Input: Bone is usually anisotropic with different stiffness and strength in different directions, but normally there are no extremely weak directions.

Bone

anisotropic

stiffness

strength


Input: Therefore, suitable porous metals will approximate the stiffness of surrounding bones, making them effective for load transfer and alleviating the stress shielding effect.

porous metals

stiffness

stress shielding


Input: The key characteristics to design porous metallic implants include the careful selection of porosity, pore size, and pore interconnectivity, aiming to achieve satisfactory clinical outcomes.

design

metallic

implants

porosity

pore

pore size


Input: These structural features have a profound effect on mechanical properties and biological performance of the metallic implants.

mechanical properties

performance

metallic

implants


Input: Bone regeneration in porous implants in vivo involves recruitment and penetration of cells from the surrounding bone tissue and vascularization.

Bone regeneration

penetration

vascularization

porous implants

cells

bone


Input: Higher porosity may facilitate these processes and benefit the bone ingrowth.

porosity

processes

bone ingrowth


Input: For instance, more bone ingrowth was found in porous titanium coatings of higher porosity after the implants were placed into a canine model for 8 weeks.

bone ingrowth

porous

porosity

coatings

implants

canine model


Input: Similarly, bone ingrowth was shown to be deeper and greater in porous polymer scaffolds of higher porosity.

bone ingrowth

be

polymer

porous

porosity


Input: The influence of pore size on the bone ingrowth is still controversial in literature.

pore size

bone ingrowth


Input: The optimal pore size for mineralized bone ingrowth is claimed to be 100in the research by Itala.

pore size

bone ingrowth

research

be


Input: They implanted triangle-shaped titanium implants of different plate thickness with pore size ranging from 50 to 125 into rabbit femur and found that there was no clear lower limit of pore size for consistent bone ingrowth.

implanted

titanium implants

pore size

pore size

limit

bone ingrowth


Input: Recently Braem assessed the feasibility of early bone ingrowth into a predominantly microporous Ti coating in the compact bone of rabbit tibiae and found that new bone formed in micropores of less than 10 Large pores are believed to favour vascularization.

feasibility

bone ingrowth

vascularization

microporous

pores

coating

compact

bone

bone


Input: Bai suggested an upper limit of pore size for vascularization, 400 beyond which no significant difference was observed with increasing pore size.

limit

vascularization

pore size

pore size


Input: Kuboki found that, when the pore size ranged from 300 to 400 the implantation of porous hydroxyapatite scaffolds into rats showed higher alkaline phosphates activity, osteocalcin content and bone ingrowth.

pore size

implantation

porous hydroxyapatite scaffolds

alkaline phosphates

osteocalcin

bone ingrowth


Input: However, Naoya implanted 300 600 and 900 AM manufactured porous Ti scaffolds into rabbit tibia and they found 600 and 900 scaffolds demonstrated significantly higher bone ingrowth than 300 scaffolds.

implanted

AM

porous

scaffolds

scaffolds

scaffolds

tibia

bone ingrowth


Input: In addition to vascularization, specific surface area of scaffolds is another essential factor with respect to fixation ability.

vascularization

surface area

scaffolds


Input: Scaffolds with smaller pores are considered to have larger surface area and therefore more space for bone tissue ingrowth.

Scaffolds

pores

surface area

bone tissue ingrowth


Input: Another important feature of bone implants is the permeability of the porous metal since the transportation of cells, nutrients and growth factors require the flow of blood through the porous scaffolds.

feature

porous scaffolds

bone implants

cells

permeability

porous metal


Input: In simple terms, permeability is characterised by using gradient pressure to push liquid through porous material.

simple

permeability

pressure

porous material


Input: Zhang stated that permeability may influence vascular invasion and the supply of nutrients required to sustain cell growth and may also provide an outlet for the removal of cell debris, thereby increasing its osteoconductive potential.

permeability

osteoconductive potential

vascular invasion

cell growth

cell debris


Input: High permeability of titanium implants enhances the osseointegration process.

permeability

osseointegration

titanium implants


Input: Further research on the effect of permeability of porous metallic implants is in demand.

research

permeability

porous metallic implants


Input: In summary, porosity, pore size and pore interconnectivity are key factors that will significantly influence the mechanical properties and biological performance of scaffolds such as bone ingrowth and transportation of cells and nutrients.

porosity

pore

pore size

mechanical properties

biological performance of scaffolds

as

cells


Input: For example, increasing the porosity may enhance the biological processes, but it can decrease the stiffness and strength drastically.

porosity

stiffness

strength

biological processes


Input: Therefore, finding the optimal topologies for scaffolds is of critical importance.

topologies

scaffolds


Input: However, conventional CAD-based design techniques are inefficient and usually fail to obtain the optimal scaffold design because a prohibitively large number of trials would be required in order to achieve a balanced performance, e.g., desirable stiffness and good permeability.

CAD-based design

scaffold

design

be

performance

stiffness

permeability


Input: On the contrary, topology optimization techniques are capable of quickly finding the optimal topologies which satisfy multiple objectives and constraints simultaneously to provide site-specific biological performance.

topology optimization

topologies

performance


Input: 3 Topological design of porous metallic structures for orthopaedic implants 3.1 Porous metallic implants and topology optimization techniques As mentioned previously, bone is a 3D inhomogeneous structure with elaborate features from macro-to nano-scales.

Topological design

porous metallic structures

topology optimization

3D inhomogeneous structure

nano-scales

orthopaedic implants

Porous metallic implants

As

bone


Input: While it is impossible, and perhaps unnecessary, to recreate all details of natural bone in the porous metallic implant, ideally the implant should have similar hierarchical configurations on multiple scales.

bone

porous metallic implant

implant


Input: It is essential that the implant should possess properties similar to the host bone and the ambient tissue.

implant

properties

host bone

ambient tissue


Input: This calls for a well-established design methodology integrating structural stiffness with fluid permeability to allow the implant to have both adequate rigidity to resist the physical loading and sufficient permeability to transfer cells, nutrients, etc.

design

stiffness

fluid permeability

permeability

implant

cells


Input: Fully solid metals, e.g.

metals


Input: Such a stiffness mismatch is regarded as one of the most significant problems in implant design as the resulting stress shielding would often lead to implantation failures.

stiffness

stress shielding

as

as

lead

implant

design

implantation


Input: Recently, porous metals were used in orthopaedic surgeries to replace damaged bones.

porous metals

orthopaedic

damaged bones


Input: Porous scaffolds are geometrically similar to natural hard tissues which are composed of constituting materials penetrated by interconnected pores.

Porous scaffolds

materials

pores


Input: Porous metals can be designed to duplicate the properties of bones if their structures could be designed digitally and fabricated using advanced manufacturing technology.

Porous metals

be

be

properties

fabricated

manufacturing technology


Input: Conventional porous scaffolds typically consist of a vast number of randomly shaped pores in different sizes and therefore it is almost impossible to quantitatively analyse their properties.

porous scaffolds

pores

quantitatively

properties


Input: To obtain a simplified model, researchers usually assume that scaffolds are constructed of periodically-repeating unit cells along all directions and the architecture of the micro unit cells can distinctly define the macro properties of the scaffolds.

model

unit cells

micro unit cells

scaffolds

macro

scaffolds

architecture


Input: Typical traditional design strategies of periodic bone scaffolds include Computer Aided Design, image-based design and implicit surfaces, as illustrated in 3.

design

design

implicit surfaces

bone scaffolds

Computer Aided Design

as


Input: CAD-based design are obtained by using various CAD tools.

CAD-based design

CAD


Input: Computer-aided system for tissue scaffolds is a further development based on these scaffold libraries, aiming to efficiently automate the entire design process for desired topologies.

scaffolds

scaffold

design process

topologies


Input: Bio-inspired design is an alternative to improve the mechanical performance of bone scaffolds and enrich the scaffold library.

Bio-inspired design

scaffold

mechanical

bone scaffolds


Input: Other CAD-based approaches may also be used in designing scaffolds.

be

scaffolds


Input: Image-based design, as proposed by Hollister, is based on Computed Tomography or Magnetic Resonance Image data for reconstruction of a defect.

design

as

Computed Tomography

Magnetic Resonance Image data

reconstruction

defect


Input: It uses Boolean combination of defect image and architecture image to create 3D scaffold image.

defect

image

architecture


Input: Implicit surface modelling uses single mathematical equations to freely introduce pore shapes such as triply periodic minimal surfaces, which is highly flexible in designing scaffolds.

Implicit surface

scaffolds

mathematical equations

surfaces

pore

as


Input: CAD-based randomization approach starts from cell elements to fill a specific volume in computer software, where standard cell elements are usually packaged while new cell elements can also be created.

CAD-based randomization

computer

cell elements

specific volume

cell elements

cell elements

standard

be


Input: This method can effectively imitate real bones by the randomization process, thus promoting the bone attachment and bone cell in-growth, as well as increasing the damage tolerance.

process

bone attachment

bone cell

as

as

damage tolerance


Input: While the aforementioned methods enable scaffolds to obtain desirable stiffness and permeability, these approaches demand a vast number of attempts to achieve anticipated properties.

scaffolds

stiffness

permeability

properties


Input: One of the main challenges in the application of porous scaffolds to orthopaedic implants is the adaptation of their mechanical and biomedical properties to those of natural bones.

porous scaffolds

orthopaedic implants

mechanical

biomedical


Input: The implanted scaffolds are placed in a complex environment and their performance is affected by many factors.

implanted

performance


Input: Some of them such as high permeability and good stiffness are competing with each other since a larger pore size is obtained usually at the cost of a lower mechanical strength.

as

permeability

stiffness

mechanical strength

pore size


Input: Hence, to increase the mass transfer, while retaining a strong supporting framework, there is a need to maintain a delicate trade-off between the porosity of the fabricated scaffold and its strength.

framework

fabricated

porosity

strength


Input: Topology optimization a mathematical method capable of rearranging the materials to attain desired properties while satisfying prescribed constraints can complement the trial-and-error approach and provide a powerful tool to design complex scaffolds with features on multiple scales.

Topology optimization

design

scaffolds

mathematical

materials

properties

trial-and-error

tool


Input: It is a branch of computational mechanics and was originally developed in structural engineering.

structural engineering


Input: It has been widely used for designing structures and materials for desirable mechanical performance and physical properties.

materials

mechanical

physical properties


Input: Through two decades of development, this method has gone far beyond the traditional structural engineering context.

structural engineering


Input: Typically, there are two ways to define a structure in topology optimization.

structure

topology optimization


Input: The first is a point-by-point description in which a void or a solid phase in a local element is represented by an elemental density.

void

phase

local element

density


Input: The Evolutionary Structural Optimization and the Solid Isotropic Material with Penalization methods use this type of description and have gained considerable success in solving a wide range of engineering optimization problems.

