How good is steel really?

The added atoms present in low alloy steel complicate the matter still further, since their presence interferes with the formation of the ferrite crystals in that types of small hard crystals involving some of the additives form between the ferrite crystals, and some of the additive atoms become included within the ferrite structures. The sizes of the ferrite and hard crystals, and the distance between the hard crystals each have distributions which may be determined by measurement for a given specimen. These changes are directly responsible for the increase in the potential mechanical resistance of the steel to deformation under applied stress, thought of as improvement in its fitness for a structural purpose. The manner of deformation under load is affected by several mechanisms. Initially the deformation is elastic and almost fully recoverable up to the point called the elastic limit, where permanent deformation starts to occur. If the application and release of a substantial fraction of this stress takes place for a very large number of 'cycles', it is found that some of the irregularities within the steel start to increase in size, with each cycle producing a microscopic increase. This is called 'fatigue'. Defects below a certain size do not grow by fatigue; and for those of greater size that do grow, their rate of growth increases with their size, and also the larger the stress cycles, the smaller is the total number of cycles to cause eventual failure. At sufficiently high temperatures the application of stress within the elastic limit produces a very slow yielding, due to thermally induced migration of atoms within the steel, which takes place in three identifiable stages, collectively known as 'creep'. At lower design or working temperatures, and at stresses within the elastic limit, some chemical agents which may be present at the steel surface react with the surfaces of the metallic grains in the steel causing them no longer to be joined. This process is called 'stress corrosion cracking'. Where a component is significantly weakened by loss of thickness due to straightforward corrosion, a given load will cause an increased deflection. Beyond the elastic limit, permanent deformation starts to occur. For a brittle steel, cleavage fracture eventually occurs at the ultimate tensile stress in which the grains either break apart or separate cleanly. For thin or small ductile steel components under tensile stress, the poisson effect or lateral contraction which accompanies the stretching means that compressive stresses are generated within the steel which act perpendicularly to each other. As the stress level is increased, thin layers of the steel move with respect to one another at an angle of 45 degrees to the direction of the contraction. The application of a brittle lacquer to the surface of a component can make the lines of slippage clearly visible. These very thin lines, only a few atoms wide are known as 'shear bands' or Luder's lines. This process is accompanied by thinning of the component perpendicular to the direction of the applied stress. As this process progresses, the true stress within the steel necessary to produce further deformation is observed to increase monotonically until eventual breakage. Some representative figures for A533B steel at 20 degress centigrade are:
True strain percent TrueStress Mpa
0.5455
1.0460
1.5475
2.5520
3.5557
4.5585
5.5607
6.5625
7.5637
8.5650
9.5610
10.0613
We shall take 455MPa as the yield stress and 650MPa as the ultimate tensile stress for thin sections, although these figures are reduced at working temperatures. In thick or large ductile steel components, the application of tensile stress beyond the elastic limit tends to generate internal 'tri-axial' stresses tending to tear the material apart. As the stress is increased, microscopic cavities form around some of the small hard crystallites. These 'microvoids' are irregular oblate ellipsoidal in shape with their long diameters parallel to the direction of the principal applied stress. As the stress increases these voids increase in size and are said to 'coalesce' as they join together (Refs.2 & 19).

stable tearing animation

Crude animation of the ductile fracture process.

scanning electron micrograph of ductile fracture surface

Scanning Electron Micrograph of Ductile Fracture Surface

Figure 2, reference 24, 304 stainless steel, which is very ductile
Some of the crystallites which initiated the defects are visible

