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mechanical_property_of_materials.pdf

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MECHANICAL_PROPERTY_OF_MATERIALS
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Mechanical Properties of Materials Stress ( 应力) and Strain ( 应变): If a load applied to the material is static or changing slowly with time and it is applied uniformly on the surface of interest, then we can test the behavior of the material under applied load by a test called “stress-strain” test. The ways of applying load are summarized in the figure below: The “true” stress ( ?) is defined as: ?=F/A, where F=force applied to the sample at any given instant and A = current cross-sectional area ( 断面面积 )of the sample. The “ture” stain (ε) is defined as: ε = ln (l 1 /l 0 ), where l 1is the current gauge length ( 标距长度、量计长度) and l 0 the original gauge length of the sample. True stress ( 真应力) and true strain ( 真应变) provide the most accurate description of what actually happens to the material during testing and so are widely used in materials science. For engineering design, however, there are two problems. Firstly, true stress requires knowledge of the value of A throughout the test, whereas in real world applications the designer of structures chooses an initial cross sectional area (A 0 ). Secondly true strain is not very easy to visualize ( 形象化). ? Consequently for engineering applications an “engineering” stress (s) ( 工程应力) and strain (e) are used in place of true stress and true strain: s = F/A 0and e = (l 1 -l 0 )/l 0, , in which F is the instantaneous load applied perpendicular to the specimen cross-section, in units of newtons (N), and A 0is the original cross-sectional area before any load is applied. the different between true stress and engineering stress: Engineering stress assumes that the area a force is acting upon remains constant, true stress takes into account the variation in the cross sectional area as a result of the stress induced deformation (strain) of a material. ? Stress has a unit ( 物理单位) of Pa (i.e. N/m 2 ) and strain is dimensionless ( 无量纲的). The concept of a stress is clearly closely related to that of pressure. Using the definitions of stress and strain given above, the load versus elongation curve produced by the tensile test can be converted into true stress-strain or engineering stress-stain curves. Using these curves, it is now possible to describe the mechanical properties of metals and alloys. (a) tensile ( 拉力,张力) test: a sample is gradually elongated to failure ( 失效) and the tensile force required to elongate the sample is measured using a load cell ( 载 荷传感器 )throughout the test. The result is a plot of tensile force versus elongation ( 延伸率). (b) Compressive load produces contraction and a negative ( 负的) linear strain. (c) Shear ( 剪切的) strain (d) Torsional ( 扭转的,扭力的) deformation ( 变形,形变, 畸变 ) Tension test ( 拉伸试验) is the most common. A typical specimen is: Typically L=4 x d (diameter) L=2 in (50 mm) Test continues usually till the specimen is permanantly deformed or fractured. apparatus ( 器具、仪器) crosshead ( 十字压头) load cell (载荷传感器) extensometer ( 伸长计) Elastic Deformation ( 弹性变形): is observed when stress and strain are proportional ( 成比例的). Hooke’s Law: E= modulus of elasticity ( 弹性模量) or Young’s modulus (GPa or psi) for metals E=45 (for magnesium, 镁) - 407GPa (for tungsten, 钨 ). For ceramic materials E= 70-500GPa for polymers E=0.007-4 GPa E is a measure of material’s stiffness ( 刚度) or materials resistance to elastic deformation. The greater the modulus, the stiffer the material or the smaller the elastic strain that results from the application of a given stress. Thus, for Example, in selecting a material for the springs ( 弹簧)of a vehicle, stiffness would be a key engineering design criterion. ? Elastic deformation is nonpermanent, which means that when the applied load is released, the piece returns to its original shape. As shown in the stress-strain plot, application of the load corresponds to moving from the original up and along the straight line. Upon release of the load, the line is traversed in the opposite direction, back to the origin. There are some materials (e.g. gray cast iron, concrete, and many polymers) for which this initial elastic portion of the stress-strain curve is not linear; hence, it is not possible to determine a modulus of elasticity as described above. For this nonlinear behavior, either tangent ( 正切的、切线的) or secant modulus ( 割线模量) is normally used. Tangent modulus is taken as the slope of the stress-strain curve at some specified level of stress, while secant modulus represents the slope of a secant drawn from the origin to some given point of the stress-strain curve. ? On exceeding a certain stress, known as the “yield stress” or “yield strength” ( ? yor s yin ture and engineering stress respectively), the stress-strain curve ceases to be