classification, SMA clamp and melt and solder tube/capsule-based self-healing are classified as liquid-assisted healing, whereas nano-SMA dispersoid-based self-healing is classified as solid-state healing. Tasan et al. [38] have classified the SHMMCs based on the characteristic length scale of the healed damage. According to their classification, nano-SMA dispersoid-based healing is classified as nanoscale healing, whereas SMA clamp and melt and solder tube/capsule-based healing is classified as macroscale healing. Based on autonomy, SHMMCs can be classified as autonomous or nonautonomous [38]. The autonomous SHMMCs do not require external intervention to repair the damage, whereas nonautonomous SHMMCs do require external intervention, such as the application of heat. According to this classification, nano-SMA dispersoid-based healing is classified as autonomous healing, whereas SMA clamp and melt and solder tube/capsule-based healing is classified as nonautonomous healing. Table 1 shows the classification of self-healing metal matrix composites. The SMA clamp-and-melt-based self-healing concept stands out as the most promising among the macroscale mechanisms because of its ability for limitless repetition. In contrast, the solder tube/capsule-based self-healing approach utilizes encapsulated solder materials that are released to fill and repair cracks. While offering localized healing, its success depends on the careful selection of host matrix and solder materials. The nano-SMA dispersoid-based self-healing mechanism offers a precise nanoscale healing potential but relies on specific material combinations to achieve the desired nanosized coherent particles with shape-memory effects [38].
Table 1. Classification of self-healing metal matrix composites.

