近幾年，積層製造也稱為快速成型或3D列印是個蓬勃發展的產業。因為其具有一些特點，例如:減少製程步驟、客製化複雜結構，適合來製造仿生的植入物。其中又以人體骨頭的應用最為廣泛研究。然而，骨頭是主要承受人類運動的部位，會隨著年齡、性別與部位而改變的孔洞結構。因此，多種的仿生植入物的機械性質與孔洞結構之關係研究其為重要。

在此研究中，我們分別使用積層製造中的選擇性雷射熔融法(SLM)和電子束熔融法(EBM)製備出仿生植入孔洞骨材。以高生物相容性的Ti-6Al-4V合金作為實驗的材料。

第一，藉由電腦輔助設計(CAD)不同孔隙度的結構，並且以Ti-6Al-4V金屬粉體，利用選擇性雷射熔融法(SLM)製備出Ti-6Al-4V孔洞結構。並在詳細的形貌觀察與CAD模型比較、物理性質測量、機械性質量測後，推導出其相關的關係。因為雷射束寬化和雷射熔融邊界效應，在CAD模型與孔洞SLM試片差異為在SLM試片有較大的支架與較小的孔洞。而在高孔隙率試片具有較多孔洞密度下，此差異會較為明顯而導致設計的孔隙度會大於實際的孔洞試片之孔隙率。若縮小雷射束與粉體大小，能降低此差異性。然而用SLM技術製備出的Ti-6Al-4V結構為具有較高的硬度利於抗磨耗性，有利於人體骨材之應用。隨著孔洞結構之孔隙率提高，其機械性質(彈性模數與降伏強度)會隨之降低，而彈性模數能匹配到人體骨頭，避免應力遮蔽效應之風險。利用Gibson and Ashby方程式，利用SLM技術製備的孔洞材料其孔洞率與機械性質的關係式可被描述與預測。

根據許多先前的研究，高孔隙率的孔洞結構，能有效降低應力遮蔽問題，但其機械強度也是會隨之降低。第二部分，利用EBM製備出高孔隙率的孔洞Ti-6Al-4V結構，並探討其物理性質、機械性質。從此研究結果的得知，當藉由提高孔洞支架與孔洞大小，其孔洞率幾乎維持相近的高孔隙率80%。而利用EBM製備出高孔隙率的孔洞結構其彈性模數，也相當匹配到人體海綿骨材的彈性模數。但從結果可以發現，較大支架的孔洞試片能增強其耐破裂能力。因此我們推導出孔洞支架與其破壞能量之關係式，從關係式可以發現當孔洞支架寬度小於401微米時，其孔洞結構幾乎無法承受能量而破壞。然而積層製造(AM)因其基本上為粉末冶金的技術，其孔洞試片具有粗糙度的表面，其會造成應力集中，而提早破壞。因此，在此研究中推導出孔洞支架寬度和粗糙度之比例對應到破壞能量之關係式，從關係式可以發現當支架寬度越大，其粗糙度對破壞能量影響越小，對於支架寬度約為650微米時，其最大接受之表面粗糙度不能大於91微米，否則孔洞結構也幾乎無法承受能量而破壞。

將實驗結果導入物理公式並推演出SLM與EBM製備出的孔洞結構對應之機械性質的關係式，期待以此關係式可在使用此技術製備出的仿生植入物，能在材料被應用前來預估其機械性質，有效提高其實際應用的價值。

In recent years, additive manufacture (AM), or called as rapid prototyping or 3D printing, has become a flourishing industry suitable to fabricate bio-implants, due to the benefits such as the reduction in process steps, complexity of parts, and customization. Among of them, the application of human bone has been most widely studied. However, the bone is a porous structure, subjected to wide variations as a result of human movement and inevitable changes with age, sex, and location. Therefore, it is important to study the relationship between the porous structure and mechanical properties of various bionic implants.

In this study, we used the selective laser melting (SLM) and electron beam melting (EBM) methods to produce porous structures of bone bio-implants. The highly biocompatible Ti-6Al-4V alloy was applied as experimental.

For the first part, using Ti-6Al-4V alloy powders, the Ti-6Al-4V porous samples were fabricated by SLM, with the help from computer-aided design (CAD) for different porosities. Compared with the CAD models and porous samples fabricated by SLM, the relevant relationships are characterized with morphology, physical properties and mechanical properties. The difference between the CAD model and porous SLM parts leads to the larger ligament widths and smaller pore sizes for SLM parts, due to the laser beam broadening and laser melting edge effects. Due to the higher porosity samples with a higher pore number density, this difference between the CAD model and porous SLM parts could be more obvious, so that the designed porosity will be greater than that of the actual porosity of porous samples. The difference can be reduced by decreasing the size of laser beam and the used powders. The structure of Ti-6Al-4V prepared by SLM was seen to possess higher hardness favorable for wear resistance and beneficial for the application of human bone implant. The mechanical properties (elastic modulus and yield strength) of porous SLM parts decrease with increasing porosity, matching well with the human bone. In terms of the matched elastic modulus, it can avoid the risk of stress shielding effect. By applying the Gibson and Ashby model, the relationship between porosity and mechanical properties of SLM porous foams can be described and predicted.

