第講 斷裂力學導論

1、第講 斷裂力學導論斷裂力學從材料力學、彈性力學發(fā)展起來固體力學中最活躍的研究領域?qū)嵱眯裕捍罅康墓こ虘靡笱芯坎牧掀茐?；跨學科：力學、材料、物理、環(huán)境、分析計算方法、測試技術(shù)；科學、工程結(jié)合形形色色的斷裂現(xiàn)象韌性試件的斷裂Facts on Liberty ShipsThere 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 ar

2、e sea-worthy.The hulls of Liberty Ships fractured without warning, mainly in the North Atlantic.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

3、prevented by employing higher quality steels and improvement of the design of the ship.The Aloha Boeing 737 AccidentOn 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).一個不斷發(fā)展的學科： 強度問題、裂紋問題、斷裂問題、疲勞、損傷、分析和規(guī)范、結(jié)構(gòu)

4、完整性問題 ，等等損傷分布結(jié)構(gòu)完整性和壽命評估系統(tǒng)從強度理論到裂紋力學應力狀態(tài)和主應力參數(shù)強度函數(shù)Some Criteria predict materials failure by yielding, others by fractureA given material may fail by yielding or fracture strength depending on its properties and the state of stressFailure criterion for isotropic material is expressed as the principal

5、 normal stresses have reached a critical failure strength (c ) f (1, 2, 3) = c孔洞導致應力集中 - Inglis理論Fracture stress for realistic materialInglis (1913) analyzed for the flat plate with an elliptical hole with major axis 2a and minor axis 2b, subjected to far end stress The stress at the tip of the majo

6、r axis (point A) is given by The ratio is defined as the stress concentration factor, When a = b, it is a circular hole, thenWhen b is very very small, Inglis define radius of curvature as And the tip stress as Inglis理論推廣到裂紋玻璃纖維的斷裂強度（示意圖）Griffith關(guān)于裂紋擴展的概念A A Griffith laid the foundations of modern f

7、racture mechanics by designing a criterion for fast fracture. He assumed that pre-existing flaws propagate under 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 wh

8、ich a crack advances. Griffiths Energy balance approach (Contd.)Griffith proposed that There is a simple energy 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 s

9、urfaceGriffith theory establishes theoretical strength of brittle material and relationship between fracture strength and flaw size a 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 o

10、n an element ds on elliptic hole is relaxed from to zero. The elastic strain energy released per unit width due to introduction of a crack of length 2a is given by (2.15) Griffiths Energy balance approach (Contd.)External work = (2.16)The potential or internal energy of the body is Due to creation o

11、f new surface increase in surface energy is (2.17)The total elastic energy of the cracked plate is (2.18) Griffiths Energy balance approach (Contd.)The variation of with crack extension should be minimum Denoting as during fracture (2.19) for plane stress (2.20) for plane strainThe Griffith theory i

12、s obeyed by materials which fail in a completely brittle elastic manner, e.g. glass, mica, diamond and refractory metals. Griffiths Energy balance approach (Contd.)Griffith extrapolated surface tension values of soda lime glass from high temperature to obtain the value at room temperature as Using v

13、alue 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 important 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

14、 considered to be propagation- (rather than nucleation-) controlled; this is a serious short-coming of the theory. Modification for Ductile MaterialsFor 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

15、, the proportionality constant can be used to evaluate gs (provided E is known) and if 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

16、accompanies crack propagation even though fracture is macroscopically brittle; The released 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 expressionWhere gprepresents energy expended i

17、n plastic work. Typically for cleavage in metallic materials gp=104 J/m2 and gs=1 J/m2. Since gp gs we have Strain Energy Release RateThe 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 w

18、hen reaches a critical value which is denoted . At fracture we have so that One disadvantage of using is that in order to determine it is necessary to know E as well as . This can be a problem with some materials, eg polymers and composites, where varies with composition and processing. In practice, it is usually more convenient to combine E and in a single fracture toughness parameter where . Then can be simply determined experiment