Self-Healing Mechanism

Phase Transformation Involved during Healing

Characteristic Length Scale of the Healed Damage

Autonomy

SMA clamp-and-melt-based self-healing

Liquid-assisted healing

Macroscale healing

Nonautonomous

Solder tube/capsule-based self-healing

Liquid-assisted healing

Macroscale healing

Nonautonomous

Nano-SMA dispersoid-based self-healing

Solid-state healing

Nanoscale healing

Autonomous

3. Synthesis of Shape Memory Alloy Reinforced Self-Healing Metal Matrix Composites

This entry will consider the following alloys analyzed as matrixes in previous studies:
  • Sn-13at.%Bi [39]
  • Mg-5.7at.%Zn-2.7at.%Al [39]
  • Al-Si, Al-Cu, and Al-Cu-Si [34]
  • Al-3at.%Si [40]
  • Sn-20wt.%Bi [41][42]
  • Sn-13wt.%Bi [43]
  • Bi-10wt.%Sn [41][42]
  • Zn-0.8Al-0.015Cu [44]
  • AA2014 (an aluminum alloy consisting of Al-Cu-Si-Mn-Mg-Fe) [45][46]
The influence of design factors such as SMA volume fraction, pre-strain of SMA wires, and healing temperature on the healing of SHMMCs has not been thoroughly investigated. Poormir et al. [43][47] and Srivastava et al. [45] conducted experimental studies using the Taguchi method [48] to investigate the impact of design factors, including volume fraction, diameter and pre-strain of SMA, specimen size, and healing temperature, on the healing process of SMA-reinforced SHMMCs.
Manuel [39][49] developed proof-of-concept self-healing composites by using a Tin-based metal matrix (Sn-13at.%Bi) and equiatomic NiTi SMA wires. One percent volume fraction of continuous, uniaxially oriented NiTi SMA wires was used as reinforcement. Surface treatment techniques, including electropolishing of the SMA wires in a solution of 5% perchloric acid and 95% acetic acid, followed by a 5 nm gold sputter-coating, were employed to enhance the bonding between the NiTi SMA wires and the metal matrix. Specially designed clamps were used to maintain tension in the wires during casting, and the clamp/wire assembly was placed in a heated graphite mold coated with boron nitride (BN). BN spray treatment was applied to both the crucibles and molds to prevent carbide formation and facilitate the casting process. The specimens obtained from the casting process were subsequently cooled to room temperature through air-cooling.
Misra [41] fabricated SHMMC made of a Sn-20wt.%Bi matrix with 20% volume fraction pre-strained NiTi wires reinforcement. The NiTi wires underwent etching and flux treatment to enhance the bonding between the metal matrix and NiTi reinforcement. Following the fabrication of single fiber composites through the dip coating of NiTi wire in Sn-20wt.%Bi, the pressure infiltration technique was employed to introduce NiTi wires with a high-volume fraction into the metal matrix. The purpose of fabricating single fiber composites was to avoid wire charring and embrittlement during the pressure infiltration process. Charring can compromise wire properties and effectiveness as reinforcement, while high temperatures and pressures during infiltration can induce wire embrittlement, reducing overall strength, toughness, and durability of the composite material.
Poormir et al. [47] fabricated SHMMCs composed of a Sn-13wt.%Bi matrix with 0.78, 1.55, and 2.33% volume fraction NiTi strip reinforcement. Casting was used as a fabrication technique because of the equipment availability and ease of process control. A metallic mold with internal fixtures was designed and constructed to ensure proper placement of the continuous reinforcement uniaxially within the matrix. The casting process involved melting tin and bismuth in a stainless-steel crucible at 300 °C and pouring the molten alloy into the mold to create bending test samples. However, the presence of a stable titanium oxide layer on the surface of the NiTi strip reduced its wettability, leading to lower interface strength. To overcome this, the SMA strips were treated by immersing them in an aquatic acid solution of 4.8%HF-10.5%HNO3 for 5 min to remove the oxide layer.
Ferguson et al. [44] fabricated NiTi-reinforced Zinc Alloy ZA-8 (Zn-0.8Al-0.015Cu) composite by Casting technique. Two types of samples, namely the “loop” and “rod” types, were fabricated to investigate the relative effectiveness of two methods for load transfer from the reinforcement to the matrix material. The first method involved transferring the load directly by establishing interfacial bonding between the matrix and reinforcement, while the second method relied on the indirect transfer through a mechanical connection to a bolt integrated within the matrix. For fabricating the "loop" sample, the NiTi wires were treated by fluxing in an aqueous solution of 4.8%HF-10.5%HNO3 for 5 minutes, followed by washing in distilled water, drying, and coating with Indalloy Flux #2 for 3 min to enhance the bonding between the reinforcement and matrix. The NiTi wires were then trained by heating them in a preform-frame made of steel bars (100 mm × 20 mm × 2 mm) and threaded steel rods (5 mm diameter) to 500 °C for 1 h, followed by quenching in room temperature water for 5 times, in order to create a permanent looping structure that could act as structural support for load transfer. Before casting, the inner bolts were removed, and the frame was positioned in a permanent steel mold, both of which had been preheated to a temperature of 150 °C. Preheating helps to minimize thermal shocks, improve mold filling, enhance the flowability of the molten alloy, and promote proper solidification of the material during casting. Additionally, preheating can also aid in reducing any potential defects or inconsistencies in the final casted product. The ZA-8 alloy was melted at 600 °C for 1 hour in a BN-coated graphite crucible before being poured into the preheated mold with the preform. The crucible was coated with BN to prevent carbide formation and enhance castability. The resulting synthesized looped sample had reported dimensions of 12.7 mm in thickness and 38.1 mm in width. For the "rod" type sample, threaded steel rods and steel bars of the same dimensions as those used for the looped sample were employed as a frame to fabricate the wound SMA preform. The as-received NiTi wires were used without any surface treatment for fabricating this type of sample. The rod samples were fabricated using identical melting and casting techniques as the looped samples. The dimensions of the synthesized rod sample were reported as 12.1 mm in thickness (or 12.7 mm for the second sample) and 34.9 mm in width.