According to many previous studies, the porous samples with high porosity can effectively reduce the stress shielding problem, but mechanical strength would also be reduced. For the second part, the high porosity of porous Ti-6Al-4V samples are fabricated by EBM, and the physical and mechanical properties are characterized. The results indicate that the porosity of porous parts can be as high as near 80% by increasing the ligament and pore size. The elastic modulus of such EBM porous Ti-6Al-4V structure with high porosity is found to match well with that of the human cancellous bone. However, it can obviously be seen that the higher ligament width of porous samples will enhance the endurance to fracture. Therefore, the relationship between the ligament width and work of fracture is systematically studied. According to the relation, it is concluded that when the ligament width is smaller than 401 μm, the porous structure cannot bear any strength for fracture. However, because the AM is basically a powder metallurgy technique, the porous samples would be inherent with rough surface, prone to cause stress concentration and premature fracture. Therefore, the relationship between the ratio of the ligament width and surface roughness corresponding to the fracture energy is derived in this study. From this relation, the fracture energy of porous samples with the larger ligament width will be less affected by the surface roughness. For an average ligament width of about 650 μm, the maximum acceptable surface roughness cannot be greater than 91 μm; otherwise, the porous sample can barely withstand the energy to fracture.

The experimental results are imported into the physical formulae and the relationships between the mechanical properties corresponding to the porous structure prepared by SLM and EBM are deduced. It is expected that these relationships can be used to prepare bionic implants using those processes to estimate its mechanical properties before the implants can be applied, effectively increase the value of their practical application.

論文審定書 i
誌謝 ii
中文摘要 v
Abstract vii
Content x
List of tables xv
List of figures xviii
Chapter 1 Introduction 1
1.1 Additive manufacturing 1
1.2 Porous materials 2
1.3 Motivation 3
Chapter 2 Background and literature review 5
2.1 Introduction of additive manufacturing technology 5
2.2 Classification the AM process 5
2.2.1 Liquid polymer systems 5
2.2.1.1 Stereolithography (SL) 6
2.2.1.2 Solid ground curing (SGC) 6
2.2.2 Molten material systems 7
2.2.2.1 Fused deposition modeling (FDM) 7
2.2.2.2 Shape deposition manufacturing (SDM) 8
2.2.3 Solid sheet systems 8
2.2.3.1 Laminated object manufacturing (LOM) 8
2.2.3.2 Solid foil polymerization (SFP) 9
2.2.4 Discrete particles systems 9
2.2.4.1 Selective laser sintering (SLS) 9
2.2.4.2 Selective laser melting (SLM) 10
2.2.4.2 Electron beam melting (EBM) 11
2.3 Characteristics and formation of AM metal powders 12
2.4 Metal and its alloys for biomedical materials 13
2.5 Mechanical properties of biomedical materials 14
2.5.1 Stress shielding effect 14
2.5.2 Wear resistance 16
2.5.3 Fracture toughness 16
2.6 Introduction of titanium (Ti) and alloys 20
2.6.1 Alpha (α) stabilizers and α-type Ti-based alloys 21
2.6.2 Beta (β) stabilizers and β-type Ti-based alloys 22
2.6.3 α+β Ti-based alloys 23
2.7 Porous titanium and its alloys 24
2.8 Fabrication methods for porous Ti-based alloys 25
2.8.1 Loose sintering of powder 26
2.8.2 Space holder method 27
2.8.3 Spark plasma sintering 28
2.8.4 Multilayer porous titanium 30
2.8.5 Additive manufacturing 30
2.9 Mechanical properties for porous Ti-based alloys fabricated by AM 31
Chapter 3 Experimental procedures 35
3.1 Raw material of Ti-6Al-4V powders 35
3.2 CAD design on porous structure 36
3.3 Porous Ti-6Al-4V alloys fabricated by SLM of AM 37
3.4 Porous Ti-6Al-4V alloys fabricated by EBM of AM 38
3.5 Property measurements and analyses 39
3.5.1 X-ray diffraction 39
3.5.2 Porosity measurement 39
3.5.3 Scanning electron microscopy 40
3.5.4 Microhardness testing 40
3.5.5 Compression testing 41
3.5.6 Micro computed tomography 41
Chapter 4 Results and Discussion 43
4.1 As-received Ti-6Al-4V powders 43
4.1.1 X-ray diffraction analysis 43
4.1.2 SEM/EDS analysis 43
4.2 Porous foams fabricated by SLM 44
4.2.1 Porosity analysis 45
4.2.2 X-ray diffraction 46
4.2.3 SEM/EDS analysis 47
4.2.4 Comparison between CAD models and porous foams 48
4.2.5 Compression testing and micro-CT analysis 50
4.2.6 Microhardness analysis 55
4.3 Porous foams fabricated by EBM 56
4.3.1 Porosity analysis 56
4.3.2 X-ray diffraction analysis 57
4.3.3 SEM/EDS analysis 58
4.3.4 Compression testing and micro-CT analysis 59
4.3.5 Microhardness analysis 64
4.4 Comparison between SLM porous foams and EBM porous foams 65
Chapter 5 Summary and Conclusions 69
Chapter 6 Suggestions for Future Research 72
References 73
Tables 88
Figures 111

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