Chapter 9Failure of MaterialsIntroductionFailure of engineering materials is a bad thing causing life and economic losses, and also interfering with the availability of products and servicesUsual reasons for the failure: improper materials selection and processing, inadequate design of the component, misuseIt is the responsibility of engineers to expect and plan for possible failure, and when failure occurs, to find out its reasons and take proper measures against future incidentsTopics: simple fracture, fundamentals of fracture mechanics, impact fracture testing, ductile-to-brittle transition, fatigue, and creepFundamentals of FractureSimple fracture is the separation of a body into two or more pieces in response to an applied stress at low temperatures (relative to the melting temperature)The applied stress: tensile, compressive, shear, or torsionalTwo fracture modes: ductile and brittle, depending on the ability of a material to experience plastic deformationAny fracture process involves two steps crack formation and propagation. Ductile fracture is corresponding to extensive plastic deformation near advancing cracks and relatively slow crack propagation rate (stable), showing considerable deformation on fracture surfaces (rough); brittle fracture to little plastic deformation and fast crack propagation rate (unstable), showing no apparent deformation on fracture surfaces (smooth) Brittle fracture often cause disasters because there is no warning signal before fracture and it is a very fast process. However, ductile fracture develops slowly and there is warning signal (considerable plastic deformation) before fractureDuctile fracture is always desirable. Under normal conditions, most metal alloys are ductile, but ceramics are considerably brittle and polymers may exhibit both types of fracture Ductile Fracture (1) Features of ductile fractureMacroscopically Necking down to a pointSome neckingHighly ductile Considerable deformationModerately ductile Some deformationDuctile Fracture (2)Microscopically Initial neckingMicrovoids formationCoalescence of microvoids to a crackCrack propagationFinal shear fracture at a 45o angle relative to the tensile directionThe fracture surface has a fibrous appearanceCupConeDuctile Fracture (3)Cup-and-cone fracture in aluminum Ductile Fracture (4) Typical ductile fracture surface appearance (microscopically) - 1Sowing many dimplesSEM photographDuctile Fracture (5) Typical ductile fracture surface appearance (microscopically) - 2Brittle Fracture (1)No necking, no apparent plastic deformationCrack propagation nearly perpendicular to the applied stress - flat fracture surface Brittle fracture in a steelBrittle Fracture (2)Fracture surface markings for brittle fractureWith naked eyes: V-shaped markings near the center of fracture surface which point back towards the origin of the crackWith naked eyes: ridges which radiate from the origin of the crackBrittle Fracture (3)For most brittle materials, crack propagation is along specific crystal planes. The planes are called cleavage planes and the fracture is call cleavage fracture. This type of fracture is Transgranular fractureGrainy or faceted texture seen in the SEM micrographSEM fractograph for a cleavage fractureTransgranular fractureCrack propagation is along grain boundaries - Intergranular fractureBrittle Fracture (5)(d)SEM fractographs for intergranular fracture (3-D nature of grains is present)Brittle Fracture (6)An oil tank that fractured in a brittle manner by crack propagation around its girthPrinciples of Fracture Mechanics (1) Brittle fracture of normally ductile materials requires us to have a good understanding of the mechanisms of fracture. To do this, we need to know the knowledge of fracture mechanicsConcerned with the relationship between material properties, stress level, crack-producing flaws, and crack propagation mechanisms Stress ConcentrationMeasured fracture strengths for most brittle materials much lower than their theoretically calculated values on the basis of atomic bonding energiesBecause of microscopic flaws or cracks, which always exist at the surfaces and in the interior of a materialAn applied stress may be concentrated at the crack tip, the magnitude of which is dependent on crack orientation and geometry Principles of Fracture Mechanics (2)The maximum stress at the crack tip: Showing the stress concentration around a crackCurvature Radius For a microcrack, (a/t)1/2 may be very large, leading to a very large m, i.e., a very large stress concentration The ratio m/ o is denoted as the stress concentration factor KtPrinciples of Fracture Mechanics (3)It is seen from the above that stress concentration occursNot only at microscopic flaws or cracksbut also at macroscopic internal defects like voids, at sharp corners or at notches In additionThe effect of a stress raiser is more significant in brittle materials than in ductile ones At the crack tip, the stress concentration factor decreases because the curvature radius increases due to plastic deformation, relieving the stress concentrationFor a brittle material, there is nearly no plastic deformation occurring at the crack tip. Thus the theoretical stress concentration factor will resultFor a ductile material, plastic deformation occurs when the maximum stress m exceeds the yield strength Principles of Fracture Mechanics (4)According to principles of fracture mechanics, the critical stress required for crack propagation, c, is given byE = modulus of elasticity s = specific surface energy (surface energy per unit area)a = half the length of an internal crackFor a brittle material, when an applied tensile stress exceeds the critical stress, the crack will propagate, leading to failure For the defect-free metallic or ceramic whisker, what about its measured fracture strength?Question:Principles of Fracture Mechanics (5)Fracture ToughnessIn the light of principles of fracture mechanics, the relation of the critical stress for crack propagation (c ) to the crack length (a) can be expressed as where Kc is the fracture toughness in units of (MPa m1/2), and Y is a parameter associated with both crack and specimen sizes and geometries as well as the manner of load applicationKc is a material property, which is the measure of the materials resistance to brittle fracture when a crack existsPrinciples of Fracture Mechanics (6)An internal crack in a plate of infinite widthA surface crack in a plate of semi-infinite widthY = 1.0Y = 1.1Principles of Fracture Mechanics (7)When the specimen is not thick enough compared with the crack length, the value of Kc changes with specimen thickness When the specimen is sufficiently thick, the value of Kc will no longer change with specimen thickness (a constant). Under these conditions, a condition of plane strain exists around the crack tip, i.e. there is no strain component perpendicular to the front and back facesThe Kc value in this plane strain condition is called the plane strain fracture toughness KIc, which is defined as Principles of Fracture Mechanics (8)Mode I, opening or tensile modeMode II, sliding modeMode III, tearing modeThree modes of crack surface displacement Principles of Fracture Mechanics (9)Main factors influencing the plane strain fracture toughnessTemperature KIc decreases with decreasing temperatureStrain rate KIc decreases with increasing strain rateMicrostructure KIc increases with reducing grain size (toughening). An increase in yield strength brought about by solid solution strengthening, precipitation hardening, or strain hardening causes a corresponding decrease in KIc (embrittling) Embrittlement Hardening embrittlement brittleness increases with strengtheningNon-hardening embrittlement brittleness increases without strengtheningPrinciples of Fracture Mechanics (10)Principles of Fracture Mechanics (11)Design using fracture toughnessAccording to three variables must be considered concerning the possibility for fracture of a structural component: the fracture toughness (KIc), the applied stress (), and the crack size (a)In engineering design, if KIc and a are specified by application constraints, the design applied stress must beIf KIc and are specified by application requirements, the critical crack size may be determined byNon-destructive evaluation (NDE) techniques can be used to detect the cracks to determine whether or not the crack size has reached the critical valueImpact Fracture TestingBBB