Fisher et al. [40] fabricated NiTi-reinforced SHMMC by casting (Al-3at.%Si matrix reinforced with two vol% NiTi SMA wires). The fabrication process involved several steps. Initially, a master alloy was prepared by melting high-purity aluminum (99.99% purity, Alfa Aesar, Haverhill, MA, USA) and silicon (99.9999% purity, Alfa Aesar) at 850 °C until a homogenous liquid solution was formed. This master alloy was then cast into a graphite mold. Subsequently, the appropriate proportions of the master alloy and aluminum were melted at 750 °C to form a liquid solution, obtaining an Al-3at.%Si alloy matrix. To fabricate the SHMMCs, the molten matrix material was poured into a specially designed graphite mold that was coated with BN and equipped with a wire holder containing pre-aligned NiTi wires (Ni-49.3at.%Ti, Ø = 0.87 mm, Memry Corporation, Bethel, CT, USA). Prior to casting, the mold was heated to 350 °C to ensure proper temperature conditions. Finally, the cast SHMMC sample was allowed to cool, and subsequent heat treatment was conducted at 592 °C for 24 h to achieve the desired post-healing microstructure.
Srivastava et al. [45] fabricated a hybrid SHMMCs consisting of an AA2014 matrix reinforced with NiTi wires (Ni55Ti45) and solder alloy (Sn60Pb40). To fabricate the composite, a customized steel split die pattern was utilized. First, a steel frame was wound with pre-strained NiTi wires and annealed at 500 °C for 10 min. After that, quenching of the NiTi wires was conducted in cold water at 20 °C so that the NiTi wires memorized their cold state shape. Next, an AA2014 ingot was melted in the melting furnace at 800 °C. The melt was poured directly into the mold cavity, containing a steel frame and wound pre-aligned NiTi wires in the die. The die was designed to allow space for longitudinally filling the solder alloy reinforcement throughout the length of the sample. The solder alloy was loaded externally into the mold, and the opposite end of the hole was sealed with refractory cement to prevent solder alloy drainage during the subsequent healing heat treatment of the composite.
Sharma et al. [50] successfully fabricated a NiTi-reinforced SHMMC using the semi-solid metal process via the rapid slurry formation (RSF) technique, ensuring careful handling to preserve the self-healing effect. The synthesis involved several steps, starting with the preparation of A356 alloy using the RSF process, where a graphite crucible was filled with the alloy billet and subjected to an electrical resistance furnace. Equiatomic NiTi wires were etched, pickled, and coated with molten A356 alloy to enhance their integration with the matrix. These wires were randomly placed in the semi-solid slurry of A356 alloy using a scope, and the slurry–wire mixture was compressed inside a hydraulic press mold to form the composite material. Rapid quenching in water preserved the microstructure and improved the mechanical properties of the alloy. Testing and characterization were performed on the prepared self-healing material. The quenched samples were reheated below the recrystallization temperature to relieve internal stresses, rectify microvoids, and enhance the integration of the reinforcement with the matrix. Controlled heating at a specific temperature induced a phase transformation in the NiTi wire, effectively training it in a new orientation. Additionally, surface finishing processes were applied to enhance the alloy’s surface. The sample was then subjected to controlled loading, resulting in the creation of the first crack. Maintaining the structural integrity allowed for subsequent recoverability analysis. By placing the cracked and bent sample in a muffle furnace at 363.15 K for 5 min, the activation temperature of the shape memory alloy was reached, causing austenite to transform into martensite and providing the necessary restoring force for partial closure of the crack. The synthesis process aimed to achieve an SHMMC with improved mechanical properties and crack closure capabilities through the incorporation of NiTi wires and the design of the A356 alloy matrix to undergo partial liquefaction at the healing temperature.
Rohatgi was granted three patents [51][52][53] that introduced the concept of incorporating macro, micro, and nano-sized SMA particles and fibers into metal matrices to induce self-healing characteristics in fabricated composites. The healing mechanism of SHMMCs involves the phase transformation of SMAs, which is associated with shape change that generates compressive forces on the matrix, effectively closing and healing cracks in the material. The patents proposed various methods for triggering self-healing in localized areas, such as electromagnetic induction, microwave, ultrasonic, ballistic, and laser energy. The patents also put forth a range of solidification techniques for the synthesis of SHMMCs, including stir mixing, squeeze casting, pressure and pressureless infiltration, powder metallurgy, and hybrid methods that incorporate stir mixing, wetting agents, ultrasonic mixing, and squeeze casting.
In the future manufacturing of SHMMCs, several techniques, ideas, and employed procedures can be explored to overcome existing challenges. These include additive manufacturing processes such as 3D printing, which offer precise control over material deposition and the ability to incorporate self-healing agents at specific locations. Advanced surface engineering techniques, such as surface modification and coatings, can be employed to enhance the bonding and interaction between the matrix and reinforcement materials, improving the overall healing performance. Nanotechnology can be utilized to design and synthesize nanostructured reinforcements with tailored properties, enabling better integration and interaction with the matrix. Smart manufacturing approaches, such as the integration of sensors and feedback systems, can be adopted to monitor and control the healing process in real time, ensuring optimal healing efficiency. Multi-scale reinforcements, combining different sizes and types of reinforcements, can be employed to achieve synergistic effects and enhance the overall healing capabilities of SHMMCs. Advanced characterization techniques, such as in situ imaging and analysis, can provide valuable insights into the healing mechanisms and help optimize the material design. Hybrid manufacturing processes that combine different fabrication techniques, such as casting, forging, and additive manufacturing, can be developed to leverage the advantages of each method and improve the overall manufacturing efficiency. Sustainable manufacturing practices, including the use of recycled materials and energy-efficient processes, can be implemented to reduce the environmental impact of SHMMC production. Computational modeling and simulation can be employed to predict and optimize the healing behavior of SHMMCs, enabling virtual testing and design optimization before physical fabrication.

