Mechanical behaviour of materials


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Mechanical behaviour of materials

  1. 1. Chapter 1 Various Types of Damage Abstract This chapter is an introduction in which the various kinds of damage are shortly described and classified. Any component in a structure is subjected to various loadings. They can be forces or deformations, aggressive environment, high or low temperatures. These can be permanent or variable. They can damage components and eventually destroy them. Such events can be costly or even catastrophic. It is then of great importance to be able to predict the occurrence of damages and of their evolution and so to understand their mechanism. Indeed, failures of components and structures are always linked with the presence of defects at various scales. It is interesting to note that this was understood even before the developments of mechanics from the eighteenth century on. Montaigne,1 in chapter 14 of the second volume of the Essays, “As Our Mind Refrains Itself”, writes in 1588: “In the same way who will presuppose an evenly strong string everywhere, it is impossible of all impossibilities that it breaks; for where do you want that the fault starts? And to fracture everywhere together, it is not in nature.”2 In this volume, we will but illustrate this statement. Aggressive environments can produce corrosions of various sorts. The ensuing destructions are extremely large and detrimental. However, when acting without being combined with mechanical loadings, they are out of the scope of this volume. Mechanical loadings can lead to excessive deformations of components. They can result from buckling or plastic instability. These phenomena happen when 1 Michel Eyquem de Montaigne (1533–1592) was a French writer and philosopher. 2 Comme notre esprit s’empesche soy-mesmes: “ : : : Pareillement qui pr´esupposera une fisselle ´egalement forte partout, il est impossibl´e de toute impossibilit´e qu’elle rompe; car par oJu voulez- vous que la fauc´ee commence? Et de rompre par tout ensemble, il n’est pas en nature”. A less literal translation could be: “Let us imagine an evenly strong string; it is absolutely impossible that it breaks, because where do you want a defect to be initiated? And breaking everywhere at the same time is not a natural thing.” D. Franc¸ois et al., Mechanical Behaviour of Materials, Solid Mechanics and Its Applications 191, DOI 10.1007/978-94-007-4930-6 1, © Springer ScienceCBusiness Media Dordrecht 2013 1
  2. 2. 2 1 Various Types of Damage Table 1.1 Various types of damage Fracture type Volume damage Mixed damage Surface damage Sudden Cleavage Liquid metal embrittlement (Hg, Cd, Ga)Cavities (Trans or intergranular) Delayed Creep Creep fatigue Fatigue Irradiation embrittlement Wear Impurities embrittlement Stress corrosion Hydrogen embrittlement Corrosion fatigue Wear – Fretting-Fatigue an increasing deformation takes place without an increase of the applied forces. Ratcheting is another way to produce excessive deformations. However important for the stability of structures, we will not deal with these types of collapses. Nevertheless, plastic instabilities at various scales need to be considered in the occurrence of damages, so that we will have to account for them in several sections of this book. The basic treatment of plastic instability can be found in chapter 3 of the first volume. Damage is due to initiation and development of surfaces, cracks or cavities at various scales. Their origin lies in microscopic defects of various kinds. They can be distributed within the volume of the material or on its surface only. They can grow and coalesce. In this way macroscopic cracks are created. These can propagate more or less slowly and eventually in a catastrophic fashion. The various types of damage, which bring up more or less precise notions in the mind of the reader, are listed and classified in Table 1.1. The multiplication or the growth of these defects lead to the development of cracks and finally to fracture. We must be able to calculate the loads needed for the various steps in the evolution of damage and cracking, so as to predict when a failure would take place. The first step, very often the most critical one, is the initiation of damage. This requires the production of surface energy, that is the breaking of atomic bonds. This needs a high local stress. In most cases, homogeneous loading is insufficient. Local stress raisers must be present. Thus, we need to relate the local stress and strain fields at their level to the macroscopic mechanical loadings. Chapter 2 of the first volume gives treatments of this kind of problems. Damage initiations at various locations leads to a distribution of defects within the bulk or on the surface, depending on the mechanism. Lazar’ Katchanov and Yurii Rabotnov3 proposed, for the treatment of creep rupture, a method to deal with small, distributed defects within the volume of the material. This is damage mechanics. 3 Lazar’ Markovich Katchanov (1914–1993) and Yurii Nikolaievich Rabotnov (1914–1985) were Russian professors in solid mechanics.
