CHAPTER 2 Mechanical Behavior, Testing, and Manufacturing Properties of Materials 材料的機械行為、測試及製造特性

Working Medium of Manufacturing Process Force Heat Light Acoustics(聲音、音響) Electricity Chemistry Biology

室溫時材料之相對機械性質(Relative Mechanical Properties of Materials at Room Temperature)

Tensile-Test Specimen and Machine (b) Figure 2.1 (a) A standard tensile-test specimen before and after pulling, showing original and final gage lengths. (b) A typical tensile-testing machine.

應力應變曲線（Stress-Strain Curve） P-δ；σ-ε 彈性區經過放大 斜率=E 比例限、彈性限、降伏強度 Offset=0.2% 反覆循環負荷之曲線形狀 曲線下面積＝材料韌性 necking E Figure 2.2 A typical stress- strain curve obtained from a tension test, showing various features.

Tension Test P A0 l0 l A Necking (Fig. 2.2) Spring back (Fig. 2.3) Eng. stress True. stress Eng. strain True strain l l0 A A0 P Necking (Fig. 2.2) Spring back (Fig. 2.3) Engineering strain= True strain= Engineering stress= True stress=

Loading and Unloading of Tensile-Test Specimen Figure 2.3 Schematic illustration of the loading and the unloading of a tensile- test specimen. Note that, during unloading, the curve follows a path parallel to the original elastic slope.

Mechanical Properties of Various Materials at Room Temperature

利於進行製造的材料 : B Exmple A B B材質塑性區大，降伏強度低，較易進入加工區域。 (然而A較易滿足設計需求，強度大) True stress True strain B

Ch 2.2.2 Ductility 延性 Elongation = （伸長量） Reduction of area = （面積縮率、斷面縮率）

Elongation versus % Area Reduction Figure 2.4 Approximate relationship between elongation and tensile reduction of area for various groups of metals.

n : strain-hardening exponent Ch 2.2.4 應力-應變曲線之建立 Stress-strain curves True stress n : strain-hardening exponent (n=0，表示沒有加工硬化現象) True strain

Typical Values for K and n at Room Temperature

各種不同金屬在常溫下的True Stress-True Strain Curves Figure 2.6 True stress-true strain curves in tension at room temperature for various metals. The curves start at a finite level of stress: The elastic regions have too steep a slope to be shown in this figure, and so each curve starts at the yield stress, Y, of the material.

Prove ε= n at necking Ch 2.2.5 ? e = At necking: Necking UTS

2.2.6 溫度效應 Temperature Effects on Stress-Strain Curves Figure 2.7 Typical effects of temperature on stress-strain curves. Note that temperature affects the modulus of elasticity, the yield stress, the ultimate tensile strength, and the toughness (area under the curve) of materials. T↑，則ductility↑， yield stress 和 modulus of elasticity↓ (因為T↑，原子動能↑，容易克服差排障礙，延展性佳)

2.2.7變形速率的影響 Effect of Strain Rate on Ultimate Tensile Strength 表2.3

2.2.7變形速率的影響 Effect of Strain Rate on Ultimate Tensile Strength Figure 2.8 The effect of strain rate on the ultimate tensile strength for aluminum. Note that, as the temperature increases, the slopes of the curves increase; thus, strength becomes more and more sensitive to strain rate as temperature increases. Source: J. H. Hollomon. strain rate ↑ tensile strength↑ （應變硬化） 直線斜率m：應變硬化敏感度指數，Temp ↑m ↑,m大可以延緩necking發生，應用在金屬薄板的成形。

2.2.7變形速率的影響 Effect of Strain Rate on Ultimate Tensile Strength 超塑性（superplasticity）:某些材料在拉伸試驗時，頸縮及破壞前，發生大量的均質伸長變形量，這種變形量從幾百個百分比到兩千個百分比之間。例如：口香糖、玻璃、熱塑性塑膠、Zn-Al合金及鈦合金。

2.2.8 靜液壓的影響 （Hydrostatic pressure effects ) 壓力：幾個ATM到3.5GPa(500KST)，液壓增加時，材料破壞時的應變量會大量增加（不容易破壞）。 脆性材料之金屬成形：液壓擠製、粉末冶金壓製。 當加工製造stress超過材料破裂點，可使用下列方法避免： 加溫 加液靜壓 (Hydrostatic Pressure Effect):脆性材料加工

2.2.9 輻射的影響（Radition effects ) 暴露在高能量輻射下：鋼料及其他種類金屬會發生降伏應力、抗拉強度及硬度會增加；延展性及韌性會減少。塑膠材料對其機械性質也有不好的影響。

2.3 壓縮 (Compression) 桶形失真（barreling）:摩擦力

2.3 壓縮 (Compression) Figure 2.9 Disk test on a brittle material( 陶瓷、玻璃 ), showing the direction of loading and the fracture path.

2.3 壓縮 (Compression) 蒲辛格效應（Bauschinger effect 1881）:金屬受拉力進入到塑性狀態，將負荷釋放再施以壓縮應力，此時，壓縮的降伏應力值比拉伸時低許多。 應變軟化（strain softening）、作工軟化（work softening ）:因負荷的方向轉換，使降伏應力值下降。

2.4 扭 轉 (Torsion) Disk and Torsion-Test Specimens Figure 2.10 Typical torsion-test specimen; it is mounted between the two heads of a testing machine and twisted. Note the shear deformation of an element in the reduced section of the specimen.