3.1. Reinforcement-Metal Wettability

Wettability is a critical factor in the development of SMA-reinforced SHMMCs as it directly influences the interaction between the liquid matrix and SMA reinforcements. It determines the matrix’s ability to penetrate and wet the SMA reinforcements, which significantly affects the quality and performance of the composite. Achieving good wettability is crucial as it promotes effective bonding and facilitates load transfer between the matrix and reinforcements. However, it is important to note that wettability and bonding are not synonymous terms. While excellent wettability, characterized by a low contact angle, is an essential requirement, it does not guarantee a strong bond at the interface. Good wettability can coexist with a weak van der Waals-type low-energy bond [54][55]. Therefore, additional factors such as surface chemistry, interfacial reactions, and mechanical interlocking contribute to the overall bonding strength in SHMMCs.
The poor wettability of metal matrix with NiTi SMA is a significant concern in the development of SHMMCs, which has been addressed by various researchers through different approaches. Manuel [39][49] proposed electrochemical etching of the SMA followed by sputter coating it with gold (Au) to improve wettability. Electroless coating with copper (Cu) [56] or removal of the oxide with an etchant or a flux [57][58][59] have also been explored to enhance wettability. Ruzek [60] investigated pressure infiltration with an electroless copper coating to improve the wetting behavior of the NiTi surface. However, coating-based approaches have shown limitations because of diffusion of the metal coating into the alloy matrix, resulting in interface deterioration with aging and thermal cycling, making them less popular for solder matrices. Ruzek [60] reported that electroless Cu-coated SMAs exhibit persistent fiber pullout rather than crack bridging in the solder–SMA composite, indicating poor interfacial strength. Pressure infiltration alone can partially overcome non-wetting forces, but because of a lack of bonding, a good fiber–matrix interface cannot be obtained. Good bonding between the matrix and SMA reinforcement was achieved by Misra et al. [41][42], Poormir et al. [43][47], and Ferguson et al. [44] using an etchant (4.8%HF-10.5%HNO3) to remove the oxide layer from SMA reinforcement. Misra et al. [41][42], and Ferguson et al. [44] conducted an additional step after etching the SMA reinforcement that further enhanced the wettability of the reinforcement with the metal matrix. A phosphoric acid-based flux was applied after etching the SMA reinforcement to remove surface oxides, perform pickling, and enhance surface energy. This flux aimed to prepare the reinforcement for subsequent processing and enhance bonding with the matrix material. The metal matrix and reinforcement bond most effectively when both etching and fluxing have been applied.

