## Features

Failure Assessment of Cracked Components

- Relation to codes and standards
- Failure assessment diagram (FAD)
- Fatigue crack growth
- Leak before break assessment
- Leak area calculations
- Stress intensity factors
- Reference stress
- Material data input
- Probabilistic calculations

### Relation to codes and standards

Structural integrity assessment performed using VERB is achieved to be according to the state-of-the-art, as VERB follows the basic assessment procedures incorporated in the most failure assessment codes and standards, such as FITNET, SINTAP, R6, BS 7910, API 579, German FKM Guideline, ASME B&PVC Section XI. To facilitate a comparison between different codes and/or to assure the compatibility of component’s assessment with a particular procedure, code specific failure criteria (analytical equation for the FAD failure line, safety factors) are implemented in VERB.

### Failure assessment diagram (FAD)

The failure assessment diagram (FAD) approach is preferably used in fracture mechanics analyses of components subjected to static loading. The FAD based approach can be regarded as an approximate method for calculating the elastic-plastic J-integral.

The FAD is a plot of the failure line, f(Lr), versus an assessment point (or a set of assessment points) representing the component state. The shape of the failure line depends upon the material strain hardening. The coodinates of assessment point(s) are defined via the normalized elastic stress intensity factor and the reference stress (or plastic limit load). Both crack initiation and ductile tearing can be treated by means of FAD.

### Fatigue crack growth

Fatigue crack propagation can be calculated at constant or variable amplitude loading. The latter can be specified by providing

- load spectrum parameters, or
- rainflow matrix, or
- load history sequence.

Crack growth is calculated by integrating an appropriate fatigue crack growth (FCG) equation, or a set of respective equations for the case of simultaneous crack propagation in different directions (e.g. part-elliptical surface crack, embedded crack), using the Euler or the Runge-Kutta integration algorithm. The integration accuracy is controlled by optional settings.

Fatigue crack growth rates versus the stress intensity factor range can be defined by an equation or as a data table. The following FCG equation types are available in VERB:

- Paris-Erdogan’s equation
- Bilinear law
- Tabulated data
- NASGRO equation
- Forman’s equation
- Erdogan-Ratwani’s equation

Several parameter sets corresponding to different stress ratios, R_{K}, can be specified for the first three input options. Crack growth rates at an arbitrary R_{K} value are then determined by linear interpolation on the double logarithmic scale. Other analytical equations – NASGRO, Forman and Erdogan-Ratwani - explicitly include the R_{K} dependency.

### Leak before break assessment

Leak before break (LBB) analysis applies to pressurized cylindrical and spherical vessels containing surface cracks of finite length. The LBB diagram demonstrates whether the growth of such cracks in the depth and length directions can potentially result in a catastrophic failure (break) of the component at the onset of crack penetration through the wall.

### Leak area calculations

Leak area (crack opening area) calculations complement the LBB assessment and apply to through-thickness cracks in cylindrical and spherical components. Calculations are performed according to different analytical solutions from the literature.

### Stress intensity factors

VERB employs accurate, verified analytical solutions for stress intensity factors. Most of the solutions implemented in the program are derived from numerical calculations (finite-element or boundary-element methods) based on the weight function or polynomial influence function technique. In the latter case, both one-dimensional and two-dimensional stress gradients in the prospective crack plane can be treated. Solutions for 2D stress profiles are available for semi-elliptical cracks in plates and cylinders, as well as for quarter-elliptical cracks in plates.

Using the polynomial influence functions, the accuracy of stress intensity factor calculations essentially depends on the accuracy of stress approximation by respective polynomials. VERB provides graphical tools and setting options to control and optimize the polynomial fit accuracy.

The expert release of VERB includes multiple stress intensity factor solutions for most crack models. This feature is useful, in particular, for judging the accuracy of calculations or in case of violating validity ranges for a particular solution.

### Reference stress

Reference stress or plastic limit load is an additional parameter employed in the FAD assessment. Since the accuracy of a reference stress solution cannot easily be evaluated, as in case of stress intensity factors, VERB incorporates most recent results of finite-element analyses from the literature and includes alternative solutions (expert release only) from different failure assessment codes.

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