linear and the material begins to undergo permanent “plastic” deformation. In the plastic region of the stress-strain curve, it is apparent that the stress required to continue plastic deformation is higher than that required to make the material yield. This phenomenon is called “working hardening” ( 加工硬 化) or “strain hardening”( 形变硬化). ? In the true stress-strain curve, it can be seen that work hardening actually continue right up until failure at the failure stress. In contrast the engineering stress-strain curve shows a maximum stress, the “ultimate tensile stress” (UTS) ( 最大抗张 应力), prior to final failure. During final failure, the sample starts to “neck” down to failure and this not account for when A 0 , rather than A, is used to calculate a stress. Nonetheless, for a design engineer, the UTS is a very useful datum and the UTS is normally used as the measure of the “tensile strength” of a material. Mechanical Behavior of Materials Metals: Elastic deformation (弹性变形)of metallic materials is usually upto strains of about 0.005. Beyond this point, the stress and strain are no longer proportional and deformation of the material becomes permanent and nonrecoverable. This is called plastic deformation (塑性变形). From an atomic perspective, plastic deformation corresponds to the breaking of bonds with original atom neighbors and reforming bonds with new neighbors. This permanent deformation for metals is accomplished by means of a process called slip (滑移), which involves the motion of dislocations (位错). 13 F ? bonds stretch return to initial 1. Initial 2. Small load 3. Unload Elastic means reversible. Elastic Deformation 14 1. Initial 2. Small load 3. Unload Plastic means permanent. F ? linear elastic linear elastic ? plastic Plastic Deformation (Metals) Tensile properties of Metals: 1) Yielding and yield strength (屈服强度) Most structures are designed to ensure that only elastic deformation will result when a stress is applied. Therefore it is useful to know the stress level at which plastic deformation begins or where the yielding occurs. Yielding and yield strength 1. Yielding (屈服): the phenomenon that plastic deformation begins. 2. Proportional limit ( 比例极限): the point of the initial departure from linearity of the stress-strain curve. 3. Yield strength: the stress corresponding to the intersection of the line, which parallels to the elastic portion of the stress-strain curve at some specified strain offset ( 应变截距), usually 0.002. Three concepts: If the transition from elastic to plastic behavior is gradual, the point of yielding may be determined as the initial departure from linearity (P=proportional limit). In cases where it is difficult to determine this point (P point) precisely, a conventional approach is used. A straight line is constructed parallel to the elastic deformation line at a strain offset ( 应变截 距) usually 0.002. The stress correspoding to this point is yield strength ( ? y ). For the materials having nonlinear elastic region, yield strength is defined as the stress required to produce some amount of strain ( ?=0.005). For the materials showing a behavior like in Figure b, the yield strength is the average of the upper and lower limits. The magnitude of yield strength is a measure of material’s resistance to plastic deformation. Yield strength may range from 35 MPa for a low-strength aluminum ( 铝) to 1400 MPa for high-strength steels. Tensile strength ( 拉 伸 强度) ? The strength at the maximum on the engineering stress-strain curve. ? correspond to the maximum stress that can be sustained by a structure in tension; if this stress is applied and maintained, fracture will result. ? All deformation up to this point is uniform throughout the narrow region of the tensile specimen. Concept: ? After yield, the stress necessary to continue plastic deformation in metals increases to a maximum, and then decreases to the eventual fracture. The tensile strength TS (MPa) is the stress at the maximum on the engineering stress-strain curve. This corresponds to the maximum stress that can be sustained by a structure in tension; if this stress is applied and maintained, fracture will result. ? All deformation up to this point is uniform throughout the narrow region of the tensile sample. However, at the maximum stress, a small constriction or neck begins to form at some point, and all subsequent deformation is confined at this neck. This phenomenon is termed “necking”, and fracture ultimately occurs at the neck. The fracture strength corresponds to the stress at fracture. 2) Tensile strength : M is the stress at the maximum point of the stress-strain curve. F is the fracture point. necking Tensile strength may vary from 50 MPa for an aluminum to as high as 3000 MPa for the high-strength steels. For applications, the yield strength is usually a more important property than the tensile strength. This is because by the time a stress corresponding to the tensile strength has been applied, often a structure has Experienced so much plastic deformation that it is useless. 