Issue 53

S. Kirin et alii, Frattura ed Integrità Strutturale, 53 (2020) 345-352; DOI: 10.3221/IGF-ESIS.53.27 348 R ISK MATRIX hen observing the risk, possible consequences for the people, property, environment and reputation of the company should be considered. In the suggested model, we proposed a combination of qualitative and quantitative approach to the assessment of potential consequences, as given in Tab. 1 in the form of risk matrix, [7, 11]. Other aspects of risk based structural integrity assessment is given in [3-11]. As already shown in the case of pressure vessels that would cause air strike and significant damage, probably with fatalities, [7, 11], this is the case also with eventual penstock failure. The indirect damage would be the total stoppage of a reversible hydroelectric power plant for long period of time. Therefore, potential consequence in the case of penstock failure is certainly the highest one, category 5, since it would cause the collapse of the entire power plant. Anyhow, the approach adopted here will not consider event frequency when probability is evaluated, since it has no relevance to the case considered. Instead, engineering approach will be applied, based on fracture mechanics concept, i.e. Failure Assessment Diagram (FAD), as described for different applications in [3-11]. F AILURE A SSESSMENT D IAGRAM APPLICATION ailure Assessment Diagram, in its simplest form, i.e. level 1 as shown Fig. 3, enables one of the most efficient ways to assess structural integrity of a cracked component made of elastic-plastic material, such as HSLA steel. Basically, FAD indicates safe and unsafe position of a point corresponding to a given stress state for a cracked component, divided by so-called limit curve, Fig. 3: 1/2 2 8 ln sec 2 r r r K S S                (1) where S r = S n / S c and K r = K I / K Ic , S n stands for stress in net cross section, S c for the critical stress (Yield Strenght, Tensile Strength or any value in-between), K I for the stress intensity factor and K Ic for its critical value, i.e. fracture toughness. Figure 3: Failure Assessment Diagram, including assessment points for edge cracks. Using experience and results of previous testing of the prototype, [1,2], two axial surface cracks are analysed here, both with length 90 mm, one with depth 11.75 mm (¼ of penstock thickness, 47 mm), and the other one with depth 23.5 mm (½ of penstock thickness). Two loading cases are analysed, one being 9.02 MPa (design pressure), and the other one 12.05 MPa (hydrostatic proof testing pressure, 33.3% higher). Conservative assumption would be to consider cross-section as being just where the crack is, i.e. 90 mm wide and 47 mm deep (minus the crack depths), i.e. ¾ or ½ of the original value, and use formulas for an edge crack, whereas S c is taken as average value of YS and TS, i.e. 750 MPa:  S n is taken as 536 MPa, for „1/4“ crack and 804 MPa for „1/2“ crack, with remote stress 402 MPa for p=9.02 MPa and 536 MPa for p=12.05 MPa.  S r = S n / S c =536/750= 0.71 for p=9.02 MPa, 0.95 for p=12.05 MPa and „1/4“ crack. W F