Fast fracture

The fracture surfaces, revealed when the tube is broken open, are found to be smooth with a rippled appearance characteristic of fatigue. This type of behavior is sometimes known as leak before break. On the other hand, if the material lacks toughness, the propagation of the fatigue crack may be intermpted part way through the wall by the intervention of fast fracture, resulting in what is sometimes known as the break before leak mode of failure. 

The life of a component, as measured in a fatigue test, is the number of cycles needed to initiate a crack and cause it to propagate across the wall until it intersects the outside surface or until fast fracture intervenes. 

One of the most important appHcations of LEFM is to estimate the critical crack or defect size which causes fast fracture to occur. This occurs when the value of iCin a stmcture becomes equal to the plain strain fracture toughness, of the material the critical crack size, for a given stress and fracture toughness, is then given by equation 31. 

Eor an impact strength of 34 J (25 ft-lbf) the equivalent fracture toughness (150) is approximately 120 MPay. The fracture toughness dictates the critical size of crack above which fast fracture intervenes, so the smaller its value the smaller the critical crack and hence the greater significance of the transverse impact requirement specified by Manning. 

We shall now examine material selection for a pressure vessel able to contain a gas at pressure p, first minimising the weight, and then the cost. We shall seek a design that will not fail by plastic collapse (i.e. general yield). But we must be cautious structures can also fail by fast fracture, by fatigue, and by corrosion superimposed on these other modes of failure. We shall discuss these in Chapters 13, 15 and 23. Here we shall assume that plastic collapse is our only problem. 

If we then introduce a flaw into the system, by poking a pin into the inflated balloon, the balloon will explode, and all this energy will be released. The membrane fails by fast fracture, even though well below its yield strength. But if we introduce a flaw of the same dimensions into a system with less energy in it, as when we poke our pin into a partially inflated balloon, the flaw is stable and fast fracture does not occur. Finally, if we blow up the punctured balloon progressively, we eventually reach a pressure at which it suddenly bursts. In other words, we have arrived at a critical balloon pressure at which our pin-sized flaw is just unstable, and fast fracture just occurs. Why is this ... 

From what we have said already, we can write down an energy balance which must be met if the crack is to advance, and fast fracture is to occur. Suppose a crack of length fl in a material of thickness t advances by 8a, then we require that work done by loads > change of elastic energy + energy absorbed at the crack tip, i.e. 

The plate shown in Fig. 13.2 is clamped under tension so that its upper and lower ends are fixed. Since the ends cannot move, the forces acting on them can do no work, and 8W = 0. Accordingly, our energy formula gives, for the onset of fast fracture. 

As the crack grows, the plate becomes less stiff, and relaxes so that the applied forces move and do work. 8W is therefore finite and positive. However, is now positive also (it turns out that some of 8W goes into increasing the strain energy of the plate) and our final result for fast fracture is in fact found to be unchanged. 

Let us now return to our condition for the onset of fast fracture, knowing it to be general for engineering structures... 

The left-hand side of our equation says that fast fracture will occur when, in a material subjected to a stress a, a crack reaches some critical size a or, alternatively, when material containing cracks of size a is subjected to some critical stress cr. The right-hand side of our result depends on material properties only E is obviously a material constant, and G, the energy required to generate unit area of crack, again must depend only on the basic properties of our material. Thus, the important point about the equation is that the critical combination of stress and crack length at which fast fracture commences is a material constant. 

The term a Tra crops up so frequently in discussing fast fracture that it is usually abbreviated to a single symbol, K, having units MN m " it is called, somewhat unclearly, the stress intensity factor. Fast fracture therefore occurs when... 

In Chapter 13 we showed that, if a material contains a crack, and is sufficiently stressed, the crack becomes unstable and grows - at up to the speed of sound in the material -to cause catastrophically rapid fracture, or fast fracture at a stress less than the yield stress. We were able to quantify this phenomenon and obtained a relationship for the onset of fast fracture... 

Some materials, like glass, have low and K, and crack easily ductile metals have high Gf and and are very resistant to fast-fracture polymers have intermediate G, but can be made tougher by making them into composites and (finally) many metals, when cold, become brittle - that is, G and fall with temperature. How can we explain these important observations ... 

Fig. 14.1. Before it broke, this steel bolt held o seat onto its mounting at Milan airport. Whenever someone sat down, the lower part of the cross-section went into tension, causing a crack to grow there by metal fatigue (Chapter 15 crack No. 1). When someone got up again, the upper part went into tension, causing fatigue crack No. 2 to grow. Eventually the bolt failed by fast fracture from the larger of the two fatigue cracks. The victim was able to escape with the fractured bolt ...

Case studies in fast fracture and fatigue failure... 

While liquid was being unloaded from the tank a fast fracture occurred in one of the circumferential welds and the cap was blown off the end of the shell. In order to decant... 

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