If a large defect is present in a stressed thick ductile component, the stress not being carried by the material immediately adjacent to the defect is carried by other material in the vicinity. This is in addition to the load which that other material would have carried in the absence of the large defect. Thus it can be seen that as the applied stress is increased without limit, the size of the initial defect will increase progressively as the material in its vicinity carries the highest stress level and yields and fails preferentially. This process, if it occurs, is called 'stable tearing'. Some success has been achieved in mathematical simulation of this process using 'finite element modelling.'(Ref.19) It is imagined that as the size of the defect increases so this effect is compounded until the all of the remaining material, known as the 'uncracked ligament' fails at or near to its ultimate stress. The total hoop load per unit height in the cylindrical wall of the Sizewell 'B' pressure vessel is given by the product of the internal pressure and the inner radius, so that the thickness of the uncracked ligament for which this would be the ultimate load is less than 5.5 cm., only about a quarter of the wall thickness. Unfortunately, this means that the vessel is most unlikely to leak by this route, before failure occurs. The question of what is the maximum crack size which is safe against catastrophic failure is absolutely vital. The effect referred to above in which the stress in the vicinity of the edge or tip of a fatigue crack is increased above the stress at the same point in the absence of the crack is called 'stress concentration', and one experimentally based formula supposes that the load unsupported by the cracked material is carried by the nearby material within a fixed distance S cm. of the tip of the crack. As the crack grows this additional load increases until the total load on the material within the distance S cm. reaches the ultimate load, at which point catastrophic failure of a pressurized vessel ensues. No test of this hypothesis on a full size PWR vessel containing water at 325 degrees centigrade, and with a crack increasing in size by this mechanism, has been tried. The stable tearing theory postulates that at this point of instability, all that happens is that stable tearing begins and as the strength of the material increases by work hardening, further increase of the size of the crack is inhibited until either further growth occurs by another mechanism, or the applied pressure load is increased further. Measured values of S for thin- walled vessels are in the range of a few centimetres. Apart from the measurements of S, there have been no full size tests to destruction of pressurized ductile thick walled vessels. Simulated tests of spinning rotors have been used to explore crack growth under stress of a heated cylinder stressed both by rotational stress and by the simultaneous application of cold water to its inner surface whilst rotating. The crack sizes used in these tests were less than one quarter of the wall thickness. Apart from the crack size, the assessment of the safety of the Sizewell 'B' reactor pressure vessel against disruptive explosion relies upon innumerable tests of several types of small samples, combined with analytical methods of application. In some of these tests a slowly increasing force is applied by some kind of machine to a cracked component. The shape of the test sample and its prior treatment are specified, for example a pre machined crack may be 'sharpened' by stress cycling fatigue. The shape of the specimen component often includes features which are intended to maintain straightness of the line of the crack front within it. The slow rate of increase of the loading force in the actual test is often specified. Test specimen temperature is one of the independent variables. The magnitudes of the applied force and the deflection of the point of application are measured and recorded. Sometimes the angle or opening distance of the crack are measured and recorded. The electrical resistance of the specimen may be used to give an indication of any advance of the crack or other change in the dimensions of the test component. Fields of increasing stress and strain result within both the machine and the component. Amounts of mechanical energy are stored within the machine and the sample. Most tests are said to be using 'fixed grips', a descriptor implying that the mechanical energy stored in the loading machine is small as compared with the mechanical energy stored in the test specimen during the test, and all mechanical energy stored in the machine is disregarded. Thus test results of applied force and deflection show that as tests proceed beyond the elastic limit, a point of maximum applied force is reached after which the applied force decreases with further deflection. Observations made of advance of the crack tip during the test show that for A533B steel, about two millimetres of crack tip advance occur before the point of maximum applied force is reached. This is described as the 'stable tearing of a critical crack'.

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What happens when steel runs out of strength?

In a real component, in which the loading force is applied by the pressure of water at 325 degrees centigrade, and a crack had advanced to the point of maximum strength, any further crack growth would lead to instability, for the force applied would not be reduced as it was by the non- availability of mechanical energy stored in the stressing system of the above described tests. Here are the results of some of these tests together with the shapes of the test samples used to generate them.

COMPACT TENSION SPECIMEN TESTS

compact test results ct specimen shape

THREE POINT BEND SPECIMEN TESTS

tpb results tpb specimen shape

SINGLE EDGE-NOTCHED TENSION SPECIMEN TESTS

sent test results sent specimen shape

DOUBLE EDGE-NOTCHED TENSION SPECIMEN TESTS

dent test results dent specimen shape


if these images are not displayed,
the source diagrams can be viewed
on pages 390 and 413 of reference 19

In each and every case the load can be seen to decrease well before the separation had increased by more than three millimetres, or less than one fifth of an inch.Imagine that the loading in these tests had been applied by adding weights to a scale pan. In every case the scale pan would have fallen as soon as the maximum load point was passed. After these tests, the progress of crack growth within the specimens is marked by oxidation colouring of the exposed surface, after which the specimen is chilled to make it brittle and then broken in the brittle state so as to expose the marked crack for measurement of the distance of crack advance, which is found to be linearly related to the change in specimen shape. In the case of A533B steel, two millimetres of stable crack 'tearing' is all that has been found.

These curves, taken from reference 19, are experimental data for A533b steel (Joyce and Link, 1994) for the four types of specimen. The applied stress P (load per unit thickness) is plotted against the increase in the distance between the points of application of the load (in millimetres) from the starting value in each case.

In the case of the single edge-notched tension specimen results it is interesting to note that the average material stress in the absence of the crack would have been 283 mega pascals, which can be seen to be well below the true yield stress given above of 455 mega pascals; and the average stress on the ligament remaining in the presence of the crack at maximum is 705 mega pascals, which is above the true ultimate failure stress given above of 650 mega pascals. The effect of the crack increasing the average stress from below the yield stress to above the ultimate failure stress can be clearly seen.

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