Structural Optimization

Isotropic Material

range

engineering


Input: In the field of computational material design, the topology optimization approach is termed as an homogenizationmethod because the homogenization method is used to calculate the effective properties of a unit cell and the material distribution is rearranged through topology optimization to enable the material to attain target properties.

material

as

material

material

design

topology optimization

topology optimization

homogenization method

properties

unit cell

distribution

properties


Input: The seminal work of inverse homogenization was conducted by Sigmund in the 1990s for the design of materials with prescribed elastic properties.

homogenization

design

materials

elastic


Input: Thereafter, great achievements were obtained in the design of exceptional material properties including negative thermal expansion coefficient and negative refraction index.

design

material properties

thermal expansion coefficient

refraction index


Input: Later, this method was extended to the design of scaffold materials with their stiffness matrices matching those of anisotropic native bones.

design

scaffold

materials

stiffness matrices

anisotropic


Input: By using the SIMP based structural optimization, Guest and Prevost developed a topology optimization technique to find a scaffold with pores in the shape of a Schwartz primitive structure, resulting in the maximum permeability.

structural optimization

topology optimization

scaffold

pores

permeability

Schwartz primitive structure


Input: They also combined bulk modulus and permeability in a single objective function and tailored these two competing properties in a multi-physics optimization problem.

bulk modulus

permeability

properties

optimization


Input: Using a similar density-based optimization method, scaffolds with elastic tensors similar to those of natural bones were designed; and the performance of these scaffolds in subsequent tissue ingrowth was investigated.

optimization

elastic tensors

performance

scaffolds

designed

scaffolds


Input: It is found that bone remodeling is at its best when the scaffold elastic tensor matches or is slightly higher than the elastic properties of the host bone.

bone

host bone

scaffold

elastic tensor

elastic


Input: The last row in 3 shows the porous structures with the maximum bulk and shear moduli, respectively, at a given porosity.

porous

shear moduli

porosity


Input: These unit cells were obtained using the Bi-directional Evolutionary Structural Optimization method, which shows faster convergence and unambiguous material definition.

unit cells

Structural Optimization method

material


Input: The BESO method, which allows the material to be added and removed simultaneously during the optimization process, is an extension of the original evolutionary ESO method proposed by Xie and Steven.

BESO method

optimization

material

be


Input: As shown in 3 on topology optimization, various unit cells with maximal bulk modulus, maximal shear modulus, prescribed stiffness ratios in three directions, and functionally graded structures can be obtained through the BESO method.

As

be

topology optimization

functionally graded structures

unit cells

BESO method

bulk modulus

shear modulus

stiffness


Input: The second class of topology optimization methods, represented by the level-set algorithm, focus on tracking phase boundaries.

topology optimization

algorithm

phase boundaries


Input: The level-set method provides an effective technique to represent smooth boundaries and to control topology changes.

smooth boundaries

topology


Input: A variational level-set technique for periodic material design problems governed by Navierand Maxwell's equations was developed to attain material with maximal permeability.

material

material

design

permeability


Input: Level-set topology optimization enables the no-slip boundary condition of fluids in Stokes flow to be naturally satisfied.

topology optimization

boundary condition

fluids

be


Input: Periodic structures of scaffolds with the maximal effective diffusivity aimed at providing an ideal environment for nutrient transportation were studied by a level-set based optimization method.

scaffolds

diffusivity

optimization


Input: There have been tremendous advances in recent years in the area of using topology optimization techniques to design multi-functional materials with periodic structures, as shown in a comprehensive review by Cadman.

area

topology optimization

design

materials

as


Input: Several of these developments are directly related to the design of scaffolds.

design

scaffolds


Input: Both stiffness and diffusive transport properties were considered by Hollister and Challis.

stiffness

transport

properties


Input: Using topology optimization, Hollister and co-workers also created an interbody fusion cage for improved arthrodesis.

topology optimization

fusion

arthrodesis


Input: The outcomes of their research were used in clinic to support bone regeneration for craniofacial reconstruction.

research

bone regeneration

clinic

support

craniofacial reconstruction


Input: 3.2 Constraints in structural design for additive manufacturing Although AM can theoretically produce structures in any shape, the quality of the structures may vary significantly depending on the design and fabrication parameters.

structural design

design

additive manufacturing

AM

fabrication

quality


Input: Therefore, it is necessary to consider the processability of the designed parts during the topological design process, including the constraints and limitations of AM technologies.

designed

topological design

process

AM technologies


Input: However, there is still limited research on creating design guidelines to achieve this goal.

research

design


Input: Kranz experimentally investigated the restrictions of Laser Additive Manufacturing of Ti6Al4V and presented a comprehensive structured catalogue.

Laser Additive Manufacturing


Input: In their research, restrictions and recommendations were presented based on experimental measurements of different characteristics such as cavities, walls, bores, gap, hollow cylinder, overhangs and support structures.

research

experimental

as

overhangs

support structures


Input: They also found that the quality of AM parts was highly dependent on the materials, machines and process parameters.

quality

materials

process parameters

AM parts

machines


Input: Therefore, similar guidelines could be achieved through similar methodology on different material systems.

be

material

methodology


Input: Among many parameters, frequently discussed one includes overhanging structures, which may lead to some undesirable defects.

parameters

overhanging structures

defects

lead


Input: In an AM process, the overhanging structure is not supported by solidified section or bottom substrate when it is being built.

AM process

overhanging structure

substrate


Input: Therefore, the overhanging structure is strongly influenced by the orientation of building-).

overhanging structure

orientation


Input: Therefore, the critical fabrication angle is of great importance since it determines the form of overhanging structure, hence the processability.

critical fabrication angle

overhanging structure


Input: 4 shows the sketch of a circular pore with overhanging arc AB, which can be processable if the fabrication angle were larger than the critical value c. Otherwise, supporting structures have to be used, which are normally avoided to prevent damage of parts in post-processing.

pore

damage

overhanging arc

AB

be

be

fabrication

post-processing


Input: A better choice in design is to adopt structures with special geometrical arrangement such as an octahedral lattice, whose lateral schematic is shown in 4.

design

as

lattice


Input: When the downward sloping surface CD has a larger fabrication angle than the critical angle c, no supporting structures are required.

surface

CD

c

fabrication

critical angle


Input: There were also attempts to design structures so that they could be fabricated using AM without support.

design

be

AM

support


Input: This approach is interesting and useful, but may not be generally applicable to scaffold designs.

be

scaffold

designs


Input: Other researchers examined the suitability of using SIMP and BESO topology optimization algorithms to design structures for AM.

BESO topology optimization algorithms

design

AM


Input: 4 Current status of AM and topology optimization in producing porous metallic structures AM technologies are superior to conventional fabrication techniques for producing porous metallic implants with complex and customized structures, as shown in 5.

AM

AM technologies

fabrication

topology optimization

porous metallic structures

porous metallic implants

as


Input: In addition to the geometric flexibility, composites with two or more phases can be manufactured.

flexibility

composites

be


Input: These advantages enable AM to become a promising tool for the production of biomedical implant devices, controlled drug delivery systems, and engineered tissues.

AM

production

tool

biomedical implant devices


Input: Examples include artificial joints and load-bearing implants produced by AM using biocompatible materials such as hydroxyapatite, Ti, Ta and Coalloys and customized prostheses such as intervertebral spacers.

artificial joints

implants

load-bearing

AM

biocompatible materials

as

Ti

Ta

as


Input: There has been growing research interest in using topology optimization to design bone scaffolds and orthopaedic implants, however significant challenges still remain before these concepts could be used in clinical practice.

research

topology optimization

design

bone scaffolds

orthopaedic implants

clinical practice

be


Input: An important issue that may not be neglected when applying topology optimization to scaffold design is to consider the differences in physical, chemical and mechanical properties of base materials produced by AM and conventional fabrication techniques.

be

topology optimization

scaffold

design

mechanical properties

materials

AM

fabrication


Input: The material property in AM process may greatly affect the final topological shape of scaffold, which may differ from the original CAD model obtained from topology optimization.

material property

AM process

scaffold

topology optimization

CAD model


Input: Moreover, good understanding of the change in mechanical properties in AM process may assist more accurate optimal design in topology optimization procedure.

mechanical properties

AM process

accurate

design

topology optimization


Input: This section will review the status of research on AM fabrication of three main families of alloys and the application of topology optimization.

research

AM

alloys

topology optimization


Input: 4.1 Biocompatible Ti alloys Metals in biological systems may experience corrosion and release ions, which may result in many adverse physiological effects.

Biocompatible Ti alloys Metals

biological systems

corrosion


Input: Therefore, the biocompatibility of any implant must be quantified to decrease the patient's risk and the failure of the implantation.

biocompatibility

implant

be

failure

implantation


Input: The cytotoxicity of typical surgical implant alloys and pure metals have been broadly studied in the past decades.

cytotoxicity

implant

alloys

pure metals


Input: It is now commonly accepted that vanadium may cause sterile abscess and aluminium may cause scar tissue, whereas titanium, zirconium, niobium and tantalum exhibit excellent biocompatibility.

vanadium

aluminium

titanium

zirconium

niobium

tantalum

sterile abscess

scar tissue

biocompatibility


Input: Another important motivation behind the design of biocompatible Ti alloys is the opportunity to decrease the modulus of Ti alloys by adding elements.

design

biocompatible Ti alloys

Ti alloys

elements


Input: As mentioned above, the elements should be biocompatible.

As

elements

be


Input: Various Ti alloys composed of low modulus biocompatible elements were developed.

Ti alloys

biocompatible elements


Input: These alloys exhibited lower modulus than the commonly used Ti6Al4V.

alloys


Input: One example is Ti13Nb13Zr, which showed improved bone biocompatibility and a modulus of 79 GPa.

bone

biocompatibility

GPa


Input: Other Ti alloys which exhibited lower modulus included Ti29Nb13Ta4.6Zr and Ti35Nb5Ta7Zr.

Ti alloys


Input: In recent years, AM produced porous Ti alloy scaffolds were widely reported with Ti6Al4V in dominance, such as the Ti6Al4V implants in sheep cervical spine in 5.

