AF Flex Anchor, and Cryo Anchor

The double wall pipe support anchor design is unique, and used to provide a fixed anchor point for the inner pipe. Generally it is recommended to also fix the outer pipe close to this location, by means of standard fixed piping clamps on the outer pipe. Countless failures of welded fixed supports in double wall piping have led us to develop this fairly simple, but incredibly robust double wall pipe support. The engineering aspect of this design is the fixing point of the inner pipe allows the piping designer to “reset” all displacements and movements from this point.

The unique nozzle loading properties inherent in the special design allow for far higher and predictable nozzle loading allowances, compared to weldings, and all fixed supports are delivered with nozzle loading specifications. The double wall pipe support anchor available for all typical double wall pipe dimensions, and in any materials. Please enquire for specifications, costings and delivery times.

The AF Flex anchor is now available in a cryogenic edition, which insulates the inner pipe from the outer pipe, whilst providing the same level of fixed support between the inner and outer pipe.

Design

The structural behavior of the double wall pipe support anchor has been investigated through Finite Element Analyses (FEA), using the Ansys Ver. 15.0 code. Reference has been made to the following documents:

[1] ASME VIII – Div. 2 – Part. 5 – Design By Analysis

[2] ASME II – Part. D – Materials

The simulations have been carried out using an elastic-plastic analysis approach. The aim of the analyses is to assess the structural integrity of the weld connections against static and cyclic loads. The static analyses should check the protection against plastic collapse and local failure, while the effects of cycling loads should be checked through a ratcheting analysis (accumulation of plastic strain, if any).

Static analyses – protection against plastic collapse and local failure

The protection against plastic collapse and local failure must be carried out using the Load and Resistance Factor Design approach, i.e. using a proper combination of factored loads, in which the factorization coefficient depends on the load case under investigation. The protection against plastic collapse is verified if the simulation converges in presence of the ultimate factored loads (highest design coefficient). The protection against local failure is verified if the equivalent plastic strain e_P is smaller than the limiting tri-axial strain e_L, in every location of the model. e_P is a direct result of the elastic plastic analysis, while e_L is defined as

in which e_Lu, a_sl, m₂ are material dependent parameters, while s₁, s₂, s₃, s_eq are the principal stress components, and the equivalent stress, respectively.

Here no external design loads (apart from inner pressure) are assigned, by consequence the maximum allowable axial force, bending and torsion moments have been calculated. Further details will be given in the following paragraphs.

Hydrostatic test
	Local criterion – protection against local failure	Global criterion – protection against plastic collapse
Inner pressure	2.3	2.3
End cap force	2.3	2.3
Design conditions
	Local criterion – protection against local failure	Global criterion – protection against plastic collapse
Inner pressure	1.7	2.4
End cap force	1.7	2.4
External forces and moments	1.7	2.4

Tab. 2.1 design factors for the loads combination. The end cap force has been calculated on the basis of the inner pressure

Preliminary: calculation of the maximum allowable bending moment for double wall pipe support anchor

The external bending moment force coming from the pipe-line is not known, by consequence a maximum allowable bending moment has been calculated, according to the following strategy: in a three time steps simulation, in which the connection preload is acting at the first time step, apply the design pressure p_D = 42 MPa and the corresponding end cap force at the second time step, then make the external bending moment increase from zero up to a maximum value until:

failure of the local criterion in a model location (initially unknown

Finally apply to the calculated value a safety factor of 0.588 (1/1.7) for the double wall pipe support.

One half of the model has been considered, and the bending moment has been applied along the z direction. The bending moment has been applied using a remote point attachment.

Preliminary: calculation of the maximum allowable axial forcedouble wall pipe support anchor

As for the previous load case the external axial force on the double wall pipe support is not known. The maximum allowable axial force has been calculated using a three step simulation. The joint is closed at the first time step, then, at the second time step (T = 1 to T = 2), the pressure increases from zero to the design value, and so the corresponding end cap force. At the third time step the pressure stands constant, while the axial force is made increases until

local weld failure

As before, when the failure point has been found a safety factor of 0.588 (1/1.7) as been applied to the failure axial load. The ASME verification has been performed using the calculated maximum allowable axial force. The half mesh model has been used for this preliminary analysis, with the same boundary conditions of LC I: in particular the axial load shown in Fig. 7.1 has been applied.

LC V – Ratcheting analysis

The accumulation of plastic strain due to a repeated loading and unloading cycles has been investigated: here the maximum allowable external axial force and the maximum allowable bending moment, calculated at the previous paragraphs, have been applied to the halved model at the same time. The torsion has been neglected. A suitable Ansys thermal load makes the analysis temperature vary between design (loading half-cycle) and room (unloading half-cycle) temperatures.

A loading cycle exists in this application and on the subsequent removal of the mentioned loads, together with the inner pressure and the end cap force). 10 cycles have been simulated, using the half model of the double wall pipe support anchor.

Material model for the ratcheting analysis

ASME VIII Div. 2 provides general rules for performing the ratcheting analysis, in particular the use of a bilinear kinematic hardening material model for the non-linear analysis. However it’s well known from literature that the bilinear kinematic hardening model is not able to capture ratcheting: in case of an uni-axial loading plastic deformations are not accumulated, and in case of a biaxial loading plastic shakedown always occurs. This is due to the fact that the definition of the back-stress component in the model does not contain a memory term. Instead the Chaboche model is able to capture the ratcheting effects. Here the back-stress component is represented by a sum of M non-linear terms a⁽ⁱ⁾, i.e.

(1)

Here y = +1 for tension and -1 for compression, C_i and g_i are material dependent properties, e_p is the plastic strain, and e_p0 is the initial plastic strain. The static stress strain curve follows from [1]:

(2)

in which s_Y is the initial yield strength. The cyclic strain curve is given by by

(3)

in which s_a is the stress range of the hysteresis curve, and e_ap the plastic strain range. Since the C_i and g_i are constant, it is possible to estimate them through a fit of the experimental hysteresis loop, or, when this is not experimentally available, using a nonlinear fit of the experimental stress versus strain static curve. Indeed by considering an zero initial plastic strain e_p0 = 0, a zero initial back-stress a₀ = 0, the static stress versus strain tension curve turns out to be

(4)

Here no experimental data are available, nor from a tension test, nor from a cyclic test. For this reason the theoretical static stress versus strain curves generated according to Ref. [1] have been used to calculate the Chaboche coefficients. The resulting Chaboche coefficients are listed in Tab. 9.1.1 (romm and design temperature). Depending on the quality of the fit two or three back-stress terms have been retained. The initial yield strength has been evaluated from the theoretical curves at the limit of the (s, e) curves. An example of the fit quality is shown in Fig. 2.2.1: the number of the Chaboche coefficients is driven by the final quality of the fit.