材料科学基础第七章.doc

第七章 力学性质一、学习目的对于工程师来说，了解不同的材料力学性质如何被测量以及这些性质所代表的内容，是他们的职责所在。他们可能会被要求应用预先规定的材料进行结构或者组分设计，从而使得这些材料不会发生可承受之外的变形或者断裂。二、本章的主要内容1 定义工程应力与工程应变。2 陈述Hooke定律，并且指出保证定律有效所遵循的条件。3 定义泊松比。4 已知工程应力应变曲线图，确定（a）弹性模量；(b)屈服强度（残余应变0.002时）；（c）拉伸强度；（d）估算延伸百分比。5 对于一个延性柱体样品的拉伸形变，描述样品直至断裂的剖面的变化过程。6 对于一个承受张力并直至断裂的材料，根据其延展百分比与面积还原率来计算材料的延展度。7 根据三点负荷法，计算陶瓷棒弯曲至断裂的弯曲强度。8 描绘出聚合物材料中所观察到的三种典型应力应变特性的示意图。9 给出两种最常见的硬度测量技术，并指出二者的不同。10(a)指出并简要描述两种不同的显微硬度测量技术；（b）列举这些技术一般被应用的情况。11计算延展性材料的工作应力。三、重要术语和概念Anelasticity: 滞弹性In most engineering materials, elastic deformation will continue after the stress application, and upon load release some finite time is required for complete recovery. This time-dependent elastic behavior is known as anelasticity.应力施加后，大多数工程材料弹性形变都会持续，并且撤去加载，样品的完全回复也需要一定的时间。这种与时间相关的弹性行为称为滞弹性。Design stress: 设计应力For static situations and when ductile materials are used, design stress, d, is taken as the calculated stress level c (on the basis of the estimated maximum load) multiplied by a design factor, N, that is d= Nc, where N is greater than unity.对于静态条件以及延展性材料的情况下，设计应力d是计算的应力c（即估算的最大载荷）乘以一个设计因子N，即d= Nc，其中N大于1。Ductility: 延伸度Ductility is a measure of the degree of plastic deformation that has been sustained at fracture. 延伸度是指材料在断裂时发生的塑性形变程度的量度。Elastic deformation: 弹性形变Deformation in which stress and strain are proportional is called elastic deformation. Elastic deformation is nonpermanent, which means that when the applied load is released, the piece returns to its original shape.应力与应变成正比关系的形变称为弹性形变。弹性形变是非永久性的，即撤去加载后，样品可恢复初始的形状。Elastic recovery：弹性回复Elastic recovery means that when the applied load is released, the piece returns to its original shape.弹性回复是指当样品所受应力撤销后，其完全回复到初始形状的现象。Elastomer: 弹性体Elastomer is a class of polymers whose deformation displayed by strain-stress curve is totally elastic, i.e., large recoverable strains produced at low stress levels. 弹性体是聚合物的一个种类，它的应力应变曲线表明其变形是完全弹性的，即很低的应力变化就会产生很大的可回复应变。Engineering strain: 工程应变Engineering strain is defined according to = (li-l0)/l0 = l/l0, in which l0 is the original length before any load is applied, and li is the instantaneous length. Sometimes the quantity li-l0 is denoted as l, and is the deformation elongation or change in length at some instant, as referenced to the original length. Engineering strain is unitless.工程应变由方程 = (li-l0)/l0 = l/l0定义，这里l0是样品加载前的初始长度，li是加载瞬间的长度，有时li-l0也用l来表示，即代表与初始长度相比较，某一时刻样品形变的延长率或长度的变化。工程应变是没有单位的。Engineering stress: 工程应力Engineering stress is defined by the relationship = F/A0, in which F is the instantaneous load applied perpendicular to the specimen cross section, in units of newtons (N), and A0 is the original cross-sectional area before any load is applied (m2). The units of engineering stress are megapascals, MPa.工程应力的定义为 = F/A0，这里F是加载在垂直样品横截面的瞬间载荷，单位为牛顿，A0是加载前样品的初始横截面积（单位m2），工程应力单位为MPa。Flexural strength: 抗弯强度For the brittle ceramic materials, flexural strengths are determined by the stress at fracture in transverse bending tests.对脆性陶瓷材料来说，抗弯强度即为横向弯曲试验中样品断裂时的应力。Hardness: 硬度Hardness is a measure of the resistance to localize plastic deformation.