AM

porous Ti alloy scaffolds

as

implants

cervical spine


Input: Ryan combined the multi-stage AM technology with the powder metallurgy process to produce porous Ti alloy scaffolds using wax templates generated by CAD.

AM technology

powder metallurgy

porous Ti alloy scaffolds

wax

CAD


Input: The pore size of their designs ranged from 200 to 400 and the porosity reached 66.8%.

pore size

designs

porosity


Input: This method could achieve controlled porous structure and ensure high resolution in manufacturing.

porous

high resolution

manufacturing


Input: The resulting microstructure and surface roughness were similar to parts manufactured by conventional methods.

microstructure

manufactured

surface roughness


Input: This method could also be extended to the fabrication of other metallic structures which are difficult to be directly made by AM.

be

be

fabrication

AM

metallic structures


Input: Murr manufactured different porous Ti6Al4V implants using AM based on micro-CT scan and CAD models built by Materialise software.

manufactured

software

porous

implants

AM

micro-CT scan

CAD models


Input: They studied the influence of geometric features of unit cells on the mechanical properties of the porous structures and found that when the porosity changed from 59% to 88%, the elastic modulus decreased from 3.03 to 0.58 GPa, which proved that the elastic modulus of porous metals could be readily adjusted through the porosity.

unit cells

mechanical properties

porous

porosity

elastic modulus

GPa

elastic modulus

porosity

porous metals

be


Input: Similarly Pattanyak studied porous Ti implants based on micro-CT scan on human cancellous bones, which focused on structures with complicated internal structures for bone ingrowth applications.

porous

internal structures

implants

bone ingrowth applications

micro-CT scan

cancellous bones


Input: The implants were manufactured via SLM using Ti powder of less than 45 in size.

implants

manufactured

SLM

Ti powder


Input: They found that the compressive strength decreased from 120 to 35 MPa when the porosity changed from 55% to 75%.

compressive strength

porosity

MPa


Input: Hollander produced a variety of Ti6Al4V implants, ranging from porous cylinder to solid human vertebra model with irregular shapes.

implants

porous

model


Input: Porous Ti6Al4V structures were shown to be effective in supporting cell growth and new bone tissue growth, and cell based study suggested that Ti6Al4V possesses high cyto-biocompatibility.

Porous Ti6Al4V structures

be

cell growth

bone tissue growth

cell based study

cyto-biocompatibility


Input: In vitro studies were performed with porous Ti6Al4V structures.

porous Ti6Al4V structures


Input: Cell spreading and proliferation were observed across the entire surface and inside the porous structure.

Cell

surface

porous


Input: Porous Ti6Al4V scaffolds were found performing well in animal models since induced new bone growth and osseointegration were achieved on both bare and surface-coated porous Ti6Al4V structures.

Porous

osseointegration

scaffolds

bone growth

surface-coated porous Ti6Al4V structures


Input: Although porous Ti6Al4V had been widely studied, the potential release of toxic ions led researchers towards looking for safer alternative alloys.

porous

led

alloys


Input: Therefore, Ti alloys such as Ti24Nb4Zr8Sn, Ti7.5Mo and Ti40Nb were designed and fabricated by AM, which exhibited comparable mechanical properties to their counterparts by conventional manufacturing approaches.

Ti alloys

as

designed

fabricated

mechanical properties

AM

conventional manufacturing


Input: There was significant research interest in using topology optimization for the design of porous Ti alloy scaffolds.

research

topology optimization

design

porous Ti alloy scaffolds


Input: While early works mainly focused on the theoretical consideration of the structural design of the unit cells, recent efforts put more emphasis on integrating topology optimization with AM, e.g.

theoretical

unit cells

structural design

topology optimization

AM


Input: Refs.. 4.2 Shape memory alloys Shape Memory Alloys are capable of regaining their original shape after severe deformations when stimulated by external environments.

Shape memory alloys

Alloys

deformations


Input: Due to this unique property, SMAs have found their way in orthopaedic implant applications.

property

SMAs

orthopaedic implant


Input: Typical SMAs include NiTi or nitinol which normally contains approximately 50 at% Ni and 50 at% Ti.

SMAs

NiTi

nitinol

Ni

Ti


Input: The shape memory effect in NiTi comes from the austenite/martensite phase transformation since martensite is a low temperature stable phase with the absence of stress whereas austenite is a high temperature stable phase.

shape memory effect

temperature stable phase

stress

temperature stable phase

NiTi

austenite/martensite phase transformation

martensite

austenite


Input: Currently, more than 90% of all commercial SMAs are based on NiTi and its ternary alloys-NiTiCu and NiTiNb.

SMAs

NiTi

ternary alloys

NiTiNb


Input: Solid NiTi has a modulus of 48 GPa, which is much lower than other Ti alloys.

NiTi

Ti alloys

GPa


Input: Furthermore, NiTi allows for relatively large reversible deformation of up to 8%.

NiTi

deformation


Input: NiTi has higher stiffness than bone under tendon, and is able to deform over a large strain range at an almost constant stress.

NiTi

stiffness

strain

stress

bone

tendon

range


Input: Due to these characteristics, NiTi has been widely used in medical devices, such as surgical tools, stents, orthodontic wires, plates and staples for bone fractures.

NiTi

as

medical devices

orthodontic

tools

stents

bone fractures


Input: Main attractive features of SMAs are: capability to recover the original shape after large deformation, capability to recover the original shape from a stable deformed shape when heated and a high damping capacity.

SMAs

deformation

capacity

deformed shape


Input: For biomedical applications, the presence of Ni in NiTi has been a continuous concern since Ni is one of the highest sensitivities in metallic allergy tests.

biomedical applications

Ni

NiTi

Ni

metallic

sensitivities


Input: Therefore, attempts were made either to develop surface modification techniques or to use substitution elements to mitigate this effect without sacrificing the biocompatibility.

surface modification

elements

biocompatibility


Input: For example, TiNb and the related TiNbX system were developed which exhibited elastic strains as high as 4.2%.

TiNb

as

as

elastic


Input: Common methods for making porous NiTi structures are based on powder metallurgy and self-propagating high temperature synthesis of a mixture of elemental powders or pre-alloyed NiTi powder with space holding materials.

porous

NiTi

powders

NiTi

powder metallurgy

temperature

materials


Input: After removing space holding materials at relatively low temperature, the structures are further sintered at high temperature.

materials

temperature

temperature

sintered


Input: Due to high reactivity of Ti and Ni, the sintering of porous structures is normally done in high vacuum.

Ti

Ni

sintering

porous


Input: However, these methods have difficulties in precisely controlling the porous structures of NiTi, i.e., pore size and pore shape.

porous

pore

NiTi

pore size


Input: To overcome this problem, AM technologies such as SLM have been used to produce NiTi implants.

AM technologies

as

NiTi

implants


Input: It was shown that AM produced NiTi parts exhibited similar mechanical properties as those fabricated by conventional methods such as casting.

AM

NiTi

as

as

mechanical properties

fabricated


Input: In contrary to the substantial research on Ti alloys, no reports on the application of topology optimization in the design of SMA scaffolds involving AM fabrication can be found in the literature up to date.

research

Ti alloys

be

topology optimization

design

SMA scaffolds

AM


Input: 4.3 Biodegradable metals Biodegradable materials, including both polymer-based and metal-based ones, are used for some medical implants which will gradually degrade in human body over a period of time.

Biodegradable metals

Biodegradable materials

medical implants


Input: In some clinical cases, biomaterials are only needed temporarily in the body and are expected to support the healing process and to disappear after the healing process is completed.

biomaterials

support

process

process


Input: 5 shows a biodegradable Mg stent after expansion.

biodegradable Mg stent


Input: Compared to polymer-based materials, biodegradable metals have higher stiffness and strength, and are more suitable for load bearing conditions.

materials

biodegradable metals

stiffness

strength


Input: As the degradable alloys are expected to degrade inside human body, the main compositions of the alloys should be metallic elements that can be metabolized, and demonstrate appropriate degradation rates in the human body.

As

alloys

be

elements

be

degradable alloys

degradation rates


Input: Due to its unique characteristics, Mg alloys were used to manufacture cardiovascular stents and bone screws.

Mg alloys

manufacture

cardiovascular stents

bone screws


Input: The degradable magnesium alloy bone screws were found clinically equivalent to the conventional Ti screws; and no foreign body reaction, osteolysis, or systemic inflammatory reaction were observed for the Mg alloy screws.

magnesium alloy

Ti

Mg alloy

bone screws

osteolysis


Input: A key parameter that needs to be considered in designing a biodegradable metallic implant is its degradation rate in human body.

parameter

be

biodegradable metallic implant

degradation rate


Input: Pure Mg is known to have a fast degradation in high chloride physiological environment but it may produce hydrogen gas at a high rate from corrosion, which can not be dealt with by the host tissue.

Pure Mg

be

degradation

gas

corrosion


Input: Fe-based biodegradable materials are known to exhibit a slow degradation rate.

biodegradable materials

degradation rate


Input: Animal tests showed that large portions of the pure Fe stent remained intact in the blood vessels 12 months post-surgery.

Fe

blood vessels


Input: Alloying is a typical method to adjust the degradation rate of a metal.

Alloying

degradation rate

metal


Input: For instance, by adding elements such as Y, Sr, Zn, Zr and Ca, Mg alloys were shown to have much lower degradation rates in comparison with pure Mg.

elements

as

Sr

Zn

Zr

Ca

Mg alloys

pure Mg

degradation rates


Input: Such alloys also exhibited high strength, which is desirable for load-bearing applications.

alloys

strength

load-bearing


Input: In addition to alloying, amorphous structures like metallic glass alloys MgZnCa showed low degradation rate and high strength.

alloying

amorphous structures

metallic glass alloys MgZnCa

degradation rate

strength


Input: However, metallic glass alloys are generally difficult to manufacture, which would add the cost to the application of this type of material.

metallic glass

alloys

material

manufacture


Input: Porous Mg alloy implants were investigated as temporary bone replacements in an animal model.

Porous

Mg alloy

as

implants

bone

model


Input: They were shown to be able to enhance bone remodelling and appropriate host response.

be

bone remodelling


Input: However, porous Mg alloys degrade too rapidly in vivo, which may leave subcutaneous gas cavities.

porous

Mg alloys

subcutaneous

gas


Input: Since an open porous implant has large surface area, only alloys with slow degradation rate should be considered for making the porous structure, e.g.

porous implant

surface area

alloys

be

degradation rate

porous


Input: Mg-4 wt.% Y.

