Stress Categorization & Linearization

BS 7910 Clause 6.4 — SCL Numerical Linearization & Residual Stress Estimation

1. Primary vs. Secondary Stress according to BS 7910

In fracture mechanics and Failure Assessment Diagram (FAD) assessments, it is critical to distinguish between primary and secondary stresses:

• Primary Stress (Primary, P): Non-self-limiting stresses developed by external loads, directly driving plastic collapse. In a FAD, it affects both the loading ratio L_r (x-axis) and fracture ratio K_r (y-axis).
• Secondary Stress (Secondary, Q): Self-limiting stresses developed by structural constraints or thermal/welding residual gradients. They are automatically relieved upon local cracking or plastic deformation. In a FAD, they only affect K_r (y-axis).

2. Membrane and Bending Stress Definitions

Along the thickness path x (from inner surface x=0 to outer surface x=B), the membrane stress \sigma_m and bending stress \sigma_b are mathematically defined as:

\sigma_m = \frac{1}{B} \int_0^B \sigma(x) \mathrm{d}x \sigma_b = \frac{6}{B^2} \int_0^B \sigma(x) \left( \frac{B}{2} - x \right) \mathrm{d}x

3. Flaw Height Range Linearization (BS 7910 Fig 6.1(b))

Where highly localized stress gradients exist near the surface (e.g., thermal shock or weld toe notch), it is permissible to fit the stress distribution conservatively only over the flaw height range [0, a] and extrapolate across the remaining wall thickness B.

4. Estimation of Welding Residual Secondary Stress

In the absence of actual measurements, the secondary weld residual membrane stress Q_m can be conservatively estimated as:

• As-welded: Q_m = \sigma_Y (where \sigma_Y is the material yield strength);
• Post-Weld Heat Treatment (PWHT): Parallel flaws are reduced to 0.2\sigma_Y; transverse flaws are reduced to 0.3\sigma_Y (or 0.4\sigma_Y if stress relieved between 550°C and 580°C).

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