The reliability of high-duty components in nuclear, aerospace, petrochemical or locomotion industry may be approached on the base of two distinct engineering views.
The traditional one, aims to guarantee a "safe" operational life under prescribed operational circumstances. This is the "safe-life" approach, which has been developed continuously since Wöhler experiments on fatigue of railway axes until the early 50th. This approach has been developed for safe-life prediction under progressive cumulative damage induced by fatigue, corrosion, creep, irradiation, wear or even natural ageing. Safety factors are applied to experimentally derived endurance to failure in order to state the safe operational life. The adherence to this approach, widely used nowadays in conventional engineering implies the retirement or replacement of involved components and structures as the safe life has been reached. The product built-in reliability is based only on the inspection performed during fabrication, in order to assure "defect-free" quality before operation. This approach which one could state as "Elysian"seeks for perfection in fabrication. Its basic message is "no defects!".
Unfortunately, in real life it can not be maintained. To many practitioners it seems dangerous not to consider the possibility of overlooking initial defects or defects generated during operation. Many catastrophic failures, especially in aerospace field have highlighted the inconsistency of the safe-life procedure.
As a result, a new design, fabrication and maintenance philosophy has emerged in the high-tech industry which put emphasise on safe operation even in the presence of defects, which may exist from the beginning or, develop by cumulative damage during operation. This new engineering philosophy is focused on the "damage-tolerance" (up to a certain extent) within a specified time intervals bounded by in-service inspections. Under this rationale, inspections intervals dictate the repair or retirement of damaged components or the whole structure. The reliability of the product may be thus significantly enhanced at reasonable costs.
The damage-tolerant approach while recognising that the risk of failures can not be completely excluded can contribute to minimise the failure risk down to tolerable levels (between 10-4 to 10-6 probability of failure) by combining the knowledge and reasoning of designer, production and quality assurance people, beginning from manufacture and in-service inspection until the component retirement.
It follows that inspection reliability coupled with explicite failure risk quantification play a central role in a successful application of damage-tolerant philosophy.
It is obvious that the most dangerous failure event in a plant or load-bearing structure is associated with fracture. Fracture occurs when external loading exceeds the material strength. The loading versus material strength trade-off is strongly influenced by the presence of defects among which the crack-like flaws are most pernicious. As concerns fracture process, one must account that the key factors pertaining to loading, material strength and defects size and their location assume in real circumstances a statistical variation which can be quantified in a probabilistic format.
Although consideration of failure risk in probabilistic terms is often unappealing to engineering and inspection community, it represents a firm trend for future developments. Probabilistic approach enables a much closer representation of reality than a currently accepted deterministic analysis which assumes that inputs are known exactly or can be represented by conservative upper and lower bounds /6/.
The physical modelling of fracture process is based on Fracture Mechanics (FM) principles, a new field of technology that aims to quantify the conditions under which an existing crack in a structural element extends to failure under operational loading. According to FM principles, applied to brittle materials under static loading, failure occurs when a compounded parameter (the stress intensity factor, SIF), K, function of applied stress ( and crack size a, attains a critical value Kc - the fracture toughness, a material characteristic. Hence, fracture occurs if:
This basic FM criterion, pertinent for predominatly elastic circumstance before fracture, derives from the first principle of thermodynamics. Accordingly, the initiation of unstable crack extension occurs when the strain energy release rate equals the energy that is necessary for the creation of new free surfaces along the front crack under extension.
While Kc as material characteristic is determined by well established laboratory technique, K is assessed by analytical or numerical solutions according to the geometry of the structural element in interaction with the crack size and loading. Generally, K assumes a functional form:
where Y (.) is a geometrical correction factor. For a through thickness crack in a large body, Y = 1.
Under static loading, the scatter in the crack size (and location) dominates the random pattern of the fracture process. Under repeated loading, with random variation of stresses from cycle-to-cycle, there is an interaction effect with statistical scatter of the crack size.
As concerns the scatter of the crack size it has an objective "intrinsic" distribution as result of manufacturing processes and in service operational circumstances. This can be described by a random variable with the probability density (PD), fa (a). However, scatter of the observed crack size s, is influenced by the uncertainty which stems from NDT technique (process, instrumentation, human factor). One can define a probability of detection (POD), in terms of repartition function PD and its associated PD, fD (s). It follows that PD of the size of existing defects fa(a) can be inferred from the PD derived from NDT, fs (s) and the POD, PD:
Many research programs are now under development for deriving information on POD related to the physical principles underlying the NDT procedure.
|
As concerns the intrinsic PD of the crack size, a favoured description has been given by Marshal [9] in terms of exponential distribution:
see Eq. (4)
where aDm is the mean value of the crack size in the population of defects.
Under static loading circumstances ( = const) and a crack population of sufficiently small crack size in comparison with the size of the structural element, (Y=1), the PD of SIF, fK (K), follows from conjunction of Eqs (2) and (4). A Rayleigh distribution results /10/: see Eq. (5)
where Km  am is SIF related to the mean crack size, a m . The simplest probabilistic fracture mechanics interpretation that retains, however, the trend pattern may be put forward by considering in the failure criterion, Eq (1) a deterministic value of the fracture toughness K c =K o . Under the assumption that, at least, one crack exists in the considered structural element, the probability of the event described by Eq (1), i.e. of failure, is: see Eq. (6)
and combined with Eq (5) an explicit relationship results /10/ by Eq. (7).
Equation (7) enables to outline the philosophy of probabilistic risk assessment by "sensitivity analysis". Figure 4 illustrates the probability of fracture of a structural component under homogeneous traction loading , the statistical distribution of the through thickness crack size being described by an exponential rule, Eq (4), with a m = 6,25 mm, a value recommended by Marshal for nuclear power reactor pressure vessels, as result of PISC - round robin investigation. This exemplification implies also that at least one crack exists in the component.
According to the outlined parametric analysis it is obvious that a range exists where a small stress increase may lead to an important increase of failure risk. The benefit from increasing material fracture toughness is clearly illustrate in Fig. 4 by the decrease in failure probability.
If the component contains n - cracks of size variability described by f a (a), Eq (4), and accounting on P f , Eq. (7), the probability of fracture associated with the presence of a single crack, then from the consideration of all routes of failure, the probability of fracture is given by Eq. (8).
|  
Fig. 4: Sensitivity Curves of Probability of Fracture
|
An increase in the number of defects enhances the failure probability since there are more chances to have at least one crack above the critical size.
Probabilistic fracture mechanics procedures have been developed for elastic - plastic circumstance as is the case of current structural steels. Failure Assessment Diagram (FAD) or R6-Procedure [11] is at the base of a FADSIM-Computer Code developed for this purpose. This approach of failure risk has been applied to a post-factum analysis of a large storage vessel failure. By modelling the crack size at fracture initiation by a normal distribution (mean value of crack size inferred from measurements on fractured fragments) and the fracture toughness uncertainty according to a 3-parameters Weibull distribution (Ko = 150 MPa m Ka = 200 MPa m and b = 4) a probability of fracture of nearly 50 %, has been evinced demonstrating the imminence of fracture. A sensitivity probabilistic analysis have outlined the deleterious effect of high stress concentration at the failed welded joint, combined with the excessive crack depth as a result of stress corrosion crack extension. The lack of in-service NDT monitoring prevented to acknowledge in due time, the high potential of failure.
See Mr. Cioclov during his presentation.