Y


Input: The element yttrium helps promote grain refinement, thus resulting in a slow degradation and sufficient cyto-compatibility.

element

grain refinement

degradation

cyto-compatibility


Input: Nguyen manufactured porous Mg alloys using SLM and suggested that the dimension, surface morphology and the oxygen pick-up of the laser-melted Mg were strongly dependent on the laser processing parameters.

manufactured

laser processing

Mg alloys

oxygen

Mg

SLM

dimension

surface morphology


Input: Due to the high evaporation rate at elevated temperatures, few attempts were made to fabricate Mg scaffolds directly using AM.

evaporation rate

temperatures

fabricate

AM

scaffolds


Input: Instead, a technique combining 3D printing and gravity casting was shown to be effective in producing topologically-ordered porous Mg structures, where a porous NaCl mould was created using SLM and then Mg alloy was cast into the mould.

3D printing

casting

SLM

cast

be

Mg

NaCl

Mg alloy

porous

porous

mould

mould


Input: After removing the NaCl, porous Mg structure with porosity of 41% and pore size of 1 mm was obtained.

NaCl

Mg

porous

porosity

pore size

mm


Input: The compressive strength of the porous Mg was reported to be 13 MPa, which is comparable to porous Mg produced by powder metallurgy.

compressive strength

porous

porous

Mg

be

Mg

MPa

powder metallurgy


Input: A review on porous biodegradable metals for hard tissue scaffolds can be found in Ref.. A theoretical study of topological design of polymeric scaffolds considering the effect of biodegradation was conducted by Chen.

porous

biodegradable metals

be

hard tissue scaffolds

theoretical

topological design

polymeric scaffolds


Input: No reports on the application of topology optimization in the design of biodegradable metallic scaffolds involving AM fabrication have appeared in the literature so far.

topology optimization

design

biodegradable metallic scaffolds

AM


Input: 5 Heat-treatment and surface modification of porous metallic structures produced by AM 5.1 Heat-treatment The mechanical properties of AM produced materials depend heavily on the processing parameters, including building layer thickness, scan speed, energy density and focal offset distance.

surface modification

AM

AM

porous metallic structures

mechanical properties

materials

parameters

building layer thickness

scan speed

energy density

focal offset distance


Input: Usually AM produced materials have relatively high yield stress and ultimate tensile strength, but a relatively low ductility.

AM

materials

yield stress

ultimate tensile strength

ductility


Input: In order to improve the mechanical properties of AM produced porous biomaterials so that they can mimic the human tissues and fulfil the desired functions, post-treatment is of critical importance.

mechanical properties

AM

post-treatment

porous

biomaterials

mimic


Input: It is known that the microstructures of as-built materials by AM are very different from those by traditional casting or forging approaches.

microstructures

materials

AM

casting

forging


Input: AM is a layer-wise build-up process with high cooling rates that lead to significant internal thermal stresses in the structure.

AM

process

structure

cooling rates

lead

thermal stresses


Input: During the building process, the scanning by either a laser or an electron beam may cause the instabilities of the melt pool, resulting in increased porosity and high surface roughness.

building process

scanning

electron beam

laser

melt pool

porosity

surface roughness


Input: The post-treatment process also enables the reduction of thermal stresses in AM produced structures.

post-treatment

AM

reduction

thermal stresses


Input: For Ti6Al4V, post heat-treatment is typically performed within the + region, which can control the morphology and size of the without significantly influencing the prior-grain size.

post heat-treatment

morphology


Input: A proper heat-treatment process may substantially improve the mechanical properties of AM produced materials.

process

mechanical properties

materials

AM


Input: Thone observed significant improvement in ductility and fatigue strength after heat-treatment of SLM produced Ti6Al4V.

ductility

fatigue strength

SLM


Input: They revealed that the tensile strength of heat-treated Ti6Al4V slightly decreased from 1080 MPa to 945 MPa but the elongation at failure increased significantly from 1.6% to 11.6%, along with remarkably prolonged fatigue life of parts from 28,900 to 290,000 cycles.

tensile strength

elongation

fatigue life

heat-treated

MPa

MPa

failure


Input: The improvements in the mechanical properties after post heat-treatment are mainly due to the elimination of thermal stresses and the changes of microstructures.

mechanical properties

post heat-treatment

thermal stresses

microstructures


Input: On the other hand, an adequate selection of AM processing variables can facilitate in-situ heat treatment.

AM

in-situ heat


Input: The microstructure of Ti6Al4V made by SLM is often dominated by martensite due to rapid cooling, which can be decomposed to lamellar + structure during SLM process by tuning the processing variables.

microstructure

lamellar

structure

process

martensite

be

SLM

cooling

SLM


Input: After the optimization of processing conditions, Xu produced Ti6Al4V with comparable or better mechanical properties than forged Ti6Al4V.

optimization

mechanical properties


Input: 5.2 Surface modification Surface modification plays an important role in enhancing the biological performance of AM produced porous biomaterials, particularly bioactivity and biocompatibility.

Surface modification

Surface

biological performance of AM

porous

bioactivity

biocompatibility

biomaterials


Input: Ti alloys are normally covered by one layer of 3nm thick native oxide, namely TiO2, which provides excellent chemical inertness, corrosion resistance and biocompatibility.

Ti alloys

oxide

layer

chemical inertness

biocompatibility

corrosion resistance


Input: In the human body, Ti alloy implants may experience non-specific protein adsorption and interrogation of neutrophils and macrophages, which may attract fibroblasts to an encapsulation process.

Ti alloy implants

adsorption

neutrophils

encapsulation

macrophages

fibroblasts


Input: To ensure an effective biological bond between Ti alloy implants and surrounding bones, surface modification is essential to improve the conductivity of bones or the bioactivity of titanium.

Ti alloy implants

surface modification

conductivity

bioactivity

titanium


Input: The surface morphology of Ti alloy implants depends on the history of material processing.

surface morphology

Ti alloy implants

material


Input: For AM produced porous Ti alloys, powders tend to become small liquid spheres when heated up by laser or electron beams.

AM

porous

alloys

powders

laser

electron beams


Input: Such a effect is a complex metallurgical process that leads to a rough surface and residual powder particles.

metallurgical

surface

particles

residual powder


Input: These loosely connected powder particles can be removed through blasting or other post-processing methods before implantation.

powder particles

be

post-processing

implantation


Input: Surface modification or activation of Ti surface can be achieved by various techniques such as plasma spray, physical or chemical vapour deposition, ion implantation, electrochemical oxidation, acidic or alkali etching, solheat-treatment, and surface machining or grinding.

Surface modification

etching

machining

grinding

Ti

be

as

surface

ion implantation

electrochemical oxidation

surface

vapour deposition


Input: For porous metallic structures, there are two main approaches, based on surface coating and surface corrosion.

porous metallic structures

surface

surface

corrosion

coating


Input: A popular coating-based method is solprocess, which is a simple yet versatile method for creating oxide coatings at relatively low temperatures.

simple

oxide coatings

temperatures


Input: For implants with a complex topology, dip coating is normally used.

implants

topology

dip coating


Input: The solprocess may deposit thin inorganic coatings.

coatings


Input: The chemical composition and microstructures of the coating can be better controlled by the solprocess than by other methods.

chemical composition

microstructures

be

coating


Input: Brie used solto form a bioceramic coating on porous Ti6Al7Nb implants.

bioceramic coating

porous

implants


Input: The coating uniformly covered the external and internal surfaces of the implants; and the coated porous structures exhibited improved biocompatibility.

coating

implants

coated

surfaces

biocompatibility


Input: Other methods include electrolytic deposition and plasma spray.

electrolytic deposition

plasma spray


Input: ED can produce CaP coatings having a thickness of a few microns to several hundred microns, which can be controlled by applying appropriate current density and processing time.

ED

CaP coatings

be

density


Input: This may also assist to control the surface morphology of CaP coatings from needle-like to plate-like structures.

surface morphology

CaP coatings


Input: Coating through ED can produce uniformly and fully covered surface, which makes it suitable for functionalizing porous structures.

Coating

ED

surface

porous


Input: Chai found that the bioactivity of the CaP coated Ti6Al4V scaffold to) was significantly improved and it was possible to produce osteoinductive for the repair of bone defects.

bioactivity

coated

scaffold

osteoinductive

bone defects


Input: Corrosion-based surface treatment involves interfacial chemical reactions of structures in corrosive solution.

surface treatment

interfacial chemical reactions

corrosive solution


Input: Such chemical processes include alkali treatment, acid etching and anodization treatments.

processes

alkali treatment

acid etching

anodization treatments


Input: 5 to show the surface morphology of scaffold before and after HCl etching treatment.

surface morphology

scaffold

etching


Input: The chemical reaction may produce a thin oxide layer on the surface of the metal, usually resulting in improved bioactivity.

chemical reaction

surface

oxide

metal

layer

bioactivity


Input: The thickness of the active layer can be controlled from tens of nanometer to hundreds of microns by adjusting processing variables.

layer

be

nanometer


Input: Alkali treatment was initially introduced by Kim to improve the bioactivity of Ti implants owing to a biologically active bone-like apatite layer on Ti surface.

Alkali treatment

bioactivity

Ti implants

bone-like apatite layer

Ti

surface


Input: Anodization is a mature electrochemical process capable of producing protective layers on the metal surface with adjustable surface microstructure and crystal structure.

Anodization

electrochemical process

protective layers

metal

surface microstructure

crystal structure


Input: Special care should be taken with regard to the possible negative effect on mechanical properties after corrosion-based surface treatment.

be

mechanical properties

surface treatment


Input: It was reported that alkali treatment might result in the deterioration of mechanical strength of porous Ti alloy scaffolds and also cause the embrittlement of the struts in the scaffolds.

alkali treatment

mechanical strength

embrittlement

porous Ti alloy scaffolds

scaffolds

struts


Input: 6 Challenges and future directions Additive manufacturing provides unprecedented opportunities for producing customized medical implants as this technology can fabricate structures of complex external shapes and intricate internal architectures.

Additive manufacturing

fabricate

medical implants

as

technology

internal architectures


Input: Topology optimization has become a powerful digital tool for the design of optimal structures and materials.

