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1、断裂力学断裂力学 第一讲第一讲 导论：导论： 什么是断裂力学？什么是断裂力学？ 断裂力学研究什么？断裂力学研究什么？ 断裂力学和材料力学有什么联系和区别？断裂力学和材料力学有什么联系和区别？ 从强度理论到断裂理论从强度理论到断裂理论 断裂力学和破坏力学（断裂力学和破坏力学（failure )之间的关系之间的关系 断裂力学 从材料力学、弹性力学发展起来 固体力学中最活跃的研究领域 实用性：大量的工程应用要求研究材料破坏； 跨学科：力学、材料、物理、环境、分析计算方 法、测试技术； 科学、工程结合 形形色色的断裂现象 疲劳断裂疲劳断裂 脆性断裂脆性断裂 断裂的扳手断裂的扳手 韧性试件的断裂 Lib
2、erty Ships in WWII Facts on Liberty Ships There were 2,751 Liberty Ships manufactured between 1941-1945. Cracks propagated in 400 of these ships including 145 catastrophic failures; only 2 exist today which are sea-worthy. The hulls of Liberty Ships fractured without warning, mainly in the North Atl
3、antic. These are the first ships mass produced with welds. The low temperatures of the North Atlantic caused the steel to be brittle. Fractures occurred mainly in the vicinity of stress raisers. The problem may be prevented by employing higher quality steels and improvement of the design of the ship
4、. The Aloha Boeing 737 Accident On April 28, 1988, part of the fuselage of a Boeing 737 failed after 19 years of service. The failure was caused by fatigue (multi-site damage). The Aloha Boeing 737 Accident 一个不断发展的学科：一个不断发展的学科： 强度问题、裂纹问题、断裂问 题、疲劳、损伤、分析和规范、 结构完整性问题 ，等等 损伤分布 与裂纹共生的结构 工程问题: 结构承载能力 (Str
5、uctural safety and integrity). 结构承载时间 (Durability). 结构可信度 (Reliability). 安全性评估 (Confidence level). 经济问题: 建造成本和获取手段 (capital or acquisition cost); 运行代价 (operational cost)，废弃代价 (disposal/recycling cost) 成本优化和使用寿命优化 (Optimize capital costs and life cycle cost) 结构完整性和寿命评估系统 从强度理论到裂纹力学从强度理论到裂纹力学 应力状态和主应力
6、参数应力状态和主应力参数 强度函数强度函数 常用的强度准则 最大主应力准则； 最大剪切应力准则； 最大主应变准则； 最大总应变能准则； 最大畸变应变能准则； 最大Von Mises应力准则； Etc. 孔洞导致应力集中 - Inglis理论 Fracture stress for realistic material Inglis (1913) analyzed for the flat plate with an elliptical hole with major axis 2a and minor axis 2b, subjected to far end stress The stre
7、ss at the tip of the major axis (point A) is given by The ratio is defined as the stress concentration factor, When a = b, it is a circular hole, then When b is very very small, Inglis define radius of curvature as And the tip stress as m 2a 1 b m t k t k3. 2 b a m a 12 Inglis理论推广到裂纹 玻璃纤维的断裂强度（示意图）
8、Griffith关于裂纹扩展的概念关于裂纹扩展的概念 Griffiths Energy balance approach First documented paper on fracture (1920) Considered as father of Fracture Mechanics A A Griffith laid the foundations of modern fracture mechanics by designing a criterion for fast fracture. He assumed that pre- existing flaws propagate u
9、nder the influence of an applied stress only if the total energy of the system is thereby reduced. Thus, Griffiths theory is not concerned with crack tip processes or the micromechanisms by which a crack advances. Griffiths Energy balance approach (Contd.) Griffith proposed that There is a simple en
10、ergy balance consisting of the decrease in potential energy with in the stressed body due to crack extension and this decrease is balanced by increase in surface energy due to increased crack surface Griffith theory establishes theoretical strength of brittle material and relationship between fractu
11、re strength and flaw size a f Griffiths Energy balance approach (Contd.) The initial strain energy for the uncracked plate per thickness is (2.14) On creating a crack of size 2a, the tensile force on an element ds on elliptic hole is relaxed from to zero. The elastic strain energy released per unit
12、width due to introduction of a crack of length 2a is given by (2.15) 2 i A UdA 2E a 1 a2 0 U4dx v dx where displacement va sin E using xa cos 22 a a U E Griffiths Energy balance approach (Contd.) External work = (2.16) The potential or internal energy of the body is Due to creation of new surface in
13、crease in surface energy is (2.17) The total elastic energy of the cracked plate is (2.18) w UFdy, where F= resultant force = area =total relative displacement piaw U =U +U -U s U = 4a 222 ts A a UdAFdy4a 2EE Griffiths Energy balance approach (Contd.) The variation of with crack extension should be
14、minimum Denoting as during fracture (2.19) for plane stress (2.20) for plane strain t U 2 t s dU2a 040 daE f 1/2 s f 2E a 1/2 s f 2 2E a(1) The Griffith theory is obeyed by materials which fail in a completely brittle elastic manner, e.g. glass, mica, diamond and refractory metals. Griffiths Energy
15、balance approach (Contd.) Griffith extrapolated surface tension values of soda lime glass from high temperature to obtain the value at room temperature as Using value of E = 62GPa,The value of as 0.15 From the experimental study on spherical vessels he calculated as 0.25 0.28 However, it is importan
16、t to note that according to the Griffith theory, it is impossible to initiate brittle fracture unless pre- existing defects are present, so that fracture is always considered to be propagation- (rather than nucleation-) controlled; this is a serious short-coming of the theory. 2 s 0.54J/m . 1/2 s 2E
17、 MPa m. 1/2 s c 2E a MPa m. Modification for Ductile Materials For more ductile materials (e.g. metals and plastics) it is found that the functional form of the Griffith relationship is still obeyed, i.e. . However, the proportionality constant can be used to evaluate s (provided E is known) and if
18、this is done, one finds the value is many orders of magnitude higher than what is known to be the true value of the surface energy (which can be determined by other means). For these materials plastic deformation accompanies crack propagation even though fracture is macroscopically brittle; The rele
19、ased strain energy is then largely dissipated by producing localized plastic flow at the crack tip. Irwin and Orowan modified the Griffith theory and came out with an expression Where prepresents energy expended in plastic work. Typically for cleavage in metallic materials p=104 J/m2 and s=1 J/m2. S
20、ince p s we have 1/2 sp f 2E() a 1/2 p f 2E a 1/2 f a Strain Energy Release Rate The strain energy release rate usually referred to Note that the strain energy release rate is respect to crack length and most definitely not time. Fracture occurs when reaches a critical value which is denoted . At fracture we have so that One disadvantage of using is that in order to determi
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