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Metal Casting Technologies : March 2006
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18 www.metals.rala.com.au Optimize Core Performance TECHNICAL FEATURE In thicker material (as seen in Figure 2b) the material is only free to contract near the free surfaces, hence through the thickness stresses develop at the notch and the stress system is triaxial. The material can not contract in the z direction. Strain is only possible in the y and x directions: this is called the Plane Strain condition. The importance of Plane Strain conditions in conducting fracture toughness tests is outlined later. STRESS INTENSITY FACTOR, K. Rather than use values of G to describe toughness it is more convenient to determine and use a parameter called the Stress Intensity Factor, K. This is derived from analysis of the stress systems developed around a crack tip (4, 5). In the general case for Plane Stress this analysis shows that EG = K2, hence the fracture equation introduced above can be written as: Fracture stress σ f x √πa = √EGc = Kc For Plane Strain conditions and tensile (mode I) crack opening (see below) the equation is then: σf√πa=KIc Where KIc is the critical value of the Stress Intensity Factor required for fracture and is called the Fracture Toughness. A correction factor, normally denoted by Y, has to be applied to this relationship to allow for the effects of the geometry of the test piece or component that contains the flaw (4-6). The stress required to cause fracture of the part by fast propagation of the flaw is thus seen to depend on the flaw size, a, and the fracture toughness of the material, Klc according to: The conventional unit for fracture toughness is MPa√m (MNm-3/2) but some data from the US is in ksi√in. If we know the size of a pre-existing defect, from suitable NDT examination, together with the fracture toughness of the material and the geometry of loading we can calculate the stress that would cause fracture, and thus set a maximum safe working stress for the material with this particular defect size. Alternatively we can calculate a maximum allowable defect size based on the intended working stress of the component. Allowances can also be made in these calculations for the shape of the defect. FRACTURE TOUGHNESS TESTING As shown in Figure 3, there are 3 basic modes of applying stress in fracture testing. Tensile loading is designated Mode I, whilst Modes II and III involve shear. In each case the relevant fracture toughness index (KIc, KIIc or KIIIc ) is determined by application of the loading across a pre-cracked notch and measurement of the load at which the crack begins to propagate. The pre- cracking is achieved by producing a fatigue crack of known length at the root of the notch. The root radius of this crack must be smaller than a limiting value below which crack sharpness has no further effect on crack propagation. Normally low stress fatigue conditions are standardized to produce a crack of known length with a root radius smaller than the limiting value for the material. Fatigue cracks are the most damaging cracks in terms of the sharpness at the crack tip. During subsequent loading the fatigue crack blunts to the critical value, which is structure dependent. Hence a fracture toughness test measures the resistance of the material to the propagation of the sharpest possible crack for that material. Testing is carried out using a test piece that is large enough to give plane strain conditions so that there is maximum plastic constraint at the notch, and that the measured fracture toughness value is independent of specimen size. Since tensile loading is likely to be the most damaging, most testing is performed using Mode I opening to determine the fracture toughness index as KIc. As for other forms of mechanical testing there are standard test procedures that must be followed in relation to size and shape of specimen, fatigue pre- cracking, crack opening, and validity of the measured toughness value (6). The most common procedures use three point loading of a single edge notched (SENB) bend test sample or a compact tension (CTS) specimen as shown in Figure 4(a) and (b). In each case the degree of crack growth is monitored using a clip type strain gauge. This produces a force-displacement record that enables the load at which the crack begins to propagate in an unstable manner. As outlined above, for the test to be valid the test specimen must have sufficient section thickness to ensure plane strain conditions. Although more difficult to machine the main advantage of the CTS type test piece is that it requires less material for a valid test than the SENB specimen. Figure 3. Three modes of crack opening -- Left to right: Mode I Tensile, Mode II Plane Shear, and Mode III Anti-plane Shear. Figure 4. Test specimens used to measure fracture toughness. (a) Three-point bend single edge notch (b) Compact tension. a b
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