Topology optimization

design

optimal structures

tool

materials


Input: The integration of these two technologies sees a promising future in designing and manufacturing biocompatible orthopaedic implants with desired mechanical properties and minimal side effects on patients in clinical applications.

technologies

mechanical properties

manufacturing

biocompatible orthopaedic implants

clinical applications


Input: Key challenges and future directions in integrating the two technologies are as follows: i) A comprehensive and reliable database containing detailed information on the mechanical and biological properties of human bones is yet to be established.

technologies

properties

as

be

database

mechanical


Input: This database should include properties of bones for different age, gender groups and at different locations.

database

properties


Input: Such information is required as the design of the topology optimization process.

as

design

topology optimization process


Input: ii) Sophisticated topology optimization algorithms capable of dealing with multi-functional designs on multiple length scales simultaneously needs to be developed.

topology optimization

designs

algorithms

length scales

be


Input: Preliminary studies along this line can be found in Refs.. iii) Topological design of the lattice structures that can be easily produced by AM and exhibit anisotropic mechanical properties similar to human bones is another promising direction, despite that the fact that there has been extensive research on topology optimization based on continuum models.

be

be

Topological design

lattice structures

topology optimization

AM

anisotropic

properties

research

continuum models


Input: iv) Constraints and limitations of current AM technologies, such as the critical angle of the overhanging structure and the difficulty in removing the supporting structure, should be involved in newly-developed topology optimization algorithms so that the designs could actually be fabricated by AM.

AM technologies

AM

as

be

be

critical angle

topology optimization

designs

overhanging structure

structure

algorithms


Input: v) The long-term in vivo material/biological performance of porous metallic implants that are designed through topology optimization techniques and produced by AM needs to be rigorously assessed in order to ascertain the advantages and drawbacks of such implants.

v

be

performance

porous metallic implants

implants

designed

topology optimization

AM


Input: vi) Novel alloying systems capable of enhancing the mechanical and biological performance of porous metallic implants are in great demand, together with new post-treatment technologies for improving the bioactivity and biocompatibility.

alloying

mechanical

porous metallic implants

performance

post-treatment

bioactivity

biocompatibility


Input: 7 Conclusions In this paper, the current status of the topological design of porous metallic implants and the fabrication of such implants using additive manufacturing is reviewed.

topological design

porous metallic implants

implants

fabrication

additive manufacturing


Input: First the mechanical properties of human bones are discussed.

mechanical properties


Input: Then it is demonstrated that topology optimization is a powerful digital tool that can be used to obtain optimal internal architectures for porous implants which not only satisfy multifunctional requirements but also mimic human bones.

topology optimization

tool

mimic

be

internal architectures

porous implants


Input: Furthermore it is shown that additive manufacturing is the most promising and disruptive technology in the fabrication of porous orthopaedic implants designed through topology optimization.

additive manufacturing

fabrication

technology

porous orthopaedic implants

designed

topology optimization


Input: To further improve the mechanical and biological performance of these structures, both post-treatment and surface modification are necessary.

mechanical

performance

post-treatment

surface modification


Input: Based on these discussions, challenges and future directions of the integration topology optimization with additive manufacturing are identified.

topology optimization

additive manufacturing


Input: This review provides useful information to researchers and practitioners who are working in various areas of the truly multidisciplinary topic of bone implant design and fabrication Additive manufacturing of polymer-fiber composites has transformed AM into a robust manufacturing paradigm and enabled producing highly customized parts with significantly improved mechanical properties, compared to un-reinforced polymers.

areas

bone implant

fabrication

Additive manufacturing

AM

manufacturing

polymer-fiber composites

polymers

mechanical properties


Input: Almost all commercially available AM methods could benefit from various fiber reinforcement techniques.

AM

fiber reinforcement


Input: Recent developments in 3D printing methods of fiber reinforced polymers, namely, fused deposition modeling, laminated object manufacturing, stereolithography, extrusion, and selective laser sintering are reviewed in this study to understand the trends and future directions in the respective areas.

3D printing

fused deposition modeling

laminated object manufacturing

stereolithography

extrusion

selective laser sintering

fiber reinforced polymers

trends

areas


Input: In addition to extra strength, fibers have also been used in 4D printing to control and manipulate the change of shape or swelling after 3D printing, right out of the printing bed.

strength

fibers

4D printing

3D printing

swelling

bed


Input: Although AM of fiber/polymer composites are increasingly developing and under intense attention, there are some issues needed to be addressed including void formation, poor adhesion of fibers and matrix, blockage due to filler inclusion, increased curing time, modelling, simulation, etc.

AM

composites

be

fibers

inclusion

void

adhesion

curing time

modelling

simulation


Input: Additive manufacturing, also known as 3D printing, is defined asa process of adding materials to fabricate objects from three-dimensional models in successive layers, versus traditional subtractive manufacturing methods.

Additive manufacturing

3D printing

fabricate

traditional subtractive manufacturing

as

process

materials

three-dimensional models


Input: Numerous novel AM processes have been developed over the span of more than 20years of AM development with applications in aerospace, automotive, biomedical, digital art, architectural design, etc.

AM processes

AM

aerospace

automotive

biomedical

art

design


Input: There has been an exponential increase in AM technology in recent years and it continues to grow due to its versatility and low cost for rapid prototyping and manufacturing applications.

AM technology

manufacturing

rapid prototyping


Input: All of these features, combined with AMcustomizability to fabricate complex monolithic structures and geometries, with micrometer resolution, helped AM grow to a multibillion-dollar industry.

fabricate

AM

monolithic structures

geometries

micrometer resolution

industry


Input: To date, the dominant part of the 3D printing industry has immensely relied on single material printing.

3D printing

material


Input: This issue, paired with limited choices of available resins compatible with commercial printers, has severely limited variations in the physical and chemical properties of 3D printed objects.

resins

printers

variations

properties

3D printed


Input: These limitations have led to development of multi-material printers with partial control on material composition and properties, offering layered composite materials.

led

multi-material

composition

properties

material

composite materials


Input: Furthermore, multiple printing heads have allowed printing blended composites with functional and variable features.

printing heads

composites


Input: 3D printing of fiber reinforced composites is currently conducted by stereolithography, laminated object manufacturing, fused deposition modeling, selective laser sintering, and extrusion.

3D printing

stereolithography

laminated object manufacturing

fused deposition modeling

selective laser sintering

extrusion

fiber reinforced composites


Input: This is one of the hottest topics in the field of additive manufacturing and is under intense attention.

additive manufacturing


Input: This also offers significant improvement in mechanical properties, however, it requires a complex procedure to be manufactured and is difficult to be incorporated into processing.

mechanical properties

be

be


Input: Implementing the traditional methods of composite manufacturing in AM is not practical and new technologies are needed to assist with the development of new AM methods.

composite manufacturing

AM

AM

technologies


Input: Advances in development of composite 3D printers have not prevented development in pre-blended materials with fillers such as nanoparticles, carbon nanotubes, fibers and graphene in order to achieve unique characteristics and capabilities.

composite

as

carbon nanotubes

fibers

graphene

3D printers

materials


Input: Fiber reinforcement, in particular, appears to be an attractive filler to improve the properties of polymers.

Fiber reinforcement

be

polymers

properties


Input: Pre-blended materials using discontinuous fibers asan additive have been under intense investigation asa suitable alternative to multi-head printers with complex and costly designs.

materials

fibers

additive

printers

designs


Input: These additive based materials exhibit unique characteristics and capabilities, depending on the additive used.

additive

additive

materials


Input: Suitable mechanical, electrical, or thermal properties can be accomplished in an inexpensive manner.

mechanical

electrical

thermal properties

be


Input: Polymers, in particular, have been the center of attention due to ease of production and availability.

Polymers

production


Input: The 3D printing industry primarily involves polymers in various forms, such as reactive, liquid solutions, and thermoplastic melts.

3D printing

polymers

as

thermoplastic


Input: These benefits, joined by enhancements from fiber reinforcement, offer a favorable combination for future development of AM technology.

fiber reinforcement

AM technology


Input: In addition, almost all of the existing AM methods can be benefited from fiber reinforcement.

AM

be

fiber reinforcement


Input: Although fiber reinforcement in 3D printing sounds promising, there are numerous issues which need to be resolved.

fiber reinforcement

3D printing

be


Input: Namely, the effect of fibers on resolution, agglomerate formation, heterogeneous composite formation, blockage of printer heads, non-adhesion, and increased curing times.

fibers

resolution

curing times

agglomerate formation

heterogeneous composite formation

printer


Input: This paper reviews recent advances in AM of polymer based fiber reinforced composites and potential methods for modelling and analysis of these 3D printed structures.

AM

3D printed

polymer

fiber reinforced composites

modelling


Input: Latest development and improvement to existing methods will be reviewed in detail, in order to understand the challenges in 3D printing of polymer composites with fiber reinforcement.

be

polymer composites

3D printing

fiber reinforcement


Input: 3D printing of fiber reinforced polymer composites Fiber reinforcement can greatly improve the properties of 3D printed parts with polymer matrix.

3D printing

fiber reinforced polymer composites

Fiber

polymer

properties

3D printed parts


Input: Fiber orientation and void content of composites are the main concerns in 3D printing of these composites.

Fiber orientation

void

composites

composites

3D printing


Input: Most of the commercially available 3D printing techniques would benefit from fiber reinforcement.

3D printing

fiber reinforcement


Input: In this section, all of these techniques for 3D printing of polymer-fiber composites are reviewed in detail to demonstrate their strengths and weaknesses in additive manufacturing of polymer-fiber composites.

3D printing

additive manufacturing

polymer-fiber composites

polymer-fiber composites

strengths


Input: These methods are FDM, LOM, SL, extrusion, and SLS.

FDM

LOM

SL

extrusion

SLS


Input: 2.1 Fused deposition modeling FDM is currently the most applied AM technology, according to WohlerReport from Stratasys, Inc. Commercial FDM machines held 41.5% of the market share, with the total of 15,000 FDM machines sold by the end of 2010.