3) Ductility (延展性): It is a measure of the degree of plastic deformation that has been sustained at fracture. A material that experiences very little or no plastic deformation upon fracture is termed brittle (脆性). Ductility may be expressed quantitatively as either percent elongation( 延 伸率 ) or percent reduction in area ( 断面收缩率 ). l fand A fare length and area at the fracture. ? “Ductile” materials are those that can undergo plastic deformation and so the greater the extent of plastic deformation, the higher the “ductility”. The engineering strain to failure is a common measure of ductility. Note that if l 1is measured after the sample has failed, then the elastic portion of the sample’s elongation will be removed, since the applied load is removed when the sample fails. Thus only plastic and not elastic deformation will contribute to an l 1measured after failure. ? A knowledge of the ductility of materials is important for at least two reasons. First, it indicates to a designer the degree to which a structure will deform plastically before fracture. Second, it specifies the degree of allowable deformation during fabrication operations. The mechanical properties of the materials are sensitive to any prior deformation, presence of impurities ( 杂质),heat treatment to which the materials have been subjected. The modulus of elasticity is one mechanical parameter that is insensitive to these treatments. The magnitudes of both yield and tensile strengths decline with increasing temperature; just the reverse holds for ductility --- it usually increases with temperature. Stress-Strain Diagram Strain ( ) (e/Lo) 4 1 2 3 5 Elastic Region Plastic Region Strain Hardening Fracture ultimate tensile strength Elastic region slope=Young’s(elastic) modulus yield strength Plastic region ultimate tensile strength strain hardening fracture necking yield strength UTS ? y ? E ? E ? ? 1 2 y E ? ? Stress-Strain Curve (cont) ? Elastic Region (Point 1 –2) - The material will return to its original shape after the material is unloaded( like a rubber band). - The stress is linearly proportional to the strain in this region. E ?: Stress(psi) E : Elastic modulus (Young’s Modulus) (psi) : Strain (in/in) - Point 2 : Yield Strength : a point where permanent deformation occurs. ( If it is passed, the material will no longer return to its original length.) E ? or ? Tensile Strength (Point 3) - The largest value of stress on the diagram is called Tensile Strength(TS) or Ultimate Tensile Strength (UTS) - It is the maximum stress which the material can support without breaking. ? Fracture (Point 5) - If the material is stretched beyond Point 3, the stress decreases as necking and non-uniform deformation occur. - Fracture will finally occur at Point 5. Stress-Strain Curve (cont) 28 Room T values a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered Yield Strength: Comparison 29 Room T values Based on data in Table B4, Callister 6e. a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered AFRE, GFRE, & CFRE = aramid, glass, & carbon fiber-reinforced epoxy composites, with 60 vol% fibers. Tensile Strength: Comparison 30 0.2 8 0.6 1 Magnesium, Aluminum Platinum Silver, Gold Tantalum Zinc, Ti Steel, Ni Molybdenum Graphite Si crystal Glass-soda Concrete Si nitride Al oxide PC Wood( grain) AFRE( fibers)* CFRE* GFRE* Glass fibers only Carbon fibers only Aramid fibers only Epoxy only 0.4 0.8 2 4 6 10 20 40 60 80 100 200 600 800 1000 1200 400 Tin Cu alloys TungstenSi carbide Diamond PTFE HDPE LDPE PP Polyester PS PET CFRE( fibers)* GFRE( fibers)* GFRE(|| fibers)* AFRE(|| fibers)* CFRE(|| fibers)* Metals Alloys Graphite Ceramics Semicond Polymers Composites /fibers E(GPa) 10 9Pa Composite data based on reinforced epoxy with 60 vol% of aligned carbon (CFRE), aramid (AFRE), or glass (GFRE) fibers. Young’s Moduli: Comparison Toughness is a mechanical term( 术语). Loosely speaking, It is a measure of the ability of a material to absorb energy up to fracture. Specimen geometry( 几何形状) as well as the manner of load application are important in toughness determinations. ? For dynamic (high strain rate) loading conditions and when a notch is present, notch toughness ( 缺口韧性) is assessed by using an impact ( 冲击) test. ? For the static situation, toughness may be ascertained from the results of a tensile stress-strain test. ? It is the area under the strain-stress curve up to the point of fracture. Toughness (韧性) 32 Toughness Lower toughness: ceramics Higher toughness: metals Toughness is the ability to absorb energy up to fracture (energy per unit volume of material). For a material to be tough, it must display both strength and ductility. Approximated by the area under the stress-strain curve. smaller toughn
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