3.2. Negative Coefficient of Thermal Expansion (CTE) Materials as Reinforcements for SHMMCs

The use of negative coefficient of thermal expansion (CTE) materials as reinforcement SHMMCs, as proposed by Manuel in a patent [61], presents an interesting concept with potential benefits for crack repair. The two-stage crack repair process involving crack closure from the contraction of the contracting constituent, followed by crack repair during partial liquefaction of the matrix material, is intriguing. However, the application of this concept is currently in the developmental stage, and experimental demonstration of self-healing ability is lacking. The authors reported that the contracting constituent can be either SMA materials (nickel–titanium-based alloys, including high-temperature modifications such as Ti(NiPt), (TiHf)Ni, Ti(NiPd), Ti(NiAu), NiTiSn, and the like, indium–titanium-based alloys, nickel–gallium-based alloys, nickel–aluminum-based alloys, copper-based alloys (e.g., copper–zinc–aluminum alloys, copper–aluminum–nickel alloys, and copper–tin and copper–gold alloys), silver–cadmium-based alloys, gold–cadmium-based alloys, manganese–copper-based alloys, indium–cadmium-based alloys, iron-based alloys, (e.g., iron–palladium-based alloys, iron–platinum-based alloys, iron–chromium alloys, and iron–manganese alloys), and the like) or materials that have a negative CTE (examples of materials that exhibit negative CTE are cubic zirconium tungstate (ZrW2O8), members of the AM2O8 family of materials (where A = Zr or Hf, M = Mo or W), and ZrV2O7; A2(MO4)3 is also an example of controllable negative thermal CTE). ALLVAR alloy 30 [62] and trifluoroscandium (ScF3) [63] also exhibit negative thermal expansion. Carbon fibers [64] show negative CTE between 20 °C and 500 °C. Quartz (SiO2) and a number of zeolites [65][66] also show negative CTE over certain temperature ranges.
One limitation of the concept is the availability of suitable materials with negative CTE for reinforcement. While a variety of materials are listed as examples of negative CTE materials, the practicality of using these materials as reinforcement in SHMMCs needs to be further investigated. The availability, cost, and processability of these materials may pose challenges in their practical implementation. Another limitation is the lack of experimental demonstration of self-healing ability using negative CTE materials as reinforcement. Although the concept of exerting compressive force at the cracked surfaces during healing using negative CTE materials is intriguing, there is a need for rigorous experimental testing to validate the effectiveness of this approach. The mechanism and extent of crack closure, partial liquefaction of the matrix material, and subsequent healing need to be systematically studied to understand the feasibility and limitations of this approach. Furthermore, the concept of using negative CTE materials for crack repair in SHMMCs may require careful consideration of the thermal properties and compatibility between the reinforcement and matrix material. Mismatch in thermal properties, such as CTE, between the reinforcement and matrix material may result in residual stresses, which could affect the overall performance and reliability of the composite. The potential for interface debonding, reduced mechanical properties, and premature failure because of residual stresses should be carefully evaluated.

3.3. Thermodynamics of Solidification and Healing

Understanding the thermodynamics of solidification and healing is crucial for the development and optimization of SMA-reinforced SHMMCs. Solidification transforms the molten metal matrix into a solid-state during cooling, facilitating the healing mechanism. By heating the composite above the SMA’s phase transformation temperature, partial melting of the matrix alloy occurs, allowing it to infiltrate cracks and initiate healing. It is crucial to maintain a specific volume ratio of dendrites to eutectic in the matrix alloy, which ensures that the crack cavities are adequately infiltrated by a liquid phase after heating and healing, thereby providing sufficient capillary pressure [1]. As the SMA returns to its original shape and clamps the crack, the partially molten matrix alloy solidifies, sealing the crack and enabling self-healing.
(a)
Partial Melting and Solidification
Equilibrium phase diagrams for multicomponent material mixtures are valuable tools for predicting the formation of thermodynamically stable phases across various temperature, pressure, and composition ranges. These diagrams provide insights into the phase behavior of the mixtures and aid in understanding the stability of different phases under different conditions. The renowned Gibbs phase rule [67][68][69][70], formulated by American physicist Josiah Willard Gibbs in his seminal work “On the Equilibrium of Heterogeneous Substances”, published in parts between 1875 and 1878 [71], relates the number of phases present (P), the degrees of freedom (F), and the number of components (C) under constant pressure as:
P + F = C + 2      (1)
The Gibbs phase rule (given as Equation (1)) allows for the prediction of the degrees of freedom and the number of phases present in a binary system. The rule predicts that in the Sn-Bi system (C = 2, P + F = 4), two-phase regions (P = 2) with two degrees of freedom (F = 2) can exist. 
For a fixed composition in a binary eutectic phase diagram, upon increasing the temperature, melting in the alloy will initiate beyond the solidus temperature and completely melt just above the liquidus temperature. At a specific composition in the phase diagram, the liquidus and solidus temperatures of the alloy coincide and reach their minimum, resulting in congruent melting akin to pure metal. This composition is referred to as the eutectic composition, and the temperature is known as the eutectic melting point. In the Sn-Bi eutectic system, the eutectic composition is approximately Sn-57wt.%Bi, and the eutectic melting point is around 139 °C [72][73]. A binary eutectic alloy has a lower melting point in its eutectic composition than either of its constituent elements. Choosing an alloy with a eutectic phase is essential for designing the matrix of SMA-reinforced SHMMCs. Crystals of the primary phase initiate nucleation and growth when the matrix alloy is cooled from the liquid into a liquid–solid two-phase region, except at eutectic compositions. The lever rule [67][69][70] allows for the design of the matrix alloy for SHMMCs with a predictable liquid fraction required for the healing of the composite at a given temperature. Conversely, the temperature corresponding to a fixed liquid fraction of the matrix alloy for a given composition can also be calculated by using the equations of the solidus and liquidus lines and the lever rule. It is worth noting that designing the matrix alloy for SHMMCs using the equilibrium phase diagram assumes ideal equilibrium conditions that are rarely found in real systems. Nevertheless, this strategy serves as a reliable starting point for designing the matrix alloy for SHMMCs.
(b)
Nonequilibrium Solidification
The melting and solidification of matrix alloys, including Sn-Bi in SHMMCs, rarely achieve equilibrium conditions because of the time-dependent kinetic processes such as diffusion [70][74][75]. Micro-segregation occurs across dendrites because of the nonequilibrium solidification of the matrix alloy. During solidification, the resulting liquid becomes enriched in solute, leading to constitutional undercooling ahead of the solidification front. Initially, a spherical solid nucleus forms in the undercooled region of the melt, but as it grows, the spherical morphology becomes unstable, resulting in non-planar (dendritic, columnar) solidification fronts caused by perturbations. As dendrites continue to grow, the inter-dendritic liquid becomes progressively enriched in solute, approaching the eutectic composition. Assuming limited diffusion in the solid, complete mixing in the liquid phase, and equilibrium at the solid-liquid interface, Scheil’s equation (Equation (2)) can be employed to determine the solute distribution within a solidified bar [70][74][75][76]. Scheil’s equation, also known as the nonequilibrium lever rule, is given by:
CS* = k CO (1 − fS) k − 1    (2)
where CS* is the concentration of the solute in the solid, CO the initial concentration of the liquid, k the partition coefficient, and fS the fractional distance (solidified) along the bar.
A nonequilibrium solidification microstructure is beneficial in designing the matrix alloy of SHMMCs. This is because, within the matrix alloy, there will always be inter-dendritic eutectic phases that possess a lower melting point compared to the surrounding matrix. These eutectic phases are capable of melting first, thereby providing a healing liquid that acts as a “welding” agent during the healing process of an off-eutectic composition of matrix alloy. This unique characteristic facilitates the effective repair of cracks or defects in the SHMMCs, enhancing their structural integrity.
(c)
Thermodynamics of Healing
Self-healing is a nonequilibrium process in which the restoring thermodynamic force (e.g., diffusion) causes healing by shifting the system away from thermodynamic equilibrium [1]. The healing of the SMA-reinforced SHMMCs can be viewed as a self-organization process that results in increased orderliness or decreased entropy of the material. Placing the system in a metastable state causes it to deviate from thermodynamic equilibrium. When degradation occurs in a system, it breaks the fragile metastable equilibrium and drives the system to its new, most stable state. Metastability is achieved in an SMA-reinforced SHMMC by prestraining the SMA, by heating that causes the phase transformation, and by designing the matrix to partially liquefy at the healing temperature. When heat is applied to the system, the martensitic–austenitic phase transformation of the SMA recovers the strain, resulting in compressive force to the matrix and crack clamping. Furthermore, partial liquefaction of the matrix welds the crack/void via wetting and capillary interactions between the eutectic liquid and the crack/void. These two phenomena result in a more stable configuration for SMA-reinforced SHMMCs by decreasing the entropy (increasing the orderliness) at higher scales. During healing, the entropy production at a particular scale is compensated for by entropy production at another level. Though the orderliness of the SMA-reinforced SHMMC as observed during healing grows (entropy decreases), the excess entropy should be produced at the lower scale. Hence, the strain of the reinforced SMA and volume fraction of liquid during healing can be considered as healing parameters necessary for driving self-healing.