硬度是材料抵抗局部塑性形变的量度。Modulus of elasticity: 弹性模量For most metals that are stressed in tension and at relatively low levels, stress and strain are proportional to each other through the relationship = E. This is known as Hookes law, and the constant of proportionality E (GPa) is the modulus of elasticity, or Youngs modulus.大多数金属在较低的拉力作用下，应力和应变成正比关系，可表达为 = E，这就是胡克定理，比例常数E（GPa）就是弹性模量，或杨氏模量。Plastic deformation: 塑性形变As the material is deformed beyond the strain that elastic deformation persists, the stress is no longer proportional to strain, and permanent, nonrecoverable, or plastic deformation occurs. 当材料的形变超出弹性形变发生的范围，其应力将不再与应变成正比，永久的、不可回复的形变发生，即为塑性形变。Poissons ratio: 泊松比Poissons ratio represents the negative ratio of transverse and longitudinal strains.泊松比的定义为样品横向应变与轴向应变的相反数。Proportional limit: 比例极限For metals that experience the gradual elastic-plastic transition, the point of yielding is determined as the initial departure from linearity of the stress-strain curve and this is sometimes called the proportional limit.对于金属逐步的弹塑性形变转变，其屈服点确定为应力应变曲线非线性关系的开始，这个点也被称为比例极限。Resilience: 弹性Resilience is the capacity of a material to absorb energy during elastic deformation.弹性是指材料在弹性形变中吸收能量的能力。Safe stress: 安全应力Safe stress is based on the yielding strength of the material and is defined as the yield strength divided by a factor of safety, N, or w=y/N.安全应力是基于材料的屈服强度，它定义为屈服强度除以一个安全因子N，或w=y/N。Tensile strength: 抗拉强度Tensile strength corresponds to the maximum tensile stress that may be sustained by a specimen. 抗拉强度是指样品可能承受的最大拉伸应力。Toughness: 韧性Toughness is a measure of the ability of a material to absorb energy up to fracture.韧性是指材料在断裂前所能吸收能量的量度True strain: 真应变True stain T is defined by T=ln(li/l0), in which l0 is the original length before any load is applied, and li is the instantaneous length.真应变T的定义为T=ln(li/l0)，其中l0是样品加载前的初始长度，li是瞬间长度。True stress: 真应力True stress T is defined as the load F divided by the instantaneous cross-sectional area Ai over which deformation is occurring, or T = F/Ai.真应力T定义为形变发生时，载荷F与瞬间横截面积Ai的比值，或者T = F/Ai。Yielding: 屈服For metals, the phenomenon of yielding occurs at the onset of plastic or permanent deformation.金属的屈服是指塑性或者永久形变开始发生的现象。Yield strength: 屈服强度Yielding strength is indicative of the stress at which plastic deformation begins.屈服强度是指塑性形变开始发生时的应力。四、主要例题、习题的分析例7.1 一个铜板最初长度为305 nm，受到276 MPa的应力的拉伸，假如发生的形变是完全弹性的，则伸长量最终为多少？解：因为形变是弹性的，根据公式7.5，应变与应力有关，更进一步说，通过公式7.2=(li-l0)/l0=l/l0，伸长值l与初始长度l0有关。结合这两个表达式，可以解得l有：和l0的值分别为276MPa和305mm，由表7.1可知铜的杨氏模量E为110GPa，将以上值代入表达式可得到伸长值为例7.2 在一个直径为10mm的圆柱型黄铜棒的长轴方向施加一个拉应力，假设所产生的形变为完全弹性，那么使得直径产生2.510-3mm的改变所需要的载荷为多少。解：当作用力F被施加到样品上时，样品在Z方向将被拉长，同时直径在x方向上将减少d=2.510-3mm。在x方向的应变为：这个值为负，因为直径是减小的。随后应用公式7.8计算Z方向的应变。黄铜的泊松比为0.34，因此应用公式7.5和弹性模量可以计算施加的应力，弹性模量如表7.1为97 GPa，则：最后，由公式7.1可以确定所施加的力为：例7.3 由图7.12所给出的黄铜样品的拉伸应力应变行为，确定：(a)弹性模量；(b)残余应变为0.002时的屈服强度；(c)初始直径为12.8mm的圆柱型样品所能承受的最大载荷；(d)若样品的初始长度为250mm，则承载拉伸应力345GPa时其长度的变化。解：(a)弹性模量是指应力应变曲线的弹性或初始线性部分的斜率。为了便于计算，图7.12插图中的应变轴被拉伸。此线性部分的斜率是其宽度除以其高度，或者是其应力的变化除以相应的应变的变化，其数学表达式为：因为线性部分通过原点，则1和1为零。如果我们选取2为150MPa，那么2的值为0.0016。因此：此值很接近表7.1中所给的黄铜的弹性模量值。(b)0.002残余应变线已经由插图给出，它与应力应变曲线的交