Fused deposition modeling

FDM

AM technology

FDM

FDM

Stratasys


Input: The key elements of the FDM system include material feed mechanism, liquefier, print head, gantry, and build surface.

elements

FDM

material feed mechanism

print head

build surface


Input: Several process parameters are essential in FDM, including bead width, air gap, model build temperature, and raster orientation.

process parameters

model

FDM

bead width

build

raster orientation


Input: The effects of raster orientation on tensile and compression test results have been investigated in detail.

raster orientation

tensile

compression test


Input: The temperature distribution during the FDM process can be monitored by IR camera.

temperature

distribution

FDM

be

IR

camera


Input: The surface roughness and cross section shape of the FDM fabricated parts are under intense study.

surface roughness

cross section

fabricated

FDM


Input: 1 and 2 illustrate the bonding mechanism in the FDM of polymer composites along cross-section of printed parts.

bonding mechanism

FDM

polymer composites


Input: Several building rules have been proposed to improve the strength and accuracy of the FDM printed parts, such as build parts to ensure tensile loads are carried axially along printed directions, deal with the stress concentration at corners, use negative air gap to increase both strength and stiffness, consider that small bead width leads to extra printing time and better surface quality, be aware the part accuracy affected by the build orientation, and realize that tensile loaded area tends to fail easier than compression loaded area.

strength

strength

stiffness

tensile

compression

accuracy

tensile loads

stress concentration

bead width

accuracy

FDM

as

be

surface quality

build orientation

area

area


Input: Recently, fiber reinforcement in FDM has been very popular amongst researchers.

fiber reinforcement

FDM


Input: Most of the efforts have focused on development of filaments with short fiber additives.

filaments

short fiber

additives


Input: Inclusion of fibers in filament reduces tape swelling at the printing head during deposition and increases the stiffness.

Inclusion

fibers

filament

swelling

deposition

printing head

stiffness


Input: Glass fiber reinforced polypropylene was evaluated by Carneiro, Silva and showed 30% and 40% improvement for the modulus and strength, respectively, compared to pure PP.

Glass fiber reinforced polypropylene

pure PP

strength


Input: Vapor grown carbon fibers and single wall carbon nanotubes were compounded with acrylonitrile butadiene styrene for the FDM process.

carbon fibers

single wall carbon nanotubes

acrylonitrile butadiene styrene

FDM


Input: The VGCFs can be easily aligned by the extrusion process.

be

extrusion process


Input: Tensile strength of 5wt% of VGCFs and SWNTs filled FDM parts increased 18% and 31%, respectively.

Tensile strength

SWNTs

FDM


Input: However, the strain to failure of printed parts reinforced with VGCFs and SWNTs was dramatically decreased.

strain

failure

reinforced

SWNTs


Input: ABS containing oriented VGCFs and SWNTs exhibited modulus improvements up to 93%.

ABS

SWNTs


Input: The fiber orientation can be observed in 3.

fiber orientation

be


Input: Thermotropic liquid crystalline polymers with excellent tensile strength, such as ABS and polypropylene, were used in fiber reinforced FDM parts in order to overcome the drawbacks of low aspect ratio of fiber in short fiber filled parts.

Thermotropic liquid crystalline polymers

as

ABS

polypropylene

fiber

fiber

short fiber

tensile strength

FDM

aspect ratio


Input: Processing temperature was one of the important parameters which affects the surface morphology of TLCP and its mechanical behavior.

temperature

parameters

surface morphology

mechanical


Input: Higher carbon fiber ratio has a high maximum decomposition temperature, thus providing high thermal stability.

carbon fiber

maximum decomposition temperature

thermal stability


Input: Ning, Cong evaluated the effect of weight ratio and length of carbon fiber on physical properties of the FDM samples with ABS matrix.

weight

carbon fiber

ABS matrix

physical properties

FDM


Input: The 5 and 7.5wt% carbon fiber content showed the best improvement in tensile strength and Young's modulus, respectively.

carbon fiber

tensile strength


Input: These researchers have also concluded that longer carbon fibers can increase tensile strength and Young's modulus at the expense of toughness and ductility.

carbon fibers

tensile strength

toughness

ductility


Input: As described in 4, with aligned carbon fiber during the FDM process, 30wt% CF-ABS composites exhibited great improvement in strength and Youngmodulus.

As

carbon fiber

composites

FDM

strength

Youngmodulus


Input: These printed CF-ABS parts exhibit specific strength higher than Aluminum.

specific strength

Aluminum


Input: The triangular channels between beads decreased by incorporating carbon fibers due to the reduced die-swell and increased thermal conductivity.

beads

carbon fibers

thermal conductivity


Input: However, inclusion of carbon fiber into the feedstock caused internal voids inside of the beads responsible for stress concentration, resulting in failure at lower stresses.

inclusion

carbon fiber

feedstock

internal voids

failure

beads

stress concentration


Input: It can be seen in 5 that the FDM samples exhibited significant pore formation, with internal voids, as well as voids formed between the deposited beads during printing.

be

as

as

FDM

pore

internal voids

deposited beads


Input: Continuous fiber reinforcement is currently one of the biggest challenges researchers face in 3D printing of polymer composites.

Continuous fiber reinforcement

polymer composites

face

3D printing


Input: It offers significant improvement in mechanical properties compared to discontinuous fibers, however, there is still no robust and standard paradigm developed for 3D printing of continuous fiber composites.

mechanical properties

standard

fibers

continuous fiber composites

3D printing


Input: Recently, Matsuzaki, Ueda developed an innovative technique for in-nozzle impregnation of continuous fiber and thermoplastic matrix.

impregnation

continuous fiber

thermoplastic matrix


Input: The resin filament and fiber were supplied separately, before heating and mixing in the printing head.

resin filament

fiber

heating

mixing

printing head


Input: The schematic of this process demonstrating the printing head and continuous fiber integration is presented in 6.

process

printing head

continuous fiber


Input: Carbon fibers and twisted yarns of natural jute fibers were used as reinforcement.

Carbon fibers

fibers

as


Input: Superiority of continuous fiber composites versus short fiber reinforcement and other 3D printing methods can be observed in 7.

continuous fiber composites

short fiber reinforcement

be

3D printing


Input: Namiki, Ueda implemented the same technique for printing polyactic acid /carbon fiber composite parts.

fiber composite


Input: Some gaps were reported between PLA filaments, which can be reduced by increasing the resolution.

PLA filaments

be

resolution


Input: Tensile strength of continuous carbon fiber reinforced PLA prepared by FDM, as reported by Li, Li, can reach up to 91MPa, while in the case of short carbon fiber, it is only 68MPa.

Tensile strength

continuous carbon fiber

PLA

as

Li

Li

short carbon fiber

FDM


Input: Weak bonding between PLA and carbon fiber can significantly affect the mechanical properties in this method, however, surface modification of carbon fiber bundle with methylene dichloride and PLA particles improved adhesion and increased tensile and flexural strength.

bonding

mechanical properties

particles

PLA

carbon fiber

carbon fiber

methylene dichloride

PLA

surface modification

adhesion

tensile

flexural strength


Input: 8 presents the ultimate tensile and flexural strength of pure PLA, carbon fiber-PLA, and modified carbon fiber-PLA.

tensile

flexural strength

PLA

carbon fiber-PLA

carbon fiber-PLA


Input: Green circles in 8 indicate different phases of the tensile process, namely, loading of the PLA material between fixture and test sample at the beginning of the test and a slight drop of the curve slope due to fiber-matrix interface debonding.

tensile

process

sample

interface

PLA material

fixture


Input: Marked circles in 8 signify the process of load change from resin to fiber at the beginning of the test.

process

resin

fiber


Input: The next circle in 8 shows the plastic elongation of PLA polymer chains that continue to bear load after the failure of carbon fibers.

plastic

PLA

carbon fibers

elongation

failure


Input: Tian, Liu performed a systemic analysis on interface and performance of printed continuous carbon fiber reinforced PLA composites and the effect of process parameters on the temperature and pressure in the process.

interface

performance

process parameters

pressure

process

continuous carbon fiber

PLA composites

temperature


Input: 9 shows cross-section of the tensile bar and continuous fibers in the fracture surface, and 10 demonstrates the capability of this method in 3D printing large curvatures, without losing the continuous fiber reinforcement.

tensile bar

continuous fibers

continuous fiber reinforcement

fracture

3D printing


Input: Melenka, Cheung evaluated continuous Kevlar fiber-reinforced 3D printed Nylon structures using commercial desktop printers in order to predict the tensile properties.

continuous Kevlar fiber-reinforced

3D printed

printers

tensile properties


Input: Stiffness and ultimate strength showed significant increase with high volume of fiber reinforcement.

Stiffness

ultimate strength

volume

fiber reinforcement


Input: Carbon fibers were placed between layers of 3D printed polymer to improve strength and fatigue life, while thermal treatment was performed to further increase the mechanical properties.

Carbon fibers

3D printed

thermal treatment

strength

fatigue life

mechanical properties


Input: However, Van Der Klift, Koga showed that increasing the number of carbon fiber layers results in larger void areas, which had negative effect on the tensile strength.

carbon fiber

void

areas

tensile strength


Input: Impregnation of plastics into the fiber bundle could be achieved in the temperature range of 200Layer thickness of 0.4and hatch spacing of about 0.6mm guaranteed bonding strength between lines and layers.

Impregnation

plastics

fiber bundle

be

temperature range

hatch spacing

bonding strength


Input: These parameters could achieve maximum flexural strength of 335MPa and flexural modulus of 30GPa.

parameters

flexural strength


Input: 2.2 Laminated object manufacturing In LOM, which was developed by Helisys of Torrance, CA and shipped in 1991, 3D parts are manufactured by cutting 2D cross-sections with a laser or cutter and sequentially laminating the sheets.

Laminated object manufacturing

LOM

cutting

Helisys of Torrance

CA

sheets

3D parts

manufactured

laser


Input: Paper, metals, plastics, fabrics, synthetic materials, and composites are amongst the materials that can be utilized in LOM.

metals

plastics

synthetic materials

composites

be

materials

LOM


Input: Polymer matrix composites of C-shaped panels were directly fabricated by curved LOM.

Polymer matrix composites

fabricated

LOM


Input: A vacuum thermoforming apparatus was applied to bond commercial prepregs.

vacuum thermoforming

prepregs


Input: The shear strength of fabricated composites was measured to be approximately 24.8MPa, which was suggested by the authors to be acceptable for normal applications.

shear strength

fabricated

composites

be

be


Input: The LOM process was applied to print 3D parts of unidirectional and continuous glass fibers with 52and epoxy matrix.

LOM

print

3D parts

unidirectional

continuous glass fibers

epoxy matrix


Input: The final part and its cross section are presented in 13.

cross section


Input: Decent interfacial bonding was shown by interlayer microstructures of LOM polymer composites.

interfacial bonding

interlayer microstructures

LOM polymer composites


Input: The major issue for the LOM process was the incapability of the heat roller to bring parts to full consolidation and cure.