3.4. The Impact of Reinforcement on the Solidification Process in SMA-Reinforced SHMMCs

The impact of reinforcement on the solidification process in SMA-reinforced SHMMCs encompasses a range of factors, including how the wettability of the reinforcement affects the solidified microstructure of the composite [76][77], how the reinforcement affects the viscosity and fluidity of the melts during nucleation and growth [78][79][80][81], and how micro-segregation occurs during solidification [78]. When SMAs are presented in the liquid matrix, i.e., Sn-Bi, they can have several effects on the solidification of castings: acting as a solute and diffusion barrier, thereby altering the curvature of the solid–liquid interface; catalyzing heterogeneous nucleation of the solid phase from the melt on the SMA, which reduces the grain size; reducing the latent heat required for solidification, thereby increasing the solidification rate; decreasing the viscosity and fluidity of the melt and giving it thixotropic properties under certain conditions; restricting fluid convection because of the narrow interstices between the SMAs, which influences the solidification structure; affecting morphological instabilities such as planar-to-cellular dendritic solidification; influencing the dendrite structure; affecting grain size because of the heterogeneous nucleation or restricted spaces between the SMAs that restrict growth; and affecting micro-segregation in the matrix [77]. 

References

  1. Nosonovsky, M.; Rohatgi, P.K. Biomimetics in Materials Science: Self-Healing, Self-Lubricating, and Self-Cleaning Materials; Springer: New York, NY, USA, 2012.
  2. van der Zwaag, S. (Ed.) An Introduction to Material Design Principles: Damage Prevention versus Damage Management. In Self Healing Materials: An Alternative Approach to 20 Centuries of Materials Science; Springer: Dordrecht, The Netherlands, 2007; pp. 1–18.
  3. Goyal, M.; Agarwal, S.N.; Bhatnagar, N. A Review on Self-Healing Polymers for Applications in Spacecraft and Construction of Roads. J. Appl. Polym. Sci. 2022, 139, e52816.
  4. Wang, Y.; Jiang, D.; Zhang, L.; Li, B.; Sun, C.; Yan, H.; Wu, Z.; Liu, H.; Zhang, J.; Fan, J.; et al. Hydrogen Bonding Derived Self-Healing Polymer Composites Reinforced with Amidation Carbon Fibers. Nanotechnology 2019, 31, 025704.
  5. Jiang, Y.; Qiu, L.; Juarez-Perez, E.J.; Ono, L.K.; Hu, Z.; Liu, Z.; Wu, Z.; Meng, L.; Wang, Q.; Qi, Y. Reduction of Lead Leakage from Damaged Lead Halide Perovskite Solar Modules Using Self-Healing Polymer-Based Encapsulation. Nat. Energy 2019, 4, 585–593.
  6. Trask, R.S.; Williams, H.R.; Bond, I.P. Self-Healing Polymer Composites: Mimicking Nature to Enhance Performance. Bioinspir. Biomim. 2007, 2, P1.
  7. Hia, I.L.; Vahedi, V.; Pasbakhsh, P. Self-Healing Polymer Composites: Prospects, Challenges, and Applications. Polym. Rev. 2016, 56, 225–261.
  8. Thakur, V.K.; Kessler, M.R. Self-Healing Polymer Nanocomposite Materials: A Review. Polymer 2015, 69, 369–383.
  9. Wang, S.; Urban, M.W. Self-Healing Polymers. Nat. Rev. Mater. 2020, 5, 562–583.
  10. Blaiszik, B.J.; Kramer, S.L.B.; Olugebefola, S.C.; Moore, J.S.; Sottos, N.R.; White, S.R. Self-Healing Polymers and Composites. Annu. Rev. Mater. Res. 2010, 40, 179–211.
  11. Zhai, L.; Narkar, A.; Ahn, K. Self-Healing Polymers with Nanomaterials and Nanostructures. Nano Today 2020, 30, 100826.
  12. Li, C.-H.; Zuo, J.-L. Self-Healing Polymers Based on Coordination Bonds. Adv. Mater. 2020, 32, 1903762.
  13. Lai, J.-C.; Jia, X.-Y.; Wang, D.-P.; Deng, Y.-B.; Zheng, P.; Li, C.-H.; Zuo, J.-L.; Bao, Z. Thermodynamically Stable Whilst Kinetically Labile Coordination Bonds Lead to Strong and Tough Self-Healing Polymers. Nat. Commun. 2019, 10, 1164.
  14. Sun, J.; Liu, C.; Zhang, R.; Gong, F.; Wang, C.; Li, G. Comprehensive Effect of the Mechanical Properties, Laminated Structure and Healing Conditions on the Self-Healing Behaviors of Laminated Al2O3-MgO Ceramic Composites. Ceram. Int. 2019, 45, 13597–13604.
  15. Wang, B.; Tu, R.; Wei, Y.; Cai, H. Self-Healing of SiC-Al2O3-B4C Ceramic Composites at Low Temperatures. Materials 2022, 15, 652.
  16. Aouadi, S.M.; Gu, J.; Berman, D. Self-Healing Ceramic Coatings That Operate in Extreme Environments: A Review. J. Vac. Sci. Technol. A 2020, 38, 050802.
  17. Greil, P. Self-Healing Engineering Ceramics with Oxidation-Induced Crack Repair. Adv. Eng. Mater. 2020, 22, 1901121.
  18. Perrot, G.; Couégnat, G.; Ricchiuto, M.; Vignoles, G.L. Image-Based Numerical Modeling of Self-Healing in a Ceramic-Matrix Minicomposite. Ceramics 2019, 2, 308–326.
  19. Xue, C.; Li, W.; Li, J.; Tam, V.W.Y.; Ye, G. A Review Study on Encapsulation-Based Self-Healing for Cementitious Materials. Struct. Concr. 2019, 20, 198–212.
  20. Justo-Reinoso, I.; Heath, A.; Gebhard, S.; Paine, K. Aerobic Non-Ureolytic Bacteria-Based Self-Healing Cementitious Composites: A Comprehensive Review. J. Build. Eng. 2021, 42, 102834.
  21. Shah, K.W.; Huseien, G.F. Biomimetic Self-Healing Cementitious Construction Materials for Smart Buildings. Biomimetics 2020, 5, 47.
  22. Wang, X.F.; Yang, Z.H.; Fang, C.; Han, N.X.; Zhu, G.M.; Tang, J.N.; Xing, F. Evaluation of the Mechanical Performance Recovery of Self-Healing Cementitious Materials—Its Methods and Future Development: A Review. Constr. Build. Mater. 2019, 212, 400–421.
  23. Li, V.C.; Lim, Y.M.; Chan, Y.-W. Feasibility Study of a Passive Smart Self-Healing Cementitious Composite. Compos. Part B Eng. 1998, 29, 819–827.
