Estudios e investigaciones respecto al currículo como texto

Material toughness can be thought of as the resistance of the material to crack propagation in the presence of a notch. Fracture mechanics is a method of

characterizing fracture behavior in terms of material toughness, flaw size, and stress level. This is heavy duty stuff. The faint of heart, the unastute, the unstable, and all Texas A & M graduates should turn back now before we dive into the morass of

fracture mechanics and they suffer mental overload. We'll meet you again at the start of the next section.

All metals contain flaws. These flaws may be the result of processing, alloying, etc. They may be macroscopic and thus easily detectable by nondestructive

examination, or they may be microscopic and be undetectable. Fracture mechanics permits us to examine the stability of flaws in materials, analyze their growth, and to predict the size at which catastrophic failure will occur. The fracture mechanics approach that we’ll look at first is based upon the linear-elastic theory of metals. The linear-elastic fracture mechanics approach (or LEFM) is suitable for materials that are normally ductile, but become brittle in the presence of a flaw. These materials are often referred to as ductile, crack sensitive. Ductile, crack sensitive materials include high strength ferritic steels, titanium alloys, and high strength aluminum alloys.

Mode I Mode II Mode III

ksi in

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Figure 8: Displacement Modes

Now some preliminaries. Plane strain describes the state of stress that characterizes thick or brittle parts in which the stress adjacent to a flaw is tri-axial tension (material next to a crack tip, for example, is under a tensile stress in the X, Y, and Z directions). A part in a plane strain condition that contains a flaw (such as a crack) is subject to rapid and complete fracture if it is loaded such that the stress intensity adjacent to the flaw exceeds a certain critical value. If such a part is slowly loaded, the flaw will grow because the restraining effects of the bulk of the material and the Poisson effect of metal minimizes the amount of local yielding that can occur. The strain energy will be absorbed by the material up to a certain point after which any additional stress will result in rapid fracture.

The basis of fracture mechanics is that the stress field ahead of a sharp crack can be described by a single parameter K, the stress intensity factor. K has units of and is a function of the stress level and the flaw size. Unstable crack growth will occur whenever K reaches a certain critical value (designated K )._c

There are three possible displacement modes for crack propagation (see Figure 8). Mode I, in which the applied stress is normal to the crack surfaces, has received the greatest attention because it is associated with many catastrophic structural failures.

The elastic-stress field distribution at the tip of a crack in Mode I is shown in Figure 9. This figure shows that the distribution of the stress field adjacent to the crack tip is invariant for structural components that are loaded in Mode I. The stress intensity factor that describes the magnitude of the elastic stress field in Mode I is designated K ._I The magnitude of K is affected by the applied stress, the crack size and configuration,_I and the structural configuration of the part, however, none of these factors will change the stress field distribution ahead of the crack tip. As a consequence, this analysis can be applied to different structural configurations (see Figure 10). Note that in all the examples in Figure 10, K is dependent on the nominal stress and the square root of theI

)y K₁ 2%r COS  2 1sin 3 2 sin  2

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Figure 9:

Elastic Stress Field At A Crack Tip

Fracture toughness is a measure of a material's resistance to crack propagation in the presence of a notch. It is a material property just like tensile strength or hardness. Fracture toughness values are dependent on the type of material, environment, loading rate, and the type of constraint. The fracture toughness value that we test our materials for is K . K is the critical stress intensity factor for static, Mode I loading and plane_{Ic Ic} strain conditions.

K₁ ) a BW 1.77 1.77 2a W 2 K₁ PR t %a 1  1.61 a2 Rt ½ K1 ) a BW 1.99  0.36 2a w 2.12 2a w 2  3.42 2a w 3

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Figure 10: K For Different Crack GeometriesI

Through Thickness, Center Crack

Through Thickness Crack In Pressurized Cylinder

Double Edge Crack

"Sir, while I'm not an old mossback, I'm no spring chicken either. How dare you try to foist this rigmarole off on me as having some import? I am sure that there are legions of academicians working for our customers who make a handsome living by perpetuating this nonsense amongst themselves. Undoubtedly their survival is

attributable only to the fact that they have managed to convince their superiors that this claptrap is vital to their common well-being. By obfuscating the already difficult to understand so that only they can interpret its meanings, this cabal has permanently

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Figure 11: Material Selection Based On K_Ic

entrenched themselves within our customers organizations. I am a simple, but honest man. What does this technical trivia have to do with me? Either enlighten me as to its meaning or let us go forth together and root out these charlatans before the disease spreads! What does it all mean?"

Good question. Here's the answer. Just as our engineers must always select a material that has a yield strength well above the nominal stress that a given part will see in service, they must select a material that has a K value well above the maximum KIc I

that will be induced in the part as it is loaded in service. In order to calculate the maximum K value, the engineer assumes that the part may contain a flaw up to aI

certain size, but no larger. This can be verified in the actual part through nondestructive examination. As long as the value of K (which is dependent on the magnitude of the_I applied stress and the size of flaw for a given part) is below the K value of the materialIc

used to make the part, the flaw will not grow catastrophically. If, however, the

combination of flaw size and applied stress is such that the K value exceeds K in a_{I Ic} given part, the flaw will propagate through the part in a brittle fracture mode (see Figure 11).