LOM

heat roller

consolidation

cure


Input: It is helpful to increase the interface strength and reduce void contents to under 5% by a post consolidation cycle.

interface

void

consolidation


Input: Sonmez and Hahn studied heat transfer and stress in LOM to understand the effect of process parameters on the resulting stress and temperature distributions.

heat transfer

process parameters

distributions

stress

stress

LOM

temperature


Input: Large rollers were more favorable for bonding, due to a less concentrated stress distribution.

bonding

stress distribution


Input: Recently, a new method called laser assisted AM for continuous fiber reinforced thermoplastic composites was developed by researchers at Kansas State University, with the motivation of reducing the waste associated with LOM.

laser

AM

LOM

continuous fiber reinforced thermoplastic

composites


Input: The authors proposed using prepreg tape instead of pre-cut prepreg sheet.

prepreg

prepreg


Input: The tape strips were placed layer by layer using a CO2 laser beam and consolidation roller, prior to laser cutting of each layer.

layer by layer

consolidation

beam

laser cutting

layer


Input: 14 demonstrates this process schematically, as well as its tensile properties in comparison with various AM and conventional methods of composite manufacturing.

process

as

as

tensile properties

AM

composite manufacturing


Input: This method exhibits superior mechanical properties due to continuous fiber reinforcement, high fiber weight ratio, minimized void content, and superior interfacial bonding.

mechanical properties

interfacial bonding

continuous fiber reinforcement

fiber weight ratio

minimized void content


Input: 2.3 Stereolithography The 3D parts fabricated by SL exhibit weak mechanical properties, which hinder their further applications as functional components under loading conditions.

Stereolithography

SL

3D parts

mechanical properties

as

components


Input: However, adding fibers to the resin can increase the potential of SL in 3D printing functional components.

fibers

resin

SL

3D printing

components


Input: Although continuous fiber is ideal for reinforcement, high weight ratio of short fibers can yield comparable results, however, their efficiency is limited due to fracture during mixing, random orientation, and un-even length.

continuous fiber

short fibers

reinforcement

weight

fracture

mixing

orientation


Input: Multi-wall carbon nanotubes with a low weight ratio were mixed in SL resin by mechanical mixing and ultrasonic dispersion.

carbon nanotubes

resin

weight

SL

mechanical mixing

ultrasonic dispersion


Input: The tensile strength and fracture strength were increased by 5.7% and 26%, respectively, by adding 0.025wt% MWNTs.

tensile strength

fracture


Input: Carbon fiber has been successfully applied to reinforce polymers, however, the primary issue for utilizing carbon fiber in SL is that it is opaque to the UV light.

Carbon fiber

polymers

carbon fiber

SL

UV light


Input: Consequently, regions of the resin blocked by carbon fibers remains uncured by UV light.

resin

carbon fibers

UV light


Input: Using glass fiber instead of carbon fiber can be beneficial for decreasing the opacity to UV light.

glass fiber

carbon fiber

be

UV light


Input: The SL plus vacuum cast process was investigated to improve the tensile strength.

SL

vacuum cast

process

tensile strength


Input: Tensile samples produced by SL and polymer-glass fiber nonwoven-polymer sandwich structures were introduced by vacuum cast, which showed a significant increase of 36% in ultimate tensile strength and 11% increase in stiffness.

Tensile

ultimate tensile strength

stiffness

samples

SL

vacuum cast

fiber

sandwich structures


Input: The viscosity of the resin, especially at low shear rates, increased in the composite resins with significant volume fractions of fibers.

viscosity

resin

composite resins

fibers

volume fractions


Input: The surface coating of fibers can effectively reduce the viscosity, which is an advantage which allows processing of resins with higher fiber concentrations.

surface

coating

fibers

resins

viscosity

fiber concentrations


Input: Laser scanning based SL was used to add 20vol% of short glass fibers into an acrylic based photo polymer.

Laser

SL

glass fibers

acrylic

polymer


Input: 15 shows the microstructures of molded and laser-scanned specimen with 20vol% glass fiber.

microstructures

glass fiber


Input: Fiber filled composites represents a higher elastic modulus and ultimate tensile strength.

Fiber filled composites

elastic modulus

ultimate tensile strength


Input: The shrinkage of fiber reinforced composites was also observed to be lower than their non-reinforced counterparts.

shrinkage

fiber reinforced composites

be


Input: Dual porlymerization scheme, including UV radiation and thermal treatments, was proposed to cure resins containing a high volume ratio of carbon fibers.

UV

cure

volume

radiation

thermal treatments

carbon fibers


Input: It was estimated that one quarter of resin remains uncured, which was primarily inside of carbon fibers.

resin

carbon fibers


Input: After an hour of thermal treatment, the tensile strength was increased by 95%.

thermal treatment

tensile strength


Input: Llewellyn-Jones, Drinkwater used ultrasonic manipulation to distribute glass microfibers in the resin.

ultrasonic manipulation

glass microfibers

resin


Input: A variety of fiber orientation angles were achieved, demonstrating the versatility of the process.

fiber orientation

process


Input: This method allows smart material fabrication, such as resin-filled capsules for self-healing or piezoelectric particles for energy harvesting.

material

as

fabrication

particles

energy harvesting


Input: 2.4 Extrusion Extrusion, as one of the most recent developments in 3D printing, emerged to overcome the limitations of the FDM method with its versatility and cost-effectiveness.

Extrusion

3D printing

FDM

as


Input: In this AM technique, layers of the material solution are directly deposited in a volatile solvent to produce freeform 3D structures.

AM technique

material

freeform 3D


Input: Lightweight cellular carbon fiber and SiC whiskers filled composites have been demonstrated by applying 3D extrusion printing method, as described in 16.

Lightweight

cellular carbon fiber

SiC whiskers

composites

as


Input: Epoxy-based inks, which exhibited the desired viscoelasticity and long pot-life in the absence and presence of highly anisotropic carbon fibers, were prepared.

Epoxy-based inks

fibers

viscoelasticity

anisotropic


Input: The SiC-filled and SiC/C filled transverse specimens showed a substantial increase in Youngmodulus, over the pure resin from 2.66 to 10.61 and 8.06 respectively.

Youngmodulus

pure resin


Input: Tensile strength of printed composites was comparable to the cast epoxy resin samples, with longitudinal specimens exhibiting slightly higher strength than that the transverse specimens.

Tensile strength

strength

composites

resin

cast


Input: 17 shows a comparison in tensile strength of 3D printed tensile bars, using various fillers, as well as their microstructure.

tensile strength

3D printed

as

as

microstructure


Input: PLA/MWNTs composite was used to fabricate conductive 3D microstructures, with arbitrary shapes as small as 100with a method called liquid deposition modeling.

composite

as

as

fabricate

deposition modeling


Input: 2.5 Selective laser sintering SLS is a powder based AM process.

Selective laser sintering

AM process

powder


Input: The laser scans the powder bed, layer by layer, to form a 3D structure, as demonstrated in 18.

laser scans

powder bed

layer by layer

3D structure

as


Input: It mainly deals with wax, ceramics, metals and polymers.

wax

ceramics

metals

polymers


Input: Major polymers used by SLS include nylon, i.e.

polymers

nylon

SLS


Input: polyamide, crystalline thermoplastics: polyethylene, PEEK, and PCL.

polyamide

crystalline thermoplastics

polyethylene

PEEK

PCL


Input: SLS can be categorized in solid state sintering, liquid phase sintering-partial melting, full melting, and chemically induced binding.

SLS

solid state sintering

melting

melting

be

liquid phase


Input: SSS is a thermal process that occurs at temperatures between TMelt /2 and TMelt, where TMelt is the melting temperature.

process

temperatures

melting temperature


Input: In liquid phase sintering-partial melting, usually the binder material becomes liquefied, while structural material remains solid.

liquid phase

melting

binder

material


Input: The full melting technique melts the powder entirely and exhibits properties comparable to those of bulk material.

melting

powder

material

properties


Input: It can be applied to a wide variety of materials, however, the long process time and preheating of powders is necessary.

be

powders

materials

process time

preheating


Input: 1 lists the range of materials and their associated binding mechanism in SLS.

range

materials

mechanism

SLS


Input: CNT was added in Polyamide 12 in order to improve the mechanical behaviors.

CNT

Polyamide 12

mechanical


Input: The laser sintered parts had 13% greater flexural modulus, 10.9% higher flexural strength, and 54% larger Youngmodulus.

laser

flexural strength

Youngmodulus


Input: The crystallization temperature of PA12-CNT powder was increased, compared to the pure PA12, which was responsible in hindering the movement of PA12 chains by the interfacial force between CNTs and PA12.

crystallization

powder

pure PA12

CNTs

interfacial force


Input: However, the porosity also increased in the CNT composites.

porosity

CNT composites


Input: MWNTs were also mixed with PA12 for the investigation of its effect on mechanical properties.

mechanical properties


Input: Goodridge, Shofner also confirmed enhancement in mechanical properties of PA12 with inclusion of CNT, exhibiting 22% increase in storage modulus.

mechanical properties

inclusion

CNT


Input: A high volume ratio of carbon fiber was added into PA12.

volume

carbon fiber


Input: CNT-coated PA12 also improved heat conduction and heat absorption compared to pure PA12.. Furthermore, simulation results on laser sintering of PA12-CNT suggested that inclusion of CNT helps the laser heat to be conducted wider and deeper into the powder bed.

inclusion

CNT

be

heat conduction

heat absorption

simulation

laser sintering

laser heat

powder bed


Input: The result of these simulations can be observed in 19.

simulations

be


Input: Uniform distribution of carbon fibers and good interfacial adhesion between fibers and matrix was achieved by pre-modification of carbon fibers through oxidation.

distribution

carbon fibers

fibers

carbon fibers

adhesion

oxidation


Input: By adding the maximum weight ratio of carbon fibers, the flexural strength and flexural modulus were enhanced 114% and 243.4%, respectively.

weight

carbon fibers

flexural strength


Input: Glass beads were used asadditives in SLS of Nylon powders, in order to determine the mechanical properties, as a function of material composition.

