Ductile fracture, 2.20

Crystals of ductile materials usually fracture in one of two ways. Either  

a neck develops so that the crystal tapers down to a chisel edge, known as rupture if the reduction in cross-sectional area is 100% or 

slip is concentrated in a narrow zone making an angle of about 45° with the tensile axis, which leads to what is called slipping off or shearing. 

Rupture is characteristic of single crystals of high purity, while shearing is more commonly observed in single crystals of alloys and also in pure polycrystalline materials. 

In materials of nominal purity small holes and cracks are formed when necking starts. These holes and cracks are produced during deformation at inclusions and, possibly, by dislocation interactions. In cylindrical specimens the formation of the neck is accompanied by the setting up of a triaxial stress system in the neck the forces between adjacent transverse sections of the neck have trajectories that follow the profile of the neck and will, therefore, have components normal to the specimen axis. This triaxial stress system may be considered as a hydrostatic stress plus a longitudinal stress. The former does not produce plastic deformation and so the material is effectively hardened. Any holes that are formed in the neck are able to grow transversely more rapidly than they can axially and so are able to coalesce, leading to an internal fracture surface at the centre of the minimum cross-section. The formation of this internal surface is followed by shearing on a surface of maximum shear stress. This surface is conical and the result is the so-called cup and cone fracture, typical of the fracture of many metallic materials at room temperature. 

When the material exhibits a ductile behavior in impact fracture, unstable fracture does not occur. The crack propagation is generally completely stable. 

To explain this inconsistency in the case of fracture with ductile behavior, another approach taking into account the crack initiation and crack propagation energies in the material is needed and has been proposed [18,19]. This approach assumes that the fracture energy of the polymer with ductile behavior varies linearly with crack extension and is given by 

From this equation, one can obtain G from the intercept and Ta from the slope of the U/A versus A plot. 

Since Wf = U and A = It, Equation (14) is similar to Equation (12). It has therefore been argued [23] that the impact fracture energy at crack initiation in polymers with ductile behavior G is rather the essential fracture work we. Furthermore, the second parameter representing the variation of the impact fracture energy during stable crack growth, T, has been attributed to the work dissipated in the outer plastic zone and is not related to the fracture process [23]. 

It can be seen that with the same fracture energy at crack initiation of 10 kJ/m2, the energy required to break this sample can vary from 0.116 to 0.406 J, depending on the character of crack propagation. This example demonstrates how a single fracture parameter can be misleading in determining the impact performance of a polymer. 

Simple fracture is the separation of a body into two or more pieces in response to an imposed stress that is static (i.e., constant or slowly changing with time) and at temperatures that are low relative to the melting temperatnre of the material. Fracture can also occur from fatigue (when cyclic stresses are imposed) and creep (time-dependent deformation, normally at elevated temperatnres) the topics of fatigue and creep are covered later in this chapter (Sections 8.7 throngh 8.15). Althongh applied stresses may be tensile, compressive, shear, or torsional (or combinations of these), the present discussion wiU be confined to fractnres that resnlt from uniaxial tensile loads. For metals, two fracture ductile fracture, modes are possible ductile and brittle. Classification is based on the ability of a material 

Ductile and brittle are relative terms whether a particular fracture is one mode or the other depends on the sitnation. DnctUity may be qnantified in terms of percent elongation (Equation 6.11) and percent rednction in area (Eqnation 6.12). Furthermore, ductility is a function of temperatnre of the material, the strain rate, and the stress state. The disposition of normally dnctile materials to fail in a brittle maimer is discussed in Section 8.6. 

Figpre 8 J Stages in the cup-and-cone fracture, (a) Initial necking. (b) Small cavity formation, (c) Coalescence of cavities to form a crack, (d) Crack propagation, (e) Final shear fractnre at a 45° angle relative to the tensile direction. 

To develop a general theory and investigate the stability or instability of existing cracks in some known geometries, a connection with Griffith s postulate is made. Consider an energy balance  

Sources Adapted from Brostow, W. and R. D. Corneliussen, Failure of Plastics, Hanser Publishers, Munich, West Germany, 1986 Engineering Plastics, Engineering Materials Handbook, Vol. 2, ASM, Metals Park, OH, 1988. 

FIGURE 5.14 Values of fracture toughness for finite-width plates. (Adapted from Shigley, J. E. and C. R. Mischke, Mechanical Engineering Design, 5th ed., McGraw-Hill, New York, 1989, 5.22, p. 224.). 