  3. 3. 1 Various Types of Damage 3 It considers that, owing to the presence of these defects, the effective stress is higher than the applied stress so that the elastic moduli of a damaged material are lowered. The effective stress is then introduced in the usual constitutive equations. Some care is needed in the use of damage mechanics, restricted to the case of distributed defects within the bulk, avoiding its extension outside of the limits of its basic hypotheses. We will give some notions about damage mechanics in dealing with creep rupture and with the fracture of concrete. The coalescence of distributed defects, or the development of a single one, can lead to the formation of a crack. When cracks are present, strain concentrations exist near their tips. The propagation of cracks depends of course on these concentrations. Their calculation is made possible by the theory of fracture mechanics. It allows determining of the critical size of cracks resulting in fracture. The next chapter will be devoted to this most important subject. The local approach to fracture mechanics consists in relating the macroscopic critical condition for crack propagation to the microscopic critical conditions near the crack tip for microscopic defects (cleavages or cavities) to nucleate, grow and coalesce. This synthesis of fracture mechanics and microscopic treatments allows better predictions of fracture and understanding of the influence of the microstructures of materials. The elements of microstructure are not uniformly distributed. Precipitates and inclusions are more or less dispersed within grains, the sizes and orientations of which are not uniform. For this reason statistical analysis will be needed in many cases for a sound treatment of damage and fracture. One of the main tools, which we will use, is based on the weakest link model. It leads to the statistics of Weibull,4 which plays an important role in fracture theories. To better understand Table 1.1, it is necessary to recall here elements, which are tackled in chapter 1 of the first volume. Damage of a material results from the development of new surfaces. On the atomic scale three basic types of damage can be envisaged (Fig. 1.1): cleavage, slip with formation of surface steps, and creation of cavities resulting from diffusion of vacancies. The term cleavage is used only in connection with crystalline materials, but an analogous mechanism, the breaking of bonds normal to the plane of the crack (called mode I in fracture mechanics), is responsible for the crazing of polymers, and for the fracture of concrete and glass. This is also the case for intergranular fractures, which occur in grain boundaries nearly perpendicular to the crack opening displacement. Slip is responsible for plastic deformation as was studied in Chap. 3 of Volume I. This can lead to the structural instability of necking or plastic collapse as mentioned above. Plastic deformation can also lead to the formation of small internal cavities in the material, which can grow, coalesce and finally cause fracture. Again, that can take place within the grains or at the grain boundaries. 4 Ernst Hjalmar Wallodi Weibull (1887–1979) was a Swedish engineer.
  4. 4. 4 1 Various Types of Damage Fig. 1.1 Atomic scale damage: (a) cleavage; (b) slip; (c) appearance of cavities Under cyclic loading slip is not perfectly reversible: after a time it can cause deteriorations, which are most often taking place at the surface, ending with fatigue failure. Corrosion can interact with slip mechanisms of damage either under static loading, leading to stress-corrosion, or cyclic loading, producing corrosion fatigue. A particular kind of aggressive environment is made of liquid metals (Hg, Cd, Ga), which affect the surface energy and can lead to sudden fractures from liquid metal embrittlement. Wear results from mechanical loadings as well in many instances of chemical aggressions. The last mechanism at the atomic scale shown in Fig. 1.1 can occur only when the temperature is high enough for vacancies to diffuse; it is the dominant effect in creep at high temperatures. The creation of vacancies occurs also when neutron irradiation creates a large excess of vacancies over the equilibrium concentration. But irradiation embrittle- ment results also from the number of other defects created in the atomic structure.
  5. 5. 1 Various Types of Damage 5 The diffusion of impurities, in particular to grain boundaries, reducing their fracture energy, or creating precipitates, can produce impurities embrittlement. This results in intergranular cracking. The fast diffusion of hydrogen, faster than the diffusion of other elements, and also the fact that the coalescence of hydrogen atoms produces gas bubbles and not solid precipitates, confer specific characteristics to hydrogen embrittlement. Chapter 2 of this volume will be devoted to fracture mechanics, introducing notions such as the strain energy release rate, stress intensity factor, the crack opening displacement, the energy rate (or J integral) of Rice and Cherepanov. Chapter 3 will deal with cleavage fracture including a study of the mechanisms at the microscopic scale as well as the ensuing macroscopic fracture conditions. It will also include various embrittlement mechanisms: impurities, hydrogen and irradiation embrittlements. Chapter 4 will treat ductile fracture mechanisms of cavities nucleation, growth and coalescence. The preceding developments will allow us, in Chap. 5, to consider the brittle ductile transition, an important aspect of the fracture of carbon steels in particular. Chapter 6 will be devoted to fatigue, once again envisaged both at the micro- scopic and at the macroscopic levels. It will treat the initiation of fatigue and the propagation of cracks under cyclic loadings. Chapter 7 will deal with environment assisted damage. It will include stress corrosion, liquid metal embrittlement and corrosion fatigue. Creep-fatigue-oxidation phenomena will be studied in Chap. 8. Chapter 9 will cover friction and wear. Contact mechanics will first be developed in order to understand the phenomena taking place at the interface between rubbing materials Finally, fracture of non-metallic materials such as glass, ceramics, concrete, polymers and composites will be tackled in Chap. 10.