Ductile materials

In moie ductile materials the assumptions of linear elastic fracture mechanics (LEFM) are not vahd because the material yields more at the crack tip, so that... 

Fig. 3. Pressure expansion curve for thick-waHed cylinder made of ductile material (5).

Criteria of Elastic Failure. Of the criteria of elastic failure which have been formulated, the two most important for ductile materials are the maximum shear stress criterion and the shear strain energy criterion. According to the former criterion, from equation 7... 

The use of the single parameter, K, to define the stress field at the crack tip is justified for brittle materials, but its extension to ductile materials is based on the assumption that although some plasticity may occur at the tip the surrounding linear elastic stress field is the controlling parameter. 

This concept is explained by Figure 12 which shows the uniaxial stress— strain curve for a ductile material such as carbon steel. If the stress level is at the yield stress B or above, the problem is no longer a linear one. 

Gutting Mills. The machines applying stress by cutting are described in Figure 3e. They are usually employed for size reduction of ductile materials such as plastics, vegetables, and animal products. 

J. A. Coppola and C. H. McMurtry, "Substitution of Ceramics for Ductile Materials ia Design," National Symposium on Ceramics in the Service of Man, Carnegie Institution, Washington, D.C., 1976. 

Hydraulic piston-type compactors for collection vehicles, on-site compactors, and transfer-station compactors roll crushers used to fracture brittle materials and to crush tin and aluminum cans and other ductile materials... 

Alloys of antimony, tin, and arsenic offer hmited improvement in mechanical properties, but the usefulness of lead is limited primarily because of its poor structural qualities. It has a low melting point and a high coefficient of expansion, and it is a veiy ductile material that will creep under a tensile stress as low as 1 MPa (145 IbFin"). 

Highly ductile materials tend to be more resistant to thermal fatigue and also seem more resistant to crack initiation and propagation. 

Cavitation typically produces sharp, jagged, spongelike metal loss, even in ductile materials. The affected region is free of deposits and accumulated corrosion products if cavitation has been recent. 

Tensile stresses stimulate void growth, and subsequent loss in local strength of the material, hence simulating spall in ductile materials. 

Sketch curves of the nominal stress against nominal strain obtained from tensile tests on (a) a typical ductile material, (b) a typical non-ductile material. The following data were obtained in a tensile test on a specimen with 50 mm gauge length and a cross-sectional area of 160 mm. ... 

W. E. C. Creyke, I. E. J. Sainsbury, and R. Morrell, Design with Non-ductile Materials, Applied Science, Publishers, 1982. 

For ductile materials subjected to pure shear, the reliability is the probabilistic requirement to avoid shear yielding ... 

Of all the theories dealing with the prediction of yielding in complex stress systems, the Distortion Energy Theory (also called the von Mises Failure Theory) agrees best with experimental results for ductile materials, for example mild steel and aluminium (Collins, 1993 Edwards and McKee, 1991 Norton, 1996 Shigley and Mischke, 1996). Its formulation is given in equation 4.57. The right-hand side of the equation is the effective stress, L, for the stress system. 

Using von Mises Theory from equation 4.58, the probabilistic requirement, P, to avoid yield in a ductile material, but under a biaxial stress system, is used to determine the reliability, R, as ... 

Not all fracture is by crack propagation. Highly ductile materials stressed at high temperature will eventually break by the growth, through absorption of lattice vacancies, of plastic voids. This shades into the phenomenon of superplasticity, which was examined in Section 4.2.5. 

Another approach to the question of resistance to crack growth is to consider the extent to which yielding occurs prior to fracture. In a ductile material it has been found that yielding occurs at the crack tip and this has the effect of blunting the crack. The extent of the plastic zone (see Fig. 2.70) is given by... 

A ductile material can be stretched uniformly only when stable flow occurs. The stable flow of materials has been investigated by Hart who described the transition from the stable to unstable flow. The beginning of geometrical instability and localisation of strain is the limit of the stable flow. At temperatures above 0.5 T (at equilibrium between recovery and hardening) the strain rate sensitivity parameter "m" may be derived from the expression ... 

Since the surface energy term will usually be negligible by comparison with the plastic work term in the stress corrosion of ductile materials, it may be neglected. The remaining terms may be derived from fracture mechanics and conventional electrochemical conditions and, for the various boundary conditions indicated by West result in... 

One way of looking at the fracture characteristics of a ductile material is by measuring the amount of plasticity at a crack tip prior to crack propagation (Fig. 8.84). One test which measures this is the crack-tip opening displacement (CTOD), 5. Wells has found that 6 can be related to the strain energy release rate, G, by the formula ... 

A more universal fracture characteristic for use with ductile materials is the J integral . This is similar to CTOD but relates a volume integral to a surface integral and is independent of the path of the integral it can be classed as a material property. The J integral can also be used to predict critical stress levels for known crack lengths or vice versa. 

Whereas ductile materials, such as iron and mild steel, are often considered not to crack when charged with hydrogen and subjected to a tensile stress below the yield stress, the position is different with high-strength ferrous alloys where, depending on the strength of the steel and the hydrogen content, failure may occur well below the yield stress. However, the fracture process is not instantaneous and there is a time delay before cracks are... 

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