For fracture initiation, the kinetic energy 11, is 0 and IdA) 0 for initiation to occur 

For constant fracture resistance R (Griffith theory for a brittle elastic material), 

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Fig. 13. Transition between ductile fracture and brittle fracture when Al QFe Gd metallic glass is aimealed at 170°C.

Answers Structure-sensitive properties yield strength, hardness, tensile strength, ductility, fracture toughness, fatigue strength, creep strength, corrosion resistance. 

Ductility Fracture toughness (MPa m ) Melting temperature IK) Specific heat u kg K- j Thermal conductivity (Wm K ] Thermal expansion coefficient (MK j... 

If crack propagation occurs by dissolution at an active crack tip, with the crack sides rendered inactive by filming, the maintenance of film-free conditions may be dependent not only upon the electrochemical conditions but also upon the rate at which metal is exposed at the crack tip by plastic strain. Thus, it may not be stress, per se, but the strain rate that it produces, that is important, as indicated in equation (8.8). Clearly, at sufficiently high strain rates a ductile fracture may be propagated faster than the electrochemical reactions can occur whereby a stress-corrosion crack is propagated, but as the strain rate is decreased so will stress-corrosion crack propagation be facilitated. However, further decreases in strain rate will eventually result in a situation where the rate at which new surface is created by straining does not exceed the rate at which the surface is rendered inactive and hence stress corrosion may effectively cease. 

Hydrogen can increase the stress required to emit dislocations from the crack tip, thereby making ductile fracture more difficult. 

Materials with a high yield stress tend to go through the ductile to brittle transition at higher temperatures. This property has led to the assumption that true brittle fracture, unlike ductile fracture, is not accompanied by the motion of dislocations. The validity of this assumption is sometimes confirmed by the appearance of brittle fractures, which show essentially no ductility. 

In thermal fatigue, a ductile fracture usually occurs, characterized by considerable plastic deformation, the tearing of metal, and an appreciable expenditure of energy—as occurs when a strip of metal is repeatedly bent. 

D-type WT boiler design Dual-amine technology program Dual-chelant programs Dual-temperature systems inhibitor requirements Ductile fracture... 

Tough fracture, which is alternatively known as ductile fracture, by contrast, gives the type of behaviour illustrated in Figure 7.2. After the maximum in the stress-strain plot has been reached, there is a substantial amount of yielding, before the sample eventually breaks. 

The term fracture implies fragmentation of a solid body into two or more bodies under the action of stress. Two main types of fracture mode are observed in solids. The first is ductile fracture which is the failure of a material after it has undergone a considerable amount of plastic deformation. The other is brittle fracture which is the failure of a material without undergoing practically any plastic deformation. The type of failure which occurs depends largely on the nature of the material and its condition however, failure is also affected by... 

In addition to plastic deformation, materials may fail by either brittle fracture or ductile fracture fracture being the separation of a body into two or more parts. 

Dual nickel, 9 820—821 Dual-pressure processes, in nitric acid production, 17 175, 177, 179 Dual-solvent fractional extraction, 10 760 Dual Ziegler catalysts, for LLDPE production, 20 191 Dubinin-Radushkevich adsorption isotherm, 1 626, 627 Dubnium (Db), l 492t Ductile (nodular) iron, 14 522 Ductile brittle transition temperature (DBTT), 13 487 Ductile cast iron, 22 518—519 Ductile fracture, as failure mechanism, 26 983 Ductile iron... 

Figure 13. Impact energy at 100% ductile fracture temperature, which is shelf energy, as a function of REM-to-sulfur ratio retained in the 80,000 psi steel. Note the progressive effect of increasing REM additions on the transverse impacts while the longitudinal values remain virtually unchanged. The X points represent untreated steel.

We seek to nnderstand the response of a material to an applied stress. In Chapter 4, we saw how a flnid responds to a shearing stress through the application of Newton s Law of Viscosity [Eq. (4.3)]. In this chapter, we examine other types of stresses, snch as tensile and compressive, and describe the response of solids (primarily) to these stresses. That response usually takes on one of several forms elastic, inelastic, viscoelastic, plastic (ductile), fracture, or time-dependent creep. We will see that Newton s Law will be useful in describing some of these responses and that the concepts of stress (applied force per unit area) and strain (change in dimensions) are universal to these topics. 

Figure 5.35 Schematic illustration of (a) rupture, (b) ductile fracture, and (c) brittle fracture. Reprinted, by permission, from W. Callister, Materials Science and Engineering An Introduction, 5th ed., p. 186. Copyright 2000 by John Wiley Sons, Inc.

Figure 13. Schematic drawing of force - deformation curve for brittle and ductile fracture (adapted from ref. 71).

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