Glass beads

Nylon

as

material

SLS

mechanical properties

composition


Input: Zhu, Yan proposed a novel method to prepare high-performance carbon fibers/PA12/epoxy ternary composites by infiltrating the porous green carbon fibers/PA12 parts built by SLS, with high-performance thermosetting epoxy resin, prior to curing the resin; this process is described in 20.

carbon

composites

carbon

epoxy

resin

infiltrating

process

porous

SLS

curing


Input: The end result is a ternary composite system with novolac epoxy resin, reinforced with carbon fibers coated with a thin 595nm layer of PA12.

ternary composite system

novolac epoxy resin

carbon fibers

reinforced

layer


Input: This method with 33% volume fraction of carbon fibers yielded an ultimate tensile strength of 101.03MPa and a flexural strength of 153.43MPa.

volume fraction

carbon fibers

ultimate tensile strength

flexural strength


Input: 3 Four-Dimensional printing of active Polymer-Fiber composites Addition of fiber in 3D printed polymers is not always for improving the mechanical properties.

Polymer-Fiber composites

fiber

3D printed

mechanical properties


Input: Fibers, as well other additives, are also used in manufacturing of smart composites, to control the structure transformation.

Fibers

as

additives

composites

manufacturing

structure


Input: This implementation in 3D printing opened a new field called 4D printing.

3D printing

4D printing


Input: 4D printing refers to a multi-material printing with the ability to transform over time or change its shape after the printing.

4D printing

multi-material printing


Input: These structures can be programmable and transformed from one or two dimensional structures to 3D objects.

be

3D objects


Input: Recent advances in AM made precise placement of material at micro-scale during 3D printing of complex structures possible.

AM

3D printing

material

micro-scale

complex structures


Input: This allows implementing programmable and computational material in AM in order to control the shape of the material after printing.

material

material

AM


Input: These materials can change their shape under light, temperature change, or immersion into a solvent.

materials

temperature


Input: 3D printing technology has enabled active material to achieve an even higher complexity and accuracy.

3D printing technology

material

complexity

accuracy


Input: Fiber additives play an important role in 4D printing; controlling the fiber alignment allows programmable transformation, right out of the printing bed.

Fiber additives

4D printing

fiber alignment

bed


Input: Ge, Qi developed a method to print thermomechanically programmable composites with complex shapes.

Ge

composites

print

complex shapes


Input: The matrix and fibers used were an elastomer and a glassy polymer, with tailored thermomechanical behavior, respectively.

fibers

elastomer

polymer

thermomechanical


Input: 21 demonstrates the process in which the inkjet deposited material on the bed, prior to photopolymerization of the film by UV light, forms a layer.

process

inkjet

photopolymerization

material

bed

UV light

layer


Input: Gladman, Matsumoto printed plant-inspired architectures, with a hydrogel composite ink, composed of stiff cellulose fibrils embedded in a soft acrylamide matrix.

hydrogel composite

cellulose fibrils

acrylamide matrix


Input: Alignment of cellulose fibrils controlled the swelling of the 3D printed part upon immersion in water.

cellulose fibrils

swelling

3D printed part


Input: These structures are programmable based on the printing direction and orientation of embedded cellulose fibrils inside the structure.

orientation

structure

cellulose fibrils


Input: 4 Modeling and analytical techniques Polymer-fiber composites produced by AM can be analyzed using existing theories based on the manufacturing technique and the reinforcement type.

Modeling

Polymer-fiber composites

be

AM

manufacturing

reinforcement


Input: Existing macro and micro mechanical modelling techniques can be applied to AM with slight modifications.

macro

mechanical modelling

be

AM


Input: Microstructure of 3D printed parts often differ from those prepared by traditional manufacturing methods and with the immerging of new AM methods, there is a demand for modelling and analysis of these structures.

Microstructure

3D printed parts

traditional manufacturing

AM

modelling


Input: 4.1 Short fiber composite theories There are several theories for predicting the properties of short fiber composites.

Short fiber composite

short fiber composites

properties


Input: Depending on their assumptions, they can be applied to various 3D printing methods.

be

3D printing


Input: Fibers alignment, shape, length, and its bonding with the matrix are crucial in accuracy of the modelling.

Fibers alignment

bonding

accuracy

modelling


Input: The modified rule of mixtures is the simplest method to predict the tensile properties of short fiber composites, by assuming perfect fiberinterfacial bonding.

rule of mixtures

fiberinterfacial bonding

tensile properties

short fiber composites


Input: MROM is given by cu = 1 2 V f fu + V m m where 1 2 is fiber efficiency factor for the strength of the composite, in which, 1 and 2 are the fiber orientation and fiber length factors, respectively; cu and fu are ultimate strength of the composite and fiber, respectively; V f and V m represent the volume fraction of the fiber and matrix; and m is the matrix stress at the composite failure.

cu

V

V

composite

cu

composite

fiber

V

V

fiber

f

f

fiber efficiency factor

strength

ultimate strength

fiber orientation

fiber length factors

volume fraction

matrix stress

composite failure


Input: If the fiber length is equal to L and uniform, fiber orientation factor is equal to 1 and fiber length factor is given by the critical fiber length, r f is fiber radius, and i is interfacial shear stress between matrix and fibers.

fiber length

fiber orientation

fiber length factor

fiber radius

critical fiber length

interfacial shear stress

f

fibers


Input: In order to consider the effect of fiber orientation and non-uniform fiber length in the model, 1 and 2 should be modified.

fiber orientation

fiber length

model

be


Input: Modified Kelly and Tyson model proposed for fibers shorter and longer than the critical fiber length with considering fiber orientation, as follows.

model

fibers

as

critical fiber length

fiber orientation


Input: However, fiber orientation factor 1 in this model is fitted empirically.

fiber orientation

model


Input: Fu and Lauke used two probability density functions for modelling the fiber length and fiber orientation distributions with the intention of predicting the elastic properties.

probability density functions

fiber length

distributions

modelling

fiber orientation

elastic


Input: There are various theories for predicting the stiffness properties of short-fiber composites.

stiffness

properties

composites


Input: The Morimodel is another well-known theory that considers a non-dilute composite containing many identical spheroidal particles.

composite

particles


Input: It is assumed that the composite experiences an average stress different from that of the applied stress.

composite

average

stress


Input: Longitudinal and transverse elastic moduli in Morimodel are where V f is the volume fraction of filler and m is the Poissonratio of the matrix; A1, A2, A3, A4, A5, and A are functions of the Eshelbytensor and the properties of the fiber and the matrix, with more explanation given in.

elastic moduli

V

fiber

f

volume fraction

properties


Input: In theory, the aforementioned equations for short fiber composites, can be used to model 3D printed parts, however, length and orientation of the fibers used in the process should match the assumptions.

short fiber composites

be

fibers

model

orientation

process

3D printed parts


Input: FDM, SLS, and extrusion with short fiber reinforcement can be modeled with these analytical methods.

FDM

SLS

extrusion

short fiber reinforcement

be


Input: However, 3D printed parts often contain considerable fraction of void content and modifications may be necessary when applying these methods on additive manufacturing.

3D printed parts

fraction

void

be

additive manufacturing


Input: Void in composite materials are comprehensively explained in.

Void

composite materials


Input: 4.2 Classical laminate plate theory CLPT is an extension of the classical plate theory for isotropic and homogeneous materials with some modifications to reflect the inhomogeneity of orthotropic materials in thickness direction.

Classical laminate plate theory

classical plate theory

materials

isotropic

homogeneous materials

orthotropic


Input: CLTP is applicable to all 3D printed parts that exhibit orthogonal behavior.

3D printed parts


Input: Here, we present a brief summary of CLPT for laminated plates consisting of multiple unidirectional laminae.

laminated plates

unidirectional laminae


Input: The stiffness matrix of each ply can be described as.

stiffness matrix

be

as


Input: Transformed reduced stiffness matrix for various fiber orientation can be computed using transformation matrix as follow, and is the angle of the fiber reinforcement.

stiffness matrix

fiber orientation

fiber reinforcement

be

as

transformation matrix


Input: Then, in-plane, coupling, and bending stiffness matrices can be obtained by, respectively where z represents the vertical position in the ply from the midplane.

bending

be

vertical

midplane


Input: Finally, we can write a connection between the applied loads and the associated strains in the laminate, as follows, N M = A B B D 0 where N is normal stress resultants, M is moment resultants, 0 represent strain term in midplane, and is the twist of the laminated plate.

laminate

midplane

as

N

B

N

stress

strain

laminated plate


Input: The strain along the plate thickness can be given by, x y xy = x 0 y 0 xy 0 + z x y xy Additionally, by using the same principle, CLPT can be applied to evaluate the strength and elastic constants of FDM printed parts with void content.

strain

strength

be

y

y

y

be

elastic constants

FDM

void


Input: As mentioned earlier, FDM process is associated with void formation between printing beads, which needs to be considered in the modeling.

As

be

FDM

void

beads

modeling


Input: In the method developed by Rodriguez, Thomas for ABS materials, The FDM part is defined as an unidirectional ABScomposite with a laminate structure.

ABS materials

as

FDM

unidirectional

laminate


Input: This structure is consisting of vertically stacked layers with contiguous material and voids.

structure

voids

material


Input: The unidirectional elastic constants are given as and represent the elastic modulus, shear modulus and Poissonratio of the extruded polymer used in the FDM process.

unidirectional

elastic constants

as

elastic modulus

shear modulus

extruded

FDM


Input: The 1 is the area void density in the plane normal to filament direction.

area void density

filament


Input: This method was used in various works for single material FDM parts containing void, however, certain modifications are needed in order to apply it to multi-material 3D printing.

material

FDM

multi-material 3D printing

void


Input: More information regarding void in composite structures can be found in.

void

composite structures

be


Input: 4.3 Finite element method FEM is particularly interesting for modelling 3D printed part due to its flexibility in analyzing complex geometries in both macro and micro scale.

Finite element method

FEM

complex geometries

macro and micro scale

modelling

3D printed part

flexibility


Input: It can be applied to continuous and short fiber 3D printed composites.

be

short fiber

3D printed


Input: The primary distinction of most composites by AM is the significant void content that needs to be incorporated into the respective finite element model.

composites

be

AM

void

finite element model


Input: Perhaps the most appealing approaches for mechanical modelling of fiber composites are homogenization, which was described briefly in CLPT, and unit-cell based methods.

mechanical modelling

fiber composites

homogenization


Input: Both approaches can be implemented in FEM, thus, applicable to all AM methods.

be

FEM

AM


Input: Conversely, there has been a lack of attention to modelling of these processes, and with increasing the popularity of 3D printing among practitioners, the need for simulation of the 3D printing process is certain.

modelling

simulation

processes

3D printing

3D printing