2.5 彎曲（撓曲）Bending （Flexure） Figure 2.11 Two bend-test methods for brittle materials: (a) three-point bending; (b) four-point bending. The areas on the beams represent the bending-moment diagrams, described in texts on mechanics of solids. Note the region of constant maximum bending moment in (b); by contrast, the maximum bending moment occurs only at the center of the specimen in (a). 硬脆材料通常都使用bending實驗量測材料性質 (因為tension實驗不易進行)

Ch 2.6 硬度（Hardness） Brinell (布氏硬度 1900):HB P對表面積的比值 設備便宜且方便，所以產業界常用 Brinell (布氏硬度 1900):HB P對表面積的比值 Rockwell (洛氏硬度 1922):HR 深度 Vickers (維氏硬度 1922)：HV 深度 Knoop (克氏硬度)：HK Load極小(5-25kg)， 做微硬度測試，可用於薄脆試件。 Scleroscope (蕭氏硬度)：反跳高度、大面積 Mohs (莫氏硬度 1822)：互相摩擦， 值1（滑 石）-10（鑽石）。 Durometer 硬度測試計 Hot hardness 熱硬度

Hardness Tests Figure 2.12 General characteristics of hardness-testing methods and formulas for calculating hardness. The quantity P is the load applied. Source: H. W. Hayden, et al., The Structure and Properties of Materials, Vol. III (John Wiley & Sons, 1965).

Brinell Testing Figure 2.13 Indentation geometry in Brinell testing; (a) annealed metal; (b) work-hardened metal; (c) deformation of mild steel under a spherical indenter. Note that the depth of the permanently deformed zone is about one order of magnitude larger than the depth of indentation. For a hardness test to be valid, this zone should be fully developed in the material. Source: M. C. Shaw and C. T. Yang. (c)

Hardness Conversion Chart Figure 2.14 Chart for converting various hardness scales. Note the limited range of most scales. Because of the many factors involved, these conversions are approximate. 硬度測試對照表 HRC機械工業常用(範圍對應鋼材) HRC55以上是很硬的鋼材

Ch 2.6.2 硬度和強度（Hardness and strength） Hardness is linearly proportional to Strength (UTS) UTS [MPa] = 3.5 (HB) Eq. ( 2.13) UTS [psi] = 500 (HB) Eq. ( 2.14)

2.7 疲勞（Fatigue） 疲勞破壞：工件在未達到靜態負荷時的降伏應力下，發生破裂。 金屬的疲勞限與其極限抗拉強度（UTS）有關，鋼料約為1/2，鋁則無（以107）。如下圖2.15

2.7 疲勞（Fatigue）S-N Curves

2.7 疲勞（Fatigue）S-N Curves Figure 2.15 Typical S-N curves for two metals. Note that, unlike steel, aluminum does not have an endurance limit.

Endurance Limit/Tensile Strength versus Tensile Strength Figure 2.16 Ratio of endurance limit to tensile strength for various metals, as a function of tensile strength. Because aluminum does not have an endurance limit, the correlation for aluminum are based on a specific number of cycles, as is seen in Fig. 2.15.

2.8 潛變（Creep） 潛變：機械零件在長時間承受一靜態負荷時所進行的永久變形，原因為晶界滑移（grain-boundary sliding）。例如：熱塑性塑膠及橡膠會在任何溫度下進行潛變。鉛會在室溫定力下潛變、老房子的玻璃。 鋁合金（200度C）、高熔點金屬（1500度C） 應力釋放（stress relaxation）：螺栓、卯釘、guy wires

2.8 潛變（Creep） 潛變曲線：分三階段

2.9 衝擊（ Impact ） Impact Test Specimens Figure 2.18 Impact test specimens: (a) Charpy; 簡支樑 (b) Izod. 懸臂樑

Ch 2.10 材料在製造過程及使用中的破壞與斷裂 破裂 破裂 破裂面 走向 Figure 2.19、2.20

Ch 2.10 材料在製造過程及使用中的破壞與斷裂

Ch 2.10 材料在製造過程及使用中的破壞與斷裂

2.10.1延性破壞（Ductile fracture) 圖2.21 2.22

2.10.1延性破壞（Ductile fracture) 杯錐狀斷裂（Cup-and-cone fracture）：空孔累積、生長合併。

2.10.1延性破壞（Ductile fracture) 雜質的影響

轉換溫度（ Transition Temperature ） Figure 2.24 Schematic illustration of transition temperature in metals. transition temperature 通常比室溫低許多，材料在低溫易發生破壞 (TITANIC!)

2.10.2 脆性破壞（Brittle fracture） 圖2.26

2.10.2 脆性破壞（Brittle fracture） 疲勞破壞 海灘標記（beach marks）

2.10.2 脆性破壞（Brittle fracture） 疲勞破壞 改善： 1.珠擊、滾桶磨光。 2.表面硬化。 3.降低表面溝槽、缺陷提高精度。 4.選擇適當材料，降低雜質、空孔及不純物。

疲勞破壞

2.11 殘留應力（Residual Stresses）

2.11 殘留應力（Residual Stresses） 殘留應力原因：加工、溫度梯度… 殘留拉應力→降低疲勞壽命、破壞強度 加工形成之殘留應力，一段時間後→應力破壞（stress cracking） 降低殘留應力：退火（annealing）、反向變形、室溫長時間放置（溫度上升可以縮短時間）

Ch 2.12 功、熱及溫度上升 Ch 2.12 製程中所受的限制 heat work 溫度(須避免熱漲冷縮造成尺寸形狀失準) 應變(須避免破裂產生) work heat Stored energy (5~30%)

Ch 2.12 Example: P 100 mm given: find: solution:

P 100 mm