DNV-RP-F112 HISC Calculation

Calculations — Nominal Stress Components

Three nominal stress components are computed at the outer fibre of the critical cross-section:

• Hoop stress σ_h — from internal pressure using the Lamé thin-wall approximation: σ_h = P_d × D_i / (2t). This is the dominant pressure-induced stress in a cylindrical section.
• Axial stress σ_ax — from end-cap pressure thrust plus the applied axial force: σ_ax = F_ax/A_cs + P_d × D_i² / (4t × (D_o + D_i)/2 × 2). For simplicity, pressure end-cap contribution is combined with the direct axial term using the full cross-sectional area.
• Bending stress σ_b — from the applied moment: σ_b = M_b / Z_s.

The axial pressure end-cap stress is included correctly by adding P_d×A_bore/A_cs, where A_bore = π/4 × D_i².

Calculations — Total Principal Stresses

The maximum longitudinal stress at the outer compression/tension fibre combines the axial and bending contributions. The radial stress σ_r at the outside surface is zero (free surface in contact with seawater). The three principal stresses are:

• σ₁ = σ_h (hoop — largest tensile principal)
• σ₂ = σ_ax + σ_b (combined longitudinal at worst fibre)
• σ₃ = 0 (radial, at outside surface)

DNV-RP-F112 Cl. 4.3 also imposes a limit on the maximum principal stress σ₁ ≤ 0.9 × R_p0.2, independent of the equivalent stress check. The SCF is applied to amplify the local stress before comparison with the HISC limit.

Calculations — Local (SCF-Amplified) Stresses

At a geometric discontinuity or weld toe, the SCF amplifies all stress components equally (conservative assumption — peak stress approach per DNV-RP-F112 Cl. 4.3). The locally amplified principal stresses become σ_1,loc = SCF × σ₁ and σ_2,loc = SCF × σ₂. These local values are used in both the von Mises equivalent stress check and the maximum principal stress check.

Calculations — Von Mises Equivalent Stress

The von Mises equivalent stress σ_eq is computed from the three principal stresses using the standard expression:

σ_eq = √( ½ × [(σ₁−σ₂)² + (σ₂−σ₃)² + (σ₃−σ₁)²] )

With σ_3,loc = 0 (free outer surface), this reduces to: σ_eq = √(σ_1,loc² − σ_1,loc×σ_2,loc + σ_2,loc²). This is the primary acceptance-criterion stress per DNV-RP-F112 Cl. 4.2.

Calculations — Maximum Principal Stress Check (DNV-RP-F112 Cl. 4.3)

In addition to the von Mises criterion, DNV-RP-F112 imposes an absolute upper limit on the maximum principal stress. This is to prevent the local stress at any point from exceeding 90% of the proof strength — even if the equivalent stress criterion is satisfied. The limit is independent of f_cp and f_tg:

σ_1,loc ≤ σ_1,allow = 0.9 × R_p0.2

Results — Acceptance Criteria

Two acceptance criteria from DNV-RP-F112 are checked:

1. Von Mises criterion: σ_eq ≤ σ_HISC
2. Maximum principal stress criterion: σ_1,loc ≤ σ_1,allow

Utilisation ratios are calculated for each check. A utilisation ratio ≤ 1.00 indicates the criterion is satisfied. A ratio > 1.00 indicates failure — the geometry, loading, SCF, or CP potential must be revised.

Interpretation of Results

The von Mises utilisation ratio UR_vM compares the SCF-amplified equivalent stress at the critical location to the HISC-derated allowable stress. A value below 1.00 confirms the component is not at risk of HISC initiation under the specified loading and CP conditions. Values approaching 1.00 should trigger a review of the SCF (through FEA) or a review of the CP design.

The principal stress utilisation ratio UR_p1 checks that the hoop stress — which is typically the largest principal stress in a pressurised cylinder — does not breach the absolute 0.9 × SMYS ceiling. This check can govern in thick-walled or high-pressure components where the hoop stress alone is large.

If either utilisation ratio exceeds 1.00, the designer should consider one or more of the following remedial actions:

• Increase wall thickness t to reduce pressure-induced stresses.
• Reduce the design pressure or operating envelope.
• Improve geometric transitions to reduce the SCF (detailed FEA per DNV-RP-F112 Appendix A).
• Adjust the CP system design to maintain E_cp in the range −0.80 V to −0.90 V where possible, which raises f_cp from 0.72 to 0.80 or 0.90.
• Consider a material with higher proof strength within the superduplex family (subject to PREN and hardness limits per NORSOK MDS).

Note that the DNV-RP-F112 framework applies only to cathodically protected superduplex components. Components not in contact with seawater or not connected to a CP system are not subject to HISC per this RP, but may still require assessment under other hydrogen embrittlement or stress corrosion cracking criteria.

Assumptions & Limitations

• Thin-wall (Lamé) hoop stress formula is used; valid when D_o/t ≥ 10. For thick-walled sections (D_o/t < 10), Lamé thick-wall equations or FEA should be used.
• The SCF is applied uniformly to all stress components — this is conservative. A component-specific FEA-based hot-spot stress approach (DNV-RP-F112 Appendix A) can yield a lower SCF.
• f_cp values are taken from DNV-RP-F112 Table 4-1 (2008 edition with 2021 clarifications). Always verify the applicable edition with the project specification.
• The thickness gradient factor f_tg is evaluated using the tabulated threshold approach. Smooth tapered transitions demonstrated by FEA may justify f_tg = 1.00.
• Residual stresses (e.g. from welding) are not explicitly included — the SCF ≥ 1.5 requirement for weld toes per the RP is intended to partially account for weld residual stress.
• This assessment covers the static HISC criterion only. Fatigue under cyclic loading with CP present requires a separate HISC-fatigue assessment per DNV-RP-F112 Cl. 5.
• Material must meet PREN ≥ 40, ferrite content 35–65%, and hardness ≤ 32 HRC per NORSOK MDS D-54 or equivalent to be classified as standard superduplex for use with this RP.
• Only the outer-surface (maximum hoop + maximum bending) location is assessed here. Other critical locations (weld root, bore surface) may require separate assessments.