  24. Dry, C. Matrix Cracking Repair and Filling Using Active and Passive Modes for Smart Timed Release of Chemicals from Fibers into Cement Matrices. Smart Mater. Struct. 1994, 3, 118–123.
  25. Danish, A.; Mosaberpanah, M.A.; Usama Salim, M. Past and Present Techniques of Self-Healing in Cementitious Materials: A Critical Review on Efficiency of Implemented Treatments. J. Mater. Res. Technol. 2020, 9, 6883–6899.
  26. Fernandez, C.A.; Correa, M.; Nguyen, M.-T.; Rod, K.A.; Dai, G.L.; Cosimbescu, L.; Rousseau, R.; Glezakou, V.-A. Progress and Challenges in Self-Healing Cementitious Materials. J. Mater. Sci. 2021, 56, 201–230.
  27. van Dijk, N.; van der Zwaag, S. Self-Healing Phenomena in Metals. Adv. Mater. Interfaces 2018, 5, 1800226.
  28. Lester, B.T.; Baxevanis, T.; Chemisky, Y.; Lagoudas, D.C. Review and Perspectives: Shape Memory Alloy Composite Systems. Acta Mech. 2015, 226, 3907–3960.
  29. Das, R.; Melchior, C.; Karumbaiah, K.M. 11-Self-Healing Composites for Aerospace Applications. In Advanced Composite Materials for Aerospace Engineering; Rana, S., Fangueiro, R., Eds.; Woodhead Publishing: Sawston, UK, 2016; pp. 333–364.
  30. An, S.; Yoon, S.S.; Lee, M.W. Self-Healing Structural Materials. Polymers 2021, 13, 2297.
  31. Tan, Y.J.; Wu, J.; Li, H.; Tee, B.C.K. Self-Healing Electronic Materials for a Smart and Sustainable Future. ACS Appl. Mater. Interfaces 2018, 10, 15331–15345.
  32. Bartlett, M.D.; Dickey, M.D.; Majidi, C. Self-Healing Materials for Soft-Matter Machines and Electronics. NPG Asia Mater. 2019, 11, 21.
  33. Fisher, C.R. Design of Liquid-Assisted Self-Healing Metal-Matrix Composites. Ph.D. Thesis, University of Florida, Gainesville, FL, USA, 2013.
  34. Wright, M.C.; Manuel, M.; Wallace, T. Fatigue Resistance of Liquid-Assisted Self-Repairing Aluminum Alloys Reinforced with Shape Memory Alloys. NASA/TM-2013-216629, 1 September 2013. Available online: https://ntrs.nasa.gov/citations/20140013299 (accessed on 6 January 2023).
  35. Lagoudas, D.C. Shape Memory Alloys: Modeling and Engineering Applications; SpringerScience+Business Media, LLC: New York, NY, USA, 2008.
  36. Antonucci, V.; Martone, A. Chapter 2—Phenomenology of Shape Memory Alloys. In Shape Memory Alloy Engineering; Lecce, L., Concilio, A., Eds.; Butterworth-Heinemann: Boston, MA, USA, 2015; pp. 33–56.
  37. Manuel, M.V. Principles of Self-Healing in Metals and Alloys: An Introduction. In Self-Healing Materials; John Wiley & Sons, Ltd.: Hoboken, NJ, USA, 2008; pp. 251–265.
  38. Grabowski, B.; Tasan, C.C. Self-Healing Metals. In Self-Healing Materials; Hager, M.D., van der Zwaag, S., Schubert, U.S., Eds.; Springer International Publishing: Cham, Switzerland, 2016; pp. 387–407.
  39. Manuel, M.V. Design of a Biomimetic Self-Healing Alloy Composite. Ph.D. Thesis, Northwestern University, Evanston, IL, USA, 2007.
  40. Fisher, C.R.; Henderson, H.B.; Kesler, M.S.; Zhu, P.; Bean, G.E.; Wright, M.C.; Newman, J.A.; Brinson, L.C.; Figueroa, O.; Manuel, M.V. Repairing Large Cracks and Reversing Fatigue Damage in Structural Metals. Appl. Mater. Today 2018, 13, 64–68.
  41. Misra, S.K. Shape Memory Alloy Reinforced Self-Healing Metal Matrix Composites. Master’s Thesis, The University of Wisconsin-Milwaukee, Milwaukee, WI, USA, 2013.
  42. Salowitz, N.; Misra, S.; Haider, M.I.; Povolo, M.; Rohatgi, P. Investigation into the Performance of NiTi Shape Memory Alloy Wire Reinforced Sn-Bi Self-Healing Metal Matrix Composite. Materials 2022, 15, 2970.
  43. Poormir, M.A.; Khalili, S.M.R.; Eslami-Farsani, R. Optimal Design of a Bio-Inspired Self-Healing Metal Matrix Composite Reinforced with NiTi Shape Memory Alloy Strips. J. Intell. Mater. Syst. Struct. 2018, 29, 3972–3982.
  44. Ferguson, J.B.; Schultz, B.F.; Rohatgi, P.K. Zinc Alloy ZA-8/Shape Memory Alloy Self-Healing Metal Matrix Composite. Mater. Sci. Eng. A 2015, 620, 85–88.
  45. Srivastava, V.; Gupta, M. Experimental Assessment of Self-Healing Nature in Aluminum-Based Smart Composites with NiTi Wires and Solder Alloy as Healing Agents through Taguchi Approach. J. Intell. Mater. Syst. Struct. 2020, 31, 2101–2116.
  46. Srivastava, V.; Gupta, M. Evaluation and Prediction of Self-Healing Assessments for AA2014 Based Hybrid Smart Composite Structures: A Novel Fuzzy Logic Approach. Int. J. Eng. 2022, 35, 1841–1857.
  47. Poormir, M.A.; Khalili, S.M.R.; Eslami-Farsani, R. Investigation of the Self-Healing Behavior of Sn-Bi Metal Matrix Composite Reinforced with NiTi Shape Memory Alloy Strips Under Flexural Loading. JOM 2018, 70, 806–810.
  48. Freddi, A.; Salmon, M. Introduction to the Taguchi Method. In Design Principles and Methodologies: From Conceptualization to First Prototyping with Examples and Case Studies; Freddi, A., Salmon, M., Eds.; Springer International Publishing: Cham, Switzerland, 2019; pp. 159–180.
  49. Manuel, M.V.; Olson, G.B. Biomimetic Self-Healing Metals. In Proceedings of the First International Conference on Self Healing Materials, Noordwijk, The Netherlands, 18–20 April 2007.
  50. Sharma, S.; Nandan, G.; Tyagi, R.; Rohtagi, P. Fabrication, Testing, and Microstructural Analysis of Nitinol-Based Self-Healing Metal Matrix Composite of A356 Alloy Cast by Semi-Solid Metal Processing. Adv. Mater. Process. Technol. 2023, 1–13.
  51. Rohatgi, P.K. Self Healing Lead, Tin, and Their Alloys, and Solders, Incorporating Shape Memory Alloys, Reactive Particles and Hollow Vascular Networks. U.S. Patent 10,161,026, 25 December 2018.