HISC Assessment of Superduplex Stainless Steel — DNV-RP-F112

This worksheet performs a Hydrogen-Induced Stress Cracking (HISC) assessment for superduplex stainless steel (SDSS) components under cathodic protection (CP), in accordance with DNV-RP-F112 (edition 2008, with 2021 amendments).

HISC is a form of hydrogen embrittlement that can occur in high-strength duplex and superduplex stainless steels when simultaneously subjected to: (1) cathodic protection potentials more negative than −0.80 V_Ag/AgCl, (2) sustained tensile stress, and (3) a susceptible microstructure. DNV-RP-F112 provides a deterministic design framework to prevent HISC failure in subsea pressure-containing components.

The recommended practice limits the allowable design stress as a fraction of the material's 0.2% proof strength, with additional derating factors for stress concentration, wall-thickness gradients, and hydrogen charging intensity. The key acceptance criterion is that the equivalent stress at any point must not exceed the HISC design stress limit.

This worked example covers a superduplex component (e.g. a subsea valve body, connector, or fitting) under combined internal pressure and external loading, assessed against the DNV-RP-F112 principal stress and equivalent stress acceptance criteria.

Inputs — Material Properties

Superduplex stainless steel (e.g. UNS S32760 / S32750) is specified. The key mechanical property governing the HISC assessment is the specified minimum 0.2% proof strength (SMYS), R_p0.2, which is used as the reference stress for calculating all allowable limits. The ultimate tensile strength (UTS) is also required to verify the material grade.

Inputs — Geometry

The component wall thickness t and the relevant section dimensions are needed to compute membrane and bending stress components, and to evaluate whether a thickness gradient derating is required. The thickness ratio between adjacent sections (t_thick/t_thin) is used by DNV-RP-F112 Cl. 4.4 to determine an additional reduction factor f_tg.

Inputs — Applied Loads

The assessment requires the design internal pressure P_d (maximum allowable operating pressure × design factor), the axial force F_ax, and the bending moment M_b applied to the cross-section. These are combined to give membrane, bending, and hoop stresses at the critical location.

Inputs — Stress Concentration and CP Potential

DNV-RP-F112 requires a stress concentration factor SCF (also denoted K_t) to be applied wherever geometric discontinuities, notches, or weld toes are present. The recommended minimum value when no detailed FEA or fatigue analysis has been performed is SCF = 1.0 (smooth geometry); weld toes typically range from 1.5 to 3.0.

The cathodic protection potential E_cp (referenced to Ag/AgCl/seawater) determines the hydrogen-charging intensity factor f_cp. DNV-RP-F112 defines three CP potential bands with corresponding allowable stress fractions.

DNV-RP-F112 — Allowable Stress Fraction f_cp

Clause 4.2 of DNV-RP-F112 defines the CP-potential-dependent allowable stress fraction f_cp as follows:

• −0.80 V ≥ E_cp > −0.90 V : f_cp = 0.90 (mild hydrogen charging)
• −0.90 V ≥ E_cp > −1.05 V : f_cp = 0.80 (moderate hydrogen charging)
• E_cp ≤ −1.05 V : f_cp = 0.72 (severe hydrogen charging / overprotection)

The design potential of −1.05 V falls at the boundary of the severe band; the conservative value f_cp = 0.72 is therefore adopted, consistent with DNV-RP-F112 Table 4-1.

DNV-RP-F112 — Thickness Gradient Factor f_tg

When the assessed section is thicker than an adjacent section, a local stress concentration exists at the transition. DNV-RP-F112 Cl. 4.4 defines a thickness gradient derating factor based on the thickness ratio R_t = t / t_adj:

• R_t ≤ 1.5 : f_tg = 1.00 (no derating)
• 1.5 < R_t ≤ 2.0 : f_tg = 0.90
• R_t > 2.0 : f_tg = 0.80

The ratio t / t_adj = 30/20 = 1.50, which sits exactly at the threshold. In accordance with a conservative interpretation, f_tg = 0.90 is adopted here. If detailed FEA demonstrates a smooth transition, f_tg = 1.00 may be justified.

HISC Design Stress Limit — DNV-RP-F112 Cl. 4.1

The HISC design stress limit σ_HISC is the maximum allowable equivalent stress (von Mises) at the critical point, accounting for both hydrogen-charging severity and thickness-gradient effects. From DNV-RP-F112 Equation (4.1):

σ_HISC = f_cp × f_tg × R_p0.2

where R_p0.2 is the SMYS, f_cp is the CP potential factor, and f_tg is the thickness gradient factor. This limit replaces the conventional yield-based allowable — the philosophy is that HISC can initiate at stresses well below yield if hydrogen charging is active, so the proof strength must be derated accordingly.

Calculations — Cross-Section Properties

The mid-wall diameter and cross-sectional area of the pipe section are needed to convert the applied forces into nominal stresses. The mid-wall diameter is D_m = D_o − t, the cross-sectional metal area is A = π/4 × (D_o² − D_i²), and the section modulus for bending is Z = π/32 × (D_o⁴ − D_i⁴) / D_o.