  52. Rohatgi, P.K. Self Healing Metals and Alloys—Including Structural Alloys and Self-Healing Solders. U.S. Patent 8,518,531, 27 August 2013.
  53. Rohatgi, P.K. Self-Healing Aluminum Alloys Incorporating Shape Metal Alloys and Reactive Particles. U.S. Patent 9,435,014, 6 September 2016.
  54. Chawla, K.K. Composite Materials; Springer: New York, NY, USA, 2012.
  55. Chawla, N.; Chawla, K.K. Metal Matrix Composites; Springer: New York, NY, USA, 2013.
  56. Mysore, K.; Chan, D.; Bhate, D.; Subbarayan, G.; Dutta, I.; Gupta, V.; Zhao, J.; Edwards, D. Aging-Informed Behavior of Sn3.8Ag0.7Cu Solder Alloys. In Proceedings of the 2008 11th Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems, Orlando, FL, USA, 28–31 May 2008; pp. 870–875.
  57. Dutta, I.; Pan, D.; Ma, S.; Majumdar, B.S.; Harris, S. Role of Shape-Memory Alloy Reinforcements on Strain Evolution in Lead-Free Solder Joints. J. Electron. Mater. 2006, 35, 1902–1913.
  58. Coughlin, J.P.; Williams, J.J.; Crawford, G.A.; Chawla, N. Interfacial Reactions in Model NiTi Shape Memory Alloy Fiber-Reinforced Sn Matrix ‘Smart’ Composites. Metall. Mater. Trans. A 2009, 40, 176–184.
  59. Coughlin, J.P.; Williams, J.J.; Chawla, N. Mechanical Behavior of NiTi Shape Memory Alloy Fiber Reinforced Sn Matrix ‘Smart’ Composites. J. Mater. Sci. 2009, 44, 700–707.
  60. Ruzek, A. Synthesis and Characterization of Metallic Systems with Potential for Self-Healing. Master’s Thesis, The University of Wisconsin-Milwaukee, Milwaukee, WI, USA, 2009.
  61. Manuel, M.V.; Fisher, C.R.; Wright, M.C. Self-Repairing Metal Alloy Matrix Composites, Methods of Manufacture and Use Thereof and Articles Comprising the Same. U.S. Patent 10,597,761, 24 March 2020.
  62. Monroe, J.A.; McAllister, J.S.; Content, D.S.; Zgarba, J.; Huerta, X.; Karaman, I. Negative Thermal Expansion ALLVAR Alloys for Telescopes. In Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation III; SPIE: Bellingham, WA, USA, 2018; pp. 202–212.
  63. Greve, B.K.; Martin, K.L.; Lee, P.L.; Chupas, P.J.; Chapman, K.W.; Wilkinson, A.P. Pronounced Negative Thermal Expansion from a Simple Structure: Cubic ScF3. J. Am. Chem. Soc. 2010, 132, 15496–15498.
  64. Kude, Y.; Sohda, Y. Thermal Management of Carbon-Carbon Composites by Functionally Graded Fiber Arrangement Technique. In Functionally Graded Materials 1996; Shiota, I., Miyamoto, Y., Eds.; Elsevier Science B.V.: Amsterdam, The Netherlands, 1997; pp. 239–244.
  65. Lightfoot, P.; Woodcock, D.A.; Maple, M.J.; Villaescusa, L.A.; Wright, P.A. The Widespread Occurrence of Negative Thermal Expansion in Zeolites. J. Mater. Chem. 2001, 11, 212–216.
  66. Attfield, M.P. Strong Negative Thermal Expansion in Siliceous Faujasite. Chem. Commun. 1998, 5, 601–602.
  67. Callister, W.D.; Rethwisch, D.G. Materials Science and Engineering: An Introduction; Wiley: Hoboken, NJ, USA, 2013.
  68. Hosford, W.F. Physical Metallurgy; CRC Press: Boca Raton, FL, USA, 2010.
  69. Smallman, R.E. Modern Physical Metallurgy; Elsevier: Amsterdam, The Netherlands, 2016.
  70. Haidemenopoulos, G.N. Physical Metallurgy: Principles and Design; CRC Press: Boca Raton, FL, USA, 2018.
  71. Ott, J.B.; Boerio-Goates, J. Chemical Thermodynamics: Principles and Applications: Principles and Applications; Academic Press: London, UK; San Diego, CA, USA, 2000.
  72. Gaskell, D.R.; Laughlin, D.E. Introduction to the Thermodynamics of Materials; CRC Press: Boca Raton, FL, USA, 2017.
  73. Yeh, C.-H.; Chang, L.-S.; Straumal, B.B. Wetting Transition of Grain Boundaries in the Sn-Rich Part of the Sn–Bi Phase Diagram. J. Mater. Sci. 2011, 46, 1557–1562.
  74. Abbaschian, R.; Reed-Hill, R.E. Physical Metallurgy Principles—SI Version; Cengage Learning: Boston, MA, USA, 2009.
  75. Porter, D.A.; Easterling, K.E.; Easterling, K.E. Phase Transformations in Metals and Alloys (Revised Reprint); CRC Press: Boca Raton, FL, USA, 2009.
  76. Flemings, M.C. Solidification Processing; McGraw-Hill College: New York, NY, USA, 1974.
  77. Rohatgi, P.K.; Ajay Kumar, P.; Chelliah, N.M.; Rajan, T.P.D. Solidification Processing of Cast Metal Matrix Composites Over the Last 50 Years and Opportunities for the Future. JOM 2020, 72, 2912–2926.
  78. Mortensen, A.; Jin, I. Solidification Processing of Metal Matrix Composites. Int. Mater. Rev. 1992, 37, 101–128.
  79. Stefanescu, D.M. Solidification of Metal Matrix Composites. In Science and Engineering of Casting Solidification; Stefanescu, D.M., Ed.; Springer International Publishing: Cham, Switzerland, 2015; pp. 305–341.
  80. Rohatgi, P.K.; Asthana, R.; Das, S. Solidification, Structures, and Properties of Cast Metal-Ceramic Particle Composites. Int. Met. Rev. 1986, 31, 115–139.
  81. Kunnen, J. General Viscosity-Composition Relationship for Dispersions, Solutions and Binary Liquid Systems. Rheol. Acta 1984, 23, 424–434.
More
© Text is available under the terms and conditions of the Creative Commons Attribution (CC BY) license; additional terms may apply. By using this site, you agree to the Terms and Conditions and Privacy Policy.
Upload a video for this entry
Information
Subjects: Engineering, Aerospace
Contributors MDPI registered users' name will be linked to their SciProfiles pages. To register with us, please refer to https://encyclopedia.pub/register :
Masum Bellah
,
Michael Nosonovsky
,
Pradeep Rohatgi
View Times: 547
Revisions: 3 times (View History)
Update Date: 10 Aug 2023
Table of Contents
    1000/1000
    Hot Most Recent
    ScholarVision Creations
    Feedback